llama.cpp/ggml.c

#define _GNU_SOURCE // Defines CLOCK_MONOTONIC on Linux
#define _CRT_SECURE_NO_DEPRECATE // Disables ridiculous "unsafe" warnigns on Windows

#include "ggml.h"

#ifdef GGML_USE_K_QUANTS
#include "k_quants.h"
#endif

#if defined(_MSC_VER) || defined(__MINGW32__)
#include <malloc.h> // using malloc.h with MSC/MINGW
#elif !defined(__FreeBSD__) && !defined(__NetBSD__) && !defined(__OpenBSD__)
#include <alloca.h>
#endif

#include <assert.h>
#include <errno.h>
#include <time.h>
#include <math.h>
#include <stdlib.h>
#include <string.h>
#include <stdint.h>
#include <inttypes.h>
#include <stdio.h>
#include <float.h>
#include <limits.h>
#include <stdarg.h>

#ifdef GGML_USE_METAL
#include <unistd.h>
#endif

// if C99 - static_assert is noop
// ref: https://stackoverflow.com/a/53923785/4039976
#ifndef static_assert
#define static_assert(cond, msg) struct global_scope_noop_trick
#endif

#if defined(_MSC_VER)
// disable "possible loss of data" to avoid hundreds of casts
// we should just be careful :)
#pragma warning(disable: 4244 4267)
#endif

#if defined(_WIN32)

#include <windows.h>

typedef volatile LONG atomic_int;
typedef atomic_int atomic_bool;

static void atomic_store(atomic_int* ptr, LONG val) {
    InterlockedExchange(ptr, val);
}
static LONG atomic_load(atomic_int* ptr) {
    return InterlockedCompareExchange(ptr, 0, 0);
}
static LONG atomic_fetch_add(atomic_int* ptr, LONG inc) {
    return InterlockedExchangeAdd(ptr, inc);
}
static LONG atomic_fetch_sub(atomic_int* ptr, LONG dec) {
    return atomic_fetch_add(ptr, -(dec));
}

typedef HANDLE pthread_t;

typedef DWORD thread_ret_t;
static int pthread_create(pthread_t* out, void* unused, thread_ret_t(*func)(void*), void* arg) {
    (void) unused;
    HANDLE handle = CreateThread(NULL, 0, (LPTHREAD_START_ROUTINE) func, arg, 0, NULL);
    if (handle == NULL)
    {
        return EAGAIN;
    }

    *out = handle;
    return 0;
}

static int pthread_join(pthread_t thread, void* unused) {
    (void) unused;
    return (int) WaitForSingleObject(thread, INFINITE);
}

static int sched_yield (void) {
    Sleep (0);
    return 0;
}
#else
#include <pthread.h>
#include <stdatomic.h>

typedef void* thread_ret_t;

#include <sys/types.h>
#include <sys/stat.h>
#include <unistd.h>

#endif

// __FMA__ and __F16C__ are not defined in MSVC, however they are implied with AVX2/AVX512
#if defined(_MSC_VER) && (defined(__AVX2__) || defined(__AVX512F__))
#ifndef __FMA__
#define __FMA__
#endif
#ifndef __F16C__
#define __F16C__
#endif
#ifndef __SSE3__
#define __SSE3__
#endif
#endif

#ifdef __HAIKU__
#define static_assert(cond, msg) _Static_assert(cond, msg)
#endif

/*#define GGML_PERF*/
#define GGML_DEBUG 0
#define GGML_GELU_FP16
#define GGML_GELU_QUICK_FP16
#define GGML_SILU_FP16

#define GGML_SOFT_MAX_UNROLL 4
#define GGML_VEC_DOT_UNROLL  2

//
// logging
//

#if (GGML_DEBUG >= 1)
#define GGML_PRINT_DEBUG(...) printf(__VA_ARGS__)
#else
#define GGML_PRINT_DEBUG(...)
#endif

#if (GGML_DEBUG >= 5)
#define GGML_PRINT_DEBUG_5(...) printf(__VA_ARGS__)
#else
#define GGML_PRINT_DEBUG_5(...)
#endif

#if (GGML_DEBUG >= 10)
#define GGML_PRINT_DEBUG_10(...) printf(__VA_ARGS__)
#else
#define GGML_PRINT_DEBUG_10(...)
#endif

#define GGML_PRINT(...) printf(__VA_ARGS__)

#ifdef GGML_USE_ACCELERATE
// uncomment to use vDSP for soft max computation
// note: not sure if it is actually faster
//#define GGML_SOFT_MAX_ACCELERATE
#endif

#if UINTPTR_MAX == 0xFFFFFFFF
    #define GGML_MEM_ALIGN 4
#else
    #define GGML_MEM_ALIGN 16
#endif

//
// logging
//

#if (GGML_DEBUG >= 1)
#define GGML_PRINT_DEBUG(...) printf(__VA_ARGS__)
#else
#define GGML_PRINT_DEBUG(...)
#endif

#if (GGML_DEBUG >= 5)
#define GGML_PRINT_DEBUG_5(...) printf(__VA_ARGS__)
#else
#define GGML_PRINT_DEBUG_5(...)
#endif

#if (GGML_DEBUG >= 10)
#define GGML_PRINT_DEBUG_10(...) printf(__VA_ARGS__)
#else
#define GGML_PRINT_DEBUG_10(...)
#endif

#define GGML_PRINT(...) printf(__VA_ARGS__)

//
// end of logging block
//

#if defined(_MSC_VER) || defined(__MINGW32__)
#define GGML_ALIGNED_MALLOC(size)  _aligned_malloc(size, GGML_MEM_ALIGN)
#define GGML_ALIGNED_FREE(ptr)     _aligned_free(ptr)
#else
inline static void* ggml_aligned_malloc(size_t size) {
    void* aligned_memory = NULL;
#ifdef GGML_USE_METAL
    int result = posix_memalign(&aligned_memory, getpagesize(), size);
#else
    int result = posix_memalign(&aligned_memory, GGML_MEM_ALIGN, size);
#endif
    if (result != 0) {
        // Handle allocation failure
        const char *error_desc = "unknown allocation error";
        switch (result) {
            case EINVAL:
                error_desc = "invalid alignment value";
                break;
            case ENOMEM:
                error_desc = "insufficient memory";
                break;
        }
        GGML_PRINT("%s: %s (attempted to allocate %6.2f MB)\n",
            __func__, error_desc, size/(1024.0*1024.0));
        return NULL;
    }
    return aligned_memory;
}
#define GGML_ALIGNED_MALLOC(size)  ggml_aligned_malloc(size)
#define GGML_ALIGNED_FREE(ptr)     free(ptr)
#endif

#define UNUSED GGML_UNUSED
#define SWAP(x, y, T) do { T SWAP = x; x = y; y = SWAP; } while (0)

//
// tensor access macros
//

#define GGML_TENSOR_UNARY_OP_LOCALS \
    GGML_TENSOR_LOCALS(int64_t, ne0, src0, ne); \
    GGML_TENSOR_LOCALS(size_t,  nb0, src0, nb); \
    GGML_TENSOR_LOCALS(int64_t, ne,  dst,  ne); \
    GGML_TENSOR_LOCALS(size_t,  nb,  dst,  nb);

#define GGML_TENSOR_BINARY_OP_LOCALS \
    GGML_TENSOR_LOCALS(int64_t, ne0, src0, ne); \
    GGML_TENSOR_LOCALS(size_t,  nb0, src0, nb); \
    GGML_TENSOR_LOCALS(int64_t, ne1, src1, ne); \
    GGML_TENSOR_LOCALS(size_t,  nb1, src1, nb); \
    GGML_TENSOR_LOCALS(int64_t, ne,  dst,  ne); \
    GGML_TENSOR_LOCALS(size_t,  nb,  dst,  nb);

#if defined(GGML_USE_ACCELERATE)
#include <Accelerate/Accelerate.h>
#if defined(GGML_USE_CLBLAST) // allow usage of CLBlast alongside Accelerate functions
#include "ggml-opencl.h"
#endif
#elif defined(GGML_USE_OPENBLAS)
#if defined(GGML_BLAS_USE_MKL)
#include <mkl.h>
#else
#include <cblas.h>
#endif
#elif defined(GGML_USE_CUBLAS)
#include "ggml-cuda.h"
#elif defined(GGML_USE_CLBLAST)
#include "ggml-opencl.h"
#endif

#undef MIN
#undef MAX
#define MIN(a, b) ((a) < (b) ? (a) : (b))
#define MAX(a, b) ((a) > (b) ? (a) : (b))

// floating point type used to accumulate sums
typedef double ggml_float;

// 16-bit float
// on Arm, we use __fp16
// on x86, we use uint16_t
#ifdef __ARM_NEON

// if YCM cannot find <arm_neon.h>, make a symbolic link to it, for example:
//
//   $ ln -sfn /Library/Developer/CommandLineTools/usr/lib/clang/13.1.6/include/arm_neon.h ./src/
//
#include <arm_neon.h>

#define GGML_COMPUTE_FP16_TO_FP32(x) ((float) (x))
#define GGML_COMPUTE_FP32_TO_FP16(x) (x)

#define GGML_FP16_TO_FP32(x) ((float) (x))
#define GGML_FP32_TO_FP16(x) (x)

#else

#ifdef __wasm_simd128__
#include <wasm_simd128.h>
#else
#ifdef __POWER9_VECTOR__
#include <altivec.h>
#undef bool
#define bool _Bool
#else
#if defined(_MSC_VER) || defined(__MINGW32__)
#include <intrin.h>
#else
#if !defined(__riscv)
#include <immintrin.h>
#endif
#endif
#endif
#endif

#ifdef __F16C__

#ifdef _MSC_VER
#define GGML_COMPUTE_FP16_TO_FP32(x) _mm_cvtss_f32(_mm_cvtph_ps(_mm_cvtsi32_si128(x)))
#define GGML_COMPUTE_FP32_TO_FP16(x) _mm_extract_epi16(_mm_cvtps_ph(_mm_set_ss(x), 0), 0)
#else
#define GGML_COMPUTE_FP16_TO_FP32(x) _cvtsh_ss(x)
#define GGML_COMPUTE_FP32_TO_FP16(x) _cvtss_sh(x, 0)
#endif

#elif defined(__POWER9_VECTOR__)

#define GGML_COMPUTE_FP16_TO_FP32(x) ggml_compute_fp16_to_fp32(x)
#define GGML_COMPUTE_FP32_TO_FP16(x) ggml_compute_fp32_to_fp16(x)
/* the inline asm below is about 12% faster than the lookup method */
#define GGML_FP16_TO_FP32(x) GGML_COMPUTE_FP16_TO_FP32(x)
#define GGML_FP32_TO_FP16(x) GGML_COMPUTE_FP32_TO_FP16(x)

static inline float ggml_compute_fp16_to_fp32(ggml_fp16_t h) {
    register float f;
    register double d;
    __asm__(
        "mtfprd %0,%2\n"
        "xscvhpdp %0,%0\n"
        "frsp %1,%0\n" :
        /* temp */ "=d"(d),
        /* out */  "=f"(f):
        /* in */   "r"(h));
    return f;
}

static inline ggml_fp16_t ggml_compute_fp32_to_fp16(float f) {
    register double d;
    register ggml_fp16_t r;
    __asm__( /* xscvdphp can work on double or single precision */
        "xscvdphp %0,%2\n"
        "mffprd %1,%0\n" :
        /* temp */ "=d"(d),
        /* out */  "=r"(r):
        /* in */   "f"(f));
    return r;
}

#else

// FP16 <-> FP32
// ref: https://github.com/Maratyszcza/FP16

static inline float fp32_from_bits(uint32_t w) {
    union {
        uint32_t as_bits;
        float as_value;
    } fp32;
    fp32.as_bits = w;
    return fp32.as_value;
}

static inline uint32_t fp32_to_bits(float f) {
    union {
        float as_value;
        uint32_t as_bits;
    } fp32;
    fp32.as_value = f;
    return fp32.as_bits;
}

static inline float ggml_compute_fp16_to_fp32(ggml_fp16_t h) {
    const uint32_t w = (uint32_t) h << 16;
    const uint32_t sign = w & UINT32_C(0x80000000);
    const uint32_t two_w = w + w;

    const uint32_t exp_offset = UINT32_C(0xE0) << 23;
#if defined(__STDC_VERSION__) && (__STDC_VERSION__ >= 199901L) || defined(__GNUC__) && !defined(__STRICT_ANSI__)
    const float exp_scale = 0x1.0p-112f;
#else
    const float exp_scale = fp32_from_bits(UINT32_C(0x7800000));
#endif
    const float normalized_value = fp32_from_bits((two_w >> 4) + exp_offset) * exp_scale;

    const uint32_t magic_mask = UINT32_C(126) << 23;
    const float magic_bias = 0.5f;
    const float denormalized_value = fp32_from_bits((two_w >> 17) | magic_mask) - magic_bias;

    const uint32_t denormalized_cutoff = UINT32_C(1) << 27;
    const uint32_t result = sign |
        (two_w < denormalized_cutoff ? fp32_to_bits(denormalized_value) : fp32_to_bits(normalized_value));
    return fp32_from_bits(result);
}

static inline ggml_fp16_t ggml_compute_fp32_to_fp16(float f) {
#if defined(__STDC_VERSION__) && (__STDC_VERSION__ >= 199901L) || defined(__GNUC__) && !defined(__STRICT_ANSI__)
    const float scale_to_inf = 0x1.0p+112f;
    const float scale_to_zero = 0x1.0p-110f;
#else
    const float scale_to_inf = fp32_from_bits(UINT32_C(0x77800000));
    const float scale_to_zero = fp32_from_bits(UINT32_C(0x08800000));
#endif
    float base = (fabsf(f) * scale_to_inf) * scale_to_zero;

    const uint32_t w = fp32_to_bits(f);
    const uint32_t shl1_w = w + w;
    const uint32_t sign = w & UINT32_C(0x80000000);
    uint32_t bias = shl1_w & UINT32_C(0xFF000000);
    if (bias < UINT32_C(0x71000000)) {
        bias = UINT32_C(0x71000000);
    }

    base = fp32_from_bits((bias >> 1) + UINT32_C(0x07800000)) + base;
    const uint32_t bits = fp32_to_bits(base);
    const uint32_t exp_bits = (bits >> 13) & UINT32_C(0x00007C00);
    const uint32_t mantissa_bits = bits & UINT32_C(0x00000FFF);
    const uint32_t nonsign = exp_bits + mantissa_bits;
    return (sign >> 16) | (shl1_w > UINT32_C(0xFF000000) ? UINT16_C(0x7E00) : nonsign);
}

#define GGML_COMPUTE_FP16_TO_FP32(x) ggml_compute_fp16_to_fp32(x)
#define GGML_COMPUTE_FP32_TO_FP16(x) ggml_compute_fp32_to_fp16(x)

#endif // __F16C__

#endif // __ARM_NEON

//
// global data
//

// precomputed gelu table for f16 (128 KB)
static ggml_fp16_t table_gelu_f16[1 << 16];

// precomputed quick gelu table for f16 (128 KB)
static ggml_fp16_t table_gelu_quick_f16[1 << 16];

// precomputed silu table for f16 (128 KB)
static ggml_fp16_t table_silu_f16[1 << 16];

// precomputed exp table for f16 (128 KB)
static ggml_fp16_t table_exp_f16[1 << 16];

// precomputed f32 table for f16 (256 KB)
static float table_f32_f16[1 << 16];

#if defined(__ARM_NEON) || defined(__wasm_simd128__)
#define B1(c,s,n)  0x ## n ## c ,  0x ## n ## s
#define B2(c,s,n) B1(c,s,n ## c), B1(c,s,n ## s)
#define B3(c,s,n) B2(c,s,n ## c), B2(c,s,n ## s)
#define B4(c,s,n) B3(c,s,n ## c), B3(c,s,n ## s)
#define B5(c,s,n) B4(c,s,n ## c), B4(c,s,n ## s)
#define B6(c,s,n) B5(c,s,n ## c), B5(c,s,n ## s)
#define B7(c,s,n) B6(c,s,n ## c), B6(c,s,n ## s)
#define B8(c,s  ) B7(c,s,     c), B7(c,s,     s)

// precomputed tables for expanding 8bits to 8 bytes:
static const uint64_t table_b2b_0[1 << 8] = { B8(00, 10) }; // ( b) << 4
static const uint64_t table_b2b_1[1 << 8] = { B8(10, 00) }; // (!b) << 4
#endif

// On ARM NEON, it's quicker to directly convert x -> x instead of calling into ggml_lookup_fp16_to_fp32,
// so we define GGML_FP16_TO_FP32 and GGML_FP32_TO_FP16 elsewhere for NEON.
// This is also true for POWER9.
#if !defined(GGML_FP16_TO_FP32) || !defined(GGML_FP32_TO_FP16)

inline static float ggml_lookup_fp16_to_fp32(ggml_fp16_t f) {
    uint16_t s;
    memcpy(&s, &f, sizeof(uint16_t));
    return table_f32_f16[s];
}

#define GGML_FP16_TO_FP32(x) ggml_lookup_fp16_to_fp32(x)
#define GGML_FP32_TO_FP16(x) GGML_COMPUTE_FP32_TO_FP16(x)

#endif

// note: do not use these inside ggml.c
// these are meant to be used via the ggml.h API
float ggml_fp16_to_fp32(ggml_fp16_t x) {
    return (float) GGML_FP16_TO_FP32(x);
}

ggml_fp16_t ggml_fp32_to_fp16(float x) {
    return GGML_FP32_TO_FP16(x);
}

void ggml_fp16_to_fp32_row(const ggml_fp16_t * x, float * y, int n) {
    for (int i = 0; i < n; i++) {
        y[i] = GGML_FP16_TO_FP32(x[i]);
    }
}

void ggml_fp32_to_fp16_row(const float * x, ggml_fp16_t * y, int n) {
    int i = 0;
#if defined(__F16C__)
    for (; i + 7 < n; i += 8) {
        __m256 x_vec = _mm256_loadu_ps(x + i);
        __m128i y_vec = _mm256_cvtps_ph(x_vec, _MM_FROUND_TO_NEAREST_INT);
        _mm_storeu_si128((__m128i *)(y + i), y_vec);
    }
    for(; i + 3 < n; i += 4) {
        __m128 x_vec = _mm_loadu_ps(x + i);
        __m128i y_vec = _mm_cvtps_ph(x_vec, _MM_FROUND_TO_NEAREST_INT);
        _mm_storel_epi64((__m128i *)(y + i), y_vec);
    }
#endif
    for (; i < n; i++) {
        y[i] = GGML_FP32_TO_FP16(x[i]);
    }
}

//
// timing
//

#if defined(_MSC_VER) || defined(__MINGW32__)
static int64_t timer_freq, timer_start;
void ggml_time_init(void) {
    LARGE_INTEGER t;
    QueryPerformanceFrequency(&t);
    timer_freq = t.QuadPart;

    // The multiplication by 1000 or 1000000 below can cause an overflow if timer_freq
    // and the uptime is high enough.
    // We subtract the program start time to reduce the likelihood of that happening.
    QueryPerformanceCounter(&t);
    timer_start = t.QuadPart;
}
int64_t ggml_time_ms(void) {
    LARGE_INTEGER t;
    QueryPerformanceCounter(&t);
    return ((t.QuadPart-timer_start) * 1000) / timer_freq;
}
int64_t ggml_time_us(void) {
    LARGE_INTEGER t;
    QueryPerformanceCounter(&t);
    return ((t.QuadPart-timer_start) * 1000000) / timer_freq;
}
#else
void ggml_time_init(void) {}
int64_t ggml_time_ms(void) {
    struct timespec ts;
    clock_gettime(CLOCK_MONOTONIC, &ts);
    return (int64_t)ts.tv_sec*1000 + (int64_t)ts.tv_nsec/1000000;
}

int64_t ggml_time_us(void) {
    struct timespec ts;
    clock_gettime(CLOCK_MONOTONIC, &ts);
    return (int64_t)ts.tv_sec*1000000 + (int64_t)ts.tv_nsec/1000;
}
#endif

int64_t ggml_cycles(void) {
    return clock();
}

int64_t ggml_cycles_per_ms(void) {
    return CLOCKS_PER_SEC/1000;
}

#ifdef GGML_PERF
#define ggml_perf_time_ms()       ggml_time_ms()
#define ggml_perf_time_us()       ggml_time_us()
#define ggml_perf_cycles()        ggml_cycles()
#define ggml_perf_cycles_per_ms() ggml_cycles_per_ms()
#else
#define ggml_perf_time_ms()       0
#define ggml_perf_time_us()       0
#define ggml_perf_cycles()        0
#define ggml_perf_cycles_per_ms() 0
#endif


//
// cache line
//

#if defined(__cpp_lib_hardware_interference_size)
#define CACHE_LINE_SIZE hardware_destructive_interference_size
#else
#if defined(__POWER9_VECTOR__)
#define CACHE_LINE_SIZE 128
#else
#define CACHE_LINE_SIZE 64
#endif
#endif

static const size_t CACHE_LINE_SIZE_F32 = CACHE_LINE_SIZE/sizeof(float);

//
// quantization
//

#define MM256_SET_M128I(a, b) _mm256_insertf128_si256(_mm256_castsi128_si256(b), (a), 1)

#if defined(__AVX__) || defined(__AVX2__) || defined(__AVX512F__) || defined(__SSSE3__)
// multiply int8_t, add results pairwise twice
static inline __m128i mul_sum_i8_pairs(const __m128i x, const __m128i y) {
    // Get absolute values of x vectors
    const __m128i ax = _mm_sign_epi8(x, x);
    // Sign the values of the y vectors
    const __m128i sy = _mm_sign_epi8(y, x);
    // Perform multiplication and create 16-bit values
    const __m128i dot = _mm_maddubs_epi16(ax, sy);
    const __m128i ones = _mm_set1_epi16(1);
    return _mm_madd_epi16(ones, dot);
}

#if __AVX__ || __AVX2__ || __AVX512F__
// horizontally add 8 floats
static inline float hsum_float_8(const __m256 x) {
    __m128 res = _mm256_extractf128_ps(x, 1);
    res = _mm_add_ps(res, _mm256_castps256_ps128(x));
    res = _mm_add_ps(res, _mm_movehl_ps(res, res));
    res = _mm_add_ss(res, _mm_movehdup_ps(res));
    return _mm_cvtss_f32(res);
}

// horizontally add 8 int32_t
static inline int hsum_i32_8(const __m256i a) {
    const __m128i sum128 = _mm_add_epi32(_mm256_castsi256_si128(a), _mm256_extractf128_si256(a, 1));
    const __m128i hi64 = _mm_unpackhi_epi64(sum128, sum128);
    const __m128i sum64 = _mm_add_epi32(hi64, sum128);
    const __m128i hi32  = _mm_shuffle_epi32(sum64, _MM_SHUFFLE(2, 3, 0, 1));
    return _mm_cvtsi128_si32(_mm_add_epi32(sum64, hi32));
}

// horizontally add 4 int32_t
static inline int hsum_i32_4(const __m128i a) {
    const __m128i hi64 = _mm_unpackhi_epi64(a, a);
    const __m128i sum64 = _mm_add_epi32(hi64, a);
    const __m128i hi32  = _mm_shuffle_epi32(sum64, _MM_SHUFFLE(2, 3, 0, 1));
    return _mm_cvtsi128_si32(_mm_add_epi32(sum64, hi32));
}

#if defined(__AVX2__) || defined(__AVX512F__)
// spread 32 bits to 32 bytes { 0x00, 0xFF }
static inline __m256i bytes_from_bits_32(const uint8_t * x) {
    uint32_t x32;
    memcpy(&x32, x, sizeof(uint32_t));
    const __m256i shuf_mask = _mm256_set_epi64x(
            0x0303030303030303, 0x0202020202020202,
            0x0101010101010101, 0x0000000000000000);
    __m256i bytes = _mm256_shuffle_epi8(_mm256_set1_epi32(x32), shuf_mask);
    const __m256i bit_mask = _mm256_set1_epi64x(0x7fbfdfeff7fbfdfe);
    bytes = _mm256_or_si256(bytes, bit_mask);
    return _mm256_cmpeq_epi8(bytes, _mm256_set1_epi64x(-1));
}

// Unpack 32 4-bit fields into 32 bytes
// The output vector contains 32 bytes, each one in [ 0 .. 15 ] interval
static inline __m256i bytes_from_nibbles_32(const uint8_t * rsi)
{
    const __m128i tmp = _mm_loadu_si128((const __m128i *)rsi);
    const __m256i bytes = MM256_SET_M128I(_mm_srli_epi16(tmp, 4), tmp);
    const __m256i lowMask = _mm256_set1_epi8( 0xF );
    return _mm256_and_si256(lowMask, bytes);
}

// add int16_t pairwise and return as float vector
static inline __m256 sum_i16_pairs_float(const __m256i x) {
    const __m256i ones = _mm256_set1_epi16(1);
    const __m256i summed_pairs = _mm256_madd_epi16(ones, x);
    return _mm256_cvtepi32_ps(summed_pairs);
}

static inline __m256 mul_sum_us8_pairs_float(const __m256i ax, const __m256i sy) {
#if __AVXVNNI__
    const __m256i zero = _mm256_setzero_si256();
    const __m256i summed_pairs = _mm256_dpbusd_epi32(zero, ax, sy);
    return _mm256_cvtepi32_ps(summed_pairs);
#else
    // Perform multiplication and create 16-bit values
    const __m256i dot = _mm256_maddubs_epi16(ax, sy);
    return sum_i16_pairs_float(dot);
#endif
}

// multiply int8_t, add results pairwise twice and return as float vector
static inline __m256 mul_sum_i8_pairs_float(const __m256i x, const __m256i y) {
#if __AVXVNNIINT8__
    const __m256i zero = _mm256_setzero_si256();
    const __m256i summed_pairs = _mm256_dpbssd_epi32(zero, x, y);
    return _mm256_cvtepi32_ps(summed_pairs);
#else
    // Get absolute values of x vectors
    const __m256i ax = _mm256_sign_epi8(x, x);
    // Sign the values of the y vectors
    const __m256i sy = _mm256_sign_epi8(y, x);
    return mul_sum_us8_pairs_float(ax, sy);
#endif
}

static inline __m128i packNibbles( __m256i bytes )
{
    // Move bits within 16-bit lanes from 0000_abcd_0000_efgh into 0000_0000_abcd_efgh
#if __AVX512F__
    const __m256i bytes_srli_4 = _mm256_srli_epi16(bytes, 4);   // 0000_0000_abcd_0000
    bytes = _mm256_or_si256(bytes, bytes_srli_4);               // 0000_abcd_abcd_efgh
    return _mm256_cvtepi16_epi8(bytes);                         // abcd_efgh
#else
    const __m256i lowByte = _mm256_set1_epi16( 0xFF );
    __m256i high = _mm256_andnot_si256( lowByte, bytes );
    __m256i low = _mm256_and_si256( lowByte, bytes );
    high = _mm256_srli_epi16( high, 4 );
    bytes = _mm256_or_si256( low, high );

    // Compress uint16_t lanes into bytes
    __m128i r0 = _mm256_castsi256_si128( bytes );
    __m128i r1 = _mm256_extracti128_si256( bytes, 1 );
    return _mm_packus_epi16( r0, r1 );
#endif
}
#elif defined(__AVX__)
// spread 32 bits to 32 bytes { 0x00, 0xFF }
static inline __m256i bytes_from_bits_32(const uint8_t * x) {
    uint32_t x32;
    memcpy(&x32, x, sizeof(uint32_t));
    const __m128i shuf_maskl = _mm_set_epi64x(0x0101010101010101, 0x0000000000000000);
    const __m128i shuf_maskh = _mm_set_epi64x(0x0303030303030303, 0x0202020202020202);
    __m128i bytesl = _mm_shuffle_epi8(_mm_set1_epi32(x32), shuf_maskl);
    __m128i bytesh = _mm_shuffle_epi8(_mm_set1_epi32(x32), shuf_maskh);
    const __m128i bit_mask = _mm_set1_epi64x(0x7fbfdfeff7fbfdfe);
    bytesl = _mm_or_si128(bytesl, bit_mask);
    bytesh = _mm_or_si128(bytesh, bit_mask);
    bytesl = _mm_cmpeq_epi8(bytesl, _mm_set1_epi64x(-1));
    bytesh = _mm_cmpeq_epi8(bytesh, _mm_set1_epi64x(-1));
    return MM256_SET_M128I(bytesh, bytesl);
}

// Unpack 32 4-bit fields into 32 bytes
// The output vector contains 32 bytes, each one in [ 0 .. 15 ] interval
static inline __m256i bytes_from_nibbles_32(const uint8_t * rsi)
{
    // Load 16 bytes from memory
    __m128i tmpl = _mm_loadu_si128((const __m128i *)rsi);
    __m128i tmph = _mm_srli_epi16(tmpl, 4);
    const __m128i lowMask = _mm_set1_epi8(0xF);
    tmpl = _mm_and_si128(lowMask, tmpl);
    tmph = _mm_and_si128(lowMask, tmph);
    return MM256_SET_M128I(tmph, tmpl);
}

// add int16_t pairwise and return as float vector
static inline __m256 sum_i16_pairs_float(const __m128i xh, const __m128i xl) {
    const __m128i ones = _mm_set1_epi16(1);
    const __m128i summed_pairsl = _mm_madd_epi16(ones, xl);
    const __m128i summed_pairsh = _mm_madd_epi16(ones, xh);
    const __m256i summed_pairs = MM256_SET_M128I(summed_pairsh, summed_pairsl);
    return _mm256_cvtepi32_ps(summed_pairs);
}

static inline __m256 mul_sum_us8_pairs_float(const __m256i ax, const __m256i sy) {
    const __m128i axl = _mm256_castsi256_si128(ax);
    const __m128i axh = _mm256_extractf128_si256(ax, 1);
    const __m128i syl = _mm256_castsi256_si128(sy);
    const __m128i syh = _mm256_extractf128_si256(sy, 1);
    // Perform multiplication and create 16-bit values
    const __m128i dotl = _mm_maddubs_epi16(axl, syl);
    const __m128i doth = _mm_maddubs_epi16(axh, syh);
    return sum_i16_pairs_float(doth, dotl);
}

// multiply int8_t, add results pairwise twice and return as float vector
static inline __m256 mul_sum_i8_pairs_float(const __m256i x, const __m256i y) {
    const __m128i xl = _mm256_castsi256_si128(x);
    const __m128i xh = _mm256_extractf128_si256(x, 1);
    const __m128i yl = _mm256_castsi256_si128(y);
    const __m128i yh = _mm256_extractf128_si256(y, 1);
    // Get absolute values of x vectors
    const __m128i axl = _mm_sign_epi8(xl, xl);
    const __m128i axh = _mm_sign_epi8(xh, xh);
    // Sign the values of the y vectors
    const __m128i syl = _mm_sign_epi8(yl, xl);
    const __m128i syh = _mm_sign_epi8(yh, xh);
    // Perform multiplication and create 16-bit values
    const __m128i dotl = _mm_maddubs_epi16(axl, syl);
    const __m128i doth = _mm_maddubs_epi16(axh, syh);
    return sum_i16_pairs_float(doth, dotl);
}

static inline __m128i packNibbles( __m128i bytes1, __m128i bytes2 )
{
    // Move bits within 16-bit lanes from 0000_abcd_0000_efgh into 0000_0000_abcd_efgh
    const __m128i lowByte = _mm_set1_epi16( 0xFF );
    __m128i high = _mm_andnot_si128( lowByte, bytes1 );
    __m128i low = _mm_and_si128( lowByte, bytes1 );
    high = _mm_srli_epi16( high, 4 );
    bytes1 = _mm_or_si128( low, high );
    high = _mm_andnot_si128( lowByte, bytes2 );
    low = _mm_and_si128( lowByte, bytes2 );
    high = _mm_srli_epi16( high, 4 );
    bytes2 = _mm_or_si128( low, high );

    return _mm_packus_epi16( bytes1, bytes2);
}
#endif
#elif defined(__SSSE3__)
// horizontally add 4x4 floats
static inline float hsum_float_4x4(const __m128 a, const __m128 b, const __m128 c, const __m128 d) {
    __m128 res_0 =_mm_hadd_ps(a, b);
    __m128 res_1 =_mm_hadd_ps(c, d);
    __m128 res =_mm_hadd_ps(res_0, res_1);
    res =_mm_hadd_ps(res, res);
    res =_mm_hadd_ps(res, res);

    return _mm_cvtss_f32(res);
}
#endif // __AVX__ || __AVX2__ || __AVX512F__
#endif // defined(__AVX__) || defined(__AVX2__) || defined(__AVX512F__) || defined(__SSSE3__)

#if defined(__ARM_NEON)

#if !defined(__aarch64__)

inline static uint16_t vaddvq_u8(uint8x16_t v) {
    return
        (uint16_t)vgetq_lane_u8(v, 0)  + (uint16_t)vgetq_lane_u8(v, 1)  +
        (uint16_t)vgetq_lane_u8(v, 2)  + (uint16_t)vgetq_lane_u8(v, 3)  +
        (uint16_t)vgetq_lane_u8(v, 4)  + (uint16_t)vgetq_lane_u8(v, 5)  +
        (uint16_t)vgetq_lane_u8(v, 6)  + (uint16_t)vgetq_lane_u8(v, 7)  +
        (uint16_t)vgetq_lane_u8(v, 8)  + (uint16_t)vgetq_lane_u8(v, 9)  +
        (uint16_t)vgetq_lane_u8(v, 10) + (uint16_t)vgetq_lane_u8(v, 11) +
        (uint16_t)vgetq_lane_u8(v, 12) + (uint16_t)vgetq_lane_u8(v, 13) +
        (uint16_t)vgetq_lane_u8(v, 14) + (uint16_t)vgetq_lane_u8(v, 15);
}

inline static int16_t vaddvq_s8(int8x16_t v) {
    return
        (int16_t)vgetq_lane_s8(v, 0)  + (int16_t)vgetq_lane_s8(v, 1)  +
        (int16_t)vgetq_lane_s8(v, 2)  + (int16_t)vgetq_lane_s8(v, 3)  +
        (int16_t)vgetq_lane_s8(v, 4)  + (int16_t)vgetq_lane_s8(v, 5)  +
        (int16_t)vgetq_lane_s8(v, 6)  + (int16_t)vgetq_lane_s8(v, 7)  +
        (int16_t)vgetq_lane_s8(v, 8)  + (int16_t)vgetq_lane_s8(v, 9)  +
        (int16_t)vgetq_lane_s8(v, 10) + (int16_t)vgetq_lane_s8(v, 11) +
        (int16_t)vgetq_lane_s8(v, 12) + (int16_t)vgetq_lane_s8(v, 13) +
        (int16_t)vgetq_lane_s8(v, 14) + (int16_t)vgetq_lane_s8(v, 15);
}

inline static int32_t vaddvq_s16(int16x8_t v) {
    return
        (int32_t)vgetq_lane_s16(v, 0) + (int32_t)vgetq_lane_s16(v, 1) +
        (int32_t)vgetq_lane_s16(v, 2) + (int32_t)vgetq_lane_s16(v, 3) +
        (int32_t)vgetq_lane_s16(v, 4) + (int32_t)vgetq_lane_s16(v, 5) +
        (int32_t)vgetq_lane_s16(v, 6) + (int32_t)vgetq_lane_s16(v, 7);
}

inline static uint32_t vaddvq_u16(uint16x8_t v) {
    return
        (uint32_t)vgetq_lane_u16(v, 0) + (uint32_t)vgetq_lane_u16(v, 1) +
        (uint32_t)vgetq_lane_u16(v, 2) + (uint32_t)vgetq_lane_u16(v, 3) +
        (uint32_t)vgetq_lane_u16(v, 4) + (uint32_t)vgetq_lane_u16(v, 5) +
        (uint32_t)vgetq_lane_u16(v, 6) + (uint32_t)vgetq_lane_u16(v, 7);
}

inline static int32_t vaddvq_s32(int32x4_t v) {
    return vgetq_lane_s32(v, 0) + vgetq_lane_s32(v, 1) + vgetq_lane_s32(v, 2) + vgetq_lane_s32(v, 3);
}

inline static float vaddvq_f32(float32x4_t v) {
    return vgetq_lane_f32(v, 0) + vgetq_lane_f32(v, 1) + vgetq_lane_f32(v, 2) + vgetq_lane_f32(v, 3);
}

inline static float vminvq_f32(float32x4_t v) {
    return
        MIN(MIN(vgetq_lane_f32(v, 0), vgetq_lane_f32(v, 1)),
            MIN(vgetq_lane_f32(v, 2), vgetq_lane_f32(v, 3)));
}

inline static float vmaxvq_f32(float32x4_t v) {
    return
        MAX(MAX(vgetq_lane_f32(v, 0), vgetq_lane_f32(v, 1)),
            MAX(vgetq_lane_f32(v, 2), vgetq_lane_f32(v, 3)));
}

inline static int32x4_t vcvtnq_s32_f32(float32x4_t v) {
    int32x4_t res;

    res[0] = roundf(vgetq_lane_f32(v, 0));
    res[1] = roundf(vgetq_lane_f32(v, 1));
    res[2] = roundf(vgetq_lane_f32(v, 2));
    res[3] = roundf(vgetq_lane_f32(v, 3));

    return res;
}

#endif
#endif

#define QK4_0 32
typedef struct {
    ggml_fp16_t d;          // delta
    uint8_t qs[QK4_0 / 2];  // nibbles / quants
} block_q4_0;
static_assert(sizeof(block_q4_0) == sizeof(ggml_fp16_t) + QK4_0 / 2, "wrong q4_0 block size/padding");

#define QK4_1 32
typedef struct {
    ggml_fp16_t d;          // delta
    ggml_fp16_t m;          // min
    uint8_t qs[QK4_1 / 2];  // nibbles / quants
} block_q4_1;
static_assert(sizeof(block_q4_1) == 2 * sizeof(ggml_fp16_t) + QK4_1 / 2, "wrong q4_1 block size/padding");

#define QK5_0 32
typedef struct {
    ggml_fp16_t d;         // delta
    uint8_t qh[4];         // 5-th bit of quants
    uint8_t qs[QK5_0 / 2]; // nibbles / quants
} block_q5_0;
static_assert(sizeof(block_q5_0) == sizeof(ggml_fp16_t) + sizeof(uint32_t) + QK5_0 / 2, "wrong q5_0 block size/padding");

#define QK5_1 32
typedef struct {
    ggml_fp16_t d;         // delta
    ggml_fp16_t m;         // min
    uint8_t qh[4];         // 5-th bit of quants
    uint8_t qs[QK5_1 / 2]; // nibbles / quants
} block_q5_1;
static_assert(sizeof(block_q5_1) == 2 * sizeof(ggml_fp16_t) + sizeof(uint32_t) + QK5_1 / 2, "wrong q5_1 block size/padding");

#define QK8_0 32
typedef struct {
    ggml_fp16_t d;         // delta
    int8_t  qs[QK8_0];     // quants
} block_q8_0;
static_assert(sizeof(block_q8_0) == sizeof(ggml_fp16_t) + QK8_0, "wrong q8_0 block size/padding");

#define QK8_1 32
typedef struct {
    float d;               // delta
    float s;               // d * sum(qs[i])
    int8_t  qs[QK8_1];     // quants
} block_q8_1;
static_assert(sizeof(block_q8_1) == 2*sizeof(float) + QK8_1, "wrong q8_1 block size/padding");

// reference implementation for deterministic creation of model files
static void quantize_row_q4_0_reference(const float * restrict x, block_q4_0 * restrict y, int k) {
    static const int qk = QK4_0;

    assert(k % qk == 0);

    const int nb = k / qk;

    for (int i = 0; i < nb; i++) {
        float amax = 0.0f; // absolute max
        float max  = 0.0f;

        for (int j = 0; j < qk; j++) {
            const float v = x[i*qk + j];
            if (amax < fabsf(v)) {
                amax = fabsf(v);
                max  = v;
            }
        }

        const float d  = max / -8;
        const float id = d ? 1.0f/d : 0.0f;

        y[i].d = GGML_FP32_TO_FP16(d);

        for (int j = 0; j < qk/2; ++j) {
            const float x0 = x[i*qk + 0    + j]*id;
            const float x1 = x[i*qk + qk/2 + j]*id;

            const uint8_t xi0 = MIN(15, (int8_t)(x0 + 8.5f));
            const uint8_t xi1 = MIN(15, (int8_t)(x1 + 8.5f));

            y[i].qs[j]  = xi0;
            y[i].qs[j] |= xi1 << 4;
        }
    }
}

static void quantize_row_q4_0(const float * restrict x, void * restrict y, int k) {
    quantize_row_q4_0_reference(x, y, k);
}

static void quantize_row_q4_1_reference(const float * restrict x, block_q4_1 * restrict y, int k) {
    const int qk = QK4_1;

    assert(k % qk == 0);

    const int nb = k / qk;

    for (int i = 0; i < nb; i++) {
        float min = FLT_MAX;
        float max = -FLT_MAX;

        for (int j = 0; j < qk; j++) {
            const float v = x[i*qk + j];

            if (v < min) min = v;
            if (v > max) max = v;
        }

        const float d  = (max - min) / ((1 << 4) - 1);
        const float id = d ? 1.0f/d : 0.0f;

        y[i].d = GGML_FP32_TO_FP16(d);
        y[i].m = GGML_FP32_TO_FP16(min);

        for (int j = 0; j < qk/2; ++j) {
            const float x0 = (x[i*qk + 0    + j] - min)*id;
            const float x1 = (x[i*qk + qk/2 + j] - min)*id;

            const uint8_t xi0 = MIN(15, (int8_t)(x0 + 0.5f));
            const uint8_t xi1 = MIN(15, (int8_t)(x1 + 0.5f));

            y[i].qs[j]  = xi0;
            y[i].qs[j] |= xi1 << 4;
        }
    }
}

static void quantize_row_q4_1(const float * restrict x, void * restrict y, int k) {
    quantize_row_q4_1_reference(x, y, k);
}

static void quantize_row_q5_0_reference(const float * restrict x, block_q5_0 * restrict y, int k) {
    static const int qk = QK5_0;

    assert(k % qk == 0);

    const int nb = k / qk;

    for (int i = 0; i < nb; i++) {
        float amax = 0.0f; // absolute max
        float max  = 0.0f;

        for (int j = 0; j < qk; j++) {
            const float v = x[i*qk + j];
            if (amax < fabsf(v)) {
                amax = fabsf(v);
                max  = v;
            }
        }

        const float d  = max / -16;
        const float id = d ? 1.0f/d : 0.0f;

        y[i].d = GGML_FP32_TO_FP16(d);

        uint32_t qh = 0;

        for (int j = 0; j < qk/2; ++j) {
            const float x0 = x[i*qk + 0    + j]*id;
            const float x1 = x[i*qk + qk/2 + j]*id;

            const uint8_t xi0 = MIN(31, (int8_t)(x0 + 16.5f));
            const uint8_t xi1 = MIN(31, (int8_t)(x1 + 16.5f));

            y[i].qs[j] = (xi0 & 0x0F) | ((xi1 & 0x0F) << 4);

            // get the 5-th bit and store it in qh at the right position
            qh |= ((xi0 & 0x10) >> 4) << (j + 0);
            qh |= ((xi1 & 0x10) >> 4) << (j + qk/2);
        }

        memcpy(&y[i].qh, &qh, sizeof(qh));
    }
}

static void quantize_row_q5_0(const float * restrict x, void * restrict y, int k) {
    quantize_row_q5_0_reference(x, y, k);
}

static void quantize_row_q5_1_reference(const float * restrict x, block_q5_1 * restrict y, int k) {
    const int qk = QK5_1;

    assert(k % qk == 0);

    const int nb = k / qk;

    for (int i = 0; i < nb; i++) {
        float min = FLT_MAX;
        float max = -FLT_MAX;

        for (int j = 0; j < qk; j++) {
            const float v = x[i*qk + j];

            if (v < min) min = v;
            if (v > max) max = v;
        }

        const float d  = (max - min) / ((1 << 5) - 1);
        const float id = d ? 1.0f/d : 0.0f;

        y[i].d = GGML_FP32_TO_FP16(d);
        y[i].m = GGML_FP32_TO_FP16(min);

        uint32_t qh = 0;

        for (int j = 0; j < qk/2; ++j) {
            const float x0 = (x[i*qk + 0    + j] - min)*id;
            const float x1 = (x[i*qk + qk/2 + j] - min)*id;

            const uint8_t xi0 = (uint8_t)(x0 + 0.5f);
            const uint8_t xi1 = (uint8_t)(x1 + 0.5f);

            y[i].qs[j] = (xi0 & 0x0F) | ((xi1 & 0x0F) << 4);

            // get the 5-th bit and store it in qh at the right position
            qh |= ((xi0 & 0x10) >> 4) << (j + 0);
            qh |= ((xi1 & 0x10) >> 4) << (j + qk/2);
        }

        memcpy(&y[i].qh, &qh, sizeof(y[i].qh));
    }
}

static void quantize_row_q5_1(const float * restrict x, void * restrict y, int k) {
    quantize_row_q5_1_reference(x, y, k);
}

// reference implementation for deterministic creation of model files
static void quantize_row_q8_0_reference(const float * restrict x, block_q8_0 * restrict y, int k) {
    assert(k % QK8_0 == 0);
    const int nb = k / QK8_0;

    for (int i = 0; i < nb; i++) {
        float amax = 0.0f; // absolute max

        for (int j = 0; j < QK8_0; j++) {
            const float v = x[i*QK8_0 + j];
            amax = MAX(amax, fabsf(v));
        }

        const float d = amax / ((1 << 7) - 1);
        const float id = d ? 1.0f/d : 0.0f;

        y[i].d = GGML_FP32_TO_FP16(d);

        for (int j = 0; j < QK8_0; ++j) {
            const float x0 = x[i*QK8_0 + j]*id;

            y[i].qs[j] = roundf(x0);
        }
    }
}

static void quantize_row_q8_0(const float * restrict x, void * restrict vy, int k) {
    assert(QK8_0 == 32);
    assert(k % QK8_0 == 0);
    const int nb = k / QK8_0;

    block_q8_0 * restrict y = vy;

#if defined(__ARM_NEON)
    for (int i = 0; i < nb; i++) {
        float32x4_t srcv [8];
        float32x4_t asrcv[8];
        float32x4_t amaxv[8];

        for (int j = 0; j < 8; j++) srcv[j]  = vld1q_f32(x + i*32 + 4*j);
        for (int j = 0; j < 8; j++) asrcv[j] = vabsq_f32(srcv[j]);

        for (int j = 0; j < 4; j++) amaxv[2*j] = vmaxq_f32(asrcv[2*j], asrcv[2*j+1]);
        for (int j = 0; j < 2; j++) amaxv[4*j] = vmaxq_f32(amaxv[4*j], amaxv[4*j+2]);
        for (int j = 0; j < 1; j++) amaxv[8*j] = vmaxq_f32(amaxv[8*j], amaxv[8*j+4]);

        const float amax = vmaxvq_f32(amaxv[0]);

        const float d = amax / ((1 << 7) - 1);
        const float id = d ? 1.0f/d : 0.0f;

        y[i].d = GGML_FP32_TO_FP16(d);

        for (int j = 0; j < 8; j++) {
            const float32x4_t v  = vmulq_n_f32(srcv[j], id);
            const int32x4_t   vi = vcvtnq_s32_f32(v);

            y[i].qs[4*j + 0] = vgetq_lane_s32(vi, 0);
            y[i].qs[4*j + 1] = vgetq_lane_s32(vi, 1);
            y[i].qs[4*j + 2] = vgetq_lane_s32(vi, 2);
            y[i].qs[4*j + 3] = vgetq_lane_s32(vi, 3);
        }
    }
#elif defined(__wasm_simd128__)
    for (int i = 0; i < nb; i++) {
        v128_t srcv [8];
        v128_t asrcv[8];
        v128_t amaxv[8];

        for (int j = 0; j < 8; j++) srcv[j]  = wasm_v128_load(x + i*32 + 4*j);
        for (int j = 0; j < 8; j++) asrcv[j] = wasm_f32x4_abs(srcv[j]);

        for (int j = 0; j < 4; j++) amaxv[2*j] = wasm_f32x4_max(asrcv[2*j], asrcv[2*j+1]);
        for (int j = 0; j < 2; j++) amaxv[4*j] = wasm_f32x4_max(amaxv[4*j], amaxv[4*j+2]);
        for (int j = 0; j < 1; j++) amaxv[8*j] = wasm_f32x4_max(amaxv[8*j], amaxv[8*j+4]);

        const float amax = MAX(MAX(wasm_f32x4_extract_lane(amaxv[0], 0),
                                   wasm_f32x4_extract_lane(amaxv[0], 1)),
                               MAX(wasm_f32x4_extract_lane(amaxv[0], 2),
                                   wasm_f32x4_extract_lane(amaxv[0], 3)));

        const float d = amax / ((1 << 7) - 1);
        const float id = d ? 1.0f/d : 0.0f;

        y[i].d = GGML_FP32_TO_FP16(d);

        for (int j = 0; j < 8; j++) {
            const v128_t v  = wasm_f32x4_mul(srcv[j], wasm_f32x4_splat(id));
            const v128_t vi = wasm_i32x4_trunc_sat_f32x4(v);

            y[i].qs[4*j + 0] = wasm_i32x4_extract_lane(vi, 0);
            y[i].qs[4*j + 1] = wasm_i32x4_extract_lane(vi, 1);
            y[i].qs[4*j + 2] = wasm_i32x4_extract_lane(vi, 2);
            y[i].qs[4*j + 3] = wasm_i32x4_extract_lane(vi, 3);
        }
    }
#elif defined(__AVX2__) || defined(__AVX__)
    for (int i = 0; i < nb; i++) {
        // Load elements into 4 AVX vectors
        __m256 v0 = _mm256_loadu_ps( x );
        __m256 v1 = _mm256_loadu_ps( x + 8 );
        __m256 v2 = _mm256_loadu_ps( x + 16 );
        __m256 v3 = _mm256_loadu_ps( x + 24 );
        x += 32;

        // Compute max(abs(e)) for the block
        const __m256 signBit = _mm256_set1_ps( -0.0f );
        __m256 maxAbs = _mm256_andnot_ps( signBit, v0 );
        maxAbs = _mm256_max_ps( maxAbs, _mm256_andnot_ps( signBit, v1 ) );
        maxAbs = _mm256_max_ps( maxAbs, _mm256_andnot_ps( signBit, v2 ) );
        maxAbs = _mm256_max_ps( maxAbs, _mm256_andnot_ps( signBit, v3 ) );

        __m128 max4 = _mm_max_ps( _mm256_extractf128_ps( maxAbs, 1 ), _mm256_castps256_ps128( maxAbs ) );
        max4 = _mm_max_ps( max4, _mm_movehl_ps( max4, max4 ) );
        max4 = _mm_max_ss( max4, _mm_movehdup_ps( max4 ) );
        const float maxScalar = _mm_cvtss_f32( max4 );

        // Quantize these floats
        const float d = maxScalar / 127.f;
        y[i].d = GGML_FP32_TO_FP16(d);
        const float id = ( maxScalar != 0.0f ) ? 127.f / maxScalar : 0.0f;
        const __m256 mul = _mm256_set1_ps( id );

        // Apply the multiplier
        v0 = _mm256_mul_ps( v0, mul );
        v1 = _mm256_mul_ps( v1, mul );
        v2 = _mm256_mul_ps( v2, mul );
        v3 = _mm256_mul_ps( v3, mul );

        // Round to nearest integer
        v0 = _mm256_round_ps( v0, _MM_ROUND_NEAREST );
        v1 = _mm256_round_ps( v1, _MM_ROUND_NEAREST );
        v2 = _mm256_round_ps( v2, _MM_ROUND_NEAREST );
        v3 = _mm256_round_ps( v3, _MM_ROUND_NEAREST );

        // Convert floats to integers
        __m256i i0 = _mm256_cvtps_epi32( v0 );
        __m256i i1 = _mm256_cvtps_epi32( v1 );
        __m256i i2 = _mm256_cvtps_epi32( v2 );
        __m256i i3 = _mm256_cvtps_epi32( v3 );

#if defined(__AVX2__)
        // Convert int32 to int16
        i0 = _mm256_packs_epi32( i0, i1 );	// 0, 1, 2, 3,  8, 9, 10, 11,  4, 5, 6, 7, 12, 13, 14, 15
        i2 = _mm256_packs_epi32( i2, i3 );	// 16, 17, 18, 19,  24, 25, 26, 27,  20, 21, 22, 23, 28, 29, 30, 31
                                            // Convert int16 to int8
        i0 = _mm256_packs_epi16( i0, i2 );	// 0, 1, 2, 3,  8, 9, 10, 11,  16, 17, 18, 19,  24, 25, 26, 27,  4, 5, 6, 7, 12, 13, 14, 15, 20, 21, 22, 23, 28, 29, 30, 31

        // We got our precious signed bytes, but the order is now wrong
        // These AVX2 pack instructions process 16-byte pieces independently
        // The following instruction is fixing the order
        const __m256i perm = _mm256_setr_epi32( 0, 4, 1, 5, 2, 6, 3, 7 );
        i0 = _mm256_permutevar8x32_epi32( i0, perm );

        _mm256_storeu_si256((__m256i *)y[i].qs, i0);
#else
        // Since we don't have in AVX some necessary functions,
        // we split the registers in half and call AVX2 analogs from SSE
        __m128i ni0 = _mm256_castsi256_si128( i0 );
        __m128i ni1 = _mm256_extractf128_si256( i0, 1);
        __m128i ni2 = _mm256_castsi256_si128( i1 );
        __m128i ni3 = _mm256_extractf128_si256( i1, 1);
        __m128i ni4 = _mm256_castsi256_si128( i2 );
        __m128i ni5 = _mm256_extractf128_si256( i2, 1);
        __m128i ni6 = _mm256_castsi256_si128( i3 );
        __m128i ni7 = _mm256_extractf128_si256( i3, 1);

        // Convert int32 to int16
        ni0 = _mm_packs_epi32( ni0, ni1 );
        ni2 = _mm_packs_epi32( ni2, ni3 );
        ni4 = _mm_packs_epi32( ni4, ni5 );
        ni6 = _mm_packs_epi32( ni6, ni7 );
        // Convert int16 to int8
        ni0 = _mm_packs_epi16( ni0, ni2 );
        ni4 = _mm_packs_epi16( ni4, ni6 );

        _mm_storeu_si128((__m128i *)(y[i].qs +  0), ni0);
        _mm_storeu_si128((__m128i *)(y[i].qs + 16), ni4);
#endif
    }
#else
    // scalar
    quantize_row_q8_0_reference(x, y, k);
#endif
}

// reference implementation for deterministic creation of model files
static void quantize_row_q8_1_reference(const float * restrict x, block_q8_1 * restrict y, int k) {
    assert(QK8_1 == 32);
    assert(k % QK8_1 == 0);
    const int nb = k / QK8_1;

    for (int i = 0; i < nb; i++) {
        float amax = 0.0f; // absolute max

        for (int j = 0; j < QK8_1; j++) {
            const float v = x[i*QK8_1 + j];
            amax = MAX(amax, fabsf(v));
        }

        const float d = amax / ((1 << 7) - 1);
        const float id = d ? 1.0f/d : 0.0f;

        y[i].d = d;

        int sum = 0;

        for (int j = 0; j < QK8_1/2; ++j) {
            const float v0 = x[i*QK8_1           + j]*id;
            const float v1 = x[i*QK8_1 + QK8_1/2 + j]*id;

            y[i].qs[          j] = roundf(v0);
            y[i].qs[QK8_1/2 + j] = roundf(v1);

            sum += y[i].qs[          j];
            sum += y[i].qs[QK8_1/2 + j];
        }

        y[i].s = sum*d;
    }
}

static void quantize_row_q8_1(const float * restrict x, void * restrict vy, int k) {
    assert(k % QK8_1 == 0);
    const int nb = k / QK8_1;

    block_q8_1 * restrict y = vy;

#if defined(__ARM_NEON)
    for (int i = 0; i < nb; i++) {
        float32x4_t srcv [8];
        float32x4_t asrcv[8];
        float32x4_t amaxv[8];

        for (int j = 0; j < 8; j++) srcv[j]  = vld1q_f32(x + i*32 + 4*j);
        for (int j = 0; j < 8; j++) asrcv[j] = vabsq_f32(srcv[j]);

        for (int j = 0; j < 4; j++) amaxv[2*j] = vmaxq_f32(asrcv[2*j], asrcv[2*j+1]);
        for (int j = 0; j < 2; j++) amaxv[4*j] = vmaxq_f32(amaxv[4*j], amaxv[4*j+2]);
        for (int j = 0; j < 1; j++) amaxv[8*j] = vmaxq_f32(amaxv[8*j], amaxv[8*j+4]);

        const float amax = vmaxvq_f32(amaxv[0]);

        const float d = amax / ((1 << 7) - 1);
        const float id = d ? 1.0f/d : 0.0f;

        y[i].d = d;

        int32x4_t accv = vdupq_n_s32(0);

        for (int j = 0; j < 8; j++) {
            const float32x4_t v  = vmulq_n_f32(srcv[j], id);
            const int32x4_t   vi = vcvtnq_s32_f32(v);

            y[i].qs[4*j + 0] = vgetq_lane_s32(vi, 0);
            y[i].qs[4*j + 1] = vgetq_lane_s32(vi, 1);
            y[i].qs[4*j + 2] = vgetq_lane_s32(vi, 2);
            y[i].qs[4*j + 3] = vgetq_lane_s32(vi, 3);

            accv = vaddq_s32(accv, vi);
        }

        y[i].s = d * vaddvq_s32(accv);
    }
#elif defined(__wasm_simd128__)
    for (int i = 0; i < nb; i++) {
        v128_t srcv [8];
        v128_t asrcv[8];
        v128_t amaxv[8];

        for (int j = 0; j < 8; j++) srcv[j]  = wasm_v128_load(x + i*32 + 4*j);
        for (int j = 0; j < 8; j++) asrcv[j] = wasm_f32x4_abs(srcv[j]);

        for (int j = 0; j < 4; j++) amaxv[2*j] = wasm_f32x4_max(asrcv[2*j], asrcv[2*j+1]);
        for (int j = 0; j < 2; j++) amaxv[4*j] = wasm_f32x4_max(amaxv[4*j], amaxv[4*j+2]);
        for (int j = 0; j < 1; j++) amaxv[8*j] = wasm_f32x4_max(amaxv[8*j], amaxv[8*j+4]);

        const float amax = MAX(MAX(wasm_f32x4_extract_lane(amaxv[0], 0),
                                   wasm_f32x4_extract_lane(amaxv[0], 1)),
                               MAX(wasm_f32x4_extract_lane(amaxv[0], 2),
                                   wasm_f32x4_extract_lane(amaxv[0], 3)));

        const float d = amax / ((1 << 7) - 1);
        const float id = d ? 1.0f/d : 0.0f;

        y[i].d = d;

        v128_t accv = wasm_i32x4_splat(0);

        for (int j = 0; j < 8; j++) {
            const v128_t v  = wasm_f32x4_mul(srcv[j], wasm_f32x4_splat(id));
            const v128_t vi = wasm_i32x4_trunc_sat_f32x4(v);

            y[i].qs[4*j + 0] = wasm_i32x4_extract_lane(vi, 0);
            y[i].qs[4*j + 1] = wasm_i32x4_extract_lane(vi, 1);
            y[i].qs[4*j + 2] = wasm_i32x4_extract_lane(vi, 2);
            y[i].qs[4*j + 3] = wasm_i32x4_extract_lane(vi, 3);

            accv = wasm_i32x4_add(accv, vi);
        }

        y[i].s = d * (wasm_i32x4_extract_lane(accv, 0) +
                      wasm_i32x4_extract_lane(accv, 1) +
                      wasm_i32x4_extract_lane(accv, 2) +
                      wasm_i32x4_extract_lane(accv, 3));
    }
#elif defined(__AVX2__) || defined(__AVX__)
    for (int i = 0; i < nb; i++) {
        // Load elements into 4 AVX vectors
        __m256 v0 = _mm256_loadu_ps( x );
        __m256 v1 = _mm256_loadu_ps( x + 8 );
        __m256 v2 = _mm256_loadu_ps( x + 16 );
        __m256 v3 = _mm256_loadu_ps( x + 24 );
        x += 32;

        // Compute max(abs(e)) for the block
        const __m256 signBit = _mm256_set1_ps( -0.0f );
        __m256 maxAbs = _mm256_andnot_ps( signBit, v0 );
        maxAbs = _mm256_max_ps( maxAbs, _mm256_andnot_ps( signBit, v1 ) );
        maxAbs = _mm256_max_ps( maxAbs, _mm256_andnot_ps( signBit, v2 ) );
        maxAbs = _mm256_max_ps( maxAbs, _mm256_andnot_ps( signBit, v3 ) );

        __m128 max4 = _mm_max_ps( _mm256_extractf128_ps( maxAbs, 1 ), _mm256_castps256_ps128( maxAbs ) );
        max4 = _mm_max_ps( max4, _mm_movehl_ps( max4, max4 ) );
        max4 = _mm_max_ss( max4, _mm_movehdup_ps( max4 ) );
        const float maxScalar = _mm_cvtss_f32( max4 );

        // Quantize these floats
        const float d = maxScalar / 127.f;
        y[i].d = d;
        const float id = ( maxScalar != 0.0f ) ? 127.f / maxScalar : 0.0f;
        const __m256 mul = _mm256_set1_ps( id );

        // Apply the multiplier
        v0 = _mm256_mul_ps( v0, mul );
        v1 = _mm256_mul_ps( v1, mul );
        v2 = _mm256_mul_ps( v2, mul );
        v3 = _mm256_mul_ps( v3, mul );

        // Round to nearest integer
        v0 = _mm256_round_ps( v0, _MM_ROUND_NEAREST );
        v1 = _mm256_round_ps( v1, _MM_ROUND_NEAREST );
        v2 = _mm256_round_ps( v2, _MM_ROUND_NEAREST );
        v3 = _mm256_round_ps( v3, _MM_ROUND_NEAREST );

        // Convert floats to integers
        __m256i i0 = _mm256_cvtps_epi32( v0 );
        __m256i i1 = _mm256_cvtps_epi32( v1 );
        __m256i i2 = _mm256_cvtps_epi32( v2 );
        __m256i i3 = _mm256_cvtps_epi32( v3 );

#if defined(__AVX2__)
        // Compute the sum of the quants and set y[i].s
        y[i].s = d * hsum_i32_8(_mm256_add_epi32(_mm256_add_epi32(i0, i1), _mm256_add_epi32(i2, i3)));

        // Convert int32 to int16
        i0 = _mm256_packs_epi32( i0, i1 );	// 0, 1, 2, 3,  8, 9, 10, 11,  4, 5, 6, 7, 12, 13, 14, 15
        i2 = _mm256_packs_epi32( i2, i3 );	// 16, 17, 18, 19,  24, 25, 26, 27,  20, 21, 22, 23, 28, 29, 30, 31
                                            // Convert int16 to int8
        i0 = _mm256_packs_epi16( i0, i2 );	// 0, 1, 2, 3,  8, 9, 10, 11,  16, 17, 18, 19,  24, 25, 26, 27,  4, 5, 6, 7, 12, 13, 14, 15, 20, 21, 22, 23, 28, 29, 30, 31

        // We got our precious signed bytes, but the order is now wrong
        // These AVX2 pack instructions process 16-byte pieces independently
        // The following instruction is fixing the order
        const __m256i perm = _mm256_setr_epi32( 0, 4, 1, 5, 2, 6, 3, 7 );
        i0 = _mm256_permutevar8x32_epi32( i0, perm );

        _mm256_storeu_si256((__m256i *)y[i].qs, i0);
#else
        // Since we don't have in AVX some necessary functions,
        // we split the registers in half and call AVX2 analogs from SSE
        __m128i ni0 = _mm256_castsi256_si128( i0 );
        __m128i ni1 = _mm256_extractf128_si256( i0, 1);
        __m128i ni2 = _mm256_castsi256_si128( i1 );
        __m128i ni3 = _mm256_extractf128_si256( i1, 1);
        __m128i ni4 = _mm256_castsi256_si128( i2 );
        __m128i ni5 = _mm256_extractf128_si256( i2, 1);
        __m128i ni6 = _mm256_castsi256_si128( i3 );
        __m128i ni7 = _mm256_extractf128_si256( i3, 1);

        // Compute the sum of the quants and set y[i].s
        const __m128i s0 = _mm_add_epi32(_mm_add_epi32(ni0, ni1), _mm_add_epi32(ni2, ni3));
        const __m128i s1 = _mm_add_epi32(_mm_add_epi32(ni4, ni5), _mm_add_epi32(ni6, ni7));
        y[i].s = d * hsum_i32_4(_mm_add_epi32(s0, s1));

        // Convert int32 to int16
        ni0 = _mm_packs_epi32( ni0, ni1 );
        ni2 = _mm_packs_epi32( ni2, ni3 );
        ni4 = _mm_packs_epi32( ni4, ni5 );
        ni6 = _mm_packs_epi32( ni6, ni7 );
        // Convert int16 to int8
        ni0 = _mm_packs_epi16( ni0, ni2 );
        ni4 = _mm_packs_epi16( ni4, ni6 );

        _mm_storeu_si128((__m128i *)(y[i].qs +  0), ni0);
        _mm_storeu_si128((__m128i *)(y[i].qs + 16), ni4);
#endif
    }
#else
    // scalar
    quantize_row_q8_1_reference(x, y, k);
#endif
}

static void dequantize_row_q4_0(const block_q4_0 * restrict x, float * restrict y, int k) {
    static const int qk = QK4_0;

    assert(k % qk == 0);

    const int nb = k / qk;

    for (int i = 0; i < nb; i++) {
        const float d = GGML_FP16_TO_FP32(x[i].d);

        for (int j = 0; j < qk/2; ++j) {
            const int x0 = (x[i].qs[j] & 0x0F) - 8;
            const int x1 = (x[i].qs[j] >>   4) - 8;

            y[i*qk + j + 0   ] = x0*d;
            y[i*qk + j + qk/2] = x1*d;
        }
    }
}

static void dequantize_row_q4_1(const block_q4_1 * restrict x, float * restrict y, int k) {
    static const int qk = QK4_1;

    assert(k % qk == 0);

    const int nb = k / qk;

    for (int i = 0; i < nb; i++) {
        const float d = GGML_FP16_TO_FP32(x[i].d);
        const float m = GGML_FP16_TO_FP32(x[i].m);

        for (int j = 0; j < qk/2; ++j) {
            const int x0 = (x[i].qs[j] & 0x0F);
            const int x1 = (x[i].qs[j] >>   4);

            y[i*qk + j + 0   ] = x0*d + m;
            y[i*qk + j + qk/2] = x1*d + m;
        }
    }
}

static void dequantize_row_q5_0(const block_q5_0 * restrict x, float * restrict y, int k) {
    static const int qk = QK5_0;

    assert(k % qk == 0);

    const int nb = k / qk;

    for (int i = 0; i < nb; i++) {
        const float d = GGML_FP16_TO_FP32(x[i].d);

        uint32_t qh;
        memcpy(&qh, x[i].qh, sizeof(qh));

        for (int j = 0; j < qk/2; ++j) {
            const uint8_t xh_0 = ((qh >> (j +  0)) << 4) & 0x10;
            const uint8_t xh_1 = ((qh >> (j + 12))     ) & 0x10;

            const int32_t x0 = ((x[i].qs[j] & 0x0F) | xh_0) - 16;
            const int32_t x1 = ((x[i].qs[j] >>   4) | xh_1) - 16;

            y[i*qk + j + 0   ] = x0*d;
            y[i*qk + j + qk/2] = x1*d;
        }
    }
}

static void dequantize_row_q5_1(const block_q5_1 * restrict x, float * restrict y, int k) {
    static const int qk = QK5_1;

    assert(k % qk == 0);

    const int nb = k / qk;

    for (int i = 0; i < nb; i++) {
        const float d = GGML_FP16_TO_FP32(x[i].d);
        const float m = GGML_FP16_TO_FP32(x[i].m);

        uint32_t qh;
        memcpy(&qh, x[i].qh, sizeof(qh));

        for (int j = 0; j < qk/2; ++j) {
            const uint8_t xh_0 = ((qh >> (j +  0)) << 4) & 0x10;
            const uint8_t xh_1 = ((qh >> (j + 12))     ) & 0x10;

            const int x0 = (x[i].qs[j] & 0x0F) | xh_0;
            const int x1 = (x[i].qs[j] >>   4) | xh_1;

            y[i*qk + j + 0   ] = x0*d + m;
            y[i*qk + j + qk/2] = x1*d + m;
        }
    }
}

static void dequantize_row_q8_0(const void * restrict vx, float * restrict y, int k) {
    static const int qk = QK8_0;

    assert(k % qk == 0);

    const int nb = k / qk;

    const block_q8_0 * restrict x = vx;

    for (int i = 0; i < nb; i++) {
        const float d = GGML_FP16_TO_FP32(x[i].d);

        for (int j = 0; j < qk; ++j) {
            y[i*qk + j] = x[i].qs[j]*d;
        }
    }
}

static void ggml_vec_dot_f32(const int n, float * restrict s, const float * restrict x, const float * restrict y);
static void ggml_vec_dot_f16(const int n, float * restrict s, ggml_fp16_t * restrict x, ggml_fp16_t * restrict y);
static void ggml_vec_dot_q4_0_q8_0(const int n, float * restrict s, const void * restrict vx, const void * restrict vy);
static void ggml_vec_dot_q4_1_q8_1(const int n, float * restrict s, const void * restrict vx, const void * restrict vy);
static void ggml_vec_dot_q5_0_q8_0(const int n, float * restrict s, const void * restrict vx, const void * restrict vy);
static void ggml_vec_dot_q5_1_q8_1(const int n, float * restrict s, const void * restrict vx, const void * restrict vy);
static void ggml_vec_dot_q8_0_q8_0(const int n, float * restrict s, const void * restrict vx, const void * restrict vy);

static const ggml_type_traits_t type_traits[GGML_TYPE_COUNT] = {
    [GGML_TYPE_F32] = {
        .vec_dot                  = (ggml_vec_dot_t) ggml_vec_dot_f32,
        .vec_dot_type             = GGML_TYPE_F32,
    },
    [GGML_TYPE_F16] = {
        .to_float                 = (ggml_to_float_t) ggml_fp16_to_fp32_row,
        .from_float               = (ggml_from_float_t) ggml_fp32_to_fp16_row,
        .from_float_reference     = (ggml_from_float_t) ggml_fp32_to_fp16_row,
        .vec_dot                  = (ggml_vec_dot_t) ggml_vec_dot_f16,
        .vec_dot_type             = GGML_TYPE_F16,
    },
    [GGML_TYPE_Q4_0] = {
        .to_float                 = (ggml_to_float_t) dequantize_row_q4_0,
        .from_float               = quantize_row_q4_0,
        .from_float_reference     = (ggml_from_float_t) quantize_row_q4_0_reference,
        .vec_dot                  = ggml_vec_dot_q4_0_q8_0,
        .vec_dot_type             = GGML_TYPE_Q8_0,
    },
    [GGML_TYPE_Q4_1] = {
        .to_float                 = (ggml_to_float_t) dequantize_row_q4_1,
        .from_float               = quantize_row_q4_1,
        .from_float_reference     = (ggml_from_float_t) quantize_row_q4_1_reference,
        .vec_dot                  = ggml_vec_dot_q4_1_q8_1,
        .vec_dot_type             = GGML_TYPE_Q8_1,
    },
    [GGML_TYPE_Q5_0] = {
        .to_float                 = (ggml_to_float_t) dequantize_row_q5_0,
        .from_float               = quantize_row_q5_0,
        .from_float_reference     = (ggml_from_float_t) quantize_row_q5_0_reference,
        .vec_dot                  = ggml_vec_dot_q5_0_q8_0,
        .vec_dot_type             = GGML_TYPE_Q8_0,
    },
    [GGML_TYPE_Q5_1] = {
        .to_float                 = (ggml_to_float_t) dequantize_row_q5_1,
        .from_float               = quantize_row_q5_1,
        .from_float_reference     = (ggml_from_float_t) quantize_row_q5_1_reference,
        .vec_dot                  = ggml_vec_dot_q5_1_q8_1,
        .vec_dot_type             = GGML_TYPE_Q8_1,
    },
    [GGML_TYPE_Q8_0] = {
        .to_float                 = dequantize_row_q8_0,
        .from_float               = quantize_row_q8_0,
        .from_float_reference     = (ggml_from_float_t) quantize_row_q8_0_reference,
        .vec_dot                  = ggml_vec_dot_q8_0_q8_0,
        .vec_dot_type             = GGML_TYPE_Q8_0,
    },
    [GGML_TYPE_Q8_1] = {
        .from_float               = quantize_row_q8_1,
        .from_float_reference     = (ggml_from_float_t) quantize_row_q8_1_reference,
        .vec_dot_type             = GGML_TYPE_Q8_1,
    },
#ifdef GGML_USE_K_QUANTS
    [GGML_TYPE_Q2_K] = {
        .to_float                 = (ggml_to_float_t) dequantize_row_q2_K,
        .from_float               = quantize_row_q2_K,
        .from_float_reference     = (ggml_from_float_t) quantize_row_q2_K_reference,
        .vec_dot                  = ggml_vec_dot_q2_K_q8_K,
        .vec_dot_type             = GGML_TYPE_Q8_K,
    },
    [GGML_TYPE_Q3_K] = {
        .to_float                 = (ggml_to_float_t) dequantize_row_q3_K,
        .from_float               = quantize_row_q3_K,
        .from_float_reference     = (ggml_from_float_t) quantize_row_q3_K_reference,
        .vec_dot                  = ggml_vec_dot_q3_K_q8_K,
        .vec_dot_type             = GGML_TYPE_Q8_K,
    },
    [GGML_TYPE_Q4_K] = {
        .to_float                 = (ggml_to_float_t) dequantize_row_q4_K,
        .from_float               = quantize_row_q4_K,
        .from_float_reference     = (ggml_from_float_t) quantize_row_q4_K_reference,
        .vec_dot                  = ggml_vec_dot_q4_K_q8_K,
        .vec_dot_type             = GGML_TYPE_Q8_K,
    },
    [GGML_TYPE_Q5_K] = {
        .to_float                 = (ggml_to_float_t) dequantize_row_q5_K,
        .from_float               = quantize_row_q5_K,
        .from_float_reference     = (ggml_from_float_t) quantize_row_q5_K_reference,
        .vec_dot                  = ggml_vec_dot_q5_K_q8_K,
        .vec_dot_type             = GGML_TYPE_Q8_K,
    },
    [GGML_TYPE_Q6_K] = {
        .to_float                 = (ggml_to_float_t) dequantize_row_q6_K,
        .from_float               = quantize_row_q6_K,
        .from_float_reference     = (ggml_from_float_t) quantize_row_q6_K_reference,
        .vec_dot                  = ggml_vec_dot_q6_K_q8_K,
        .vec_dot_type             = GGML_TYPE_Q8_K,
    },
    [GGML_TYPE_Q8_K] = {
        .from_float               = quantize_row_q8_K,
    }
#endif
};

// For internal test use
ggml_type_traits_t ggml_internal_get_type_traits(enum ggml_type i) {
    GGML_ASSERT(i < GGML_TYPE_COUNT);
    return type_traits[i];
}


//
// simd mappings
//

// we define a common set of C macros which map to specific intrinsics based on the current architecture
// we then implement the fundamental computation operations below using only these macros
// adding support for new architectures requires to define the corresponding SIMD macros
//
// GGML_F32_STEP / GGML_F16_STEP
//   number of elements to process in a single step
//
// GGML_F32_EPR / GGML_F16_EPR
//   number of elements to fit in a single register
//

#if defined(__ARM_NEON) && defined(__ARM_FEATURE_FMA)

#define GGML_SIMD

// F32 NEON

#define GGML_F32_STEP 16
#define GGML_F32_EPR  4

#define GGML_F32x4              float32x4_t
#define GGML_F32x4_ZERO         vdupq_n_f32(0.0f)
#define GGML_F32x4_SET1(x)      vdupq_n_f32(x)
#define GGML_F32x4_LOAD         vld1q_f32
#define GGML_F32x4_STORE        vst1q_f32
#define GGML_F32x4_FMA(a, b, c) vfmaq_f32(a, b, c)
#define GGML_F32x4_ADD          vaddq_f32
#define GGML_F32x4_MUL          vmulq_f32
#define GGML_F32x4_REDUCE_ONE(x) vaddvq_f32(x)
#define GGML_F32x4_REDUCE(res, x)              \
{                                              \
    int offset = GGML_F32_ARR >> 1;            \
    for (int i = 0; i < offset; ++i) {         \
        x[i] = vaddq_f32(x[i], x[offset+i]);   \
    }                                          \
    offset >>= 1;                              \
    for (int i = 0; i < offset; ++i) {         \
        x[i] = vaddq_f32(x[i], x[offset+i]);   \
    }                                          \
    offset >>= 1;                              \
    for (int i = 0; i < offset; ++i) {         \
        x[i] = vaddq_f32(x[i], x[offset+i]);   \
    }                                          \
    res = GGML_F32x4_REDUCE_ONE(x[0]);         \
}

#define GGML_F32_VEC        GGML_F32x4
#define GGML_F32_VEC_ZERO   GGML_F32x4_ZERO
#define GGML_F32_VEC_SET1   GGML_F32x4_SET1
#define GGML_F32_VEC_LOAD   GGML_F32x4_LOAD
#define GGML_F32_VEC_STORE  GGML_F32x4_STORE
#define GGML_F32_VEC_FMA    GGML_F32x4_FMA
#define GGML_F32_VEC_ADD    GGML_F32x4_ADD
#define GGML_F32_VEC_MUL    GGML_F32x4_MUL
#define GGML_F32_VEC_REDUCE GGML_F32x4_REDUCE

// F16 NEON

#if defined(__ARM_FEATURE_FP16_VECTOR_ARITHMETIC)
    #define GGML_F16_STEP 32
    #define GGML_F16_EPR  8

    #define GGML_F16x8              float16x8_t
    #define GGML_F16x8_ZERO         vdupq_n_f16(0.0f)
    #define GGML_F16x8_SET1(x)      vdupq_n_f16(x)
    #define GGML_F16x8_LOAD         vld1q_f16
    #define GGML_F16x8_STORE        vst1q_f16
    #define GGML_F16x8_FMA(a, b, c) vfmaq_f16(a, b, c)
    #define GGML_F16x8_ADD          vaddq_f16
    #define GGML_F16x8_MUL          vmulq_f16
    #define GGML_F16x8_REDUCE(res, x)                             \
    {                                                             \
        int offset = GGML_F16_ARR >> 1;                           \
        for (int i = 0; i < offset; ++i) {                        \
            x[i] = vaddq_f16(x[i], x[offset+i]);                  \
        }                                                         \
        offset >>= 1;                                             \
        for (int i = 0; i < offset; ++i) {                        \
            x[i] = vaddq_f16(x[i], x[offset+i]);                  \
        }                                                         \
        offset >>= 1;                                             \
        for (int i = 0; i < offset; ++i) {                        \
            x[i] = vaddq_f16(x[i], x[offset+i]);                  \
        }                                                         \
        const float32x4_t t0 = vcvt_f32_f16(vget_low_f16 (x[0])); \
        const float32x4_t t1 = vcvt_f32_f16(vget_high_f16(x[0])); \
        res = (ggml_float) vaddvq_f32(vaddq_f32(t0, t1));         \
    }

    #define GGML_F16_VEC                GGML_F16x8
    #define GGML_F16_VEC_ZERO           GGML_F16x8_ZERO
    #define GGML_F16_VEC_SET1           GGML_F16x8_SET1
    #define GGML_F16_VEC_LOAD(p, i)     GGML_F16x8_LOAD(p)
    #define GGML_F16_VEC_STORE(p, r, i) GGML_F16x8_STORE(p, r[i])
    #define GGML_F16_VEC_FMA            GGML_F16x8_FMA
    #define GGML_F16_VEC_ADD            GGML_F16x8_ADD
    #define GGML_F16_VEC_MUL            GGML_F16x8_MUL
    #define GGML_F16_VEC_REDUCE         GGML_F16x8_REDUCE
#else
    // if FP16 vector arithmetic is not supported, we use FP32 instead
    // and take advantage of the vcvt_ functions to convert to/from FP16

    #define GGML_F16_STEP 16
    #define GGML_F16_EPR  4

    #define GGML_F32Cx4              float32x4_t
    #define GGML_F32Cx4_ZERO         vdupq_n_f32(0.0f)
    #define GGML_F32Cx4_SET1(x)      vdupq_n_f32(x)
    #define GGML_F32Cx4_LOAD(x)      vcvt_f32_f16(vld1_f16(x))
    #define GGML_F32Cx4_STORE(x, y)  vst1_f16(x, vcvt_f16_f32(y))
    #define GGML_F32Cx4_FMA(a, b, c) vfmaq_f32(a, b, c)
    #define GGML_F32Cx4_ADD          vaddq_f32
    #define GGML_F32Cx4_MUL          vmulq_f32
    #define GGML_F32Cx4_REDUCE       GGML_F32x4_REDUCE

    #define GGML_F16_VEC                GGML_F32Cx4
    #define GGML_F16_VEC_ZERO           GGML_F32Cx4_ZERO
    #define GGML_F16_VEC_SET1           GGML_F32Cx4_SET1
    #define GGML_F16_VEC_LOAD(p, i)     GGML_F32Cx4_LOAD(p)
    #define GGML_F16_VEC_STORE(p, r, i) GGML_F32Cx4_STORE(p, r[i])
    #define GGML_F16_VEC_FMA            GGML_F32Cx4_FMA
    #define GGML_F16_VEC_ADD            GGML_F32Cx4_ADD
    #define GGML_F16_VEC_MUL            GGML_F32Cx4_MUL
    #define GGML_F16_VEC_REDUCE         GGML_F32Cx4_REDUCE
#endif

#elif defined(__AVX__)

#define GGML_SIMD

// F32 AVX

#define GGML_F32_STEP 32
#define GGML_F32_EPR  8

#define GGML_F32x8         __m256
#define GGML_F32x8_ZERO    _mm256_setzero_ps()
#define GGML_F32x8_SET1(x) _mm256_set1_ps(x)
#define GGML_F32x8_LOAD    _mm256_loadu_ps
#define GGML_F32x8_STORE   _mm256_storeu_ps
#if defined(__FMA__)
    #define GGML_F32x8_FMA(a, b, c) _mm256_fmadd_ps(b, c, a)
#else
    #define GGML_F32x8_FMA(a, b, c) _mm256_add_ps(_mm256_mul_ps(b, c), a)
#endif
#define GGML_F32x8_ADD     _mm256_add_ps
#define GGML_F32x8_MUL     _mm256_mul_ps
#define GGML_F32x8_REDUCE(res, x)                                 \
{                                                                 \
    int offset = GGML_F32_ARR >> 1;                               \
    for (int i = 0; i < offset; ++i) {                            \
        x[i] = _mm256_add_ps(x[i], x[offset+i]);                  \
    }                                                             \
    offset >>= 1;                                                 \
    for (int i = 0; i < offset; ++i) {                            \
        x[i] = _mm256_add_ps(x[i], x[offset+i]);                  \
    }                                                             \
    offset >>= 1;                                                 \
    for (int i = 0; i < offset; ++i) {                            \
        x[i] = _mm256_add_ps(x[i], x[offset+i]);                  \
    }                                                             \
    const __m128 t0 = _mm_add_ps(_mm256_castps256_ps128(x[0]),    \
                                 _mm256_extractf128_ps(x[0], 1)); \
    const __m128 t1 = _mm_hadd_ps(t0, t0);                        \
    res = _mm_cvtss_f32(_mm_hadd_ps(t1, t1));                     \
}
// TODO: is this optimal ?

