ggml : a faster version for Q4_1 x Q8_0 dot products (#1083)

* A faster version for Q4_1 x Q8_0 dot products

The idea nehind being that Q8_0 quantized
values get used many times in the matrix multiplications
where they are involved. In the current implementations,
when we are evaluating the dot products, we need to compute
the sum of the quants in the Q8_0 vector, so the same
operation is repeated many times. Here we pre-compute
the sum during Q8_0 quantization, store it in the
now modified block_q8_0 struct, and then reuse this
result in the subsequent dot products.

In a synthetic benchmark (just compute a bunch of dot
products), this change speeds up the Q4_1 * Q8_0 dot
product by 80%, making the performance identical to
Q4_0 * Q8_0.

In practical application, I see a ~15% gain in speed for
token prediction on M2, and ~5% gain on Ryzen 7950X.
The speed gain in the prompt evaluation is much bigger
(around 50%).

I have only done the change for the scalar version,
ARM_NEON, and AVX2, so we still need an AVX implementation.

* Cleaning up

---------

Co-authored-by: Iwan Kawrakow <iwan.kawrakow@gmail.com>

ggml.c

@@ -657,9 +657,10 @@ static_assert(sizeof(block_q4_3) == 2 * sizeof(ggml_fp16_t) + QK4_3 / 2, "wrong
 #define QK8_0 32
 typedef struct {
     float   d;          // delta
+    float   s;          // d * sum(qs[i])
     int8_t  qs[QK8_0];  // quants
 } block_q8_0;
-static_assert(sizeof(block_q8_0) == sizeof(float) + QK8_