#define GGML_F32_VEC        GGML_F32x8
#define GGML_F32_VEC_ZERO   GGML_F32x8_ZERO
#define GGML_F32_VEC_SET1   GGML_F32x8_SET1
#define GGML_F32_VEC_LOAD   GGML_F32x8_LOAD
#define GGML_F32_VEC_STORE  GGML_F32x8_STORE
#define GGML_F32_VEC_FMA    GGML_F32x8_FMA
#define GGML_F32_VEC_ADD    GGML_F32x8_ADD
#define GGML_F32_VEC_MUL    GGML_F32x8_MUL
#define GGML_F32_VEC_REDUCE GGML_F32x8_REDUCE

// F16 AVX

#define GGML_F16_STEP 32
#define GGML_F16_EPR  8

// F16 arithmetic is not supported by AVX, so we use F32 instead

#define GGML_F32Cx8             __m256
#define GGML_F32Cx8_ZERO        _mm256_setzero_ps()
#define GGML_F32Cx8_SET1(x)     _mm256_set1_ps(x)

#if defined(__F16C__)
// the  _mm256_cvt intrinsics require F16C
#define GGML_F32Cx8_LOAD(x)     _mm256_cvtph_ps(_mm_loadu_si128((__m128i *)(x)))
#define GGML_F32Cx8_STORE(x, y) _mm_storeu_si128((__m128i *)(x), _mm256_cvtps_ph(y, 0))
#else
static inline __m256 __avx_f32cx8_load(ggml_fp16_t *x) {
    float tmp[8];

    for (int i = 0; i < 8; i++) {
        tmp[i] = GGML_FP16_TO_FP32(x[i]);
    }

    return _mm256_loadu_ps(tmp);
}
static inline void __avx_f32cx8_store(ggml_fp16_t *x, __m256 y) {
    float arr[8];

    _mm256_storeu_ps(arr, y);

    for (int i = 0; i < 8; i++)
        x[i] = GGML_FP32_TO_FP16(arr[i]);
}
#define GGML_F32Cx8_LOAD(x)     __avx_f32cx8_load(x)
#define GGML_F32Cx8_STORE(x, y) __avx_f32cx8_store(x, y)
#endif

#define GGML_F32Cx8_FMA         GGML_F32x8_FMA
#define GGML_F32Cx8_ADD         _mm256_add_ps
#define GGML_F32Cx8_MUL         _mm256_mul_ps
#define GGML_F32Cx8_REDUCE      GGML_F32x8_REDUCE

#define GGML_F16_VEC                GGML_F32Cx8
#define GGML_F16_VEC_ZERO           GGML_F32Cx8_ZERO
#define GGML_F16_VEC_SET1           GGML_F32Cx8_SET1
#define GGML_F16_VEC_LOAD(p, i)     GGML_F32Cx8_LOAD(p)
#define GGML_F16_VEC_STORE(p, r, i) GGML_F32Cx8_STORE(p, r[i])
#define GGML_F16_VEC_FMA            GGML_F32Cx8_FMA
#define GGML_F16_VEC_ADD            GGML_F32Cx8_ADD
#define GGML_F16_VEC_MUL            GGML_F32Cx8_MUL
#define GGML_F16_VEC_REDUCE         GGML_F32Cx8_REDUCE

#elif defined(__POWER9_VECTOR__)

#define GGML_SIMD

// F32 POWER9

#define GGML_F32_STEP 32
#define GGML_F32_EPR  4

#define GGML_F32x4              vector float
#define GGML_F32x4_ZERO         0.0f
#define GGML_F32x4_SET1         vec_splats
#define GGML_F32x4_LOAD(p)      vec_xl(0, p)
#define GGML_F32x4_STORE(p, r)  vec_xst(r, 0, p)
#define GGML_F32x4_FMA(a, b, c) vec_madd(b, c, a)
#define GGML_F32x4_ADD          vec_add
#define GGML_F32x4_MUL          vec_mul
#define GGML_F32x4_REDUCE(res, x)              \
{                                              \
    int offset = GGML_F32_ARR >> 1;            \
    for (int i = 0; i < offset; ++i) {         \
        x[i] = vec_add(x[i], x[offset+i]);     \
    }                                          \
    offset >>= 1;                              \
    for (int i = 0; i < offset; ++i) {         \
        x[i] = vec_add(x[i], x[offset+i]);     \
    }                                          \
    offset >>= 1;                              \
    for (int i = 0; i < offset; ++i) {         \
        x[i] = vec_add(x[i], x[offset+i]);     \
    }                                          \
    res = vec_extract(x[0], 0) +               \
          vec_extract(x[0], 1) +               \
          vec_extract(x[0], 2) +               \
          vec_extract(x[0], 3);                \
}

#define GGML_F32_VEC        GGML_F32x4
#define GGML_F32_VEC_ZERO   GGML_F32x4_ZERO
#define GGML_F32_VEC_SET1   GGML_F32x4_SET1
#define GGML_F32_VEC_LOAD   GGML_F32x4_LOAD
#define GGML_F32_VEC_STORE  GGML_F32x4_STORE
#define GGML_F32_VEC_FMA    GGML_F32x4_FMA
#define GGML_F32_VEC_ADD    GGML_F32x4_ADD
#define GGML_F32_VEC_MUL    GGML_F32x4_MUL
#define GGML_F32_VEC_REDUCE GGML_F32x4_REDUCE

// F16 POWER9
#define GGML_F16_STEP       GGML_F32_STEP
#define GGML_F16_EPR        GGML_F32_EPR
#define GGML_F16_VEC        GGML_F32x4
#define GGML_F16_VEC_ZERO   GGML_F32x4_ZERO
#define GGML_F16_VEC_SET1   GGML_F32x4_SET1
#define GGML_F16_VEC_FMA    GGML_F32x4_FMA
#define GGML_F16_VEC_REDUCE GGML_F32x4_REDUCE
// Use vec_xl, not vec_ld, in case the load address is not aligned.
#define GGML_F16_VEC_LOAD(p, i) (i & 0x1) ?                   \
  vec_extract_fp32_from_shorth(vec_xl(0, p - GGML_F16_EPR)) : \
  vec_extract_fp32_from_shortl(vec_xl(0, p))
#define GGML_ENDIAN_BYTE(i) ((unsigned char *)&(uint16_t){1})[i]
#define GGML_F16_VEC_STORE(p, r, i)                             \
  if (i & 0x1)                                                  \
    vec_xst(vec_pack_to_short_fp32(r[i - GGML_ENDIAN_BYTE(1)],  \
                                   r[i - GGML_ENDIAN_BYTE(0)]), \
            0, p - GGML_F16_EPR)

#elif defined(__wasm_simd128__)

#define GGML_SIMD

// F32 WASM

#define GGML_F32_STEP 16
#define GGML_F32_EPR  4

#define GGML_F32x4              v128_t
#define GGML_F32x4_ZERO         wasm_f32x4_splat(0.0f)
#define GGML_F32x4_SET1(x)      wasm_f32x4_splat(x)
#define GGML_F32x4_LOAD         wasm_v128_load
#define GGML_F32x4_STORE        wasm_v128_store
#define GGML_F32x4_FMA(a, b, c) wasm_f32x4_add(wasm_f32x4_mul(b, c), a)
#define GGML_F32x4_ADD          wasm_f32x4_add
#define GGML_F32x4_MUL          wasm_f32x4_mul
#define GGML_F32x4_REDUCE(res, x)                  \
{                                                  \
    int offset = GGML_F32_ARR >> 1;                \
    for (int i = 0; i < offset; ++i) {             \
        x[i] = wasm_f32x4_add(x[i], x[offset+i]);  \
    }                                              \
    offset >>= 1;                                  \
    for (int i = 0; i < offset; ++i) {             \
        x[i] = wasm_f32x4_add(x[i], x[offset+i]);  \
    }                                              \
    offset >>= 1;                                  \
    for (int i = 0; i < offset; ++i) {             \
        x[i] = wasm_f32x4_add(x[i], x[offset+i]);  \
    }                                              \
    res = wasm_f32x4_extract_lane(x[0], 0) +       \
          wasm_f32x4_extract_lane(x[0], 1) +       \
          wasm_f32x4_extract_lane(x[0], 2) +       \
          wasm_f32x4_extract_lane(x[0], 3);        \
}

#define GGML_F32_VEC        GGML_F32x4
#define GGML_F32_VEC_ZERO   GGML_F32x4_ZERO
#define GGML_F32_VEC_SET1   GGML_F32x4_SET1
#define GGML_F32_VEC_LOAD   GGML_F32x4_LOAD
#define GGML_F32_VEC_STORE  GGML_F32x4_STORE
#define GGML_F32_VEC_FMA    GGML_F32x4_FMA
#define GGML_F32_VEC_ADD    GGML_F32x4_ADD
#define GGML_F32_VEC_MUL    GGML_F32x4_MUL
#define GGML_F32_VEC_REDUCE GGML_F32x4_REDUCE

// F16 WASM

#define GGML_F16_STEP 16
#define GGML_F16_EPR  4

inline static v128_t __wasm_f16x4_load(const ggml_fp16_t * p) {
    float tmp[4];

    tmp[0] = GGML_FP16_TO_FP32(p[0]);
    tmp[1] = GGML_FP16_TO_FP32(p[1]);
    tmp[2] = GGML_FP16_TO_FP32(p[2]);
    tmp[3] = GGML_FP16_TO_FP32(p[3]);

    return wasm_v128_load(tmp);
}

inline static void __wasm_f16x4_store(ggml_fp16_t * p, v128_t x) {
    float tmp[4];

    wasm_v128_store(tmp, x);

    p[0] = GGML_FP32_TO_FP16(tmp[0]);
    p[1] = GGML_FP32_TO_FP16(tmp[1]);
    p[2] = GGML_FP32_TO_FP16(tmp[2]);
    p[3] = GGML_FP32_TO_FP16(tmp[3]);
}

#define GGML_F16x4             v128_t
#define GGML_F16x4_ZERO        wasm_f32x4_splat(0.0f)
#define GGML_F16x4_SET1(x)     wasm_f32x4_splat(x)
#define GGML_F16x4_LOAD(x)     __wasm_f16x4_load(x)
#define GGML_F16x4_STORE(x, y) __wasm_f16x4_store(x, y)
#define GGML_F16x4_FMA         GGML_F32x4_FMA
#define GGML_F16x4_ADD         wasm_f32x4_add
#define GGML_F16x4_MUL         wasm_f32x4_mul
#define GGML_F16x4_REDUCE(res, x)                  \
{                                                  \
    int offset = GGML_F16_ARR >> 1;                \
    for (int i = 0; i < offset; ++i) {             \
        x[i] = wasm_f32x4_add(x[i], x[offset+i]);  \
    }                                              \
    offset >>= 1;                                  \
    for (int i = 0; i < offset; ++i) {             \
        x[i] = wasm_f32x4_add(x[i], x[offset+i]);  \
    }                                              \
    offset >>= 1;                                  \
    for (int i = 0; i < offset; ++i) {             \
        x[i] = wasm_f32x4_add(x[i], x[offset+i]);  \
    }                                              \
    res = wasm_f32x4_extract_lane(x[0], 0) +       \
          wasm_f32x4_extract_lane(x[0], 1) +       \
          wasm_f32x4_extract_lane(x[0], 2) +       \
          wasm_f32x4_extract_lane(x[0], 3);        \
}

#define GGML_F16_VEC                GGML_F16x4
#define GGML_F16_VEC_ZERO           GGML_F16x4_ZERO
#define GGML_F16_VEC_SET1           GGML_F16x4_SET1
#define GGML_F16_VEC_LOAD(p, i)     GGML_F16x4_LOAD(p)
#define GGML_F16_VEC_STORE(p, r, i) GGML_F16x4_STORE(p, r[i])
#define GGML_F16_VEC_FMA            GGML_F16x4_FMA
#define GGML_F16_VEC_ADD            GGML_F16x4_ADD
#define GGML_F16_VEC_MUL            GGML_F16x4_MUL
#define GGML_F16_VEC_REDUCE         GGML_F16x4_REDUCE

#elif defined(__SSE3__)

#define GGML_SIMD

// F32 SSE

#define GGML_F32_STEP 32
#define GGML_F32_EPR  4

#define GGML_F32x4         __m128
#define GGML_F32x4_ZERO    _mm_setzero_ps()
#define GGML_F32x4_SET1(x) _mm_set1_ps(x)
#define GGML_F32x4_LOAD    _mm_loadu_ps
#define GGML_F32x4_STORE   _mm_storeu_ps
#if defined(__FMA__)
    // TODO: Does this work?
    #define GGML_F32x4_FMA(a, b, c) _mm_fmadd_ps(b, c, a)
#else
    #define GGML_F32x4_FMA(a, b, c) _mm_add_ps(_mm_mul_ps(b, c), a)
#endif
#define GGML_F32x4_ADD     _mm_add_ps
#define GGML_F32x4_MUL     _mm_mul_ps
#define GGML_F32x4_REDUCE(res, x)                                 \
{                                                                 \
    int offset = GGML_F32_ARR >> 1;                               \
    for (int i = 0; i < offset; ++i) {                            \
        x[i] = _mm_add_ps(x[i], x[offset+i]);                     \
    }                                                             \
    offset >>= 1;                                                 \
    for (int i = 0; i < offset; ++i) {                            \
        x[i] = _mm_add_ps(x[i], x[offset+i]);                     \
    }                                                             \
    offset >>= 1;                                                 \
    for (int i = 0; i < offset; ++i) {                            \
        x[i] = _mm_add_ps(x[i], x[offset+i]);                     \
    }                                                             \
    const __m128 t0 = _mm_hadd_ps(x[0], x[0]);                    \
    res = _mm_cvtss_f32(_mm_hadd_ps(t0, t0));                     \
}
// TODO: is this optimal ?

#define GGML_F32_VEC        GGML_F32x4
#define GGML_F32_VEC_ZERO   GGML_F32x4_ZERO
#define GGML_F32_VEC_SET1   GGML_F32x4_SET1
#define GGML_F32_VEC_LOAD   GGML_F32x4_LOAD
#define GGML_F32_VEC_STORE  GGML_F32x4_STORE
#define GGML_F32_VEC_FMA    GGML_F32x4_FMA
#define GGML_F32_VEC_ADD    GGML_F32x4_ADD
#define GGML_F32_VEC_MUL    GGML_F32x4_MUL
#define GGML_F32_VEC_REDUCE GGML_F32x4_REDUCE

// F16 SSE

#define GGML_F16_STEP 32
#define GGML_F16_EPR  4

static inline __m128 __sse_f16x4_load(ggml_fp16_t *x) {
    float tmp[4];

    tmp[0] = GGML_FP16_TO_FP32(x[0]);
    tmp[1] = GGML_FP16_TO_FP32(x[1]);
    tmp[2] = GGML_FP16_TO_FP32(x[2]);
    tmp[3] = GGML_FP16_TO_FP32(x[3]);

    return _mm_loadu_ps(tmp);
}

static inline void __sse_f16x4_store(ggml_fp16_t *x, __m128 y) {
    float arr[4];

    _mm_storeu_ps(arr, y);

    x[0] = GGML_FP32_TO_FP16(arr[0]);
    x[1] = GGML_FP32_TO_FP16(arr[1]);
    x[2] = GGML_FP32_TO_FP16(arr[2]);
    x[3] = GGML_FP32_TO_FP16(arr[3]);
}

#define GGML_F32Cx4             __m128
#define GGML_F32Cx4_ZERO        _mm_setzero_ps()
#define GGML_F32Cx4_SET1(x)     _mm_set1_ps(x)
#define GGML_F32Cx4_LOAD(x)     __sse_f16x4_load(x)
#define GGML_F32Cx4_STORE(x, y) __sse_f16x4_store(x, y)
#define GGML_F32Cx4_FMA         GGML_F32x4_FMA
#define GGML_F32Cx4_ADD         _mm_add_ps
#define GGML_F32Cx4_MUL         _mm_mul_ps
#define GGML_F32Cx4_REDUCE      GGML_F32x4_REDUCE

#define GGML_F16_VEC                 GGML_F32Cx4
#define GGML_F16_VEC_ZERO            GGML_F32Cx4_ZERO
#define GGML_F16_VEC_SET1            GGML_F32Cx4_SET1
#define GGML_F16_VEC_LOAD(p, i)      GGML_F32Cx4_LOAD(p)
#define GGML_F16_VEC_STORE(p, r, i)  GGML_F32Cx4_STORE(p, r[i])
#define GGML_F16_VEC_FMA             GGML_F32Cx4_FMA
#define GGML_F16_VEC_ADD             GGML_F32Cx4_ADD
#define GGML_F16_VEC_MUL             GGML_F32Cx4_MUL
#define GGML_F16_VEC_REDUCE          GGML_F32Cx4_REDUCE

#endif

// GGML_F32_ARR / GGML_F16_ARR
//   number of registers to use per step
#ifdef GGML_SIMD
#define GGML_F32_ARR (GGML_F32_STEP/GGML_F32_EPR)
#define GGML_F16_ARR (GGML_F16_STEP/GGML_F16_EPR)
#endif

//
// fundamental operations
//

inline static void ggml_vec_set_i8(const int n, int8_t * x, const int8_t v) { for (int i = 0; i < n; ++i) x[i] = v; }

inline static void ggml_vec_set_i16(const int n, int16_t * x, const int16_t v) { for (int i = 0; i < n; ++i) x[i] = v; }

inline static void ggml_vec_set_i32(const int n, int32_t * x, const int32_t v) { for (int i = 0; i < n; ++i) x[i] = v; }

inline static void ggml_vec_set_f16(const int n, ggml_fp16_t * x, const int32_t v) { for (int i = 0; i < n; ++i) x[i] = v; }

inline static void ggml_vec_add_f32 (const int n, float * z, const float * x, const float * y) { for (int i = 0; i < n; ++i) z[i]  = x[i] + y[i]; }
inline static void ggml_vec_add1_f32(const int n, float * z, const float * x, const float   v) { for (int i = 0; i < n; ++i) z[i]  = x[i] + v;    }
inline static void ggml_vec_acc_f32 (const int n, float * y, const float * x)                  { for (int i = 0; i < n; ++i) y[i] += x[i];        }
inline static void ggml_vec_acc1_f32(const int n, float * y, const float   v)                  { for (int i = 0; i < n; ++i) y[i] += v;           }
inline static void ggml_vec_sub_f32 (const int n, float * z, const float * x, const float * y) { for (int i = 0; i < n; ++i) z[i]  = x[i] - y[i]; }
inline static void ggml_vec_set_f32 (const int n, float * x, const float   v)                  { for (int i = 0; i < n; ++i) x[i]  = v;           }
inline static void ggml_vec_cpy_f32 (const int n, float * y, const float * x)                  { for (int i = 0; i < n; ++i) y[i]  = x[i];        }
inline static void ggml_vec_neg_f32 (const int n, float * y, const float * x)                  { for (int i = 0; i < n; ++i) y[i]  = -x[i];       }
inline static void ggml_vec_mul_f32 (const int n, float * z, const float * x, const float * y) { for (int i = 0; i < n; ++i) z[i]  = x[i]*y[i];   }
inline static void ggml_vec_div_f32 (const int n, float * z, const float * x, const float * y) { for (int i = 0; i < n; ++i) z[i]  = x[i]/y[i];   }

static void ggml_vec_dot_f32(const int n, float * restrict s, const float * restrict x, const float * restrict y) {
#ifdef GGML_SIMD
    float sumf = 0.0f;
    const int np = (n & ~(GGML_F32_STEP - 1));

    GGML_F32_VEC sum[GGML_F32_ARR] = { GGML_F32_VEC_ZERO };

    GGML_F32_VEC ax[GGML_F32_ARR];
    GGML_F32_VEC ay[GGML_F32_ARR];

    for (int i = 0; i < np; i += GGML_F32_STEP) {
        for (int j = 0; j < GGML_F32_ARR; j++) {
            ax[j] = GGML_F32_VEC_LOAD(x + i + j*GGML_F32_EPR);
            ay[j] = GGML_F32_VEC_LOAD(y + i + j*GGML_F32_EPR);

            sum[j] = GGML_F32_VEC_FMA(sum[j], ax[j], ay[j]);
        }
    }

    // reduce sum0..sum3 to sum0
    GGML_F32_VEC_REDUCE(sumf, sum);

    // leftovers
    for (int i = np; i < n; ++i) {
        sumf += x[i]*y[i];
    }
#else
    // scalar
    ggml_float sumf = 0.0;
    for (int i = 0; i < n; ++i) {
        sumf += (ggml_float)(x[i]*y[i]);
    }
#endif

    *s = sumf;
}

static void ggml_vec_dot_f16(const int n, float * restrict s, ggml_fp16_t * restrict x, ggml_fp16_t * restrict y) {
    ggml_float sumf = 0.0;

#if defined(GGML_SIMD)
    const int np = (n & ~(GGML_F16_STEP - 1));

    GGML_F16_VEC sum[GGML_F16_ARR] = { GGML_F16_VEC_ZERO };

    GGML_F16_VEC ax[GGML_F16_ARR];
    GGML_F16_VEC ay[GGML_F16_ARR];

    for (int i = 0; i < np; i += GGML_F16_STEP) {
        for (int j = 0; j < GGML_F16_ARR; j++) {
            ax[j] = GGML_F16_VEC_LOAD(x + i + j*GGML_F16_EPR, j);
            ay[j] = GGML_F16_VEC_LOAD(y + i + j*GGML_F16_EPR, j);

            sum[j] = GGML_F16_VEC_FMA(sum[j], ax[j], ay[j]);
        }
    }

    // reduce sum0..sum3 to sum0
    GGML_F16_VEC_REDUCE(sumf, sum);

    // leftovers
    for (int i = np; i < n; ++i) {
        sumf += (ggml_float)(GGML_FP16_TO_FP32(x[i])*GGML_FP16_TO_FP32(y[i]));
    }
#else
    for (int i = 0; i < n; ++i) {
        sumf += (ggml_float)(GGML_FP16_TO_FP32(x[i])*GGML_FP16_TO_FP32(y[i]));
    }
#endif

    *s = sumf;
}

static void ggml_vec_dot_q4_0_q8_0(const int n, float * restrict s, const void * restrict vx, const void * restrict vy) {
    const int qk = QK8_0;
    const int nb = n / qk;

    assert(n % qk == 0);
    assert(nb % 2 == 0);

    const block_q4_0 * restrict x = vx;
    const block_q8_0 * restrict y = vy;

#if defined(__ARM_NEON)
    float32x4_t sumv0 = vdupq_n_f32(0.0f);
    float32x4_t sumv1 = vdupq_n_f32(0.0f);

    for (int i = 0; i < nb; i += 2) {
        const block_q4_0 * restrict x0 = &x[i + 0];
        const block_q4_0 * restrict x1 = &x[i + 1];
        const block_q8_0 * restrict y0 = &y[i + 0];
        const block_q8_0 * restrict y1 = &y[i + 1];

        const uint8x16_t m4b = vdupq_n_u8(0x0F);
        const int8x16_t  s8b = vdupq_n_s8(0x8);

        const uint8x16_t v0_0 = vld1q_u8(x0->qs);
        const uint8x16_t v0_1 = vld1q_u8(x1->qs);

        // 4-bit -> 8-bit
        const int8x16_t v0_0l = vreinterpretq_s8_u8(vandq_u8  (v0_0, m4b));
        const int8x16_t v0_0h = vreinterpretq_s8_u8(vshrq_n_u8(v0_0, 4));
        const int8x16_t v0_1l = vreinterpretq_s8_u8(vandq_u8  (v0_1, m4b));
        const int8x16_t v0_1h = vreinterpretq_s8_u8(vshrq_n_u8(v0_1, 4));

        // sub 8
        const int8x16_t v0_0ls = vsubq_s8(v0_0l, s8b);
        const int8x16_t v0_0hs = vsubq_s8(v0_0h, s8b);
        const int8x16_t v0_1ls = vsubq_s8(v0_1l, s8b);
        const int8x16_t v0_1hs = vsubq_s8(v0_1h, s8b);

        // load y
        const int8x16_t v1_0l = vld1q_s8(y0->qs);
        const int8x16_t v1_0h = vld1q_s8(y0->qs + 16);
        const int8x16_t v1_1l = vld1q_s8(y1->qs);
        const int8x16_t v1_1h = vld1q_s8(y1->qs + 16);

#if defined(__ARM_FEATURE_DOTPROD)
        // dot product into int32x4_t
        const int32x4_t p_0 = vdotq_s32(vdotq_s32(vdupq_n_s32(0), v0_0ls, v1_0l), v0_0hs, v1_0h);
        const int32x4_t p_1 = vdotq_s32(vdotq_s32(vdupq_n_s32(0), v0_1ls, v1_1l), v0_1hs, v1_1h);

        sumv0 = vmlaq_n_f32(sumv0, vcvtq_f32_s32(p_0), GGML_FP16_TO_FP32(x0->d)*GGML_FP16_TO_FP32(y0->d));
        sumv1 = vmlaq_n_f32(sumv1, vcvtq_f32_s32(p_1), GGML_FP16_TO_FP32(x1->d)*GGML_FP16_TO_FP32(y1->d));
#else
        const int16x8_t pl0l = vmull_s8(vget_low_s8 (v0_0ls), vget_low_s8 (v1_0l));
        const int16x8_t pl0h = vmull_s8(vget_high_s8(v0_0ls), vget_high_s8(v1_0l));
        const int16x8_t ph0l = vmull_s8(vget_low_s8 (v0_0hs), vget_low_s8 (v1_0h));
        const int16x8_t ph0h = vmull_s8(vget_high_s8(v0_0hs), vget_high_s8(v1_0h));

        const int16x8_t pl1l = vmull_s8(vget_low_s8 (v0_1ls), vget_low_s8 (v1_1l));
        const int16x8_t pl1h = vmull_s8(vget_high_s8(v0_1ls), vget_high_s8(v1_1l));
        const int16x8_t ph1l = vmull_s8(vget_low_s8 (v0_1hs), vget_low_s8 (v1_1h));
        const int16x8_t ph1h = vmull_s8(vget_high_s8(v0_1hs), vget_high_s8(v1_1h));

        const int32x4_t pl0 = vaddq_s32(vpaddlq_s16(pl0l), vpaddlq_s16(pl0h));
        const int32x4_t ph0 = vaddq_s32(vpaddlq_s16(ph0l), vpaddlq_s16(ph0h));
        const int32x4_t pl1 = vaddq_s32(vpaddlq_s16(pl1l), vpaddlq_s16(pl1h));
        const int32x4_t ph1 = vaddq_s32(vpaddlq_s16(ph1l), vpaddlq_s16(ph1h));

        sumv0 = vmlaq_n_f32(sumv0, vcvtq_f32_s32(vaddq_s32(pl0, ph0)), GGML_FP16_TO_FP32(x0->d)*GGML_FP16_TO_FP32(y0->d));
        sumv1 = vmlaq_n_f32(sumv1, vcvtq_f32_s32(vaddq_s32(pl1, ph1)), GGML_FP16_TO_FP32(x1->d)*GGML_FP16_TO_FP32(y1->d));
#endif
    }

    *s = vaddvq_f32(sumv0) + vaddvq_f32(sumv1);
#elif defined(__AVX2__)
    // Initialize accumulator with zeros
    __m256 acc = _mm256_setzero_ps();

    // Main loop
    for (int i = 0; i < nb; ++i) {
        /* Compute combined scale for the block */
        const __m256 d = _mm256_set1_ps( GGML_FP16_TO_FP32(x[i].d) * GGML_FP16_TO_FP32(y[i].d) );

        __m256i bx = bytes_from_nibbles_32(x[i].qs);

        // Now we have a vector with bytes in [ 0 .. 15 ] interval. Offset them into [ -8 .. +7 ] interval.
        const __m256i off = _mm256_set1_epi8( 8 );
        bx = _mm256_sub_epi8( bx, off );

        __m256i by = _mm256_loadu_si256((const __m256i *)y[i].qs);

        const __m256 q = mul_sum_i8_pairs_float(bx, by);

        /* Multiply q with scale and accumulate */
        acc = _mm256_fmadd_ps( d, q, acc );
    }

    *s = hsum_float_8(acc);
#elif defined(__AVX__)
    // Initialize accumulator with zeros
    __m256 acc = _mm256_setzero_ps();

    // Main loop
    for (int i = 0; i < nb; ++i) {
        // Compute combined scale for the block
        const __m256 d = _mm256_set1_ps( GGML_FP16_TO_FP32(x[i].d) * GGML_FP16_TO_FP32(y[i].d) );

        const __m128i lowMask = _mm_set1_epi8(0xF);
        const __m128i off = _mm_set1_epi8(8);

        const __m128i tmp = _mm_loadu_si128((const __m128i *)x[i].qs);

        __m128i bx = _mm_and_si128(lowMask, tmp);
        __m128i by = _mm_loadu_si128((const __m128i *)y[i].qs);
        bx = _mm_sub_epi8(bx, off);
        const __m128i i32_0 = mul_sum_i8_pairs(bx, by);

        bx = _mm_and_si128(lowMask, _mm_srli_epi64(tmp, 4));
        by = _mm_loadu_si128((const __m128i *)(y[i].qs + 16));
        bx = _mm_sub_epi8(bx, off);
        const __m128i i32_1 = mul_sum_i8_pairs(bx, by);

        // Convert int32_t to float
        __m256 p = _mm256_cvtepi32_ps(MM256_SET_M128I(i32_0, i32_1));

        // Apply the scale, and accumulate
        acc = _mm256_add_ps(_mm256_mul_ps( d, p ), acc);
    }

    *s = hsum_float_8(acc);
#elif defined(__SSSE3__)
    // set constants
    const __m128i lowMask = _mm_set1_epi8(0xF);
    const __m128i off = _mm_set1_epi8(8);

    // Initialize accumulator with zeros
    __m128 acc_0 = _mm_setzero_ps();
    __m128 acc_1 = _mm_setzero_ps();
    __m128 acc_2 = _mm_setzero_ps();
    __m128 acc_3 = _mm_setzero_ps();

    // First round without accumulation
    {
        _mm_prefetch(&x[0] + sizeof(block_q4_0), _MM_HINT_T0);
        _mm_prefetch(&y[0] + sizeof(block_q8_0), _MM_HINT_T0);

        // Compute combined scale for the block 0 and 1
        const __m128 d_0_1 = _mm_set1_ps( GGML_FP16_TO_FP32(x[0].d) * GGML_FP16_TO_FP32(y[0].d) );

        const __m128i tmp_0_1 = _mm_loadu_si128((const __m128i *)x[0].qs);

        __m128i bx_0 = _mm_and_si128(lowMask, tmp_0_1);
        __m128i by_0 = _mm_loadu_si128((const __m128i *)y[0].qs);
        bx_0 = _mm_sub_epi8(bx_0, off);
        const __m128i i32_0 = mul_sum_i8_pairs(bx_0, by_0);

        __m128i bx_1 = _mm_and_si128(lowMask, _mm_srli_epi64(tmp_0_1, 4));
        __m128i by_1 = _mm_loadu_si128((const __m128i *)(y[0].qs + 16));
        bx_1 = _mm_sub_epi8(bx_1, off);
        const __m128i i32_1 = mul_sum_i8_pairs(bx_1, by_1);

        _mm_prefetch(&x[1] + sizeof(block_q4_0), _MM_HINT_T0);
        _mm_prefetch(&y[1] + sizeof(block_q8_0), _MM_HINT_T0);

        // Compute combined scale for the block 2 and 3
        const __m128 d_2_3 = _mm_set1_ps( GGML_FP16_TO_FP32(x[1].d) * GGML_FP16_TO_FP32(y[1].d) );

        const __m128i tmp_2_3 = _mm_loadu_si128((const __m128i *)x[1].qs);

        __m128i bx_2 = _mm_and_si128(lowMask, tmp_2_3);
        __m128i by_2 = _mm_loadu_si128((const __m128i *)y[1].qs);
        bx_2 = _mm_sub_epi8(bx_2, off);
        const __m128i i32_2 = mul_sum_i8_pairs(bx_2, by_2);

        __m128i bx_3 = _mm_and_si128(lowMask, _mm_srli_epi64(tmp_2_3, 4));
        __m128i by_3 = _mm_loadu_si128((const __m128i *)(y[1].qs + 16));
        bx_3 = _mm_sub_epi8(bx_3, off);
        const __m128i i32_3 = mul_sum_i8_pairs(bx_3, by_3);

        // Convert int32_t to float
        __m128 p0 = _mm_cvtepi32_ps(i32_0);
        __m128 p1 = _mm_cvtepi32_ps(i32_1);
        __m128 p2 = _mm_cvtepi32_ps(i32_2);
        __m128 p3 = _mm_cvtepi32_ps(i32_3);

        // Apply the scale
        acc_0 = _mm_mul_ps( d_0_1, p0 );
        acc_1 = _mm_mul_ps( d_0_1, p1 );
        acc_2 = _mm_mul_ps( d_2_3, p2 );
        acc_3 = _mm_mul_ps( d_2_3, p3 );
    }

    // Main loop
    for (int i = 2; i < nb; i+=2) {
        _mm_prefetch(&x[i] + sizeof(block_q4_0), _MM_HINT_T0);
        _mm_prefetch(&y[i] + sizeof(block_q8_0), _MM_HINT_T0);

        // Compute combined scale for the block 0 and 1
        const __m128 d_0_1 = _mm_set1_ps( GGML_FP16_TO_FP32(x[i].d) * GGML_FP16_TO_FP32(y[i].d) );

        const __m128i tmp_0_1 = _mm_loadu_si128((const __m128i *)x[i].qs);

        __m128i bx_0 = _mm_and_si128(lowMask, tmp_0_1);
        __m128i by_0 = _mm_loadu_si128((const __m128i *)y[i].qs);
        bx_0 = _mm_sub_epi8(bx_0, off);
        const __m128i i32_0 = mul_sum_i8_pairs(bx_0, by_0);

        __m128i bx_1 = _mm_and_si128(lowMask, _mm_srli_epi64(tmp_0_1, 4));
        __m128i by_1 = _mm_loadu_si128((const __m128i *)(y[i].qs + 16));
        bx_1 = _mm_sub_epi8(bx_1, off);
        const __m128i i32_1 = mul_sum_i8_pairs(bx_1, by_1);

        _mm_prefetch(&x[i] + 2 * sizeof(block_q4_0), _MM_HINT_T0);
        _mm_prefetch(&y[i] + 2 * sizeof(block_q8_0), _MM_HINT_T0);

        // Compute combined scale for the block 2 and 3
        const __m128 d_2_3 = _mm_set1_ps( GGML_FP16_TO_FP32(x[i + 1].d) * GGML_FP16_TO_FP32(y[i + 1].d) );

        const __m128i tmp_2_3 = _mm_loadu_si128((const __m128i *)x[i + 1].qs);

        __m128i bx_2 = _mm_and_si128(lowMask, tmp_2_3);
        __m128i by_2 = _mm_loadu_si128((const __m128i *)y[i + 1].qs);
        bx_2 = _mm_sub_epi8(bx_2, off);
        const __m128i i32_2 = mul_sum_i8_pairs(bx_2, by_2);

        __m128i bx_3 = _mm_and_si128(lowMask, _mm_srli_epi64(tmp_2_3, 4));
        __m128i by_3 = _mm_loadu_si128((const __m128i *)(y[i + 1].qs + 16));
        bx_3 = _mm_sub_epi8(bx_3, off);
        const __m128i i32_3 = mul_sum_i8_pairs(bx_3, by_3);

        // Convert int32_t to float
        __m128 p0 = _mm_cvtepi32_ps(i32_0);
        __m128 p1 = _mm_cvtepi32_ps(i32_1);
        __m128 p2 = _mm_cvtepi32_ps(i32_2);
        __m128 p3 = _mm_cvtepi32_ps(i32_3);

        // Apply the scale
        __m128 p0_d = _mm_mul_ps( d_0_1, p0 );
        __m128 p1_d = _mm_mul_ps( d_0_1, p1 );
        __m128 p2_d = _mm_mul_ps( d_2_3, p2 );
        __m128 p3_d = _mm_mul_ps( d_2_3, p3 );

        // Acummulate
        acc_0 = _mm_add_ps(p0_d, acc_0);
        acc_1 = _mm_add_ps(p1_d, acc_1);
        acc_2 = _mm_add_ps(p2_d, acc_2);
        acc_3 = _mm_add_ps(p3_d, acc_3);
    }

    *s = hsum_float_4x4(acc_0, acc_1, acc_2, acc_3);
#else
    // scalar
    float sumf = 0.0;

    for (int i = 0; i < nb; i++) {
        int sumi = 0;

        for (int j = 0; j < qk/2; ++j) {
            const int v0 = (x[i].qs[j] & 0x0F) - 8;
            const int v1 = (x[i].qs[j] >>   4) - 8;

            sumi += (v0 * y[i].qs[j]) + (v1 * y[i].qs[j + qk/2]);
        }

        sumf += sumi*GGML_FP16_TO_FP32(x[i].d)*GGML_FP16_TO_FP32(y[i].d);
    }

    *s = sumf;
#endif
}

static void ggml_vec_dot_q4_1_q8_1(const int n, float * restrict s, const void * restrict vx, const void * restrict vy) {
    const int qk = QK8_1;
    const int nb = n / qk;

    assert(n % qk == 0);
    assert(nb % 2 == 0);

    const block_q4_1 * restrict x = vx;
    const block_q8_1 * restrict y = vy;

    // TODO: add WASM SIMD
#if defined(__ARM_NEON)
    float32x4_t sumv0 = vdupq_n_f32(0.0f);
    float32x4_t sumv1 = vdupq_n_f32(0.0f);

    float summs = 0;

    for (int i = 0; i < nb; i += 2) {
        const block_q4_1 * restrict x0 = &x[i + 0];
        const block_q4_1 * restrict x1 = &x[i + 1];
        const block_q8_1 * restrict y0 = &y[i + 0];
        const block_q8_1 * restrict y1 = &y[i + 1];

        summs += GGML_FP16_TO_FP32(x0->m) * y0->s + GGML_FP16_TO_FP32(x1->m) * y1->s;

        const uint8x16_t m4b = vdupq_n_u8(0x0F);

        const uint8x16_t v0_0 = vld1q_u8(x0->qs);
        const uint8x16_t v0_1 = vld1q_u8(x1->qs);

        // 4-bit -> 8-bit
        const int8x16_t v0_0l = vreinterpretq_s8_u8(vandq_u8  (v0_0, m4b));
        const int8x16_t v0_0h = vreinterpretq_s8_u8(vshrq_n_u8(v0_0, 4));
        const int8x16_t v0_1l = vreinterpretq_s8_u8(vandq_u8  (v0_1, m4b));
        const int8x16_t v0_1h = vreinterpretq_s8_u8(vshrq_n_u8(v0_1, 4));

        // load y
        const int8x16_t v1_0l = vld1q_s8(y0->qs);
        const int8x16_t v1_0h = vld1q_s8(y0->qs + 16);
        const int8x16_t v1_1l = vld1q_s8(y1->qs);
        const int8x16_t v1_1h = vld1q_s8(y1->qs + 16);

#if defined(__ARM_FEATURE_DOTPROD)
        // dot product into int32x4_t
        const int32x4_t p_0 = vdotq_s32(vdotq_s32(vdupq_n_s32(0), v0_0l, v1_0l), v0_0h, v1_0h);
        const int32x4_t p_1 = vdotq_s32(vdotq_s32(vdupq_n_s32(0), v0_1l, v1_1l), v0_1h, v1_1h);

        sumv0 = vmlaq_n_f32(sumv0, vcvtq_f32_s32(p_0), GGML_FP16_TO_FP32(x0->d)*y0->d);
        sumv1 = vmlaq_n_f32(sumv1, vcvtq_f32_s32(p_1), GGML_FP16_TO_FP32(x1->d)*y1->d);
#else
        const int16x8_t pl0l = vmull_s8(vget_low_s8 (v0_0l), vget_low_s8 (v1_0l));
        const int16x8_t pl0h = vmull_s8(vget_high_s8(v0_0l), vget_high_s8(v1_0l));
        const int16x8_t ph0l = vmull_s8(vget_low_s8 (v0_0h), vget_low_s8 (v1_0h));
        const int16x8_t ph0h = vmull_s8(vget_high_s8(v0_0h), vget_high_s8(v1_0h));

        const int16x8_t pl1l = vmull_s8(vget_low_s8 (v0_1l), vget_low_s8 (v1_1l));
        const int16x8_t pl1h = vmull_s8(vget_high_s8(v0_1l), vget_high_s8(v1_1l));
        const int16x8_t ph1l = vmull_s8(vget_low_s8 (v0_1h), vget_low_s8 (v1_1h));
        const int16x8_t ph1h = vmull_s8(vget_high_s8(v0_1h), vget_high_s8(v1_1h));

        const int32x4_t pl0 = vaddq_s32(vpaddlq_s16(pl0l), vpaddlq_s16(pl0h));
        const int32x4_t ph0 = vaddq_s32(vpaddlq_s16(ph0l), vpaddlq_s16(ph0h));
        const int32x4_t pl1 = vaddq_s32(vpaddlq_s16(pl1l), vpaddlq_s16(pl1h));
        const int32x4_t ph1 = vaddq_s32(vpaddlq_s16(ph1l), vpaddlq_s16(ph1h));

        sumv0 = vmlaq_n_f32(sumv0, vcvtq_f32_s32(vaddq_s32(pl0, ph0)), GGML_FP16_TO_FP32(x0->d)*y0->d);
        sumv1 = vmlaq_n_f32(sumv1, vcvtq_f32_s32(vaddq_s32(pl1, ph1)), GGML_FP16_TO_FP32(x1->d)*y1->d);
#endif
    }

    *s = vaddvq_f32(sumv0) + vaddvq_f32(sumv1) + summs;
#elif defined(__AVX2__) || defined(__AVX__)
    // Initialize accumulator with zeros
    __m256 acc = _mm256_setzero_ps();

    float summs = 0;

    // Main loop
    for (int i = 0; i < nb; ++i) {
        const float d0 = GGML_FP16_TO_FP32(x[i].d);
        const float d1 = y[i].d;

        summs += GGML_FP16_TO_FP32(x[i].m) * y[i].s;

        const __m256 d0v = _mm256_set1_ps( d0 );
        const __m256 d1v = _mm256_set1_ps( d1 );

        // Compute combined scales
        const __m256 d0d1 = _mm256_mul_ps( d0v, d1v );

        // Load 16 bytes, and unpack 4 bit fields into bytes, making 32 bytes
        const __m256i bx = bytes_from_nibbles_32(x[i].qs);
        const __m256i by = _mm256_loadu_si256( (const __m256i *)y[i].qs );

        const __m256 xy = mul_sum_us8_pairs_float(bx, by);

        // Accumulate d0*d1*x*y
#if defined(__AVX2__)
        acc = _mm256_fmadd_ps( d0d1, xy, acc );
#else
        acc = _mm256_add_ps( _mm256_mul_ps( d0d1, xy ), acc );
#endif
    }

    *s = hsum_float_8(acc) + summs;
#else
    // scalar
    float sumf = 0.0;

    for (int i = 0; i < nb; i++) {
        int sumi = 0;

        for (int j = 0; j < qk/2; ++j) {
            const int v0 = (x[i].qs[j] & 0x0F);
            const int v1 = (x[i].qs[j] >>   4);

            sumi += (v0 * y[i].qs[j]) + (v1 * y[i].qs[j + qk/2]);
        }

        sumf += (GGML_FP16_TO_FP32(x[i].d)*y[i].d)*sumi + GGML_FP16_TO_FP32(x[i].m)*y[i].s;
    }

    *s = sumf;
#endif
}

static void ggml_vec_dot_q5_0_q8_0(const int n, float * restrict s, const void * restrict vx, const void * restrict vy) {
    const int qk = QK8_0;
    const int nb = n / qk;

    assert(n % qk == 0);
    assert(nb % 2 == 0);
    assert(qk == QK5_0);

    const block_q5_0 * restrict x = vx;
    const block_q8_0 * restrict y = vy;

#if defined(__ARM_NEON)
    float32x4_t sumv0 = vdupq_n_f32(0.0f);
    float32x4_t sumv1 = vdupq_n_f32(0.0f);

    uint32_t qh0;
    uint32_t qh1;

    uint64_t tmp0[4];
    uint64_t tmp1[4];

    for (int i = 0; i < nb; i += 2) {
        const block_q5_0 * restrict x0 = &x[i];
        const block_q5_0 * restrict x1 = &x[i + 1];
        const block_q8_0 * restrict y0 = &y[i];
        const block_q8_0 * restrict y1 = &y[i + 1];

        const uint8x16_t m4b = vdupq_n_u8(0x0F);

        // extract the 5th bit via lookup table ((!b) << 4)
        memcpy(&qh0, x0->qh, sizeof(qh0));
        memcpy(&qh1, x1->qh, sizeof(qh1));

        tmp0[0] = table_b2b_1[(qh0 >>  0) & 0xFF];
        tmp0[1] = table_b2b_1[(qh0 >>  8) & 0xFF];
        tmp0[2] = table_b2b_1[(qh0 >> 16) & 0xFF];
        tmp0[3] = table_b2b_1[(qh0 >> 24)       ];

        tmp1[0] = table_b2b_1[(qh1 >>  0) & 0xFF];
        tmp1[1] = table_b2b_1[(qh1 >>  8) & 0xFF];
        tmp1[2] = table_b2b_1[(qh1 >> 16) & 0xFF];
        tmp1[3] = table_b2b_1[(qh1 >> 24)       ];

        const int8x16_t qhl0 = vld1q_s8((const int8_t *)(tmp0 + 0));
        const int8x16_t qhh0 = vld1q_s8((const int8_t *)(tmp0 + 2));
        const int8x16_t qhl1 = vld1q_s8((const int8_t *)(tmp1 + 0));
        const int8x16_t qhh1 = vld1q_s8((const int8_t *)(tmp1 + 2));

        const uint8x16_t v0_0 = vld1q_u8(x0->qs);
        const uint8x16_t v0_1 = vld1q_u8(x1->qs);

        // 4-bit -> 8-bit
        int8x16_t v0_0l = vreinterpretq_s8_u8(vandq_u8  (v0_0, m4b));
        int8x16_t v0_0h = vreinterpretq_s8_u8(vshrq_n_u8(v0_0, 4));
        int8x16_t v0_1l = vreinterpretq_s8_u8(vandq_u8  (v0_1, m4b));
        int8x16_t v0_1h = vreinterpretq_s8_u8(vshrq_n_u8(v0_1, 4));

        // add high bit and sub 16 (equivalent to sub 0x10 when bit is zero)
        const int8x16_t v0_0lf = vsubq_s8(v0_0l, qhl0);
        const int8x16_t v0_0hf = vsubq_s8(v0_0h, qhh0);
        const int8x16_t v0_1lf = vsubq_s8(v0_1l, qhl1);
        const int8x16_t v0_1hf = vsubq_s8(v0_1h, qhh1);

        // load y
        const int8x16_t v1_0l = vld1q_s8(y0->qs);
        const int8x16_t v1_0h = vld1q_s8(y0->qs + 16);
        const int8x16_t v1_1l = vld1q_s8(y1->qs);
        const int8x16_t v1_1h = vld1q_s8(y1->qs + 16);

#if defined(__ARM_FEATURE_DOTPROD)
        sumv0 = vmlaq_n_f32(sumv0, vcvtq_f32_s32(vaddq_s32(
                        vdotq_s32(vdupq_n_s32(0), v0_0lf, v1_0l),
                        vdotq_s32(vdupq_n_s32(0), v0_0hf, v1_0h))), GGML_FP16_TO_FP32(x0->d)*GGML_FP16_TO_FP32(y0->d));
        sumv1 = vmlaq_n_f32(sumv1, vcvtq_f32_s32(vaddq_s32(
                        vdotq_s32(vdupq_n_s32(0), v0_1lf, v1_1l),
                        vdotq_s32(vdupq_n_s32(0), v0_1hf, v1_1h))), GGML_FP16_TO_FP32(x1->d)*GGML_FP16_TO_FP32(y1->d));
#else
        const int16x8_t pl0l = vmull_s8(vget_low_s8 (v0_0lf), vget_low_s8 (v1_0l));
        const int16x8_t pl0h = vmull_s8(vget_high_s8(v0_0lf), vget_high_s8(v1_0l));
        const int16x8_t ph0l = vmull_s8(vget_low_s8 (v0_0hf), vget_low_s8 (v1_0h));
        const int16x8_t ph0h = vmull_s8(vget_high_s8(v0_0hf), vget_high_s8(v1_0h));

        const int16x8_t pl1l = vmull_s8(vget_low_s8 (v0_1lf), vget_low_s8 (v1_1l));
        const int16x8_t pl1h = vmull_s8(vget_high_s8(v0_1lf), vget_high_s8(v1_1l));
        const int16x8_t ph1l = vmull_s8(vget_low_s8 (v0_1hf), vget_low_s8 (v1_1h));
        const int16x8_t ph1h = vmull_s8(vget_high_s8(v0_1hf), vget_high_s8(v1_1h));

        const int32x4_t pl0 = vaddq_s32(vpaddlq_s16(pl0l), vpaddlq_s16(pl0h));
        const int32x4_t ph0 = vaddq_s32(vpaddlq_s16(ph0l), vpaddlq_s16(ph0h));
        const int32x4_t pl1 = vaddq_s32(vpaddlq_s16(pl1l), vpaddlq_s16(pl1h));
        const int32x4_t ph1 = vaddq_s32(vpaddlq_s16(ph1l), vpaddlq_s16(ph1h));

        sumv0 = vmlaq_n_f32(sumv0, vcvtq_f32_s32(vaddq_s32(pl0, ph0)), GGML_FP16_TO_FP32(x0->d)*GGML_FP16_TO_FP32(y0->d));
        sumv1 = vmlaq_n_f32(sumv1, vcvtq_f32_s32(vaddq_s32(pl1, ph1)), GGML_FP16_TO_FP32(x1->d)*GGML_FP16_TO_FP32(y1->d));
#endif
    }

    *s = vaddvq_f32(sumv0) + vaddvq_f32(sumv1);
#elif defined(__wasm_simd128__)
    v128_t sumv = wasm_f32x4_splat(0.0f);

    uint32_t qh;
    uint64_t tmp[4];

    // TODO: check if unrolling this is better
    for (int i = 0; i < nb; ++i) {
        const block_q5_0 * restrict x0 = &x[i];
        const block_q8_0 * restrict y0 = &y[i];

        const v128_t m4b  = wasm_i8x16_splat(0x0F);

        // extract the 5th bit
        memcpy(&qh, x0->qh, sizeof(qh));

        tmp[0] = table_b2b_1[(qh >>  0) & 0xFF];
        tmp[1] = table_b2b_1[(qh >>  8) & 0xFF];
        tmp[2] = table_b2b_1[(qh >> 16) & 0xFF];
        tmp[3] = table_b2b_1[(qh >> 24)       ];

        const v128_t qhl = wasm_v128_load(tmp + 0);
        const v128_t qhh = wasm_v128_load(tmp + 2);

        const v128_t v0 = wasm_v128_load(x0->qs);

        // 4-bit -> 8-bit
        const v128_t v0l = wasm_v128_and (v0, m4b);
        const v128_t v0h = wasm_u8x16_shr(v0, 4);

        // add high bit and sub 16 (equivalent to sub 0x10 when bit is zero)
        const v128_t v0lf = wasm_i8x16_sub(v0l, qhl);
        const v128_t v0hf = wasm_i8x16_sub(v0h, qhh);

        // load y
        const v128_t v1l = wasm_v128_load(y0->qs);
        const v128_t v1h = wasm_v128_load(y0->qs + 16);

        // int8x16 -> int16x8
        const v128_t v0lfl = wasm_i16x8_extend_low_i8x16 (v0lf);
        const v128_t v0lfh = wasm_i16x8_extend_high_i8x16(v0lf);
        const v128_t v0hfl = wasm_i16x8_extend_low_i8x16 (v0hf);
        const v128_t v0hfh = wasm_i16x8_extend_high_i8x16(v0hf);

        const v128_t v1ll = wasm_i16x8_extend_low_i8x16 (v1l);
        const v128_t v1lh = wasm_i16x8_extend_high_i8x16(v1l);
        const v128_t v1hl = wasm_i16x8_extend_low_i8x16 (v1h);
        const v128_t v1hh = wasm_i16x8_extend_high_i8x16(v1h);

        // dot product
        sumv = wasm_f32x4_add(sumv, wasm_f32x4_mul(wasm_f32x4_convert_i32x4(
                        wasm_i32x4_add(
                            wasm_i32x4_add(wasm_i32x4_dot_i16x8(v0lfl, v1ll),
                                           wasm_i32x4_dot_i16x8(v0lfh, v1lh)),
                            wasm_i32x4_add(wasm_i32x4_dot_i16x8(v0hfl, v1hl),
                                           wasm_i32x4_dot_i16x8(v0hfh, v1hh)))),
                    wasm_f32x4_splat(GGML_FP16_TO_FP32(x0->d) * GGML_FP16_TO_FP32(y0->d))));
    }

    *s = wasm_f32x4_extract_lane(sumv, 0) + wasm_f32x4_extract_lane(sumv, 1) +
         wasm_f32x4_extract_lane(sumv, 2) + wasm_f32x4_extract_lane(sumv, 3);
#elif defined(__AVX2__)
    // Initialize accumulator with zeros
    __m256 acc = _mm256_setzero_ps();

    // Main loop
    for (int i = 0; i < nb; i++) {
        /* Compute combined scale for the block */
        const __m256 d = _mm256_set1_ps(GGML_FP16_TO_FP32(x[i].d) * GGML_FP16_TO_FP32(y[i].d));

        __m256i bx = bytes_from_nibbles_32(x[i].qs);
        __m256i bxhi = bytes_from_bits_32(x[i].qh);
        bxhi = _mm256_andnot_si256(bxhi, _mm256_set1_epi8((char)0xF0));
        bx = _mm256_or_si256(bx, bxhi);

        __m256i by = _mm256_loadu_si256((const __m256i *)y[i].qs);

        const __m256 q = mul_sum_i8_pairs_float(bx, by);

        /* Multiply q with scale and accumulate */
        acc = _mm256_fmadd_ps(d, q, acc);
    }

    *s = hsum_float_8(acc);
#elif defined(__AVX__)
    // Initialize accumulator with zeros
    __m256 acc = _mm256_setzero_ps();
    __m128i mask = _mm_set1_epi8((char)0xF0);

    // Main loop
    for (int i = 0; i < nb; i++) {
        /* Compute combined scale for the block */
        const __m256 d = _mm256_set1_ps(GGML_FP16_TO_FP32(x[i].d) * GGML_FP16_TO_FP32(y[i].d));

        __m256i bx = bytes_from_nibbles_32(x[i].qs);
        const __m256i bxhi = bytes_from_bits_32(x[i].qh);
        __m128i bxhil = _mm256_castsi256_si128(bxhi);
        __m128i bxhih = _mm256_extractf128_si256(bxhi, 1);
        bxhil = _mm_andnot_si128(bxhil, mask);
        bxhih = _mm_andnot_si128(bxhih, mask);
        __m128i bxl = _mm256_castsi256_si128(bx);
        __m128i bxh = _mm256_extractf128_si256(bx, 1);
        bxl = _mm_or_si128(bxl, bxhil);
        bxh = _mm_or_si128(bxh, bxhih);
        bx = MM256_SET_M128I(bxh, bxl);

        const __m256i by = _mm256_loadu_si256((const __m256i *)y[i].qs);

        const __m256 q = mul_sum_i8_pairs_float(bx, by);

        /* Multiply q with scale and accumulate */
        acc = _mm256_add_ps(_mm256_mul_ps(d, q), acc);
    }

    *s = hsum_float_8(acc);
#else
    // scalar
    float sumf = 0.0;

    for (int i = 0; i < nb; i++) {
        uint32_t qh;
        memcpy(&qh, x[i].qh, sizeof(qh));

        int sumi = 0;

        for (int j = 0; j < qk/2; ++j) {
            const uint8_t xh_0 = ((qh & (1u << (j + 0 ))) >> (j + 0 )) << 4;
            const uint8_t xh_1 = ((qh & (1u << (j + 16))) >> (j + 12));

            const int32_t x0 = ((x[i].qs[j] & 0x0F) | xh_0) - 16;
            const int32_t x1 = ((x[i].qs[j] >>   4) | xh_1) - 16;

            sumi += (x0 * y[i].qs[j]) + (x1 * y[i].qs[j + qk/2]);
        }

        sumf += (GGML_FP16_TO_FP32(x[i].d)*GGML_FP16_TO_FP32(y[i].d)) * sumi;
    }

    *s = sumf;
#endif
}

static void ggml_vec_dot_q5_1_q8_1(const int n, float * restrict s, const void * restrict vx, const void * restrict vy) {
    const int qk = QK8_1;
    const int nb = n / qk;

    assert(n % qk == 0);
    assert(nb % 2 == 0);
    assert(qk == QK5_1);

    const block_q5_1 * restrict x = vx;
    const block_q8_1 * restrict y = vy;

#if defined(__ARM_NEON)
    float32x4_t sumv0 = vdupq_n_f32(0.0f);
    float32x4_t sumv1 = vdupq_n_f32(0.0f);

    float summs0 = 0.0f;
    float summs1 = 0.0f;

    uint32_t qh0;
    uint32_t qh1;

    uint64_t tmp0[4];
    uint64_t tmp1[4];

    for (int i = 0; i < nb; i += 2) {
        const block_q5_1 * restrict x0 = &x[i];
        const block_q5_1 * restrict x1 = &x[i + 1];
        const block_q8_1 * restrict y0 = &y[i];
        const block_q8_1 * restrict y1 = &y[i + 1];

        const uint8x16_t m4b = vdupq_n_u8(0x0F);

        summs0 += GGML_FP16_TO_FP32(x0->m) * y0->s;
        summs1 += GGML_FP16_TO_FP32(x1->m) * y1->s;

        // extract the 5th bit via lookup table ((b) << 4)
        memcpy(&qh0, x0->qh, sizeof(qh0));
        memcpy(&qh1, x1->qh, sizeof(qh1));

        tmp0[0] = table_b2b_0[(qh0 >>  0) & 0xFF];
        tmp0[1] = table_b2b_0[(qh0 >>  8) & 0xFF];
        tmp0[2] = table_b2b_0[(qh0 >> 16) & 0xFF];
        tmp0[3] = table_b2b_0[(qh0 >> 24)       ];

        tmp1[0] = table_b2b_0[(qh1 >>  0) & 0xFF];
        tmp1[1] = table_b2b_0[(qh1 >>  8) & 0xFF];
        tmp1[2] = table_b2b_0[(qh1 >> 16) & 0xFF];
        tmp1[3] = table_b2b_0[(qh1 >> 24)       ];

        const int8x16_t qhl0 = vld1q_s8((const int8_t *)(tmp0 + 0));
        const int8x16_t qhh0 = vld1q_s8((const int8_t *)(tmp0 + 2));
        const int8x16_t qhl1 = vld1q_s8((const int8_t *)(tmp1 + 0));
        const int8x16_t qhh1 = vld1q_s8((const int8_t *)(tmp1 + 2));

        const uint8x16_t v0_0 = vld1q_u8(x0->qs);
        const uint8x16_t v0_1 = vld1q_u8(x1->qs);

        // 4-bit -> 8-bit
        const int8x16_t v0_0l = vreinterpretq_s8_u8(vandq_u8  (v0_0, m4b));
        const int8x16_t v0_0h = vreinterpretq_s8_u8(vshrq_n_u8(v0_0, 4));
        const int8x16_t v0_1l = vreinterpretq_s8_u8(vandq_u8  (v0_1, m4b));
        const int8x16_t v0_1h = vreinterpretq_s8_u8(vshrq_n_u8(v0_1, 4));

        // add high bit
        const int8x16_t v0_0lf = vorrq_s8(v0_0l, qhl0);
        const int8x16_t v0_0hf = vorrq_s8(v0_0h, qhh0);
        const int8x16_t v0_1lf = vorrq_s8(v0_1l, qhl1);
        const int8x16_t v0_1hf = vorrq_s8(v0_1h, qhh1);

        // load y
        const int8x16_t v1_0l = vld1q_s8(y0->qs);
        const int8x16_t v1_0h = vld1q_s8(y0->qs + 16);
        const int8x16_t v1_1l = vld1q_s8(y1->qs);
        const int8x16_t v1_1h = vld1q_s8(y1->qs + 16);

#if defined(__ARM_FEATURE_DOTPROD)
        sumv0 = vmlaq_n_f32(sumv0, vcvtq_f32_s32(vaddq_s32(
                        vdotq_s32(vdupq_n_s32(0), v0_0lf, v1_0l),
                        vdotq_s32(vdupq_n_s32(0), v0_0hf, v1_0h))), GGML_FP16_TO_FP32(x0->d)*y0->d);
        sumv1 = vmlaq_n_f32(sumv1, vcvtq_f32_s32(vaddq_s32(
                        vdotq_s32(vdupq_n_s32(0), v0_1lf, v1_1l),
                        vdotq_s32(vdupq_n_s32(0), v0_1hf, v1_1h))), GGML_FP16_TO_FP32(x1->d)*y1->d);
#else
        const int16x8_t pl0l = vmull_s8(vget_low_s8 (v0_0lf), vget_low_s8 (v1_0l));
        const int16x8_t pl0h = vmull_s8(vget_high_s8(v0_0lf), vget_high_s8(v1_0l));
        const int16x8_t ph0l = vmull_s8(vget_low_s8 (v0_0hf), vget_low_s8 (v1_0h));
        const int16x8_t ph0h = vmull_s8(vget_high_s8(v0_0hf), vget_high_s8(v1_0h));

        const int16x8_t pl1l = vmull_s8(vget_low_s8 (v0_1lf), vget_low_s8 (v1_1l));
        const int16x8_t pl1h = vmull_s8(vget_high_s8(v0_1lf), vget_high_s8(v1_1l));
        const int16x8_t ph1l = vmull_s8(vget_low_s8 (v0_1hf), vget_low_s8 (v1_1h));
        const int16x8_t ph1h = vmull_s8(vget_high_s8(v0_1hf), vget_high_s8(v1_1h));

        const int32x4_t pl0 = vaddq_s32(vpaddlq_s16(pl0l), vpaddlq_s16(pl0h));
        const int32x4_t ph0 = vaddq_s32(vpaddlq_s16(ph0l), vpaddlq_s16(ph0h));
        const int32x4_t pl1 = vaddq_s32(vpaddlq_s16(pl1l), vpaddlq_s16(pl1h));
        const int32x4_t ph1 = vaddq_s32(vpaddlq_s16(ph1l), vpaddlq_s16(ph1h));

        sumv0 = vmlaq_n_f32(sumv0, vcvtq_f32_s32(vaddq_s32(pl0, ph0)), GGML_FP16_TO_FP32(x0->d)*y0->d);
        sumv1 = vmlaq_n_f32(sumv1, vcvtq_f32_s32(vaddq_s32(pl1, ph1)), GGML_FP16_TO_FP32(x1->d)*y1->d);
#endif
    }

    *s = vaddvq_f32(sumv0) + vaddvq_f32(sumv1) + summs0 + summs1;
#elif defined(__wasm_simd128__)
    v128_t sumv = wasm_f32x4_splat(0.0f);

    float summs = 0.0f;

    uint32_t qh;
    uint64_t tmp[4];

    // TODO: check if unrolling this is better
    for (int i = 0; i < nb; ++i) {
        const block_q5_1 * restrict x0 = &x[i];
        const block_q8_1 * restrict y0 = &y[i];

        summs += GGML_FP16_TO_FP32(x0->m) * y0->s;

        const v128_t m4b = wasm_i8x16_splat(0x0F);

        // extract the 5th bit
        memcpy(&qh, x0->qh, sizeof(qh));

        tmp[0] = table_b2b_0[(qh >>  0) & 0xFF];
        tmp[1] = table_b2b_0[(qh >>  8) & 0xFF];
        tmp[2] = table_b2b_0[(qh >> 16) & 0xFF];
        tmp[3] = table_b2b_0[(qh >> 24)       ];

        const v128_t qhl = wasm_v128_load(tmp + 0);
        const v128_t qhh = wasm_v128_load(tmp + 2);

        const v128_t v0 = wasm_v128_load(x0->qs);

        // 4-bit -> 8-bit
        const v128_t v0l = wasm_v128_and (v0, m4b);
        const v128_t v0h = wasm_u8x16_shr(v0, 4);

        // add high bit
        const v128_t v0lf = wasm_v128_or(v0l, qhl);
        const v128_t v0hf = wasm_v128_or(v0h, qhh);

        // load y
        const v128_t v1l = wasm_v128_load(y0->qs);
        const v128_t v1h = wasm_v128_load(y0->qs + 16);

        // int8x16 -> int16x8
        const v128_t v0lfl = wasm_i16x8_extend_low_i8x16 (v0lf);
        const v128_t v0lfh = wasm_i16x8_extend_high_i8x16(v0lf);
        const v128_t v0hfl = wasm_i16x8_extend_low_i8x16 (v0hf);
        const v128_t v0hfh = wasm_i16x8_extend_high_i8x16(v0hf);

        const v128_t v1ll = wasm_i16x8_extend_low_i8x16 (v1l);
        const v128_t v1lh = wasm_i16x8_extend_high_i8x16(v1l);
        const v128_t v1hl = wasm_i16x8_extend_low_i8x16 (v1h);
        const v128_t v1hh = wasm_i16x8_extend_high_i8x16(v1h);

        // dot product
        sumv = wasm_f32x4_add(sumv,
                wasm_f32x4_mul(wasm_f32x4_convert_i32x4(wasm_i32x4_add(
                            wasm_i32x4_add(wasm_i32x4_dot_i16x8(v0lfl, v1ll),
                                           wasm_i32x4_dot_i16x8(v0lfh, v1lh)),
                            wasm_i32x4_add(wasm_i32x4_dot_i16x8(v0hfl, v1hl),
                                           wasm_i32x4_dot_i16x8(v0hfh, v1hh)))),
                    wasm_f32x4_splat(GGML_FP16_TO_FP32(x0->d) * y0->d)));
    }

    *s = wasm_f32x4_extract_lane(sumv, 0) + wasm_f32x4_extract_lane(sumv, 1) +
         wasm_f32x4_extract_lane(sumv, 2) + wasm_f32x4_extract_lane(sumv, 3) + summs;
#elif defined(__AVX2__)
    // Initialize accumulator with zeros
    __m256 acc = _mm256_setzero_ps();

    float summs = 0.0f;

    // Main loop
    for (int i = 0; i < nb; i++) {
        const __m256 dx = _mm256_set1_ps(GGML_FP16_TO_FP32(x[i].d));

        summs += GGML_FP16_TO_FP32(x[i].m) * y[i].s;

        __m256i bx = bytes_from_nibbles_32(x[i].qs);
        __m256i bxhi = bytes_from_bits_32(x[i].qh);
        bxhi = _mm256_and_si256(bxhi, _mm256_set1_epi8(0x10));
        bx = _mm256_or_si256(bx, bxhi);

        const __m256 dy = _mm256_set1_ps(y[i].d);
        const __m256i by = _mm256_loadu_si256((const __m256i *)y[i].qs);

        const __m256 q = mul_sum_us8_pairs_float(bx, by);

        acc = _mm256_fmadd_ps(q, _mm256_mul_ps(dx, dy), acc);
    }

    *s = hsum_float_8(acc) + summs;
#elif defined(__AVX__)
    // Initialize accumulator with zeros
    __m256 acc = _mm256_setzero_ps();
    __m128i mask = _mm_set1_epi8(0x10);

    float summs = 0.0f;

    // Main loop
    for (int i = 0; i < nb; i++) {
        const __m256 dx = _mm256_set1_ps(GGML_FP16_TO_FP32(x[i].d));

        summs += GGML_FP16_TO_FP32(x[i].m) * y[i].s;

        __m256i bx = bytes_from_nibbles_32(x[i].qs);
        const __m256i bxhi = bytes_from_bits_32(x[i].qh);
        __m128i bxhil = _mm256_castsi256_si128(bxhi);
        __m128i bxhih = _mm256_extractf128_si256(bxhi, 1);
        bxhil = _mm_and_si128(bxhil, mask);
        bxhih = _mm_and_si128(bxhih, mask);
        __m128i bxl = _mm256_castsi256_si128(bx);
        __m128i bxh = _mm256_extractf128_si256(bx, 1);
        bxl = _mm_or_si128(bxl, bxhil);
        bxh = _mm_or_si128(bxh, bxhih);
        bx = MM256_SET_M128I(bxh, bxl);

        const __m256 dy = _mm256_set1_ps(y[i].d);
        const __m256i by = _mm256_loadu_si256((const __m256i *)y[i].qs);

        const __m256 q = mul_sum_us8_pairs_float(bx, by);

        acc = _mm256_add_ps(_mm256_mul_ps(q, _mm256_mul_ps(dx, dy)), acc);
    }

    *s = hsum_float_8(acc) + summs;
#else
    // scalar
    float sumf = 0.0;

    for (int i = 0; i < nb; i++) {
        uint32_t qh;
        memcpy(&qh, x[i].qh, sizeof(qh));

        int sumi = 0;

        for (int j = 0; j < qk/2; ++j) {
            const uint8_t xh_0 = ((qh >> (j +  0)) << 4) & 0x10;
            const uint8_t xh_1 = ((qh >> (j + 12))     ) & 0x10;

            const int32_t x0 = (x[i].qs[j] & 0xF) | xh_0;
            const int32_t x1 = (x[i].qs[j] >>  4) | xh_1;

            sumi += (x0 * y[i].qs[j]) + (x1 * y[i].qs[j + qk/2]);
        }

        sumf += (GGML_FP16_TO_FP32(x[i].d)*y[i].d)*sumi + GGML_FP16_TO_FP32(x[i].m)*y[i].s;
    }

    *s = sumf;
#endif
}

static void ggml_vec_dot_q8_0_q8_0(const int n, float * restrict s, const void * restrict vx, const void * restrict vy) {
    const int qk = QK8_0;
    const int nb = n / qk;

    assert(n % qk == 0);
    assert(nb % 2 == 0);

    const block_q8_0 * restrict x = vx;
    const block_q8_0 * restrict y = vy;

#if defined(__ARM_NEON)
    float32x4_t sumv0 = vdupq_n_f32(0.0f);
    float32x4_t sumv1 = vdupq_n_f32(0.0f);

    for (int i = 0; i < nb; i += 2) {
        const block_q8_0 * restrict x0 = &x[i + 0];
        const block_q8_0 * restrict x1 = &x[i + 1];
        const block_q8_0 * restrict y0 = &y[i + 0];
        const block_q8_0 * restrict y1 = &y[i + 1];

        const int8x16_t x0_0 = vld1q_s8(x0->qs);
        const int8x16_t x0_1 = vld1q_s8(x0->qs + 16);
        const int8x16_t x1_0 = vld1q_s8(x1->qs);
        const int8x16_t x1_1 = vld1q_s8(x1->qs + 16);

        // load y
        const int8x16_t y0_0 = vld1q_s8(y0->qs);
        const int8x16_t y0_1 = vld1q_s8(y0->qs + 16);
        const int8x16_t y1_0 = vld1q_s8(y1->qs);
        const int8x16_t y1_1 = vld1q_s8(y1->qs + 16);

#if defined(__ARM_FEATURE_DOTPROD)
        sumv0 = vmlaq_n_f32(sumv0, vcvtq_f32_s32(vaddq_s32(
                        vdotq_s32(vdupq_n_s32(0), x0_0, y0_0),
                        vdotq_s32(vdupq_n_s32(0), x0_1, y0_1))), GGML_FP16_TO_FP32(x0->d)*GGML_FP16_TO_FP32(y0->d));

        sumv1 = vmlaq_n_f32(sumv1, vcvtq_f32_s32(vaddq_s32(
                        vdotq_s32(vdupq_n_s32(0), x1_0, y1_0),
                        vdotq_s32(vdupq_n_s32(0), x1_1, y1_1))), GGML_FP16_TO_FP32(x1->d)*GGML_FP16_TO_FP32(y1->d));

#else
        const int16x8_t p0_0 = vmull_s8(vget_low_s8 (x0_0), vget_low_s8 (y0_0));
        const int16x8_t p0_1 = vmull_s8(vget_high_s8(x0_0), vget_high_s8(y0_0));
        const int16x8_t p0_2 = vmull_s8(vget_low_s8 (x0_1), vget_low_s8 (y0_1));
        const int16x8_t p0_3 = vmull_s8(vget_high_s8(x0_1), vget_high_s8(y0_1));

        const int16x8_t p1_0 = vmull_s8(vget_low_s8 (x1_0), vget_low_s8 (y1_0));
        const int16x8_t p1_1 = vmull_s8(vget_high_s8(x1_0), vget_high_s8(y1_0));
        const int16x8_t p1_2 = vmull_s8(vget_low_s8 (x1_1), vget_low_s8 (y1_1));
        const int16x8_t p1_3 = vmull_s8(vget_high_s8(x1_1), vget_high_s8(y1_1));

        const int32x4_t p0 = vaddq_s32(vpaddlq_s16(p0_0), vpaddlq_s16(p0_1));
        const int32x4_t p1 = vaddq_s32(vpaddlq_s16(p0_2), vpaddlq_s16(p0_3));
        const int32x4_t p2 = vaddq_s32(vpaddlq_s16(p1_0), vpaddlq_s16(p1_1));
        const int32x4_t p3 = vaddq_s32(vpaddlq_s16(p1_2), vpaddlq_s16(p1_3));

        sumv0 = vmlaq_n_f32(sumv0, vcvtq_f32_s32(vaddq_s32(p0, p1)), GGML_FP16_TO_FP32(x0->d)*GGML_FP16_TO_FP32(y0->d));
        sumv1 = vmlaq_n_f32(sumv1, vcvtq_f32_s32(vaddq_s32(p2, p3)), GGML_FP16_TO_FP32(x1->d)*GGML_FP16_TO_FP32(y1->d));
#endif
    }

    *s = vaddvq_f32(sumv0) + vaddvq_f32(sumv1);
#elif defined(__AVX2__) || defined(__AVX__)
    // Initialize accumulator with zeros
    __m256 acc = _mm256_setzero_ps();

    // Main loop
    for (int i = 0; i < nb; ++i) {
        // Compute combined scale for the block
        const __m256 d = _mm256_set1_ps(GGML_FP16_TO_FP32(x[i].d) * GGML_FP16_TO_FP32(y[i].d));
        __m256i bx = _mm256_loadu_si256((const __m256i *)x[i].qs);
        __m256i by = _mm256_loadu_si256((const __m256i *)y[i].qs);

        const __m256 q = mul_sum_i8_pairs_float(bx, by);

        // Multiply q with scale and accumulate
#if defined(__AVX2__)
        acc = _mm256_fmadd_ps( d, q, acc );
#else
        acc = _mm256_add_ps( _mm256_mul_ps( d, q ), acc );
#endif
    }

    *s = hsum_float_8(acc);
#else
    // scalar
    float sumf = 0.0;

    for (int i = 0; i < nb; i++) {
        int sumi = 0;

        for (int j = 0; j < qk; j++) {
            sumi += x[i].qs[j]*y[i].qs[j];
        }

        sumf += sumi*(GGML_FP16_TO_FP32(x[i].d)*GGML_FP16_TO_FP32(y[i].d));
    }

    *s = sumf;
#endif
}

// compute GGML_VEC_DOT_UNROLL dot products at once
// xs - x row stride in bytes
inline static void ggml_vec_dot_f16_unroll(const int n, const int xs, float * restrict s, void * restrict xv, ggml_fp16_t * restrict y) {
    ggml_float sumf[GGML_VEC_DOT_UNROLL] = { 0.0 };

    ggml_fp16_t * restrict x[GGML_VEC_DOT_UNROLL];

    for (int i = 0; i < GGML_VEC_DOT_UNROLL; ++i) {
        x[i] = (ggml_fp16_t *) ((char *) xv + i*xs);
    }

#if defined(GGML_SIMD)
    const int np = (n & ~(GGML_F16_STEP - 1));

    GGML_F16_VEC sum[GGML_VEC_DOT_UNROLL][GGML_F16_ARR] = { { GGML_F16_VEC_ZERO } };

    GGML_F16_VEC ax[GGML_F16_ARR];
    GGML_F16_VEC ay[GGML_F16_ARR];

    for (int i = 0; i < np; i += GGML_F16_STEP) {
        for (int j = 0; j < GGML_F16_ARR; j++) {
            ay[j] = GGML_F16_VEC_LOAD(y + i + j*GGML_F16_EPR, j);

            for (int k = 0; k < GGML_VEC_DOT_UNROLL; ++k) {
                ax[j] = GGML_F16_VEC_LOAD(x[k] + i + j*GGML_F16_EPR, j);

                sum[k][j] = GGML_F16_VEC_FMA(sum[k][j], ax[j], ay[j]);
            }
        }
    }

    // reduce sum0..sum3 to sum0
    for (int k = 0; k < GGML_VEC_DOT_UNROLL; ++k) {
        GGML_F16_VEC_REDUCE(sumf[k], sum[k]);
    }

    // leftovers
    for (int i = np; i < n; ++i) {
        for (int j = 0; j < GGML_VEC_DOT_UNROLL; ++j) {
            sumf[j] += (ggml_float)(GGML_FP16_TO_FP32(x[j][i])*GGML_FP16_TO_FP32(y[i]));
        }
    }
#else
    for (int i = 0; i < n; ++i) {
        for (int j = 0; j < GGML_VEC_DOT_UNROLL; ++j) {
            sumf[j] += (ggml_float)(GGML_FP16_TO_FP32(x[j][i])*GGML_FP16_TO_FP32(y[i]));
        }
    }
#endif

    for (int i = 0; i < GGML_VEC_DOT_UNROLL; ++i) {
        s[i] = sumf[i];
    }
}

inline static void ggml_vec_mad_f32(const int n, float * restrict y, const float * restrict x, const float v) {
#if defined(GGML_SIMD)
    const int np = (n & ~(GGML_F32_STEP - 1));

    GGML_F32_VEC vx = GGML_F32_VEC_SET1(v);

    GGML_F32_VEC ax[GGML_F32_ARR];
    GGML_F32_VEC ay[GGML_F32_ARR];

    for (int i = 0; i < np; i += GGML_F32_STEP) {
        for (int j = 0; j < GGML_F32_ARR; j++) {
            ax[j] = GGML_F32_VEC_LOAD(x + i + j*GGML_F32_EPR);
            ay[j] = GGML_F32_VEC_LOAD(y + i + j*GGML_F32_EPR);
            ay[j] = GGML_F32_VEC_FMA(ay[j], ax[j], vx);

            GGML_F32_VEC_STORE(y + i + j*GGML_F32_EPR, ay[j]);
        }
    }

    // leftovers
    for (int i = np; i < n; ++i) {
        y[i] += x[i]*v;
    }
#else
    // scalar
    for (int i = 0; i < n; ++i) {
        y[i] += x[i]*v;
    }
#endif
}

//inline static void ggml_vec_scale_f32(const int n, float * y, const float   v) { for (int i = 0; i < n; ++i) y[i] *= v;          }
inline static void ggml_vec_scale_f32(const int n, float * y, const float   v) {
#if defined(GGML_SIMD)
    const int np = (n & ~(GGML_F32_STEP - 1));

    GGML_F32_VEC vx = GGML_F32_VEC_SET1(v);

    GGML_F32_VEC ay[GGML_F32_ARR];

    for (int i = 0; i < np; i += GGML_F32_STEP) {
        for (int j = 0; j < GGML_F32_ARR; j++) {
            ay[j] = GGML_F32_VEC_LOAD(y + i + j*GGML_F32_EPR);
            ay[j] = GGML_F32_VEC_MUL(ay[j], vx);

            GGML_F32_VEC_STORE(y + i + j*GGML_F32_EPR, ay[j]);
        }
    }

    // leftovers
    for (int i = np; i < n; ++i) {
        y[i] *= v;
    }
#else
    // scalar
    for (int i = 0; i < n; ++i) {
        y[i] *= v;
    }
#endif
}

inline static void ggml_vec_norm_f32 (const int n, float * s, const float * x) { ggml_vec_dot_f32(n, s, x, x); *s = sqrtf(*s);   }
inline static void ggml_vec_sqr_f32  (const int n, float * y, const float * x) { for (int i = 0; i < n; ++i) y[i] = x[i]*x[i];   }
inline static void ggml_vec_sqrt_f32 (const int n, float * y, const float * x) { for (int i = 0; i < n; ++i) y[i] = sqrtf(x[i]); }
inline static void ggml_vec_log_f32  (const int n, float * y, const float * x) { for (int i = 0; i < n; ++i) y[i] = logf(x[i]);   }
inline static void ggml_vec_abs_f32  (const int n, float * y, const float * x) { for (int i = 0; i < n; ++i) y[i] = fabsf(x[i]); }
inline static void ggml_vec_sgn_f32  (const int n, float * y, const float * x) { for (int i = 0; i < n; ++i) y[i] = (x[i] > 0.f) ? 1.f : ((x[i] < 0.f) ? -1.f : 0.f); }
inline static void ggml_vec_step_f32 (const int n, float * y, const float * x) { for (int i = 0; i < n; ++i) y[i] = (x[i] > 0.f) ? 1.f : 0.f; }
inline static void ggml_vec_tanh_f32 (const int n, float * y, const float * x) { for (int i = 0; i < n; ++i) y[i] = tanhf(x[i]);  }
inline static void ggml_vec_elu_f32  (const int n, float * y, const float * x) { for (int i = 0; i < n; ++i) y[i] = (x[i] > 0.f) ? x[i] : expf(x[i])-1; }
inline static void ggml_vec_relu_f32 (const int n, float * y, const float * x) { for (int i = 0; i < n; ++i) y[i] = (x[i] > 0.f) ? x[i] : 0.f; }

static const float GELU_COEF_A    = 0.044715f;
static const float GELU_QUICK_COEF    = -1.702f;
static const float SQRT_2_OVER_PI = 0.79788456080286535587989211986876f;

inline static float ggml_gelu_f32(float x) {
    return 0.5f*x*(1.0f + tanhf(SQRT_2_OVER_PI*x*(1.0f + GELU_COEF_A*x*x)));
}

inline static void ggml_vec_gelu_f16(const int n, ggml_fp16_t * y, const ggml_fp16_t * x) {
    const uint16_t * i16 = (const uint16_t *) x;
    for (int i = 0; i < n; ++i) {
        y[i] = table_gelu_f16[i16[i]];
    }
}

#ifdef GGML_GELU_FP16
inline static void ggml_vec_gelu_f32(const int n, float * y, const float * x) {
    uint16_t t;
    for (int i = 0; i < n; ++i) {
        ggml_fp16_t fp16 = GGML_FP32_TO_FP16(x[i]);
        memcpy(&t, &fp16, sizeof(uint16_t));
        y[i] = GGML_FP16_TO_FP32(table_gelu_f16[t]);
    }
}
#else
inline static void ggml_vec_gelu_f32(const int n, float * y, const float * x) {
    for (int i = 0; i < n; ++i) {
        y[i] = ggml_gelu_f32(x[i]);
    }
}
#endif

inline static float ggml_gelu_quick_f32(float x) {
    return x*(1.0f/(1.0f+expf(GELU_QUICK_COEF*x)));
}

//inline static void ggml_vec_gelu_quick_f16(const int n, ggml_fp16_t * y, const ggml_fp16_t * x) {
//    const uint16_t * i16 = (const uint16_t *) x;
//    for (int i = 0; i < n; ++i) {
//        y[i] = table_gelu_quick_f16[i16[i]];
//    }
//}

#ifdef GGML_GELU_QUICK_FP16
inline static void ggml_vec_gelu_quick_f32(const int n, float * y, const float * x) {
    uint16_t t;
    for (int i = 0; i < n; ++i) {
        ggml_fp16_t fp16 = GGML_FP32_TO_FP16(x[i]);
        memcpy(&t, &fp16, sizeof(uint16_t));
        y[i] = GGML_FP16_TO_FP32(table_gelu_quick_f16[t]);
    }
}
#else
inline static void ggml_vec_gelu_quick_f32(const int n, float * y, const float * x) {
    for (int i = 0; i < n; ++i) {
        y[i] = ggml_gelu_quick_f32(x[i]);
    }
}
#endif

// Sigmoid Linear Unit (SiLU) function
inline static float ggml_silu_f32(float x) {
    return x/(1.0f + expf(-x));
}

//inline static void ggml_vec_silu_f16(const int n, ggml_fp16_t * y, const ggml_fp16_t * x) {
//    const uint16_t * i16 = (const uint16_t *) x;
//    for (int i = 0; i < n; ++i) {
//        y[i] = table_silu_f16[i16[i]];
//    }
//}

#ifdef GGML_SILU_FP16
inline static void ggml_vec_silu_f32(const int n, float * y, const float * x) {
    uint16_t t;
    for (int i = 0; i < n; ++i) {
        ggml_fp16_t fp16 = GGML_FP32_TO_FP16(x[i]);
        memcpy(&t, &fp16, sizeof(uint16_t));
        y[i] = GGML_FP16_TO_FP32(table_silu_f16[t]);
    }
}
#else
inline static void ggml_vec_silu_f32(const int n, float * y, const float * x) {
    for (int i = 0; i < n; ++i) {
        y[i] = ggml_silu_f32(x[i]);
    }
}
#endif

inline static float ggml_silu_backward_f32(float x, float dy) {
    const float s = 1.0f/(1.0f + expf(-x));
    return dy*s*(1.0f + x*(1.0f - s));
}

#ifdef GGML_SILU_FP16
inline static void ggml_vec_silu_backward_f32(const int n, float * dx, const float * x, const float * dy) {
    for (int i = 0; i < n; ++i) {
        // we did not use x[i] to compute forward silu but its f16 equivalent
        // take derivative at f16 of x[i]:
        ggml_fp16_t fp16 = GGML_FP32_TO_FP16(x[i]);
        float usedx = GGML_FP16_TO_FP32(fp16);
        dx[i] = ggml_silu_backward_f32(usedx, dy[i]);
    }
}
#else
inline static void ggml_vec_silu_backward_f32(const int n, float * dx, const float * x, const float * dy) {
    for (int i = 0; i < n; ++i) {
        dx[i] = ggml_silu_backward_f32(x[i], dy[i]);
    }
}
#endif

inline static void ggml_vec_sum_f32(const int n, float * s, const float * x) {
#ifndef GGML_USE_ACCELERATE
    ggml_float sum = 0.0;
    for (int i = 0; i < n; ++i) {
        sum += (ggml_float)x[i];
    }
    *s = sum;
#else
    vDSP_sve(x, 1, s, n);
#endif
}

inline static void ggml_vec_sum_ggf(const int n, ggml_float * s, const float * x) {
    ggml_float sum = 0.0;
    for (int i = 0; i < n; ++i) {
        sum += (ggml_float)x[i];
    }
    *s = sum;
}

inline static void ggml_vec_max_f32(const int n, float * s, const float * x) {
#ifndef GGML_USE_ACCELERATE
    float max = -INFINITY;
    for (int i = 0; i < n; ++i) {
        max = MAX(max, x[i]);
    }
    *s = max;
#else
    vDSP_maxv(x, 1, s, n);
#endif
}

inline static void ggml_vec_norm_inv_f32(const int n, float * s, const float * x) {
    ggml_vec_norm_f32(n, s, x);
    *s = 1.f/(*s);
}

inline static void ggml_vec_argmax_f32(const int n, int * s, const float * x) {
    float max = -INFINITY;
    int idx = 0;
    for (int i = 0; i < n; ++i) {
        max = MAX(max, x[i]);
        if (max == x[i]) { idx = i; }
    }
    *s = idx;
}

//
// data types
//

static const int GGML_BLCK_SIZE[GGML_TYPE_COUNT] = {
    [GGML_TYPE_F32]  = 1,
    [GGML_TYPE_F16]  = 1,
    [GGML_TYPE_Q4_0] = QK4_0,
    [GGML_TYPE_Q4_1] = QK4_1,
    [GGML_TYPE_Q5_0] = QK5_0,
    [GGML_TYPE_Q5_1] = QK5_1,
    [GGML_TYPE_Q8_0] = QK8_0,
    [GGML_TYPE_Q8_1] = QK8_1,
#ifdef GGML_USE_K_QUANTS
    [GGML_TYPE_Q2_K] = QK_K,
    [GGML_TYPE_Q3_K] = QK_K,
    [GGML_TYPE_Q4_K] = QK_K,
    [GGML_TYPE_Q5_K] = QK_K,
    [GGML_TYPE_Q6_K] = QK_K,
    [GGML_TYPE_Q8_K] = QK_K,
#endif
    [GGML_TYPE_I8]   = 1,
    [GGML_TYPE_I16]  = 1,
    [GGML_TYPE_I32]  = 1,
};
static_assert(GGML_TYPE_COUNT == 19, "GGML_BLCK_SIZE is outdated");

static const size_t GGML_TYPE_SIZE[GGML_TYPE_COUNT] = {
    [GGML_TYPE_F32]  = sizeof(float),
    [GGML_TYPE_F16]  = sizeof(ggml_fp16_t),
    [GGML_TYPE_Q4_0] = sizeof(block_q4_0),
    [GGML_TYPE_Q4_1] = sizeof(block_q4_1),
    [GGML_TYPE_Q5_0] = sizeof(block_q5_0),
    [GGML_TYPE_Q5_1] = sizeof(block_q5_1),
    [GGML_TYPE_Q8_0] = sizeof(block_q8_0),
    [GGML_TYPE_Q8_1] = sizeof(block_q8_1),
#ifdef GGML_USE_K_QUANTS
    [GGML_TYPE_Q2_K] = sizeof(block_q2_K),
    [GGML_TYPE_Q3_K] = sizeof(block_q3_K),
    [GGML_TYPE_Q4_K] = sizeof(block_q4_K),
    [GGML_TYPE_Q5_K] = sizeof(block_q5_K),
    [GGML_TYPE_Q6_K] = sizeof(block_q6_K),
    [GGML_TYPE_Q8_K] = sizeof(block_q8_K),
#endif
    [GGML_TYPE_I8]   = sizeof(int8_t),
    [GGML_TYPE_I16]  = sizeof(int16_t),
    [GGML_TYPE_I32]  = sizeof(int32_t),
};
static_assert(GGML_TYPE_COUNT == 19, "GGML_TYPE_SIZE is outdated");


static const char * GGML_TYPE_NAME[GGML_TYPE_COUNT] = {
    [GGML_TYPE_F32]  = "f32",
    [GGML_TYPE_F16]  = "f16",
    [GGML_TYPE_Q4_0] = "q4_0",
    [GGML_TYPE_Q4_1] = "q4_1",
    [GGML_TYPE_Q5_0] = "q5_0",
    [GGML_TYPE_Q5_1] = "q5_1",
    [GGML_TYPE_Q8_0] = "q8_0",
    [GGML_TYPE_Q8_1] = "q8_1",
    [GGML_TYPE_Q2_K] = "q2_K",
    [GGML_TYPE_Q3_K] = "q3_K",
    [GGML_TYPE_Q4_K] = "q4_K",
    [GGML_TYPE_Q5_K] = "q5_K",
    [GGML_TYPE_Q6_K] = "q6_K",
    [GGML_TYPE_Q8_K] = "q8_K",
    [GGML_TYPE_I8]   = "i8",
    [GGML_TYPE_I16]  = "i16",
    [GGML_TYPE_I32]  = "i32",
};
static_assert(GGML_TYPE_COUNT == 19, "GGML_TYPE_NAME is outdated");

static bool GGML_IS_QUANTIZED[GGML_TYPE_COUNT] = {
    [GGML_TYPE_F32]  = false,
    [GGML_TYPE_F16]  = false,
    [GGML_TYPE_Q4_0] = true,
    [GGML_TYPE_Q4_1] = true,
    [GGML_TYPE_Q5_0] = true,
    [GGML_TYPE_Q5_1] = true,
    [GGML_TYPE_Q8_0] = true,
    [GGML_TYPE_Q8_1] = true,
    [GGML_TYPE_Q2_K] = true,
    [GGML_TYPE_Q3_K] = true,
    [GGML_TYPE_Q4_K] = true,
    [GGML_TYPE_Q5_K] = true,
    [GGML_TYPE_Q6_K] = true,
    [GGML_TYPE_Q8_K] = true,
    [GGML_TYPE_I8]   = false,
    [GGML_TYPE_I16]  = false,
    [GGML_TYPE_I32]  = false,
};
static_assert(GGML_TYPE_COUNT == 19, "GGML_IS_QUANTIZED is outdated");

static const char * GGML_OP_NAME[GGML_OP_COUNT] = {
    "NONE",

    "DUP",
    "ADD",
    "ADD1",
    "ACC",
    "SUB",
    "MUL",
    "DIV",
    "SQR",
    "SQRT",
    "LOG",
    "SUM",
    "SUM_ROWS",
    "MEAN",
    "ARGMAX",
    "REPEAT",
    "REPEAT_BACK",
    "ABS",
    "SGN",
    "NEG",
    "STEP",
    "TANH",
    "ELU",
    "RELU",
    "GELU",
    "GELU_QUICK",
    "SILU",
    "SILU_BACK",
    "NORM",
    "RMS_NORM",
    "RMS_NORM_BACK",

    "MUL_MAT",
    "OUT_PROD",

    "SCALE",
    "SET",
    "CPY",
    "CONT",
    "RESHAPE",
    "VIEW",
    "PERMUTE",
    "TRANSPOSE",
    "GET_ROWS",
    "GET_ROWS_BACK",
    "DIAG",
    "DIAG_MASK_INF",
    "DIAG_MASK_ZERO",
    "SOFT_MAX",
    "SOFT_MAX_BACK",
    "ROPE",
    "ROPE_BACK",
    "ALIBI",
    "CLAMP",
    "CONV_1D",
    "CONV_2D",

    "FLASH_ATTN",
    "FLASH_FF",
    "FLASH_ATTN_BACK",
    "WIN_PART",
    "WIN_UNPART",

    "MAP_UNARY",
    "MAP_BINARY",

    "MAP_CUSTOM1",
    "MAP_CUSTOM2",
    "MAP_CUSTOM3",

    "CROSS_ENTROPY_LOSS",
    "CROSS_ENTROPY_LOSS_BACK",
};

static_assert(GGML_OP_COUNT == 66, "GGML_OP_COUNT != 66");

static const char * GGML_OP_SYMBOL[GGML_OP_COUNT] = {
    "none",

    "x",
    "x+y",
    "x+y",
    "view(x,nb,offset)+=y->x",
    "x-y",
    "x*y",
    "x/y",
    "x^2",
    "√x",
    "log(x)",
    "Σx",
    "Σx_k",
    "Σx/n",
    "argmax(x)",
    "repeat(x)",
    "repeat_back(x)",
    "abs(x)",
    "sgn(x)",
    "-x",
    "step(x)",
    "tanh(x)",
    "elu(x)",
    "relu(x)",
    "gelu(x)",
    "gelu_quick(x)",
    "silu(x)",
    "silu_back(x)",
    "norm(x)",
    "rms_norm(x)",
    "rms_norm_back(x)",

    "X*Y",
    "X*Y",

    "x*v",
    "y-\\>view(x)",
    "x-\\>y",
    "cont(x)",
    "reshape(x)",
    "view(x)",
    "permute(x)",
    "transpose(x)",
    "get_rows(x)",
    "get_rows_back(x)",
    "diag(x)",
    "diag_mask_inf(x)",
    "diag_mask_zero(x)",
    "soft_max(x)",
    "soft_max_back(x)",
    "rope(x)",
    "rope_back(x)",
    "alibi(x)",
    "clamp(x)",
    "conv_1d(x)",
    "conv_2d(x)",

    "flash_attn(x)",
    "flash_ff(x)",
    "flash_attn_back(x)",
    "win_part(x)",
    "win_unpart(x)",

    "f(x)",
    "f(x,y)",

    "custom(x)",
    "custom(x,y)",
    "custom(x,y,z)",

    "cross_entropy_loss(x,y)",
    "cross_entropy_loss_back(x,y)",
};

static_assert(GGML_OP_COUNT == 66, "GGML_OP_COUNT != 66");

static_assert(sizeof(struct ggml_object)%GGML_MEM_ALIGN == 0, "ggml_object size must be a multiple of GGML_MEM_ALIGN");
static_assert(sizeof(struct ggml_tensor)%GGML_MEM_ALIGN == 0, "ggml_tensor size must be a multiple of GGML_MEM_ALIGN");

// WARN:
// Mis-confguration can lead to problem that's hard to reason about:
// * At best  it crash or talks nosense.
// * At worst it talks slightly difference but hard to perceive.
//
// An op has to enable INIT or FINALIZE when any of it's branch needs that pass.
// Take care about compile options (e.g., GGML_USE_xxx).
static bool GGML_OP_HAS_INIT    [GGML_OP_COUNT] = { 0 };
static bool GGML_OP_HAS_FINALIZE[GGML_OP_COUNT] = { 0 };

static void ggml_setup_op_has_task_pass(void) {
    {   // INIT
        bool * p = GGML_OP_HAS_INIT;

        p[GGML_OP_ACC                    ] = true;
        p[GGML_OP_MUL_MAT                ] = true;
        p[GGML_OP_OUT_PROD               ] = true;
        p[GGML_OP_SET                    ] = true;
        p[GGML_OP_GET_ROWS_BACK          ] = true;
        p[GGML_OP_DIAG_MASK_INF          ] = true;
        p[GGML_OP_DIAG_MASK_ZERO         ] = true;
        p[GGML_OP_CONV_1D                ] = true;
        p[GGML_OP_CONV_2D                ] = true;
        p[GGML_OP_FLASH_ATTN_BACK        ] = true;
        p[GGML_OP_CROSS_ENTROPY_LOSS     ] = true;
    }

    {   // FINALIZE
        bool * p = GGML_OP_HAS_FINALIZE;

        p[GGML_OP_CROSS_ENTROPY_LOSS     ] = true;
    }
}

//
// ggml context
//

struct ggml_context {
    size_t mem_size;
    void * mem_buffer;
    bool   mem_buffer_owned;
    bool   no_alloc;
    bool   no_alloc_save; // this is used to save the no_alloc state when using scratch buffers

    int    n_objects;

    struct ggml_object * objects_begin;
    struct ggml_object * objects_end;

    struct ggml_scratch scratch;
    struct ggml_scratch scratch_save;
};

struct ggml_context_container {
    bool used;

    struct ggml_context context;
};

//
// NUMA support
//

#define GGML_NUMA_MAX_NODES 8
#define GGML_NUMA_MAX_CPUS 512

struct ggml_numa_node {
    uint32_t cpus[GGML_NUMA_MAX_CPUS]; // hardware threads on this node
    uint32_t n_cpus;
};

struct ggml_numa_nodes {
    struct ggml_numa_node nodes[GGML_NUMA_MAX_NODES];
    uint32_t n_nodes;
    uint32_t total_cpus; // hardware threads on system
};

//
// ggml state
//

struct ggml_state {
    struct ggml_context_container contexts[GGML_MAX_CONTEXTS];
    struct ggml_numa_nodes numa;
};

// global state
static struct ggml_state g_state;
static atomic_int g_state_barrier = 0;

// barrier via spin lock
inline static void ggml_critical_section_start(void) {
    int processing = atomic_fetch_add(&g_state_barrier, 1);

    while (processing > 0) {
        // wait for other threads to finish
        atomic_fetch_sub(&g_state_barrier, 1);
        sched_yield(); // TODO: reconsider this
        processing = atomic_fetch_add(&g_state_barrier, 1);
    }
}

// TODO: make this somehow automatically executed
//       some sort of "sentry" mechanism
inline static void ggml_critical_section_end(void) {
    atomic_fetch_sub(&g_state_barrier, 1);
}

void ggml_numa_init(void) {
    if (g_state.numa.n_nodes > 0) {
        fprintf(stderr, "ggml_numa_init: NUMA already initialized\n");

        return;
    }

#ifdef __linux__
    struct stat st;
    char path[256];
    int rv;

    // enumerate nodes
    while (g_state.numa.n_nodes < GGML_NUMA_MAX_NODES) {
        rv = snprintf(path, sizeof(path), "/sys/devices/system/node/node%u", g_state.numa.n_nodes);
        GGML_ASSERT(rv > 0 && (unsigned)rv < sizeof(path));
        if (stat(path, &st) != 0) { break; }
        ++g_state.numa.n_nodes;
    }

    // enumerate CPUs
    while (g_state.numa.total_cpus < GGML_NUMA_MAX_CPUS) {
        rv = snprintf(path, sizeof(path), "/sys/devices/system/cpu/cpu%u", g_state.numa.total_cpus);
        GGML_ASSERT(rv > 0 && (unsigned)rv < sizeof(path));
        if (stat(path, &st) != 0) { break; }
        ++g_state.numa.total_cpus;
    }

    GGML_PRINT_DEBUG("found %u numa nodes, %u CPUs\n", g_state.numa.n_nodes, g_state.numa.total_cpus);

    if (g_state.numa.n_nodes < 1 || g_state.numa.total_cpus < 1) {
        g_state.numa.n_nodes = 0;
        return;
    }

    for (uint32_t n = 0; n < g_state.numa.n_nodes; ++n) {
        struct ggml_numa_node * node = &g_state.numa.nodes[n];
        GGML_PRINT_DEBUG("CPUs on node %u:", n);
        node->n_cpus = 0;
        for (uint32_t c = 0; c < g_state.numa.total_cpus; ++c) {
            rv = snprintf(path, sizeof(path), "/sys/devices/system/node/node%u/cpu%u", n, c);
            GGML_ASSERT(rv > 0 && (unsigned)rv < sizeof(path));
            if (stat(path, &st) == 0) {
                node->cpus[node->n_cpus++] = c;
                GGML_PRINT_DEBUG(" %u", c);
            }
        }
        GGML_PRINT_DEBUG("\n");
    }

    if (ggml_is_numa()) {
        FILE *fptr = fopen("/proc/sys/kernel/numa_balancing", "r");
        if (fptr != NULL) {
            char buf[42];
            if (fgets(buf, sizeof(buf), fptr) && strncmp(buf, "0\n", sizeof(buf)) != 0) {
                GGML_PRINT("WARNING: /proc/sys/kernel/numa_balancing is enabled, this has been observed to impair performance\n");
            }
            fclose(fptr);
        }
    }
#else
    // TODO
#endif
}

bool ggml_is_numa(void) {
    return g_state.numa.n_nodes > 1;
}

////////////////////////////////////////////////////////////////////////////////

void ggml_print_object(const struct ggml_object * obj) {
    GGML_PRINT(" - ggml_object: offset = %zu, size = %zu, next = %p\n",
            obj->offs, obj->size, (const void *) obj->next);
}

void ggml_print_objects(const struct ggml_context * ctx) {
    struct ggml_object * obj = ctx->objects_begin;

    GGML_PRINT("%s: objects in context %p:\n", __func__, (const void *) ctx);

    while (obj != NULL) {
        ggml_print_object(obj);
        obj = obj->next;
    }

    GGML_PRINT("%s: --- end ---\n", __func__);
}

int64_t ggml_nelements(const struct ggml_tensor * tensor) {
    static_assert(GGML_MAX_DIMS == 4, "GGML_MAX_DIMS is not 4 - update this function");

    return tensor->ne[0]*tensor->ne[1]*tensor->ne[2]*tensor->ne[3];
}

int64_t ggml_nrows(const struct ggml_tensor * tensor) {
    static_assert(GGML_MAX_DIMS == 4, "GGML_MAX_DIMS is not 4 - update this function");

    return tensor->ne[1]*tensor->ne[2]*tensor->ne[3];
}

size_t ggml_nbytes(const struct ggml_tensor * tensor) {
    static_assert(GGML_MAX_DIMS == 4, "GGML_MAX_DIMS is not 4 - update this function");

    // this should handle cases where the tensor is not contiguous in memory
    // probaby just:
    //
    //     return tensor->ne[3]*tensor->nb[3]
    //
    // is enough, but just in case, adding the second part

    return MAX(tensor->ne[3]*tensor->nb[3], (ggml_nelements(tensor)*GGML_TYPE_SIZE[tensor->type])/GGML_BLCK_SIZE[tensor->type]);
}

size_t ggml_nbytes_split(const struct ggml_tensor * tensor, int nrows_split) {
    static_assert(GGML_MAX_DIMS == 4, "GGML_MAX_DIMS is not 4 - update this function");

    return (nrows_split*tensor->ne[0]*GGML_TYPE_SIZE[tensor->type])/GGML_BLCK_SIZE[tensor->type];
}

int ggml_blck_size(enum ggml_type type) {
    return GGML_BLCK_SIZE[type];
}

size_t ggml_type_size(enum ggml_type type) {
    return GGML_TYPE_SIZE[type];
}

float ggml_type_sizef(enum ggml_type type) {
    return ((float)(GGML_TYPE_SIZE[type]))/GGML_BLCK_SIZE[type];
}

const char * ggml_type_name(enum ggml_type type) {
    return GGML_TYPE_NAME[type];
}

const char * ggml_op_name(enum ggml_op op) {
    return GGML_OP_NAME[op];
}

size_t ggml_element_size(const struct ggml_tensor * tensor) {
    return GGML_TYPE_SIZE[tensor->type];
}

static inline bool ggml_is_scalar(const struct ggml_tensor * tensor) {
    static_assert(GGML_MAX_DIMS == 4, "GGML_MAX_DIMS is not 4 - update this function");

    return tensor->ne[0] == 1 && tensor->ne[1] == 1 && tensor->ne[2] == 1 && tensor->ne[3] == 1;
}

static inline bool ggml_is_vector(const struct ggml_tensor * tensor) {
    static_assert(GGML_MAX_DIMS == 4, "GGML_MAX_DIMS is not 4 - update this function");

    return tensor->ne[1] == 1 && tensor->ne[2] == 1 && tensor->ne[3] == 1;
}

static inline bool ggml_is_matrix(const struct ggml_tensor * tensor) {
    static_assert(GGML_MAX_DIMS == 4, "GGML_MAX_DIMS is not 4 - update this function");

    return tensor->ne[2] == 1 && tensor->ne[3] == 1;
}

static inline bool ggml_can_mul_mat(const struct ggml_tensor * t0, const struct ggml_tensor * t1) {
    static_assert(GGML_MAX_DIMS == 4, "GGML_MAX_DIMS is not 4 - update this function");

    return
        (t0->ne[0] == t1->ne[0])  &&
        (t0->ne[2] == t1->ne[2])  &&
        (t0->ne[3] == t1->ne[3]);
}

static inline bool ggml_can_out_prod(const struct ggml_tensor * t0, const struct ggml_tensor * t1) {
    static_assert(GGML_MAX_DIMS == 4, "GGML_MAX_DIMS is not 4 - update this function");

    return
        (t0->ne[1] == t1->ne[1])  &&
        (t0->ne[2] == t1->ne[2])  &&
        (t0->ne[3] == t1->ne[3]);
}

bool ggml_is_quantized(enum ggml_type type) {
    return GGML_IS_QUANTIZED[type];
}

enum ggml_type ggml_ftype_to_ggml_type(enum ggml_ftype ftype) {
    enum ggml_type wtype = GGML_TYPE_COUNT;

    switch (ftype) {
        case GGML_FTYPE_ALL_F32:              wtype = GGML_TYPE_F32;   break;
        case GGML_FTYPE_MOSTLY_F16:           wtype = GGML_TYPE_F16;   break;
        case GGML_FTYPE_MOSTLY_Q4_0:          wtype = GGML_TYPE_Q4_0;  break;
        case GGML_FTYPE_MOSTLY_Q4_1:          wtype = GGML_TYPE_Q4_1;  break;
        case GGML_FTYPE_MOSTLY_Q5_0:          wtype = GGML_TYPE_Q5_0;  break;
        case GGML_FTYPE_MOSTLY_Q5_1:          wtype = GGML_TYPE_Q5_1;  break;
        case GGML_FTYPE_MOSTLY_Q8_0:          wtype = GGML_TYPE_Q8_0;  break;
        case GGML_FTYPE_MOSTLY_Q2_K:          wtype = GGML_TYPE_Q2_K;  break;
        case GGML_FTYPE_MOSTLY_Q3_K:          wtype = GGML_TYPE_Q3_K;  break;
        case GGML_FTYPE_MOSTLY_Q4_K:          wtype = GGML_TYPE_Q4_K;  break;
        case GGML_FTYPE_MOSTLY_Q5_K:          wtype = GGML_TYPE_Q5_K;  break;
        case GGML_FTYPE_MOSTLY_Q6_K:          wtype = GGML_TYPE_Q6_K;  break;
        case GGML_FTYPE_UNKNOWN:              wtype = GGML_TYPE_COUNT; break;
        case GGML_FTYPE_MOSTLY_Q4_1_SOME_F16: wtype = GGML_TYPE_COUNT; break;
    }

    GGML_ASSERT(wtype != GGML_TYPE_COUNT);

    return wtype;
}

size_t ggml_tensor_overhead(void) {
    return GGML_OBJECT_SIZE + GGML_TENSOR_SIZE + 16;
}

bool ggml_is_transposed(const struct ggml_tensor * tensor) {
    return tensor->nb[0] > tensor->nb[1];
}

bool ggml_is_contiguous(const struct ggml_tensor * tensor) {
    static_assert(GGML_MAX_DIMS == 4, "GGML_MAX_DIMS is not 4 - update this function");

    return
        tensor->nb[0] == GGML_TYPE_SIZE[tensor->type] &&
        tensor->nb[1] == (tensor->nb[0]*tensor->ne[0])/GGML_BLCK_SIZE[tensor->type] &&
        tensor->nb[2] == tensor->nb[1]*tensor->ne[1] &&
        tensor->nb[3] == tensor->nb[2]*tensor->ne[2];
}

bool ggml_is_permuted(const struct ggml_tensor * tensor) {
    static_assert(GGML_MAX_DIMS == 4, "GGML_MAX_DIMS is not 4 - update this function");

    return tensor->nb[0] > tensor->nb[1] || tensor->nb[1] > tensor->nb[2] || tensor->nb[2] > tensor->nb[3];
}

static inline bool ggml_is_padded_1d(const struct ggml_tensor * tensor) {
    static_assert(GGML_MAX_DIMS == 4, "GGML_MAX_DIMS is not 4 - update this function");

    return
        tensor->nb[0] == GGML_TYPE_SIZE[tensor->type] &&
        tensor->nb[2] == tensor->nb[1]*tensor->ne[1] &&
        tensor->nb[3] == tensor->nb[2]*tensor->ne[2];
}

static inline bool ggml_are_same_shape(const struct ggml_tensor * t0, const struct ggml_tensor * t1) {
    static_assert(GGML_MAX_DIMS == 4, "GGML_MAX_DIMS is not 4 - update this function");

    return
        (t0->ne[0] == t1->ne[0] ) &&
        (t0->ne[1] == t1->ne[1] ) &&
        (t0->ne[2] == t1->ne[2] ) &&
        (t0->ne[3] == t1->ne[3] );
}

// check if t1 can be represented as a repeatition of t0
static inline bool ggml_can_repeat(const struct ggml_tensor * t0, const struct ggml_tensor * t1) {
    static_assert(GGML_MAX_DIMS == 4, "GGML_MAX_DIMS is not 4 - update this function");

    return
        (t1->ne[0]%t0->ne[0] == 0) &&
        (t1->ne[1]%t0->ne[1] == 0) &&
        (t1->ne[2]%t0->ne[2] == 0) &&
        (t1->ne[3]%t0->ne[3] == 0);
}

static inline bool ggml_can_repeat_rows(const struct ggml_tensor * t0, const struct ggml_tensor * t1) {
    static_assert(GGML_MAX_DIMS == 4, "GGML_MAX_DIMS is not 4 - update this function");

    return (t0->ne[0] == t1->ne[0]) && ggml_can_repeat(t0, t1);
}

static inline int ggml_up32(int n) {
    return (n + 31) & ~31;
}

//static inline int ggml_up64(int n) {
//    return (n + 63) & ~63;
//}

static inline int ggml_up(int n, int m) {
    // assert m is a power of 2
    GGML_ASSERT((m & (m - 1)) == 0);
    return (n + m - 1) & ~(m - 1);
}

// assert that pointer is aligned to GGML_MEM_ALIGN
#define ggml_assert_aligned(ptr) \
    GGML_ASSERT(((uintptr_t) (ptr))%GGML_MEM_ALIGN == 0)

////////////////////////////////////////////////////////////////////////////////

struct ggml_context * ggml_init(struct ggml_init_params params) {
    // make this function thread safe
    ggml_critical_section_start();

    static bool is_first_call = true;

    if (is_first_call) {
        // initialize time system (required on Windows)
        ggml_time_init();

        // initialize GELU, Quick GELU, SILU and EXP F32 tables
        {
            const uint64_t t_start = ggml_time_us(); UNUSED(t_start);

            ggml_fp16_t ii;
            for (int i = 0; i < (1 << 16); ++i) {
                uint16_t ui = i;
                memcpy(&ii, &ui, sizeof(ii));
                const float f = table_f32_f16[i] = GGML_COMPUTE_FP16_TO_FP32(ii);
                table_gelu_f16[i] = GGML_FP32_TO_FP16(ggml_gelu_f32(f));
                table_gelu_quick_f16[i] = GGML_FP32_TO_FP16(ggml_gelu_quick_f32(f));
                table_silu_f16[i] = GGML_FP32_TO_FP16(ggml_silu_f32(f));
                table_exp_f16[i]  = GGML_FP32_TO_FP16(expf(f));
            }

            const uint64_t t_end = ggml_time_us(); UNUSED(t_end);

            GGML_PRINT_DEBUG("%s: GELU, Quick GELU, SILU and EXP tables initialized in %f ms\n", __func__, (t_end - t_start)/1000.0f);
        }

        // initialize g_state
        {
            const uint64_t t_start = ggml_time_us(); UNUSED(t_start);

            g_state = (struct ggml_state) {
                /*.contexts =*/ { { 0 } },
                /*.numa =*/ {
                    .n_nodes = 0,
                    .total_cpus = 0,
                },
            };

            for (int i = 0; i < GGML_MAX_CONTEXTS; ++i) {
                g_state.contexts[i].used = false;
            }

            const uint64_t t_end = ggml_time_us(); UNUSED(t_end);

            GGML_PRINT_DEBUG("%s: g_state initialized in %f ms\n", __func__, (t_end - t_start)/1000.0f);
        }

#if defined(GGML_USE_CUBLAS)
        ggml_init_cublas();
#elif defined(GGML_USE_CLBLAST)
        ggml_cl_init();
#endif

        ggml_setup_op_has_task_pass();

        is_first_call = false;
    }

    // find non-used context in g_state
    struct ggml_context * ctx = NULL;

    for (int i = 0; i < GGML_MAX_CONTEXTS; i++) {
        if (!g_state.contexts[i].used) {
            g_state.contexts[i].used = true;
            ctx = &g_state.contexts[i].context;

            GGML_PRINT_DEBUG("%s: found unused context %d\n", __func__, i);
            break;
        }
    }

    if (ctx == NULL) {
        GGML_PRINT_DEBUG("%s: no unused context found\n", __func__);

        ggml_critical_section_end();

        return NULL;
    }

    const size_t mem_size = (params.mem_size + GGML_MEM_ALIGN - 1) & ~(GGML_MEM_ALIGN - 1);

    *ctx = (struct ggml_context) {
        /*.mem_size           =*/ mem_size,
        /*.mem_buffer         =*/ params.mem_buffer ? params.mem_buffer : GGML_ALIGNED_MALLOC(mem_size),
        /*.mem_buffer_owned   =*/ params.mem_buffer ? false : true,
        /*.no_alloc           =*/ params.no_alloc,
        /*.no_alloc_save      =*/ params.no_alloc,
        /*.n_objects          =*/ 0,
        /*.objects_begin      =*/ NULL,
        /*.objects_end        =*/ NULL,
        /*.scratch            =*/ { 0, 0, NULL, },
        /*.scratch_save       =*/ { 0, 0, NULL, },
    };

    GGML_ASSERT(ctx->mem_buffer != NULL);

    ggml_assert_aligned(ctx->mem_buffer);

    GGML_PRINT_DEBUG("%s: context initialized\n", __func__);

    ggml_critical_section_end();

    return ctx;
}

void ggml_free(struct ggml_context * ctx) {
    // make this function thread safe
    ggml_critical_section_start();

    bool found = false;

    for (int i = 0; i < GGML_MAX_CONTEXTS; i++) {
        if (&g_state.contexts[i].context == ctx) {
            g_state.contexts[i].used = false;

            GGML_PRINT_DEBUG("%s: context %d with %d objects has been freed. memory used = %zu\n",
                    __func__, i, ctx->n_objects, ctx->objects_end->offs + ctx->objects_end->size);

            if (ctx->mem_buffer_owned) {
                GGML_ALIGNED_FREE(ctx->mem_buffer);
            }

            found = true;
            break;
        }
    }

    if (!found) {
        GGML_PRINT_DEBUG("%s: context not found\n", __func__);
    }

    ggml_critical_section_end();
}

size_t ggml_used_mem(const struct ggml_context * ctx) {
    return ctx->objects_end == NULL ? 0 : ctx->objects_end->offs + ctx->objects_end->size;
}

size_t ggml_set_scratch(struct ggml_context * ctx, struct ggml_scratch scratch) {
    const size_t result = ctx->scratch.data ? ctx->scratch.offs : 0;

    ctx->scratch = scratch;

    return result;
}

void ggml_set_no_alloc(struct ggml_context * ctx, bool no_alloc) {
    ctx->no_alloc = no_alloc;
}

void * ggml_get_mem_buffer(const struct ggml_context * ctx) {
    return ctx->mem_buffer;
}

size_t ggml_get_mem_size(const struct ggml_context * ctx) {
    return ctx->mem_size;
}

size_t ggml_get_max_tensor_size(const struct ggml_context * ctx) {
    size_t max_size = 0;

    struct ggml_object * obj = ctx->objects_begin;

    while (obj != NULL) {
        struct ggml_tensor * tensor = (struct ggml_tensor *) ((char *) ctx->mem_buffer + obj->offs);

        const size_t size = ggml_nbytes(tensor);

        if (max_size < size) {
            max_size = size;
        }

        obj = obj->next;
    }

    return max_size;
}

// IMPORTANT:
// when creating "opt" tensors, always save and load the scratch buffer
// this is an error prone process, but it is necessary to support inplace
// operators when using scratch buffers
// TODO: implement a better way
void ggml_scratch_save(struct ggml_context * ctx) {
    // this is needed to allow opt tensors to store their data
    // TODO: again, need to find a better way
    ctx->no_alloc_save = ctx->no_alloc;
    ctx->no_alloc      = false;

    ctx->scratch_save = ctx->scratch;
    ctx->scratch.data = NULL;
}

void ggml_scratch_load(struct ggml_context * ctx) {
    ctx->no_alloc = ctx->no_alloc_save;

    ctx->scratch = ctx->scratch_save;
}

////////////////////////////////////////////////////////////////////////////////

struct ggml_tensor * ggml_new_tensor_impl(
        struct ggml_context * ctx,
        enum   ggml_type type,
        int    n_dims,
        const int64_t* ne,
        void*  data) {
    // always insert objects at the end of the context's memory pool
    struct ggml_object * obj_cur = ctx->objects_end;

    const size_t cur_offs = obj_cur == NULL ? 0 : obj_cur->offs;
    const size_t cur_size = obj_cur == NULL ? 0 : obj_cur->size;
    const size_t cur_end  = cur_offs + cur_size;

    size_t size_needed = 0;

    if (data == NULL && !ctx->no_alloc) {
        size_needed += GGML_TYPE_SIZE[type]*(ne[0]/GGML_BLCK_SIZE[type]);
        for (int i = 1; i < n_dims; i++) {
            size_needed *= ne[i];
        }
        // align to GGML_MEM_ALIGN
        size_needed = ((size_needed + GGML_MEM_ALIGN - 1)/GGML_MEM_ALIGN)*GGML_MEM_ALIGN;
    }

    char * const mem_buffer = ctx->mem_buffer;
    struct ggml_object * const obj_new = (struct ggml_object *)(mem_buffer + cur_end);

    if (ctx->scratch.data == NULL || data != NULL) {
        size_needed += GGML_TENSOR_SIZE;

        if (cur_end + size_needed + GGML_OBJECT_SIZE > ctx->mem_size) {
            GGML_PRINT("%s: not enough space in the context's memory pool (needed %zu, available %zu)\n",
                    __func__, cur_end + size_needed + GGML_OBJECT_SIZE, ctx->mem_size);
            assert(false);
            return NULL;
        }

        *obj_new = (struct ggml_object) {
            .offs = cur_end + GGML_OBJECT_SIZE,
            .size = size_needed,
            .next = NULL,
        };
    } else {
        if (ctx->scratch.offs + size_needed > ctx->scratch.size) {
            GGML_PRINT("%s: not enough space in the scratch memory pool (needed %zu, available %zu)\n",
                    __func__, ctx->scratch.offs + size_needed, ctx->scratch.size);
            assert(false);
            return NULL;
        }

        if (cur_end + GGML_TENSOR_SIZE + GGML_OBJECT_SIZE > ctx->mem_size) {
            GGML_PRINT("%s: not enough space in the context's memory pool (needed %zu, available %zu)\n",
                    __func__, cur_end + GGML_TENSOR_SIZE + GGML_OBJECT_SIZE, ctx->mem_size);
            assert(false);
            return NULL;
        }

        data = (char * const) ctx->scratch.data + ctx->scratch.offs;

        *obj_new = (struct ggml_object) {
            .offs = cur_end + GGML_OBJECT_SIZE,
            .size = GGML_TENSOR_SIZE,
            .next = NULL,
        };

        //printf("scratch offs = %zu, size_needed = %zu\n", ctx->scratch.offs, size_needed);

        ctx->scratch.offs += size_needed;
    }

    if (obj_cur != NULL) {
        obj_cur->next = obj_new;
    } else {
        // this is the first object in this context
        ctx->objects_begin = obj_new;
    }

    ctx->objects_end = obj_new;

    //printf("%s: inserted new object at %zu, size = %zu\n", __func__, cur_end, obj_new->size);

    struct ggml_tensor * const result = (struct ggml_tensor *)(mem_buffer + obj_new->offs);

    ggml_assert_aligned(result);

    *result = (struct ggml_tensor) {
        /*.type         =*/ type,
        /*.backend      =*/ GGML_BACKEND_CPU,
        /*.n_dims       =*/ n_dims,
        /*.ne           =*/ { 1, 1, 1, 1 },
        /*.nb           =*/ { 0, 0, 0, 0 },
        /*.op           =*/ GGML_OP_NONE,
        /*.is_param     =*/ false,
        /*.grad         =*/ NULL,
        /*.src0         =*/ NULL,
        /*.src1         =*/ NULL,
        /*.opt          =*/ { NULL },
        /*.perf_runs    =*/ 0,
        /*.perf_cycles  =*/ 0,
        /*.perf_time_us =*/ 0,
        /*.data         =*/ (data == NULL && !ctx->no_alloc) ? (void *)(result + 1) : data,
        /*.name         =*/ { 0 },
        /*.extra        =*/ NULL,
        /*.padding      =*/ { 0 },
    };

    // TODO: this should not be needed as long as we don't rely on aligned SIMD loads
    //ggml_assert_aligned(result->data);

    for (int i = 0; i < n_dims; i++) {
        result->ne[i] = ne[i];
    }

    result->nb[0] = GGML_TYPE_SIZE[type];
    result->nb[1] = result->nb[0]*(result->ne[0]/GGML_BLCK_SIZE[type]);
    for (int i = 2; i < GGML_MAX_DIMS; i++) {
        result->nb[i] = result->nb[i - 1]*result->ne[i - 1];
    }

    ctx->n_objects++;

    return result;
}

struct ggml_tensor * ggml_new_tensor(
        struct ggml_context * ctx,
        enum   ggml_type type,
        int    n_dims,
        const int64_t * ne) {
    return ggml_new_tensor_impl(ctx, type, n_dims, ne, NULL);
}

struct ggml_tensor * ggml_new_tensor_1d(
        struct ggml_context * ctx,
        enum   ggml_type type,
        int64_t ne0) {
    return ggml_new_tensor(ctx, type, 1, &ne0);
}

struct ggml_tensor * ggml_new_tensor_2d(
        struct ggml_context * ctx,
        enum   ggml_type type,
        int64_t ne0,
        int64_t ne1) {
    const int64_t ne[2] = { ne0, ne1 };
    return ggml_new_tensor(ctx, type, 2, ne);
}

struct ggml_tensor * ggml_new_tensor_3d(
        struct ggml_context * ctx,
        enum   ggml_type type,
        int64_t ne0,
        int64_t ne1,
        int64_t ne2) {
    const int64_t ne[3] = { ne0, ne1, ne2 };
    return ggml_new_tensor(ctx, type, 3, ne);
}

struct ggml_tensor * ggml_new_tensor_4d(
        struct ggml_context * ctx,
        enum   ggml_type type,
        int64_t ne0,
        int64_t ne1,
        int64_t ne2,
        int64_t ne3) {
    const int64_t ne[4] = { ne0, ne1, ne2, ne3 };
    return ggml_new_tensor(ctx, type, 4, ne);
}

struct ggml_tensor * ggml_new_i32(struct ggml_context * ctx, int32_t value) {
    ggml_scratch_save(ctx);

    struct ggml_tensor * result = ggml_new_tensor_1d(ctx, GGML_TYPE_I32, 1);

    ggml_scratch_load(ctx);

    ggml_set_i32(result, value);

    return result;
}

struct ggml_tensor * ggml_new_f32(struct ggml_context * ctx, float value) {
    ggml_scratch_save(ctx);

    struct ggml_tensor * result = ggml_new_tensor_1d(ctx, GGML_TYPE_F32, 1);

    ggml_scratch_load(ctx);

    ggml_set_f32(result, value);

    return result;
}

struct ggml_tensor * ggml_dup_tensor(struct ggml_context * ctx, const struct ggml_tensor * src) {
    return ggml_new_tensor_impl(ctx, src->type, src->n_dims, src->ne, NULL);
}

struct ggml_tensor * ggml_set_zero(struct ggml_tensor * tensor) {
    memset(tensor->data, 0, ggml_nbytes(tensor));
    return tensor;
}

struct ggml_tensor * ggml_set_i32 (struct ggml_tensor * tensor, int32_t value) {
    const int n     = ggml_nrows(tensor);
    const int nc    = tensor->ne[0];
    const size_t n1 = tensor->nb[1];

    char * const data = tensor->data;

    switch (tensor->type) {
        case GGML_TYPE_I8:
            {
                assert(tensor->nb[0] == sizeof(int8_t));
                for (int i = 0; i < n; i++) {
                    ggml_vec_set_i8(nc, (int8_t *)(data + i*n1), value);
                }
            } break;
        case GGML_TYPE_I16:
            {
                assert(tensor->nb[0] == sizeof(int16_t));
                for (int i = 0; i < n; i++) {
                    ggml_vec_set_i16(nc, (int16_t *)(data + i*n1), value);
                }
            } break;
        case GGML_TYPE_I32:
            {
                assert(tensor->nb[0] == sizeof(int32_t));
                for (int i = 0; i < n; i++) {
                    ggml_vec_set_i32(nc, (int32_t *)(data + i*n1), value);
                }
            } break;
        case GGML_TYPE_F16:
            {
                assert(tensor->nb[0] == sizeof(ggml_fp16_t));
                for (int i = 0; i < n; i++) {
                    ggml_vec_set_f16(nc, (ggml_fp16_t *)(data + i*n1), value);
                }
            } break;
        case GGML_TYPE_F32:
            {
                assert(tensor->nb[0] == sizeof(float));
                for (int i = 0; i < n; i++) {
                    ggml_vec_set_f32(nc, (float *)(data + i*n1), value);
                }
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }

    return tensor;
}

struct ggml_tensor * ggml_set_f32(struct ggml_tensor * tensor, float value) {
    const int n     = ggml_nrows(tensor);
    const int nc    = tensor->ne[0];
    const size_t n1 = tensor->nb[1];

    char * const data = tensor->data;

    switch (tensor->type) {
        case GGML_TYPE_I8:
            {
                assert(tensor->nb[0] == sizeof(int8_t));
                for (int i = 0; i < n; i++) {
                    ggml_vec_set_i8(nc, (int8_t *)(data + i*n1), value);
                }
            } break;
        case GGML_TYPE_I16:
            {
                assert(tensor->nb[0] == sizeof(int16_t));
                for (int i = 0; i < n; i++) {
                    ggml_vec_set_i16(nc, (int16_t *)(data + i*n1), value);
                }
            } break;
        case GGML_TYPE_I32:
            {
                assert(tensor->nb[0] == sizeof(int32_t));
                for (int i = 0; i < n; i++) {
                    ggml_vec_set_i32(nc, (int32_t *)(data + i*n1), value);
                }
            } break;
        case GGML_TYPE_F16:
            {
                assert(tensor->nb[0] == sizeof(ggml_fp16_t));
                for (int i = 0; i < n; i++) {
                    ggml_vec_set_f16(nc, (ggml_fp16_t *)(data + i*n1), value);
                }
            } break;
        case GGML_TYPE_F32:
            {
                assert(tensor->nb[0] == sizeof(float));
                for (int i = 0; i < n; i++) {
                    ggml_vec_set_f32(nc, (float *)(data + i*n1), value);
                }
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }

    return tensor;
}

int32_t ggml_get_i32_1d(const struct ggml_tensor * tensor, int i) {
    switch (tensor->type) {
        case GGML_TYPE_I8:
            {
                GGML_ASSERT(tensor->nb[0] == sizeof(int8_t));
                return ((int8_t *)(tensor->data))[i];
            } break;
        case GGML_TYPE_I16:
            {
                GGML_ASSERT(tensor->nb[0] == sizeof(int16_t));
                return ((int16_t *)(tensor->data))[i];
            } break;
        case GGML_TYPE_I32:
            {
                GGML_ASSERT(tensor->nb[0] == sizeof(int32_t));
                return ((int32_t *)(tensor->data))[i];
            } break;
        case GGML_TYPE_F16:
            {
                GGML_ASSERT(tensor->nb[0] == sizeof(ggml_fp16_t));
                return GGML_FP16_TO_FP32(((ggml_fp16_t *)(tensor->data))[i]);
            } break;
        case GGML_TYPE_F32:
            {
                GGML_ASSERT(tensor->nb[0] == sizeof(float));
                return ((float *)(tensor->data))[i];
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }

    return 0.0f;
}

void ggml_set_i32_1d(const struct ggml_tensor * tensor, int i, int32_t value) {
    switch (tensor->type) {
        case GGML_TYPE_I8:
            {
                GGML_ASSERT(tensor->nb[0] == sizeof(int8_t));
                ((int8_t *)(tensor->data))[i] = value;
            } break;
        case GGML_TYPE_I16:
            {
                GGML_ASSERT(tensor->nb[0] == sizeof(int16_t));
                ((int16_t *)(tensor->data))[i] = value;
            } break;
        case GGML_TYPE_I32:
            {
                GGML_ASSERT(tensor->nb[0] == sizeof(int32_t));
                ((int32_t *)(tensor->data))[i] = value;
            } break;
        case GGML_TYPE_F16:
            {
                GGML_ASSERT(tensor->nb[0] == sizeof(ggml_fp16_t));
                ((ggml_fp16_t *)(tensor->data))[i] = GGML_FP32_TO_FP16(value);
            } break;
        case GGML_TYPE_F32:
            {
                GGML_ASSERT(tensor->nb[0] == sizeof(float));
                ((float *)(tensor->data))[i] = value;
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

float ggml_get_f32_1d(const struct ggml_tensor * tensor, int i) {
    switch (tensor->type) {
        case GGML_TYPE_I8:
            {
                GGML_ASSERT(tensor->nb[0] == sizeof(int8_t));
                return ((int8_t *)(tensor->data))[i];
            } break;
        case GGML_TYPE_I16:
            {
                GGML_ASSERT(tensor->nb[0] == sizeof(int16_t));
                return ((int16_t *)(tensor->data))[i];
            } break;
        case GGML_TYPE_I32:
            {
                GGML_ASSERT(tensor->nb[0] == sizeof(int32_t));
                return ((int32_t *)(tensor->data))[i];
            } break;
        case GGML_TYPE_F16:
            {
                GGML_ASSERT(tensor->nb[0] == sizeof(ggml_fp16_t));
                return GGML_FP16_TO_FP32(((ggml_fp16_t *)(tensor->data))[i]);
            } break;
        case GGML_TYPE_F32:
            {
                GGML_ASSERT(tensor->nb[0] == sizeof(float));
                return ((float *)(tensor->data))[i];
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }

    return 0.0f;
}

void ggml_set_f32_1d(const struct ggml_tensor * tensor, int i, float value) {
    switch (tensor->type) {
        case GGML_TYPE_I8:
            {
                GGML_ASSERT(tensor->nb[0] == sizeof(int8_t));
                ((int8_t *)(tensor->data))[i] = value;
            } break;
        case GGML_TYPE_I16:
            {
                GGML_ASSERT(tensor->nb[0] == sizeof(int16_t));
                ((int16_t *)(tensor->data))[i] = value;
            } break;
        case GGML_TYPE_I32:
            {
                GGML_ASSERT(tensor->nb[0] == sizeof(int32_t));
                ((int32_t *)(tensor->data))[i] = value;
            } break;
        case GGML_TYPE_F16:
            {
                GGML_ASSERT(tensor->nb[0] == sizeof(ggml_fp16_t));
                ((ggml_fp16_t *)(tensor->data))[i] = GGML_FP32_TO_FP16(value);
            } break;
        case GGML_TYPE_F32:
            {
                GGML_ASSERT(tensor->nb[0] == sizeof(float));
                ((float *)(tensor->data))[i] = value;
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

void * ggml_get_data(const struct ggml_tensor * tensor) {
    return tensor->data;
}

float * ggml_get_data_f32(const struct ggml_tensor * tensor) {
    assert(tensor->type == GGML_TYPE_F32);
    return (float *)(tensor->data);
}

const char * ggml_get_name(const struct ggml_tensor * tensor) {
    return tensor->name;
}

struct ggml_tensor * ggml_set_name(struct ggml_tensor * tensor, const char * name) {
    strncpy(tensor->name, name, sizeof(tensor->name));
    tensor->name[sizeof(tensor->name) - 1] = '\0';
    return tensor;
}

struct ggml_tensor * ggml_format_name(struct ggml_tensor * tensor, const char * fmt, ...) {
    va_list args;
    va_start(args, fmt);
    vsnprintf(tensor->name, sizeof(tensor->name), fmt, args);
    va_end(args);
    return tensor;
}

struct ggml_tensor * ggml_view_tensor(
        struct ggml_context * ctx,
        const struct ggml_tensor * src) {
    struct ggml_tensor * result = ggml_new_tensor_impl(ctx, src->type, src->n_dims, src->ne, src->data);
    ggml_format_name(result, "%s (view)", src->name);

    result->nb[0] = src->nb[0];
    result->nb[1] = src->nb[1];
    result->nb[2] = src->nb[2];
    result->nb[3] = src->nb[3];

    return result;
}

struct ggml_tensor * ggml_get_tensor(struct ggml_context * ctx, const char * name) {
    struct ggml_object * obj = ctx->objects_begin;

    char * const mem_buffer = ctx->mem_buffer;

    while (obj != NULL) {
        struct ggml_tensor * cur = (struct ggml_tensor *)(mem_buffer + obj->offs);
        if (strcmp(cur->name, name) == 0) {
            return cur;
        }

        obj = obj->next;
    }

    return NULL;
}

////////////////////////////////////////////////////////////////////////////////

// ggml_dup

struct ggml_tensor * ggml_dup_impl(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        bool inplace) {
    bool is_node = false;

    if (!inplace && (a->grad)) {
        is_node = true;
    }

    struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);

    result->op   = GGML_OP_DUP;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;

    return result;
}

struct ggml_tensor * ggml_dup(
        struct ggml_context * ctx,
        struct ggml_tensor * a) {
    return ggml_dup_impl(ctx, a, false);
}

struct ggml_tensor * ggml_dup_inplace(
        struct ggml_context * ctx,
        struct ggml_tensor * a) {
    return ggml_dup_impl(ctx, a, true);
}

// ggml_add

struct ggml_tensor * ggml_add_impl(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        struct ggml_tensor * b,
        bool inplace) {
    GGML_ASSERT(ggml_are_same_shape(a, b));

    bool is_node = false;

    if (a->grad || b->grad) {
        is_node = true;
    }

    struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);

    result->op   = GGML_OP_ADD;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = b;

    return result;
}

struct ggml_tensor * ggml_add(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        struct ggml_tensor * b) {
    return ggml_add_impl(ctx, a, b, false);
}

struct ggml_tensor * ggml_add_inplace(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        struct ggml_tensor * b) {
    return ggml_add_impl(ctx, a, b, true);
}

// ggml_add1

struct ggml_tensor * ggml_add1_impl(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        struct ggml_tensor * b,
        bool inplace) {
    GGML_ASSERT(ggml_is_scalar(b));
    GGML_ASSERT(ggml_is_padded_1d(a));

    bool is_node = false;

    if (a->grad || b->grad) {
        is_node = true;
    }

    struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);

    result->op   = GGML_OP_ADD1;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = b;

    return result;
}

struct ggml_tensor * ggml_add1(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        struct ggml_tensor * b) {
    return ggml_add1_impl(ctx, a, b, false);
}

struct ggml_tensor * ggml_add1_inplace(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        struct ggml_tensor * b) {
    return ggml_add1_impl(ctx, a, b, true);
}

// ggml_acc

struct ggml_tensor * ggml_acc_impl(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        struct ggml_tensor * b,
        size_t               nb1,
        size_t               nb2,
        size_t               nb3,
        size_t               offset,
        bool inplace) {
    GGML_ASSERT(ggml_nelements(b) <= ggml_nelements(a));
    GGML_ASSERT(ggml_is_contiguous(a));
    GGML_ASSERT(a->type == GGML_TYPE_F32);
    GGML_ASSERT(b->type == GGML_TYPE_F32);

    bool is_node = false;

    if (!inplace && (a->grad || b->grad)) {
        is_node = true;
    }

    struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);

    ggml_scratch_save(ctx);

    struct ggml_tensor * c = ggml_new_tensor_1d(ctx, GGML_TYPE_I32, 5);

    ((int32_t *) c->data)[0] = nb1;
    ((int32_t *) c->data)[1] = nb2;
    ((int32_t *) c->data)[2] = nb3;
    ((int32_t *) c->data)[3] = offset;
    ((int32_t *) c->data)[4] = inplace ? 1 : 0;

    ggml_scratch_load(ctx);

    result->op   = GGML_OP_ACC;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = b;
    result->opt[0] = c;

    return result;
}

struct ggml_tensor * ggml_acc(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        struct ggml_tensor * b,
        size_t               nb1,
        size_t               nb2,
        size_t               nb3,
        size_t               offset) {
    return ggml_acc_impl(ctx, a, b, nb1, nb2, nb3, offset, false);
}

struct ggml_tensor * ggml_acc_inplace(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        struct ggml_tensor * b,
        size_t               nb1,
        size_t               nb2,
        size_t               nb3,
        size_t               offset) {
    return ggml_acc_impl(ctx, a, b, nb1, nb2, nb3, offset, true);
}

// ggml_sub

struct ggml_tensor * ggml_sub_impl(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        struct ggml_tensor * b,
        bool inplace) {
    GGML_ASSERT(ggml_are_same_shape(a, b));

    bool is_node = false;

    if (!inplace && (a->grad || b->grad)) {
        is_node = true;
    }

    struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);

    result->op   = GGML_OP_SUB;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = b;

    return result;
}

struct ggml_tensor * ggml_sub(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        struct ggml_tensor * b) {
    return ggml_sub_impl(ctx, a, b, false);
}

struct ggml_tensor * ggml_sub_inplace(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        struct ggml_tensor * b) {
    return ggml_sub_impl(ctx, a, b, true);
}

// ggml_mul

struct ggml_tensor * ggml_mul_impl(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        struct ggml_tensor * b,
        bool inplace) {
    // TODO: support less-strict constraint
    //       GGML_ASSERT(ggml_can_repeat(b, a));
    GGML_ASSERT(ggml_can_repeat_rows(b, a));

    bool is_node = false;

    if (!inplace && (a->grad || b->grad)) {
        // TODO: support backward pass for broadcasting
        GGML_ASSERT(ggml_are_same_shape(a, b));
        is_node = true;
    }

    if (inplace) {
        GGML_ASSERT(is_node == false);
    }

    struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);

    result->op   = GGML_OP_MUL;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = b;

    return result;
}

struct ggml_tensor * ggml_mul(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        struct ggml_tensor  * b) {
    return ggml_mul_impl(ctx, a, b, false);
}

struct ggml_tensor * ggml_mul_inplace(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        struct ggml_tensor  * b) {
    return ggml_mul_impl(ctx, a, b, true);
}

// ggml_div

struct ggml_tensor * ggml_div_impl(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        struct ggml_tensor * b,
        bool inplace) {
    GGML_ASSERT(ggml_are_same_shape(a, b));

    bool is_node = false;

    if (!inplace && (a->grad || b->grad)) {
        is_node = true;
    }

    if (inplace) {
        GGML_ASSERT(is_node == false);
    }

    struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);

    result->op   = GGML_OP_DIV;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = b;

    return result;
}

struct ggml_tensor * ggml_div(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        struct ggml_tensor  * b) {
    return ggml_div_impl(ctx, a, b, false);
}

struct ggml_tensor * ggml_div_inplace(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        struct ggml_tensor  * b) {
    return ggml_div_impl(ctx, a, b, true);
}

// ggml_sqr

struct ggml_tensor * ggml_sqr_impl(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        bool inplace) {
    bool is_node = false;

    if (!inplace && (a->grad)) {
        is_node = true;
    }

    struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);

    result->op   = GGML_OP_SQR;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;

    return result;
}

struct ggml_tensor * ggml_sqr(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    return ggml_sqr_impl(ctx, a, false);
}

struct ggml_tensor * ggml_sqr_inplace(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    return ggml_sqr_impl(ctx, a, true);
}

// ggml_sqrt

struct ggml_tensor * ggml_sqrt_impl(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        bool inplace) {
    bool is_node = false;

    if (!inplace && (a->grad)) {
        is_node = true;
    }

    struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);

    result->op   = GGML_OP_SQRT;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;

    return result;
}

struct ggml_tensor * ggml_sqrt(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    return ggml_sqrt_impl(ctx, a, false);
}

struct ggml_tensor * ggml_sqrt_inplace(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    return ggml_sqrt_impl(ctx, a, true);
}


// ggml_log

struct ggml_tensor * ggml_log_impl(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        bool inplace) {
    bool is_node = false;

    if (!inplace && (a->grad)) {
        is_node = true;
    }

    struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);

    result->op   = GGML_OP_LOG;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;

    return result;
}

struct ggml_tensor * ggml_log(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    return ggml_log_impl(ctx, a, false);
}

struct ggml_tensor * ggml_log_inplace(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    return ggml_log_impl(ctx, a, true);
}

// ggml_sum

struct ggml_tensor * ggml_sum(
        struct ggml_context * ctx,
        struct ggml_tensor * a) {
    bool is_node = false;

    if (a->grad) {
        is_node = true;
    }

    struct ggml_tensor * result = ggml_new_tensor_1d(ctx, a->type, 1);

    result->op   = GGML_OP_SUM;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;

    return result;
}


// ggml_sum_rows

struct ggml_tensor * ggml_sum_rows(
        struct ggml_context * ctx,
        struct ggml_tensor * a) {
    bool is_node = false;

    if (a->grad) {
        is_node = true;
    }

    int64_t ne[4] = {1,1,1,1};
    for (int i=1; i<a->n_dims; ++i) {
        ne[i] = a->ne[i];
    }

    struct ggml_tensor * result = ggml_new_tensor(ctx, a->type, a->n_dims, ne);

    result->op   = GGML_OP_SUM_ROWS;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;

    return result;
}

// ggml_mean

struct ggml_tensor * ggml_mean(
        struct ggml_context * ctx,
        struct ggml_tensor * a) {
    bool is_node = false;

    if (a->grad) {
        GGML_ASSERT(false); // TODO: implement
        is_node = true;
    }

    int64_t ne[GGML_MAX_DIMS] = { 1, a->ne[1], a->ne[2], a->ne[3] };
    struct ggml_tensor * result = ggml_new_tensor(ctx, GGML_TYPE_F32, a->n_dims, ne);

    result->op   = GGML_OP_MEAN;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;

    return result;
}

// ggml_argmax

struct ggml_tensor * ggml_argmax(
        struct ggml_context * ctx,
        struct ggml_tensor * a) {
    GGML_ASSERT(ggml_is_matrix(a));
    bool is_node = false;

    if (a->grad) {
        GGML_ASSERT(false);
        is_node = true;
    }

    int64_t ne[GGML_MAX_DIMS] = { a->ne[1], 1, 1, 1 };
    struct ggml_tensor * result = ggml_new_tensor(ctx, GGML_TYPE_I32, a->n_dims, ne);

    result->op   = GGML_OP_ARGMAX;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;

    return result;
}

// ggml_repeat

struct ggml_tensor * ggml_repeat(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        struct ggml_tensor * b) {
    GGML_ASSERT(ggml_can_repeat(a, b));

    bool is_node = false;

    if (a->grad) {
        is_node = true;
    }

    if (ggml_are_same_shape(a, b) && !is_node) {
        return a;
    }

    struct ggml_tensor * result = ggml_new_tensor(ctx, a->type, b->n_dims, b->ne);

    result->op   = GGML_OP_REPEAT;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = b;

    return result;
}

// ggml_repeat_back

struct ggml_tensor * ggml_repeat_back(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        struct ggml_tensor * b) {
    GGML_ASSERT(ggml_can_repeat(b, a));

    bool is_node = false;

    if (a->grad) {
        is_node = true;
    }

    if (ggml_are_same_shape(a, b) && !is_node) {
        return a;
    }

    struct ggml_tensor * result = ggml_new_tensor(ctx, a->type, b->n_dims, b->ne);

    result->op   = GGML_OP_REPEAT_BACK;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = b;

    return result;
}

// ggml_abs

struct ggml_tensor * ggml_abs_impl(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        bool inplace) {
    bool is_node = false;

    if (!inplace && (a->grad)) {
        is_node = true;
    }

    struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);

    result->op   = GGML_OP_ABS;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;

    return result;
}

struct ggml_tensor * ggml_abs(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    return ggml_abs_impl(ctx, a, false);
}

struct ggml_tensor * ggml_abs_inplace(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    return ggml_abs_impl(ctx, a, true);
}


// ggml_sgn

struct ggml_tensor * ggml_sgn_impl(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        bool inplace) {
    bool is_node = false;

    if (!inplace && (a->grad)) {
        is_node = true;
    }

    struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);

    result->op   = GGML_OP_SGN;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;

    return result;
}

struct ggml_tensor * ggml_sgn(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    return ggml_sgn_impl(ctx, a, false);
}

struct ggml_tensor * ggml_sgn_inplace(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    return ggml_sgn_impl(ctx, a, true);
}

// ggml_neg

struct ggml_tensor * ggml_neg_impl(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        bool inplace) {
    bool is_node = false;

    if (!inplace && (a->grad)) {
        is_node = true;
    }

    struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);

    result->op   = GGML_OP_NEG;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;

    return result;
}

struct ggml_tensor * ggml_neg(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    return ggml_neg_impl(ctx, a, false);
}

struct ggml_tensor * ggml_neg_inplace(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    return ggml_neg_impl(ctx, a, true);
}

// ggml_step

struct ggml_tensor * ggml_step_impl(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        bool inplace) {
    bool is_node = false;

    if (!inplace && (a->grad)) {
        is_node = true;
    }

    struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);

    result->op   = GGML_OP_STEP;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;

    return result;
}

struct ggml_tensor * ggml_step(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    return ggml_step_impl(ctx, a, false);
}

struct ggml_tensor * ggml_step_inplace(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    return ggml_step_impl(ctx, a, true);
}

// ggml_tanh

struct ggml_tensor * ggml_tanh_impl(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        bool inplace) {
    bool is_node = false;

    if (!inplace && (a->grad)) {
        is_node = true;
    }

    struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);

    result->op   = GGML_OP_TANH;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;

    return result;
}

struct ggml_tensor * ggml_tanh(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    return ggml_tanh_impl(ctx, a, false);
}

struct ggml_tensor * ggml_tanh_inplace(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    return ggml_tanh_impl(ctx, a, true);
}

// ggml_elu

struct ggml_tensor * ggml_elu_impl(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        bool inplace) {
    bool is_node = false;

    if (!inplace && (a->grad)) {
        is_node = true;
    }

    struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);

    result->op   = GGML_OP_ELU;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;

    return result;
}

struct ggml_tensor * ggml_elu(
    struct ggml_context * ctx,
    struct ggml_tensor  * a) {
    return ggml_elu_impl(ctx, a, false);
}

struct ggml_tensor * ggml_elu_inplace(
    struct ggml_context * ctx,
    struct ggml_tensor  * a) {
    return ggml_elu_impl(ctx, a, true);
}

// ggml_relu

struct ggml_tensor * ggml_relu_impl(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        bool inplace) {
    bool is_node = false;

    if (!inplace && (a->grad)) {
        is_node = true;
    }

    struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);

    result->op   = GGML_OP_RELU;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;

    return result;
}

struct ggml_tensor * ggml_relu(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    return ggml_relu_impl(ctx, a, false);
}

struct ggml_tensor * ggml_relu_inplace(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    return ggml_relu_impl(ctx, a, true);
}

// ggml_gelu

struct ggml_tensor * ggml_gelu_impl(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        bool inplace) {
    bool is_node = false;

    if (!inplace && (a->grad)) {
        is_node = true;
    }

    struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);

    result->op   = GGML_OP_GELU;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;

    return result;
}

struct ggml_tensor * ggml_gelu(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    return ggml_gelu_impl(ctx, a, false);
}

struct ggml_tensor * ggml_gelu_inplace(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    return ggml_gelu_impl(ctx, a, true);
}

// ggml_gelu_quick

struct ggml_tensor * ggml_gelu_quick_impl(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        bool inplace) {
    bool is_node = false;

    if (!inplace && (a->grad)) {
        is_node = true;
    }

    struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);

    result->op   = GGML_OP_GELU_QUICK;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;

    return result;
}

struct ggml_tensor * ggml_gelu_quick(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    return ggml_gelu_quick_impl(ctx, a, false);
}

struct ggml_tensor * ggml_gelu_quick_inplace(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    return ggml_gelu_quick_impl(ctx, a, true);
}

// ggml_silu

struct ggml_tensor * ggml_silu_impl(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        bool inplace) {
    bool is_node = false;

    if (!inplace && (a->grad)) {
        is_node = true;
    }

    struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);

    result->op   = GGML_OP_SILU;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;

    return result;
}

struct ggml_tensor * ggml_silu(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    return ggml_silu_impl(ctx, a, false);
}

struct ggml_tensor * ggml_silu_inplace(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    return ggml_silu_impl(ctx, a, true);
}

// ggml_silu_back

struct ggml_tensor * ggml_silu_back(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        struct ggml_tensor  * b) {
    bool is_node = false;

    if (a->grad || b->grad) {
        // TODO: implement backward
        is_node = true;
    }

    struct ggml_tensor * result = ggml_dup_tensor(ctx, a);

    result->op   = GGML_OP_SILU_BACK;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = b;

    return result;
}

// ggml_norm

struct ggml_tensor * ggml_norm_impl(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        bool inplace) {
    bool is_node = false;

    if (!inplace && (a->grad)) {
        GGML_ASSERT(false); // TODO: implement backward
        is_node = true;
    }

    struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);

    result->op   = GGML_OP_NORM;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL; // TODO: maybe store epsilon here?

    return result;
}

struct ggml_tensor * ggml_norm(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    return ggml_norm_impl(ctx, a, false);
}

struct ggml_tensor * ggml_norm_inplace(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    return ggml_norm_impl(ctx, a, true);
}

struct ggml_tensor * ggml_rms_norm_impl(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        bool inplace) {
    bool is_node = false;

    if (!inplace && (a->grad)) {
        is_node = true;
    }

    struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);

    result->op   = GGML_OP_RMS_NORM;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL; // TODO: maybe store epsilon here?

    return result;
}

struct ggml_tensor * ggml_rms_norm(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    return ggml_rms_norm_impl(ctx, a, false);
}

struct ggml_tensor * ggml_rms_norm_inplace(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    return ggml_rms_norm_impl(ctx, a, true);
}

struct ggml_tensor * ggml_rms_norm_back(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        struct ggml_tensor  * b) {
    bool is_node = false;

    if (a->grad) {
        // TODO: implement backward
        is_node = true;
    }

    struct ggml_tensor * result = ggml_dup_tensor(ctx, a);

    result->op   = GGML_OP_RMS_NORM_BACK;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = b;

    return result;
}


// ggml_mul_mat

struct ggml_tensor * ggml_mul_mat(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        struct ggml_tensor  * b) {
    GGML_ASSERT(ggml_can_mul_mat(a, b));
    GGML_ASSERT(!ggml_is_transposed(a));

    bool is_node = false;

    if (a->grad || b->grad) {
        is_node = true;
    }

    const int64_t ne[4] = { a->ne[1], b->ne[1], a->ne[2], b->ne[3] };
    struct ggml_tensor * result = ggml_new_tensor(ctx, GGML_TYPE_F32, MIN(a->n_dims, b->n_dims), ne);

    result->op   = GGML_OP_MUL_MAT;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = b;

    return result;
}

// ggml_out_prod

struct ggml_tensor * ggml_out_prod(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        struct ggml_tensor  * b) {
    GGML_ASSERT(ggml_can_out_prod(a, b));
    GGML_ASSERT(!ggml_is_transposed(a));

    bool is_node = false;

    if (a->grad || b->grad) {
        is_node = true;
    }

    const int64_t ne[4] = { a->ne[0], b->ne[0], a->ne[2], b->ne[3] };
    struct ggml_tensor * result = ggml_new_tensor(ctx, GGML_TYPE_F32, MIN(a->n_dims, b->n_dims), ne);

    result->op   = GGML_OP_OUT_PROD;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = b;

    return result;
}

// ggml_scale

struct ggml_tensor * ggml_scale_impl(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        struct ggml_tensor  * b,
        bool inplace) {
    GGML_ASSERT(ggml_is_scalar(b));
    GGML_ASSERT(ggml_is_padded_1d(a));

    bool is_node = false;

    if (a->grad || b->grad) {
        is_node = true;
    }

    struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);

    result->op   = GGML_OP_SCALE;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = b;

    return result;
}

struct ggml_tensor * ggml_scale(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        struct ggml_tensor * b) {
    return ggml_scale_impl(ctx, a, b, false);
}

struct ggml_tensor * ggml_scale_inplace(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        struct ggml_tensor * b) {
    return ggml_scale_impl(ctx, a, b, true);
}

// ggml_set

struct ggml_tensor * ggml_set_impl(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        struct ggml_tensor  * b,
        size_t                nb1,
        size_t                nb2,
        size_t                nb3,
        size_t                offset,
        bool inplace) {
    GGML_ASSERT(ggml_nelements(a) >= ggml_nelements(b));

    bool is_node = false;

    if (a->grad || b->grad) {
        is_node = true;
    }

    // make a view of the destination
    struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);

    ggml_scratch_save(ctx);

    struct ggml_tensor * c = ggml_new_tensor_1d(ctx, GGML_TYPE_I32, 5);

    (( int32_t * ) c->data)[0] = nb1;
    (( int32_t * ) c->data)[1] = nb2;
    (( int32_t * ) c->data)[2] = nb3;
    (( int32_t * ) c->data)[3] = offset;
    (( int32_t * ) c->data)[4] = inplace ? 1 : 0;

    ggml_scratch_load(ctx);

    result->op   = GGML_OP_SET;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = b;
    result->opt[0] = c;

    return result;
}

struct ggml_tensor * ggml_set(
        struct ggml_context * ctx,
        struct ggml_tensor *  a,
        struct ggml_tensor *  b,
        size_t                nb1,
        size_t                nb2,
        size_t                nb3,
        size_t                offset) {
    return ggml_set_impl(ctx, a, b, nb1, nb2, nb3, offset, false);
}

struct ggml_tensor * ggml_set_inplace(
        struct ggml_context * ctx,
        struct ggml_tensor *  a,
        struct ggml_tensor *  b,
        size_t                nb1,
        size_t                nb2,
        size_t                nb3,
        size_t                offset) {
    return ggml_set_impl(ctx, a, b, nb1, nb2, nb3, offset, true);
}

struct ggml_tensor * ggml_set_1d(
        struct ggml_context * ctx,
        struct ggml_tensor *  a,
        struct ggml_tensor *  b,
        size_t                offset) {
    return ggml_set_impl(ctx, a, b, a->nb[1], a->nb[2], a->nb[3], offset, false);
}

struct ggml_tensor * ggml_set_1d_inplace(
        struct ggml_context * ctx,
        struct ggml_tensor *  a,
        struct ggml_tensor *  b,
        size_t                offset) {
    return ggml_set_impl(ctx, a, b, a->nb[1], a->nb[2], a->nb[3], offset, true);
}

struct ggml_tensor * ggml_set_2d(
        struct ggml_context * ctx,
        struct ggml_tensor *  a,
        struct ggml_tensor *  b,
        size_t                nb1,
        size_t                offset) {
    return ggml_set_impl(ctx, a, b, nb1, a->nb[2], a->nb[3], offset, false);
}

struct ggml_tensor * ggml_set_2d_inplace(
        struct ggml_context * ctx,
        struct ggml_tensor *  a,
        struct ggml_tensor *  b,
        size_t                nb1,
        size_t                offset) {
    return ggml_set_impl(ctx, a, b, nb1, a->nb[2], a->nb[3], offset, false);
}


// ggml_cpy

struct ggml_tensor * ggml_cpy_impl(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        struct ggml_tensor  * b,
        bool inplace) {
    GGML_ASSERT(ggml_nelements(a) == ggml_nelements(b));

    bool is_node = false;

    if (!inplace && (a->grad || b->grad)) {
        is_node = true;
    }

    // make a view of the destination
    struct ggml_tensor * result = ggml_view_tensor(ctx, b);
    if (strlen(b->name) > 0) {
        ggml_format_name(result, "%s (copy of %s)", b->name, a->name);
    } else {
        ggml_format_name(result, "%s (copy)", a->name);
    }

    result->op   = GGML_OP_CPY;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = b;

    return result;
}

struct ggml_tensor * ggml_cpy(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        struct ggml_tensor * b) {
    return ggml_cpy_impl(ctx, a, b, false);
}

struct ggml_tensor * ggml_cpy_inplace(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        struct ggml_tensor * b) {
    return ggml_cpy_impl(ctx, a, b, true);
}

// ggml_cont

struct ggml_tensor * ggml_cont_impl(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        bool inplace) {
    bool is_node = false;

    if (!inplace && a->grad) {
        is_node = true;
    }

    struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);
    ggml_format_name(result, "%s (cont)", a->name);

    result->op   = GGML_OP_CONT;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;

    return result;
}

struct ggml_tensor * ggml_cont(
        struct ggml_context * ctx,
        struct ggml_tensor * a) {
    return ggml_cont_impl(ctx, a, false);
}

struct ggml_tensor * ggml_cont_inplace(
        struct ggml_context * ctx,
        struct ggml_tensor * a) {
    return ggml_cont_impl(ctx, a, true);
}

// ggml_reshape

struct ggml_tensor * ggml_reshape(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        struct ggml_tensor * b) {
    GGML_ASSERT(ggml_is_contiguous(a));
    GGML_ASSERT(ggml_is_contiguous(b));
    GGML_ASSERT(ggml_nelements(a) == ggml_nelements(b));

    bool is_node = false;

    if (a->grad) {
        is_node = true;
    }

    if (b->grad) {
        // gradient propagation is not supported
        //GGML_ASSERT(false);
    }

    struct ggml_tensor * result = ggml_new_tensor_impl(ctx, a->type, b->n_dims, b->ne, a->data);
    ggml_format_name(result, "%s (reshaped)", a->name);

    result->op   = GGML_OP_RESHAPE;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;

    return result;
}

struct ggml_tensor * ggml_reshape_1d(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        int64_t               ne0) {
    GGML_ASSERT(ggml_is_contiguous(a));
    GGML_ASSERT(ggml_nelements(a) == ne0);

    bool is_node = false;

    if (a->grad) {
        is_node = true;
    }

    const int64_t ne[1] = { ne0 };
    struct ggml_tensor * result = ggml_new_tensor_impl(ctx, a->type, 1, ne, a->data);
    ggml_format_name(result, "%s (reshaped)", a->name);

    result->op   = GGML_OP_RESHAPE;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;

    return result;
}

struct ggml_tensor * ggml_reshape_2d(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        int64_t               ne0,
        int64_t               ne1) {
    GGML_ASSERT(ggml_is_contiguous(a));
    GGML_ASSERT(ggml_nelements(a) == ne0*ne1);

    bool is_node = false;

    if (a->grad) {
        is_node = true;
    }

    const int64_t ne[2] = { ne0, ne1 };
    struct ggml_tensor * result = ggml_new_tensor_impl(ctx, a->type, 2, ne, a->data);
    ggml_format_name(result, "%s (reshaped)", a->name);

    result->op   = GGML_OP_RESHAPE;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;

    return result;
}

struct ggml_tensor * ggml_reshape_3d(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        int64_t               ne0,
        int64_t               ne1,
        int64_t               ne2) {
    GGML_ASSERT(ggml_is_contiguous(a));
    GGML_ASSERT(ggml_nelements(a) == ne0*ne1*ne2);

    bool is_node = false;

    if (a->grad) {
        is_node = true;
    }

    const int64_t ne[3] = { ne0, ne1, ne2 };
    struct ggml_tensor * result = ggml_new_tensor_impl(ctx, a->type, 3, ne, a->data);
    ggml_format_name(result, "%s (reshaped)", a->name);

    result->op   = GGML_OP_RESHAPE;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;

    return result;
}


struct ggml_tensor * ggml_reshape_4d(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        int64_t               ne0,
        int64_t               ne1,
        int64_t               ne2,
        int64_t               ne3) {
    GGML_ASSERT(ggml_is_contiguous(a));
    GGML_ASSERT(ggml_nelements(a) == ne0*ne1*ne2*ne3);

    bool is_node = false;

    if (a->grad) {
        is_node = true;
    }

    const int64_t ne[4] = { ne0, ne1, ne2, ne3 };
    struct ggml_tensor * result = ggml_new_tensor_impl(ctx, a->type, 4, ne, a->data);
    ggml_format_name(result, "%s (reshaped)", a->name);

    result->op   = GGML_OP_RESHAPE;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;

    return result;
}

// ggml_view_1d

struct ggml_tensor * ggml_view_1d(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        int64_t               ne0,
        size_t                offset) {

    bool is_node = false;

    if (a->grad) {
        is_node = true;
    }

    struct ggml_tensor * result = ggml_new_tensor_impl(ctx, a->type, 1, &ne0, (char *) a->data + offset);
    ggml_format_name(result, "%s (view)", a->name);

    ggml_scratch_save(ctx);

    struct ggml_tensor * offs = ggml_new_tensor_1d(ctx, GGML_TYPE_I32, 2);
    ggml_set_name(offs, "offset");
    memcpy(offs->data, &offset, 2*sizeof(int32_t));

    ggml_scratch_load(ctx);

    result->op   = GGML_OP_VIEW;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;
    result->opt[0] = offs;

    return result;
}

// ggml_view_2d

struct ggml_tensor * ggml_view_2d(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        int64_t               ne0,
        int64_t               ne1,
        size_t                nb1,
        size_t                offset) {

    bool is_node = false;

    if (a->grad) {
        is_node = true;
    }

    const int64_t ne[GGML_MAX_DIMS] = { ne0, ne1, 1, 1 };

    struct ggml_tensor * result = ggml_new_tensor_impl(ctx, a->type, 2, ne, (char *) a->data + offset);
    ggml_format_name(result, "%s (view)", a->name);

    ggml_scratch_save(ctx);

    struct ggml_tensor * offs = ggml_new_tensor_1d(ctx, GGML_TYPE_I32, 2);
    ggml_set_name(offs, "offset");
    memcpy(offs->data, &offset, 2*sizeof(int32_t));

    ggml_scratch_load(ctx);

    result->nb[1] = nb1;
    result->nb[2] = result->nb[1]*ne1;
    result->nb[3] = result->nb[2];

    result->op   = GGML_OP_VIEW;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;
    result->opt[0] = offs;

    return result;
}

// ggml_view_3d

struct ggml_tensor * ggml_view_3d(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        int64_t               ne0,
        int64_t               ne1,
        int64_t               ne2,
        size_t                nb1,
        size_t                nb2,
        size_t                offset) {

    bool is_node = false;

    if (a->grad) {
        is_node = true;
    }

    const int64_t ne[GGML_MAX_DIMS] = { ne0, ne1, ne2, 1 };

    struct ggml_tensor * result = ggml_new_tensor_impl(ctx, a->type, 3, ne, (char *) a->data + offset);
    ggml_format_name(result, "%s (view)", a->name);

    ggml_scratch_save(ctx);

    struct ggml_tensor * offs = ggml_new_tensor_1d(ctx, GGML_TYPE_I32, 2);
    ggml_set_name(offs, "offset");
    memcpy(offs->data, &offset, 2*sizeof(int32_t));

    ggml_scratch_load(ctx);

    result->nb[1] = nb1;
    result->nb[2] = nb2;
    result->nb[3] = result->nb[2]*ne2;

    result->op   = GGML_OP_VIEW;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;
    result->opt[0] = offs;

    return result;
}

// ggml_view_4d

struct ggml_tensor * ggml_view_4d(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        int64_t               ne0,
        int64_t               ne1,
        int64_t               ne2,
        int64_t               ne3,
        size_t                nb1,
        size_t                nb2,
        size_t                nb3,
        size_t                offset) {

    bool is_node = false;

    if (a->grad) {
        is_node = true;
    }

    const int64_t ne[GGML_MAX_DIMS] = { ne0, ne1, ne2, ne3 };

    struct ggml_tensor * result = ggml_new_tensor_impl(ctx, a->type, 4, ne, (char *) a->data + offset);
    ggml_format_name(result, "%s (view)", a->name);

    ggml_scratch_save(ctx);

    struct ggml_tensor * offs = ggml_new_tensor_1d(ctx, GGML_TYPE_I32, 2);
    ggml_set_name(offs, "offset");
    memcpy(offs->data, &offset, 2*sizeof(int32_t));

    ggml_scratch_load(ctx);

    result->nb[1] = nb1;
    result->nb[2] = nb2;
    result->nb[3] = nb3;

    result->op   = GGML_OP_VIEW;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;
    result->opt[0] = offs;

    return result;
}

// ggml_permute

struct ggml_tensor * ggml_permute(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        int                   axis0,
        int                   axis1,
        int                   axis2,
        int                   axis3) {
    GGML_ASSERT(axis0 >= 0 && axis0 < GGML_MAX_DIMS);
    GGML_ASSERT(axis1 >= 0 && axis1 < GGML_MAX_DIMS);
    GGML_ASSERT(axis2 >= 0 && axis2 < GGML_MAX_DIMS);
    GGML_ASSERT(axis3 >= 0 && axis3 < GGML_MAX_DIMS);

    GGML_ASSERT(axis0 != axis1);
    GGML_ASSERT(axis0 != axis2);
    GGML_ASSERT(axis0 != axis3);
    GGML_ASSERT(axis1 != axis2);
    GGML_ASSERT(axis1 != axis3);
    GGML_ASSERT(axis2 != axis3);

    bool is_node = false;

    if (a->grad) {
        is_node = true;
    }

    struct ggml_tensor * result = ggml_view_tensor(ctx, a);
    ggml_format_name(result, "%s (permuted)", a->name);

    int ne[GGML_MAX_DIMS];
    int nb[GGML_MAX_DIMS];

    ne[axis0] = a->ne[0];
    ne[axis1] = a->ne[1];
    ne[axis2] = a->ne[2];
    ne[axis3] = a->ne[3];

    nb[axis0] = a->nb[0];
    nb[axis1] = a->nb[1];
    nb[axis2] = a->nb[2];
    nb[axis3] = a->nb[3];

    result->ne[0] = ne[0];
    result->ne[1] = ne[1];
    result->ne[2] = ne[2];
    result->ne[3] = ne[3];

    result->nb[0] = nb[0];
    result->nb[1] = nb[1];
    result->nb[2] = nb[2];
    result->nb[3] = nb[3];

    result->op   = GGML_OP_PERMUTE;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;

    if (is_node) {
        ggml_scratch_save(ctx);

        struct ggml_tensor * b = ggml_new_tensor_1d(ctx, GGML_TYPE_I32, 4);

        ((int32_t *) b->data)[0] = axis0;
        ((int32_t *) b->data)[1] = axis1;
        ((int32_t *) b->data)[2] = axis2;
        ((int32_t *) b->data)[3] = axis3;

        ggml_scratch_load(ctx);

        result->opt[0] = b;
    }

    return result;
}

// ggml_transpose

struct ggml_tensor * ggml_transpose(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    bool is_node = false;

    if (a->grad) {
        is_node = true;
    }

    struct ggml_tensor * result = ggml_view_tensor(ctx, a);
    ggml_format_name(result, "%s (transposed)", a->name);

    result->ne[0] = a->ne[1];
    result->ne[1] = a->ne[0];

    result->nb[0] = a->nb[1];
    result->nb[1] = a->nb[0];

    result->op   = GGML_OP_TRANSPOSE;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;

    return result;
}

// ggml_get_rows

struct ggml_tensor * ggml_get_rows(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        struct ggml_tensor  * b) {
    GGML_ASSERT(ggml_is_matrix(a) && ggml_is_vector(b) && b->type == GGML_TYPE_I32);

    bool is_node = false;

    if (a->grad || b->grad) {
        is_node = true;
    }

    // TODO: implement non F32 return
    //struct ggml_tensor * result = ggml_new_tensor_2d(ctx, a->type, a->ne[0], b->ne[0]);
    struct ggml_tensor * result = ggml_new_tensor_2d(ctx, GGML_TYPE_F32, a->ne[0], b->ne[0]);

    result->op   = GGML_OP_GET_ROWS;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = b;

    return result;
}

// ggml_get_rows_back

struct ggml_tensor * ggml_get_rows_back(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        struct ggml_tensor  * b,
        struct ggml_tensor  * c) {
    GGML_ASSERT(ggml_is_matrix(a) && ggml_is_vector(b) && b->type == GGML_TYPE_I32);
    GGML_ASSERT(ggml_is_matrix(c) && (a->ne[0] == c->ne[0]));

    bool is_node = false;

    if (a->grad || b->grad) {
        is_node = true;
    }

    // TODO: implement non F32 return
    //struct ggml_tensor * result = ggml_new_tensor_2d(ctx, a->type, a->ne[0], b->ne[0]);
    struct ggml_tensor * result = ggml_new_tensor_2d(ctx, GGML_TYPE_F32, c->ne[0], c->ne[1]);

    result->op   = GGML_OP_GET_ROWS_BACK;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = b;
    result->opt[0] = c;

    return result;
}

// ggml_diag

struct ggml_tensor * ggml_diag(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    GGML_ASSERT(a->ne[1] == 1);
    bool is_node = false;

    if (a->grad) {
        is_node = true;
    }

    const int64_t ne[4] = { a->ne[0], a->ne[0], a->ne[2], a->ne[3] };
    struct ggml_tensor * result = ggml_new_tensor(ctx, a->type, MAX(a->n_dims, 2), ne);

    result->op   = GGML_OP_DIAG;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;

    return result;
}


// ggml_diag_mask_inf

struct ggml_tensor * ggml_diag_mask_inf_impl(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        int                   n_past,
        bool                  inplace) {
    bool is_node = false;

    if (a->grad) {
        is_node = true;
    }

    struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);

    ggml_scratch_save(ctx);

    struct ggml_tensor * b = ggml_new_tensor_1d(ctx, GGML_TYPE_I32, 2);

    ((int32_t *) b->data)[0] = n_past;
    ((int32_t *) b->data)[1] = inplace ? 1 : 0;

    ggml_scratch_load(ctx);

    result->op   = GGML_OP_DIAG_MASK_INF;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = b;

    return result;
}

struct ggml_tensor * ggml_diag_mask_inf(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        int                   n_past) {
    return ggml_diag_mask_inf_impl(ctx, a, n_past, false);
}


struct ggml_tensor * ggml_diag_mask_inf_inplace(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        int                   n_past) {
    return ggml_diag_mask_inf_impl(ctx, a, n_past, true);
}

// ggml_diag_mask_zero

struct ggml_tensor * ggml_diag_mask_zero_impl(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        int                   n_past,
        bool                  inplace) {
    bool is_node = false;

    if (a->grad) {
        is_node = true;
    }

    struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);

    ggml_scratch_save(ctx);

    struct ggml_tensor * b = ggml_new_tensor_1d(ctx, GGML_TYPE_I32, 2);
    ggml_set_name(b, "n_past, inplace");

    ((int32_t *) b->data)[0] = n_past;
    ((int32_t *) b->data)[1] = inplace ? 1 : 0;

    ggml_scratch_load(ctx);

    result->op   = GGML_OP_DIAG_MASK_ZERO;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = b;

    return result;
}

struct ggml_tensor * ggml_diag_mask_zero(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        int                   n_past) {
    return ggml_diag_mask_zero_impl(ctx, a, n_past, false);
}

struct ggml_tensor * ggml_diag_mask_zero_inplace(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        int                   n_past) {
    return ggml_diag_mask_zero_impl(ctx, a, n_past, true);
}

// ggml_soft_max

struct ggml_tensor * ggml_soft_max_impl(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        bool                  inplace) {
    bool is_node = false;

    if (a->grad) {
        is_node = true;
    }

    struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);

    result->op   = GGML_OP_SOFT_MAX;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;

    return result;
}

struct ggml_tensor * ggml_soft_max(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    return ggml_soft_max_impl(ctx, a, false);
}

struct ggml_tensor * ggml_soft_max_inplace(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    return ggml_soft_max_impl(ctx, a, true);
}


// ggml_soft_max_back

struct ggml_tensor * ggml_soft_max_back_impl(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        struct ggml_tensor  * b,
        bool                  inplace) {
    bool is_node = false;

    if (a->grad || b->grad) {
        is_node = true; // TODO : implement backward pass
    }

    struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);

    result->op   = GGML_OP_SOFT_MAX_BACK;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = b;

    return result;
}

struct ggml_tensor * ggml_soft_max_back(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        struct ggml_tensor  * b) {
    return ggml_soft_max_back_impl(ctx, a, b, false);
}

struct ggml_tensor * ggml_soft_max_back_inplace(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        struct ggml_tensor  * b) {
    return ggml_soft_max_back_impl(ctx, a, b, true);
}

// ggml_rope

struct ggml_tensor * ggml_rope_impl(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        int                   n_past,
        int                   n_dims,
        int                   mode,
        int                   n_ctx,
        bool                  inplace) {
    GGML_ASSERT(n_past >= 0);
    bool is_node = false;

    if (a->grad) {
        is_node = true;
    }

    struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);

    ggml_scratch_save(ctx);

    struct ggml_tensor * b = ggml_new_tensor_1d(ctx, GGML_TYPE_I32, 4);

    ((int32_t *) b->data)[0] = n_past;
    ((int32_t *) b->data)[1] = n_dims;
    ((int32_t *) b->data)[2] = mode;
    ((int32_t *) b->data)[3] = n_ctx;

    ggml_scratch_load(ctx);

    result->op   = GGML_OP_ROPE;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = b;

    return result;
}

struct ggml_tensor * ggml_rope(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        int                   n_past,
        int                   n_dims,
        int                   mode,
        int                   n_ctx) {
    return ggml_rope_impl(ctx, a, n_past, n_dims, mode, n_ctx, false);
}

struct ggml_tensor * ggml_rope_inplace(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        int                   n_past,
        int                   n_dims,
        int                   mode,
        int                   n_ctx) {
    return ggml_rope_impl(ctx, a, n_past, n_dims, mode, n_ctx, true);
}

// ggml_rope_back

struct ggml_tensor * ggml_rope_back(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        int                   n_past,
        int                   n_dims,
        int                   mode) {
    GGML_ASSERT(n_past >= 0);
    GGML_ASSERT((mode & 4) == 0 && "ggml_rope_back() for ChatGLM not implemented yet");

    bool is_node = false;

    if (a->grad) {
        is_node = false; // TODO: implement backward
    }

    struct ggml_tensor * result = ggml_dup_tensor(ctx, a);

    ggml_scratch_save(ctx);

    struct ggml_tensor * b = ggml_new_tensor_1d(ctx, GGML_TYPE_I32, 3);
    ggml_set_name(b, "n_past, n_dims, mode");

    ((int32_t *) b->data)[0] = n_past;
    ((int32_t *) b->data)[1] = n_dims;
    ((int32_t *) b->data)[2] = mode;

    ggml_scratch_load(ctx);

    result->op   = GGML_OP_ROPE_BACK;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = b;

    return result;
}

// ggml_alibi

struct ggml_tensor * ggml_alibi(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        int                   n_past,
        int                   n_head,
        float                 bias_max) {
    GGML_ASSERT(n_past >= 0);
    bool is_node = false;

    if (a->grad) {
        GGML_ASSERT(false); // TODO: implement backward
        is_node = true;
    }

    // TODO: when implement backward, fix this:
    //struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);
    struct ggml_tensor * result = ggml_view_tensor(ctx, a);

    ggml_scratch_save(ctx);

    struct ggml_tensor * b = ggml_new_tensor_1d(ctx, GGML_TYPE_I32, 3);

    ((int32_t *) b->data)[0] = n_past;
    ((int32_t *) b->data)[1] = n_head;
    GGML_ASSERT(sizeof(float) == sizeof(int32_t));
    (((float *) b->data)[2]) = bias_max;

    ggml_scratch_load(ctx);

    result->op   = GGML_OP_ALIBI;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = b;

    return result;
}

// ggml_clamp

struct ggml_tensor * ggml_clamp(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        float                 min,
        float                 max) {
    bool is_node = false;

    if (a->grad) {
        GGML_ASSERT(false); // TODO: implement backward
        is_node = true;
    }

    // TODO: when implement backward, fix this:
    struct ggml_tensor * result = ggml_view_tensor(ctx, a);

    ggml_scratch_save(ctx);

    struct ggml_tensor * b = ggml_new_tensor_1d(ctx, GGML_TYPE_F32, 2);

    ((float *) b->data)[0] = min;
    ((float *) b->data)[1] = max;

    ggml_scratch_load(ctx);

    result->op   = GGML_OP_CLAMP;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = b;

    return result;
}

// ggml_conv_1d

static int64_t ggml_calc_conv_output_size(int64_t ins, int64_t ks, int s, int p, int d) {
    return (ins + 2 * p - d * (ks - 1) - 1) / s + 1;
}

GGML_API struct ggml_tensor * ggml_conv_1d(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        struct ggml_tensor  * b,
        int                   s0,
        int                   p0,
        int                   d0) {
    GGML_ASSERT(ggml_is_matrix(b));
    GGML_ASSERT(a->ne[1] == b->ne[1]);
    bool is_node = false;

    if (a->grad || b->grad) {
        GGML_ASSERT(false); // TODO: implement backward
        is_node = true;
    }

    const int64_t ne[4] = {
        ggml_calc_conv_output_size(b->ne[0], a->ne[0], s0, p0, d0),
        a->ne[2], 1, 1,
    };
    struct ggml_tensor* result = ggml_new_tensor(ctx, GGML_TYPE_F32, 2, ne);

    ggml_scratch_save(ctx);
    struct ggml_tensor* c = ggml_new_tensor_1d(ctx, GGML_TYPE_I32, 3);
    ((int32_t*)c->data)[0] = s0;
    ((int32_t*)c->data)[1] = p0;
    ((int32_t*)c->data)[2] = d0;
    ggml_scratch_load(ctx);

    result->op = GGML_OP_CONV_1D;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = b;
    result->opt[0] = c;

    return result;
}

// ggml_conv_2d

struct ggml_tensor* ggml_conv_2d(
    struct ggml_context* ctx,
    struct ggml_tensor * a,
    struct ggml_tensor * b,
    int                  s0,
    int                  s1,
    int                  p0,
    int                  p1,
    int                  d0,
    int                  d1) {

    GGML_ASSERT(b->ne[3] == 1);
    GGML_ASSERT(a->ne[2] == b->ne[2]);
    bool is_node = false;

    if (a->grad || b->grad) {
        GGML_ASSERT(false); // TODO: implement backward
        is_node = true;
    }

    const int64_t ne[4] = {
        ggml_calc_conv_output_size(b->ne[0], a->ne[0], s0, p0, d0),
        ggml_calc_conv_output_size(b->ne[1], a->ne[1], s1, p1, d1),
        a->ne[3], 1,
    };
    struct ggml_tensor* result = ggml_new_tensor(ctx, GGML_TYPE_F32, 4, ne);

    ggml_scratch_save(ctx);
    struct ggml_tensor* c = ggml_new_tensor_1d(ctx, GGML_TYPE_I32, 6);
    ((int32_t*)c->data)[0] = s0;
    ((int32_t*)c->data)[1] = s1;
    ((int32_t*)c->data)[2] = p0;
    ((int32_t*)c->data)[3] = p1;
    ((int32_t*)c->data)[4] = d0;
    ((int32_t*)c->data)[5] = d1;
    ggml_scratch_load(ctx);

    result->op = GGML_OP_CONV_2D;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = b;
    result->opt[0] = c;

    return result;

}

// ggml_conv_1d_ph

struct ggml_tensor* ggml_conv_1d_ph(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        struct ggml_tensor  * b,
        int                   s,
        int                   d) {
    return ggml_conv_1d(ctx, a, b, s, a->ne[0] / 2, d);
}

// ggml_flash_attn

struct ggml_tensor * ggml_flash_attn(
        struct ggml_context * ctx,
        struct ggml_tensor  * q,
        struct ggml_tensor  * k,
        struct ggml_tensor  * v,
        bool                  masked) {
    GGML_ASSERT(ggml_can_mul_mat(k, q));
    // TODO: check if vT can be multiplied by (k*qT)

    bool is_node = false;

    if (q->grad || k->grad || v->grad) {
        is_node = true;
    }

    //struct ggml_tensor * result = ggml_dup_tensor(ctx, q);
    struct ggml_tensor * result = ggml_new_tensor(ctx, GGML_TYPE_F32, 4, q->ne);

    result->op   = GGML_OP_FLASH_ATTN;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = q;
    result->src1 = k;
    result->opt[0] = v;
    result->opt[1] = ggml_new_i32(ctx, masked ? 1 : 0);

    return result;
}

// ggml_flash_ff

struct ggml_tensor * ggml_flash_ff(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        struct ggml_tensor  * b0,
        struct ggml_tensor  * b1,
        struct ggml_tensor  * c0,
        struct ggml_tensor  * c1) {
    GGML_ASSERT(ggml_can_mul_mat(b0, a));
    // TODO: more checks

    bool is_node = false;

    if (a->grad || b0->grad || b1->grad || c0->grad || c1->grad) {
        is_node = true;
    }

    //struct ggml_tensor * result = ggml_dup_tensor(ctx, a);
    struct ggml_tensor * result = ggml_new_tensor(ctx, GGML_TYPE_F32, 4, a->ne);

    result->op   = GGML_OP_FLASH_FF;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = b0;
    result->opt[0] = b1;
    result->opt[1] = c0;
    result->opt[2] = c1;

    return result;
}

// ggml_flash_attn_back

struct ggml_tensor * ggml_flash_attn_back(
        struct ggml_context * ctx,
        struct ggml_tensor  * q,
        struct ggml_tensor  * k,
        struct ggml_tensor  * v,
        struct ggml_tensor  * d,
        bool                  masked) {
    GGML_ASSERT(ggml_can_mul_mat(k, q));
    // TODO: check if vT can be multiplied by (k*qT)

    // d shape [D,N,ne2,ne3]
    // q shape [D,N,ne2,ne3]
    // k shape [D,M,ne2,ne3]
    // v shape [M,D,ne2,ne3]

    const int64_t   D = q->ne[0];
    const int64_t   N = q->ne[1];
    const int64_t   M = k->ne[1];
    const int64_t ne2 = q->ne[2];
    const int64_t ne3 = q->ne[3];

    GGML_ASSERT(k->ne[0] == D);
    GGML_ASSERT(v->ne[0] == M);
    GGML_ASSERT(v->ne[1] == D);
    GGML_ASSERT(d->ne[0] == D);
    GGML_ASSERT(d->ne[1] == N);
    GGML_ASSERT(k->ne[2] == ne2);
    GGML_ASSERT(k->ne[3] == ne3);
    GGML_ASSERT(v->ne[2] == ne2);
    GGML_ASSERT(v->ne[3] == ne3);
    GGML_ASSERT(d->ne[2] == ne2);
    GGML_ASSERT(d->ne[3] == ne3);

    bool is_node = false;

    if (q->grad || k->grad || v->grad) {
        // when using this operation (in backwards pass) these grads are set.
        // we don't want to create (big) grad of our result, so is_node is false.
        is_node = false;
    }

    // store gradients of q, k and v as continuous tensors concatenated in result.
    // q shape[D,N,ne2,ne3] ; k shape [D,M,ne2,ne3] ; v shape [M,D,ne2,ne3]
    // gradq->data = result->data
    // gradk->data = result->data + nb0*D*N*ne2*ne3
    // gradv->data = result->data + nb0*D*N*ne2*ne3 + nb0*D*M*ne2*ne3
    // note: v and gradv are actually transposed, i.e. v->ne[0] != D.
    int64_t ne[4] = {D,M+N+M,ne2,ne3};

    struct ggml_tensor * result = ggml_new_tensor(ctx, GGML_TYPE_F32, 4, ne);

    result->op   = GGML_OP_FLASH_ATTN_BACK;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = q;
    result->src1 = k;
    result->opt[0] = v;
    result->opt[1] = d;
    result->opt[2] = ggml_new_i32(ctx, masked ? 1 : 0);

    return result;
}

// ggml_win_part

struct ggml_tensor * ggml_win_part(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        int                   w) {
    GGML_ASSERT(a->ne[3] == 1);
    GGML_ASSERT(a->type  == GGML_TYPE_F32);

    bool is_node = false;

    if (a->grad) {
        GGML_ASSERT(false); // TODO: implement backward
        is_node = true;
    }

    // padding
    const int px = (w - a->ne[1]%w)%w;
    const int py = (w - a->ne[2]%w)%w;

    const int npx = (px + a->ne[1])/w;
    const int npy = (py + a->ne[2])/w;
    const int np  = npx*npy;

    const int64_t ne[4] = { a->ne[0], w, w, np, };

    struct ggml_tensor * result = ggml_new_tensor(ctx, GGML_TYPE_F32, 4, ne);

    ggml_scratch_save(ctx);

    struct ggml_tensor * b = ggml_new_tensor_1d(ctx, GGML_TYPE_I32, 3);

    ((int32_t *) b->data)[0] = npx;
    ((int32_t *) b->data)[1] = npy;
    ((int32_t *) b->data)[2] = w;

    ggml_scratch_load(ctx);

    result->op   = GGML_OP_WIN_PART;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;
    result->opt[0] = b;

    return result;
}

// ggml_win_unpart

struct ggml_tensor * ggml_win_unpart(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        int                   w0,
        int                   h0,
        int                   w) {
    GGML_ASSERT(a->type == GGML_TYPE_F32);

    bool is_node = false;

    if (a->grad) {
        GGML_ASSERT(false); // TODO: implement backward
        is_node = true;
    }

    const int64_t ne[4] = { a->ne[0], w0, h0, 1, };
    struct ggml_tensor * result = ggml_new_tensor(ctx, GGML_TYPE_F32, 3, ne);

    ggml_scratch_save(ctx);

    struct ggml_tensor * b = ggml_new_tensor_1d(ctx, GGML_TYPE_I32, 1);

    ((int32_t *) b->data)[0] = w;

    ggml_scratch_load(ctx);

    result->op   = GGML_OP_WIN_UNPART;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;
    result->opt[0] = b;

    return result;
}

// ggml_map_unary

struct ggml_tensor * ggml_map_unary_impl_f32(
        struct ggml_context        * ctx,
        struct ggml_tensor         * a,
        const  ggml_unary_op_f32_t fun,
        bool   inplace) {
    bool is_node = false;

    if (!inplace && a->grad) {
        is_node = true;
    }

    struct ggml_tensor *result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);

    ggml_scratch_save(ctx);

    struct ggml_tensor * addr_tensor = ggml_new_tensor_1d(ctx, GGML_TYPE_I32, sizeof(void *) / sizeof(int32_t));
    *((void (**)(void))addr_tensor->data) = (void (*)(void))fun;

    ggml_scratch_load(ctx);

    result->op = GGML_OP_MAP_UNARY;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->opt[0] = addr_tensor;

    return result;
}

struct ggml_tensor * ggml_map_unary_f32(
        struct ggml_context        * ctx,
        struct ggml_tensor         * a,
        const  ggml_unary_op_f32_t fun) {
    return ggml_map_unary_impl_f32(ctx, a, fun, false);
}

struct ggml_tensor * ggml_map_unary_inplace_f32(
        struct ggml_context        * ctx,
        struct ggml_tensor         * a,
        const  ggml_unary_op_f32_t fun) {
    return ggml_map_unary_impl_f32(ctx, a, fun, true);
}

// ggml_map_binary

struct ggml_tensor * ggml_map_binary_impl_f32(
        struct ggml_context         * ctx,
        struct ggml_tensor          * a,
        struct ggml_tensor          * b,
        const  ggml_binary_op_f32_t fun,
        bool   inplace) {
    GGML_ASSERT(ggml_are_same_shape(a, b));

    bool is_node = false;

    if (!inplace && (a->grad || b->grad)) {
        is_node = true;
    }

    struct ggml_tensor *result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);

    ggml_scratch_save(ctx);

    struct ggml_tensor * addr_tensor = ggml_new_tensor_1d(ctx, GGML_TYPE_I32, sizeof(void *) / sizeof(int32_t));
    *((void (**)(void))addr_tensor->data) = (void (*)(void))fun;

    ggml_scratch_load(ctx);

    result->op = GGML_OP_MAP_BINARY;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = b;
    result->opt[0] = addr_tensor;

    return result;
}

struct ggml_tensor * ggml_map_binary_f32(
        struct ggml_context         * ctx,
        struct ggml_tensor          * a,
        struct ggml_tensor          * b,
        const  ggml_binary_op_f32_t fun) {
    return ggml_map_binary_impl_f32(ctx, a, b, fun, false);
}

struct ggml_tensor * ggml_map_binary_inplace_f32(
        struct ggml_context         * ctx,
        struct ggml_tensor          * a,
        struct ggml_tensor          * b,
        const  ggml_binary_op_f32_t fun) {
    return ggml_map_binary_impl_f32(ctx, a, b, fun, true);
}

// ggml_map_custom1

struct ggml_tensor * ggml_map_custom1_impl_f32(
        struct ggml_context          * ctx,
        struct ggml_tensor           * a,
        const  ggml_custom1_op_f32_t   fun,
        bool   inplace) {
    bool is_node = false;

    if (!inplace && a->grad) {
        is_node = true;
    }

    struct ggml_tensor *result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);

    ggml_scratch_save(ctx);

    struct ggml_tensor * addr_tensor = ggml_new_tensor_1d(ctx, GGML_TYPE_I32, sizeof(void *) / sizeof(int32_t));
    *((void (**)(void))addr_tensor->data) = (void (*)(void))fun;

    ggml_scratch_load(ctx);

    result->op = GGML_OP_MAP_CUSTOM1;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->opt[0] = addr_tensor;

    return result;
}

struct ggml_tensor * ggml_map_custom1_f32(
        struct ggml_context          * ctx,
        struct ggml_tensor           * a,
        const  ggml_custom1_op_f32_t   fun) {
    return ggml_map_custom1_impl_f32(ctx, a, fun, false);
}

struct ggml_tensor * ggml_map_custom1_inplace_f32(
        struct ggml_context          * ctx,
        struct ggml_tensor           * a,
        const  ggml_custom1_op_f32_t   fun) {
    return ggml_map_custom1_impl_f32(ctx, a, fun, true);
}

// ggml_map_custom2

struct ggml_tensor * ggml_map_custom2_impl_f32(
        struct ggml_context          * ctx,
        struct ggml_tensor           * a,
        struct ggml_tensor           * b,
        const  ggml_custom2_op_f32_t   fun,
        bool   inplace) {
    bool is_node = false;

    if (!inplace && (a->grad || b->grad)) {
        is_node = true;
    }

    struct ggml_tensor *result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);

    ggml_scratch_save(ctx);

    struct ggml_tensor * addr_tensor = ggml_new_tensor_1d(ctx, GGML_TYPE_I32, sizeof(void *) / sizeof(int32_t));
    *((void (**)(void))addr_tensor->data) = (void (*)(void))fun;

    ggml_scratch_load(ctx);

    result->op = GGML_OP_MAP_CUSTOM2;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = b;
    result->opt[0] = addr_tensor;

    return result;
}

struct ggml_tensor * ggml_map_custom2_f32(
        struct ggml_context          * ctx,
        struct ggml_tensor           * a,
        struct ggml_tensor           * b,
        const  ggml_custom2_op_f32_t   fun) {
    return ggml_map_custom2_impl_f32(ctx, a, b, fun, false);
}

struct ggml_tensor * ggml_map_custom2_inplace_f32(
        struct ggml_context          * ctx,
        struct ggml_tensor           * a,
        struct ggml_tensor           * b,
        const  ggml_custom2_op_f32_t   fun) {
    return ggml_map_custom2_impl_f32(ctx, a, b, fun, true);
}

// ggml_map_custom3

struct ggml_tensor * ggml_map_custom3_impl_f32(
        struct ggml_context          * ctx,
        struct ggml_tensor           * a,
        struct ggml_tensor           * b,
        struct ggml_tensor           * c,
        const  ggml_custom3_op_f32_t   fun,
        bool   inplace) {
    bool is_node = false;

    if (!inplace && (a->grad || b->grad || c->grad)) {
        is_node = true;
    }

    struct ggml_tensor *result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);

    ggml_scratch_save(ctx);

    struct ggml_tensor * addr_tensor = ggml_new_tensor_1d(ctx, GGML_TYPE_I32, sizeof(void *) / sizeof(int32_t));
    *((void (**)(void))addr_tensor->data) = (void (*)(void))fun;

    ggml_scratch_load(ctx);

    result->op = GGML_OP_MAP_CUSTOM3;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = b;
    result->opt[0] = addr_tensor;
    result->opt[1] = c;

    return result;
}

struct ggml_tensor * ggml_map_custom3_f32(
        struct ggml_context          * ctx,
        struct ggml_tensor           * a,
        struct ggml_tensor           * b,
        struct ggml_tensor           * c,
        const  ggml_custom3_op_f32_t   fun) {
    return ggml_map_custom3_impl_f32(ctx, a, b, c, fun, false);
}

struct ggml_tensor * ggml_map_custom3_inplace_f32(
        struct ggml_context          * ctx,
        struct ggml_tensor           * a,
        struct ggml_tensor           * b,
        struct ggml_tensor           * c,
        const  ggml_custom3_op_f32_t   fun) {
    return ggml_map_custom3_impl_f32(ctx, a, b, c, fun, true);
}

// ggml_cross_entropy_loss

struct ggml_tensor * ggml_cross_entropy_loss(
        struct ggml_context         * ctx,
        struct ggml_tensor          * a,
        struct ggml_tensor          * b) {
    GGML_ASSERT(ggml_are_same_shape(a, b));
    bool is_node = false;

    if (a->grad || b->grad) {
        is_node = true;
    }

    struct ggml_tensor * result = ggml_new_tensor_1d(ctx, a->type, 1);

    result->op   = GGML_OP_CROSS_ENTROPY_LOSS;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = b;

    return result;
}

// ggml_cross_entropy_loss_back

struct ggml_tensor * ggml_cross_entropy_loss_back(
        struct ggml_context         * ctx,
        struct ggml_tensor          * a,
        struct ggml_tensor          * b,
        struct ggml_tensor          * c) {
    GGML_ASSERT(ggml_are_same_shape(a, b));
    GGML_ASSERT(ggml_is_scalar(c));

    struct ggml_tensor * result = ggml_dup_tensor(ctx, a);

    result->op   = GGML_OP_CROSS_ENTROPY_LOSS_BACK;
    result->grad = NULL;
    result->src0 = a;
    result->src1 = b;
    result->opt[0] = c;

    return result;
}

////////////////////////////////////////////////////////////////////////////////

void ggml_set_param(
        struct ggml_context * ctx,
        struct ggml_tensor * tensor) {
    tensor->is_param = true;

    GGML_ASSERT(tensor->grad == NULL);
    tensor->grad = ggml_dup_tensor(ctx, tensor);
}

// ggml_compute_forward_dup

static void ggml_compute_forward_dup_same_cont(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    GGML_ASSERT(ggml_nelements(dst) == ggml_nelements(src0));
    GGML_ASSERT(ggml_is_contiguous(dst) && ggml_is_contiguous(src0));
    GGML_ASSERT(src0->type == dst->type);

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const size_t nb00 = src0->nb[0];
    const size_t nb0 = dst->nb[0];

    const int ith = params->ith; // thread index
    const int nth = params->nth; // number of threads

    // parallelize by elements
    const int ne = ggml_nelements(dst);
    const int dr = (ne + nth - 1) / nth;
    const int ie0 = dr * ith;
    const int ie1 = MIN(ie0 + dr, ne);

    if (ie0 < ie1) {
        memcpy(
            ((char *)  dst->data + ie0*nb0),
            ((char *) src0->data + ie0*nb00),
            (ie1 - ie0) * GGML_TYPE_SIZE[src0->type]);
    }

}
static void ggml_compute_forward_dup_f16(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    GGML_ASSERT(ggml_nelements(dst) == ggml_nelements(src0));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    GGML_TENSOR_UNARY_OP_LOCALS;

    const int ith = params->ith; // thread index
    const int nth = params->nth; // number of threads

    if (ggml_is_contiguous(src0) && ggml_is_contiguous(dst) && src0->type == dst->type) {
        ggml_compute_forward_dup_same_cont(params, src0, dst);
        return;
    }

    // parallelize by rows
    const int nr = ne01;
    // number of rows per thread
    const int dr = (nr + nth - 1) / nth;
    // row range for this thread
    const int ir0 = dr * ith;
    const int ir1 = MIN(ir0 + dr, nr);

    if (src0->type == dst->type &&
        ne00 == ne0 &&
        nb00 == GGML_TYPE_SIZE[src0->type] && nb0 == GGML_TYPE_SIZE[dst->type]) {
        // copy by rows
        const size_t rs = ne00*nb00;
        for (int64_t i03 = 0; i03 < ne03; i03++) {
            for (int64_t i02 = 0; i02 < ne02; i02++) {
                for (int64_t i01 = ir0; i01 < ir1; i01++) {
                    memcpy(
                        ((char *)  dst->data + i01*nb1  + i02*nb2  + i03*nb3),
                        ((char *) src0->data + i01*nb01 + i02*nb02 + i03*nb03),
                        rs);
                }
            }
        }
        return;
    }

    // TODO: add more special-case implementations for tensor shapes/strides that can benefit from memcpy

    if (ggml_is_contiguous(dst)) {
        if (nb00 == sizeof(ggml_fp16_t)) {
            if (dst->type == GGML_TYPE_F16) {
                size_t id = 0;
                const size_t rs = ne00 * nb00;
                char * dst_ptr = (char *) dst->data;

                for (int i03 = 0; i03 < ne03; i03++) {
                    for (int i02 = 0; i02 < ne02; i02++) {
                        id += rs * ir0;
                        for (int i01 = ir0; i01 < ir1; i01++) {
                            const char * src0_ptr = (char *) src0->data + i01*nb01 + i02*nb02 + i03*nb03;
                            memcpy(dst_ptr + id, src0_ptr, rs);
                            id += rs;
                        }
                        id += rs * (ne01 - ir1);
                    }
                }
            } else if (dst->type == GGML_TYPE_F32) {
                size_t id = 0;
                float * dst_ptr = (float *) dst->data;

                for (int i03 = 0; i03 < ne03; i03++) {
                    for (int i02 = 0; i02 < ne02; i02++) {
                        id += ne00 * ir0;
                        for (int i01 = ir0; i01 < ir1; i01++) {
                            const ggml_fp16_t * src0_ptr = (ggml_fp16_t *) ((char *) src0->data + i01*nb01 + i02*nb02 + i03*nb03);
                            for (int i00 = 0; i00 < ne00; i00++) {
                                dst_ptr[id] = GGML_FP16_TO_FP32(src0_ptr[i00]);
                                id++;
                            }
                        }
                        id += ne00 * (ne01 - ir1);
                    }
                }
            } else if (type_traits[dst->type].from_float) {
                ggml_from_float_t const quantize_row_q = type_traits[dst->type].from_float;
                float * src0_f32 = (float *) params->wdata + (ne00 + CACHE_LINE_SIZE_F32) * ith;

                size_t id = 0;
                size_t rs = nb0 * (ne00 / GGML_BLCK_SIZE[dst->type]);
                char * dst_ptr = (char *) dst->data;

                for (int i03 = 0; i03 < ne03; i03++) {
                    for (int i02 = 0; i02 < ne02; i02++) {
                        id += rs * ir0;
                        for (int i01 = ir0; i01 < ir1; i01++) {
                            const ggml_fp16_t * src0_ptr = (ggml_fp16_t *) ((char *) src0->data + i01*nb01 + i02*nb02 + i03*nb03);

                            for (int i00 = 0; i00 < ne00; i00++) {
                                src0_f32[i00] = GGML_FP16_TO_FP32(src0_ptr[i00]);
                            }

                            quantize_row_q(src0_f32, dst_ptr + id, ne00);
                            id += rs;
                        }
                        id += rs * (ne01 - ir1);
                    }
                }
            } else {
                GGML_ASSERT(false); // TODO: implement
            }
        } else {
            //printf("%s: this is not optimal - fix me\n", __func__);

            if (dst->type == GGML_TYPE_F32) {
                size_t id = 0;
                float * dst_ptr = (float *) dst->data;

                for (int i03 = 0; i03 < ne03; i03++) {
                    for (int i02 = 0; i02 < ne02; i02++) {
                        id += ne00 * ir0;
                        for (int i01 = ir0; i01 < ir1; i01++) {
                            for (int i00 = 0; i00 < ne00; i00++) {
                                const ggml_fp16_t * src0_ptr = (ggml_fp16_t *) ((char *) src0->data + i00*nb00 + i01*nb01 + i02*nb02 + i03*nb03);

                                dst_ptr[id] = GGML_FP16_TO_FP32(*src0_ptr);
                                id++;
                            }
                        }
                        id += ne00 * (ne01 - ir1);
                    }
                }
            } else if (dst->type == GGML_TYPE_F16) {
                size_t id = 0;
                ggml_fp16_t * dst_ptr = (ggml_fp16_t *) dst->data;

                for (int i03 = 0; i03 < ne03; i03++) {
                    for (int i02 = 0; i02 < ne02; i02++) {
                        id += ne00 * ir0;
                        for (int i01 = ir0; i01 < ir1; i01++) {
                            for (int i00 = 0; i00 < ne00; i00++) {
                                const ggml_fp16_t * src0_ptr = (ggml_fp16_t *) ((char *) src0->data + i00*nb00 + i01*nb01 + i02*nb02 + i03*nb03);

                                dst_ptr[id] = *src0_ptr;
                                id++;
                            }
                        }
                        id += ne00 * (ne01 - ir1);
                    }
                }
            } else {
                GGML_ASSERT(false); // TODO: implement
            }
        }
        return;
    }

    // dst counters
    int64_t i10 = 0;
    int64_t i11 = 0;
    int64_t i12 = 0;
    int64_t i13 = 0;

    if (dst->type == GGML_TYPE_F16) {
        for (int64_t i03 = 0; i03 < ne03; i03++) {
            for (int64_t i02 = 0; i02 < ne02; i02++) {
                i10 += ne00 * ir0;
                while (i10 >= ne0) {
                    i10 -= ne0;
                    if (++i11 == ne1) {
                        i11 = 0;
                        if (++i12 == ne2) {
                            i12 = 0;
                            if (++i13 == ne3) {
                                i13 = 0;
                            }
                        }
                    }
                }
                for (int64_t i01 = ir0; i01 < ir1; i01++) {
                    for (int64_t i00 = 0; i00 < ne00; i00++) {
                        const char * src0_ptr = ((char *) src0->data + i00*nb00 + i01*nb01 + i02*nb02 + i03*nb03);
                              char * dst_ptr  = ((char *)  dst->data + i10*nb0  + i11*nb1  + i12*nb2  + i13*nb3);

                        memcpy(dst_ptr, src0_ptr, sizeof(ggml_fp16_t));

                        if (++i10 == ne00) {
                            i10 = 0;
                            if (++i11 == ne01) {
                                i11 = 0;
                                if (++i12 == ne02) {
                                    i12 = 0;
                                    if (++i13 == ne03) {
                                        i13 = 0;
                                    }
                                }
                            }
                        }
                    }
                }
                i10 += ne00 * (ne01 - ir1);
                while (i10 >= ne0) {
                    i10 -= ne0;
                    if (++i11 == ne1) {
                        i11 = 0;
                        if (++i12 == ne2) {
                            i12 = 0;
                            if (++i13 == ne3) {
                                i13 = 0;
                            }
                        }
                    }
                }
            }
        }
    } else if (dst->type == GGML_TYPE_F32) {
        for (int64_t i03 = 0; i03 < ne03; i03++) {
            for (int64_t i02 = 0; i02 < ne02; i02++) {
                i10 += ne00 * ir0;
                while (i10 >= ne0) {
                    i10 -= ne0;
                    if (++i11 == ne1) {
                        i11 = 0;
                        if (++i12 == ne2) {
                            i12 = 0;
                            if (++i13 == ne3) {
                                i13 = 0;
                            }
                        }
                    }
                }
                for (int64_t i01 = ir0; i01 < ir1; i01++) {
                    for (int64_t i00 = 0; i00 < ne00; i00++) {
                        const char * src0_ptr = ((char *) src0->data + i00*nb00 + i01*nb01 + i02*nb02 + i03*nb03);
                              char * dst_ptr  = ((char *)  dst->data + i10*nb0  + i11*nb1  + i12*nb2  + i13*nb3);

                        *(float *) dst_ptr = GGML_FP16_TO_FP32(*(const ggml_fp16_t *) src0_ptr);

                        if (++i10 == ne0) {
                            i10 = 0;
                            if (++i11 == ne1) {
                                i11 = 0;
                                if (++i12 == ne2) {
                                    i12 = 0;
                                    if (++i13 == ne3) {
                                        i13 = 0;
                                    }
                                }
                            }
                        }
                    }
                }
                i10 += ne00 * (ne01 - ir1);
                while (i10 >= ne0) {
                    i10 -= ne0;
                    if (++i11 == ne1) {
                        i11 = 0;
                        if (++i12 == ne2) {
                            i12 = 0;
                            if (++i13 == ne3) {
                                i13 = 0;
                            }
                        }
                    }
                }
            }
        }
    } else {
        GGML_ASSERT(false); // TODO: implement
    }
}

static void ggml_compute_forward_dup_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    GGML_ASSERT(ggml_nelements(dst) == ggml_nelements(src0));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    GGML_TENSOR_UNARY_OP_LOCALS;

    const int ith = params->ith; // thread index
    const int nth = params->nth; // number of threads

    if (ggml_is_contiguous(src0) && ggml_is_contiguous(dst) && src0->type == dst->type) {
        ggml_compute_forward_dup_same_cont(params, src0, dst);
        return;
    }

    // parallelize by rows
    const int nr = ne01;
    // number of rows per thread
    const int dr = (nr + nth - 1) / nth;
    // row range for this thread
    const int ir0 = dr * ith;
    const int ir1 = MIN(ir0 + dr, nr);

    if (src0->type == dst->type &&
        ne00 == ne0 &&
        nb00 == GGML_TYPE_SIZE[src0->type] && nb0 == GGML_TYPE_SIZE[dst->type]) {
        // copy by rows
        const size_t rs = ne00*nb00;
        for (int64_t i03 = 0; i03 < ne03; i03++) {
            for (int64_t i02 = 0; i02 < ne02; i02++) {
                for (int64_t i01 = ir0; i01 < ir1; i01++) {
                    memcpy(
                        ((char *)  dst->data + i01*nb1  + i02*nb2  + i03*nb3),
                        ((char *) src0->data + i01*nb01 + i02*nb02 + i03*nb03),
                        rs);
                }
            }
        }
        return;
    }

    if (ggml_is_contiguous(dst)) {
        // TODO: simplify
        if (nb00 == sizeof(float)) {
            if (dst->type == GGML_TYPE_F32) {
                size_t id = 0;
                const size_t rs = ne00 * nb00;
                char * dst_ptr = (char *) dst->data;

                for (int i03 = 0; i03 < ne03; i03++) {
                    for (int i02 = 0; i02 < ne02; i02++) {
                        id += rs * ir0;
                        for (int i01 = ir0; i01 < ir1; i01++) {
                            const char * src0_ptr = (char *) src0->data + i01*nb01 + i02*nb02 + i03*nb03;
                            memcpy(dst_ptr + id, src0_ptr, rs);
                            id += rs;
                        }
                        id += rs * (ne01 - ir1);
                    }
                }
            } else if (type_traits[dst->type].from_float) {
                ggml_from_float_t const quantize_row_q = type_traits[dst->type].from_float;

                size_t id = 0;
                size_t rs = nb0 * (ne00 / GGML_BLCK_SIZE[dst->type]);
                char * dst_ptr = (char *) dst->data;

                for (int i03 = 0; i03 < ne03; i03++) {
                    for (int i02 = 0; i02 < ne02; i02++) {
                        id += rs * ir0;
                        for (int i01 = ir0; i01 < ir1; i01++) {
                            const float * src0_ptr = (float *) ((char *) src0->data + i01*nb01 + i02*nb02 + i03*nb03);
                            quantize_row_q(src0_ptr, dst_ptr + id, ne00);
                            id += rs;
                        }
                        id += rs * (ne01 - ir1);
                    }
                }
            } else {
                GGML_ASSERT(false); // TODO: implement
            }
        } else {
            //printf("%s: this is not optimal - fix me\n", __func__);

            if (dst->type == GGML_TYPE_F32) {
                size_t id = 0;
                float * dst_ptr = (float *) dst->data;

                for (int i03 = 0; i03 < ne03; i03++) {
                    for (int i02 = 0; i02 < ne02; i02++) {
                        id += ne00 * ir0;
                        for (int i01 = ir0; i01 < ir1; i01++) {
                            for (int i00 = 0; i00 < ne00; i00++) {
                                const float * src0_ptr = (float *) ((char *) src0->data + i00*nb00 + i01*nb01 + i02*nb02 + i03*nb03);

                                dst_ptr[id] = *src0_ptr;
                                id++;
                            }
                        }
                        id += ne00 * (ne01 - ir1);
                    }
                }
            } else if (dst->type == GGML_TYPE_F16) {
                size_t id = 0;
                ggml_fp16_t * dst_ptr = (ggml_fp16_t *) dst->data;

                for (int i03 = 0; i03 < ne03; i03++) {
                    for (int i02 = 0; i02 < ne02; i02++) {
                        id += ne00 * ir0;
                        for (int i01 = ir0; i01 < ir1; i01++) {
                            for (int i00 = 0; i00 < ne00; i00++) {
                                const float * src0_ptr = (float *) ((char *) src0->data + i00*nb00 + i01*nb01 + i02*nb02 + i03*nb03);

                                dst_ptr[id] = GGML_FP32_TO_FP16(*src0_ptr);
                                id++;
                            }
                        }
                        id += ne00 * (ne01 - ir1);
                    }
                }
            } else {
                GGML_ASSERT(false); // TODO: implement
            }
        }

        return;
    }

    // dst counters

    int64_t i10 = 0;
    int64_t i11 = 0;
    int64_t i12 = 0;
    int64_t i13 = 0;

    if (dst->type == GGML_TYPE_F32) {
        for (int64_t i03 = 0; i03 < ne03; i03++) {
            for (int64_t i02 = 0; i02 < ne02; i02++) {
                i10 += ne00 * ir0;
                while (i10 >= ne0) {
                    i10 -= ne0;
                    if (++i11 == ne1) {
                        i11 = 0;
                        if (++i12 == ne2) {
                            i12 = 0;
                            if (++i13 == ne3) {
                                i13 = 0;
                            }
                        }
                    }
                }
                for (int64_t i01 = ir0; i01 < ir1; i01++) {
                    for (int64_t i00 = 0; i00 < ne00; i00++) {
                        const char * src0_ptr = ((char *) src0->data + i00*nb00 + i01*nb01 + i02*nb02 + i03*nb03);
                              char * dst_ptr  = ((char *)  dst->data + i10*nb0  + i11*nb1  + i12*nb2  + i13*nb3);

                        memcpy(dst_ptr, src0_ptr, sizeof(float));

                        if (++i10 == ne0) {
                            i10 = 0;
                            if (++i11 == ne1) {
                                i11 = 0;
                                if (++i12 == ne2) {
                                    i12 = 0;
                                    if (++i13 == ne3) {
                                        i13 = 0;
                                    }
                                }
                            }
                        }
                    }
                }
                i10 += ne00 * (ne01 - ir1);
                while (i10 >= ne0) {
                    i10 -= ne0;
                    if (++i11 == ne1) {
                        i11 = 0;
                        if (++i12 == ne2) {
                            i12 = 0;
                            if (++i13 == ne3) {
                                i13 = 0;
                            }
                        }
                    }
                }
            }
        }
    } else if (dst->type == GGML_TYPE_F16) {
        for (int64_t i03 = 0; i03 < ne03; i03++) {
            for (int64_t i02 = 0; i02 < ne02; i02++) {
                i10 += ne00 * ir0;
                while (i10 >= ne0) {
                    i10 -= ne0;
                    if (++i11 == ne1) {
                        i11 = 0;
                        if (++i12 == ne2) {
                            i12 = 0;
                            if (++i13 == ne3) {
                                i13 = 0;
                            }
                        }
                    }
                }
                for (int64_t i01 = ir0; i01 < ir1; i01++) {
                    for (int64_t i00 = 0; i00 < ne00; i00++) {
                        const char * src0_ptr = ((char *) src0->data + i00*nb00 + i01*nb01 + i02*nb02 + i03*nb03);
                              char * dst_ptr  = ((char *)  dst->data + i10*nb0  + i11*nb1  + i12*nb2  + i13*nb3);

                        *(ggml_fp16_t *) dst_ptr = GGML_FP32_TO_FP16(*(const float *) src0_ptr);

                        if (++i10 == ne0) {
                            i10 = 0;
                            if (++i11 == ne1) {
                                i11 = 0;
                                if (++i12 == ne2) {
                                    i12 = 0;
                                    if (++i13 == ne3) {
                                        i13 = 0;
                                    }
                                }
                            }
                        }
                    }
                }
                i10 += ne00 * (ne01 - ir1);
                while (i10 >= ne0) {
                    i10 -= ne0;
                    if (++i11 == ne1) {
                        i11 = 0;
                        if (++i12 == ne2) {
                            i12 = 0;
                            if (++i13 == ne3) {
                                i13 = 0;
                            }
                        }
                    }
                }
            }
        }
    } else {
        GGML_ASSERT(false); // TODO: implement
    }
}

static void ggml_compute_forward_dup(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    if (ggml_is_contiguous(src0) && ggml_is_contiguous(dst) && src0->type == dst->type) {
        ggml_compute_forward_dup_same_cont(params, src0, dst);
        return;
    }
    switch (src0->type) {
        case GGML_TYPE_F16:
            {
                ggml_compute_forward_dup_f16(params, src0, dst);
            } break;
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_dup_f32(params, src0, dst);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_add

static void ggml_compute_forward_add_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    GGML_ASSERT(ggml_are_same_shape(src0, src1) && ggml_are_same_shape(src0, dst));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int ith = params->ith;
    const int nth = params->nth;

    const int nr  = ggml_nrows(src0);

    GGML_TENSOR_BINARY_OP_LOCALS;

    GGML_ASSERT( nb0 == sizeof(float));
    GGML_ASSERT(nb00 == sizeof(float));

    // rows per thread
    const int dr = (nr + nth - 1)/nth;

    // row range for this thread
    const int ir0 = dr*ith;
    const int ir1 = MIN(ir0 + dr, nr);

    if (nb10 == sizeof(float)) {
        for (int ir = ir0; ir < ir1; ++ir) {
            // src0, src1 and dst are same shape => same indices
            const int i3 = ir/(ne2*ne1);
            const int i2 = (ir - i3*ne2*ne1)/ne1;
            const int i1 = (ir - i3*ne2*ne1 - i2*ne1);


#ifdef GGML_USE_ACCELERATE
            vDSP_vadd(
                    (float *) ((char *) src0->data + i3*nb03 + i2*nb02 + i1*nb01), 1,
                    (float *) ((char *) src1->data + i3*nb13 + i2*nb12 + i1*nb11), 1,
                    (float *) ((char *) dst->data  + i3*nb3  + i2*nb2  + i1*nb1 ), 1,
                    ne0);
#else
            ggml_vec_add_f32(ne0,
                    (float *) ((char *) dst->data  + i3*nb3  + i2*nb2  + i1*nb1 ),
                    (float *) ((char *) src0->data + i3*nb03 + i2*nb02 + i1*nb01),
                    (float *) ((char *) src1->data + i3*nb13 + i2*nb12 + i1*nb11));
#endif
                // }
            // }
        }
    } else {
        // src1 is not contiguous
        for (int ir = ir0; ir < ir1; ++ir) {
            // src0, src1 and dst are same shape => same indices
            const int i3 = ir/(ne2*ne1);
            const int i2 = (ir - i3*ne2*ne1)/ne1;
            const int i1 = (ir - i3*ne2*ne1 - i2*ne1);

            float * dst_ptr  = (float *) ((char *) dst->data  + i3*nb3  + i2*nb2  + i1*nb1 );
            float * src0_ptr = (float *) ((char *) src0->data + i3*nb03 + i2*nb02 + i1*nb01);
            for (int i0 = 0; i0 < ne0; i0++) {
                float * src1_ptr = (float *) ((char *) src1->data + i3*nb13 + i2*nb12 + i1*nb11 + i0*nb10);

                dst_ptr[i0] = src0_ptr[i0] + *src1_ptr;
            }
        }
    }
}

static void ggml_compute_forward_add_f16_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    GGML_ASSERT(ggml_are_same_shape(src0, src1) && ggml_are_same_shape(src0, dst));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int ith = params->ith;
    const int nth = params->nth;

    const int nr  = ggml_nrows(src0);

    GGML_TENSOR_BINARY_OP_LOCALS;

    GGML_ASSERT(src0->type == GGML_TYPE_F16);
    GGML_ASSERT(src1->type == GGML_TYPE_F32);
    GGML_ASSERT(dst->type  == GGML_TYPE_F16);

    GGML_ASSERT( nb0 == sizeof(ggml_fp16_t));
    GGML_ASSERT(nb00 == sizeof(ggml_fp16_t));

    // rows per thread
    const int dr = (nr + nth - 1)/nth;

    // row range for this thread
    const int ir0 = dr*ith;
    const int ir1 = MIN(ir0 + dr, nr);

    if (nb10 == sizeof(float)) {
        for (int ir = ir0; ir < ir1; ++ir) {
            // src0, src1 and dst are same shape => same indices
            const int i3 = ir/(ne2*ne1);
            const int i2 = (ir - i3*ne2*ne1)/ne1;
            const int i1 = (ir - i3*ne2*ne1 - i2*ne1);

            ggml_fp16_t * dst_ptr  = (ggml_fp16_t *) ((char *) dst->data  + i3*nb3  + i2*nb2  + i1*nb1);
            ggml_fp16_t * src0_ptr = (ggml_fp16_t *) ((char *) src0->data + i3*nb03 + i2*nb02 + i1*nb01);
            float *       src1_ptr = (float *)       ((char *) src1->data + i3*nb13 + i2*nb12 + i1*nb11);

            for (int i = 0; i < ne0; i++) {
                dst_ptr[i] = GGML_FP32_TO_FP16(GGML_FP16_TO_FP32(src0_ptr[i]) + src1_ptr[i]);
            }
        }
    }
    else {
        // src1 is not contiguous
        GGML_ASSERT(false);
    }
}

static void ggml_compute_forward_add_f16_f16(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    GGML_ASSERT(ggml_are_same_shape(src0, src1) && ggml_are_same_shape(src0, dst));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int ith = params->ith;
    const int nth = params->nth;

    const int nr  = ggml_nrows(src0);

    GGML_TENSOR_BINARY_OP_LOCALS;

    GGML_ASSERT(src0->type == GGML_TYPE_F16);
    GGML_ASSERT(src1->type == GGML_TYPE_F16);
    GGML_ASSERT(dst->type  == GGML_TYPE_F16);

    GGML_ASSERT( nb0 == sizeof(ggml_fp16_t));
    GGML_ASSERT(nb00 == sizeof(ggml_fp16_t));

    // rows per thread
    const int dr = (nr + nth - 1)/nth;

    // row range for this thread
    const int ir0 = dr*ith;
    const int ir1 = MIN(ir0 + dr, nr);

    if (nb10 == sizeof(ggml_fp16_t)) {
        for (int ir = ir0; ir < ir1; ++ir) {
            // src0, src1 and dst are same shape => same indices
            const int i3 = ir/(ne2*ne1);
            const int i2 = (ir - i3*ne2*ne1)/ne1;
            const int i1 = (ir - i3*ne2*ne1 - i2*ne1);

            ggml_fp16_t * dst_ptr  = (ggml_fp16_t *) ((char *) dst->data  + i3*nb3  + i2*nb2  + i1*nb1);
            ggml_fp16_t * src0_ptr = (ggml_fp16_t *) ((char *) src0->data + i3*nb03 + i2*nb02 + i1*nb01);
            ggml_fp16_t * src1_ptr = (ggml_fp16_t *) ((char *) src1->data + i3*nb13 + i2*nb12 + i1*nb11);

            for (int i = 0; i < ne0; i++) {
                dst_ptr[i] = GGML_FP32_TO_FP16(GGML_FP16_TO_FP32(src0_ptr[i]) + GGML_FP16_TO_FP32(src1_ptr[i]));
            }
        }
    }
    else {
        // src1 is not contiguous
        GGML_ASSERT(false);
    }
}

static void ggml_compute_forward_add_q_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    GGML_ASSERT(ggml_are_same_shape(src0, src1) && ggml_are_same_shape(src0, dst));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int nr  = ggml_nrows(src0);

    GGML_TENSOR_BINARY_OP_LOCALS;

    const int ith = params->ith;
    const int nth = params->nth;

    const enum ggml_type type = src0->type;
    ggml_to_float_t const dequantize_row_q = type_traits[type].to_float;
    ggml_from_float_t const quantize_row_q = type_traits[type].from_float;

    // we don't support permuted src0 or src1
    GGML_ASSERT(nb00 == GGML_TYPE_SIZE[type]);
    GGML_ASSERT(nb10 == sizeof(float));

    // dst cannot be transposed or permuted
    GGML_ASSERT(nb0 <= nb1);
    GGML_ASSERT(nb1 <= nb2);
    GGML_ASSERT(nb2 <= nb3);

    GGML_ASSERT(ggml_is_quantized(src0->type));
    GGML_ASSERT(dst->type == src0->type);
    GGML_ASSERT(src1->type == GGML_TYPE_F32);

    // rows per thread
    const int dr = (nr + nth - 1)/nth;

    // row range for this thread
    const int ir0 = dr*ith;
    const int ir1 = MIN(ir0 + dr, nr);

    float * wdata = (float *) params->wdata + (ne00 + CACHE_LINE_SIZE_F32) * ith;

    for (int ir = ir0; ir < ir1; ++ir) {
        // src0 indices
        const int i03 = ir/(ne02*ne01);
        const int i02 = (ir - i03*ne02*ne01)/ne01;
        const int i01 = (ir - i03*ne02*ne01 - i02*ne01);

        // src1 and dst are same shape as src0 => same indices
        const int i13 = i03;
        const int i12 = i02;
        const int i11 = i01;

        const int i3 = i03;
        const int i2 = i02;
        const int i1 = i01;

        void  * src0_row = (void *) ((char *) src0->data + (i01*nb01 + i02*nb02 + i03*nb03));
        float * src1_row = (float *)((char *) src1->data + (i11*nb11 + i12*nb12 + i13*nb13));
        void  * dst_row  = (void *) ((char *)  dst->data + ( i1*nb1  +  i2*nb2  +  i3*nb3));

        assert(ne00 % 32 == 0);

        // unquantize row from src0 to temp buffer
        dequantize_row_q(src0_row, wdata, ne00);
        // add src1
        ggml_vec_acc_f32(ne00, wdata, src1_row);
        // quantize row to dst
        quantize_row_q(wdata, dst_row, ne00);
    }
}

static void ggml_compute_forward_add(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_add_f32(params, src0, src1, dst);
            } break;
        case GGML_TYPE_F16:
            {
                if (src1->type == GGML_TYPE_F16) {
                    ggml_compute_forward_add_f16_f16(params, src0, src1, dst);
                }
                else if (src1->type == GGML_TYPE_F32) {
                    ggml_compute_forward_add_f16_f32(params, src0, src1, dst);
                }
                else {
                    GGML_ASSERT(false);
                }
            } break;
        case GGML_TYPE_Q4_0:
        case GGML_TYPE_Q4_1:
        case GGML_TYPE_Q5_0:
        case GGML_TYPE_Q5_1:
        case GGML_TYPE_Q8_0:
        case GGML_TYPE_Q2_K:
        case GGML_TYPE_Q3_K:
        case GGML_TYPE_Q4_K:
        case GGML_TYPE_Q5_K:
        case GGML_TYPE_Q6_K:
            {
                ggml_compute_forward_add_q_f32(params, src0, src1, dst);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_add1

static void ggml_compute_forward_add1_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    GGML_ASSERT(ggml_are_same_shape(src0, dst));
    GGML_ASSERT(ggml_is_scalar(src1));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int ith = params->ith;
    const int nth = params->nth;

    const int nr  = ggml_nrows(src0);

    GGML_TENSOR_UNARY_OP_LOCALS;

    GGML_ASSERT( nb0 == sizeof(float));
    GGML_ASSERT(nb00 == sizeof(float));

    // rows per thread
    const int dr = (nr + nth - 1)/nth;

    // row range for this thread
    const int ir0 = dr*ith;
    const int ir1 = MIN(ir0 + dr, nr);

    for (int ir = ir0; ir < ir1; ++ir) {
        // src0 and dst are same shape => same indices
        const int i3 = ir/(ne2*ne1);
        const int i2 = (ir - i3*ne2*ne1)/ne1;
        const int i1 = (ir - i3*ne2*ne1 - i2*ne1);

#ifdef GGML_USE_ACCELERATE
        UNUSED(ggml_vec_add1_f32);

        vDSP_vadd(
                (float *) ((char *) src0->data + i3*nb03 + i2*nb02 + i1*nb01), 1,
                (float *) ((char *) src1->data), 0,
                (float *) ((char *) dst->data  + i3*nb3  + i2*nb2  + i1*nb1 ), 1,
                ne0);
#else
        ggml_vec_add1_f32(ne0,
                (float *) ((char *) dst->data  + i3*nb3  + i2*nb2  + i1*nb1 ),
                (float *) ((char *) src0->data + i3*nb03 + i2*nb02 + i1*nb01),
               *(float *) src1->data);
#endif
    }
}

static void ggml_compute_forward_add1_f16_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    GGML_ASSERT(ggml_are_same_shape(src0, dst));
    GGML_ASSERT(ggml_is_scalar(src1));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    // scalar to add
    const float v = *(float *) src1->data;

    const int ith = params->ith;
    const int nth = params->nth;

    const int nr  = ggml_nrows(src0);

    GGML_TENSOR_UNARY_OP_LOCALS;

    GGML_ASSERT(src0->type == GGML_TYPE_F16);
    GGML_ASSERT(src1->type == GGML_TYPE_F32);
    GGML_ASSERT(dst->type  == GGML_TYPE_F16);

    GGML_ASSERT( nb0 == sizeof(ggml_fp16_t));
    GGML_ASSERT(nb00 == sizeof(ggml_fp16_t));

    // rows per thread
    const int dr = (nr + nth - 1)/nth;

    // row range for this thread
    const int ir0 = dr*ith;
    const int ir1 = MIN(ir0 + dr, nr);

    for (int ir = ir0; ir < ir1; ++ir) {
        // src0 and dst are same shape => same indices
        const int i3 = ir/(ne2*ne1);
        const int i2 = (ir - i3*ne2*ne1)/ne1;
        const int i1 = (ir - i3*ne2*ne1 - i2*ne1);

        ggml_fp16_t * dst_ptr  = (ggml_fp16_t *) ((char *) dst->data  + i3*nb3  + i2*nb2  + i1*nb1 );
        ggml_fp16_t * src0_ptr = (ggml_fp16_t *) ((char *) src0->data + i3*nb03 + i2*nb02 + i1*nb01);
        for (int i = 0; i < ne0; i++) {
            dst_ptr[i] = GGML_FP32_TO_FP16(GGML_FP16_TO_FP32(src0_ptr[i]) + v);
        }
    }
}

static void ggml_compute_forward_add1_f16_f16(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    GGML_ASSERT(ggml_are_same_shape(src0, dst));
    GGML_ASSERT(ggml_is_scalar(src1));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    // scalar to add
    const float v = GGML_FP16_TO_FP32(*(ggml_fp16_t *) src1->data);

    const int ith = params->ith;
    const int nth = params->nth;

    const int nr  = ggml_nrows(src0);

    GGML_TENSOR_UNARY_OP_LOCALS;

    GGML_ASSERT(src0->type == GGML_TYPE_F16);
    GGML_ASSERT(src1->type == GGML_TYPE_F16);
    GGML_ASSERT(dst->type  == GGML_TYPE_F16);

    GGML_ASSERT( nb0 == sizeof(ggml_fp16_t));
    GGML_ASSERT(nb00 == sizeof(ggml_fp16_t));

    // rows per thread
    const int dr = (nr + nth - 1)/nth;

    // row range for this thread
    const int ir0 = dr*ith;
    const int ir1 = MIN(ir0 + dr, nr);

    for (int ir = ir0; ir < ir1; ++ir) {
        // src0 and dst are same shape => same indices
        const int i3 = ir/(ne2*ne1);
        const int i2 = (ir - i3*ne2*ne1)/ne1;
        const int i1 = (ir - i3*ne2*ne1 - i2*ne1);

        ggml_fp16_t * dst_ptr  = (ggml_fp16_t *) ((char *) dst->data  + i3*nb3  + i2*nb2  + i1*nb1 );
        ggml_fp16_t * src0_ptr = (ggml_fp16_t *) ((char *) src0->data + i3*nb03 + i2*nb02 + i1*nb01);
        for (int i = 0; i < ne0; i++) {
            dst_ptr[i] = GGML_FP32_TO_FP16(GGML_FP16_TO_FP32(src0_ptr[i]) + v);
        }
    }
}

static void ggml_compute_forward_add1_q_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    GGML_ASSERT(ggml_are_same_shape(src0, dst));
    GGML_ASSERT(ggml_is_scalar(src1));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    // scalar to add
    const float v = *(float *) src1->data;

    const int ith = params->ith;
    const int nth = params->nth;

    const int nr  = ggml_nrows(src0);

    GGML_TENSOR_UNARY_OP_LOCALS;

    const enum ggml_type type = src0->type;
    ggml_to_float_t const dequantize_row_q = type_traits[type].to_float;
    ggml_from_float_t const quantize_row_q = type_traits[type].from_float;

    // we don't support permuted src0
    GGML_ASSERT(nb00 == GGML_TYPE_SIZE[type]);

    // dst cannot be transposed or permuted
    GGML_ASSERT(nb0 <= nb1);
    GGML_ASSERT(nb1 <= nb2);
    GGML_ASSERT(nb2 <= nb3);

    GGML_ASSERT(ggml_is_quantized(src0->type));
    GGML_ASSERT(dst->type == src0->type);
    GGML_ASSERT(src1->type == GGML_TYPE_F32);

    // rows per thread
    const int dr = (nr + nth - 1)/nth;

    // row range for this thread
    const int ir0 = dr*ith;
    const int ir1 = MIN(ir0 + dr, nr);

    float * wdata = (float *) params->wdata + (ne0 + CACHE_LINE_SIZE_F32) * ith;

    for (int ir = ir0; ir < ir1; ++ir) {
        // src0 and dst are same shape => same indices
        const int i3 = ir/(ne2*ne1);
        const int i2 = (ir - i3*ne2*ne1)/ne1;
        const int i1 = (ir - i3*ne2*ne1 - i2*ne1);

        void  * src0_row = (void *) ((char *) src0->data + (i1*nb01 + i2*nb02 + i3*nb03));
        void  * dst_row  = (void *) ((char *)  dst->data + (i1*nb1  + i2*nb2  + i3*nb0 ));

        assert(ne0 % 32 == 0);

        // unquantize row from src0 to temp buffer
        dequantize_row_q(src0_row, wdata, ne0);
        // add src1
        ggml_vec_acc1_f32(ne0, wdata, v);
        // quantize row to dst
        quantize_row_q(wdata, dst_row, ne0);
    }
}

static void ggml_compute_forward_add1(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_add1_f32(params, src0, src1, dst);
            } break;
        case GGML_TYPE_F16:
            {
                if (src1->type == GGML_TYPE_F16) {
                    ggml_compute_forward_add1_f16_f16(params, src0, src1, dst);
                }
                else if (src1->type == GGML_TYPE_F32) {
                    ggml_compute_forward_add1_f16_f32(params, src0, src1, dst);
                }
                else {
                    GGML_ASSERT(false);
                }
            } break;
        case GGML_TYPE_Q4_0:
        case GGML_TYPE_Q4_1:
        case GGML_TYPE_Q5_0:
        case GGML_TYPE_Q5_1:
        case GGML_TYPE_Q8_0:
        case GGML_TYPE_Q8_1:
        case GGML_TYPE_Q2_K:
        case GGML_TYPE_Q3_K:
        case GGML_TYPE_Q4_K:
        case GGML_TYPE_Q5_K:
        case GGML_TYPE_Q6_K:
            {
                ggml_compute_forward_add1_q_f32(params, src0, src1, dst);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}


// ggml_compute_forward_acc

static void ggml_compute_forward_acc_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        const struct ggml_tensor * opt0,
        struct ggml_tensor * dst) {
    GGML_ASSERT(ggml_are_same_shape(src0, dst));
    GGML_ASSERT(ggml_is_contiguous(dst) && ggml_is_contiguous(src0));

    GGML_ASSERT(opt0->type == GGML_TYPE_I32);
    GGML_ASSERT(ggml_nelements(opt0) == 5);

    // view src0 and dst with these strides and data offset inbytes during acc
    // nb0 is implicitely element_size because src0 and dst are contiguous
    size_t nb1     = ((int32_t *) opt0->data)[0];
    size_t nb2     = ((int32_t *) opt0->data)[1];
    size_t nb3     = ((int32_t *) opt0->data)[2];
    size_t offset  = ((int32_t *) opt0->data)[3];
    bool   inplace = (bool) ((int32_t *) opt0->data)[4];

    if (!inplace && (params->type == GGML_TASK_INIT)) {
        // memcpy needs to be synchronized across threads to avoid race conditions.
        // => do it in INIT phase
        memcpy(
            ((char *)  dst->data),
            ((char *) src0->data),
            ggml_nbytes(dst));
    }

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int ith = params->ith;
    const int nth = params->nth;

    const int nr = ggml_nrows(src1);
    const int nc = src1->ne[0];

    GGML_TENSOR_LOCALS(int64_t, ne1, src1, ne);
    GGML_TENSOR_LOCALS(size_t,  nb1, src1, nb);

    // src0 and dst as viewed during acc
    const size_t nb0 = ggml_element_size(src0);

    const size_t nb00 = nb0;
    const size_t nb01 = nb1;
    const size_t nb02 = nb2;
    const size_t nb03 = nb3;

    GGML_ASSERT(offset + (ne10 == 0 ? 0 : ne10-1)*nb0  + (ne11 == 0 ? 0 : ne11-1)*nb1  + (ne12 == 0 ? 0 : ne12-1)*nb2  + (ne13 == 0 ? 0 : ne13-1)*nb3  < ggml_nbytes(dst));
    GGML_ASSERT(offset + (ne10 == 0 ? 0 : ne10-1)*nb00 + (ne11 == 0 ? 0 : ne11-1)*nb01 + (ne12 == 0 ? 0 : ne12-1)*nb02 + (ne13 == 0 ? 0 : ne13-1)*nb03 < ggml_nbytes(src0));

    GGML_ASSERT(nb10 == sizeof(float));

    // rows per thread
    const int dr = (nr + nth - 1)/nth;

    // row range for this thread
    const int ir0 = dr*ith;
    const int ir1 = MIN(ir0 + dr, nr);

    for (int ir = ir0; ir < ir1; ++ir) {
        // src0 and dst are viewed with shape of src1 and offset
        // => same indices
        const int i3 = ir/(ne12*ne11);
        const int i2 = (ir - i3*ne12*ne11)/ne11;
        const int i1 = (ir - i3*ne12*ne11 - i2*ne11);

#ifdef GGML_USE_ACCELERATE
        vDSP_vadd(
                (float *) ((char *) src0->data + i3*nb03 + i2*nb02 + i1*nb01 + offset), 1,
                (float *) ((char *) src1->data + i3*nb13 + i2*nb12 + i1*nb11), 1,
                (float *) ((char *) dst->data  + i3*nb3  + i2*nb2  + i1*nb1  + offset), 1, nc);
#else
        ggml_vec_add_f32(nc,
                (float *) ((char *)  dst->data + i3*nb3  + i2*nb2  + i1*nb1  + offset),
                (float *) ((char *) src0->data + i3*nb03 + i2*nb02 + i1*nb01 + offset),
                (float *) ((char *) src1->data + i3*nb13 + i2*nb12 + i1*nb11));
#endif
    }
}

static void ggml_compute_forward_acc(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        const struct ggml_tensor * opt0,
        struct ggml_tensor * dst) {

    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_acc_f32(params, src0, src1, opt0, dst);
            } break;
        case GGML_TYPE_F16:
        case GGML_TYPE_Q4_0:
        case GGML_TYPE_Q4_1:
        case GGML_TYPE_Q5_0:
        case GGML_TYPE_Q5_1:
        case GGML_TYPE_Q8_0:
        case GGML_TYPE_Q8_1:
        case GGML_TYPE_Q2_K:
        case GGML_TYPE_Q3_K:
        case GGML_TYPE_Q4_K:
        case GGML_TYPE_Q5_K:
        case GGML_TYPE_Q6_K:
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_sub

static void ggml_compute_forward_sub_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    assert(params->ith == 0);
    assert(ggml_are_same_shape(src0, src1) && ggml_are_same_shape(src0, dst));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int nr  = ggml_nrows(src0);

    GGML_TENSOR_BINARY_OP_LOCALS;

    GGML_ASSERT( nb0 == sizeof(float));
    GGML_ASSERT(nb00 == sizeof(float));

    if (nb10 == sizeof(float)) {
        for (int ir = 0; ir < nr; ++ir) {
            // src0, src1 and dst are same shape => same indices
            const int i3 = ir/(ne2*ne1);
            const int i2 = (ir - i3*ne2*ne1)/ne1;
            const int i1 = (ir - i3*ne2*ne1 - i2*ne1);


#ifdef GGML_USE_ACCELERATE
            vDSP_vsub(
                    (float *) ((char *) src1->data + i3*nb13 + i2*nb12 + i1*nb11), 1,
                    (float *) ((char *) src0->data + i3*nb03 + i2*nb02 + i1*nb01), 1,
                    (float *) ((char *) dst->data  + i3*nb3  + i2*nb2  + i1*nb1 ), 1,
                    ne0);
#else
            ggml_vec_sub_f32(ne0,
                    (float *) ((char *) dst->data  + i3*nb3  + i2*nb2  + i1*nb1 ),
                    (float *) ((char *) src0->data + i3*nb03 + i2*nb02 + i1*nb01),
                    (float *) ((char *) src1->data + i3*nb13 + i2*nb12 + i1*nb11));
#endif
                // }
            // }
        }
    } else {
        // src1 is not contiguous
        for (int ir = 0; ir < nr; ++ir) {
            // src0, src1 and dst are same shape => same indices
            const int i3 = ir/(ne2*ne1);
            const int i2 = (ir - i3*ne2*ne1)/ne1;
            const int i1 = (ir - i3*ne2*ne1 - i2*ne1);

            float * dst_ptr  = (float *) ((char *) dst->data  + i3*nb3  + i2*nb2  + i1*nb1 );
            float * src0_ptr = (float *) ((char *) src0->data + i3*nb03 + i2*nb02 + i1*nb01);
            for (int i0 = 0; i0 < ne0; i0++) {
                float * src1_ptr = (float *) ((char *) src1->data + i3*nb13 + i2*nb12 + i1*nb11 + i0*nb10);

                dst_ptr[i0] = src0_ptr[i0] - *src1_ptr;
            }
        }
    }
}

static void ggml_compute_forward_sub(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_sub_f32(params, src0, src1, dst);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_mul

static void ggml_compute_forward_mul_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    GGML_ASSERT(ggml_can_repeat_rows(src1, src0) && ggml_are_same_shape(src0, dst));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }
    const int ith = params->ith;
    const int nth = params->nth;

#ifdef GGML_USE_CLBLAST
    if (src1->backend == GGML_BACKEND_GPU) {
        if (ith == 0) {
            ggml_cl_mul(src0, src1, dst);
        }
        return;
    }
#endif

    const int64_t nr = ggml_nrows(src0);

    GGML_TENSOR_BINARY_OP_LOCALS;

    GGML_ASSERT( nb0 == sizeof(float));
    GGML_ASSERT(nb00 == sizeof(float));
    GGML_ASSERT(ne00 == ne10);

    if (nb10 == sizeof(float)) {
        for (int64_t ir = ith; ir < nr; ir += nth) {
            // src0 and dst are same shape => same indices
            const int64_t i03 = ir/(ne02*ne01);
            const int64_t i02 = (ir - i03*ne02*ne01)/ne01;
            const int64_t i01 = (ir - i03*ne02*ne01 - i02*ne01);

            const int64_t i13 = i03 % ne13;
            const int64_t i12 = i02 % ne12;
            const int64_t i11 = i01 % ne11;

            float * dst_ptr  = (float *) ((char *) dst->data  + i03*nb3  + i02*nb2  + i01*nb1 );
            float * src0_ptr = (float *) ((char *) src0->data + i03*nb03 + i02*nb02 + i01*nb01);
            float * src1_ptr = (float *) ((char *) src1->data + i13*nb13 + i12*nb12 + i11*nb11);

#ifdef GGML_USE_ACCELERATE
            UNUSED(ggml_vec_mul_f32);

            vDSP_vmul( src0_ptr, 1, src1_ptr, 1, dst_ptr,  1, ne00);
#else
            ggml_vec_mul_f32(ne00, dst_ptr, src0_ptr, src1_ptr);
#endif
                // }
            // }
        }
    } else {
        // src1 is not contiguous
        for (int64_t ir = ith; ir < nr; ir += nth) {
            // src0 and dst are same shape => same indices
            // src1 is broadcastable across src0 and dst in i1, i2, i3
            const int64_t i03 = ir/(ne02*ne01);
            const int64_t i02 = (ir - i03*ne02*ne01)/ne01;
            const int64_t i01 = (ir - i03*ne02*ne01 - i02*ne01);

            const int64_t i13 = i03 % ne13;
            const int64_t i12 = i02 % ne12;
            const int64_t i11 = i01 % ne11;

            float * dst_ptr  = (float *) ((char *) dst->data  + i03*nb3  + i02*nb2  + i01*nb1 );
            float * src0_ptr = (float *) ((char *) src0->data + i03*nb03 + i02*nb02 + i01*nb01);

            for (int64_t i0 = 0; i0 < ne00; i0++) {
                float * src1_ptr = (float *) ((char *) src1->data + i13*nb13 + i12*nb12 + i11*nb11 + i0*nb10);

                dst_ptr[i0] = src0_ptr[i0] * (*src1_ptr);
            }
        }
    }
}

static void ggml_compute_forward_mul(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_mul_f32(params, src0, src1, dst);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_div

static void ggml_compute_forward_div_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    assert(params->ith == 0);
    assert(ggml_are_same_shape(src0, src1) && ggml_are_same_shape(src0, dst));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int nr  = ggml_nrows(src0);

    GGML_TENSOR_BINARY_OP_LOCALS;

    GGML_ASSERT( nb0 == sizeof(float));
    GGML_ASSERT(nb00 == sizeof(float));

    if (nb10 == sizeof(float)) {
        for (int ir = 0; ir < nr; ++ir) {
            // src0, src1 and dst are same shape => same indices
            const int i3 = ir/(ne2*ne1);
            const int i2 = (ir - i3*ne2*ne1)/ne1;
            const int i1 = (ir - i3*ne2*ne1 - i2*ne1);


#ifdef GGML_USE_ACCELERATE
            vDSP_vdiv(
                    (float *) ((char *) src1->data + i3*nb13 + i2*nb12 + i1*nb11), 1,
                    (float *) ((char *) src0->data + i3*nb03 + i2*nb02 + i1*nb01), 1,
                    (float *) ((char *) dst->data  + i3*nb3  + i2*nb2  + i1*nb1 ), 1,
                    ne0);
#else
            ggml_vec_div_f32(ne0,
                    (float *) ((char *) dst->data  + i3*nb3  + i2*nb2  + i1*nb1 ),
                    (float *) ((char *) src0->data + i3*nb03 + i2*nb02 + i1*nb01),
                    (float *) ((char *) src1->data + i3*nb13 + i2*nb12 + i1*nb11));
#endif
                // }
            // }
        }
    } else {
        // src1 is not contiguous
        for (int ir = 0; ir < nr; ++ir) {
            // src0, src1 and dst are same shape => same indices
            const int i3 = ir/(ne2*ne1);
            const int i2 = (ir - i3*ne2*ne1)/ne1;
            const int i1 = (ir - i3*ne2*ne1 - i2*ne1);

            float * dst_ptr  = (float *) ((char *) dst->data  + i3*nb3  + i2*nb2  + i1*nb1 );
            float * src0_ptr = (float *) ((char *) src0->data + i3*nb03 + i2*nb02 + i1*nb01);
            for (int i0 = 0; i0 < ne0; i0++) {
                float * src1_ptr = (float *) ((char *) src1->data + i3*nb13 + i2*nb12 + i1*nb11 + i0*nb10);

                dst_ptr[i0] = src0_ptr[i0] / (*src1_ptr);
            }
        }
    }
}

static void ggml_compute_forward_div(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_div_f32(params, src0, src1, dst);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_sqr

static void ggml_compute_forward_sqr_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    assert(params->ith == 0);
    assert(ggml_are_same_shape(src0, dst));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int n     = ggml_nrows(src0);
    const int nc    = src0->ne[0];

    assert( dst->nb[0] == sizeof(float));
    assert(src0->nb[0] == sizeof(float));

    for (int i = 0; i < n; i++) {
        ggml_vec_sqr_f32(nc,
                (float *) ((char *) dst->data  + i*( dst->nb[1])),
                (float *) ((char *) src0->data + i*(src0->nb[1])));
    }
}

static void ggml_compute_forward_sqr(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_sqr_f32(params, src0, dst);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_sqrt

static void ggml_compute_forward_sqrt_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    assert(params->ith == 0);
    assert(ggml_are_same_shape(src0, dst));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int n  = ggml_nrows(src0);
    const int nc = src0->ne[0];

    assert( dst->nb[0] == sizeof(float));
    assert(src0->nb[0] == sizeof(float));

    for (int i = 0; i < n; i++) {
        ggml_vec_sqrt_f32(nc,
                (float *) ((char *) dst->data  + i*( dst->nb[1])),
                (float *) ((char *) src0->data + i*(src0->nb[1])));
    }
}

static void ggml_compute_forward_sqrt(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_sqrt_f32(params, src0, dst);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}


// ggml_compute_forward_log

static void ggml_compute_forward_log_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    GGML_ASSERT(params->ith == 0);
    GGML_ASSERT(ggml_are_same_shape(src0, dst));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int n  = ggml_nrows(src0);
    const int nc = src0->ne[0];

    GGML_ASSERT( dst->nb[0] == sizeof(float));
    GGML_ASSERT(src0->nb[0] == sizeof(float));

    for (int i = 0; i < n; i++) {
        ggml_vec_log_f32(nc,
                (float *) ((char *) dst->data  + i*( dst->nb[1])),
                (float *) ((char *) src0->data + i*(src0->nb[1])));
    }
}

static void ggml_compute_forward_log(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_log_f32(params, src0, dst);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_sum

static void ggml_compute_forward_sum_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    assert(params->ith == 0);
    assert(ggml_is_scalar(dst));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    assert(ggml_is_scalar(dst));
    assert(src0->nb[0] == sizeof(float));

    GGML_TENSOR_LOCALS(int64_t, ne0, src0, ne);
    GGML_TENSOR_LOCALS(size_t,  nb0, src0, nb);

    ggml_float sum     = 0;
    ggml_float row_sum = 0;

    for (int64_t i03 = 0; i03 < ne03; i03++) {
        for (int64_t i02 = 0; i02 < ne02; i02++) {
            for (int64_t i01 = 0; i01 < ne01; i01++) {
                ggml_vec_sum_ggf(ne00,
                        &row_sum,
                        (float *) ((char *) src0->data + i01*nb01 + i02*nb02 + i03*nb03));
                sum += row_sum;
            }
        }
    }
    ((float *) dst->data)[0] = sum;
}

static void ggml_compute_forward_sum(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_sum_f32(params, src0, dst);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_sum_rows

static void ggml_compute_forward_sum_rows_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    GGML_ASSERT(params->ith == 0);

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    GGML_ASSERT(src0->nb[0] == sizeof(float));
    GGML_ASSERT(dst->nb[0] == sizeof(float));

    GGML_TENSOR_UNARY_OP_LOCALS;

    GGML_ASSERT(ne0 == 1);
    GGML_ASSERT(ne1 == ne01);
    GGML_ASSERT(ne2 == ne02);
    GGML_ASSERT(ne3 == ne03);

    for (int64_t i3 = 0; i3 < ne03; i3++) {
        for (int64_t i2 = 0; i2 < ne02; i2++) {
            for (int64_t i1 = 0; i1 < ne01; i1++) {
                float* src_row = (float *) ((char *) src0->data + i1*nb01 + i2*nb02 + i3*nb03);
                float* dst_row = (float *) ((char *) dst->data  + i1*nb1  + i2*nb2  + i3*nb3);
                float row_sum = 0;
                ggml_vec_sum_f32(ne00, &row_sum, src_row);
                dst_row[0] = row_sum;
            }
        }
    }
}

static void ggml_compute_forward_sum_rows(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_sum_rows_f32(params, src0, dst);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_mean

static void ggml_compute_forward_mean_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    assert(params->ith == 0);

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    assert(src0->nb[0] == sizeof(float));

    GGML_TENSOR_UNARY_OP_LOCALS;

    assert(ne0 == 1);
    assert(ne1 == ne01);
    assert(ne2 == ne02);
    assert(ne3 == ne03);

    UNUSED(ne0);
    UNUSED(ne1);
    UNUSED(ne2);
    UNUSED(ne3);

    for (int64_t i03 = 0; i03 < ne03; i03++) {
        for (int64_t i02 = 0; i02 < ne02; i02++) {
            for (int64_t i01 = 0; i01 < ne01; i01++) {
                ggml_vec_sum_f32(ne00,
                        (float *) ((char *)  dst->data + i01*nb1  + i02*nb2  + i03*nb3),
                        (float *) ((char *) src0->data + i01*nb01 + i02*nb02 + i03*nb03));

                *(float *) ((char *) dst->data + i01*nb1 + i02*nb2 + i03*nb3) /= (float) ne00;
            }
        }
    }
}

static void ggml_compute_forward_mean(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_mean_f32(params, src0, dst);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_argmax

static void ggml_compute_forward_argmax_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    assert(params->ith == 0);

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    assert(src0->nb[0] == sizeof(float));
    assert(dst->nb[0] == sizeof(float));

    const int64_t ne00 = src0->ne[0];
    const int64_t ne01 = src0->ne[1];

    const size_t nb01 = src0->nb[1];
    const size_t nb0 = dst->nb[0];

    for (int64_t i1 = 0; i1 < ne01; i1++) {
        float * src = (float *) ((char *) src0->data + i1*nb01);
        int32_t * dst_ = (int32_t *) ((char *)  dst->data + i1*nb0);
        int v = 0;
        ggml_vec_argmax_f32(ne00, &v, src);
        dst_[0] = v;
    }
}

static void ggml_compute_forward_argmax(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_argmax_f32(params, src0, dst);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_repeat

static void ggml_compute_forward_repeat_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    GGML_ASSERT(params->ith == 0);
    GGML_ASSERT(ggml_can_repeat(src0, dst));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    GGML_TENSOR_UNARY_OP_LOCALS;

    // guaranteed to be an integer due to the check in ggml_can_repeat
    const int nr0 = (int)(ne0/ne00);
    const int nr1 = (int)(ne1/ne01);
    const int nr2 = (int)(ne2/ne02);
    const int nr3 = (int)(ne3/ne03);

    // TODO: support for transposed / permuted tensors
    GGML_ASSERT(nb0  == sizeof(float));
    GGML_ASSERT(nb00 == sizeof(float));

    // TODO: maybe this is not optimal?
    for                         (int i3 = 0; i3 < nr3;  i3++) {
        for                     (int k3 = 0; k3 < ne03; k3++) {
            for                 (int i2 = 0; i2 < nr2;  i2++) {
                for             (int k2 = 0; k2 < ne02; k2++) {
                    for         (int i1 = 0; i1 < nr1;  i1++) {
                        for     (int k1 = 0; k1 < ne01; k1++) {
                            for (int i0 = 0; i0 < nr0;  i0++) {
                                ggml_vec_cpy_f32(ne00,
                                        (float *) ((char *)  dst->data + (i3*ne03 + k3)*nb3  + (i2*ne02 + k2)*nb2  + (i1*ne01 + k1)*nb1  + (i0*ne00)*nb0),
                                        (float *) ((char *) src0->data + (          k3)*nb03 + (          k2)*nb02 + (          k1)*nb01));
                            }
                        }
                    }
                }
            }
        }
    }
}

static void ggml_compute_forward_repeat(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_repeat_f32(params, src0, dst);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_repeat_back

static void ggml_compute_forward_repeat_back_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    GGML_ASSERT(params->ith == 0);
    GGML_ASSERT(ggml_can_repeat(dst, src0));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    GGML_TENSOR_UNARY_OP_LOCALS;

    // guaranteed to be an integer due to the check in ggml_can_repeat
    const int nr0 = (int)(ne00/ne0);
    const int nr1 = (int)(ne01/ne1);
    const int nr2 = (int)(ne02/ne2);
    const int nr3 = (int)(ne03/ne3);

    // TODO: support for transposed / permuted tensors
    GGML_ASSERT(nb0  == sizeof(float));
    GGML_ASSERT(nb00 == sizeof(float));

    if (ggml_is_contiguous(dst)) {
        ggml_vec_set_f32(ne0*ne1*ne2*ne3, dst->data, 0);
    } else {
        for         (int k3 = 0; k3 < ne3; k3++) {
            for     (int k2 = 0; k2 < ne2; k2++) {
                for (int k1 = 0; k1 < ne1; k1++) {
                    ggml_vec_set_f32(ne0,
                        (float *) ((char *) dst->data + k1*nb1 + k2*nb2 + k3*nb3),
                        0);
                }
            }
        }
    }

    // TODO: maybe this is not optimal?
    for                         (int i3 = 0; i3 < nr3; i3++) {
        for                     (int k3 = 0; k3 < ne3; k3++) {
            for                 (int i2 = 0; i2 < nr2; i2++) {
                for             (int k2 = 0; k2 < ne2; k2++) {
                    for         (int i1 = 0; i1 < nr1; i1++) {
                        for     (int k1 = 0; k1 < ne1; k1++) {
                            for (int i0 = 0; i0 < nr0; i0++) {
                                ggml_vec_acc_f32(ne0,
                                        (float *) ((char *)  dst->data + (         k3)*nb3  + (         k2)*nb2  + (         k1)*nb1),
                                        (float *) ((char *) src0->data + (i3*ne3 + k3)*nb03 + (i2*ne2 + k2)*nb02 + (i1*ne1 + k1)*nb01 + (i0*ne0)*nb00));
                            }
                        }
                    }
                }
            }
        }
    }
}

static void ggml_compute_forward_repeat_back(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_repeat_back_f32(params, src0, dst);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_abs

static void ggml_compute_forward_abs_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    assert(params->ith == 0);
    assert(ggml_are_same_shape(src0, dst));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int n  = ggml_nrows(src0);
    const int nc = src0->ne[0];

    assert(dst->nb[0]  == sizeof(float));
    assert(src0->nb[0] == sizeof(float));

    for (int i = 0; i < n; i++) {
        ggml_vec_abs_f32(nc,
                (float *) ((char *) dst->data  + i*( dst->nb[1])),
                (float *) ((char *) src0->data + i*(src0->nb[1])));
    }
}

static void ggml_compute_forward_abs(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_abs_f32(params, src0, dst);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_sgn

static void ggml_compute_forward_sgn_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    assert(params->ith == 0);
    assert(ggml_are_same_shape(src0, dst));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int n  = ggml_nrows(src0);
    const int nc = src0->ne[0];

    assert(dst->nb[0]  == sizeof(float));
    assert(src0->nb[0] == sizeof(float));

    for (int i = 0; i < n; i++) {
        ggml_vec_sgn_f32(nc,
                (float *) ((char *) dst->data  + i*( dst->nb[1])),
                (float *) ((char *) src0->data + i*(src0->nb[1])));
    }
}

static void ggml_compute_forward_sgn(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_sgn_f32(params, src0, dst);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_neg

static void ggml_compute_forward_neg_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    assert(params->ith == 0);
    assert(ggml_are_same_shape(src0, dst));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int n  = ggml_nrows(src0);
    const int nc = src0->ne[0];

    assert(dst->nb[0]  == sizeof(float));
    assert(src0->nb[0] == sizeof(float));

    for (int i = 0; i < n; i++) {
        ggml_vec_neg_f32(nc,
                (float *) ((char *) dst->data  + i*( dst->nb[1])),
                (float *) ((char *) src0->data + i*(src0->nb[1])));
    }
}

static void ggml_compute_forward_neg(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_neg_f32(params, src0, dst);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_step

static void ggml_compute_forward_step_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    assert(params->ith == 0);
    assert(ggml_are_same_shape(src0, dst));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int n  = ggml_nrows(src0);
    const int nc = src0->ne[0];

    assert(dst->nb[0]  == sizeof(float));
    assert(src0->nb[0] == sizeof(float));

    for (int i = 0; i < n; i++) {
        ggml_vec_step_f32(nc,
                (float *) ((char *) dst->data  + i*( dst->nb[1])),
                (float *) ((char *) src0->data + i*(src0->nb[1])));
    }
}

static void ggml_compute_forward_step(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_step_f32(params, src0, dst);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_tanh

static void ggml_compute_forward_tanh_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    assert(params->ith == 0);
    assert(ggml_are_same_shape(src0, dst));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int n  = ggml_nrows(src0);
    const int nc = src0->ne[0];

    assert(dst->nb[0]  == sizeof(float));
    assert(src0->nb[0] == sizeof(float));

    for (int i = 0; i < n; i++) {
        ggml_vec_tanh_f32(nc,
                (float *) ((char *) dst->data  + i*( dst->nb[1])),
                (float *) ((char *) src0->data + i*(src0->nb[1])));
    }
}

static void ggml_compute_forward_tanh(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_tanh_f32(params, src0, dst);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_elu

static void ggml_compute_forward_elu_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    assert(params->ith == 0);
    assert(ggml_are_same_shape(src0, dst));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int n  = ggml_nrows(src0);
    const int nc = src0->ne[0];

    assert(dst->nb[0]  == sizeof(float));
    assert(src0->nb[0] == sizeof(float));

    for (int i = 0; i < n; i++) {
        ggml_vec_elu_f32(nc,
                (float *) ((char *) dst->data  + i*( dst->nb[1])),
                (float *) ((char *) src0->data + i*(src0->nb[1])));
    }
}

static void ggml_compute_forward_elu(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_elu_f32(params, src0, dst);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_relu

static void ggml_compute_forward_relu_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    assert(params->ith == 0);
    assert(ggml_are_same_shape(src0, dst));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int n  = ggml_nrows(src0);
    const int nc = src0->ne[0];

    assert(dst->nb[0]  == sizeof(float));
    assert(src0->nb[0] == sizeof(float));

    for (int i = 0; i < n; i++) {
        ggml_vec_relu_f32(nc,
                (float *) ((char *) dst->data  + i*( dst->nb[1])),
                (float *) ((char *) src0->data + i*(src0->nb[1])));
    }
}

static void ggml_compute_forward_relu(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_relu_f32(params, src0, dst);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_gelu

static void ggml_compute_forward_gelu_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    GGML_ASSERT(ggml_is_contiguous(src0));
    GGML_ASSERT(ggml_is_contiguous(dst));
    GGML_ASSERT(ggml_are_same_shape(src0, dst));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int ith = params->ith;
    const int nth = params->nth;

    const int nc = src0->ne[0];
    const int nr = ggml_nrows(src0);

    // rows per thread
    const int dr = (nr + nth - 1)/nth;

    // row range for this thread
    const int ir0 = dr*ith;
    const int ir1 = MIN(ir0 + dr, nr);

    for (int i1 = ir0; i1 < ir1; i1++) {
        ggml_vec_gelu_f32(nc,
                (float *) ((char *) dst->data  + i1*( dst->nb[1])),
                (float *) ((char *) src0->data + i1*(src0->nb[1])));

#ifndef NDEBUG
        for (int k = 0; k < nc; k++) {
            const float x = ((float *) ((char *) dst->data + i1*( dst->nb[1])))[k];
            UNUSED(x);
            assert(!isnan(x));
            assert(!isinf(x));
        }
#endif
    }
}

static void ggml_compute_forward_gelu(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_gelu_f32(params, src0, dst);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_gelu_quick

static void ggml_compute_forward_gelu_quick_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    GGML_ASSERT(ggml_is_contiguous(src0));
    GGML_ASSERT(ggml_is_contiguous(dst));
    GGML_ASSERT(ggml_are_same_shape(src0, dst));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int ith = params->ith;
    const int nth = params->nth;

    const int nc = src0->ne[0];
    const int nr = ggml_nrows(src0);

    // rows per thread
    const int dr = (nr + nth - 1)/nth;

    // row range for this thread
    const int ir0 = dr*ith;
    const int ir1 = MIN(ir0 + dr, nr);

    for (int i1 = ir0; i1 < ir1; i1++) {
        ggml_vec_gelu_quick_f32(nc,
                (float *) ((char *) dst->data  + i1*( dst->nb[1])),
                (float *) ((char *) src0->data + i1*(src0->nb[1])));

#ifndef NDEBUG
        for (int k = 0; k < nc; k++) {
            const float x = ((float *) ((char *) dst->data + i1*( dst->nb[1])))[k];
            UNUSED(x);
            assert(!isnan(x));
            assert(!isinf(x));
        }
#endif
    }
}

static void ggml_compute_forward_gelu_quick(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_gelu_quick_f32(params, src0, dst);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_silu

static void ggml_compute_forward_silu_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    GGML_ASSERT(ggml_is_contiguous(src0));
    GGML_ASSERT(ggml_is_contiguous(dst));
    GGML_ASSERT(ggml_are_same_shape(src0, dst));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int ith = params->ith;
    const int nth = params->nth;

    const int nc = src0->ne[0];
    const int nr = ggml_nrows(src0);

    // rows per thread
    const int dr = (nr + nth - 1)/nth;

    // row range for this thread
    const int ir0 = dr*ith;
    const int ir1 = MIN(ir0 + dr, nr);

    for (int i1 = ir0; i1 < ir1; i1++) {
        ggml_vec_silu_f32(nc,
                (float *) ((char *) dst->data  + i1*( dst->nb[1])),
                (float *) ((char *) src0->data + i1*(src0->nb[1])));

#ifndef NDEBUG
        for (int k = 0; k < nc; k++) {
            const float x = ((float *) ((char *) dst->data + i1*( dst->nb[1])))[k];
            UNUSED(x);
            assert(!isnan(x));
            assert(!isinf(x));
        }
#endif
    }
}

static void ggml_compute_forward_silu(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_silu_f32(params, src0, dst);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}


// ggml_compute_forward_silu_back

static void ggml_compute_forward_silu_back_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * grad,
        struct ggml_tensor * dst) {
    GGML_ASSERT(ggml_is_contiguous(grad));
    GGML_ASSERT(ggml_is_contiguous(src0));
    GGML_ASSERT(ggml_is_contiguous(dst));
    GGML_ASSERT(ggml_are_same_shape(src0, dst));
    GGML_ASSERT(ggml_are_same_shape(src0, grad));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int ith = params->ith;
    const int nth = params->nth;

    const int nc = src0->ne[0];
    const int nr = ggml_nrows(src0);

    // rows per thread
    const int dr = (nr + nth - 1)/nth;

    // row range for this thread
    const int ir0 = dr*ith;
    const int ir1 = MIN(ir0 + dr, nr);

    for (int i1 = ir0; i1 < ir1; i1++) {
        ggml_vec_silu_backward_f32(nc,
                (float *) ((char *) dst->data  + i1*( dst->nb[1])),
                (float *) ((char *) src0->data + i1*(src0->nb[1])),
                (float *) ((char *) grad->data + i1*(grad->nb[1])));

#ifndef NDEBUG
        for (int k = 0; k < nc; k++) {
            const float x = ((float *) ((char *) dst->data + i1*( dst->nb[1])))[k];
            UNUSED(x);
            assert(!isnan(x));
            assert(!isinf(x));
        }
#endif
    }
}

static void ggml_compute_forward_silu_back(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * grad,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_silu_back_f32(params, src0, grad, dst);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_norm

static void ggml_compute_forward_norm_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    GGML_ASSERT(ggml_are_same_shape(src0, dst));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    GGML_ASSERT(src0->nb[0] == sizeof(float));

    const int ith = params->ith;
    const int nth = params->nth;

    GGML_TENSOR_UNARY_OP_LOCALS;

    const float eps = 1e-5f; // TODO: make this a parameter

    // TODO: optimize
    for (int64_t i03 = 0; i03 < ne03; i03++) {
        for (int64_t i02 = 0; i02 < ne02; i02++) {
            for (int64_t i01 = ith; i01 < ne01; i01 += nth) {
                const float * x = (float *) ((char *) src0->data + i01*nb01 + i02*nb02 + i03*nb03);

                ggml_float sum = 0.0;
                for (int64_t i00 = 0; i00 < ne00; i00++) {
                    sum += (ggml_float)x[i00];
                }

                float mean = sum/ne00;

                float * y = (float *) ((char *) dst->data + i01*nb1 + i02*nb2 + i03*nb3);

                ggml_float sum2 = 0.0;
                for (int64_t i00 = 0; i00 < ne00; i00++) {
                    float v = x[i00] - mean;
                    y[i00] = v;
                    sum2 += (ggml_float)(v*v);
                }

                float variance = sum2/ne00;
                const float scale = 1.0f/sqrtf(variance + eps);

                ggml_vec_scale_f32(ne00, y, scale);
            }
        }
    }
}

static void ggml_compute_forward_norm(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_norm_f32(params, src0, dst);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

static void ggml_compute_forward_rms_norm_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    GGML_ASSERT(ggml_are_same_shape(src0, dst));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    GGML_ASSERT(src0->nb[0] == sizeof(float));

    const int ith = params->ith;
    const int nth = params->nth;

    GGML_TENSOR_UNARY_OP_LOCALS;

    const float eps = 1e-6f; // TODO: make this a parameter

    // TODO: optimize
    for (int64_t i03 = 0; i03 < ne03; i03++) {
        for (int64_t i02 = 0; i02 < ne02; i02++) {
            for (int64_t i01 = ith; i01 < ne01; i01 += nth) {
                const float * x = (float *) ((char *) src0->data + i01*nb01 + i02*nb02 + i03*nb03);

                ggml_float sum = 0.0;
                for (int64_t i00 = 0; i00 < ne00; i00++) {
                    sum += (ggml_float)(x[i00] * x[i00]);
                }

                const float mean = sum/ne00;

                float * y = (float *) ((char *) dst->data + i01*nb1 + i02*nb2 + i03*nb3);

                memcpy(y, x, ne00 * sizeof(float));
                // for (int i00 = 0; i00 < ne00; i00++) {
                //     y[i00] = x[i00];
                // }

                const float scale = 1.0f/sqrtf(mean + eps);

                ggml_vec_scale_f32(ne00, y, scale);
            }
        }
    }
}

static void ggml_compute_forward_rms_norm(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_rms_norm_f32(params, src0, dst);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}


static void ggml_compute_forward_rms_norm_back_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    GGML_ASSERT(ggml_are_same_shape(src0, dst) && ggml_are_same_shape(src0, src1));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    GGML_ASSERT(src0->nb[0] == sizeof(float));

    const int ith = params->ith;
    const int nth = params->nth;

    GGML_TENSOR_BINARY_OP_LOCALS;

    const float eps = 1e-6f; // TODO: make this a parameter

    // TODO: optimize
    for (int64_t i03 = 0; i03 < ne03; i03++) {
        for (int64_t i02 = 0; i02 < ne02; i02++) {
            for (int64_t i01 = ith; i01 < ne01; i01 += nth) {
                // src1 is same shape as src0 => same indices
                const int64_t i11 = i01;
                const int64_t i12 = i02;
                const int64_t i13 = i03;

                const float * x = (float *) ((char *) src0->data + i01*nb01 + i02*nb02 + i03*nb03);
                const float * dz = (float *) ((char *) src1->data + i11*nb11 + i12*nb12 + i13*nb13);

                ggml_float sum_xx  = 0.0;
                ggml_float sum_xdz = 0.0;

                for (int64_t i00 = 0; i00 < ne00; i00++) {
                    sum_xx  += (ggml_float)(x[i00] * x[i00]);
                    sum_xdz += (ggml_float)(x[i00] * dz[i00]);
                }

                //const float mean     = (float)(sum_xx)/ne00;
                const float mean_eps = (float)(sum_xx)/ne00 + eps;
                const float sum_eps  = (float)(sum_xx) + eps*ne00;
                //const float mean_xdz = (float)(sum_xdz)/ne00;
                // we could cache rms from forward pass to improve performance.
                // to do this implement ggml_rms and compose ggml_rms_norm using ggml_rms.
                //const float rms      = sqrtf(mean_eps);
                const float rrms     = 1.0f / sqrtf(mean_eps);
                //const float scale    = -rrms/(ne00 * mean_eps); // -1/(n*rms**3)

                {
                    // z = rms_norm(x)
                    //
                    // rms_norm(src0) =
                    //     scale(
                    //         src0,
                    //         div(
                    //             1,
                    //             sqrt(
                    //                 add(
                    //                     scale(
                    //                         sum(
                    //                             sqr(
                    //                                 src0)),
                    //                         (1.0/N)),
                    //                     eps))));

                    // postorder:
                    // ## op    args         grad
                    // 00 param src0         grad[#00]
                    // 01 const 1
                    // 02 sqr   (#00)        grad[#02]
                    // 03 sum   (#02)        grad[#03]
                    // 04 const 1/N
                    // 05 scale (#03, #04)   grad[#05]
                    // 06 const eps
                    // 07 add   (#05, #06)   grad[#07]
                    // 08 sqrt  (#07)        grad[#08]
                    // 09 div   (#01,#08)    grad[#09]
                    // 10 scale (#00,#09)    grad[#10]
                    //
                    // backward pass, given grad[#10]
                    // #10: scale
                    // grad[#00] += scale(grad[#10],#09)
                    // grad[#09] += sum(mul(grad[#10],#00))
                    // #09: div
                    // grad[#08] += neg(mul(grad[#09], div(#09,#08)))
                    // #08: sqrt
                    // grad[#07] += mul(grad[#08], div(0.5, #08))
                    // #07: add
                    // grad[#05] += grad[#07]
                    // #05: scale
                    // grad[#03] += scale(grad[#05],#04)
                    // #03: sum
                    // grad[#02] += repeat(grad[#03], #02)
                    // #02:
                    // grad[#00] += scale(mul(#00, grad[#02]), 2.0)
                    //
                    // substitute and simplify:
                    // grad[#00] = scale(grad(#10), #09) + scale(mul(#00, grad[#02]), 2.0)
                    // grad[#02] = repeat(grad[#03], #02)
                    // grad[#02] = repeat(scale(grad[#05],#04), #02)
                    // grad[#02] = repeat(scale(grad[#07],#04), #02)
                    // grad[#02] = repeat(scale(mul(grad[#08], div(0.5, #08)),#04), #02)
                    // grad[#02] = repeat(scale(mul(neg(mul(grad[#09], div(#09,#08))), div(0.5, #08)),#04), #02)
                    // grad[#02] = repeat(scale(mul(neg(mul(sum(mul(grad[#10],#00)), div(#09,#08))), div(0.5, #08)),#04), #02)
                    // grad[#02] = repeat(-(sum(mul(grad[#10],#00)) * div(#09,#08) * div(0.5, #08) * (1/N)), #02)
                    // grad[#02] = repeat(-(sum(mul(grad[#10],#00)) * div(div(#01,#08),#08) * div(0.5, #08) * (1/N)), #02)
                    // grad[#02] = repeat(-(sum(mul(grad[#10],#00)) * div(1,#08*#08) * div(0.5, #08) * (1/N)), #02)
                    // grad[#02] = repeat(-(sum(mul(grad[#10],#00)) * div(1,#07) * div(0.5, #08) * (1/N)), #02)
                    // grad[#00] = scale(grad(#10), #09) + scale(mul(#00, grad[#02]), 2.0)
                    // grad[#00] = scale(grad(#10), #09) + scale(mul(#00, repeat(-(sum(mul(grad[#10],#00)) * div(1,#07) * div(0.5, #08) * (1/N)), #02)), 2.0)
                    // grad[#00] = scale(grad(#10), #09) + scale(scale(#00, -(sum(mul(grad[#10],#00)) * div(1,#07) * div(0.5, #08) * (1/N))), 2.0)
                    // grad[#00] = scale(grad(#10), #09) + scale(#00, -(sum(mul(grad[#10],#00)) * div(1,#07) * div(1,#08) * (1/N)))
                    // grad[#00] = scale(grad(#10), #09) + scale(#00, sum(mul(grad[#10],#00)) * div(1,#07*#08) * (-1/N))
                    // grad[#00] = scale(grad(#10), #09) + scale(#00, sum(mul(grad[#10],#00)) * div(1,#07*#08) * (-1/N))
                    // grad[#00] = scale(grad(#10), #09) + scale(#00, sum(mul(grad[#10],#00)) * div(1,mean_eps*rms) * (-1/N))
                    // grad[#00] = scale(grad(#10), #09) + scale(#00, sum(mul(grad[#10],#00)) * div(-1,rms*N*mean_eps))
                    // grad[#00] = scale(grad(#10), #09) + scale(#00, sum(mul(grad[#10],#00)) * div(-1,rms*N*(sum_xx/N+eps)))
                    // grad[#00] = scale(grad(#10), #09) + scale(#00, sum(mul(grad[#10],#00)) * div(-1,rms*N*sum_xx+rms*N*eps))
                    // grad[#00] = scale(dz, rrms) + scale(x, sum(mul(dz,x)) * div(-1,rms*N*mean_eps))
                    // grad[#00] = scale(dz, rrms) + scale(x, sum_xdz * div(-1,rms*N*mean_eps))
                    // a = b*c + d*e
                    // a = b*c*f/f + d*e*f/f
                    // a = (b*c*f + d*e*f)*(1/f)
                    // a = (b*c*(1/c) + d*e*(1/c))*(1/(1/c))
                    // a = (b + d*e/c)*c
                    // b = dz, c = rrms, d = x, e = sum_xdz * div(-1,rms*N*mean_eps)
                    // a = (dz + x*sum_xdz * div(-1,rms*N*mean_eps)/rrms)*rrms
                    // a = (dz + x*sum_xdz * div(-1,rms*N*mean_eps)*rms)*rrms
                    // a = (dz + x*sum_xdz * div(-rms,rms*N*mean_eps))*rrms
                    // a = (dz + x*sum_xdz * div(-1,N*mean_eps))*rrms
                    // a = (dz + x*div(-sum_xdz,N*mean_eps))*rrms
                    // a = (dz + x*div(-mean_xdz,mean_eps))*rrms
                    // grad[#00] = scale(dz + scale(x, div(-mean_xdz,mean_eps)),rrms)
                    // grad[#00] = scale(dz + scale(x, -mean_xdz/mean_eps),rrms)
                    // dx = scale(dz + scale(x, -mean_xdz/mean_eps),rrms)
                }
                // dx = scale(dz + scale(x, -mean_xdz/mean_eps),rrms)
                // post-order:
                // dx := x
                // dx := scale(dx,-mean_xdz/mean_eps)
                // dx := add(dx, dz)
                // dx := scale(dx, rrms)
                float * dx = (float *) ((char *) dst->data + i01*nb1 + i02*nb2 + i03*nb3);

                ggml_vec_cpy_f32  (ne00, dx, x);
                // ggml_vec_scale_f32(ne00, dx, -mean_xdz/mean_eps);
                ggml_vec_scale_f32(ne00, dx, (float)(-sum_xdz)/sum_eps);
                ggml_vec_acc_f32  (ne00, dx, dz);
                ggml_vec_scale_f32(ne00, dx, rrms);
            }
        }
    }
}

static void ggml_compute_forward_rms_norm_back(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_rms_norm_back_f32(params, src0, src1, dst);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}


// ggml_compute_forward_mul_mat

#if defined(GGML_USE_ACCELERATE) || defined(GGML_USE_OPENBLAS)
// helper function to determine if it is better to use BLAS or not
// for large matrices, BLAS is faster
static bool ggml_compute_forward_mul_mat_use_blas(
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
              struct ggml_tensor * dst) {
    //const int64_t ne00 = src0->ne[0];
    //const int64_t ne01 = src0->ne[1];

    const int64_t ne10 = src1->ne[0];

    const int64_t ne0 = dst->ne[0];
    const int64_t ne1 = dst->ne[1];

    // TODO: find the optimal values for these
    if (ggml_is_contiguous(src0) &&
        ggml_is_contiguous(src1) &&
        (ne0 >= 32 && ne1 >= 32 && ne10 >= 32)) {

        /*printf("BLAS: %d %d %d %d %d\n", ne0, ne1, ne10, ne00, ne01);*/
        return true;
    }

    return false;
}
#endif

static void ggml_compute_forward_mul_mat(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
              struct ggml_tensor * dst) {
    int64_t t0 = ggml_perf_time_us();
    UNUSED(t0);

    GGML_TENSOR_BINARY_OP_LOCALS;

    const int ith = params->ith;
    const int nth = params->nth;

    GGML_ASSERT(ne02 == ne12);
    GGML_ASSERT(ne03 == ne13);
    GGML_ASSERT(ne2  == ne12);
    GGML_ASSERT(ne3  == ne13);

    const enum ggml_type type = src0->type;

    ggml_vec_dot_t    const vec_dot               = type_traits[type].vec_dot;
    enum ggml_type    const vec_dot_type          = type_traits[type].vec_dot_type;
    ggml_from_float_t const from_float_to_vec_dot = type_traits[vec_dot_type].from_float;

    // we don't support permuted src0 or src1
    GGML_ASSERT(nb00 == GGML_TYPE_SIZE[type]);
    GGML_ASSERT(nb10 == sizeof(float));

    // dst cannot be transposed or permuted
    GGML_ASSERT(nb0 == sizeof(float));
    GGML_ASSERT(nb0 <= nb1);
    GGML_ASSERT(nb1 <= nb2);
    GGML_ASSERT(nb2 <= nb3);

    GGML_ASSERT(ne0 == ne01);
    GGML_ASSERT(ne1 == ne11);
    GGML_ASSERT(ne2 == ne02);
    GGML_ASSERT(ne3 == ne03);

    // nb01 >= nb00 - src0 is not transposed
    //   compute by src0 rows

#if defined(GGML_USE_CLBLAST)
    if (ggml_cl_can_mul_mat(src0, src1, dst)) {
        if (params->ith == 0 && params->type == GGML_TASK_COMPUTE) {
            ggml_cl_mul_mat(src0, src1, dst, params->wdata, params->wsize);
        }
        return;
    }
#endif

#if defined(GGML_USE_ACCELERATE) || defined(GGML_USE_OPENBLAS)
    if (ggml_compute_forward_mul_mat_use_blas(src0, src1, dst)) {
        if (params->ith != 0) {
            return;
        }

        if (params->type == GGML_TASK_INIT) {
            return;
        }

        if (params->type == GGML_TASK_FINALIZE) {
            return;
        }

        for (int64_t i03 = 0; i03 < ne03; i03++) {
            for (int64_t i02 = 0; i02 < ne02; i02++) {
                const void * x = (char *) src0->data + i03*nb03 + i02*nb02;
                const float * y = (float *) ((char *) src1->data + i02*nb12 + i03*nb13);

                float * d = (float *) ((char *) dst->data + i02*nb2 + i03*nb3);

                if (type != GGML_TYPE_F32) {
                    float * const wdata = params->wdata;
                    ggml_to_float_t const to_float = type_traits[type].to_float;

                    size_t id = 0;
                    for (int64_t i01 = 0; i01 < ne01; ++i01) {
                        to_float((char *) src0->data + i03*nb03 + i02*nb02 + i01*nb01, wdata + id, ne00);
                        id += ne00;
                    }

                    assert(id*sizeof(float) <= params->wsize);
                    x = wdata;
                }

                cblas_sgemm(CblasRowMajor, CblasNoTrans, CblasTrans,
                        ne11, ne01, ne10,
                        1.0f,    y, ne10,
                                 x, ne00,
                        0.0f,    d, ne01);
            }
        }

        //printf("CBLAS = %f ms, %d x %d x %d x %d\n", (ggml_perf_time_us() - t0)/1000.0, ne0, ne1, ne2, ne3);

        return;
    }
#endif

    if (params->type == GGML_TASK_INIT) {
        if (src1->type != vec_dot_type) {
            char * wdata = params->wdata;
            const size_t row_size = ne10*GGML_TYPE_SIZE[vec_dot_type]/GGML_BLCK_SIZE[vec_dot_type];

            for (int64_t i13 = 0; i13 < ne13; ++i13) {
                for (int64_t i12 = 0; i12 < ne12; ++i12) {
                    for (int64_t i11 = 0; i11 < ne11; ++i11) {
                        from_float_to_vec_dot((float *)((char *) src1->data + i13*nb13 + i12*nb12 + i11*nb11), (void *) wdata, ne10);
                        wdata += row_size;
                    }
                }
            }
        }

        return;
    }

    if (params->type == GGML_TASK_FINALIZE) {
        return;
    }

    // parallelize by src0 rows using ggml_vec_dot_q

    // total rows in src0
    const int nr = ne01*ne02*ne03;

    // rows per thread
    const int dr = (nr + nth - 1)/nth;

    // row range for this thread
    const int ir0 = dr*ith;
    const int ir1 = MIN(ir0 + dr, nr);

    void * wdata = (src1->type == vec_dot_type) ? src1->data : params->wdata;
    const size_t row_size = ne00*GGML_TYPE_SIZE[vec_dot_type]/GGML_BLCK_SIZE[vec_dot_type];

    for (int ir = ir0; ir < ir1; ++ir) {
        // src0 indices
        const int i03 = ir/(ne02*ne01);
        const int i02 = (ir - i03*ne02*ne01)/ne01;
        const int i01 = (ir - i03*ne02*ne01 - i02*ne01);

        const int i13 = i03;
        const int i12 = i02;

        const int i0 = i01;
        const int i2 = i02;
        const int i3 = i03;

        void * src0_row = (void *) ((char *) src0->data + (i01*nb01 + i02*nb02 + i03*nb03));
        char * src1_col =          ((char *)      wdata + (      (0 + i12*ne11 + i13*ne12*ne11)*row_size));

        float * dst_col = (float *) ((char *) dst->data + (i0*nb0 + 0*nb1 + i2*nb2 + i3*nb3));

        for (int64_t ic = 0; ic < ne11; ++ic) {
            vec_dot(ne00, &dst_col[ic*ne0], src0_row, (void *) (src1_col + ic*row_size));
        }
    }

    //int64_t t1 = ggml_time_us();
    //static int64_t acc = 0;
    //acc += t1 - t0;
    //if (t1 - t0 > 10) {
    //    printf("\n");
    //    printf("ne00 = %5d, ne01 = %5d, ne02 = %5d, ne03 = %5d\n", ne00, ne01, ne02, ne03);
    //    printf("nb00 = %5d, nb01 = %5d, nb02 = %5d, nb03 = %5d\n", nb00, nb01, nb02, nb03);
    //    printf("ne10 = %5d, ne11 = %5d, ne12 = %5d, ne13 = %5d\n", ne10, ne11, ne12, ne13);

    //    printf("XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX task %d/%d: %d us, acc = %d\n", ith, nth, (int) (t1 - t0), (int) acc);
    //}
}


// ggml_compute_forward_out_prod


static void ggml_compute_forward_out_prod_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
              struct ggml_tensor * dst) {
    int64_t t0 = ggml_perf_time_us();
    UNUSED(t0);

    GGML_TENSOR_BINARY_OP_LOCALS;

    const int ith = params->ith;
    const int nth = params->nth;

    GGML_ASSERT(ne02 == ne12);
    GGML_ASSERT(ne03 == ne13);
    GGML_ASSERT(ne2  == ne12);
    GGML_ASSERT(ne3  == ne13);

    // we don't support permuted src0 or src1
    GGML_ASSERT(nb00 == sizeof(float));

    // dst cannot be transposed or permuted
    GGML_ASSERT(nb0 == sizeof(float));
    // GGML_ASSERT(nb0 <= nb1);
    // GGML_ASSERT(nb1 <= nb2);
    // GGML_ASSERT(nb2 <= nb3);

    GGML_ASSERT(ne0 == ne00);
    GGML_ASSERT(ne1 == ne10);
    GGML_ASSERT(ne2 == ne02);
    GGML_ASSERT(ne3 == ne03);

    // nb01 >= nb00 - src0 is not transposed
    //   compute by src0 rows

    // TODO: #if defined(GGML_USE_CUBLAS) ggml_cuda_out_prod
    // TODO: #if defined(GGML_USE_ACCELERATE) || defined(GGML_USE_OPENBLAS) || defined(GGML_USE_CLBLAST)

    if (params->type == GGML_TASK_INIT) {
        ggml_vec_set_f32(ne0*ne1*ne2*ne3, dst->data, 0);
        return;
    }

    if (params->type == GGML_TASK_FINALIZE) {
        return;
    }

    // parallelize by last three dimensions

    // total rows in dst
    const int64_t nr = ne1*ne2*ne3;

    // rows per thread
    const int64_t dr = (nr + nth - 1)/nth;

    // row range for this thread
    const int64_t ir0 = dr*ith;
    const int64_t ir1 = MIN(ir0 + dr, nr);

    // dst[:,:,:,:] = 0
    // for i2,i3:
    //   for i1:
    //     for i01:
    //       for i0:
    //         dst[i0,i1,i2,i3] += src0[i0,i01,i2,i3] * src1[i1,i01,i2,i3]

    for (int64_t ir = ir0; ir < ir1; ++ir) {
        // dst indices
        const int64_t i3 = ir/(ne2*ne1);
        const int64_t i2 = (ir - i3*ne2*ne1)/ne1;
        const int64_t i1 = (ir - i3*ne2*ne1 - i2*ne1);

        const int64_t i02 = i2;
        const int64_t i03 = i3;

        //const int64_t i10 = i1;
        const int64_t i12 = i2;
        const int64_t i13 = i3;

        for (int64_t i01 = 0; i01 < ne01; ++i01) {
            const int64_t i11 = i01;

            float * s0 = (float *) ((char *) src0->data + (          i01*nb01 + i02*nb02 + i03*nb03));
            float * s1 = (float *) ((char *) src1->data + (i1*nb10 + i11*nb11 + i12*nb12 + i13*nb13));
            float * d  = (float *) ((char *)  dst->data + (          i1*nb1 + i2*nb2 + i3*nb3));

            ggml_vec_mad_f32(ne0, d, s0, *s1);
            // for (int64_t i0 = 0; i0 < ne0; ++i0) {
            //     d[i0] += s0[i0] * s1[i1];
            // }
        }
    }

    //int64_t t1 = ggml_perf_time_us();
    //static int64_t acc = 0;
    //acc += t1 - t0;
    //if (t1 - t0 > 10) {
    //    printf("\n");
    //    printf("ne00 = %5d, ne01 = %5d, ne02 = %5d, ne03 = %5d\n", ne00, ne01, ne02, ne03);
    //    printf("nb00 = %5d, nb01 = %5d, nb02 = %5d, nb03 = %5d\n", nb00, nb01, nb02, nb03);
    //    printf("ne10 = %5d, ne11 = %5d, ne12 = %5d, ne13 = %5d\n", ne10, ne11, ne12, ne13);
    //    printf("nb10 = %5d, nb11 = %5d, nb12 = %5d, nb13 = %5d\n", nb10, nb11, nb12, nb13);

    //    printf("XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX task %d/%d: %d us, acc = %d\n", ith, nth, (int) (t1 - t0), (int) acc);
    //}
}

static void ggml_compute_forward_out_prod(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_Q4_0:
        case GGML_TYPE_Q4_1:
        case GGML_TYPE_Q5_0:
        case GGML_TYPE_Q5_1:
        case GGML_TYPE_Q8_0:
        case GGML_TYPE_Q8_1:
            {
                GGML_ASSERT(false); // todo
                // ggml_compute_forward_out_prod_q_f32(params, src0, src1, dst);
            } break;
        case GGML_TYPE_F16:
            {
                GGML_ASSERT(false); // todo
                // ggml_compute_forward_out_prod_f16_f32(params, src0, src1, dst);
            } break;
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_out_prod_f32(params, src0, src1, dst);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_scale

static void ggml_compute_forward_scale_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    GGML_ASSERT(ggml_is_contiguous(src0));
    GGML_ASSERT(ggml_is_contiguous(dst));
    GGML_ASSERT(ggml_are_same_shape(src0, dst));
    GGML_ASSERT(ggml_is_scalar(src1));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    // scale factor
    const float v = *(float *) src1->data;

    const int ith = params->ith;
    const int nth = params->nth;

    const int nc = src0->ne[0];
    const int nr = ggml_nrows(src0);

    // rows per thread
    const int dr = (nr + nth - 1)/nth;

    // row range for this thread
    const int ir0 = dr*ith;
    const int ir1 = MIN(ir0 + dr, nr);

    const size_t nb01 = src0->nb[1];

    const size_t nb1 = dst->nb[1];


    for (int i1 = ir0; i1 < ir1; i1++) {
        if (dst->data != src0->data) {
            // src0 is same shape as dst => same indices
            memcpy((char *)dst->data + i1*nb1, (char *)src0->data + i1*nb01, nc * sizeof(float));
        }
        ggml_vec_scale_f32(nc, (float *) ((char *) dst->data + i1*nb1), v);
    }
}

static void ggml_compute_forward_scale(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_scale_f32(params, src0, src1, dst);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_set

static void ggml_compute_forward_set_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        const struct ggml_tensor * opt0,
        struct ggml_tensor * dst) {
    GGML_ASSERT(ggml_are_same_shape(src0, dst));
    GGML_ASSERT(ggml_is_contiguous(dst) && ggml_is_contiguous(src0));

    GGML_ASSERT(opt0->type == GGML_TYPE_I32);
    GGML_ASSERT(ggml_nelements(opt0) == 5);

    // view src0 and dst with these strides and data offset inbytes during set
    // nb0 is implicitely element_size because src0 and dst are contiguous
    size_t nb1     = ((int32_t *) opt0->data)[0];
    size_t nb2     = ((int32_t *) opt0->data)[1];
    size_t nb3     = ((int32_t *) opt0->data)[2];
    size_t offset  = ((int32_t *) opt0->data)[3];
    bool   inplace = (bool) ((int32_t *) opt0->data)[4];

    if (!inplace && (params->type == GGML_TASK_INIT)) {
        // memcpy needs to be synchronized across threads to avoid race conditions.
        // => do it in INIT phase
        memcpy(
            ((char *)  dst->data),
            ((char *) src0->data),
            ggml_nbytes(dst));
    }

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int ith = params->ith;
    const int nth = params->nth;

    const int nr = ggml_nrows(src1);
    const int nc = src1->ne[0];

    GGML_TENSOR_LOCALS(int64_t, ne1, src1, ne);
    GGML_TENSOR_LOCALS(size_t,  nb1, src1, nb);

    // src0 and dst as viewed during set
    const size_t nb0 = ggml_element_size(src0);

    const int im0 = (ne10 == 0 ? 0 : ne10-1);
    const int im1 = (ne11 == 0 ? 0 : ne11-1);
    const int im2 = (ne12 == 0 ? 0 : ne12-1);
    const int im3 = (ne13 == 0 ? 0 : ne13-1);

    GGML_ASSERT(offset + im0*nb0  + im1*nb1  + im2*nb2  + im3*nb3  <= ggml_nbytes(dst));

    GGML_ASSERT(nb10 == sizeof(float));

    // rows per thread
    const int dr = (nr + nth - 1)/nth;

    // row range for this thread
    const int ir0 = dr*ith;
    const int ir1 = MIN(ir0 + dr, nr);

    for (int ir = ir0; ir < ir1; ++ir) {
        // src0 and dst are viewed with shape of src1 and offset
        // => same indices
        const int i3 = ir/(ne12*ne11);
        const int i2 = (ir - i3*ne12*ne11)/ne11;
        const int i1 = (ir - i3*ne12*ne11 - i2*ne11);

        ggml_vec_cpy_f32(nc,
                (float *) ((char *)  dst->data + i3*nb3  + i2*nb2  + i1*nb1  + offset),
                (float *) ((char *) src1->data + i3*nb13 + i2*nb12 + i1*nb11));
    }
}

static void ggml_compute_forward_set(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        const struct ggml_tensor * opt0,
        struct ggml_tensor * dst) {

    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_set_f32(params, src0, src1, opt0, dst);
            } break;
        case GGML_TYPE_F16:
        case GGML_TYPE_Q4_0:
        case GGML_TYPE_Q4_1:
        case GGML_TYPE_Q5_0:
        case GGML_TYPE_Q5_1:
        case GGML_TYPE_Q8_0:
        case GGML_TYPE_Q8_1:
        case GGML_TYPE_Q2_K:
        case GGML_TYPE_Q3_K:
        case GGML_TYPE_Q4_K:
        case GGML_TYPE_Q5_K:
        case GGML_TYPE_Q6_K:
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_cpy

static void ggml_compute_forward_cpy(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    ggml_compute_forward_dup(params, src0, dst);
}

// ggml_compute_forward_cont

static void ggml_compute_forward_cont(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    ggml_compute_forward_dup(params, src0, dst);
}

// ggml_compute_forward_reshape

static void ggml_compute_forward_reshape(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    // NOP
    UNUSED(params);
    UNUSED(src0);
    UNUSED(dst);
}

// ggml_compute_forward_view

static void ggml_compute_forward_view(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0) {
    // NOP
    UNUSED(params);
    UNUSED(src0);
}

// ggml_compute_forward_permute

static void ggml_compute_forward_permute(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0) {
    // NOP
    UNUSED(params);
    UNUSED(src0);
}

// ggml_compute_forward_transpose

static void ggml_compute_forward_transpose(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0) {
    // NOP
    UNUSED(params);
    UNUSED(src0);
}

// ggml_compute_forward_get_rows

static void ggml_compute_forward_get_rows_q(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
              struct ggml_tensor * dst) {
    assert(params->ith == 0);

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int nc = src0->ne[0];
    const int nr = ggml_nelements(src1);
    const enum ggml_type type = src0->type;
    ggml_to_float_t const dequantize_row_q = type_traits[type].to_float;

    assert( dst->ne[0] == nc);
    assert( dst->ne[1] == nr);
    assert(src0->nb[0] == GGML_TYPE_SIZE[type]);

    for (int i = 0; i < nr; ++i) {
        const int r = ((int32_t *) src1->data)[i];

        dequantize_row_q(
                (const void *) ((char *) src0->data + r*src0->nb[1]),
                     (float *) ((char *)  dst->data + i*dst->nb[1]), nc);
    }
}

static void ggml_compute_forward_get_rows_f16(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
              struct ggml_tensor * dst) {
    assert(params->ith == 0);

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int nc = src0->ne[0];
    const int nr = ggml_nelements(src1);

    assert( dst->ne[0] == nc);
    assert( dst->ne[1] == nr);
    assert(src0->nb[0] == sizeof(ggml_fp16_t));

    for (int i = 0; i < nr; ++i) {
        const int r = ((int32_t *) src1->data)[i];

        for (int j = 0; j < nc; ++j) {
            ggml_fp16_t v = ((ggml_fp16_t *) ((char *) src0->data + r*src0->nb[1]))[j];
            ((float *) ((char *)  dst->data + i*dst->nb[1]))[j] = GGML_FP16_TO_FP32(v);
        }
    }
}

static void ggml_compute_forward_get_rows_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
              struct ggml_tensor * dst) {
    assert(params->ith == 0);

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int nc = src0->ne[0];
    const int nr = ggml_nelements(src1);

    assert( dst->ne[0] == nc);
    assert( dst->ne[1] == nr);
    assert(src0->nb[0] == sizeof(float));

    for (int i = 0; i < nr; ++i) {
        const int r = ((int32_t *) src1->data)[i];

        ggml_vec_cpy_f32(nc,
                (float *) ((char *)  dst->data + i*dst->nb[1]),
                (float *) ((char *) src0->data + r*src0->nb[1]));
    }
}

static void ggml_compute_forward_get_rows(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_Q4_0:
        case GGML_TYPE_Q4_1:
        case GGML_TYPE_Q5_0:
        case GGML_TYPE_Q5_1:
        case GGML_TYPE_Q8_0:
        case GGML_TYPE_Q8_1:
        case GGML_TYPE_Q2_K:
        case GGML_TYPE_Q3_K:
        case GGML_TYPE_Q4_K:
        case GGML_TYPE_Q5_K:
        case GGML_TYPE_Q6_K:
            {
                ggml_compute_forward_get_rows_q(params, src0, src1, dst);
            } break;
        case GGML_TYPE_F16:
            {
                ggml_compute_forward_get_rows_f16(params, src0, src1, dst);
            } break;
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_get_rows_f32(params, src0, src1, dst);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }

    //static bool first = true;
    //printf("ne0 = %d, ne1 = %d, ne2 = %d\n", dst->ne[0], dst->ne[1], dst->ne[2]);
    //if (first) {
    //    first = false;
    //} else {
    //    for (int k = 0; k < dst->ne[1]; ++k) {
    //        for (int j = 0; j < dst->ne[0]/16; ++j) {
    //            for (int i = 0; i < 16; ++i) {
    //                printf("%8.4f ", ((float *) dst->data)[k*dst->ne[0] + j*16 + i]);
    //            }
    //            printf("\n");
    //        }
    //        printf("\n");
    //    }
    //    printf("\n");
    //    exit(0);
    //}
}

// ggml_compute_forward_get_rows_back

static void ggml_compute_forward_get_rows_back_f32_f16(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        const struct ggml_tensor * opt0,
              struct ggml_tensor * dst) {
    GGML_ASSERT(params->ith == 0);
    GGML_ASSERT(ggml_are_same_shape(opt0, dst));
    GGML_ASSERT(ggml_is_contiguous(opt0));
    GGML_ASSERT(ggml_is_contiguous(dst));

    ggml_compute_forward_dup_same_cont(params, opt0, dst);

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int nc = src0->ne[0];
    const int nr = ggml_nelements(src1);

    GGML_ASSERT( dst->ne[0] == nc);
    GGML_ASSERT(src0->nb[0] == sizeof(ggml_fp16_t));

    for (int i = 0; i < nr; ++i) {
        const int r = ((int32_t *) src1->data)[i];

        for (int j = 0; j < nc; ++j) {
            ggml_fp16_t v = ((ggml_fp16_t *) ((char *) src0->data + i*src0->nb[1]))[j];
            ((float *) ((char *) dst->data + r*dst->nb[1]))[j] += GGML_FP16_TO_FP32(v);
        }
    }
}

static void ggml_compute_forward_get_rows_back_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        const struct ggml_tensor * opt0,
              struct ggml_tensor * dst) {
    GGML_ASSERT(params->ith == 0);
    GGML_ASSERT(ggml_are_same_shape(opt0, dst));
    GGML_ASSERT(ggml_is_contiguous(opt0));
    GGML_ASSERT(ggml_is_contiguous(dst));

    // ggml_compute_forward_dup_same_cont(params, opt0, dst);

    if (params->type == GGML_TASK_INIT) {
        memset(dst->data, 0, ggml_nbytes(dst));
    }

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int nc = src0->ne[0];
    const int nr = ggml_nelements(src1);

    GGML_ASSERT( dst->ne[0] == nc);
    GGML_ASSERT(src0->nb[0] == sizeof(float));

    for (int i = 0; i < nr; ++i) {
        const int r = ((int32_t *) src1->data)[i];

        ggml_vec_add_f32(nc,
                (float *) ((char *)  dst->data + r*dst->nb[1]),
                (float *) ((char *)  dst->data + r*dst->nb[1]),
                (float *) ((char *) src0->data + i*src0->nb[1]));
    }
}


static void ggml_compute_forward_get_rows_back(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        const struct ggml_tensor * opt0,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F16:
            {
                ggml_compute_forward_get_rows_back_f32_f16(params, src0, src1, opt0, dst);
            } break;
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_get_rows_back_f32(params, src0, src1, opt0, dst);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }

    //static bool first = true;
    //printf("ne0 = %d, ne1 = %d, ne2 = %d\n", dst->ne[0], dst->ne[1], dst->ne[2]);
    //if (first) {
    //    first = false;
    //} else {
    //    for (int k = 0; k < dst->ne[1]; ++k) {
    //        for (int j = 0; j < dst->ne[0]/16; ++j) {
    //            for (int i = 0; i < 16; ++i) {
    //                printf("%8.4f ", ((float *) dst->data)[k*dst->ne[0] + j*16 + i]);
    //            }
    //            printf("\n");
    //        }
    //        printf("\n");
    //    }
    //    printf("\n");
    //    exit(0);
    //}
}

// ggml_compute_forward_diag

static void ggml_compute_forward_diag_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    GGML_ASSERT(params->ith == 0);

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    // TODO: handle transposed/permuted matrices

    GGML_TENSOR_UNARY_OP_LOCALS;

    GGML_ASSERT(ne00 == ne0);
    GGML_ASSERT(ne00 == ne1);
    GGML_ASSERT(ne01 == 1);
    GGML_ASSERT(ne02 == ne2);
    GGML_ASSERT(ne03 == ne3);

    GGML_ASSERT(nb00 == sizeof(float));
    GGML_ASSERT(nb0  == sizeof(float));

    for (int i3 = 0; i3 < ne3; i3++) {
        for (int i2 = 0; i2 < ne2; i2++) {
            for (int i1 = 0; i1 < ne1; i1++) {
                float * d = (float *)((char *)  dst->data + i3*nb3  + i2*nb2 + i1*nb1);
                float * s = (float *)((char *) src0->data + i3*nb03 + i2*nb02);
                for (int i0 = 0; i0 < i1; i0++) {
                    d[i0] = 0;
                }
                d[i1] = s[i1];
                for (int i0 = i1+1; i0 < ne0; i0++) {
                    d[i0] = 0;
                }
            }
        }
    }
}

static void ggml_compute_forward_diag(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_diag_f32(params, src0, dst);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_diag_mask_inf

static void ggml_compute_forward_diag_mask_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst,
        const float value) {
    GGML_ASSERT(src1->type == GGML_TYPE_I32);
    GGML_ASSERT(ggml_nelements(src1) == 2);

    const int ith = params->ith;
    const int nth = params->nth;

    const int  n_past  =       ((int32_t *) src1->data)[0];
    const bool inplace = (bool)((int32_t *) src1->data)[1];

    GGML_ASSERT(n_past >= 0);

    if (!inplace && (params->type == GGML_TASK_INIT)) {
        // memcpy needs to be synchronized across threads to avoid race conditions.
        // => do it in INIT phase
        GGML_ASSERT(ggml_nelements(dst) == ggml_nelements(src0));
        GGML_ASSERT(ggml_is_contiguous(dst) && ggml_is_contiguous(src0));
        memcpy(
            ((char *)  dst->data),
            ((char *) src0->data),
            ggml_nbytes(dst));
    }

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    // TODO: handle transposed/permuted matrices

    const int n  = ggml_nrows(src0);
    const int nc = src0->ne[0];
    const int nr = src0->ne[1];
    const int nz = n/nr;

    GGML_ASSERT( dst->nb[0] == sizeof(float));
    GGML_ASSERT(src0->nb[0] == sizeof(float));

    for (int k = 0; k < nz; k++) {
        for (int j = ith; j < nr; j += nth) {
            for (int i = n_past; i < nc; i++) {
                if (i > n_past + j) {
                    *(float *)((char *) dst->data + k*dst->nb[2] + j*dst->nb[1] + i*dst->nb[0]) = value;
                }
            }
        }
    }
}

static void ggml_compute_forward_diag_mask_inf(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_diag_mask_f32(params, src0, src1, dst, -INFINITY);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

static void ggml_compute_forward_diag_mask_zero(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_diag_mask_f32(params, src0, src1, dst, 0);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_soft_max

static void ggml_compute_forward_soft_max_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    GGML_ASSERT(ggml_is_contiguous(src0));
    GGML_ASSERT(ggml_is_contiguous(dst));
    GGML_ASSERT(ggml_are_same_shape(src0, dst));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    // TODO: handle transposed/permuted matrices

    const int ith = params->ith;
    const int nth = params->nth;

    const int nc = src0->ne[0];
    const int nr = ggml_nrows(src0);

    // rows per thread
    const int dr = (nr + nth - 1)/nth;

    // row range for this thread
    const int ir0 = dr*ith;
    const int ir1 = MIN(ir0 + dr, nr);

    for (int i1 = ir0; i1 < ir1; i1++) {
        float *sp = (float *)((char *) src0->data + i1*src0->nb[1]);
        float *dp = (float *)((char *)  dst->data +  i1*dst->nb[1]);

#ifndef NDEBUG
        for (int i = 0; i < nc; ++i) {
            //printf("p[%d] = %f\n", i, p[i]);
            assert(!isnan(sp[i]));
        }
#endif

        float max = -INFINITY;
        ggml_vec_max_f32(nc, &max, sp);

        ggml_float sum = 0.0;

        uint16_t scvt;
        for (int i = 0; i < nc; i++) {
            if (sp[i] == -INFINITY) {
                dp[i] = 0.0f;
            } else {
                // const float val = (sp[i] == -INFINITY) ? 0.0 : exp(sp[i] - max);
                ggml_fp16_t s = GGML_FP32_TO_FP16(sp[i] - max);
                memcpy(&scvt, &s, sizeof(scvt));
                const float val = GGML_FP16_TO_FP32(table_exp_f16[scvt]);
                sum += (ggml_float)val;
                dp[i] = val;
            }
        }

        assert(sum > 0.0);

        sum = 1.0/sum;
        ggml_vec_scale_f32(nc, dp, sum);

#ifndef NDEBUG
        for (int i = 0; i < nc; ++i) {
            assert(!isnan(dp[i]));
            assert(!isinf(dp[i]));
        }
#endif
    }
}

static void ggml_compute_forward_soft_max(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_soft_max_f32(params, src0, dst);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_soft_max_back

static void ggml_compute_forward_soft_max_back_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    GGML_ASSERT(ggml_is_contiguous(src0));
    GGML_ASSERT(ggml_is_contiguous(src1));
    GGML_ASSERT(ggml_is_contiguous(dst));
    GGML_ASSERT(ggml_are_same_shape(src0, dst));
    GGML_ASSERT(ggml_are_same_shape(src1, dst));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    // TODO: handle transposed/permuted matrices

    const int ith = params->ith;
    const int nth = params->nth;

    const int nc = src0->ne[0];
    const int nr = ggml_nrows(src0);

    // rows per thread
    const int dr = (nr + nth - 1)/nth;

    // row range for this thread
    const int ir0 = dr*ith;
    const int ir1 = MIN(ir0 + dr, nr);

    for (int i1 = ir0; i1 < ir1; i1++) {
        float *dy = (float *)((char *) src0->data + i1*src0->nb[1]);
        float *y  = (float *)((char *) src1->data + i1*src1->nb[1]);
        float *dx = (float *)((char *) dst->data  + i1*dst->nb[1]);

#ifndef NDEBUG
        for (int i = 0; i < nc; ++i) {
            //printf("p[%d] = %f\n", i, p[i]);
            assert(!isnan(dy[i]));
            assert(!isnan(y[i]));
        }
#endif
        // Jii = yi - yi*yi
        // Jij = -yi*yj
        // J = diag(y)-y.T*y
        // dx = J * dy
        // dxk = sum_i(Jki * dyi)
        // dxk = sum_i(-yk*yi * dyi) - (-yk*yk)*dyk + (yk - yk*yk)*dyk
        // dxk = sum_i(-yk*yi * dyi) + yk*dyk
        // dxk = -yk * sum_i(yi * dyi) + yk*dyk
        // dxk = -yk * dot(y, dy) + yk*dyk
        // dxk = yk * (- dot(y, dy) + dyk)
        // dxk = yk * (dyk - dot(y, dy))
        //
        // post-order:
        // dot_y_dy := dot(y, dy)
        // dx := dy
        // dx := dx - dot_y_dy
        // dx := dx * y

        // linear runtime, no additional memory
        float dot_y_dy = 0;
        ggml_vec_dot_f32 (nc, &dot_y_dy, y, dy);
        ggml_vec_cpy_f32 (nc, dx, dy);
        ggml_vec_acc1_f32(nc, dx, -dot_y_dy);
        ggml_vec_mul_f32 (nc, dx, dx, y);

#ifndef NDEBUG
        for (int i = 0; i < nc; ++i) {
            assert(!isnan(dx[i]));
            assert(!isinf(dx[i]));
        }
#endif
    }
}

static void ggml_compute_forward_soft_max_back(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_soft_max_back_f32(params, src0, src1, dst);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_alibi

static void ggml_compute_forward_alibi_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    assert(params->ith == 0);

    GGML_ASSERT(src1->type == GGML_TYPE_I32);
    GGML_ASSERT(ggml_nelements(src1) == 3);

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int   n_past   = ((int32_t *) src1->data)[0];
    const int   n_head   = ((int32_t *) src1->data)[1];
    const float max_bias = ((float *)   src1->data)[2];

    assert(n_past >= 0);

    const int ne0 = src0->ne[0]; // all_seq_len = n_past + ne1
    const int ne1 = src0->ne[1]; // seq_len_without_past
    //const int ne2 = src0->ne[2]; // n_head -> this is k
    //const int ne3 = src0->ne[3]; // 1 -> bsz

    const int n  = ggml_nrows(src0);
    const int ne2_ne3 = n/ne1; // ne2*ne3

    const int nb0 = src0->nb[0];
    const int nb1 = src0->nb[1];
    const int nb2 = src0->nb[2];
    //const int nb3 = src0->nb[3];

    assert(nb0 == sizeof(float));
    assert(ne1 + n_past == ne0); (void) n_past;

    // add alibi to src0 (KQ_scaled)
    const int n_heads_log2_floor = 1 << (int) floor(log2(n_head));

    const float m0 = powf(2.0f, -(max_bias) / n_heads_log2_floor);
    const float m1 = powf(2.0f, -(max_bias / 2.0f) / n_heads_log2_floor);

    for (int i = 0; i < ne0; i++) {
        for (int j = 0; j < ne1; j++) {
            for (int k = 0; k < ne2_ne3; k++) {
                float * const src = (float *)((char *) src0->data + i*nb0 + j*nb1 + k*nb2);
                float *      pdst = (float *)((char *)  dst->data + i*nb0 + j*nb1 + k*nb2);

                // TODO: k*nb2 or k*nb3

                float m_k;

                if (k < n_heads_log2_floor) {
                    m_k = powf(m0, k + 1);
                } else {
                    m_k = powf(m1, 2 * (k - n_heads_log2_floor) + 1);
                }

                pdst[0] = (i-ne0+1) * m_k + src[0];

            }
        }
    }
}

static void ggml_compute_forward_alibi_f16(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    assert(params->ith == 0);

    GGML_ASSERT(src1->type == GGML_TYPE_I32);
    GGML_ASSERT(ggml_nelements(src1) == 3);

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int   n_past   = ((int32_t *) src1->data)[0];
    const int   n_head   = ((int32_t *) src1->data)[1];
    const float max_bias = ((float *)   src1->data)[2];

    assert(n_past >= 0);

    const int ne0 = src0->ne[0]; // all_seq_len = n_past + ne1
    const int ne1 = src0->ne[1]; // seq_len_without_past
    //const int ne2 = src0->ne[2]; // n_head -> this is k
    //const int ne3 = src0->ne[3]; // 1 -> bsz

    const int n  = ggml_nrows(src0);
    const int ne2_ne3 = n/ne1; // ne2*ne3

    const int nb0 = src0->nb[0];
    const int nb1 = src0->nb[1];
    const int nb2 = src0->nb[2];
    //const int nb3 = src0->nb[3];

    assert(nb0 == sizeof(ggml_fp16_t));
    assert(ne1 + n_past == ne0); (void) n_past;

    // add alibi to src0 (KQ_scaled)
    const int n_heads_log2_floor = 1 << (int) floor(log2(n_head));

    const float m0 = powf(2.0f, -(max_bias) / n_heads_log2_floor);
    const float m1 = powf(2.0f, -(max_bias / 2.0f) / n_heads_log2_floor);

    for (int i = 0; i < ne0; i++) {
        for (int j = 0; j < ne1; j++) {
            for (int k = 0; k < ne2_ne3; k++) {
                ggml_fp16_t * const src  = (ggml_fp16_t *)((char *) src0->data + i*nb0 + j*nb1 + k*nb2);
                      float *      pdst  =       (float *)((char *)  dst->data + i*nb0 + j*nb1 + k*nb2);

                // TODO: k*nb2 or k*nb3

                float m_k;

                if (k < n_heads_log2_floor) {
                    m_k = powf(m0, k + 1);
                } else {
                    m_k = powf(m1, 2 * (k - n_heads_log2_floor) + 1);
                }

                // we return F32
                pdst[0] = (i-ne0+1) * m_k + GGML_FP16_TO_FP32(src[0]);
            }
        }
    }
}

static void ggml_compute_forward_alibi(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F16:
            {
                ggml_compute_forward_alibi_f16(params, src0, src1, dst);
            } break;
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_alibi_f32(params, src0, src1, dst);
            } break;
        case GGML_TYPE_Q4_0:
        case GGML_TYPE_Q4_1:
        case GGML_TYPE_Q5_0:
        case GGML_TYPE_Q5_1:
        case GGML_TYPE_Q8_0:
        case GGML_TYPE_Q8_1:
        case GGML_TYPE_Q2_K:
        case GGML_TYPE_Q3_K:
        case GGML_TYPE_Q4_K:
        case GGML_TYPE_Q5_K:
        case GGML_TYPE_Q6_K:
        case GGML_TYPE_Q8_K:
        case GGML_TYPE_I8:
        case GGML_TYPE_I16:
        case GGML_TYPE_I32:
        case GGML_TYPE_COUNT:
            {
                GGML_ASSERT(false);
            } break;
    }
}


// ggml_compute_forward_clamp

static void ggml_compute_forward_clamp_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    assert(params->ith == 0);

    GGML_ASSERT(src1->type == GGML_TYPE_F32);
    GGML_ASSERT(ggml_nelements(src1) == 2);

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const float min = ((float *) src1->data)[0];
    const float max = ((float *) src1->data)[1];

    const int ith = params->ith;
    const int nth = params->nth;

    const int n  = ggml_nrows(src0);
    const int nc = src0->ne[0];

    const size_t nb00 = src0->nb[0];
    const size_t nb01 = src0->nb[1];

    const size_t nb0 = dst->nb[0];
    const size_t nb1 = dst->nb[1];

    GGML_ASSERT( nb0 == sizeof(float));
    GGML_ASSERT(nb00 == sizeof(float));

    for (int j = ith; j < n; j += nth) {
        float * dst_ptr  = (float *) ((char *)  dst->data + j*nb1);
        float * src0_ptr = (float *) ((char *) src0->data + j*nb01);

        for (int i = 0; i < nc; i++) {
            dst_ptr[i] = MAX(MIN(src0_ptr[i], max), min);
        }
    }
}

static void ggml_compute_forward_clamp(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_clamp_f32(params, src0, src1, dst);
            } break;
        case GGML_TYPE_F16:
        case GGML_TYPE_Q4_0:
        case GGML_TYPE_Q4_1:
        case GGML_TYPE_Q5_0:
        case GGML_TYPE_Q5_1:
        case GGML_TYPE_Q8_0:
        case GGML_TYPE_Q8_1:
        case GGML_TYPE_Q2_K:
        case GGML_TYPE_Q3_K:
        case GGML_TYPE_Q4_K:
        case GGML_TYPE_Q5_K:
        case GGML_TYPE_Q6_K:
        case GGML_TYPE_Q8_K:
        case GGML_TYPE_I8:
        case GGML_TYPE_I16:
        case GGML_TYPE_I32:
        case GGML_TYPE_COUNT:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_rope

static void ggml_compute_forward_rope_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    GGML_ASSERT(src1->type == GGML_TYPE_I32);
    GGML_ASSERT(ggml_nelements(src1) == 4);

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int n_past = ((int32_t *) src1->data)[0];
    const int n_dims = ((int32_t *) src1->data)[1];
    const int mode   = ((int32_t *) src1->data)[2];
    const int n_ctx  = ((int32_t *) src1->data)[3];

    assert(n_past >= 0);

    GGML_TENSOR_UNARY_OP_LOCALS;

    //printf("ne0: %d, ne1: %d, ne2: %d, ne3: %d\n", ne0, ne1, ne2, ne3);
    //printf("n_past = %d, ne2 = %d\n", n_past, ne2);

    GGML_ASSERT(nb00 == sizeof(float));

    const int ith = params->ith;
    const int nth = params->nth;

    const int nr = ggml_nrows(dst);

    GGML_ASSERT(n_dims <= ne0);
    GGML_ASSERT(n_dims % 2 == 0);

    // rows per thread
    const int dr = (nr + nth - 1)/nth;

    // row range for this thread
    const int ir0 = dr*ith;
    const int ir1 = MIN(ir0 + dr, nr);

    // row index used to determine which thread to use
    int ir = 0;

    const float theta_scale = powf(10000.0, -2.0f/n_dims);

    const bool is_neox = mode & 2;
    const bool is_glm  = mode & 4;

    for (int64_t i3 = 0; i3 < ne3; i3++) {
        for (int64_t i2 = ((mode & 1) == 0 ? 0 : n_past); i2 < ne2; i2++) {
            const int64_t p = ((mode & 1) == 0 ? n_past + i2 : i2);
            for (int64_t i1 = 0; i1 < ne1; i1++) {
                if (ir++ < ir0) continue;
                if (ir   > ir1) break;

                float theta = (float)p;

                if (is_glm) {
                    theta = MIN(p, n_ctx - 2);
                    float block_theta = MAX(p - (n_ctx - 2), 0);
                    for (int64_t i0 = 0; i0 < ne0 / 4; i0++) {
                        const float cos_theta = cosf(theta);
                        const float sin_theta = sinf(theta);
                        const float cos_block_theta = cosf(block_theta);
                        const float sin_block_theta = sinf(block_theta);

                        theta *= theta_scale;
                        block_theta *= theta_scale;

                        const float * const src = (float *)((char *) src0->data + i3*nb03 + i2*nb02 + i1*nb01 + i0*nb00);
                              float * dst_data  = (float *)((char *)  dst->data +  i3*nb3 + i2*nb2  + i1*nb1  + i0*nb0);

                        const float x0 = src[0];
                        const float x1 = src[n_dims/2];
                        const float x2 = src[n_dims];
                        const float x3 = src[n_dims/2*3];

                        dst_data[0]          = x0*cos_theta - x1*sin_theta;
                        dst_data[n_dims/2]   = x0*sin_theta + x1*cos_theta;
                        dst_data[n_dims]     = x2*cos_block_theta - x3*sin_block_theta;
                        dst_data[n_dims/2*3] = x2*sin_block_theta + x3*cos_block_theta;
                    }
                } else if (!is_neox) {
                    for (int64_t i0 = 0; i0 < ne0; i0 += 2) {
                        const float cos_theta = cosf(theta);
                        const float sin_theta = sinf(theta);

                        theta *= theta_scale;

                        const float * const src = (float *)((char *) src0->data + i3*nb03 + i2*nb02 + i1*nb01 + i0*nb00);
                              float * dst_data  = (float *)((char *)  dst->data + i3*nb3  + i2*nb2  + i1*nb1  + i0*nb0);

                        const float x0 = src[0];
                        const float x1 = src[1];

                        dst_data[0] = x0*cos_theta - x1*sin_theta;
                        dst_data[1] = x0*sin_theta + x1*cos_theta;
                    }
                } else {
                    // TODO: this is probably wrong, but I can't figure it out ..
                    // ref:  https://github.com/huggingface/transformers/blob/main/src/transformers/models/gpt_neox/modeling_gpt_neox.py#LL251C1-L294C28
                    for (int64_t ib = 0; ib < ne0/n_dims; ++ib) {
                        for (int64_t ic = 0; ic < n_dims; ic += 2) {
                            const float cos_theta = cosf(theta);
                            const float sin_theta = sinf(theta);

                            theta *= theta_scale;

                            const int64_t i0 = ib*n_dims + ic/2;

                            const float * const src = (float *)((char *) src0->data + i3*nb03 + i2*nb02 + i1*nb01 + i0*nb00);
                                  float * dst_data  = (float *)((char *)  dst->data + i3*nb3  + i2*nb2  + i1*nb1  + i0*nb0);

                            const float x0 = src[0];
                            const float x1 = src[n_dims/2];

                            dst_data[0]        = x0*cos_theta - x1*sin_theta;
                            dst_data[n_dims/2] = x0*sin_theta + x1*cos_theta;
                        }
                    }
                }
            }
        }
    }
}

static void ggml_compute_forward_rope_f16(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    GGML_ASSERT(src1->type == GGML_TYPE_I32);
    GGML_ASSERT(ggml_nelements(src1) == 4);

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int n_past = ((int32_t *) src1->data)[0];
    const int n_dims = ((int32_t *) src1->data)[1];
    const int mode   = ((int32_t *) src1->data)[2];
    const int n_ctx  = ((int32_t *) src1->data)[3];

    assert(n_past >= 0);

    GGML_TENSOR_UNARY_OP_LOCALS;

    //printf("ne0: %d, ne1: %d, ne2: %d, ne3: %d\n", ne0, ne1, ne2, ne3);
    //printf("n_past = %d, ne2 = %d\n", n_past, ne2);

    GGML_ASSERT(nb0 == sizeof(ggml_fp16_t));

    const int ith = params->ith;
    const int nth = params->nth;

    const int nr = ggml_nrows(dst);

    GGML_ASSERT(n_dims <= ne0);
    GGML_ASSERT(n_dims % 2 == 0);

    // rows per thread
    const int dr = (nr + nth - 1)/nth;

    // row range for this thread
    const int ir0 = dr*ith;
    const int ir1 = MIN(ir0 + dr, nr);

    // row index used to determine which thread to use
    int ir = 0;

    const float theta_scale = powf(10000.0, -2.0f/n_dims);

    const bool is_neox = mode & 2;
    const bool is_glm  = mode & 4;

    for (int64_t i3 = 0; i3 < ne3; i3++) {
        for (int64_t i2 = ((mode & 1) == 0 ? 0 : n_past); i2 < ne2; i2++) {
            const int64_t p = ((mode & 1) == 0 ? n_past + i2 : i2);
            for (int64_t i1 = 0; i1 < ne1; i1++) {
                if (ir++ < ir0) continue;
                if (ir   > ir1) break;

                float theta = (float)p;

                if (is_glm) {
                    theta = MIN(p, n_ctx - 2);
                    float block_theta = MAX(p - (n_ctx - 2), 0);
                    for (int64_t i0 = 0; i0 < ne0 / 4; i0++) {
                        const float cos_theta = cosf(theta);
                        const float sin_theta = sinf(theta);
                        const float cos_block_theta = cosf(block_theta);
                        const float sin_block_theta = sinf(block_theta);

                        theta *= theta_scale;
                        block_theta *= theta_scale;

                        const ggml_fp16_t * const src = (ggml_fp16_t *)((char *) src0->data + i3*nb03 + i2*nb02 + i1*nb01 + i0*nb00);
                              ggml_fp16_t * dst_data  = (ggml_fp16_t *)((char *)  dst->data +  i3*nb3 + i2*nb2  + i1*nb1  + i0*nb0);

                        const float x0 = GGML_FP16_TO_FP32(src[0]);
                        const float x1 = GGML_FP16_TO_FP32(src[n_dims/2]);
                        const float x2 = GGML_FP16_TO_FP32(src[n_dims]);
                        const float x3 = GGML_FP16_TO_FP32(src[n_dims/2*3]);

                        dst_data[0]          = GGML_FP32_TO_FP16(x0*cos_theta - x1*sin_theta);
                        dst_data[n_dims/2]   = GGML_FP32_TO_FP16(x0*sin_theta + x1*cos_theta);
                        dst_data[n_dims]     = GGML_FP32_TO_FP16(x2*cos_block_theta - x3*sin_block_theta);
                        dst_data[n_dims/2*3] = GGML_FP32_TO_FP16(x2*sin_block_theta + x3*cos_block_theta);
                    }
                } if (!is_neox) {
                    for (int64_t i0 = 0; i0 < ne0; i0 += 2) {
                        const float cos_theta = cosf(theta);
                        const float sin_theta = sinf(theta);

                        theta *= theta_scale;

                        const ggml_fp16_t * const src = (ggml_fp16_t *)((char *) src0->data + i3*nb03 + i2*nb02 + i1*nb01 + i0*nb00);
                              ggml_fp16_t * dst_data  = (ggml_fp16_t *)((char *)  dst->data + i3*nb3  + i2*nb2  + i1*nb1  + i0*nb0);

                        const float x0 = GGML_FP16_TO_FP32(src[0]);
                        const float x1 = GGML_FP16_TO_FP32(src[1]);

                        dst_data[0] = GGML_FP32_TO_FP16(x0*cos_theta - x1*sin_theta);
                        dst_data[1] = GGML_FP32_TO_FP16(x0*sin_theta + x1*cos_theta);
                    }
                } else {
                    // TODO: this is probably wrong, but I can't figure it out ..
                    // ref:  https://github.com/huggingface/transformers/blob/main/src/transformers/models/gpt_neox/modeling_gpt_neox.py#LL251C1-L294C28
                    for (int64_t ib = 0; ib < ne0/n_dims; ++ib) {
                        for (int64_t ic = 0; ic < n_dims; ic += 2) {
                            const float cos_theta = cosf(theta);
                            const float sin_theta = sinf(theta);

                            theta *= theta_scale;

                            const int64_t i0 = ib*n_dims + ic/2;

                            const ggml_fp16_t * const src = (ggml_fp16_t *)((char *) src0->data + i3*nb03 + i2*nb02 + i1*nb01 + i0*nb00);
                                  ggml_fp16_t * dst_data  = (ggml_fp16_t *)((char *)  dst->data + i3*nb3  + i2*nb2  + i1*nb1  + i0*nb0);

                            const float x0 = GGML_FP16_TO_FP32(src[0]);
                            const float x1 = GGML_FP16_TO_FP32(src[n_dims/2]);

                            dst_data[0]     = GGML_FP32_TO_FP16(x0*cos_theta - x1*sin_theta);
                            dst_data[n_dims/2] = GGML_FP32_TO_FP16(x0*sin_theta + x1*cos_theta);
                        }
                    }
                }
            }
        }
    }
}

static void ggml_compute_forward_rope(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F16:
            {
                ggml_compute_forward_rope_f16(params, src0, src1, dst);
            } break;
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_rope_f32(params, src0, src1, dst);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_rope_back

static void ggml_compute_forward_rope_back_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    assert(src1->type == GGML_TYPE_I32);
    assert(ggml_nelements(src1) == 3);

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    // y = rope(x, src1)
    // dx = rope_back(dy, src1)
    // src0 is dy, src1 contains options

    const int n_past = ((int32_t *) src1->data)[0];
    const int n_dims = ((int32_t *) src1->data)[1];
    const int mode   = ((int32_t *) src1->data)[2];

    assert(n_past >= 0);

    GGML_TENSOR_UNARY_OP_LOCALS;

    //printf("ne0: %d, ne1: %d, ne2: %d, ne3: %d\n", ne0, ne1, ne2, ne3);
    //printf("n_past = %d, ne2 = %d\n", n_past, ne2);

    assert(nb0 == sizeof(float));

    const int ith = params->ith;
    const int nth = params->nth;

    const int nr = ggml_nrows(dst);

    // rows per thread
    const int dr = (nr + nth - 1)/nth;

    // row range for this thread
    const int ir0 = dr*ith;
    const int ir1 = MIN(ir0 + dr, nr);

    // row index used to determine which thread to use
    int ir = 0;

    const float theta_scale = powf(10000.0, -2.0f/n_dims);

    const bool is_neox = mode & 2;

    for (int64_t i3 = 0; i3 < ne3; i3++) {
        for (int64_t i2 = ((mode & 1) == 0 ? 0 : n_past); i2 < ne2; i2++) {
            const int64_t p = ((mode & 1) == 0 ? n_past + i2 : i2);
            for (int64_t i1 = 0; i1 < ne1; i1++) {
                if (ir++ < ir0) continue;
                if (ir   > ir1) break;

                float theta = (float)p;

                if (!is_neox) {
                    for (int64_t i0 = 0; i0 < ne0; i0 += 2) {
                        const float cos_theta = cosf(theta);
                        const float sin_theta = sinf(theta);

                        theta *= theta_scale;

                        const float * const dy  = (float *)((char *) src0->data + i3*nb03 + i2*nb02 + i1*nb01 + i0*nb00);
                              float *       dx  = (float *)((char *)  dst->data + i3*nb3  + i2*nb2  + i1*nb1  + i0*nb0);

                        const float dy0 = dy[0];
                        const float dy1 = dy[1];

                        dx[0] =   dy0*cos_theta + dy1*sin_theta;
                        dx[1] = - dy0*sin_theta + dy1*cos_theta;
                    }
                } else {
                    for (int64_t ib = 0; ib < ne0/n_dims; ++ib) {
                        for (int64_t ic = 0; ic < n_dims; ic += 2) {
                            const float cos_theta = cosf(theta);
                            const float sin_theta = sinf(theta);

                            theta *= theta_scale;

                            const int64_t i0 = ib*n_dims + ic/2;

                            const float * const dy  = (float *)((char *) src0->data + i3*nb03 + i2*nb02 + i1*nb01 + i0*nb00);
                                  float *       dx  = (float *)((char *)  dst->data + i3*nb3  + i2*nb2  + i1*nb1  + i0*nb0);

                            const float dy0 = dy[0];
                            const float dy1 = dy[n_dims/2];

                            dx[0]        =   dy0*cos_theta + dy1*sin_theta;
                            dx[n_dims/2] = - dy0*sin_theta + dy1*cos_theta;
                        }
                    }
                }
            }
        }
    }
}

static void ggml_compute_forward_rope_back_f16(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    assert(src1->type == GGML_TYPE_I32);
    assert(ggml_nelements(src1) == 3);

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    // y = rope(x, src1)
    // dx = rope_back(dy, src1)
    // src0 is dy, src1 contains options

    const int n_past = ((int32_t *) src1->data)[0];
    const int n_dims = ((int32_t *) src1->data)[1];
    const int mode   = ((int32_t *) src1->data)[2];

    assert(n_past >= 0);

    GGML_TENSOR_UNARY_OP_LOCALS;

    //printf("ne0: %d, ne1: %d, ne2: %d, ne3: %d\n", ne0, ne1, ne2, ne3);
    //printf("n_past = %d, ne2 = %d\n", n_past, ne2);

    assert(nb0 == sizeof(ggml_fp16_t));

    const int ith = params->ith;
    const int nth = params->nth;

    const int nr = ggml_nrows(dst);

    // rows per thread
    const int dr = (nr + nth - 1)/nth;

    // row range for this thread
    const int ir0 = dr*ith;
    const int ir1 = MIN(ir0 + dr, nr);

    // row index used to determine which thread to use
    int ir = 0;

    const float theta_scale = powf(10000.0, -2.0f/n_dims);

    const bool is_neox = mode & 2;

    for (int64_t i3 = 0; i3 < ne3; i3++) {
        for (int64_t i2 = ((mode & 1) == 0 ? 0 : n_past); i2 < ne2; i2++) {
            const int64_t p = ((mode & 1) == 0 ? n_past + i2 : i2);
            for (int64_t i1 = 0; i1 < ne1; i1++) {
                if (ir++ < ir0) continue;
                if (ir   > ir1) break;

                float theta = (float)p;

                if (!is_neox) {
                    for (int64_t i0 = 0; i0 < ne0; i0 += 2) {
                        const float cos_theta = cosf(theta);
                        const float sin_theta = sinf(theta);

                        theta *= theta_scale;

                        const ggml_fp16_t * const dy  = (ggml_fp16_t *)((char *) src0->data + i3*nb03 + i2*nb02 + i1*nb01 + i0*nb00);
                              ggml_fp16_t *       dx  = (ggml_fp16_t *)((char *)  dst->data + i3*nb3  + i2*nb2  + i1*nb1  + i0*nb0);

                        const float dy0 = GGML_FP16_TO_FP32(dy[0]);
                        const float dy1 = GGML_FP16_TO_FP32(dy[1]);

                        dx[0] = GGML_FP32_TO_FP16( dy0*cos_theta + dy1*sin_theta);
                        dx[1] = GGML_FP32_TO_FP16(-dy0*sin_theta + dy1*cos_theta);
                    }
                } else {
                    for (int64_t ib = 0; ib < ne0/n_dims; ++ib) {
                        for (int64_t ic = 0; ic < n_dims; ic += 2) {
                            const float cos_theta = cosf(theta);
                            const float sin_theta = sinf(theta);

                            theta *= theta_scale;

                            const int64_t i0 = ib*n_dims + ic/2;

                            const ggml_fp16_t * const dy  = (ggml_fp16_t *)((char *) src0->data + i3*nb03 + i2*nb02 + i1*nb01 + i0*nb00);
                                  ggml_fp16_t *       dx  = (ggml_fp16_t *)((char *)  dst->data + i3*nb3  + i2*nb2  + i1*nb1  + i0*nb0);

                            const float dy0 = GGML_FP16_TO_FP32(dy[0]);
                            const float dy1 = GGML_FP16_TO_FP32(dy[n_dims/2]);

                            dx[0]        = GGML_FP32_TO_FP16( dy0*cos_theta + dy1*sin_theta);
                            dx[n_dims/2] = GGML_FP32_TO_FP16(-dy0*sin_theta + dy1*cos_theta);
                        }
                    }
                }
            }
        }
    }
}

static void ggml_compute_forward_rope_back(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F16:
            {
                ggml_compute_forward_rope_back_f16(params, src0, src1, dst);
            } break;
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_rope_back_f32(params, src0, src1, dst);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_conv_1d

static void ggml_compute_forward_conv_1d_s1_ph_f16_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
              struct ggml_tensor * dst) {
    GGML_ASSERT(src0->type == GGML_TYPE_F16);
    GGML_ASSERT(src1->type == GGML_TYPE_F32);
    GGML_ASSERT( dst->type == GGML_TYPE_F32);

    int64_t t0 = ggml_perf_time_us();
    UNUSED(t0);

    GGML_TENSOR_BINARY_OP_LOCALS;

    const int ith = params->ith;
    const int nth = params->nth;

    const int nk = ne00;
    const int nh = nk/2;

    const int ew0 = ggml_up32(ne01);

    GGML_ASSERT(ne00 % 2 == 1); // TODO: support even kernel sizes
    GGML_ASSERT(nb00 == sizeof(ggml_fp16_t));
    GGML_ASSERT(nb10 == sizeof(float));

    if (params->type == GGML_TASK_INIT) {
        // TODO: fix this memset (wsize is overestimated)
        memset(params->wdata, 0, params->wsize);

        // prepare kernel data (src0)
        {
            ggml_fp16_t * const wdata = (ggml_fp16_t *) params->wdata + 0;

            for (int64_t i02 = 0; i02 < ne02; i02++) {
                for (int64_t i01 = 0; i01 < ne01; i01++) {
                    const ggml_fp16_t * const src = (ggml_fp16_t *)((char *) src0->data + i02*nb02 + i01*nb01);
                    ggml_fp16_t * dst_data = wdata + i02*ew0*ne00;
                    for (int64_t i00 = 0; i00 < ne00; i00++) {
                        dst_data[i00*ew0 + i01] = src[i00];
                    }
                }
            }
        }

        // prepare source data (src1)
        {
            ggml_fp16_t * const wdata = (ggml_fp16_t *) params->wdata + ne02*ew0*ne00;

            for (int64_t i11 = 0; i11 < ne11; i11++) {
                const float * const src = (float *)((char *) src1->data + i11*nb11);
                ggml_fp16_t * dst_data = wdata;
                for (int64_t i10 = 0; i10 < ne10; i10++) {
                    dst_data[(i10 + nh)*ew0 + i11] = GGML_FP32_TO_FP16(src[i10]);
                }
            }
        }

        return;
    }

    if (params->type == GGML_TASK_FINALIZE) {
        return;
    }

    // total rows in dst
    const int nr = ne02;

    // rows per thread
    const int dr = (nr + nth - 1)/nth;

    // row range for this thread
    const int ir0 = dr*ith;
    const int ir1 = MIN(ir0 + dr, nr);

    for (int i1 = ir0; i1 < ir1; i1++) {
        float * dst_data = (float *)((char *) dst->data + i1*nb1);
        for (int64_t i0 = 0; i0 < ne10; ++i0) {
            dst_data[i0] = 0;
            for (int k = -nh; k <= nh; k++) {
                float v = 0.0f;
                ggml_vec_dot_f16(ew0, &v,
                        (ggml_fp16_t *) params->wdata +   i1*ew0*ne00 +      (nh + k)*ew0,
                        (ggml_fp16_t *) params->wdata + ne02*ew0*ne00 + (i0 + nh + k)*ew0);

                dst_data[i0] += v;
            }
        }
    }
}

static void ggml_compute_forward_conv_1d_s1_ph_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
              struct ggml_tensor * dst) {
    GGML_ASSERT(src0->type == GGML_TYPE_F32);
    GGML_ASSERT(src1->type == GGML_TYPE_F32);
    GGML_ASSERT( dst->type == GGML_TYPE_F32);

    int64_t t0 = ggml_perf_time_us();
    UNUSED(t0);

    GGML_TENSOR_BINARY_OP_LOCALS;

    const int ith = params->ith;
    const int nth = params->nth;

    const int nk = ne00;
    const int nh = nk/2;

    const int ew0 = ggml_up32(ne01);

    GGML_ASSERT(ne00 % 2 == 1); // TODO: support even kernel sizes
    GGML_ASSERT(nb00 == sizeof(float));
    GGML_ASSERT(nb10 == sizeof(float));

    if (params->type == GGML_TASK_INIT) {
        // TODO: fix this memset (wsize is overestimated)
        memset(params->wdata, 0, params->wsize);

        // prepare kernel data (src0)
        {
            float * const wdata = (float *) params->wdata + 0;

            for (int64_t i02 = 0; i02 < ne02; i02++) {
                for (int64_t i01 = 0; i01 < ne01; i01++) {
                    const float * const src = (float *)((char *) src0->data + i02*nb02 + i01*nb01);
                    float * dst_data = wdata + i02*ew0*ne00;
                    for (int64_t i00 = 0; i00 < ne00; i00++) {
                        dst_data[i00*ew0 + i01] = src[i00];
                    }
                }
            }
        }

        // prepare source data (src1)
        {
            float * const wdata = (float *) params->wdata + ne02*ew0*ne00;

            for (int64_t i11 = 0; i11 < ne11; i11++) {
                const float * const src = (float *)((char *) src1->data + i11*nb11);
                float * dst_data = wdata;
                for (int64_t i10 = 0; i10 < ne10; i10++) {
                    dst_data[(i10 + nh)*ew0 + i11] = src[i10];
                }
            }
        }

        return;
    }

    if (params->type == GGML_TASK_FINALIZE) {
        return;
    }

    // total rows in dst
    const int nr = ne02;

    // rows per thread
    const int dr = (nr + nth - 1)/nth;

    // row range for this thread
    const int ir0 = dr*ith;
    const int ir1 = MIN(ir0 + dr, nr);

    for (int i1 = ir0; i1 < ir1; i1++) {
        float * dst_data = (float *)((char *) dst->data + i1*nb1);
        for (int64_t i0 = 0; i0 < ne10; ++i0) {
            dst_data[i0] = 0;
            for (int k = -nh; k <= nh; k++) {
                float v = 0.0f;
                ggml_vec_dot_f32(ew0, &v,
                        (float *) params->wdata +   i1*ew0*ne00 +      (nh + k)*ew0,
                        (float *) params->wdata + ne02*ew0*ne00 + (i0 + nh + k)*ew0);

                dst_data[i0] += v;
            }
        }
    }
}

static void ggml_compute_forward_conv_1d_s1_ph(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F16:
            {
                ggml_compute_forward_conv_1d_s1_ph_f16_f32(params, src0, src1, dst);
            } break;
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_conv_1d_s1_ph_f32(params, src0, src1, dst);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

static void ggml_compute_forward_conv_1d_s2_ph_f16_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
              struct ggml_tensor * dst) {
    GGML_ASSERT(src0->type == GGML_TYPE_F16);
    GGML_ASSERT(src1->type == GGML_TYPE_F32);
    GGML_ASSERT( dst->type == GGML_TYPE_F32);

    int64_t t0 = ggml_perf_time_us();
    UNUSED(t0);

    GGML_TENSOR_BINARY_OP_LOCALS;

    const int ith = params->ith;
    const int nth = params->nth;

    const int nk = ne00;
    const int nh = nk/2;

    const int ew0 = ggml_up32(ne01);

    GGML_ASSERT(ne00 % 2 == 1); // TODO: support even kernel sizes
    GGML_ASSERT(nb00 == sizeof(ggml_fp16_t));
    GGML_ASSERT(nb10 == sizeof(float));

    if (params->type == GGML_TASK_INIT) {
        // TODO: fix this memset (wsize is overestimated)
        memset(params->wdata, 0, params->wsize);

        // prepare kernel data (src0)
        {
            ggml_fp16_t * const wdata = (ggml_fp16_t *) params->wdata + 0;

            for (int64_t i02 = 0; i02 < ne02; i02++) {
                for (int64_t i01 = 0; i01 < ne01; i01++) {
                    const ggml_fp16_t * const src = (ggml_fp16_t *)((char *) src0->data + i02*nb02 + i01*nb01);
                    ggml_fp16_t * dst_data = wdata + i02*ew0*ne00;
                    for (int64_t i00 = 0; i00 < ne00; i00++) {
                        dst_data[i00*ew0 + i01] = src[i00];
                    }
                }
            }
        }

        // prepare source data (src1)
        {
            ggml_fp16_t * const wdata = (ggml_fp16_t *) params->wdata + ne02*ew0*ne00;

            for (int64_t i11 = 0; i11 < ne11; i11++) {
                const float * const src = (float *)((char *) src1->data + i11*nb11);
                ggml_fp16_t * dst_data = wdata;
                for (int64_t i10 = 0; i10 < ne10; i10++) {
                    dst_data[(i10 + nh)*ew0 + i11] = GGML_FP32_TO_FP16(src[i10]);
                }
            }
        }

        return;
    }

    if (params->type == GGML_TASK_FINALIZE) {
        return;
    }

    // total rows in dst
    const int nr = ne02;

    // rows per thread
    const int dr = (nr + nth - 1)/nth;

    // row range for this thread
    const int ir0 = dr*ith;
    const int ir1 = MIN(ir0 + dr, nr);

    for (int i1 = ir0; i1 < ir1; i1++) {
        float * dst_data = (float *)((char *) dst->data + i1*nb1);
        for (int64_t i0 = 0; i0 < ne10; i0 += 2) {
            dst_data[i0/2] = 0;
            for (int k = -nh; k <= nh; k++) {
                float v = 0.0f;
                ggml_vec_dot_f16(ew0, &v,
                        (ggml_fp16_t *) params->wdata +   i1*ew0*ne00 +      (nh + k)*ew0,
                        (ggml_fp16_t *) params->wdata + ne02*ew0*ne00 + (i0 + nh + k)*ew0);

                dst_data[i0/2] += v;
            }
        }
    }
}

static void ggml_compute_forward_conv_1d_s2_ph_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
              struct ggml_tensor * dst) {
    GGML_ASSERT(src0->type == GGML_TYPE_F32);
    GGML_ASSERT(src1->type == GGML_TYPE_F32);
    GGML_ASSERT( dst->type == GGML_TYPE_F32);

    int64_t t0 = ggml_perf_time_us();
    UNUSED(t0);

    GGML_TENSOR_BINARY_OP_LOCALS;

    const int ith = params->ith;
    const int nth = params->nth;

    const int nk = ne00;
    const int nh = nk/2;

    const int ew0 = ggml_up32(ne01);

    GGML_ASSERT(ne00 % 2 == 1); // TODO: support even kernel sizes
    GGML_ASSERT(nb00 == sizeof(float));
    GGML_ASSERT(nb10 == sizeof(float));

    if (params->type == GGML_TASK_INIT) {
        // TODO: fix this memset (wsize is overestimated)
        memset(params->wdata, 0, params->wsize);

        // prepare kernel data (src0)
        {
            float * const wdata = (float *) params->wdata + 0;

            for (int64_t i02 = 0; i02 < ne02; i02++) {
                for (int64_t i01 = 0; i01 < ne01; i01++) {
                    const float * const src = (float *)((char *) src0->data + i02*nb02 + i01*nb01);
                    float * dst_data = wdata + i02*ew0*ne00;
                    for (int64_t i00 = 0; i00 < ne00; i00++) {
                        dst_data[i00*ew0 + i01] = src[i00];
                    }
                }
            }
        }

        // prepare source data (src1)
        {
            float * const wdata = (float *) params->wdata + ne02*ew0*ne00;

            for (int64_t i11 = 0; i11 < ne11; i11++) {
                const float * const src = (float *)((char *) src1->data + i11*nb11);
                float * dst_data = wdata;
                for (int64_t i10 = 0; i10 < ne10; i10++) {
                    dst_data[(i10 + nh)*ew0 + i11] = src[i10];
                }
            }
        }

        return;
    }

    if (params->type == GGML_TASK_FINALIZE) {
        return;
    }

    // total rows in dst
    const int nr = ne02;

    // rows per thread
    const int dr = (nr + nth - 1)/nth;

    // row range for this thread
    const int ir0 = dr*ith;
    const int ir1 = MIN(ir0 + dr, nr);

    for (int i1 = ir0; i1 < ir1; i1++) {
        float * dst_data = (float *)((char *) dst->data + i1*nb1);
        for (int64_t i0 = 0; i0 < ne10; i0 += 2) {
            dst_data[i0/2] = 0;
            for (int k = -nh; k <= nh; k++) {
                float v = 0.0f;
                ggml_vec_dot_f32(ew0, &v,
                        (float *) params->wdata +   i1*ew0*ne00 +      (nh + k)*ew0,
                        (float *) params->wdata + ne02*ew0*ne00 + (i0 + nh + k)*ew0);

                dst_data[i0/2] += v;
            }
        }
    }
}

static void ggml_compute_forward_conv_1d_s2_ph(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F16:
            {
                ggml_compute_forward_conv_1d_s2_ph_f16_f32(params, src0, src1, dst);
            } break;
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_conv_1d_s2_ph_f32(params, src0, src1, dst);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_conv_1d

static void ggml_compute_forward_conv_1d(
    const struct ggml_compute_params * params,
    const struct ggml_tensor * src0,
    const struct ggml_tensor * src1,
    const struct ggml_tensor * opt0,
    struct ggml_tensor * dst) {
    const int32_t s0 = ((const int32_t*)(opt0->data))[0];
    const int32_t p0 = ((const int32_t*)(opt0->data))[1];
    const int32_t d0 = ((const int32_t*)(opt0->data))[2];
    GGML_ASSERT(d0 == 1); // dilation not supported
    GGML_ASSERT(p0 == src0->ne[0]/2); // only half padding supported
    if (s0 == 1) {
        ggml_compute_forward_conv_1d_s1_ph(params, src0, src1, dst);
    } else if (s0 == 2) {
        ggml_compute_forward_conv_1d_s2_ph(params, src0, src1, dst);
    } else {
        GGML_ASSERT(false); // only stride 1 and 2 supported
    };
}

// ggml_compute_forward_conv_2d_sk_p0

static void ggml_compute_forward_conv_2d_sk_p0_f16_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
              struct ggml_tensor * dst) {
    GGML_ASSERT(src0->type == GGML_TYPE_F16);
    GGML_ASSERT(src1->type == GGML_TYPE_F32);
    GGML_ASSERT( dst->type == GGML_TYPE_F32);

    int64_t t0 = ggml_perf_time_us();
    UNUSED(t0);

    GGML_TENSOR_BINARY_OP_LOCALS;

    const int ith = params->ith;
    const int nth = params->nth;

    const int nk0 = ne00;
    const int nk1 = ne01;

    // size of the convolution row - the kernel size unrolled across all channels
    const int ew0 = nk0*nk1*ne02;

    GGML_ASSERT(nb00 == sizeof(ggml_fp16_t));
    GGML_ASSERT(nb10 == sizeof(float));

    if (params->type == GGML_TASK_INIT) {
        // TODO: fix this memset (wsize is overestimated)
        memset(params->wdata, 0, params->wsize);

        // prepare source data (src1)
        {
            ggml_fp16_t * const wdata = (ggml_fp16_t *) params->wdata + 0;

            for (int i12 = 0; i12 < ne12; i12++) {
                const float * const src = (float *)((char *) src1->data + i12*nb12);
                ggml_fp16_t * dst_data = wdata;

                for (int i1 = 0; i1 < ne1; i1++) {
                    for (int i0 = 0; i0 < ne0; i0++) {
                        for (int ik1 = 0; ik1 < nk1; ik1++) {
                            for (int ik0 = 0; ik0 < nk0; ik0++) {
                                dst_data[(i1*ne0 + i0)*ew0 + i12*(nk0*nk1) + ik1*nk0 + ik0] =
                                    GGML_FP32_TO_FP16(src[(i1*nk1 + ik1)*ne10 + (i0*nk0 + ik0)]);
                            }
                        }
                    }
                }
            }
        }

        return;
    }

    if (params->type == GGML_TASK_FINALIZE) {
        return;
    }

    // total patches in dst
    const int np = ne2;

    // patches per thread
    const int dp = (np + nth - 1)/nth;

    // patch range for this thread
    const int ip0 = dp*ith;
    const int ip1 = MIN(ip0 + dp, np);

    ggml_fp16_t * const wdata = (ggml_fp16_t *) params->wdata + 0;

    for (int i2 = ip0; i2 < ip1; i2++) {
        float * dst_data = (float *)((char *) dst->data + i2*nb2);

        for (int i1 = 0; i1 < ne1; ++i1) {
            for (int i0 = 0; i0 < ne0; ++i0) {
                ggml_vec_dot_f16(ew0, dst_data + i1*ne0 + i0,
                        (ggml_fp16_t *) ((char *) src0->data + i2*nb03),
                        (ggml_fp16_t *)                wdata + (i1*ne0 + i0)*ew0);
            }
        }
    }
}

static void ggml_compute_forward_conv_2d_sk_p0(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F16:
            {
                ggml_compute_forward_conv_2d_sk_p0_f16_f32(params, src0, src1, dst);
            } break;
        case GGML_TYPE_F32:
            {
                //ggml_compute_forward_conv_2d_sk_p0_f32(params, src0, src1, dst);
                GGML_ASSERT(false);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_conv_2d

static void ggml_compute_forward_conv_2d(
    const struct ggml_compute_params* params,
    const struct ggml_tensor* src0,
    const struct ggml_tensor* src1,
    const struct ggml_tensor* opt0,
    struct ggml_tensor* dst) {
    const int32_t s0 = ((const int32_t*)(opt0->data))[0];
    const int32_t s1 = ((const int32_t*)(opt0->data))[1];
    const int32_t p0 = ((const int32_t*)(opt0->data))[2];
    const int32_t p1 = ((const int32_t*)(opt0->data))[3];
    const int32_t d0 = ((const int32_t*)(opt0->data))[4];
    const int32_t d1 = ((const int32_t*)(opt0->data))[5];
    GGML_ASSERT(d0 == 1); // dilation not supported
    GGML_ASSERT(d1 == 1);
    GGML_ASSERT(p0 == 0); // padding not supported
    GGML_ASSERT(p1 == 0);

    if (s0 == src0->ne[0] && s1 == src0->ne[1]) {
        ggml_compute_forward_conv_2d_sk_p0(params, src0, src1, dst);
    }
    else {
        GGML_ASSERT(false); // only stride equal to kernel size is supported
    };
}


// ggml_compute_forward_flash_attn

static void ggml_compute_forward_flash_attn_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * q,
        const struct ggml_tensor * k,
        const struct ggml_tensor * v,
        const bool masked,
             struct ggml_tensor * dst) {
    int64_t t0 = ggml_perf_time_us();
    UNUSED(t0);

    GGML_TENSOR_LOCALS(int64_t, neq, q,   ne);
    GGML_TENSOR_LOCALS(size_t,  nbq, q,   nb);
    GGML_TENSOR_LOCALS(int64_t, nek, k,   ne);
    GGML_TENSOR_LOCALS(size_t,  nbk, k,   nb);
    GGML_TENSOR_LOCALS(int64_t, nev, v,   ne);
    GGML_TENSOR_LOCALS(size_t,  nbv, v,   nb);
    GGML_TENSOR_LOCALS(int64_t, ne,  dst, ne);
    GGML_TENSOR_LOCALS(size_t,  nb,  dst, nb);

    const int ith = params->ith;
    const int nth = params->nth;

    const int64_t D = neq0;
    const int64_t N = neq1;
    const int64_t P = nek1 - N;
    const int64_t M = P + N;

    const int Mup = ggml_up(M, GGML_SOFT_MAX_UNROLL);

    GGML_ASSERT(ne0 == D);
    GGML_ASSERT(ne1 == N);
    GGML_ASSERT(P >= 0);

    GGML_ASSERT(nbq0 == sizeof(float));
    GGML_ASSERT(nbk0 == sizeof(float));
    GGML_ASSERT(nbv0 == sizeof(float));

    GGML_ASSERT(neq0 == D);
    GGML_ASSERT(nek0 == D);
    GGML_ASSERT(nev1 == D);

    GGML_ASSERT(neq1 == N);
    GGML_ASSERT(nek1 == N + P);
    GGML_ASSERT(nev1 == D);

    // dst cannot be transposed or permuted
    GGML_ASSERT(nb0 == sizeof(float));
    GGML_ASSERT(nb0 <= nb1);
    GGML_ASSERT(nb1 <= nb2);
    GGML_ASSERT(nb2 <= nb3);

    if (params->type == GGML_TASK_INIT) {
        return;
    }

    if (params->type == GGML_TASK_FINALIZE) {
        return;
    }

    // parallelize by q rows using ggml_vec_dot_f32

    // total rows in q
    const int nr = neq1*neq2*neq3;

    // rows per thread
    const int dr = (nr + nth - 1)/nth;

    // row range for this thread
    const int ir0 = dr*ith;
    const int ir1 = MIN(ir0 + dr, nr);

    const float scale = 1.0f/sqrtf(D);

    //printf("P=%d N=%d D=%d ir0=%d ir1=%d scale = %f\n", P, N, D, ir0, ir1, scale);

    for (int ir = ir0; ir < ir1; ++ir) {
        // q indices
        const int iq3 = ir/(neq2*neq1);
        const int iq2 = (ir - iq3*neq2*neq1)/neq1;
        const int iq1 = (ir - iq3*neq2*neq1 - iq2*neq1);

        float * S = (float *) params->wdata + ith*(Mup + CACHE_LINE_SIZE_F32);

        for (int i = M; i < Mup; ++i) {
            S[i] = -INFINITY;
        }

        for (int64_t ic = 0; ic < nek1; ++ic) {
            // k indices
            const int ik3 = iq3;
            const int ik2 = iq2;
            const int ik1 = ic;

            // S indices
            const int i1 = ik1;

            ggml_vec_dot_f32(neq0,
                    S + i1,
                    (float *) ((char *) k->data + (ik1*nbk1 + ik2*nbk2 + ik3*nbk3)),
                    (float *) ((char *) q->data + (iq1*nbq1 + iq2*nbq2 + iq3*nbq3)));
        }

        // scale
        ggml_vec_scale_f32(nek1, S, scale);

        if (masked) {
            for (int64_t i = P; i < M; i++) {
                if (i > P + iq1) {
                    S[i] = -INFINITY;
                }
            }
        }

        // softmax
        {
            float max = -INFINITY;
            ggml_vec_max_f32(M, &max, S);

            ggml_float sum = 0.0;
            {
#ifdef GGML_SOFT_MAX_ACCELERATE
                max = -max;
                vDSP_vsadd(S, 1, &max, S, 1, Mup);
                vvexpf(S, S, &Mup);
                ggml_vec_sum_f32(Mup, &sum, S);
#else
                uint16_t   scvt[GGML_SOFT_MAX_UNROLL];
                ggml_float sump[GGML_SOFT_MAX_UNROLL] = { 0.0 };

                for (int i = 0; i < Mup; i += GGML_SOFT_MAX_UNROLL) {
                    float * SS = S + i;

                    for (int j = 0; j < GGML_SOFT_MAX_UNROLL; ++j) {
                        if (SS[j] == -INFINITY) {
                            SS[j] = 0.0f;
                        } else {
                            ggml_fp16_t s = GGML_FP32_TO_FP16(SS[j] - max);
                            memcpy(&scvt[j], &s, sizeof(uint16_t));
                            const float val = GGML_FP16_TO_FP32(table_exp_f16[scvt[j]]);
                            sump[j] += (ggml_float)val;
                            SS[j] = val;
                        }
                    }
                }

                for (int i = 0; i < GGML_SOFT_MAX_UNROLL; i++) {
                    sum += sump[i];
                }
#endif
            }

            assert(sum > 0.0);

            sum = 1.0/sum;
            ggml_vec_scale_f32(M, S, sum);

#ifndef NDEBUG
            for (int i = 0; i < M; ++i) {
                assert(!isnan(S[i]));
                assert(!isinf(S[i]));
            }
#endif
        }

        for (int64_t ic = 0; ic < nev1; ++ic) {
            // dst indices
            const int i1 = iq1;
            const int i2 = iq2;
            const int i3 = iq3;

            ggml_vec_dot_f32(nek1,
                    (float *) ((char *) dst->data + (ic*nb0 + i1*nb1  + i2*nb2  + i3*nb3)),
                    (float *) ((char *) v->data   + (         ic*nbv1 + i2*nbv2 + i3*nbv3)),
                    S);
        }
    }
}

static void ggml_compute_forward_flash_attn_f16(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * q,
        const struct ggml_tensor * k,
        const struct ggml_tensor * v,
        const bool masked,
             struct ggml_tensor * dst) {
    int64_t t0 = ggml_perf_time_us();
    UNUSED(t0);

    GGML_TENSOR_LOCALS(int64_t, neq, q,   ne);
    GGML_TENSOR_LOCALS(size_t,  nbq, q,   nb);
    GGML_TENSOR_LOCALS(int64_t, nek, k,   ne);
    GGML_TENSOR_LOCALS(size_t,  nbk, k,   nb);
    GGML_TENSOR_LOCALS(int64_t, nev, v,   ne);
    GGML_TENSOR_LOCALS(size_t,  nbv, v,   nb);
    GGML_TENSOR_LOCALS(int64_t, ne,  dst, ne);
    GGML_TENSOR_LOCALS(size_t,  nb,  dst, nb);

    const int ith = params->ith;
    const int nth = params->nth;

    const int64_t D = neq0;
    const int64_t N = neq1;
    const int64_t P = nek1 - N;
    const int64_t M = P + N;

    const int Mup = ggml_up(M, GGML_SOFT_MAX_UNROLL);

    GGML_ASSERT(ne0 == D);
    GGML_ASSERT(ne1 == N);
    GGML_ASSERT(P >= 0);

    GGML_ASSERT(nbq0 == sizeof(ggml_fp16_t));
    GGML_ASSERT(nbk0 == sizeof(ggml_fp16_t));
    GGML_ASSERT(nbv0 == sizeof(ggml_fp16_t));

    GGML_ASSERT(neq0 == D);
    GGML_ASSERT(nek0 == D);
    GGML_ASSERT(nev1 == D);

    GGML_ASSERT(neq1 == N);
    GGML_ASSERT(nek1 == N + P);
    GGML_ASSERT(nev1 == D);

    // dst cannot be transposed or permuted
    GGML_ASSERT(nb0 == sizeof(float));
    GGML_ASSERT(nb0 <= nb1);
    GGML_ASSERT(nb1 <= nb2);
    GGML_ASSERT(nb2 <= nb3);

    if (params->type == GGML_TASK_INIT) {
        return;
    }

    if (params->type == GGML_TASK_FINALIZE) {
        return;
    }

    // parallelize by q rows using ggml_vec_dot_f32

    // total rows in q
    const int nr = neq1*neq2*neq3;

    // rows per thread
    const int dr = (nr + nth - 1)/nth;

    // row range for this thread
    const int ir0 = dr*ith;
    const int ir1 = MIN(ir0 + dr, nr);

    const float scale = 1.0f/sqrtf(D);

    //printf("P=%d N=%d D=%d ir0=%d ir1=%d scale = %f\n", P, N, D, ir0, ir1, scale);

    for (int ir = ir0; ir < ir1; ++ir) {
        // q indices
        const int iq3 = ir/(neq2*neq1);
        const int iq2 = (ir - iq3*neq2*neq1)/neq1;
        const int iq1 = (ir - iq3*neq2*neq1 - iq2*neq1);

        float * S = (float *) params->wdata + ith*(2*Mup + CACHE_LINE_SIZE_F32);

        for (int i = M; i < Mup; ++i) {
            S[i] = -INFINITY;
        }

        if (GGML_VEC_DOT_UNROLL > 2 || nek1 % GGML_VEC_DOT_UNROLL != 0) {
            for (int64_t ic = 0; ic < nek1; ++ic) {
                // k indices
                const int ik3 = iq3;
                const int ik2 = iq2;
                const int ik1 = ic;

                // S indices
                const int i1 = ik1;

                ggml_vec_dot_f16(neq0,
                        S + i1,
                        (ggml_fp16_t *) ((char *) k->data + (ik1*nbk1 + ik2*nbk2 + ik3*nbk3)),
                        (ggml_fp16_t *) ((char *) q->data + (iq1*nbq1 + iq2*nbq2 + iq3*nbq3)));
            }
        } else {
            for (int64_t ic = 0; ic < nek1; ic += GGML_VEC_DOT_UNROLL) {
                // k indices
                const int ik3 = iq3;
                const int ik2 = iq2;
                const int ik1 = ic;

                // S indices
                const int i1 = ik1;

                ggml_vec_dot_f16_unroll(neq0, nbk1,
                        S + i1,
                        ((char *) k->data + (ik1*nbk1 + ik2*nbk2 + ik3*nbk3)),
                        (ggml_fp16_t *) ((char *) q->data + (iq1*nbq1 + iq2*nbq2 + iq3*nbq3)));
            }
        }

        // scale
        ggml_vec_scale_f32(nek1, S, scale);

        if (masked) {
            for (int64_t i = P; i < M; i++) {
                if (i > P + iq1) {
                    S[i] = -INFINITY;
                }
            }
        }

        // softmax
        {
            float max = -INFINITY;
            ggml_vec_max_f32(M, &max, S);

            ggml_float sum = 0.0;
            {
#ifdef GGML_SOFT_MAX_ACCELERATE
                max = -max;
                vDSP_vsadd(S, 1, &max, S, 1, Mup);
                vvexpf(S, S, &Mup);
                ggml_vec_sum_f32(Mup, &sum, S);
#else
                uint16_t   scvt[GGML_SOFT_MAX_UNROLL];
                ggml_float sump[GGML_SOFT_MAX_UNROLL] = { 0.0 };

                for (int i = 0; i < Mup; i += GGML_SOFT_MAX_UNROLL) {
                    float * SS = S + i;

                    for (int j = 0; j < GGML_SOFT_MAX_UNROLL; ++j) {
                        if (SS[j] == -INFINITY) {
                            SS[j] = 0.0f;
                        } else {
                            ggml_fp16_t s = GGML_FP32_TO_FP16(SS[j] - max);
                            memcpy(&scvt[j], &s, sizeof(uint16_t));
                            const float val = GGML_FP16_TO_FP32(table_exp_f16[scvt[j]]);
                            sump[j] += (ggml_float)val;
                            SS[j] = val;
                        }
                    }
                }

                for (int i = 0; i < GGML_SOFT_MAX_UNROLL; i++) {
                    sum += sump[i];
                }
#endif
            }

            assert(sum > 0.0);

            sum = 1.0/sum;
            ggml_vec_scale_f32(M, S, sum);

#ifndef NDEBUG
            for (int i = 0; i < M; ++i) {
                assert(!isnan(S[i]));
                assert(!isinf(S[i]));
            }
#endif
        }

        ggml_fp16_t * S16 = (ggml_fp16_t *) ((float *) params->wdata + ith*(2*Mup + CACHE_LINE_SIZE_F32) + Mup);

        for (int64_t i = 0; i < M; i++) {
            S16[i] = GGML_FP32_TO_FP16(S[i]);
        }

        if (GGML_VEC_DOT_UNROLL == 1 || (nev1 % GGML_VEC_DOT_UNROLL != 0)) {
            for (int64_t ic = 0; ic < nev1; ++ic) {
                // dst indices
                const int i1 = iq1;
                const int i2 = iq2;
                const int i3 = iq3;

                ggml_vec_dot_f16(nek1,
                        (float *)       ((char *) dst->data + (ic*nb0 + i1*nb1  + i2*nb2  + i3*nb3)),
                        (ggml_fp16_t *) ((char *) v->data   + (         ic*nbv1 + i2*nbv2 + i3*nbv3)),
                        S16);
            }
        } else {
            for (int64_t ic = 0; ic < nev1; ic += GGML_VEC_DOT_UNROLL) {
                // dst indices
                const int i1 = iq1;
                const int i2 = iq2;
                const int i3 = iq3;

                ggml_vec_dot_f16_unroll(nek1, nbv1,
                        (float *) ((char *) dst->data + (ic*nb0 + i1*nb1  + i2*nb2  + i3*nb3)),
                        ((char *) v->data   + (         ic*nbv1 + i2*nbv2 + i3*nbv3)),
                        S16);
            }
        }
    }
}

static void ggml_compute_forward_flash_attn(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * q,
        const struct ggml_tensor * k,
        const struct ggml_tensor * v,
        const bool masked,
        struct ggml_tensor * dst) {
    switch (q->type) {
        case GGML_TYPE_F16:
            {
                ggml_compute_forward_flash_attn_f16(params, q, k, v, masked, dst);
            } break;
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_flash_attn_f32(params, q, k, v, masked, dst);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_flash_ff

static void ggml_compute_forward_flash_ff_f16(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * a,  // F16
        const struct ggml_tensor * b0, // F16 fc_w
        const struct ggml_tensor * b1, // F32 fc_b
        const struct ggml_tensor * c0, // F16 proj_w
        const struct ggml_tensor * c1, // F32 proj_b
        struct ggml_tensor * dst) {
    int64_t t0 = ggml_perf_time_us();
    UNUSED(t0);

    GGML_TENSOR_LOCALS(int64_t, nea,  a,   ne);
    GGML_TENSOR_LOCALS(size_t,  nba,  a,   nb);
    GGML_TENSOR_LOCALS(int64_t, neb0, b0,  ne);
    GGML_TENSOR_LOCALS(size_t,  nbb0, b0,  nb);
    GGML_TENSOR_LOCALS(int64_t, neb1, b1,  ne);
    GGML_TENSOR_LOCALS(size_t,  nbb1, b1,  nb);
    GGML_TENSOR_LOCALS(int64_t, nec0, c0,  ne);
    GGML_TENSOR_LOCALS(size_t,  nbc0, c0,  nb);
    GGML_TENSOR_LOCALS(int64_t, nec1, c1,  ne);
    GGML_TENSOR_LOCALS(size_t,  nbc1, c1,  nb);
    GGML_TENSOR_LOCALS(int64_t, ne,   dst, ne);
    GGML_TENSOR_LOCALS(size_t,  nb,   dst, nb);

    const int ith = params->ith;
    const int nth = params->nth;

    const int64_t D = nea0;
    //const int64_t N = nea1;
    const int64_t M = neb01;

    GGML_ASSERT(ne0 == nea0);
    GGML_ASSERT(ne1 == nea1);
    GGML_ASSERT(ne2 == nea2);

    GGML_ASSERT(nba0  == sizeof(ggml_fp16_t));
    GGML_ASSERT(nbb00 == sizeof(ggml_fp16_t));
    GGML_ASSERT(nbb10 == sizeof(float));
    GGML_ASSERT(nbc00 == sizeof(ggml_fp16_t));
    GGML_ASSERT(nbc10 == sizeof(float));

    GGML_ASSERT(neb00 == D);
    GGML_ASSERT(neb01 == M);
    GGML_ASSERT(neb10 == M);
    GGML_ASSERT(neb11 == 1);

    GGML_ASSERT(nec00 == M);
    GGML_ASSERT(nec01 == D);
    GGML_ASSERT(nec10 == D);
    GGML_ASSERT(nec11 == 1);

    // dst cannot be transposed or permuted
    GGML_ASSERT(nb0 == sizeof(float));
    GGML_ASSERT(nb0 <= nb1);
    GGML_ASSERT(nb1 <= nb2);
    GGML_ASSERT(nb2 <= nb3);

    if (params->type == GGML_TASK_INIT) {
        return;
    }

    if (params->type == GGML_TASK_FINALIZE) {
        return;
    }

    // parallelize by a rows using ggml_vec_dot_f32

    // total rows in a
    const int nr = nea1*nea2*nea3;

    // rows per thread
    const int dr = (nr + nth - 1)/nth;

    // row range for this thread
    const int ir0 = dr*ith;
    const int ir1 = MIN(ir0 + dr, nr);

    for (int ir = ir0; ir < ir1; ++ir) {
        // a indices
        const int ia3 = ir/(nea2*nea1);
        const int ia2 = (ir - ia3*nea2*nea1)/nea1;
        const int ia1 = (ir - ia3*nea2*nea1 - ia2*nea1);

        float * S = (float *) params->wdata + ith*(2*M + CACHE_LINE_SIZE_F32);

        for (int64_t ic = 0; ic < neb01; ++ic) {
            // b0 indices
            const int ib03 = ia3;
            const int ib02 = ia2;
            const int ib01 = ic;

            // S indices
            const int i1 = ib01;

            ggml_vec_dot_f16(nea0,
                    S + i1,
                    (ggml_fp16_t *) ((char *) b0->data + (ib01*nbb01 + ib02*nbb02 + ib03*nbb03)),
                    (ggml_fp16_t *) ((char *)  a->data + ( ia1*nba1  +  ia2*nba2  +  ia3*nba3)));
        }

        ggml_vec_add_f32(neb01, S, S, (float *) b1->data);
        //ggml_vec_gelu_f32(neb01, S, S);

        ggml_fp16_t * S16 = (ggml_fp16_t *) ((float *) params->wdata + ith*(2*M + CACHE_LINE_SIZE_F32) + M);

        for (int64_t i = 0; i < M; i++) {
            S16[i] = GGML_FP32_TO_FP16(S[i]);
        }

        ggml_vec_gelu_f16(neb01, S16, S16);

        {
            // dst indices
            const int i1 = ia1;
            const int i2 = ia2;
            const int i3 = ia3;

            for (int64_t ic = 0; ic < nec01; ++ic) {

                ggml_vec_dot_f16(neb01,
                        (float *)       ((char *) dst->data + (ic*nb0 + i1*nb1   + i2*nb2   + i3*nb3)),
                        (ggml_fp16_t *) ((char *) c0->data  + (         ic*nbc01 + i2*nbc02 + i3*nbc03)),
                        S16);
            }

            ggml_vec_add_f32(nec01,
                    (float *) ((char *) dst->data + (i1*nb1 + i2*nb2 + i3*nb3)),
                    (float *) ((char *) dst->data + (i1*nb1 + i2*nb2 + i3*nb3)),
                    (float *) c1->data);
        }
    }
}

static void ggml_compute_forward_flash_ff(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * a,
        const struct ggml_tensor * b0,
        const struct ggml_tensor * b1,
        const struct ggml_tensor * c0,
        const struct ggml_tensor * c1,
        struct ggml_tensor * dst) {
    switch (b0->type) {
        case GGML_TYPE_F16:
            {
                ggml_compute_forward_flash_ff_f16(params, a, b0, b1, c0, c1, dst);
            } break;
        case GGML_TYPE_F32:
            {
                GGML_ASSERT(false); // TODO
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_flash_attn_back

static void ggml_compute_forward_flash_attn_back_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * q,
        const struct ggml_tensor * k,
        const struct ggml_tensor * v,
        const struct ggml_tensor * d,
        const bool masked,
              struct ggml_tensor * dst) {
    int64_t t0 = ggml_perf_time_us();
    UNUSED(t0);

    GGML_TENSOR_LOCALS(int64_t, neq, q,   ne);
    GGML_TENSOR_LOCALS(size_t,  nbq, q,   nb);
    GGML_TENSOR_LOCALS(int64_t, nek, k,   ne);
    GGML_TENSOR_LOCALS(size_t,  nbk, k,   nb);
    GGML_TENSOR_LOCALS(int64_t, nev, v,   ne);
    GGML_TENSOR_LOCALS(size_t,  nbv, v,   nb);
    GGML_TENSOR_LOCALS(int64_t, ned, d,   ne);
    GGML_TENSOR_LOCALS(size_t,  nbd, d,   nb);
    GGML_TENSOR_LOCALS(int64_t, ne,  dst, ne);
    GGML_TENSOR_LOCALS(size_t,  nb,  dst, nb);

    const int ith = params->ith;
    const int nth = params->nth;

    const int64_t D = neq0;
    const int64_t N = neq1;
    const int64_t P = nek1 - N;
    const int64_t M = P + N;

    const int Mup  = ggml_up(M, GGML_SOFT_MAX_UNROLL);
    const int mxDM = MAX(D, Mup);

    // GGML_ASSERT(ne0 == D);
    // GGML_ASSERT(ne1 == N);
    GGML_ASSERT(P >= 0);

    GGML_ASSERT(nbq0 == sizeof(float));
    GGML_ASSERT(nbk0 == sizeof(float));
    GGML_ASSERT(nbv0 == sizeof(float));

    GGML_ASSERT(neq0 == D);
    GGML_ASSERT(nek0 == D);
    GGML_ASSERT(nev1 == D);
    GGML_ASSERT(ned0 == D);

    GGML_ASSERT(neq1 == N);
    GGML_ASSERT(nek1 == N + P);
    GGML_ASSERT(nev1 == D);
    GGML_ASSERT(ned1 == N);

    // dst cannot be transposed or permuted
    GGML_ASSERT(nb0 == sizeof(float));
    GGML_ASSERT(nb0 <= nb1);
    GGML_ASSERT(nb1 <= nb2);
    GGML_ASSERT(nb2 <= nb3);

    if (params->type == GGML_TASK_INIT) {
        if (ith == 0) {
            memset(dst->data, 0, nb0*ne0*ne1*ne2*ne3);
        }
        return;
    }

    if (params->type == GGML_TASK_FINALIZE) {
        return;
    }

    // parallelize by q rows using ggml_vec_dot_f32

    // total rows in q
    const int nr = neq2*neq3;

    // rows per thread
    const int dr = (nr + nth - 1)/nth;

    // row range for this thread
    const int ir0 = dr*ith;
    const int ir1 = MIN(ir0 + dr, nr);

    const float scale = 1.0f/sqrtf(D);

    //printf("P=%d N=%d D=%d ir0=%d ir1=%d scale = %f\n", P, N, D, ir0, ir1, scale);

    for (int ir = ir0; ir < ir1; ++ir) {
        // q indices
        const int iq3 = ir/(neq2);
        const int iq2 = ir - iq3*neq2;
        for ( int iq1 = 0; iq1 < neq1; ++iq1) {


            // not sure about CACHE_LINE_SIZE_F32..
            // - maybe it must not be multiplied by 2 and excluded from .. in SM 1*(..) offset?
            float * S  = (float *) params->wdata + ith*2*(mxDM + CACHE_LINE_SIZE_F32) + 0*(mxDM+CACHE_LINE_SIZE_F32);
            float * SM = (float *) params->wdata + ith*2*(mxDM + CACHE_LINE_SIZE_F32) + 1*(mxDM+CACHE_LINE_SIZE_F32);

            for (int i = M; i < Mup; ++i) {
                S[i] = -INFINITY;
            }

            for (int64_t ic = 0; ic < nek1; ++ic) {
                // k indices
                const int ik3 = iq3;
                const int ik2 = iq2;
                const int ik1 = ic;

                // S indices
                const int i1 = ik1;

                ggml_vec_dot_f32(neq0,
                        S + i1,
                        (float *) ((char *) k->data + (ik1*nbk1 + ik2*nbk2 + ik3*nbk3)),
                        (float *) ((char *) q->data + (iq1*nbq1 + iq2*nbq2 + iq3*nbq3)));
            }

            // scale
            ggml_vec_scale_f32(nek1, S, scale);

            if (masked) {
                for (int64_t i = P; i < M; i++) {
                    if (i > P + iq1) {
                        S[i] = -INFINITY;
                    }
                }
            }

            // softmax
            {
                float max = -INFINITY;
                ggml_vec_max_f32(M, &max, S);

                ggml_float sum = 0.0;
                {
#ifdef GGML_SOFT_MAX_ACCELERATE
                    max = -max;
                    vDSP_vsadd(SM, 1, &max, SM, 1, Mup);
                    vvexpf(SM, SM, &Mup);
                    ggml_vec_sum_f32(Mup, &sum, SM);
#else
                    uint16_t   scvt[GGML_SOFT_MAX_UNROLL];
                    ggml_float sump[GGML_SOFT_MAX_UNROLL] = { 0.0 };

                    for (int i = 0; i < Mup; i += GGML_SOFT_MAX_UNROLL) {
                        float * SR =  S + i;
                        float * SW = SM + i;

                        for (int j = 0; j < GGML_SOFT_MAX_UNROLL; ++j) {
                            if (SR[j] == -INFINITY) {
                                SW[j] = 0.0f;
                            } else {
                                ggml_fp16_t s = GGML_FP32_TO_FP16(SR[j] - max);
                                memcpy(&scvt[j], &s, sizeof(uint16_t));
                                const float val = GGML_FP16_TO_FP32(table_exp_f16[scvt[j]]);
                                sump[j] += (ggml_float)val;
                                SW[j] = val;
                            }
                        }
                    }

                    for (int i = 0; i < GGML_SOFT_MAX_UNROLL; i++) {
                        sum += sump[i];
                    }
#endif
                }

                assert(sum > 0.0);

                sum = 1.0/sum;
                ggml_vec_scale_f32(M, SM, sum);

            }

            // step-by-step explanation
            {
                // forward-process                   shape      grads from backward process
                // parallel_for iq2,iq3:
                //  k[:D,:M,:,:]                     [D,M,:,:]  grad[k][:D,:M,iq2,iq3]  += grad[kcur]
                //  q[:D,:N,:,:]                     [D,N,:,:]  grad[q][:D,iq1,iq2,iq3] += grad[qcur]
                //  v[:M,:D,:,:]                     [M,D,:,:]  grad[v][:M,:D,iq2,iq3]  += grad[vcur]
                //  for iq1:
                //   kcur   = k[:D,:M,iq2,iq3]       [D,M,1,1]  grad[kcur] = grad[S1].T @ qcur
                //   qcur   = q[:D,iq1,iq2,iq3]      [D,1,1,1]  grad[qcur] = grad[S1]   @ kcur
                //   vcur   = v[:M,:D,iq2,iq3]       [M,D,1,1]  grad[vcur] = grad[S5].T @ S4
                //   S0     = -Inf                   [D,1,1,1]
                //  ~S1[i]  = dot(kcur[:D,i], qcur)
                //   S1     = qcur @ kcur.T          [M,1,1,1]  grad[S1]   = grad[S2] * scale
                //   S2     = S1 * scale             [M,1,1,1]  grad[S2]   = diag_mask_zero(grad[S3], P)
                //   S3     = diag_mask_inf(S2, P)   [M,1,1,1]  grad[S3]   = S4 * (grad[S4] - dot(S4, grad[S4]))
                //   S4     = softmax(S3)            [M,1,1,1]  grad[S4]   = grad[S5] @ vcur
                //  ~S5[i]  = dot(vcur[:,i], S4)
                //   S5     = S4 @ vcur.T            [D,1,1,1]  grad[S5]   = d[:D,iq1,iq2,iq3]
                //  ~dst[i,iq1,iq2,iq3]  = S5[i]              ^
                //   dst[:D,iq1,iq2,iq3] = S5                 | grad[dst[:D,iq1,iq2,iq3]] = d[:D,iq1,iq2,iq3]
                // dst                               backward-/ grad[dst]                 = d
                //
                // output gradients with their dependencies:
                //
                // grad[kcur] = grad[S1].T @ qcur
                // grad[S1]   = diag_mask_zero(grad[S3], P) * scale
                // grad[S3]   = S4 * (grad[S4] - dot(S4, grad[S4]))
                // grad[S4]   = grad[S5] @ vcur
                // grad[S4]   = d[:D,iq1,iq2,iq3] @ vcur
                // grad[qcur] = grad[S1]   @ kcur
                // grad[vcur] = grad[S5].T @ S4
                // grad[vcur] = d[:D,iq1,iq2,iq3].T @ S4
                //
                // in post-order:
                //
                // S1         = qcur @ kcur.T
                // S2         = S1 * scale
                // S3         = diag_mask_inf(S2, P)
                // S4         = softmax(S3)
                // grad[S4]   = d[:D,iq1,iq2,iq3] @ vcur
                // grad[S3]   = S4 * (grad[S4] - dot(S4, grad[S4]))
                // grad[S1]   = diag_mask_zero(grad[S3], P) * scale
                // grad[qcur] = grad[S1]   @ kcur
                // grad[kcur] = grad[S1].T @ qcur
                // grad[vcur] = d[:D,iq1,iq2,iq3].T @ S4
                //
                // using less variables (SM=S4):
                //
                // S             = diag_mask_inf(qcur @ kcur.T * scale, P)
                // SM            = softmax(S)
                // S             = d[:D,iq1,iq2,iq3] @ vcur
                // dot_SM_gradSM = dot(SM, S)
                // S             = SM * (S - dot(SM, S))
                // S             = diag_mask_zero(S, P) * scale
                //
                // grad[q][:D,iq1,iq2,iq3] += S   @ kcur
                // grad[k][:D,:M,iq2,iq3]  += S.T @ qcur
                // grad[v][:M,:D,iq2,iq3]  += d[:D,iq1,iq2,iq3].T @ SM
            }

            // S = gradSM = d[:D,iq1,iq2,iq3] @ vcur
            // S = d[:D,iq1,iq2,iq3] @ vcur
            // S[:M] += vcur[:M,ic] * d[ic,iq1,iq2,iq3]
            ggml_vec_set_f32(M, S, 0);
            for (int64_t ic = 0; ic < D; ++ic) {
                // dst indices
                const int i1 = iq1;
                const int i2 = iq2;
                const int i3 = iq3;

                ggml_vec_mad_f32(M,
                        S,
                         (float *) ((char *) v->data + (          ic*nbv1 + i2*nbv2 + i3*nbv3)),
                        *(float *) ((char *) d->data + (ic*nbd0 + i1*nbd1 + i2*nbd2 + i3*nbd3)));
            }

            // S = SM * (S - dot(SM, S))
            float dot_SM_gradSM = 0;
            ggml_vec_dot_f32 (M, &dot_SM_gradSM, SM, S);
            ggml_vec_acc1_f32(M, S, -dot_SM_gradSM);
            ggml_vec_mul_f32 (M, S, S, SM);

            // S = diag_mask_zero(S, P) * scale
            if (masked) {
                // for (int64_t i = P + iq1 + 1; i < M; i++) {
                //     S[i] = 0;
                // }
                for (int64_t i = P; i < M; i++) {
                    if (i > P + iq1) {
                        S[i] = 0;
                    }
                }
            }
            ggml_vec_scale_f32(M, S, scale);

            void * grad_q = (char *) dst->data;
            void * grad_k = (char *) dst->data + nb0*D*N*neq2*neq3;
            void * grad_v = (char *) dst->data + nb0*D*N*neq2*neq3 + nb0*D*M*neq2*neq3;

            const size_t nbgq1 = nb0*neq0;
            const size_t nbgq2 = nb0*neq0*neq1;
            const size_t nbgq3 = nb0*neq0*neq1*neq2;

            const size_t nbgk1 = nb0*nek0;
            const size_t nbgk2 = nb0*nek0*nek1;
            const size_t nbgk3 = nb0*nek0*nek1*neq2;

            const size_t nbgv1 = nb0*nev0;
            const size_t nbgv2 = nb0*nev0*nev1;
            const size_t nbgv3 = nb0*nev0*nev1*neq2;

            // S    shape [M,1]
            // SM   shape [M,1]
            // kcur shape [D,M]
            // qcur shape [D,1]
            // vcur shape [M,D]
            //
            // grad[q][:D,iq1,iq2,iq3] += S @ kcur
            // grad[q][:D,iq1,iq2,iq3] += shape[M,1] @ shape[D,M]
            // grad[q][:D,iq1,iq2,iq3] += S[ic] * kcur[:D,ic]
            //
            //// grad[q][ic,iq1,iq2,iq3] += dot(kcur[:,ic],S.T)
            //// grad[q][ic,iq1,iq2,iq3] += dot(k[:D,ic,iq2,iq3],S.T)
            for (int64_t ic = 0; ic < M; ++ic) {
                // dst indices
                const int i1 = iq1;
                const int i2 = iq2;
                const int i3 = iq3;

                ggml_vec_mad_f32(D,
                        (float *) ((char *) grad_q  + (i1*nbgq1  + i2*nbgq2  + i3*nbgq3)),
                        (float *) ((char *) k->data + (ic*nbk1   + i2*nbk2   + i3*nbk3)),
                        S[ic]);
            }

            // grad[k][:D,:M,iq2,iq3] += S.T       @ qcur
            // grad[k][:D,ic,iq2,iq3] += S.T[0,ic] * qcur[:D,0]
            // grad[k][:D,ic,iq2,iq3] += S[ic]     * qcur[:D,0]
            for (int64_t ic = 0; ic < M; ++ic) {
                // dst indices
                const int i1 = iq1;
                const int i2 = iq2;
                const int i3 = iq3;

                // ggml_vec_set_f32(D,
                //         (float *) ((char *) grad_k  + (ic*nbgk1  + i2*nbgk2  + i3*nbgk3)),
                //         0);
                ggml_vec_mad_f32(D,
                        (float *) ((char *) grad_k  + (ic*nbgk1  + i2*nbgk2  + i3*nbgk3)),
                        (float *) ((char *) q->data + (i1*nbq1   + i2*nbq2   + i3*nbq3)),
                        S[ic]);
            }

            // grad[v][:M,:D,iq2,iq3] += d[:D,iq1,iq2,iq3].T       @ SM
            // grad[v][:M,ic,iq2,iq3] += d[:D,iq1,iq2,iq3].T[0,ic] * SM[:M]
            // grad[v][:M,ic,iq2,iq3] += d[ic,iq1,iq2,iq3]         * SM[:M]
            for (int64_t ic = 0; ic < D; ++ic) {
                // dst indices
                const int i1 = iq1;
                const int i2 = iq2;
                const int i3 = iq3;

                // ggml_vec_set_f32(M,
                //         (float *) ((char *) grad_v   + (          ic*nbgv1 + i2*nbgv2 + i3*nbgv3)),
                //         0);
                ggml_vec_mad_f32(M,
                        (float *) ((char *) grad_v   + (          ic*nbgv1 + i2*nbgv2 + i3*nbgv3)),
                        SM,
                        *(float *) ((char *) d->data + (ic*nbd0 + i1*nbd1  + i2*nbd2  + i3*nbd3)));
            }
        }
    }
}

static void ggml_compute_forward_flash_attn_back(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * q,
        const struct ggml_tensor * k,
        const struct ggml_tensor * v,
        const struct ggml_tensor * d,
        const bool masked,
        struct ggml_tensor * dst) {
    switch (q->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_flash_attn_back_f32(params, q, k, v, d, masked, dst);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_win_part

static void ggml_compute_forward_win_part_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * opt0,
        struct ggml_tensor * dst) {
    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    GGML_TENSOR_LOCALS(int64_t, ne0, src0, ne);
    GGML_TENSOR_LOCALS(int64_t, ne,  dst,  ne);

    const int32_t nep0 = ((const int32_t *)(opt0->data))[0];
    const int32_t nep1 = ((const int32_t *)(opt0->data))[1];
    const int32_t w    = ((const int32_t *)(opt0->data))[2];

    assert(ne00 == ne0);
    assert(ne3  == nep0*nep1);

    // TODO: optimize / multi-thread
    for (int py = 0; py < nep1; ++py) {
        for (int px = 0; px < nep0; ++px) {
            const int64_t i3 = py*nep0 + px;
            for (int64_t i2 = 0; i2 < ne2; ++i2) {
                for (int64_t i1 = 0; i1 < ne1; ++i1) {
                    for (int64_t i0 = 0; i0 < ne0; ++i0) {
                        const int64_t i02 = py*w + i2;
                        const int64_t i01 = px*w + i1;
                        const int64_t i00 = i0;

                        const int64_t i = i3*ne2*ne1*ne0 + i2*ne1*ne0    + i1*ne0   + i0;
                        const int64_t j =                  i02*ne01*ne00 + i01*ne00 + i00;

                        if (py*w + i2 >= ne02 || px*w + i1 >= ne01) {
                            ((float *) dst->data)[i] = 0.0f;
                        } else {
                            ((float *) dst->data)[i] = ((float *) src0->data)[j];
                        }
                    }
                }
            }
        }
    }
}

static void ggml_compute_forward_win_part(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * opt0,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_win_part_f32(params, src0, opt0, dst);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_win_unpart

static void ggml_compute_forward_win_unpart_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * opt0,
        struct ggml_tensor * dst) {
    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    GGML_TENSOR_LOCALS(int64_t, ne0, src0, ne);
    GGML_TENSOR_LOCALS(int64_t, ne,  dst,  ne);

    const int32_t w = ((const int32_t *)(opt0->data))[0];

    // padding
    const int px = (w - ne1%w)%w;
    //const int py = (w - ne2%w)%w;

    const int npx = (px + ne1)/w;
    //const int npy = (py + ne2)/w;

    assert(ne0 == ne00);

    // TODO: optimize / multi-thread
    for (int64_t i2 = 0; i2 < ne2; ++i2) {
        for (int64_t i1 = 0; i1 < ne1; ++i1) {
            for (int64_t i0 = 0; i0 < ne0; ++i0) {
                const int ip2 = i2/w;
                const int ip1 = i1/w;

                const int64_t i02 = i2%w;
                const int64_t i01 = i1%w;
                const int64_t i00 = i0;

                const int64_t i = (ip2*npx + ip1)*ne02*ne01*ne00 + i02*ne01*ne00 + i01*ne00 + i00;
                const int64_t j =                                  i2*ne1*ne0    + i1*ne0   + i0;

                ((float *) dst->data)[j] = ((float *) src0->data)[i];
            }
        }
    }
}

static void ggml_compute_forward_win_unpart(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * opt0,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_win_unpart_f32(params, src0, opt0, dst);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_map_unary

static void ggml_compute_forward_map_unary_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst,
        const ggml_unary_op_f32_t fun) {
    GGML_ASSERT(ggml_are_same_shape(src0, dst));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int n  = ggml_nrows(src0);
    const int nc = src0->ne[0];

    assert( dst->nb[0] == sizeof(float));
    assert(src0->nb[0] == sizeof(float));

    for (int i = 0; i < n; i++) {
        fun(nc,
                (float *) ((char *) dst->data  + i*( dst->nb[1])),
                (float *) ((char *) src0->data + i*(src0->nb[1])));
    }
}


static void ggml_compute_forward_map_unary(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst,
        const ggml_unary_op_f32_t fun) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_map_unary_f32(params, src0, dst, fun);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_map_binary

static void ggml_compute_forward_map_binary_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst,
        const ggml_binary_op_f32_t fun) {
    assert(params->ith == 0);
    assert(ggml_are_same_shape(src0, src1) && ggml_are_same_shape(src0, dst));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int n  = ggml_nrows(src0);
    const int nc = src0->ne[0];

    assert( dst->nb[0] == sizeof(float));
    assert(src0->nb[0] == sizeof(float));
    assert(src1->nb[0] == sizeof(float));

    for (int i = 0; i < n; i++) {
        fun(nc,
                (float *) ((char *) dst->data  + i*( dst->nb[1])),
                (float *) ((char *) src0->data + i*(src0->nb[1])),
                (float *) ((char *) src1->data + i*(src1->nb[1])));
    }
}


static void ggml_compute_forward_map_binary(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst,
        const ggml_binary_op_f32_t fun) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_map_binary_f32(params, src0, src1, dst, fun);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_map_custom1

static void ggml_compute_forward_map_custom1_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * a,
        struct ggml_tensor * dst,
        const ggml_custom1_op_f32_t fun) {
    assert(params->ith == 0);

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    fun(dst, a);
}


static void ggml_compute_forward_map_custom1(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * a,
        struct ggml_tensor * dst,
        const ggml_custom1_op_f32_t fun) {
    switch (a->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_map_custom1_f32(params, a, dst, fun);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_map_custom2

static void ggml_compute_forward_map_custom2_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * a,
        const struct ggml_tensor * b,
        struct ggml_tensor * dst,
        const ggml_custom2_op_f32_t fun) {
    assert(params->ith == 0);

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    fun(dst, a, b);
}


static void ggml_compute_forward_map_custom2(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * a,
        const struct ggml_tensor * b,
        struct ggml_tensor * dst,
        const ggml_custom2_op_f32_t fun) {
    switch (a->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_map_custom2_f32(params, a, b, dst, fun);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_map_custom3

static void ggml_compute_forward_map_custom3_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * a,
        const struct ggml_tensor * b,
        const struct ggml_tensor * c,
        struct ggml_tensor * dst,
        const ggml_custom3_op_f32_t fun) {
    assert(params->ith == 0);

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    fun(dst, a, b, c);
}


static void ggml_compute_forward_map_custom3(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * a,
        const struct ggml_tensor * b,
        const struct ggml_tensor * c,
        struct ggml_tensor * dst,
        const ggml_custom3_op_f32_t fun) {
    switch (a->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_map_custom3_f32(params, a, b, c, dst, fun);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_cross_entropy_loss

static void ggml_compute_forward_cross_entropy_loss_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    GGML_ASSERT(ggml_is_contiguous(src0));
    GGML_ASSERT(ggml_is_contiguous(src1));
    GGML_ASSERT(ggml_is_scalar(dst));
    GGML_ASSERT(ggml_are_same_shape(src0, src1));

    const int ith = params->ith;
    const int nth = params->nth;

    float * sums = (float *) params->wdata;

    // TODO: handle transposed/permuted matrices
    const int nc = src0->ne[0];
    const int nr = ggml_nrows(src0);

    if (params->type == GGML_TASK_INIT) {
        if (ith == 0) {
            memset(sums, 0, sizeof(float) * (nth + nth * nc));
        }
        return;
    }

    if (params->type == GGML_TASK_FINALIZE) {
        if (ith == 0) {
            float * dp = (float *) dst->data;
            ggml_vec_sum_f32(nth, dp, sums);
            dp[0] *= -1.0f;
        }
        return;
    }

    const double eps = 1e-9;

    // rows per thread
    const int dr = (nr + nth - 1)/nth;

    // row range for this thread
    const int ir0 = dr*ith;
    const int ir1 = MIN(ir0 + dr, nr);

    for (int i1 = ir0; i1 < ir1; i1++) {
        float * s0 = (float *)((char *) src0->data + i1*src0->nb[1]);
        float * s1 = (float *)((char *) src1->data + i1*src1->nb[1]);
        float * st = (float *) params->wdata + nth + ith*nc;

#ifndef NDEBUG
        for (int i = 0; i < nc; ++i) {
            //printf("p[%d] = %f\n", i, p[i]);
            assert(!isnan(s0[i]));
            assert(!isnan(s1[i]));
        }
#endif
        // soft_max
        ggml_float sum = 0.0;
        {
            float max = -INFINITY;
            ggml_vec_max_f32(nc, &max, s0);

            uint16_t scvt;
            for (int i = 0; i < nc; i++) {
                if (s0[i] == -INFINITY) {
                    st[i] = 0.0f;
                } else {
                    // const float val = (s0[i] == -INFINITY) ? 0.0 : exp(s0[i] - max);
                    ggml_fp16_t s = GGML_FP32_TO_FP16(s0[i] - max);
                    memcpy(&scvt, &s, sizeof(scvt));
                    const float val = GGML_FP16_TO_FP32(table_exp_f16[scvt]);
                    sum += (ggml_float)val;
                    st[i] = val;
                }
            }

            assert(sum > 0.0);
            // sum = 1.0/sum;
        }
        // avoid log(0) by rescaling from [0..1] to [eps..1]
        sum = (1.0 - eps) / sum;
        ggml_vec_scale_f32(nc, st, sum);
        ggml_vec_add1_f32(nc, st, st, eps);
        ggml_vec_log_f32(nc, st, st);
        ggml_vec_mul_f32(nc, st, st, s1);

        ggml_vec_sum_f32(nc, sums + ith, st);

#ifndef NDEBUG
        for (int i = 0; i < nc; ++i) {
            assert(!isnan(st[i]));
            assert(!isinf(st[i]));
        }
#endif
    }

}

static void ggml_compute_forward_cross_entropy_loss(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_cross_entropy_loss_f32(params, src0, src1, dst);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_cross_entropy_loss_back

static void ggml_compute_forward_cross_entropy_loss_back_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        const struct ggml_tensor * opt0,
        struct ggml_tensor * dst) {
    GGML_ASSERT(ggml_is_contiguous(dst));
    GGML_ASSERT(ggml_is_contiguous(src0));
    GGML_ASSERT(ggml_is_contiguous(src1));
    GGML_ASSERT(ggml_is_contiguous(opt0));
    GGML_ASSERT(ggml_are_same_shape(src0, src1) && ggml_are_same_shape(src0, dst));

    const int64_t ith = params->ith;
    const int64_t nth = params->nth;

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const float eps = 1e-9f;

    // TODO: handle transposed/permuted matrices
    const int64_t nc = src0->ne[0];
    const int64_t nr = ggml_nrows(src0);

    // rows per thread
    const int64_t dr = (nr + nth - 1)/nth;

    // row range for this thread
    const int64_t ir0 = dr*ith;
    const int64_t ir1 = MIN(ir0 + dr, nr);

    float * d   = (float *) opt0->data;

    for (int64_t i1 = ir0; i1 < ir1; i1++) {
        float * ds0 = (float *)((char *) dst->data  + i1*dst->nb[1]);
        float * s0  = (float *)((char *) src0->data + i1*src0->nb[1]);
        float * s1  = (float *)((char *) src1->data + i1*src1->nb[1]);
        float * sm  = (float *) params->wdata + ith*nc;

#ifndef NDEBUG
        for (int i = 0; i < nc; ++i) {
            //printf("p[%d] = %f\n", i, p[i]);
            assert(!isnan(s0[i]));
            assert(!isnan(s1[i]));
        }
#endif
        // step by step explanation:
        {
            //float * sums = (float *) params->wdata;

            // forward pass with annotated gradients from backward pass
            // (built by going in reverse operation order, adding to gradients of current operation args)
            // st0 = exp(s0-max(s0))                                                       grad[st0] = grad[st1]*(1.0 - eps)/sum
                                                          // from softmax_back:            grad[s0]  = st1_k * (grad[st1]_k - dot(st1, grad[st1]))
            // ggml_vec_scale_f32(nc, st, sum);           // st1 = st0*/sum = softmax(s0)  grad[st1] = grad[st2]*(1.0 - eps)
            // ggml_vec_scale_f32(nc, st, (1.0f - eps));  // st2 = st1*(1.0 - eps)         grad[st2] = grad[st3]
            // ggml_vec_add1_f32(nc, st, st, eps);        // st3 = st2 + eps               grad[st3] = grad[st4]/st3
            // ggml_vec_log_f32(nc, st, st);              // st4 = log(st3)                grad[st4] = grad[st5] * s1
            // ggml_vec_mul_f32(nc, st, st, s1);          // st5 = st4 * s1                grad[st5] = grad[sums[ith]]
            // ggml_vec_sum_f32(nc, sums + ith, st);      // sums[ith] = st5               grad[sums[ith]] = grad[cross_entropy_loss] = -grad[cel]

            // substitute into grad[st1], because we can reuse softmax_back from this point on
            // grad[st1] = -grad[cel]*s1*(1.0 - eps)/(eps + softmax(s0)*(1.0 - eps))
            // postorder:
            // grad[st1] := softmax(s0)
            // grad[st1] := grad[st1]*(1.0 - eps)
            // grad[st1] := grad[st1] + eps
            // grad[st1] := s1 / grad[st1]
            // grad[st1] := grad[st1]*(1.0-eps)*-grad[cel]

            // src0 gradients by going through softmax_back
            // grad[s0] = st1_k * (grad[st1]_k - dot(st1, grad[st1]))
            //   from softmax_back:
            //   dxk = yk * (dyk - dot(y, dy))
            //   dot_y_dy := dot(y, dy)
            //   dx := dy
            //   dx := dx - dot_y_dy
            //   dx := dx * y
            //   postorder:
            //   dot_st1_dst1 := dot(st1, grad[st1])
            //   grad[s0] := grad[st1]
            //   grad[s0] := grad[s0] - dot_st1_dst1
            //   grad[s0] := grad[s0] * st1

            // prepend postorder from grad[st1] directly using grad[s0] as memory location, as we will grad[s0] := grad[st1]
            // sm           := softmax(s0)
            // grad[s0]     := sm*(1.0 - eps)
            // grad[s0]     := grad[s0] + eps
            // grad[s0]     := s1 / grad[s0]
            // grad[s0]     := grad[s0]*(1.0-eps)*-grad[cel]
            // dot_st1_dst1 := dot(sm, grad[s0])
            // grad[s0]     := grad[s0] - dot_st1_dst1
            // grad[s0]     := grad[s0] * sm
        }

        // soft_max
        ggml_float sum = 0.0;
        {
            float max = -INFINITY;
            ggml_vec_max_f32(nc, &max, s0);

            uint16_t scvt;
            for (int i = 0; i < nc; i++) {
                if (s0[i] == -INFINITY) {
                    sm[i] = 0.0f;
                } else {
                    // const float val = (s0[i] == -INFINITY) ? 0.0 : exp(s0[i] - max);
                    ggml_fp16_t s = GGML_FP32_TO_FP16(s0[i] - max);
                    memcpy(&scvt, &s, sizeof(scvt));
                    const float val = GGML_FP16_TO_FP32(table_exp_f16[scvt]);
                    sum += (ggml_float)val;
                    sm[i] = val;
                }
            }

            assert(sum > 0.0);
            sum = 1.0/sum;
        }

        float dot_st1_dst1 = 0;
        ggml_vec_scale_f32(nc, sm, sum);
        ggml_vec_cpy_f32  (nc, ds0, sm);
        ggml_vec_scale_f32(nc, ds0, (1.0f - eps));
        ggml_vec_add1_f32 (nc, ds0, ds0, eps);
        ggml_vec_div_f32  (nc, ds0, s1, ds0);
        ggml_vec_scale_f32(nc, ds0, -(1.0f - eps)*d[0]);
        ggml_vec_dot_f32  (nc, &dot_st1_dst1, sm, ds0);
        ggml_vec_acc1_f32 (nc, ds0, -dot_st1_dst1);
        ggml_vec_mul_f32  (nc, ds0, ds0, sm);

#ifndef NDEBUG
        for (int i = 0; i < nc; ++i) {
            assert(!isnan(sm[i]));
            assert(!isinf(sm[i]));
            assert(!isnan(ds0[i]));
            assert(!isinf(ds0[i]));
        }
#endif
    }
}

static void ggml_compute_forward_cross_entropy_loss_back(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        const struct ggml_tensor * opt0,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_cross_entropy_loss_back_f32(params, src0, src1, opt0, dst);
            } break;
        default:
            {
                GGML_ASSERT(false);
            } break;
    }
}


/////////////////////////////////

static void ggml_compute_forward(struct ggml_compute_params * params, struct ggml_tensor * tensor) {
    GGML_ASSERT(params);

#ifdef GGML_USE_CUBLAS
    bool skip_cpu = ggml_cuda_compute_forward(params, tensor);
    if (skip_cpu) {
        return;
    }
    GGML_ASSERT(tensor->src0 == NULL || tensor->src0->backend == GGML_BACKEND_CPU);
    GGML_ASSERT(tensor->src1 == NULL || tensor->src1->backend == GGML_BACKEND_CPU);
#endif // GGML_USE_CUBLAS

    switch (tensor->op) {
        case GGML_OP_DUP:
            {
                ggml_compute_forward_dup(params, tensor->src0, tensor);
            } break;
        case GGML_OP_ADD:
            {
                ggml_compute_forward_add(params, tensor->src0, tensor->src1, tensor);
            } break;
        case GGML_OP_ADD1:
            {
                ggml_compute_forward_add1(params, tensor->src0, tensor->src1, tensor);
            } break;
        case GGML_OP_ACC:
            {
                ggml_compute_forward_acc(params, tensor->src0, tensor->src1, tensor->opt[0], tensor);
            } break;
        case GGML_OP_SUB:
            {
                ggml_compute_forward_sub(params, tensor->src0, tensor->src1, tensor);
            } break;
        case GGML_OP_MUL:
            {
                ggml_compute_forward_mul(params, tensor->src0, tensor->src1, tensor);
            } break;
        case GGML_OP_DIV:
            {
                ggml_compute_forward_div(params, tensor->src0, tensor->src1, tensor);
            } break;
        case GGML_OP_SQR:
            {
                ggml_compute_forward_sqr(params, tensor->src0, tensor);
            } break;
        case GGML_OP_SQRT:
            {
                ggml_compute_forward_sqrt(params, tensor->src0, tensor);
            } break;
        case GGML_OP_LOG:
            {
                ggml_compute_forward_log(params, tensor->src0, tensor);
            } break;
        case GGML_OP_SUM:
            {
                ggml_compute_forward_sum(params, tensor->src0, tensor);
            } break;
        case GGML_OP_SUM_ROWS:
            {
                ggml_compute_forward_sum_rows(params, tensor->src0, tensor);
            } break;
        case GGML_OP_MEAN:
            {
                ggml_compute_forward_mean(params, tensor->src0, tensor);
            } break;
        case GGML_OP_ARGMAX:
            {
                ggml_compute_forward_argmax(params, tensor->src0, tensor);
            } break;
        case GGML_OP_REPEAT:
            {
                ggml_compute_forward_repeat(params, tensor->src0, tensor);
            } break;
        case GGML_OP_REPEAT_BACK:
            {
                ggml_compute_forward_repeat_back(params, tensor->src0, tensor);
            } break;
        case GGML_OP_ABS:
            {
                ggml_compute_forward_abs(params, tensor->src0, tensor);
            } break;
        case GGML_OP_SGN:
            {
                ggml_compute_forward_sgn(params, tensor->src0, tensor);
            } break;
        case GGML_OP_NEG:
            {
                ggml_compute_forward_neg(params, tensor->src0, tensor);
            } break;
        case GGML_OP_STEP:
            {
                ggml_compute_forward_step(params, tensor->src0, tensor);
            } break;
        case GGML_OP_TANH:
            {
                ggml_compute_forward_tanh(params, tensor->src0, tensor);
            } break;
        case GGML_OP_ELU:
            {
                ggml_compute_forward_elu(params, tensor->src0, tensor);
            } break;
        case GGML_OP_RELU:
            {
                ggml_compute_forward_relu(params, tensor->src0, tensor);
            } break;
        case GGML_OP_GELU:
            {
                ggml_compute_forward_gelu(params, tensor->src0, tensor);
            } break;
        case GGML_OP_GELU_QUICK:
            {
                ggml_compute_forward_gelu_quick(params, tensor->src0, tensor);
            } break;
        case GGML_OP_SILU:
            {
                ggml_compute_forward_silu(params, tensor->src0, tensor);
            } break;
        case GGML_OP_SILU_BACK:
            {
                ggml_compute_forward_silu_back(params, tensor->src0, tensor->src1, tensor);
            } break;
        case GGML_OP_NORM:
            {
                ggml_compute_forward_norm(params, tensor->src0, tensor);
            } break;
        case GGML_OP_RMS_NORM:
            {
                ggml_compute_forward_rms_norm(params, tensor->src0, tensor);
            } break;
        case GGML_OP_RMS_NORM_BACK:
            {
                ggml_compute_forward_rms_norm_back(params, tensor->src0, tensor->src1, tensor);
            } break;
        case GGML_OP_MUL_MAT:
            {
                ggml_compute_forward_mul_mat(params, tensor->src0, tensor->src1, tensor);
            } break;
        case GGML_OP_OUT_PROD:
            {
                ggml_compute_forward_out_prod(params, tensor->src0, tensor->src1, tensor);
            } break;
        case GGML_OP_SCALE:
            {
                ggml_compute_forward_scale(params, tensor->src0, tensor->src1, tensor);
            } break;
        case GGML_OP_SET:
            {
                ggml_compute_forward_set(params, tensor->src0, tensor->src1, tensor->opt[0], tensor);
            } break;
        case GGML_OP_CPY:
            {
                ggml_compute_forward_cpy(params, tensor->src0, tensor);
            } break;
        case GGML_OP_CONT:
            {
                ggml_compute_forward_cont(params, tensor->src0, tensor);
            } break;
        case GGML_OP_RESHAPE:
            {
                ggml_compute_forward_reshape(params, tensor->src0, tensor);
            } break;
        case GGML_OP_VIEW:
            {
                ggml_compute_forward_view(params, tensor->src0);
            } break;
        case GGML_OP_PERMUTE:
            {
                ggml_compute_forward_permute(params, tensor->src0);
            } break;
        case GGML_OP_TRANSPOSE:
            {
                ggml_compute_forward_transpose(params, tensor->src0);
            } break;
        case GGML_OP_GET_ROWS:
            {
                ggml_compute_forward_get_rows(params, tensor->src0, tensor->src1, tensor);
            } break;
        case GGML_OP_GET_ROWS_BACK:
            {
                ggml_compute_forward_get_rows_back(params, tensor->src0, tensor->src1, tensor->opt[0], tensor);
            } break;
        case GGML_OP_DIAG:
            {
                ggml_compute_forward_diag(params, tensor->src0, tensor);
            } break;
        case GGML_OP_DIAG_MASK_INF:
            {
                ggml_compute_forward_diag_mask_inf(params, tensor->src0, tensor->src1, tensor);
            } break;
        case GGML_OP_DIAG_MASK_ZERO:
            {
                ggml_compute_forward_diag_mask_zero(params, tensor->src0, tensor->src1, tensor);
            } break;
        case GGML_OP_SOFT_MAX:
            {
                ggml_compute_forward_soft_max(params, tensor->src0, tensor);
            } break;
        case GGML_OP_SOFT_MAX_BACK:
            {
                ggml_compute_forward_soft_max_back(params, tensor->src0, tensor->src1, tensor);
            } break;
        case GGML_OP_ROPE:
            {
                ggml_compute_forward_rope(params, tensor->src0, tensor->src1, tensor);
            } break;
        case GGML_OP_ROPE_BACK:
            {
                ggml_compute_forward_rope_back(params, tensor->src0, tensor->src1, tensor);
            } break;
        case GGML_OP_ALIBI:
            {
                ggml_compute_forward_alibi(params, tensor->src0, tensor->src1, tensor);
            } break;
        case GGML_OP_CLAMP:
            {
                ggml_compute_forward_clamp(params, tensor->src0, tensor->src1, tensor);
            } break;
        case GGML_OP_CONV_1D:
            {
                ggml_compute_forward_conv_1d(params, tensor->src0, tensor->src1, tensor->opt[0], tensor);
            } break;
        case GGML_OP_CONV_2D:
            {
                ggml_compute_forward_conv_2d(params, tensor->src0, tensor->src1, tensor->opt[0], tensor);
            } break;
        case GGML_OP_FLASH_ATTN:
            {
                const int32_t t = ggml_get_i32_1d(tensor->opt[1], 0);
                GGML_ASSERT(t == 0 || t == 1);
                const bool masked = t != 0;
                ggml_compute_forward_flash_attn(params, tensor->src0, tensor->src1, tensor->opt[0], masked, tensor);
            } break;
        case GGML_OP_FLASH_FF:
            {
                ggml_compute_forward_flash_ff(params, tensor->src0, tensor->src1, tensor->opt[0], tensor->opt[1], tensor->opt[2], tensor);
            } break;
        case GGML_OP_FLASH_ATTN_BACK:
            {
                int32_t t = ggml_get_i32_1d(tensor->opt[2], 0);
                GGML_ASSERT(t == 0 || t == 1);
                bool masked = t != 0;
                ggml_compute_forward_flash_attn_back(params, tensor->src0, tensor->src1, tensor->opt[0], tensor->opt[1], masked, tensor);
            } break;
        case GGML_OP_WIN_PART:
            {
                ggml_compute_forward_win_part(params, tensor->src0, tensor->opt[0], tensor);
            } break;
        case GGML_OP_WIN_UNPART:
            {
                ggml_compute_forward_win_unpart(params, tensor->src0, tensor->opt[0], tensor);
            } break;
        case GGML_OP_MAP_UNARY:
            {
                const ggml_unary_op_f32_t fun = *((ggml_unary_op_f32_t *)tensor->opt[0]->data);
                ggml_compute_forward_map_unary(params, tensor->src0, tensor, fun);
            }
            break;
        case GGML_OP_MAP_BINARY:
            {
                const ggml_binary_op_f32_t fun = *((ggml_binary_op_f32_t *)tensor->opt[0]->data);
                ggml_compute_forward_map_binary(params, tensor->src0, tensor->src1, tensor, fun);
            }
            break;
        case GGML_OP_MAP_CUSTOM1:
            {
                const ggml_custom1_op_f32_t fun = *((ggml_custom1_op_f32_t *)tensor->opt[0]->data);
                ggml_compute_forward_map_custom1(params, tensor->src0, tensor, fun);
            }
            break;
        case GGML_OP_MAP_CUSTOM2:
            {
                const ggml_custom2_op_f32_t fun = *((ggml_custom2_op_f32_t *)tensor->opt[0]->data);
                ggml_compute_forward_map_custom2(params, tensor->src0, tensor->src1, tensor, fun);
            }
            break;
        case GGML_OP_MAP_CUSTOM3:
            {
                const ggml_custom3_op_f32_t fun = *((ggml_custom3_op_f32_t *)tensor->opt[0]->data);
                ggml_compute_forward_map_custom3(params, tensor->src0, tensor->src1, tensor->opt[1], tensor, fun);
            }
            break;
        case GGML_OP_CROSS_ENTROPY_LOSS:
            {
                ggml_compute_forward_cross_entropy_loss(params, tensor->src0, tensor->src1, tensor);
            }
            break;
        case GGML_OP_CROSS_ENTROPY_LOSS_BACK:
            {
                ggml_compute_forward_cross_entropy_loss_back(params, tensor->src0, tensor->src1, tensor->opt[0], tensor);
            }
            break;
        case GGML_OP_NONE:
            {
                // nop
            } break;
        case GGML_OP_COUNT:
            {
                GGML_ASSERT(false);
            } break;
    }
}

////////////////////////////////////////////////////////////////////////////////

static void ggml_compute_backward(struct ggml_context * ctx, struct ggml_tensor * tensor, bool inplace) {
    struct ggml_tensor * src0 = tensor->src0;
    struct ggml_tensor * src1 = tensor->src1;

    switch (tensor->op) {
        case GGML_OP_DUP:
            {
                if (src0->grad) {
                    src0->grad = ggml_add_impl(ctx, src0->grad, tensor->grad, inplace);
                }
            } break;
        case GGML_OP_ADD:
            {
                if (src0->grad) {
                    src0->grad = ggml_add_impl(ctx, src0->grad, tensor->grad, inplace);
                }
                if (src1->grad) {
                    src1->grad = ggml_add_impl(ctx, src1->grad, tensor->grad, inplace);
                }
            } break;
        case GGML_OP_ADD1:
            {
                if (src0->grad) {
                    src0->grad = ggml_add_impl(ctx, src0->grad, tensor->grad, inplace);
                }
                if (src1->grad) {
                    src1->grad = ggml_add_impl(ctx,
                        src1->grad,
                        ggml_mean(ctx, tensor->grad), // TODO: should probably be sum instead of mean
                        inplace);
                }
            } break;
        case GGML_OP_ACC:
            {
                if (src0->grad) {
                    src0->grad = ggml_add_impl(ctx, src0->grad, tensor->grad, inplace);
                }
                if (src1->grad) {
                    GGML_ASSERT(ggml_nelements(tensor->opt[0]) == 5);
                    GGML_ASSERT(tensor->opt[0]->type == GGML_TYPE_I32);
                    const size_t nb1     = (( int32_t * ) tensor->opt[0]->data)[0];
                    const size_t nb2     = (( int32_t * ) tensor->opt[0]->data)[1];
                    const size_t nb3     = (( int32_t * ) tensor->opt[0]->data)[2];
                    const size_t offset  = (( int32_t * ) tensor->opt[0]->data)[3];

                    struct ggml_tensor * tensor_grad_view = ggml_view_4d(ctx,
                        tensor->grad,
                        src1->grad->ne[0],
                        src1->grad->ne[1],
                        src1->grad->ne[2],
                        src1->grad->ne[3],
                        nb1, nb2, nb3, offset);

                    src1->grad =
                        ggml_add_impl(ctx,
                            src1->grad,
                            ggml_reshape(ctx,
                                ggml_cont(ctx, tensor_grad_view),
                                src1->grad),
                            inplace);
                }
            } break;
        case GGML_OP_SUB:
            {
                if (src0->grad) {
                    src0->grad = ggml_add_impl(ctx, src0->grad, tensor->grad, inplace);
                }
                if (src1->grad) {
                    src1->grad = ggml_sub_impl(ctx, src1->grad, tensor->grad, inplace);
                }
            } break;
        case GGML_OP_MUL:
            {
                if (src0->grad) {
                    src0->grad =
                        ggml_add_impl(ctx,
                                src0->grad,
                                ggml_mul(ctx, src1, tensor->grad),
                                inplace);
                }
                if (src1->grad) {
                    src1->grad =
                        ggml_add_impl(ctx,
                                src1->grad,
                                ggml_mul(ctx, src0, tensor->grad),
                                inplace);
                }
            } break;
        case GGML_OP_DIV:
            {
                if (src0->grad) {
                    src0->grad =
                        ggml_add_impl(ctx,
                                src0->grad,
                                ggml_div(ctx, tensor->grad, src1),
                                inplace);
                }
                if (src1->grad) {
                    src1->grad =
                        ggml_sub_impl(ctx,
                                src1->grad,
                                ggml_mul(ctx,
                                    tensor->grad,
                                    ggml_div(ctx, tensor, src1)),
                                inplace);
                }
            } break;
        case GGML_OP_SQR:
            {
                if (src0->grad) {
                    src0->grad =
                        ggml_add_impl(ctx,
                                src0->grad,
                                ggml_scale(ctx,
                                    ggml_mul(ctx, src0, tensor->grad),
                                    ggml_new_f32(ctx, 2.0f)),
                                inplace);
                }
            } break;
        case GGML_OP_SQRT:
            {
                if (src0->grad) {
                    src0->grad =
                        ggml_add_impl(ctx,
                                src0->grad,
                                ggml_scale(ctx,
                                    ggml_div(ctx,
                                        tensor->grad,
                                        tensor),
                                    ggml_new_f32(ctx, 0.5f)),
                                inplace);
                }
            } break;
        case GGML_OP_LOG:
            {
                if (src0->grad) {
                    src0->grad =
                        ggml_add_impl(ctx,
                                src0->grad,
                                ggml_div(ctx,
                                    tensor->grad,
                                    src0),
                                inplace);
                }
            } break;
        case GGML_OP_SUM:
            {
                if (src0->grad) {
                    src0->grad =
                        ggml_add1_impl(ctx,
                                src0->grad,
                                tensor->grad,
                                inplace);
                }
            } break;
        case GGML_OP_SUM_ROWS:
            {
                if (src0->grad) {
                    src0->grad =
                        ggml_add_impl(ctx,
                                src0->grad,
                                ggml_repeat(ctx,
                                    tensor->grad,
                                    src0->grad),
                                inplace);
                }
            } break;
        case GGML_OP_MEAN:
        case GGML_OP_ARGMAX:
            {
                GGML_ASSERT(false); // TODO: implement
            } break;
        case GGML_OP_REPEAT:
            {
                // necessary for llama
                if (src0->grad) {
                    src0->grad = ggml_add_impl(ctx,
                            src0->grad,
                            ggml_repeat_back(ctx, tensor->grad, src0->grad),
                            inplace);
                }
            } break;
        case GGML_OP_REPEAT_BACK:
            {
                if (src0->grad) {
                    // TODO: test this
                    src0->grad = ggml_add_impl(ctx,
                            src0->grad,
                            ggml_repeat(ctx, tensor->grad, src0->grad),
                            inplace);
                }
            } break;
        case GGML_OP_ABS:
            {
                if (src0->grad) {
                    src0->grad =
                        ggml_add_impl(ctx,
                                src0->grad,
                                ggml_mul(ctx,
                                    ggml_sgn(ctx, src0),
                                    tensor->grad),
                                inplace);
                }
            } break;
        case GGML_OP_SGN:
            {
                if (src0->grad) {
                    // noop
                }
            } break;
        case GGML_OP_NEG:
            {
                if (src0->grad) {
                    src0->grad = ggml_sub_impl(ctx, src0->grad, tensor->grad, inplace);
                }
            } break;
        case GGML_OP_STEP:
            {
                if (src0->grad) {
                    // noop
                }
            } break;
        case GGML_OP_TANH:
            {
                GGML_ASSERT(false); // TODO: not implemented
            } break;
        case GGML_OP_ELU:
            {
                GGML_ASSERT(false); // TODO: not implemented
            } break;
        case GGML_OP_RELU:
            {
                if (src0->grad) {
                    src0->grad = ggml_sub_impl(ctx,
                            src0->grad,
                            ggml_mul(ctx,
                                ggml_step(ctx, src0),
                                tensor->grad),
                            inplace);
                }
            } break;
        case GGML_OP_GELU:
            {
                GGML_ASSERT(false); // TODO: not implemented
            } break;
        case GGML_OP_GELU_QUICK:
            {
                GGML_ASSERT(false); // TODO: not implemented
            } break;
        case GGML_OP_SILU:
            {
                // necessary for llama
                if (src0->grad) {
                    src0->grad = ggml_add_impl(ctx,
                            src0->grad,
                            ggml_silu_back(ctx, src0, tensor->grad),
                            inplace);
                }
            } break;
        case GGML_OP_SILU_BACK:
            {
                GGML_ASSERT(false); // TODO: not implemented
            } break;
        case GGML_OP_NORM:
            {
                GGML_ASSERT(false); // TODO: not implemented
            } break;
        case GGML_OP_RMS_NORM:
            {
                // necessary for llama
                if (src0->grad) {
                    src0->grad = ggml_add_impl(ctx,
                            src0->grad,
                            ggml_rms_norm_back(ctx, src0, tensor->grad),
                            inplace);
                }
            } break;
        case GGML_OP_RMS_NORM_BACK:
            {
                GGML_ASSERT(false); // TODO: not implemented
            } break;
        case GGML_OP_MUL_MAT:
            {
                // https://cs231n.github.io/optimization-2/#staged
                // # forward pass
                // s0 = np.random.randn(5, 10)
                // s1 = np.random.randn(10, 3)
                // t = s0.dot(s1)

                // # now suppose we had the gradient on t from above in the circuit
                // dt = np.random.randn(*t.shape) # same shape as t
                // ds0 = dt.dot(s1.T) #.T gives the transpose of the matrix
                // ds1 = t.T.dot(dt)

                // tensor.shape [m,p]
                // src0.shape   [n,m]
                // src1.shape   [n,p]

                // necessary for llama
                if (src0->grad) {
                    src0->grad =
                        ggml_add_impl(ctx,
                                src0->grad,
                                ggml_out_prod(ctx, // [n,m]
                                    src1,          // [n,p]
                                    tensor->grad), // [m,p]
                                inplace);
                }
                if (src1->grad) {
                    src1->grad =
                        ggml_add_impl(ctx,
                                src1->grad,
                                // ggml_mul_mat(ctx,                   // [n,p]
                                //     ggml_cont(ctx,                  // [m,n]
                                //         ggml_transpose(ctx, src0)), // [m,n]
                                //     tensor->grad),                  // [m,p]

                                // // when src0 is bigger than tensor->grad (this is mostly the case in llama),
                                // // avoid transpose of src0, rather transpose smaller tensor->grad
                                // // and then use ggml_out_prod
                                ggml_out_prod(ctx,                  // [n,p]
                                    src0,                           // [n,m]
                                    ggml_transpose(ctx,             // [p,m]
                                        tensor->grad)),             // [m,p]
                                inplace);
                }
            } break;
        case GGML_OP_OUT_PROD:
            {
                GGML_ASSERT(false); // TODO: not implemented
            } break;
        case GGML_OP_SCALE:
            {
                // necessary for llama
                if (src0->grad) {
                    src0->grad =
                        ggml_add_impl(ctx,
                            src0->grad,
                            ggml_scale_impl(ctx, tensor->grad, src1, false),
                            inplace);
                }
                if (src1->grad) {
                    src1->grad =
                        ggml_add_impl(ctx,
                            src1->grad,
                            ggml_sum(ctx, ggml_mul_impl(ctx, tensor->grad, src0, false)),
                            inplace);
                }
            } break;
        case GGML_OP_SET:
            {
                GGML_ASSERT(ggml_nelements(tensor->opt[0]) == 5);
                GGML_ASSERT(tensor->opt[0]->type == GGML_TYPE_I32);
                const size_t nb1     = (( int32_t * ) tensor->opt[0]->data)[0];
                const size_t nb2     = (( int32_t * ) tensor->opt[0]->data)[1];
                const size_t nb3     = (( int32_t * ) tensor->opt[0]->data)[2];
                const size_t offset  = (( int32_t * ) tensor->opt[0]->data)[3];

                struct ggml_tensor * tensor_grad_view = NULL;

                if (src0->grad || src1->grad) {
                    GGML_ASSERT(src0->type == tensor->type);
                    GGML_ASSERT(tensor->grad->type == tensor->type);
                    GGML_ASSERT(tensor->grad->type == src1->grad->type);

                    tensor_grad_view = ggml_view_4d(ctx,
                        tensor->grad,
                        src1->grad->ne[0],
                        src1->grad->ne[1],
                        src1->grad->ne[2],
                        src1->grad->ne[3],
                        nb1, nb2, nb3, offset);
                }

                if (src0->grad) {
                    src0->grad = ggml_add_impl(ctx,
                        src0->grad,
                        ggml_acc_impl(ctx,
                            tensor->grad,
                            ggml_neg(ctx, tensor_grad_view),
                            nb1, nb2, nb3, offset, false),
                        inplace);
                }

                if (src1->grad) {
                    src1->grad =
                        ggml_add_impl(ctx,
                            src1->grad,
                            ggml_reshape(ctx,
                                ggml_cont(ctx, tensor_grad_view),
                                src1->grad),
                            inplace);
                }
            } break;
        case GGML_OP_CPY:
            {
                // necessary for llama
                // cpy overwrites value of src1 by src0 and returns view(src1)
                // the overwriting is mathematically equivalent to:
                // tensor = src0 * 1 + src1 * 0
                if (src0->grad) {
                    // dsrc0 = dtensor * 1
                    src0->grad = ggml_add_impl(ctx, src0->grad, tensor->grad, inplace);
                }
                if (src1->grad) {
                    // dsrc1 = dtensor * 0 -> noop
                }
            } break;
        case GGML_OP_CONT:
            {
                // same as cpy
                if (src0->grad) {
                    GGML_ASSERT(ggml_is_contiguous(src0->grad));
                    GGML_ASSERT(ggml_is_contiguous(tensor->grad));
                    src0->grad = ggml_add_impl(ctx, src0->grad, tensor->grad, inplace);
                }
            } break;
        case GGML_OP_RESHAPE:
            {
                // necessary for llama
                if (src0->grad) {
                    src0->grad =
                        ggml_add_impl(ctx, src0->grad,
                            ggml_reshape(ctx, tensor->grad, src0->grad),
                        inplace);
                }
            } break;
        case GGML_OP_VIEW:
            {
                // necessary for llama
                if (src0->grad) {
                    size_t offset;

                    GGML_ASSERT(sizeof(offset) <= ggml_nbytes(tensor->opt[0]));
                    memcpy(&offset, tensor->opt[0]->data, sizeof(offset));

                    size_t nb1     = tensor->nb[1];
                    size_t nb2     = tensor->nb[2];
                    size_t nb3     = tensor->nb[3];

                    if (src0->type != src0->grad->type) {
                        // gradient is typically F32, but src0 could be other type
                        size_t ng = ggml_element_size(src0->grad);
                        size_t n0 = ggml_element_size(src0);
                        GGML_ASSERT(offset % n0 == 0);
                        GGML_ASSERT(nb1 % n0 == 0);
                        GGML_ASSERT(nb2 % n0 == 0);
                        GGML_ASSERT(nb3 % n0 == 0);
                        offset = (offset / n0) * ng;
                        nb1 = (nb1 / n0) * ng;
                        nb2 = (nb2 / n0) * ng;
                        nb3 = (nb3 / n0) * ng;
                    }

                    src0->grad = ggml_acc_impl(ctx, src0->grad, tensor->grad, nb1, nb2, nb3, offset, inplace);
                }
            } break;
        case GGML_OP_PERMUTE:
            {
                // necessary for llama
                if (src0->grad) {
                    int32_t * axes = (int32_t *) tensor->opt[0]->data;
                    int axis0 = axes[0] & 0x3;
                    int axis1 = axes[1] & 0x3;
                    int axis2 = axes[2] & 0x3;
                    int axis3 = axes[3] & 0x3;
                    int axes_backward[4] = {0,0,0,0};
                    axes_backward[axis0] = 0;
                    axes_backward[axis1] = 1;
                    axes_backward[axis2] = 2;
                    axes_backward[axis3] = 3;
                    src0->grad =
                        ggml_add_impl(ctx, src0->grad,
                            ggml_permute(ctx,
                                tensor->grad,
                                axes_backward[0],
                                axes_backward[1],
                                axes_backward[2],
                                axes_backward[3]),
                            inplace);
                }
            } break;
        case GGML_OP_TRANSPOSE:
            {
                // necessary for llama
                if (src0->grad) {
                    src0->grad =
                        ggml_add_impl(ctx, src0->grad,
                            ggml_transpose(ctx, tensor->grad),
                        inplace);
                }
            } break;
        case GGML_OP_GET_ROWS:
            {
                // necessary for llama (only for tokenizer)
                if (src0->grad) {
                    src0->grad =
                        ggml_add_impl(ctx, src0->grad,
                            ggml_get_rows_back(ctx, tensor->grad, src1, src0->grad),
                        inplace);
                }
                if (src1->grad) {
                    // noop
                }
            } break;
        case GGML_OP_GET_ROWS_BACK:
            {
                GGML_ASSERT(false); // TODO: not implemented
            } break;
        case GGML_OP_DIAG:
            {
                GGML_ASSERT(false); // TODO: not implemented
            } break;
        case GGML_OP_DIAG_MASK_INF:
            {
                // necessary for llama
                if (src0->grad) {
                    assert(src1->type == GGML_TYPE_I32);
                    assert(ggml_nelements(src1) == 2);
                    const int n_past = ((int32_t *) src1->data)[0];
                    src0->grad =
                        ggml_add_impl(ctx, src0->grad,
                            ggml_diag_mask_zero_impl(ctx, tensor->grad, n_past, false),
                        inplace);
                }
                if (src1->grad) {
                    // noop
                }
            } break;
        case GGML_OP_DIAG_MASK_ZERO:
            {
                // necessary for llama
                if (src0->grad) {
                    assert(src1->type == GGML_TYPE_I32);
                    assert(ggml_nelements(src1) == 2);
                    const int n_past = ((int32_t *) src1->data)[0];
                    src0->grad =
                        ggml_add_impl(ctx, src0->grad,
                            ggml_diag_mask_zero_impl(ctx, tensor->grad, n_past, false),
                        inplace);
                }
                if (src1->grad) {
                    // noop
                }
            } break;
        case GGML_OP_SOFT_MAX:
            {
                // necessary for llama
                if (src0->grad) {
                    src0->grad =
                        ggml_add_impl(ctx, src0->grad,
                            ggml_soft_max_back(ctx, tensor->grad, tensor),
                        inplace);
                }

            } break;
        case GGML_OP_SOFT_MAX_BACK:
            {
                GGML_ASSERT(false); // TODO: not implemented
            } break;
        case GGML_OP_ROPE:
            {
                // necessary for llama
                if (src0->grad) {
                    assert(src1->type == GGML_TYPE_I32);
                    assert(ggml_nelements(src1) == 4);
                    const int n_past = ((int32_t *) src1->data)[0];
                    const int n_dims = ((int32_t *) src1->data)[1];
                    const int mode   = ((int32_t *) src1->data)[2];
                    src0->grad = ggml_add_impl(ctx,
                            src0->grad,
                            ggml_rope_back(ctx,
                                tensor->grad,
                                n_past,
                                n_dims,
                                mode),
                            inplace);
                }
                if (src1->grad) {
                    // noop
                }
            } break;
        case GGML_OP_ROPE_BACK:
            {
                if (src0->grad) {
                    assert(src1->type == GGML_TYPE_I32);
                    assert(ggml_nelements(src1) == 4);
                    const int n_past = ((int32_t *) src1->data)[0];
                    const int n_dims = ((int32_t *) src1->data)[1];
                    const int mode   = ((int32_t *) src1->data)[2];
                    const int n_ctx  = ((int32_t *) src1->data)[3];
                    src0->grad = ggml_add_impl(ctx,
                            src0->grad,
                            ggml_rope(ctx,
                                tensor->grad,
                                n_past,
                                n_dims,
                                mode,
                                n_ctx),
                            inplace);
                }
                if (src1->grad) {
                    // noop
                }
            } break;
        case GGML_OP_ALIBI:
            {
                GGML_ASSERT(false); // TODO: not implemented
            } break;
        case GGML_OP_CLAMP:
            {
                GGML_ASSERT(false); // TODO: not implemented
            } break;
        case GGML_OP_CONV_1D:
            {
                GGML_ASSERT(false); // TODO: not implemented
            } break;
        case GGML_OP_CONV_2D:
            {
                GGML_ASSERT(false); // TODO: not implemented
            } break;
        case GGML_OP_FLASH_ATTN:
            {
                struct ggml_tensor * flash_grad = NULL;
                if (src0->grad || src1->grad || tensor->opt[0]->grad) {
                    int32_t t = ggml_get_i32_1d(tensor->opt[1], 0);
                    GGML_ASSERT(t == 0 || t == 1);
                    bool masked = t != 0;
                    flash_grad =
                        ggml_flash_attn_back(ctx,
                            src0,
                            src1,
                            tensor->opt[0],
                            tensor->grad,
                            masked);
                }

                if (src0->grad) {
                    struct ggml_tensor * grad_q = NULL;
                    const size_t nb0    = flash_grad->nb[0];
                    const size_t offset = 0;
                    switch(src0->n_dims) {
                        case 2:
                            {
                                grad_q = ggml_view_2d(ctx,
                                    flash_grad,
                                    src0->ne[0],
                                    src0->ne[1],
                                    nb0*src0->ne[0],
                                    offset);
                            } break;
                        case 3:
                            {
                                grad_q = ggml_view_3d(ctx,
                                    flash_grad,
                                    src0->ne[0],
                                    src0->ne[1],
                                    src0->ne[2],
                                    nb0*src0->ne[0],
                                    nb0*src0->ne[0]*src0->ne[1],
                                    offset);
                            } break;
                        case 4:
                            {
                                grad_q = ggml_view_4d(ctx,
                                    flash_grad,
                                    src0->ne[0],
                                    src0->ne[1],
                                    src0->ne[2],
                                    src0->ne[3],
                                    nb0*src0->ne[0],
                                    nb0*src0->ne[0]*src0->ne[1],
                                    nb0*src0->ne[0]*src0->ne[1]*src0->ne[2],
                                    offset);
                            } break;
                    }

                    src0->grad = ggml_add_impl(ctx,
                            src0->grad,
                            grad_q,
                            inplace);
                }

                if (src1->grad) {
                    struct ggml_tensor * grad_k = NULL;
                    const size_t nb0    = flash_grad->nb[0];
                    const size_t offset = nb0*src0->ne[0]*src0->ne[1]*src0->ne[2]*src0->ne[3];
                    switch(src1->n_dims) {
                        case 2:
                            {
                                grad_k = ggml_view_2d(ctx,
                                    flash_grad,
                                    src1->ne[0],
                                    src1->ne[1],
                                    nb0*src1->ne[0],
                                    offset);
                            } break;
                        case 3:
                            {
                                grad_k = ggml_view_3d(ctx,
                                    flash_grad,
                                    src1->ne[0],
                                    src1->ne[1],
                                    src1->ne[2],
                                    nb0*src1->ne[0],
                                    nb0*src1->ne[0]*src1->ne[1],
                                    offset);
                            } break;
                        case 4:
                            {
                                grad_k = ggml_view_4d(ctx,
                                    flash_grad,
                                    src1->ne[0],
                                    src1->ne[1],
                                    src1->ne[2],
                                    src1->ne[3],
                                    nb0*src1->ne[0],
                                    nb0*src1->ne[0]*src1->ne[1],
                                    nb0*src1->ne[0]*src1->ne[1]*src1->ne[2],
                                    offset);
                            } break;
                    }

                    src1->grad = ggml_add_impl(ctx,
                            src1->grad,
                            grad_k,
                            inplace);
                }

                struct ggml_tensor * opt0 = tensor->opt[0];

                if (opt0->grad) {
                    struct ggml_tensor * grad_v = NULL;
                    const size_t nb0    = flash_grad->nb[0];
                    const size_t offset = nb0*src0->ne[0]*src0->ne[1]*src0->ne[2]*src0->ne[3]
                                        + nb0*src1->ne[0]*src1->ne[1]*src1->ne[2]*src1->ne[3];
                    switch(opt0->n_dims) {
                        case 2:
                            {
                                grad_v = ggml_view_2d(ctx,
                                    flash_grad,
                                    opt0->ne[0],
                                    opt0->ne[1],
                                    nb0*opt0->ne[0],
                                    offset);
                            } break;
                        case 3:
                            {
                                grad_v = ggml_view_3d(ctx,
                                    flash_grad,
                                    opt0->ne[0],
                                    opt0->ne[1],
                                    opt0->ne[2],
                                    nb0*opt0->ne[0],
                                    nb0*opt0->ne[0]*opt0->ne[1],
                                    offset);
                            } break;
                        case 4:
                            {
                                grad_v = ggml_view_4d(ctx,
                                    flash_grad,
                                    opt0->ne[0],
                                    opt0->ne[1],
                                    opt0->ne[2],
                                    opt0->ne[3],
                                    nb0*opt0->ne[0],
                                    nb0*opt0->ne[0]*opt0->ne[1],
                                    nb0*opt0->ne[0]*opt0->ne[1]*opt0->ne[2],
                                    offset);
                            } break;
                    }

                    opt0->grad = ggml_add_impl(ctx,
                            opt0->grad,
                            grad_v,
                            inplace);
                }
            } break;
        case GGML_OP_FLASH_FF:
            {
                GGML_ASSERT(false); // not supported
            } break;
        case GGML_OP_FLASH_ATTN_BACK:
            {
                GGML_ASSERT(false); // not supported
            } break;
        case GGML_OP_WIN_PART:
        case GGML_OP_WIN_UNPART:
        case GGML_OP_MAP_UNARY:
        case GGML_OP_MAP_BINARY:
        case GGML_OP_MAP_CUSTOM1:
        case GGML_OP_MAP_CUSTOM2:
        case GGML_OP_MAP_CUSTOM3:
            {
                GGML_ASSERT(false); // not supported
            } break;
        case GGML_OP_CROSS_ENTROPY_LOSS:
            {
                if (src0->grad) {
                    src0->grad = ggml_add_impl(ctx,
                                src0->grad,
                                ggml_cross_entropy_loss_back(ctx,
                                    src0,
                                    src1,
                                    tensor->grad),
                                inplace);
                }
            } break;
        case GGML_OP_CROSS_ENTROPY_LOSS_BACK:
            {
                GGML_ASSERT(false); // not supported
            } break;
        case GGML_OP_NONE:
            {
                // nop
            } break;
        case GGML_OP_COUNT:
            {
                GGML_ASSERT(false);
            } break;
    }
}

static void ggml_visit_parents(struct ggml_cgraph * cgraph, struct ggml_tensor * node) {
    if (node->grad == NULL) {
        // this usually happens when we generate intermediate nodes from constants in the backward pass
        // it can also happen during forward pass, if the user performs computations with constants
        if (node->op != GGML_OP_NONE) {
            //GGML_PRINT_DEBUG("%s: warning: node %p has no grad, but op %d\n", __func__, (void *) node, node->op);
        }
    }

    // check if already visited
    for (int i = 0; i < cgraph->n_nodes; i++) {
        if (cgraph->nodes[i] == node) {
            return;
        }
    }

    for (int i = 0; i < cgraph->n_leafs; i++) {
        if (cgraph->leafs[i] == node) {
            return;
        }
    }

    if (node->src0) {
        ggml_visit_parents(cgraph, node->src0);
    }

    if (node->src1) {
        ggml_visit_parents(cgraph, node->src1);
    }

    for (int i = 0; i < GGML_MAX_OPT; ++i) {
        if (node->opt[i]) {
            ggml_visit_parents(cgraph, node->opt[i]);
        }
    }

    if (node->op == GGML_OP_NONE && node->grad == NULL) {
        // reached a leaf node, not part of the gradient graph (e.g. a constant)
        GGML_ASSERT(cgraph->n_leafs < GGML_MAX_NODES);

        if (strlen(node->name) == 0) {
            ggml_format_name(node, "leaf_%d", cgraph->n_leafs);
        }

        cgraph->leafs[cgraph->n_leafs] = node;
        cgraph->n_leafs++;
    } else {
        GGML_ASSERT(cgraph->n_nodes < GGML_MAX_NODES);

        if (strlen(node->name) == 0) {
            ggml_format_name(node, "node_%d", cgraph->n_nodes);
        }

        cgraph->nodes[cgraph->n_nodes] = node;
        cgraph->grads[cgraph->n_nodes] = node->grad;
        cgraph->n_nodes++;
    }
}

static void ggml_build_forward_impl(struct ggml_cgraph * cgraph, struct ggml_tensor * tensor, bool expand) {
    if (!expand) {
        cgraph->n_nodes = 0;
        cgraph->n_leafs = 0;
    }

    const int n0 = cgraph->n_nodes;
    UNUSED(n0);

    ggml_visit_parents(cgraph, tensor);

    const int n_new = cgraph->n_nodes - n0;
    GGML_PRINT_DEBUG("%s: visited %d new nodes\n", __func__, n_new);

    if (n_new > 0) {
        // the last added node should always be starting point
        GGML_ASSERT(cgraph->nodes[cgraph->n_nodes - 1] == tensor);
    }
}

void ggml_build_forward_expand(struct ggml_cgraph * cgraph, struct ggml_tensor * tensor) {
    ggml_build_forward_impl(cgraph, tensor, true);
}

struct ggml_cgraph ggml_build_forward(struct ggml_tensor * tensor) {
    struct ggml_cgraph result = {
        /*.n_nodes      =*/ 0,
        /*.n_leafs      =*/ 0,
        /*.nodes        =*/ { NULL },
        /*.grads        =*/ { NULL },
        /*.leafs        =*/ { NULL },
        /*.perf_runs    =*/ 0,
        /*.perf_cycles  =*/ 0,
        /*.perf_time_us =*/ 0,
    };

    ggml_build_forward_impl(&result, tensor, false);

    return result;
}

struct ggml_cgraph ggml_build_backward(struct ggml_context * ctx, struct ggml_cgraph * gf, bool keep) {
    struct ggml_cgraph result = *gf;

    GGML_ASSERT(gf->n_nodes > 0);

    // if we are keeping the gradient graph, we have to detach the gradient nodes from the original graph
    if (keep) {
        for (int i = 0; i < gf->n_nodes; i++) {
            struct ggml_tensor * node = gf->nodes[i];

            if (node->grad) {
                node->grad = ggml_dup_tensor(ctx, node);
                gf->grads[i] = node->grad;
            }
        }
    }

    for (int i = gf->n_nodes - 1; i >= 0; i--) {
        struct ggml_tensor * node = gf->nodes[i];

        // because we detached the grad nodes from the original graph, we can afford inplace operations
        if (node->grad) {
            ggml_compute_backward(ctx, node, keep);
        }
    }

    for (int i = gf->n_nodes - 1; i >= 0; i--) {
        struct ggml_tensor * node = gf->nodes[i];

        if (node->is_param) {
            GGML_PRINT_DEBUG("%s: found root node %p\n", __func__, (void *) node);
            ggml_build_forward_impl(&result, node->grad, true);
        }
    }

    return result;
}

//
// thread data
//
// synchronization is done via busy loops
// I tried using spin locks, but not sure how to use them correctly - the things I tried were slower than busy loops
//

#ifdef __APPLE__

//#include <os/lock.h>
//
//typedef os_unfair_lock ggml_lock_t;
//
//#define ggml_lock_init(x)    UNUSED(x)
//#define ggml_lock_destroy(x) UNUSED(x)
//#define ggml_lock_lock       os_unfair_lock_lock
//#define ggml_lock_unlock     os_unfair_lock_unlock
//
//#define GGML_LOCK_INITIALIZER OS_UNFAIR_LOCK_INIT

typedef int ggml_lock_t;

#define ggml_lock_init(x)    UNUSED(x)
#define ggml_lock_destroy(x) UNUSED(x)
#define ggml_lock_lock(x)    UNUSED(x)
#define ggml_lock_unlock(x)  UNUSED(x)

#define GGML_LOCK_INITIALIZER 0

typedef pthread_t ggml_thread_t;

#define ggml_thread_create pthread_create
#define ggml_thread_join   pthread_join

#else

//typedef pthread_spinlock_t ggml_lock_t;

//#define ggml_lock_init(x) pthread_spin_init(x, PTHREAD_PROCESS_PRIVATE)
//#define ggml_lock_destroy pthread_spin_destroy
//#define ggml_lock_lock    pthread_spin_lock
//#define ggml_lock_unlock  pthread_spin_unlock

typedef int ggml_lock_t;

#define ggml_lock_init(x)    UNUSED(x)
#define ggml_lock_destroy(x) UNUSED(x)
#if defined(__x86_64__) || (defined(_MSC_VER) && defined(_M_AMD64))
#define ggml_lock_lock(x)    _mm_pause()
#else
#define ggml_lock_lock(x)    UNUSED(x)
#endif
#define ggml_lock_unlock(x)  UNUSED(x)

#define GGML_LOCK_INITIALIZER 0

typedef pthread_t ggml_thread_t;

#define ggml_thread_create pthread_create
#define ggml_thread_join   pthread_join

#endif

// Android's libc implementation "bionic" does not support setting affinity
#if defined(__linux__) && !defined(__BIONIC__)
void set_numa_thread_affinity(int thread_n, int n_threads) {
    if (!ggml_is_numa()) {
        return;
    }

    // run thread on node_num thread_n / (threads per node)
    const int node_num = thread_n / ((n_threads + g_state.numa.n_nodes - 1) / g_state.numa.n_nodes);
    struct ggml_numa_node * node = &g_state.numa.nodes[node_num];
    size_t setsize = CPU_ALLOC_SIZE(g_state.numa.total_cpus);

    cpu_set_t * cpus = CPU_ALLOC(g_state.numa.total_cpus);
    CPU_ZERO_S(setsize, cpus);
    for (size_t i = 0; i < node->n_cpus; ++i) {
        CPU_SET_S(node->cpus[i], setsize, cpus);
    }

    int rv = pthread_setaffinity_np(pthread_self(), setsize, cpus);
    if (rv) {
            fprintf(stderr, "warning: pthread_setaffinity_np() failed: %s\n",
                    strerror(rv));
    }

    CPU_FREE(cpus);
}

void clear_numa_thread_affinity(void) {
    if (!ggml_is_numa()) {
        return;
    }

    size_t setsize = CPU_ALLOC_SIZE(g_state.numa.total_cpus);

    cpu_set_t * cpus = CPU_ALLOC(g_state.numa.total_cpus);
    CPU_ZERO_S(setsize, cpus);
    for (unsigned i = 0; i < g_state.numa.total_cpus; ++i) {
        CPU_SET_S(i, setsize, cpus);
    }

    int rv = pthread_setaffinity_np(pthread_self(), setsize, cpus);
    if (rv) {
        fprintf(stderr, "warning: pthread_setaffinity_np() failed: %s\n",
            strerror(rv));
    }

    CPU_FREE(cpus);
}
#else
// TODO: Windows etc.
// (the linux implementation may also work on BSD, someone should test)
void set_numa_thread_affinity(int thread_n, int n_threads) { UNUSED(thread_n); UNUSED(n_threads);  }
void clear_numa_thread_affinity(void) {}
#endif

struct ggml_compute_state_shared {
    const struct ggml_cgraph * cgraph;
    const struct ggml_cplan  * cplan;

    int64_t perf_node_start_cycles;
    int64_t perf_node_start_time_us;

    const int n_threads;

    // synchronization primitives
    atomic_int n_active; // num active threads
    atomic_int node_n;   // active graph node
};

struct ggml_compute_state {
    ggml_thread_t thrd;
    int ith;
    struct ggml_compute_state_shared * shared;
};

static void ggml_graph_compute_perf_stats_node(struct ggml_tensor * node, const struct ggml_compute_state_shared * st) {
    int64_t cycles_cur  = ggml_perf_cycles()  - st->perf_node_start_cycles;
    int64_t time_us_cur = ggml_perf_time_us() - st->perf_node_start_time_us;

    node->perf_runs++;
    node->perf_cycles  += cycles_cur;
    node->perf_time_us += time_us_cur;
}

static thread_ret_t ggml_graph_compute_thread(void * data) {
    struct ggml_compute_state * state = (struct ggml_compute_state *) data;

    const struct ggml_cgraph * cgraph = state->shared->cgraph;
    const struct ggml_cplan  * cplan  = state->shared->cplan;

    const int * n_tasks_arr = cplan->n_tasks;
    const int   n_threads   = state->shared->n_threads;

    set_numa_thread_affinity(state->ith, n_threads);

    int node_n = -1;

    while (true) {
        if (atomic_fetch_sub(&state->shared->n_active, 1) == 1) {
            // all other threads are finished and spinning
            // do finalize and init here so we don't have synchronize again
            struct ggml_compute_params params = {
                /*.type  =*/ GGML_TASK_FINALIZE,
                /*.ith   =*/ 0,
                /*.nth   =*/ 0,
                /*.wsize =*/ cplan->work_size,
                /*.wdata =*/ cplan->work_data,
            };

            if (node_n != -1) {
                /* FINALIZE */
                struct ggml_tensor * node = state->shared->cgraph->nodes[node_n];
                if (GGML_OP_HAS_FINALIZE[node->op]) {
                    params.nth = n_tasks_arr[node_n];
                    ggml_compute_forward(&params, node);
                    ggml_graph_compute_perf_stats_node(node, state->shared);
                }
            }

            // distribute new work or execute it direct if 1T
            while (++node_n < cgraph->n_nodes) {
                GGML_PRINT_DEBUG_5("%s: %d/%d\n", __func__, node_n, cgraph->n_nodes);

                struct ggml_tensor * node = cgraph->nodes[node_n];
                const int n_tasks = n_tasks_arr[node_n];

                state->shared->perf_node_start_cycles  = ggml_perf_cycles();
                state->shared->perf_node_start_time_us = ggml_perf_time_us();

                params.nth = n_tasks;

                /* INIT */
                if (GGML_OP_HAS_INIT[node->op]) {
                    params.type = GGML_TASK_INIT;
                    ggml_compute_forward(&params, node);
                }

                if (n_tasks == 1) {
                    // TODO: maybe push node_n to the atomic but if other threads see n_tasks is 1,
                    // they do something more efficient than spinning (?)
                    params.type = GGML_TASK_COMPUTE;
                    ggml_compute_forward(&params, node);

                    if (GGML_OP_HAS_FINALIZE[node->op]) {
                        params.type = GGML_TASK_FINALIZE;
                        ggml_compute_forward(&params, node);
                        ggml_graph_compute_perf_stats_node(node, state->shared);
                    }
                } else {
                    break;
                }
            }

            atomic_store(&state->shared->n_active, n_threads);
            atomic_store(&state->shared->node_n,   node_n);
        } else {
            // wait for other threads to finish
            const int last = node_n;
            do {
                //sched_yield();
                node_n = atomic_load(&state->shared->node_n);
            } while (node_n == last);
        }

        // check if we should stop
        if (node_n >= cgraph->n_nodes) break;

        /* COMPUTE */
        struct ggml_tensor * node = cgraph->nodes[node_n];
        const int n_tasks = n_tasks_arr[node_n];

        struct ggml_compute_params params = {
            /*.type  =*/ GGML_TASK_COMPUTE,
            /*.ith   =*/ state->ith,
            /*.nth   =*/ n_tasks,
            /*.wsize =*/ cplan->work_size,
            /*.wdata =*/ cplan->work_data,
        };

        if (state->ith < n_tasks) {
            ggml_compute_forward(&params, node);
        }
    }

    return 0;
}

struct ggml_cplan ggml_graph_plan(struct ggml_cgraph * cgraph, int n_threads) {
    if (n_threads <= 0) {
        n_threads = GGML_DEFAULT_N_THREADS;
    }

    size_t work_size = 0;

    struct ggml_cplan cplan;
    memset(&cplan, 0, sizeof(struct ggml_cplan));

    // thread scheduling for the different operations + work buffer size estimation
    for (int i = 0; i < cgraph->n_nodes; i++) {
        int n_tasks = 1;

        struct ggml_tensor * node = cgraph->nodes[i];

        switch (node->op) {
            case GGML_OP_CPY:
            case GGML_OP_DUP:
                {
                    n_tasks = n_threads;

                    size_t cur = 0;
                    if (ggml_is_quantized(node->type)) {
                        cur = GGML_TYPE_SIZE[GGML_TYPE_F32] * node->ne[0] * n_tasks;
                    }

                    work_size = MAX(work_size, cur);
                } break;
            case GGML_OP_ADD:
            case GGML_OP_ADD1:
                {
                    n_tasks = n_threads;

                    size_t cur = 0;

                    if (ggml_is_quantized(node->src0->type)) {
                        cur = GGML_TYPE_SIZE[GGML_TYPE_F32] * node->src0->ne[0] * n_tasks;
                    }

                    work_size = MAX(work_size, cur);
                } break;
            case GGML_OP_ACC:
                {
                    n_tasks = n_threads;

                    size_t cur = 0;

                    if (ggml_is_quantized(node->src0->type)) {
                        cur = GGML_TYPE_SIZE[GGML_TYPE_F32] * node->src1->ne[0] * n_tasks;
                    }

                    work_size = MAX(work_size, cur);
                } break;
            case GGML_OP_SUB:
            case GGML_OP_DIV:
            case GGML_OP_SQR:
            case GGML_OP_SQRT:
            case GGML_OP_LOG:
            case GGML_OP_SUM:
            case GGML_OP_SUM_ROWS:
            case GGML_OP_MEAN:
            case GGML_OP_ARGMAX:
            case GGML_OP_REPEAT:
            case GGML_OP_REPEAT_BACK:
            case GGML_OP_ABS:
            case GGML_OP_SGN:
            case GGML_OP_NEG:
            case GGML_OP_STEP:
            case GGML_OP_TANH:
            case GGML_OP_ELU:
            case GGML_OP_RELU:
                {
                    n_tasks = 1;
                } break;
            case GGML_OP_MUL:
            case GGML_OP_GELU:
            case GGML_OP_GELU_QUICK:
            case GGML_OP_SILU:
            case GGML_OP_SILU_BACK:
            case GGML_OP_NORM:
            case GGML_OP_RMS_NORM:
            case GGML_OP_RMS_NORM_BACK:
                {
                    n_tasks = n_threads;
                } break;
            case GGML_OP_MUL_MAT:
            case GGML_OP_OUT_PROD:
                {
                    n_tasks = n_threads;

                    // TODO: use different scheduling for different matrix sizes
                    //const int nr0 = ggml_nrows(node->src0);
                    //const int nr1 = ggml_nrows(node->src1);

                    //n_tasks = MIN(n_threads, MAX(1, nr0/128));
                    //printf("nr0 = %8d, nr1 = %8d, nr0*nr1 = %8d, n_tasks%d\n", nr0, nr1, nr0*nr1, n_tasks);

                    size_t cur = 0;
                    const enum ggml_type vec_dot_type = type_traits[node->src0->type].vec_dot_type;

#if defined(GGML_USE_CUBLAS)
                    if (ggml_cuda_can_mul_mat(node->src0, node->src1, node)) {
                        n_tasks = 1; // TODO: this actually is doing nothing
                                     //       the threads are still spinning
                    } else
#elif defined(GGML_USE_CLBLAST)
                    if (ggml_cl_can_mul_mat(node->src0, node->src1, node)) {
                        n_tasks = 1; // TODO: this actually is doing nothing
                                     //       the threads are still spinning
                        cur = ggml_cl_mul_mat_get_wsize(node->src0, node->src1, node);
                    } else
#endif
#if defined(GGML_USE_ACCELERATE) || defined(GGML_USE_OPENBLAS)
                    if (ggml_compute_forward_mul_mat_use_blas(node->src0, node->src1, node)) {
                        n_tasks = 1; // TODO: this actually is doing nothing
                                     //       the threads are still spinning
                        if (node->src0->type != GGML_TYPE_F32) {
                            // here we need memory just for single 2D matrix from src0
                            cur = GGML_TYPE_SIZE[GGML_TYPE_F32]*(node->src0->ne[0]*node->src0->ne[1]);
                        }
                    } else
#endif
                    if (node->src1->type != vec_dot_type) {
                        cur = GGML_TYPE_SIZE[vec_dot_type]*ggml_nelements(node->src1)/GGML_BLCK_SIZE[vec_dot_type];
                    } else {
                        cur = 0;
                    }

                    work_size = MAX(work_size, cur);
                } break;
            case GGML_OP_SCALE:
                {
                    n_tasks = 1;
                } break;
            case GGML_OP_SET:
            case GGML_OP_CONT:
            case GGML_OP_RESHAPE:
            case GGML_OP_VIEW:
            case GGML_OP_PERMUTE:
            case GGML_OP_TRANSPOSE:
            case GGML_OP_GET_ROWS:
            case GGML_OP_GET_ROWS_BACK:
            case GGML_OP_DIAG:
            case GGML_OP_DIAG_MASK_ZERO:
                {
                    n_tasks = 1;
                } break;
            case GGML_OP_DIAG_MASK_INF:
            case GGML_OP_SOFT_MAX:
            case GGML_OP_SOFT_MAX_BACK:
            case GGML_OP_ROPE:
            case GGML_OP_ROPE_BACK:
                {
                    n_tasks = n_threads;
                } break;
            case GGML_OP_ALIBI:
                {
                    n_tasks = 1; //TODO
                } break;
            case GGML_OP_CLAMP:
                {
                    n_tasks = 1; //TODO
                } break;
            case GGML_OP_CONV_1D:
                {
                    n_tasks = n_threads;

                    GGML_ASSERT(node->src0->ne[3] == 1);
                    GGML_ASSERT(node->src1->ne[2] == 1);
                    GGML_ASSERT(node->src1->ne[3] == 1);

                    size_t cur = 0;
                    const int nk = node->src0->ne[0];

                    if (node->src0->type == GGML_TYPE_F16 &&
                            node->src1->type == GGML_TYPE_F32) {
                        cur = sizeof(ggml_fp16_t)*(
                                nk*ggml_up32(node->src0->ne[1])*node->src0->ne[2] +
                                ( 2*(nk/2) + node->src1->ne[0])*node->src1->ne[1]
                                );
                    } else if (node->src0->type == GGML_TYPE_F32 &&
                            node->src1->type == GGML_TYPE_F32) {
                        cur = sizeof(float)*(
                                nk*ggml_up32(node->src0->ne[1])*node->src0->ne[2] +
                                ( 2*(nk/2) + node->src1->ne[0])*node->src1->ne[1]
                                );
                    } else {
                        GGML_ASSERT(false);
                    }

                    work_size = MAX(work_size, cur);
                } break;
            case GGML_OP_CONV_2D:
                {
                    n_tasks = n_threads;

                    GGML_ASSERT(node->src1->ne[3] == 1);

                    const int64_t ne00 = node->src0->ne[0]; // W
                    const int64_t ne01 = node->src0->ne[1]; // H
                    const int64_t ne02 = node->src0->ne[2]; // C
                    const int64_t ne03 = node->src0->ne[3]; // N

                    const int64_t ne10 = node->src1->ne[0]; // W
                    const int64_t ne11 = node->src1->ne[1]; // H
                    const int64_t ne12 = node->src1->ne[2]; // C

                    const int64_t nk = ne00*ne01;

                    UNUSED(ne02);
                    UNUSED(ne03);
                    UNUSED(nk);

                    size_t cur = 0;

                    if (node->src0->type == GGML_TYPE_F16 &&
                            node->src1->type == GGML_TYPE_F32) {
                        cur = sizeof(ggml_fp16_t)*(ne10*ne11*ne12);
                    } else if (node->src0->type == GGML_TYPE_F32 &&
                            node->src1->type == GGML_TYPE_F32) {
                        cur = sizeof(float)*      (ne10*ne11*ne12);
                    } else {
                        GGML_ASSERT(false);
                    }

                    work_size = MAX(work_size, cur);
                } break;
            case GGML_OP_FLASH_ATTN:
                {
                    n_tasks = n_threads;

                    size_t cur = 0;

                    const int64_t ne11 = ggml_up(node->src1->ne[1], GGML_SOFT_MAX_UNROLL);

                    if (node->src1->type == GGML_TYPE_F32) {
                        cur  = sizeof(float)*ne11*n_tasks; // TODO: this can become (n_tasks-1)
                        cur += sizeof(float)*ne11*n_tasks; // this is overestimated by x2
                    }

                    if (node->src1->type == GGML_TYPE_F16) {
                        cur  = sizeof(float)*ne11*n_tasks; // TODO: this can become (n_tasks-1)
                        cur += sizeof(float)*ne11*n_tasks; // this is overestimated by x2
                    }

                    work_size = MAX(work_size, cur);
                } break;
            case GGML_OP_FLASH_FF:
                {
                    n_tasks = n_threads;

                    size_t cur = 0;

                    if (node->src1->type == GGML_TYPE_F32) {
                        cur  = sizeof(float)*node->src1->ne[1]*n_tasks; // TODO: this can become (n_tasks-1)
                        cur += sizeof(float)*node->src1->ne[1]*n_tasks; // this is overestimated by x2
                    }

                    if (node->src1->type == GGML_TYPE_F16) {
                        cur  = sizeof(float)*node->src1->ne[1]*n_tasks; // TODO: this can become (n_tasks-1)
                        cur += sizeof(float)*node->src1->ne[1]*n_tasks; // this is overestimated by x2
                    }

                    work_size = MAX(work_size, cur);
                } break;
            case GGML_OP_FLASH_ATTN_BACK:
                {
                    n_tasks = n_threads;

                    size_t cur = 0;

                    const int64_t    D = node->src0->ne[0];
                    const int64_t ne11 = ggml_up(node->src1->ne[1], GGML_SOFT_MAX_UNROLL);
                    const int64_t mxDn = MAX(D, ne11) * 2; // *2 because of S and SM in ggml_compute_forward_flash_attn_back
                    if (node->src1->type == GGML_TYPE_F32) {
                        cur  = sizeof(float)*mxDn*n_tasks; // TODO: this can become (n_tasks-1)
                        cur += sizeof(float)*mxDn*n_tasks; // this is overestimated by x2
                    }

                    if (node->src1->type == GGML_TYPE_F16) {
                        cur  = sizeof(float)*mxDn*n_tasks; // TODO: this can become (n_tasks-1)
                        cur += sizeof(float)*mxDn*n_tasks; // this is overestimated by x2
                    }

                    work_size = MAX(work_size, cur);
                } break;
            case GGML_OP_WIN_PART:
            case GGML_OP_WIN_UNPART:
            case GGML_OP_MAP_UNARY:
            case GGML_OP_MAP_BINARY:
            case GGML_OP_MAP_CUSTOM1:
            case GGML_OP_MAP_CUSTOM2:
            case GGML_OP_MAP_CUSTOM3:
                {
                    n_tasks = 1;
                } break;
            case GGML_OP_CROSS_ENTROPY_LOSS:
                {
                    n_tasks = n_threads;

                    size_t cur = ggml_type_size(node->type)*(n_tasks + node->src0->ne[0]*n_tasks);

                    work_size = MAX(work_size, cur);
                } break;
            case GGML_OP_CROSS_ENTROPY_LOSS_BACK:
                {
                    n_tasks = n_threads;

                    size_t cur = ggml_type_size(node->type)*node->src0->ne[0]*n_tasks;

                    work_size = MAX(work_size, cur);
                } break;
            case GGML_OP_NONE:
                {
                    n_tasks = 1;
                } break;
            case GGML_OP_COUNT:
                {
                    GGML_ASSERT(false);
                } break;
        }

        cplan.n_tasks[i] = n_tasks;
    }

    if (work_size > 0) {
        work_size += CACHE_LINE_SIZE*(n_threads - 1);
    }

    cplan.n_threads = n_threads;
    cplan.work_size = work_size;
    cplan.work_data = NULL;

    return cplan;
}

void ggml_graph_compute(struct ggml_cgraph * cgraph, struct ggml_cplan * cplan) {
    {
        GGML_ASSERT(cplan);
        GGML_ASSERT(cplan->n_threads > 0);

        if (cplan->work_size > 0) {
            GGML_ASSERT(cplan->work_data);
        }

        for (int i = 0; i < cgraph->n_nodes; ++i) {
            if (cgraph->nodes[i]->op != GGML_OP_NONE) {
                GGML_ASSERT(cplan->n_tasks[i] > 0);
            }
        }
    }

    const int n_threads = cplan->n_threads;

    struct ggml_compute_state_shared state_shared = {
        /*.cgraph                  =*/ cgraph,
        /*.cgraph_plan             =*/ cplan,
        /*.perf_node_start_cycles  =*/ 0,
        /*.perf_node_start_time_us =*/ 0,
        /*.n_threads               =*/ n_threads,
        /*.n_active                =*/ n_threads,
        /*.node_n                  =*/ -1,
    };
    struct ggml_compute_state * workers = alloca(sizeof(struct ggml_compute_state)*n_threads);

    // create thread pool
    if (n_threads > 1) {
        for (int j = 1; j < n_threads; ++j) {
            workers[j] = (struct ggml_compute_state) {
                .thrd   = 0,
                .ith = j,
                .shared = &state_shared,
            };

            const int rc = ggml_thread_create(&workers[j].thrd, NULL, ggml_graph_compute_thread, &workers[j]);
            GGML_ASSERT(rc == 0);
        }
    }
    workers[0].ith = 0;
    workers[0].shared = &state_shared;

    const int64_t perf_start_cycles  = ggml_perf_cycles();
    const int64_t perf_start_time_us = ggml_perf_time_us();

    // this is a work thread too
    ggml_graph_compute_thread(&workers[0]);

    // don't leave affinity set on the main thread
    clear_numa_thread_affinity();

    // join thread pool
    if (n_threads > 1) {
        for (int j = 1; j < n_threads; j++) {
            const int rc = ggml_thread_join(workers[j].thrd, NULL);
            GGML_ASSERT(rc == 0);
        }
    }

    // performance stats (graph)
    {
        int64_t perf_cycles_cur  = ggml_perf_cycles()  - perf_start_cycles;
        int64_t perf_time_us_cur = ggml_perf_time_us() - perf_start_time_us;

        cgraph->perf_runs++;
        cgraph->perf_cycles  += perf_cycles_cur;
        cgraph->perf_time_us += perf_time_us_cur;

        GGML_PRINT_DEBUG("%s: perf (%d) - cpu = %.3f / %.3f ms, wall = %.3f / %.3f ms\n",
                __func__, cgraph->perf_runs,
                (double) perf_cycles_cur      / (double) ggml_cycles_per_ms(),
                (double) cgraph->perf_cycles  / (double) ggml_cycles_per_ms() / (double) cgraph->perf_runs,
                (double) perf_time_us_cur     / 1000.0,
                (double) cgraph->perf_time_us / 1000.0 / cgraph->perf_runs);
    }
}

void ggml_graph_reset(struct ggml_cgraph * cgraph) {
    for (int i = 0; i < cgraph->n_nodes; i++) {
        struct ggml_tensor * grad = cgraph->grads[i];

        if (grad) {
            ggml_set_zero(grad);
        }
    }
}

void ggml_graph_compute_with_ctx(struct ggml_context * ctx, struct ggml_cgraph * cgraph, int n_threads) {
    struct ggml_cplan cplan = ggml_graph_plan(cgraph, n_threads);

    struct ggml_tensor * buf = ggml_new_tensor_1d(ctx, GGML_TYPE_I8, cplan.work_size);
    GGML_ASSERT(buf);

    cplan.work_data = buf->data;

    ggml_graph_compute(cgraph, &cplan);
}

struct ggml_tensor * ggml_graph_get_tensor(struct ggml_cgraph * cgraph, const char * name) {
    for (int i = 0; i < cgraph->n_leafs; i++) {
        struct ggml_tensor * leaf = cgraph->leafs[i];

        if (strcmp(leaf->name, name) == 0) {
            return leaf;
        }
    }

    for (int i = 0; i < cgraph->n_nodes; i++) {
        struct ggml_tensor * node = cgraph->nodes[i];

        if (strcmp(node->name, name) == 0) {
            return node;
        }
    }

    return NULL;
}

static void ggml_graph_export_leaf(const struct ggml_tensor * tensor, FILE * fout) {
    const int64_t * ne = tensor->ne;
    const size_t  * nb = tensor->nb;

    fprintf(fout, "%-6s %-12s %8d %" PRId64 " %" PRId64 " %" PRId64 " %" PRId64 " %16zu %16zu %16zu %16zu %16p %32s\n",
            ggml_type_name(tensor->type),
            ggml_op_name  (tensor->op),
            tensor->n_dims,
            ne[0], ne[1], ne[2], ne[3],
            nb[0], nb[1], nb[2], nb[3],
            tensor->data,
            tensor->name);
}

static void ggml_graph_export_node(const struct ggml_tensor * tensor, const char * arg, FILE * fout) {
    const int64_t * ne = tensor->ne;
    const size_t  * nb = tensor->nb;

    fprintf(fout, "%-6s %-6s %-12s %8d %" PRId64 " %" PRId64 " %" PRId64 " %" PRId64 " %16zu %16zu %16zu %16zu %16p %32s\n",
            arg,
            ggml_type_name(tensor->type),
            ggml_op_name  (tensor->op),
            tensor->n_dims,
            ne[0], ne[1], ne[2], ne[3],
            nb[0], nb[1], nb[2], nb[3],
            tensor->data,
            tensor->name);
}

void ggml_graph_export(const struct ggml_cgraph * cgraph, const char * fname) {
    //assert(cgraph->work      == NULL);
    //assert(cgraph->work_size == 0);

    uint64_t size_eval = 0;

    // compute size of intermediate results
    // TODO: does not take into account scratch buffers !!!!
    for (int i = 0; i < cgraph->n_nodes; ++i) {
        size_eval += ggml_nbytes(cgraph->nodes[i]);
    }

    // print
    {
        FILE * fout = stdout;

        fprintf(fout, "\n");
        fprintf(fout, "%-16s %8x\n", "magic",        GGML_FILE_MAGIC);
        fprintf(fout, "%-16s %8d\n", "version",      GGML_FILE_VERSION);
        fprintf(fout, "%-16s %8d\n", "leafs",        cgraph->n_leafs);
        fprintf(fout, "%-16s %8d\n", "nodes",        cgraph->n_nodes);
        fprintf(fout, "%-16s %" PRIu64 "\n", "eval", size_eval);

        // header
        fprintf(fout, "\n");
        fprintf(fout, "%-6s %-12s %8s %8s %8s %8s %8s %16s %16s %16s %16s %16s %16s\n",
                "TYPE", "OP", "NDIMS", "NE0", "NE1", "NE2", "NE3", "NB0", "NB1", "NB2", "NB3", "DATA", "NAME");

        for (int i = 0; i < cgraph->n_leafs; ++i) {
            ggml_graph_export_leaf(cgraph->leafs[i], fout);

            GGML_ASSERT(cgraph->leafs[i]->op   == GGML_OP_NONE);
            GGML_ASSERT(cgraph->leafs[i]->src0 == NULL);
            GGML_ASSERT(cgraph->leafs[i]->src1 == NULL);
        }

        // header
        fprintf(fout, "\n");
        fprintf(fout, "%-6s %-6s %-12s %8s %8s %8s %8s %8s %16s %16s %16s %16s %8s %16s %16s\n",
                "ARG", "TYPE", "OP", "NDIMS", "NE0", "NE1", "NE2", "NE3", "NB0", "NB1", "NB2", "NB3", "NTASKS", "DATA", "NAME");

        for (int i = 0; i < cgraph->n_nodes; ++i) {
            ggml_graph_export_node(cgraph->nodes[i], "DST", fout);

            if (cgraph->nodes[i]->src0) {
                ggml_graph_export_node(cgraph->nodes[i]->src0, "SRC0", fout);
            }

            if (cgraph->nodes[i]->src1) {
                ggml_graph_export_node(cgraph->nodes[i]->src1, "SRC1", fout);
            }

            for (int j = 0; j < GGML_MAX_OPT; ++j) {
                if (cgraph->nodes[i]->opt[j]) {
                    ggml_graph_export_node(cgraph->nodes[i]->opt[j], "OPT", fout);
                }
            }

            fprintf(fout, "\n");
        }

        fprintf(fout, "\n");
    }

    // write binary data
    {
        FILE * fout = fopen(fname, "wb");

        if (!fout) {
            fprintf(stderr, "%s: failed to open %s\n", __func__, fname);
            return;
        }

        // header
        {
            const uint32_t magic   = GGML_FILE_MAGIC;
            const uint32_t version = GGML_FILE_VERSION;
            const uint32_t n_leafs = cgraph->n_leafs;
            const uint32_t nodes   = cgraph->n_nodes;

            fwrite(&magic,     sizeof(uint32_t), 1, fout);
            fwrite(&version,   sizeof(uint32_t), 1, fout);
            fwrite(&n_leafs,   sizeof(uint32_t), 1, fout);
            fwrite(&nodes,     sizeof(uint32_t), 1, fout);
            fwrite(&size_eval, sizeof(uint64_t), 1, fout);
        }

        // leafs
        {
            for (int i = 0; i < cgraph->n_leafs; ++i) {
                const struct ggml_tensor * tensor = cgraph->leafs[i];

                const uint32_t type   = tensor->type;
                const uint32_t op     = tensor->op;
                const uint32_t n_dims = tensor->n_dims;

                fwrite(&type,   sizeof(uint32_t), 1, fout);
                fwrite(&op,     sizeof(uint32_t), 1, fout);
                fwrite(&n_dims, sizeof(uint32_t), 1, fout);

                for (int j = 0; j < GGML_MAX_DIMS; ++j) {
                    const uint64_t ne = tensor->ne[j];
                    const uint64_t nb = tensor->nb[j];

                    fwrite(&ne, sizeof(uint64_t), 1, fout);
                    fwrite(&nb, sizeof(uint64_t), 1, fout);
                }

                fwrite(tensor->name, sizeof(char), GGML_MAX_NAME, fout);

                // dump the data
                // TODO: pad this to 32 byte boundary
                {
                    const size_t size = ggml_nbytes(tensor);

                    fwrite(tensor->data, sizeof(char), size, fout);
                }
            }
        }

        // nodes
        {
            for (int i = 0; i < cgraph->n_nodes; ++i) {
                const struct ggml_tensor * tensor = cgraph->nodes[i];

                const uint32_t type   = tensor->type;
                const uint32_t op     = tensor->op;
                const uint32_t n_dims = tensor->n_dims;

                fwrite(&type,   sizeof(uint32_t), 1, fout);
                fwrite(&op,     sizeof(uint32_t), 1, fout);
                fwrite(&n_dims, sizeof(uint32_t), 1, fout);

                for (int j = 0; j < GGML_MAX_DIMS; ++j) {
                    const uint64_t ne = tensor->ne[j];
                    const uint64_t nb = tensor->nb[j];

                    fwrite(&ne, sizeof(uint64_t), 1, fout);
                    fwrite(&nb, sizeof(uint64_t), 1, fout);
                }

                fwrite(tensor->name, sizeof(char), GGML_MAX_NAME, fout);

                // output the op arguments
                {
                    struct ggml_tensor * args[2 + GGML_MAX_OPT] = { NULL };

                    args[0] = tensor->src0;
                    args[1] = tensor->src1;

                    for (int j = 0; j < GGML_MAX_OPT; ++j) {
                        args[2 + j] = tensor->opt[j];
                    }

                    for (int j = 0; j < 2 + GGML_MAX_OPT; ++j) {
                        if (args[j]) {
                            int32_t idx = -1;

                            // check if leaf
                            {
                                for (int k = 0; k < cgraph->n_leafs; ++k) {
                                    if (args[j] == cgraph->leafs[k]) {
                                        idx = k;
                                        break;
                                    }
                                }
                            }

                            // check if node
                            if (idx == -1) {
                                for (int k = 0; k < cgraph->n_nodes; ++k) {
                                    if (args[j] == cgraph->nodes[k]) {
                                        idx = GGML_MAX_NODES + k;
                                        break;
                                    }
                                }
                            }

                            if (idx == -1) {
                                fprintf(stderr, "%s: failed to find tensor, arg = %d, node = %d\n", __func__, j, i);
                                return;
                            }

                            fwrite(&idx, sizeof(int32_t), 1, fout);
                        } else {
                            const int32_t nul = -1;

                            fwrite(&nul, sizeof(int32_t), 1, fout);
                        }
                    }
                }
            }
        }

        fclose(fout);
    }
}

struct ggml_cgraph ggml_graph_import(const char * fname, struct ggml_context ** ctx_data, struct ggml_context ** ctx_eval) {
    assert(*ctx_data == NULL);
    assert(*ctx_eval == NULL);

    struct ggml_cgraph result = { 0 };

    struct ggml_tensor * data = NULL;

    // read file into data
    {
        FILE * fin = fopen(fname, "rb");
        if (!fin) {
            fprintf(stderr, "%s: failed to open %s\n", __func__, fname);
            return result;
        }

        size_t fsize = 0;

        fseek(fin, 0, SEEK_END);
        fsize = ftell(fin);
        fseek(fin, 0, SEEK_SET);

        // create the data context
        {
            const size_t overhead = 1*ggml_tensor_overhead();

            struct ggml_init_params params = {
                .mem_size   = fsize + overhead,
                .mem_buffer = NULL,
                .no_alloc   = false,
            };

            *ctx_data = ggml_init(params);

            if (!*ctx_data) {
                fprintf(stderr, "%s: failed to create ggml context\n", __func__);
                fclose(fin);
                return result;
            }
        }

        data = ggml_new_tensor_1d(*ctx_data, GGML_TYPE_I8, fsize);

        {
            const size_t ret = fread(data->data, sizeof(char), fsize, fin);
            if (ret != fsize) {
                fprintf(stderr, "%s: failed to read %s\n", __func__, fname);
                fclose(fin);
                return result;
            }
        }

        fclose(fin);
    }

    // populate result
    {
        char * ptr = (char *) data->data;

        const uint32_t magic = *(const uint32_t *) ptr; ptr += sizeof(magic);

        if (magic != GGML_FILE_MAGIC) {
            fprintf(stderr, "%s: invalid magic number, got %08x\n", __func__, magic);
            return result;
        }

        const uint32_t version = *(const uint32_t *) ptr; ptr += sizeof(version);

        if (version != GGML_FILE_VERSION) {
            fprintf(stderr, "%s: invalid version number\n", __func__);
            return result;
        }

        const uint32_t n_leafs   = *(const uint32_t *) ptr; ptr += sizeof(n_leafs);
        const uint32_t n_nodes   = *(const uint32_t *) ptr; ptr += sizeof(n_nodes);
        const uint64_t size_eval = *(const uint64_t *) ptr; ptr += sizeof(size_eval);

        result.n_leafs = n_leafs;
        result.n_nodes = n_nodes;

        // create the data context
        {
            const size_t overhead = (n_leafs + n_nodes)*ggml_tensor_overhead();

            struct ggml_init_params params = {
                .mem_size   = size_eval + overhead,
                .mem_buffer = NULL,
                .no_alloc   = true,
            };

            *ctx_eval = ggml_init(params);

            if (!*ctx_eval) {
                fprintf(stderr, "%s: failed to create ggml context\n", __func__);
                return result;
            }
        }

        // leafs
        {
            uint32_t type;
            uint32_t op;
            uint32_t n_dims;

            for (uint32_t i = 0; i < n_leafs; ++i) {
                type   = *(const uint32_t *) ptr; ptr += sizeof(type);
                op     = *(const uint32_t *) ptr; ptr += sizeof(op);
                n_dims = *(const uint32_t *) ptr; ptr += sizeof(n_dims);

                int64_t ne[GGML_MAX_DIMS];
                size_t  nb[GGML_MAX_DIMS];

                for (int j = 0; j < GGML_MAX_DIMS; ++j) {
                    uint64_t ne_cur;
                    uint64_t nb_cur;

                    ne_cur = *(const uint64_t *) ptr; ptr += sizeof(ne_cur);
                    nb_cur = *(const uint64_t *) ptr; ptr += sizeof(nb_cur);

                    ne[j] = ne_cur;
                    nb[j] = nb_cur;
                }

                struct ggml_tensor * tensor = ggml_new_tensor(*ctx_eval, (enum ggml_type) type, n_dims, ne);

                tensor->op = (enum ggml_op) op;

                memcpy(tensor->name, ptr, GGML_MAX_NAME); ptr += GGML_MAX_NAME;

                tensor->data = (void *) ptr;

                for (int j = 0; j < GGML_MAX_DIMS; ++j) {
                    tensor->nb[j] = nb[j];
                }

                result.leafs[i] = tensor;

                ptr += ggml_nbytes(tensor);

                fprintf(stderr, "%s: loaded leaf %d: '%16s', %3d dims, %9zu bytes\n", __func__, i, tensor->name, n_dims, ggml_nbytes(tensor));
            }
        }

        ggml_set_no_alloc(*ctx_eval, false);

        // nodes
        {
            uint32_t type;
            uint32_t op;
            uint32_t n_dims;

            for (uint32_t i = 0; i < n_nodes; ++i) {
                type   = *(const uint32_t *) ptr; ptr += sizeof(type);
                op     = *(const uint32_t *) ptr; ptr += sizeof(op);
                n_dims = *(const uint32_t *) ptr; ptr += sizeof(n_dims);

                enum ggml_op eop = (enum ggml_op) op;

                int64_t ne[GGML_MAX_DIMS];
                size_t  nb[GGML_MAX_DIMS];

                for (int j = 0; j < GGML_MAX_DIMS; ++j) {
                    uint64_t ne_cur;
                    uint64_t nb_cur;

                    ne_cur = *(const uint64_t *) ptr; ptr += sizeof(ne_cur);
                    nb_cur = *(const uint64_t *) ptr; ptr += sizeof(nb_cur);

                    ne[j] = ne_cur;
                    nb[j] = nb_cur;
                }

                const char * ptr_name = ptr; ptr += GGML_MAX_NAME;

                const int32_t * ptr_arg_idx = (const int32_t *) ptr; ptr += (2 + GGML_MAX_OPT)*sizeof(int32_t);

                struct ggml_tensor * args[2 + GGML_MAX_OPT] = { NULL };

                // parse args
                for (int j = 0; j < 2 + GGML_MAX_OPT; ++j) {
                    const int32_t arg_idx = ptr_arg_idx[j];

                    if (arg_idx == -1) {
                        continue;
                    }

                    if (arg_idx < GGML_MAX_NODES) {
                        args[j] = result.leafs[arg_idx];
                    } else {
                        args[j] = result.nodes[arg_idx - GGML_MAX_NODES];
                    }
                }

                // create the tensor
                // "view" operations are handled differently
                // TODO: handle inplace ops - currently a copy is always made

                struct ggml_tensor * tensor = NULL;

                switch (eop) {
                    // TODO: implement other view ops
                    case GGML_OP_RESHAPE:
                        {
                            tensor = ggml_reshape_4d(*ctx_eval, args[0], ne[0], ne[1], ne[2], ne[3]);
                        } break;
                    case GGML_OP_VIEW:
                        {
                            tensor = ggml_view_4d(*ctx_eval, args[0], ne[0], ne[1], ne[2], ne[3], 0, 0, 0, 0);

                            uint64_t offs;
                            memcpy(&offs, args[2]->data, sizeof(offs));

                            tensor->data = ((char *) tensor->data) + offs;
                        } break;
                    case GGML_OP_TRANSPOSE:
                        {
                            tensor = ggml_transpose(*ctx_eval, args[0]);
                        } break;
                    case GGML_OP_PERMUTE:
                        {
                            tensor = ggml_view_4d(*ctx_eval, args[0], ne[0], ne[1], ne[2], ne[3], 0, 0, 0, 0);
                        } break;
                    default:
                        {
                            tensor = ggml_new_tensor(*ctx_eval, (enum ggml_type) type, n_dims, ne);

                            tensor->op = eop;
                        } break;
                }

                memcpy(tensor->name, ptr_name, GGML_MAX_NAME);

                for (int j = 0; j < GGML_MAX_DIMS; ++j) {
                    tensor->nb[j] = nb[j];
                }

                tensor->src0 = args[0];
                tensor->src1 = args[1];

                for (int j = 0; j < GGML_MAX_OPT; ++j) {
                    tensor->opt[j] = args[2 + j];
                }

                result.nodes[i] = tensor;

                fprintf(stderr, "%s: loaded node %d: '%16s', %3d dims, %9zu bytes\n", __func__, i, tensor->name, n_dims, ggml_nbytes(tensor));
            }
        }
    }

    return result;
}

void ggml_graph_print(const struct ggml_cgraph * cgraph) {
    int64_t perf_total_per_op_us[GGML_OP_COUNT] = {0};

    GGML_PRINT("=== GRAPH ===\n");

    GGML_PRINT_DEBUG("n_threads       = %d\n",        cgraph->n_threads);
    GGML_PRINT_DEBUG("total work size = %zu bytes\n", cgraph->work_size);

    GGML_PRINT("n_nodes = %d\n", cgraph->n_nodes);
    for (int i = 0; i < cgraph->n_nodes; i++) {
        struct ggml_tensor * node = cgraph->nodes[i];

        perf_total_per_op_us[node->op] += MAX(1, node->perf_time_us);

        GGML_PRINT(" - %3d: [ %5" PRId64 ", %5" PRId64 ", %5" PRId64 "] %16s %s (%3d) cpu = %7.3f / %7.3f ms, wall = %7.3f / %7.3f ms\n",
                i,
                node->ne[0], node->ne[1], node->ne[2],
                GGML_OP_NAME[node->op], node->is_param ? "x" : node->grad ? "g" : " ", node->perf_runs,
                (double) node->perf_cycles  / (double) ggml_cycles_per_ms(),
                (double) node->perf_cycles  / (double) ggml_cycles_per_ms() / (double) node->perf_runs,
                (double) node->perf_time_us / 1000.0,
                (double) node->perf_time_us / 1000.0 / node->perf_runs);
    }

    GGML_PRINT("n_leafs = %d\n", cgraph->n_leafs);
    for (int i = 0; i < cgraph->n_leafs; i++) {
        struct ggml_tensor * node = cgraph->leafs[i];

        GGML_PRINT(" - %3d: [ %5" PRId64 ", %5" PRId64 "] %8s\n",
                i,
                node->ne[0], node->ne[1],
                GGML_OP_NAME[node->op]);
    }

    for (int i = 0; i < GGML_OP_COUNT; i++) {
        if (perf_total_per_op_us[i] == 0) {
            continue;
        }

        GGML_PRINT("perf_total_per_op_us[%16s] = %7.3f ms\n", GGML_OP_NAME[i], (double) perf_total_per_op_us[i] / 1000.0);
    }

    GGML_PRINT("========================================\n");
}

// check if node is part of the graph
static bool ggml_graph_find(const struct ggml_cgraph * cgraph, const struct ggml_tensor * node) {
    if (cgraph == NULL) {
        return true;
    }

    for (int i = 0; i < cgraph->n_nodes; i++) {
        if (cgraph->nodes[i] == node) {
            return true;
        }
    }

    return false;
}

static struct ggml_tensor * ggml_graph_get_parent(const struct ggml_cgraph * cgraph, const struct ggml_tensor * node) {
    for (int i = 0; i < cgraph->n_nodes; i++) {
        struct ggml_tensor * parent = cgraph->nodes[i];

        if (parent->grad == node) {
            return parent;
        }
    }

    return NULL;
}

static void ggml_graph_dump_dot_node_edge(FILE * fp, const struct ggml_cgraph * gb, struct ggml_tensor * node, struct ggml_tensor * parent, const char * label)  {
    struct ggml_tensor * gparent = ggml_graph_get_parent(gb, node);
    struct ggml_tensor * gparent0 = ggml_graph_get_parent(gb, parent);
    fprintf(fp, "  \"%p\":%s -> \"%p\":%s [ arrowhead = %s; style = %s; label = \"%s\"; ]\n",
            gparent0 ? (void *) gparent0 : (void *) parent,
            gparent0 ? "g" : "x",
            gparent ? (void *) gparent : (void *) node,
            gparent ? "g" : "x",
            gparent ? "empty" : "vee",
            gparent ? "dashed" : "solid",
            label);
}

static void ggml_graph_dump_dot_leaf_edge(FILE * fp, struct ggml_tensor * node, struct ggml_tensor * parent, const char * label)  {
    fprintf(fp, "  \"%p\":%s -> \"%p\":%s [ label = \"%s\"; ]\n",
            (void *) parent, "x",
            (void *) node, "x",
            label);
}

void ggml_graph_dump_dot(const struct ggml_cgraph * gb, const struct ggml_cgraph * gf, const char * filename) {
    char color[16];

    FILE * fp = fopen(filename, "w");
    GGML_ASSERT(fp);

    fprintf(fp, "digraph G {\n");
    fprintf(fp, "  newrank = true;\n");
    fprintf(fp, "  rankdir = LR;\n");

    for (int i = 0; i < gb->n_nodes; i++) {
        struct ggml_tensor * node = gb->nodes[i];

        if (ggml_graph_get_parent(gb, node) != NULL) {
            continue;
        }

        if (node->is_param) {
            snprintf(color, sizeof(color), "yellow");
        } else if (node->grad) {
            if (ggml_graph_find(gf, node)) {
                snprintf(color, sizeof(color), "green");
            } else {
                snprintf(color, sizeof(color), "lightblue");
            }
        } else {
            snprintf(color, sizeof(color), "white");
        }

        fprintf(fp, "  \"%p\" [ "
                    "style = filled; fillcolor = %s; shape = record; "
                    "label=\"",
                (void *) node, color);

        if (strlen(node->name) > 0) {
            fprintf(fp, "%s (%s)|", node->name, ggml_type_name(node->type));
        } else {
            fprintf(fp, "(%s)|", ggml_type_name(node->type));
        }

        if (node->n_dims == 2) {
            fprintf(fp, "%d [%" PRId64 ", %" PRId64 "] | <x>%s", i, node->ne[0], node->ne[1], GGML_OP_SYMBOL[node->op]);
        } else {
            fprintf(fp, "%d [%" PRId64 ", %" PRId64 ", %" PRId64 "] | <x>%s", i, node->ne[0], node->ne[1], node->ne[2], GGML_OP_SYMBOL[node->op]);
        }

        if (node->grad) {
            fprintf(fp, " | <g>%s\"; ]\n", GGML_OP_SYMBOL[node->grad->op]);
        } else {
            fprintf(fp, "\"; ]\n");
        }
    }

    for (int i = 0; i < gb->n_leafs; i++) {
        struct ggml_tensor * node = gb->leafs[i];

        snprintf(color, sizeof(color), "pink");

        fprintf(fp, "  \"%p\" [ "
                    "style = filled; fillcolor = %s; shape = record; "
                    "label=\"<x>",
                (void *) node, color);

        if (strlen(node->name) > 0) {
            fprintf(fp, "%s (%s)|", node->name, ggml_type_name(node->type));
        } else {
            fprintf(fp, "(%s)|", ggml_type_name(node->type));
        }

        fprintf(fp, "CONST %d [%" PRId64 ", %" PRId64 "]", i, node->ne[0], node->ne[1]);
        if (ggml_nelements(node) < 5) {
            fprintf(fp, " | (");
            for (int j = 0; j < ggml_nelements(node); j++) {
                if (node->type == GGML_TYPE_I8 || node->type == GGML_TYPE_I16 || node->type == GGML_TYPE_I32) {
                    fprintf(fp, "%d", ggml_get_i32_1d(node, j));
                }
                else if (node->type == GGML_TYPE_F32 || node->type == GGML_TYPE_F16) {
                    fprintf(fp, "%.1e", (double)ggml_get_f32_1d(node, j));
                }
                else {
                    fprintf(fp, "#");
                }
                if (j < ggml_nelements(node) - 1) {
                    fprintf(fp, ", ");
                }
            }
            fprintf(fp, ")");
        }
        fprintf(fp, "\"; ]\n");
    }

    for (int i = 0; i < gb->n_nodes; i++) {
        struct ggml_tensor * node = gb->nodes[i];

        if (node->src0) {
            ggml_graph_dump_dot_node_edge(fp, gb, node, node->src0, "x");
        }

        if (node->src1) {
            ggml_graph_dump_dot_node_edge(fp, gb, node, node->src1, "y");
        }

        for (int j = 0; j < GGML_MAX_OPT; j++) {
            if (node->opt[j]) {
                char label[16];
                snprintf(label, sizeof(label), "opt %d", j);
                ggml_graph_dump_dot_node_edge(fp, gb, node, node->opt[j], label);
            }
        }
    }

    for (int i = 0; i < gb->n_leafs; i++) {
        struct ggml_tensor * node = gb->leafs[i];

        if (node->src0) {
            ggml_graph_dump_dot_leaf_edge(fp, node, node->src0, "x");
        }

        if (node->src1) {
            ggml_graph_dump_dot_leaf_edge(fp, node, node->src1, "y");
        }

        for (int j = 0; j < GGML_MAX_OPT; j++) {
            if (node->opt[j]) {
                char label[16];
                snprintf(label, sizeof(label), "opt %d", j);
                ggml_graph_dump_dot_leaf_edge(fp, node, node->opt[j], label);
            }
        }
    }

    fprintf(fp, "}\n");

    fclose(fp);

    GGML_PRINT("%s: dot -Tpng %s -o %s.png && open %s.png\n", __func__, filename, filename, filename);
}

////////////////////////////////////////////////////////////////////////////////

static void ggml_opt_set_params(int np, struct ggml_tensor * const ps[], const float * x) {
    int i = 0;
    for (int p = 0; p < np; ++p) {
        const int64_t ne = ggml_nelements(ps[p]) ;
        // TODO: add function to set tensor from array
        for (int64_t j = 0; j < ne; ++j) {
            ggml_set_f32_1d(ps[p], j, x[i++]);
        }
    }
}

static void ggml_opt_get_params(int np, struct ggml_tensor * const ps[], float * x) {
    int i = 0;
    for (int p = 0; p < np; ++p) {
        const int64_t ne = ggml_nelements(ps[p]) ;
        // TODO: add function to get all elements at once
        for (int64_t j = 0; j < ne; ++j) {
            x[i++] = ggml_get_f32_1d(ps[p], j);
        }
    }
}

static void ggml_opt_get_grad(int np, struct ggml_tensor * const ps[], float * g) {
    int i = 0;
    for (int p = 0; p < np; ++p) {
        const int64_t ne = ggml_nelements(ps[p]) ;
        // TODO: add function to get all elements at once
        for (int64_t j = 0; j < ne; ++j) {
            g[i++] = ggml_get_f32_1d(ps[p]->grad, j);
        }
    }
}

//
// ADAM
//
//   ref: https://arxiv.org/pdf/1412.6980.pdf
//

static enum ggml_opt_result ggml_opt_adam(
        struct ggml_context * ctx,
        struct ggml_opt_context * opt,
        struct ggml_opt_params params,
        struct ggml_tensor * f,
        struct ggml_cgraph * gf,
        struct ggml_cgraph * gb) {
    GGML_ASSERT(ggml_is_scalar(f));

    // these will store the parameters we want to optimize
    struct ggml_tensor * ps[GGML_MAX_PARAMS];

    int np = 0;
    int nx = 0;
    for (int i = 0; i < gf->n_nodes; ++i) {
        if (gf->nodes[i]->is_param) {
            GGML_PRINT_DEBUG("found param %d: grad->op = %d\n", np, gf->nodes[i]->grad->op);

            GGML_ASSERT(np < GGML_MAX_PARAMS);

            ps[np++] = gf->nodes[i];
            nx += ggml_nelements(gf->nodes[i]);
        }
    }

    if ((opt->params.type != params.type) || (opt->nx != nx) || (opt->params.past != params.past)) {
        int iter = opt->iter;
        ggml_opt_init(opt->ctx, opt, params, nx);
        opt->iter = iter;
    }

    // constants
    const float sched = params.adam.sched;
    const float decay = params.adam.decay * sched;
    const float alpha = params.adam.alpha * sched;
    const float beta1 = params.adam.beta1;
    const float beta2 = params.adam.beta2;
    const float eps   = params.adam.eps;

    float * x  = opt->adam.x->data;  // view of the parameters
    float * g1 = opt->adam.g1->data; // gradient
    float * g2 = opt->adam.g2->data; // gradient squared
    float * m  = opt->adam.m->data;  // first moment
    float * v  = opt->adam.v->data;  // second moment
    float * mh = opt->adam.mh->data; // first moment hat
    float * vh = opt->adam.vh->data; // second moment hat

    float * pf = params.past > 0 ? opt->adam.pf->data : NULL; // past function values

    // update view
    ggml_opt_get_params(np, ps, x);

    // compute the function value
    ggml_graph_reset  (gf);
    ggml_set_f32      (f->grad, 1.0f);

    ggml_graph_compute_with_ctx(ctx, gb, params.n_threads);

    opt->adam.fx_prev = ggml_get_f32_1d(f, 0);
    opt->adam.fx_best = opt->adam.fx_prev;
    if (pf) {
        pf[opt->iter % params.past] = opt->adam.fx_prev;
    }

    // initialize
    if (opt->just_initialized) {
        opt->adam.n_no_improvement = 0;
        opt->just_initialized = false;
    }

    float * fx_best = &opt->adam.fx_best;
    float * fx_prev = &opt->adam.fx_prev;
    int * n_no_improvement = &opt->adam.n_no_improvement;

    int iter0 = opt->iter;

    // run the optimizer
    for (int t = 0; t < params.adam.n_iter; ++t) {
        opt->iter = iter0 + t + 1;
        GGML_PRINT_DEBUG  ("=== iter %d ===\n", t);

        GGML_PRINT_DEBUG  ("f      = %10.6f\n", ggml_get_f32_1d(f, 0));
        GGML_PRINT_DEBUG_5("df/dx0 = %10.6f\n", ggml_get_f32_1d(ps[0]->grad, 0));
        GGML_PRINT_DEBUG_5("df/dx1 = %10.6f\n", ggml_get_f32_1d(ps[1]->grad, 0));

        for (int i = 0; i < np; ++i) {
            GGML_PRINT_DEBUG("param %d: %10.6f, g = %10.6f\n", i,
                    ggml_get_f32_1d(ps[i], 0), ggml_get_f32_1d(ps[i]->grad, 0));
        }

        const int64_t t_start_wall = ggml_time_us();
        const int64_t t_start_cpu = ggml_cycles();
        UNUSED(t_start_wall);
        UNUSED(t_start_cpu);

        {
            // update the gradient
            ggml_opt_get_grad(np, ps, g1);

            // m_t = beta1*m_t-1 + (1 - beta1)*g_t
            ggml_vec_scale_f32(nx, m, beta1);
            ggml_vec_mad_f32  (nx, m, g1, 1.0f - beta1);

            // g2 = g1^2
            ggml_vec_sqr_f32  (nx, g2, g1);

            // v_t = beta2*v_t-1 + (1 - beta2)*g_t^2
            ggml_vec_scale_f32(nx, v, beta2);
            ggml_vec_mad_f32  (nx, v, g2, 1.0f - beta2);

            // m^hat = m_t / (1 - beta1^t)
            // v^hat = v_t / (1 - beta2^t)
            // x_t = x_t-1 - sched*(alpha*m^hat/(sqrt(v^hat) + eps) + decay*x_t-1)
            // x_t = x_t-1 - sched*alpha*m^hat/(sqrt(v^hat) + eps) - sched*decay*x_t-1
            // x_t = x_t-1*(1-sched*decay) - sched*alpha*m^hat/(sqrt(v^hat) + eps)
            // x_t = x_t-1*(1-sched*decay) + sched*decay*(-alpha/decay)*m^hat/(sqrt(v^hat) + eps)
            // x_t = mix(x_t-1, (-alpha/decay)*m^hat/(sqrt(v^hat) + eps), sched*decay)
            ggml_vec_cpy_f32  (nx, mh, m);
            ggml_vec_cpy_f32  (nx, vh, v);

            ggml_vec_scale_f32(nx, mh, alpha/(1.0f - powf(beta1, opt->iter)));
            ggml_vec_scale_f32(nx, vh,  1.0f/(1.0f - powf(beta2, opt->iter)));

            ggml_vec_sqrt_f32 (nx, vh, vh);
            ggml_vec_acc1_f32 (nx, vh, eps);

            ggml_vec_div_f32  (nx, mh, mh, vh);
            ggml_vec_scale_f32(nx, x,  1.0f - decay);
            ggml_vec_sub_f32  (nx, x,  x,  mh);

            // update the parameters
            ggml_opt_set_params(np, ps, x);
        }

        ggml_graph_reset  (gf);
        ggml_set_f32      (f->grad, 1.0f);

        ggml_graph_compute_with_ctx(ctx, gb, params.n_threads);

        const float fx = ggml_get_f32_1d(f, 0);

        // check convergence
        if (fabsf(fx - fx_prev[0])/fx < params.adam.eps_f) {
            GGML_PRINT_DEBUG("converged\n");

            return GGML_OPT_OK;
        }

        // delta-based convergence test
        if (pf != NULL) {
            // need at least params.past iterations to start checking for convergence
            if (params.past <= iter0 + t) {
                const float rate = (pf[(iter0 + t)%params.past] - fx)/fx;

                if (fabsf(rate) < params.delta) {
                    return GGML_OPT_OK;
                }
            }

            pf[(iter0 + t)%params.past] = fx;
        }

        // check for improvement
        if (params.max_no_improvement > 0) {
            if (fx_best[0] > fx) {
                fx_best[0] = fx;
                n_no_improvement[0] = 0;
            } else {
                ++n_no_improvement[0];

                if (n_no_improvement[0] >= params.max_no_improvement) {
                    return GGML_OPT_OK;
                }
            }
        }

        fx_prev[0] = fx;

        {
            const int64_t t_end_cpu = ggml_cycles();
            GGML_PRINT_DEBUG("time iter:      %5.3f s\n", ((float)(t_end_cpu - t_start_cpu))/CLOCKS_PER_SEC);
            UNUSED(t_end_cpu);

            const int64_t t_end_wall = ggml_time_us();
            GGML_PRINT_DEBUG("wall time iter: %5.3f s\n", (t_end_wall - t_start_wall)/1e6);
            UNUSED(t_end_wall);
        }
    }

    return GGML_OPT_DID_NOT_CONVERGE;
}

//
// L-BFGS
//
// the L-BFGS implementation below is based on the following implementation:
//
//   https://github.com/chokkan/liblbfgs
//

struct ggml_lbfgs_iteration_data {
    float alpha;
    float ys;
    float * s;
    float * y;
};

static enum ggml_opt_result linesearch_backtracking(
        struct ggml_context * ctx,
        const struct ggml_opt_params * params,
        int nx,
        float * x,
        float * fx,
        float * g,
        float * d,
        float * step,
        const float * xp,
        struct ggml_tensor * f,
        struct ggml_cgraph * gf,
        struct ggml_cgraph * gb,
        const int np,
        struct ggml_tensor * ps[]) {
    int count = 0;

    float width  = 0.0f;
    float dg     = 0.0f;
    float finit  = 0.0f;
    float dginit = 0.0f;
    float dgtest = 0.0f;

    const float dec = 0.5f;
    const float inc = 2.1f;

    if (*step <= 0.f) {
        return GGML_LINESEARCH_INVALID_PARAMETERS;
    }

    // compute the initial gradient in the search direction
    ggml_vec_dot_f32(nx, &dginit, g, d);

    // make sure that d points to a descent direction
    if (0 < dginit) {
        return GGML_LINESEARCH_FAIL;
    }

    // initialize local variables
    finit = *fx;
    dgtest = params->lbfgs.ftol*dginit;

    while (true) {
        ggml_vec_cpy_f32(nx, x, xp);
        ggml_vec_mad_f32(nx, x, d, *step);

        // evaluate the function and gradient values
        {
            ggml_opt_set_params(np, ps, x);

            ggml_graph_reset  (gf);
            ggml_set_f32      (f->grad, 1.0f);

            ggml_graph_compute_with_ctx(ctx, gb, params->n_threads);

            ggml_opt_get_grad(np, ps, g);

            *fx = ggml_get_f32_1d(f, 0);
        }

        ++count;

        if (*fx > finit + (*step)*dgtest) {
            width = dec;
        } else {
            // Armijo condition is satisfied
            if (params->lbfgs.linesearch == GGML_LINESEARCH_BACKTRACKING_ARMIJO) {
                return count;
            }

            ggml_vec_dot_f32(nx, &dg, g, d);

            // check the Wolfe condition
            if (dg < params->lbfgs.wolfe * dginit) {
                width = inc;
            } else {
                if(params->lbfgs.linesearch == GGML_LINESEARCH_BACKTRACKING_WOLFE) {
                    // regular Wolfe conditions
                    return count;
                }

                if(dg > -params->lbfgs.wolfe*dginit) {
                    width = dec;
                } else {
                    // strong Wolfe condition (GGML_LINESEARCH_BACKTRACKING_STRONG_WOLFE)
                    return count;
                }
                return count;
            }
        }

        if (*step < params->lbfgs.min_step) {
            return GGML_LINESEARCH_MINIMUM_STEP;
        }
        if (*step > params->lbfgs.max_step) {
            return GGML_LINESEARCH_MAXIMUM_STEP;
        }
        if (params->lbfgs.max_linesearch <= count) {
            return GGML_LINESEARCH_MAXIMUM_ITERATIONS;
        }

        (*step) *= width;
    }

    return GGML_LINESEARCH_FAIL;
}

static enum ggml_opt_result ggml_opt_lbfgs(
        struct ggml_context * ctx,
        struct ggml_opt_context * opt,
        struct ggml_opt_params params,
        struct ggml_tensor * f,
        struct ggml_cgraph * gf,
        struct ggml_cgraph * gb) {
    if (params.lbfgs.linesearch == GGML_LINESEARCH_BACKTRACKING_WOLFE ||
        params.lbfgs.linesearch == GGML_LINESEARCH_BACKTRACKING_STRONG_WOLFE) {
        if (params.lbfgs.wolfe <= params.lbfgs.ftol || 1.f <= params.lbfgs.wolfe) {
            return GGML_OPT_INVALID_WOLFE;
        }
    }

    const int m = params.lbfgs.m;

    // these will store the parameters we want to optimize
    struct ggml_tensor * ps[GGML_MAX_PARAMS];

    int np = 0;
    int nx = 0;
    for (int i = 0; i < gf->n_nodes; ++i) {
        if (gf->nodes[i]->is_param) {
            GGML_PRINT_DEBUG("found param %d: grad->op = %d\n", np, gf->nodes[i]->grad->op);

            GGML_ASSERT(np < GGML_MAX_PARAMS);

            ps[np++] = gf->nodes[i];
            nx += ggml_nelements(gf->nodes[i]);
        }
    }

    if ((opt->params.type != params.type) || (opt->nx != nx) || (opt->params.past != params.past) || (opt->params.lbfgs.m != params.lbfgs.m)) {
        int iter = opt->iter;
        ggml_opt_init(ctx, opt, params, nx);
        opt->iter = iter;
    }

    float * x  = opt->lbfgs.x->data;  // current parameters
    float * xp = opt->lbfgs.xp->data; // previous parameters
    float * g  = opt->lbfgs.g->data;  // current gradient
    float * gp = opt->lbfgs.gp->data; // previous gradient
    float * d  = opt->lbfgs.d->data;  // search direction

    float * pf = params.past > 0 ? opt->lbfgs.pf->data : NULL; // past function values

    float fx    = 0.0f; // cost function value
    float xnorm = 0.0f; // ||x||
    float gnorm = 0.0f; // ||g||

    // initialize x from the graph nodes
    ggml_opt_get_params(np, ps, x);

    // the L-BFGS memory
    float * lm_alpha = opt->lbfgs.lmal->data;
    float * lm_ys    = opt->lbfgs.lmys->data;
    float * lm_s     = opt->lbfgs.lms->data;
    float * lm_y     = opt->lbfgs.lmy->data;

    // evaluate the function value and its gradient
    {
        ggml_opt_set_params(np, ps, x);

        ggml_graph_reset  (gf);
        ggml_set_f32      (f->grad, 1.0f);

        ggml_graph_compute_with_ctx(ctx, gb, params.n_threads);

        ggml_opt_get_grad(np, ps, g);

        fx = ggml_get_f32_1d(f, 0);
    }

    // search direction = -gradient
    ggml_vec_neg_f32(nx, d, g);

    // ||x||, ||g||
    ggml_vec_norm_f32(nx, &xnorm, x);
    ggml_vec_norm_f32(nx, &gnorm, g);

    if (xnorm < 1.0f) {
        xnorm = 1.0f;
    }

    // already optimized
    if (gnorm/xnorm <= params.lbfgs.eps) {
        return GGML_OPT_OK;
    }

    if (opt->just_initialized) {
        if (pf) {
            pf[0] = fx;
        }
        opt->lbfgs.fx_best = fx;

        // initial step
        ggml_vec_norm_inv_f32(nx, &opt->lbfgs.step, d);
        opt->lbfgs.j                = 0;
        opt->lbfgs.k                = 1;
        opt->lbfgs.end              = 0;
        opt->lbfgs.n_no_improvement = 0;
        opt->just_initialized       = false;
    }

    float * fx_best        = &opt->lbfgs.fx_best;
    float * step           = &opt->lbfgs.step;
    int * j                = &opt->lbfgs.j;
    int * k                = &opt->lbfgs.k;
    int * end              = &opt->lbfgs.end;
    int * n_no_improvement = &opt->lbfgs.n_no_improvement;

    int ls     = 0;
    int bound  = 0;

    float ys   = 0.0f;
    float yy   = 0.0f;
    float beta = 0.0f;

    int it = 0;

    while (true) {
        // store the current position and gradient vectors
        ggml_vec_cpy_f32(nx, xp, x);
        ggml_vec_cpy_f32(nx, gp, g);

        ls = linesearch_backtracking(ctx, &params, nx, x, &fx, g, d, step, xp, f, gf, gb, np, ps);

        if (ls < 0) {
            // linesearch failed - go back to the previous point and return
            ggml_vec_cpy_f32(nx, x, xp);
            ggml_vec_cpy_f32(nx, g, gp);

            return ls;
        }

        ggml_vec_norm_f32(nx, &xnorm, x);
        ggml_vec_norm_f32(nx, &gnorm, g);

        GGML_PRINT_DEBUG("f = %10.6f\n", ggml_get_f32_1d(f, 0));

        if (xnorm < 1.0f) {
            xnorm = 1.0f;
        }
        if (gnorm/xnorm <= params.lbfgs.eps) {
            // converged
            return GGML_OPT_OK;
        }

        // delta-based convergence test
        if (pf != NULL) {
            // need at least params.past iterations to start checking for convergence
            if (params.past <= k[0]) {
                const float rate = (pf[k[0]%params.past] - fx)/fx;

                if (fabsf(rate) < params.delta) {
                    return GGML_OPT_OK;
                }
            }

            pf[k[0]%params.past] = fx;
        }

        // check for improvement
        if (params.max_no_improvement > 0) {
            if (fx < fx_best[0]) {
                fx_best[0] = fx;
                n_no_improvement[0] = 0;
            } else {
                n_no_improvement[0]++;

                if (n_no_improvement[0] >= params.max_no_improvement) {
                    return GGML_OPT_OK;
                }
            }
        }

        if (params.lbfgs.n_iter != 0 && params.lbfgs.n_iter < it + 1) {
            // reached the maximum number of iterations
            return GGML_OPT_DID_NOT_CONVERGE;
        }

        // update vectors s and y:
        //   s_{k+1} = x_{k+1} - x_{k} = \step * d_{k}.
        //   y_{k+1} = g_{k+1} - g_{k}.
        //
        ggml_vec_sub_f32(nx, &lm_s[end[0]*nx], x, xp);
        ggml_vec_sub_f32(nx, &lm_y[end[0]*nx], g, gp);

        // compute scalars ys and yy:
        //     ys = y^t \cdot s    -> 1 / \rho.
        //     yy = y^t \cdot y.
        //
        ggml_vec_dot_f32(nx, &ys, &lm_y[end[0]*nx], &lm_s[end[0] *nx]);
        ggml_vec_dot_f32(nx, &yy, &lm_y[end[0]*nx], &lm_y[end[0]*nx]);

        lm_ys[end[0]] = ys;

        // find new search direction
        //   ref: https://en.wikipedia.org/wiki/Limited-memory_BFGS

        bound = (m <= k[0]) ? m : k[0];
        k[0]++;
        it++;
        end[0] = (end[0] + 1)%m;

        // initialize search direction with -g
        ggml_vec_neg_f32(nx, d, g);

        j[0] = end[0];
        for (int i = 0; i < bound; ++i) {
            j[0] = (j[0] + m - 1) % m;
            // \alpha_{j} = \rho_{j} s^{t}_{j} \cdot q_{k+1}
            ggml_vec_dot_f32(nx, &lm_alpha[j[0]], &lm_s[j[0]*nx], d);
            lm_alpha[j[0]] /= lm_ys[j[0]];
            // q_{i} = q_{i+1} - \alpha_{i} y_{i}
            ggml_vec_mad_f32(nx, d, &lm_y[j[0]*nx], -lm_alpha[j[0]]);
        }

        ggml_vec_scale_f32(nx, d, ys/yy);

        for (int i = 0; i < bound; ++i) {
            // \beta_{j} = \rho_{j} y^t_{j} \cdot \gamma_{i}
            ggml_vec_dot_f32(nx, &beta, &lm_y[j[0]*nx], d);
            beta /= lm_ys[j[0]];
            // \gamma_{i+1} = \gamma_{i} + (\alpha_{j} - \beta_{j}) s_{j}
            ggml_vec_mad_f32(nx, d, &lm_s[j[0]*nx], lm_alpha[j[0]] - beta);
            j[0] = (j[0] + 1)%m;
        }

        step[0] = 1.0;
    }

    return GGML_OPT_DID_NOT_CONVERGE;
}

struct ggml_opt_params ggml_opt_default_params(enum ggml_opt_type type) {
    struct ggml_opt_params result;

    switch (type) {
        case GGML_OPT_ADAM:
            {
                result = (struct ggml_opt_params) {
                    .type      = GGML_OPT_ADAM,
                    .n_threads = 1,
                    .past      = 0,
                    .delta     = 1e-5f,

                    .max_no_improvement = 100,

                    .print_forward_graph  = true,
                    .print_backward_graph = true,

                    .adam = {
                        .n_iter = 10000,
                        .sched  = 1.000f,
                        .decay  = 0.001f,
                        .alpha  = 0.001f,
                        .beta1  = 0.9f,
                        .beta2  = 0.999f,
                        .eps    = 1e-8f,
                        .eps_f  = 1e-5f,
                        .eps_g  = 1e-3f,
                    },
                };
            } break;
        case GGML_OPT_LBFGS:
            {
                result = (struct ggml_opt_params) {
                    .type      = GGML_OPT_LBFGS,
                    .n_threads = 1,
                    .past      = 0,
                    .delta     = 1e-5f,

                    .max_no_improvement = 0,

                    .print_forward_graph  = true,
                    .print_backward_graph = true,

                    .lbfgs = {
                        .m              = 6,
                        .n_iter         = 100,
                        .max_linesearch = 20,

                        .eps      = 1e-5f,
                        .ftol     = 1e-4f,
                        .wolfe    = 0.9f,
                        .min_step = 1e-20f,
                        .max_step = 1e+20f,

                        .linesearch = GGML_LINESEARCH_DEFAULT,
                    },
                };
            } break;
    }

    return result;
}

GGML_API void ggml_opt_init(
        struct ggml_context * ctx,
        struct ggml_opt_context * opt,
        struct ggml_opt_params params,
        int64_t nx) {
    opt->ctx = ctx;
    opt->params = params;
    opt->iter = 0;
    opt->nx = nx;
    opt->just_initialized = true;
    switch (opt->params.type) {
        case GGML_OPT_ADAM:
            {
                opt->adam.x  = ggml_new_tensor_1d(ctx, GGML_TYPE_F32, nx);
                opt->adam.g1 = ggml_new_tensor_1d(ctx, GGML_TYPE_F32, nx);
                opt->adam.g2 = ggml_new_tensor_1d(ctx, GGML_TYPE_F32, nx);
                opt->adam.m  = ggml_new_tensor_1d(ctx, GGML_TYPE_F32, nx);
                opt->adam.v  = ggml_new_tensor_1d(ctx, GGML_TYPE_F32, nx);
                opt->adam.mh = ggml_new_tensor_1d(ctx, GGML_TYPE_F32, nx);
                opt->adam.vh = ggml_new_tensor_1d(ctx, GGML_TYPE_F32, nx);
                opt->adam.pf = params.past > 0
                    ? ggml_new_tensor_1d(ctx, GGML_TYPE_F32, params.past)
                    : NULL;
                ggml_set_zero(opt->adam.x);
                ggml_set_zero(opt->adam.g1);
                ggml_set_zero(opt->adam.g2);
                ggml_set_zero(opt->adam.m);
                ggml_set_zero(opt->adam.v);
                ggml_set_zero(opt->adam.mh);
                ggml_set_zero(opt->adam.vh);
                if (opt->adam.pf) {
                    ggml_set_zero(opt->adam.pf);
                }
            } break;
        case GGML_OPT_LBFGS:
            {
                opt->lbfgs.x  = ggml_new_tensor_1d(ctx, GGML_TYPE_F32, nx);
                opt->lbfgs.xp = ggml_new_tensor_1d(ctx, GGML_TYPE_F32, nx);
                opt->lbfgs.g  = ggml_new_tensor_1d(ctx, GGML_TYPE_F32, nx);
                opt->lbfgs.gp = ggml_new_tensor_1d(ctx, GGML_TYPE_F32, nx);
                opt->lbfgs.d  = ggml_new_tensor_1d(ctx, GGML_TYPE_F32, nx);
                opt->lbfgs.pf = params.past > 0
                    ? ggml_new_tensor_1d(ctx, GGML_TYPE_F32, params.past)
                    : NULL;
                opt->lbfgs.lmal = ggml_new_tensor_1d(ctx, GGML_TYPE_F32, params.lbfgs.m);
                opt->lbfgs.lmys = ggml_new_tensor_1d(ctx, GGML_TYPE_F32, params.lbfgs.m);
                opt->lbfgs.lms  = ggml_new_tensor_2d(ctx, GGML_TYPE_F32, nx, params.lbfgs.m);
                opt->lbfgs.lmy  = ggml_new_tensor_2d(ctx, GGML_TYPE_F32, nx, params.lbfgs.m);
                ggml_set_zero(opt->lbfgs.x);
                ggml_set_zero(opt->lbfgs.xp);
                ggml_set_zero(opt->lbfgs.g);
                ggml_set_zero(opt->lbfgs.gp);
                ggml_set_zero(opt->lbfgs.d);
                if (opt->lbfgs.pf) {
                    ggml_set_zero(opt->lbfgs.pf);
                }
                ggml_set_zero(opt->lbfgs.lmal);
                ggml_set_zero(opt->lbfgs.lmys);
                ggml_set_zero(opt->lbfgs.lms);
                ggml_set_zero(opt->lbfgs.lmy);
            } break;
    }
}

enum ggml_opt_result ggml_opt(
        struct ggml_context * ctx,
        struct ggml_opt_params params,
        struct ggml_tensor * f) {
    bool free_ctx = false;
    if (ctx == NULL) {
        struct ggml_init_params params_ctx = {
            .mem_size   = 16*1024*1024,
            .mem_buffer = NULL,
            .no_alloc   = false,
        };

        ctx = ggml_init(params_ctx);
        if (ctx == NULL) {
            return GGML_OPT_NO_CONTEXT;
        }

        free_ctx = true;
    }

    enum ggml_opt_result result = GGML_OPT_OK;

    struct ggml_opt_context * opt = (struct ggml_opt_context *) alloca(sizeof(struct ggml_opt_context));

    ggml_opt_init(ctx, opt, params, 0);
    result = ggml_opt_resume(ctx, opt, f);

    if (free_ctx) {
        ggml_free(ctx);
    }

    return result;
}

enum ggml_opt_result ggml_opt_resume(
        struct ggml_context * ctx,
        struct ggml_opt_context * opt,
        struct ggml_tensor * f) {

    // build forward + backward compute graphs
    struct ggml_tensor * gfbuf = ggml_new_tensor_1d(ctx, GGML_TYPE_I32, sizeof(struct ggml_cgraph) / GGML_TYPE_SIZE[GGML_TYPE_I32]+ (sizeof(struct ggml_cgraph) % GGML_TYPE_SIZE[GGML_TYPE_I32] ? 1 : 0));
    struct ggml_tensor * gbbuf = ggml_new_tensor_1d(ctx, GGML_TYPE_I32, sizeof(struct ggml_cgraph) / GGML_TYPE_SIZE[GGML_TYPE_I32]+ (sizeof(struct ggml_cgraph) % GGML_TYPE_SIZE[GGML_TYPE_I32] ? 1 : 0));

    struct ggml_cgraph * gf = (struct ggml_cgraph *) gfbuf->data;
    struct ggml_cgraph * gb = (struct ggml_cgraph *) gbbuf->data;

    *gf = ggml_build_forward (f);
    *gb = ggml_build_backward(ctx, gf, true);

    return ggml_opt_resume_g(ctx, opt, f, gf, gb);
}

enum ggml_opt_result ggml_opt_resume_g(
        struct ggml_context * ctx,
        struct ggml_opt_context * opt,
        struct ggml_tensor * f,
        struct ggml_cgraph * gf,
        struct ggml_cgraph * gb) {

    // build forward + backward compute graphs
    enum ggml_opt_result result = GGML_OPT_OK;

    switch (opt->params.type) {
        case GGML_OPT_ADAM:
            {
                result = ggml_opt_adam(ctx, opt, opt->params, f, gf, gb);
            } break;
        case GGML_OPT_LBFGS:
            {
                result = ggml_opt_lbfgs(ctx, opt, opt->params, f, gf, gb);
            } break;
    }

    if (opt->params.print_forward_graph) {
        ggml_graph_print   (gf);
        ggml_graph_dump_dot(gf, NULL, "opt-forward.dot");
    }

    if (opt->params.print_backward_graph) {
        ggml_graph_print   (gb);
        ggml_graph_dump_dot(gb, gf, "opt-backward.dot");
    }

    return result;
}

////////////////////////////////////////////////////////////////////////////////

size_t ggml_quantize_q4_0(const float * src, void * dst, int n, int k, int64_t * hist) {
    assert(k % QK4_0 == 0);
    const int nb = k / QK4_0;

    for (int b = 0; b < n; b += k) {
        block_q4_0 * restrict y = (block_q4_0 *) dst + b/QK4_0;

        quantize_row_q4_0_reference(src + b, y, k);

        for (int i = 0; i < nb; i++) {
            for (int j = 0; j < QK4_0; j += 2) {
                const uint8_t vi0 = y[i].qs[j/2] & 0x0F;
                const uint8_t vi1 = y[i].qs[j/2] >> 4;

                hist[vi0]++;
                hist[vi1]++;
            }
        }
    }

    return (n/QK4_0*sizeof(block_q4_0));
}

size_t ggml_quantize_q4_1(const float * src, void * dst, int n, int k, int64_t * hist) {
    assert(k % QK4_1 == 0);
    const int nb = k / QK4_1;

    for (int b = 0; b < n; b += k) {
        block_q4_1 * restrict y = (block_q4_1 *) dst + b/QK4_1;

        quantize_row_q4_1_reference(src + b, y, k);

        for (int i = 0; i < nb; i++) {
            for (int j = 0; j < QK4_1; j += 2) {
                const uint8_t vi0 = y[i].qs[j/2] & 0x0F;
                const uint8_t vi1 = y[i].qs[j/2] >> 4;

                hist[vi0]++;
                hist[vi1]++;
            }
        }
    }

    return (n/QK4_1*sizeof(block_q4_1));
}

size_t ggml_quantize_q5_0(const float * src, void * dst, int n, int k, int64_t * hist) {
    assert(k % QK5_0 == 0);
    const int nb = k / QK5_0;

    for (int b = 0; b < n; b += k) {
        block_q5_0 * restrict y = (block_q5_0 *)dst + b/QK5_0;

        quantize_row_q5_0_reference(src + b, y, k);

        for (int i = 0; i < nb; i++) {
            uint32_t qh;
            memcpy(&qh, &y[i].qh, sizeof(qh));

            for (int j = 0; j < QK5_0; j += 2) {
                const uint8_t vh0 = ((qh & (1u << (j + 0 ))) >> (j + 0 )) << 4;
                const uint8_t vh1 = ((qh & (1u << (j + 16))) >> (j + 12));

                // cast to 16 bins
                const uint8_t vi0 = ((y[i].qs[j/2] & 0x0F) | vh0) / 2;
                const uint8_t vi1 = ((y[i].qs[j/2] >>   4) | vh1) / 2;

                hist[vi0]++;
                hist[vi1]++;
            }
        }
    }

    return (n/QK5_0*sizeof(block_q5_0));
}

size_t ggml_quantize_q5_1(const float * src, void * dst, int n, int k, int64_t * hist) {
    assert(k % QK5_1 == 0);
    const int nb = k / QK5_1;

    for (int b = 0; b < n; b += k) {
        block_q5_1 * restrict y = (block_q5_1 *)dst + b/QK5_1;

        quantize_row_q5_1_reference(src + b, y, k);

        for (int i = 0; i < nb; i++) {
            uint32_t qh;
            memcpy(&qh, &y[i].qh, sizeof(qh));

            for (int j = 0; j < QK5_1; j += 2) {
                const uint8_t vh0 = ((qh & (1u << (j + 0 ))) >> (j + 0 )) << 4;
                const uint8_t vh1 = ((qh & (1u << (j + 16))) >> (j + 12));

                // cast to 16 bins
                const uint8_t vi0 = ((y[i].qs[j/2] & 0x0F) | vh0) / 2;
                const uint8_t vi1 = ((y[i].qs[j/2] >>   4) | vh1) / 2;

                hist[vi0]++;
                hist[vi1]++;
            }
        }
    }

    return (n/QK5_1*sizeof(block_q5_1));
}

size_t ggml_quantize_q8_0(const float * src, void * dst, int n, int k, int64_t * hist) {
    assert(k % QK8_0 == 0);
    const int nb = k / QK8_0;

    for (int b = 0; b < n; b += k) {
        block_q8_0 * restrict y = (block_q8_0 *)dst + b/QK8_0;

        quantize_row_q8_0_reference(src + b, y, k);

        for (int i = 0; i < nb; i++) {
            for (int j = 0; j < QK8_0; ++j) {
                const int8_t vi = y[i].qs[j];

                hist[vi/16 + 8]++;
            }
        }
    }

    return (n/QK8_0*sizeof(block_q8_0));
}

size_t ggml_quantize_chunk(enum ggml_type type, const float * src, void * dst, int start, int n, int64_t * hist) {
    size_t result = 0;
    switch (type) {
        case GGML_TYPE_Q4_0:
            {
                GGML_ASSERT(start % QK4_0 == 0);
                block_q4_0 * block = (block_q4_0*)dst + start / QK4_0;
                result = ggml_quantize_q4_0(src + start, block, n, n, hist);
            } break;
        case GGML_TYPE_Q4_1:
            {
                GGML_ASSERT(start % QK4_1 == 0);
                block_q4_1 * block = (block_q4_1*)dst + start / QK4_1;
                result = ggml_quantize_q4_1(src + start, block, n, n, hist);
            } break;
        case GGML_TYPE_Q5_0:
            {
                GGML_ASSERT(start % QK5_0 == 0);
                block_q5_0 * block = (block_q5_0*)dst + start / QK5_0;
                result = ggml_quantize_q5_0(src + start, block, n, n, hist);
            } break;
        case GGML_TYPE_Q5_1:
            {
                GGML_ASSERT(start % QK5_1 == 0);
                block_q5_1 * block = (block_q5_1*)dst + start / QK5_1;
                result = ggml_quantize_q5_1(src + start, block, n, n, hist);
            } break;
        case GGML_TYPE_Q8_0:
            {
                GGML_ASSERT(start % QK8_0 == 0);
                block_q8_0 * block = (block_q8_0*)dst + start / QK8_0;
                result = ggml_quantize_q8_0(src + start, block, n, n, hist);
            } break;
#ifdef GGML_USE_K_QUANTS
        case GGML_TYPE_Q2_K:
            {
                GGML_ASSERT(start % QK_K == 0);
                block_q2_K * block = (block_q2_K*)dst + start / QK_K;
                result = ggml_quantize_q2_K(src + start, block, n, n, hist);
            } break;
        case GGML_TYPE_Q3_K:
            {
                GGML_ASSERT(start % QK_K == 0);
                block_q3_K * block = (block_q3_K*)dst + start / QK_K;
                result = ggml_quantize_q3_K(src + start, block, n, n, hist);
            } break;
        case GGML_TYPE_Q4_K:
            {
                GGML_ASSERT(start % QK_K == 0);
                block_q4_K * block = (block_q4_K*)dst + start / QK_K;
                result = ggml_quantize_q4_K(src + start, block, n, n, hist);
            } break;
        case GGML_TYPE_Q5_K:
            {
                GGML_ASSERT(start % QK_K == 0);
                block_q5_K * block = (block_q5_K*)dst + start / QK_K;
                result = ggml_quantize_q5_K(src + start, block, n, n, hist);
            } break;
        case GGML_TYPE_Q6_K:
            {
                GGML_ASSERT(start % QK_K == 0);
                block_q6_K * block = (block_q6_K*)dst + start / QK_K;
                result = ggml_quantize_q6_K(src + start, block, n, n, hist);
            } break;
#endif
        case GGML_TYPE_F16:
            {
                int elemsize = sizeof(ggml_fp16_t);
                ggml_fp32_to_fp16_row(src + start, (ggml_fp16_t *)dst + start, n);
                result = n * elemsize;
            } break;
        case GGML_TYPE_F32:
            {
                int elemsize = sizeof(float);
                result = n * elemsize;
                memcpy((uint8_t *)dst + start * elemsize, src + start, result);
            } break;
        default:
            assert(false);
    }
    return result;
}

////////////////////////////////////////////////////////////////////////////////

int ggml_cpu_has_avx(void) {
#if defined(__AVX__)
    return 1;
#else
    return 0;
#endif
}

int ggml_cpu_has_avx2(void) {
#if defined(__AVX2__)
    return 1;
#else
    return 0;
#endif
}

int ggml_cpu_has_avx512(void) {
#if defined(__AVX512F__)
    return 1;
#else
    return 0;
#endif
}

int ggml_cpu_has_avx512_vbmi(void) {
#if defined(__AVX512VBMI__)
    return 1;
#else
    return 0;
#endif
}

int ggml_cpu_has_avx512_vnni(void) {
#if defined(__AVX512VNNI__)
    return 1;
#else
    return 0;
#endif
}

int ggml_cpu_has_fma(void) {
#if defined(__FMA__)
    return 1;
#else
    return 0;
#endif
}

int ggml_cpu_has_neon(void) {
#if defined(__ARM_NEON)
    return 1;
#else
    return 0;
#endif
}

int ggml_cpu_has_arm_fma(void) {
#if defined(__ARM_FEATURE_FMA)
    return 1;
#else
    return 0;
#endif
}

int ggml_cpu_has_f16c(void) {
#if defined(__F16C__)
    return 1;
#else
    return 0;
#endif
}

int ggml_cpu_has_fp16_va(void) {
#if defined(__ARM_FEATURE_FP16_VECTOR_ARITHMETIC)
    return 1;
#else
    return 0;
#endif
}

int ggml_cpu_has_wasm_simd(void) {
#if defined(__wasm_simd128__)
    return 1;
#else
    return 0;
#endif
}

int ggml_cpu_has_blas(void) {
#if defined(GGML_USE_ACCELERATE) || defined(GGML_USE_OPENBLAS) || defined(GGML_USE_CUBLAS) || defined(GGML_USE_CLBLAST)
    return 1;
#else
    return 0;
#endif
}

int ggml_cpu_has_cublas(void) {
#if defined(GGML_USE_CUBLAS)
    return 1;
#else
    return 0;
#endif
}

int ggml_cpu_has_clblast(void) {
#if defined(GGML_USE_CLBLAST)
    return 1;
#else
    return 0;
#endif
}

int ggml_cpu_has_gpublas(void) {
    return ggml_cpu_has_cublas() || ggml_cpu_has_clblast();
}

int ggml_cpu_has_sse3(void) {
#if defined(__SSE3__)
    return 1;
#else
    return 0;
#endif
}

int ggml_cpu_has_vsx(void) {
#if defined(__POWER9_VECTOR__)
    return 1;
#else
    return 0;
#endif
}

////////////////////////////////////////////////////////////////////////////////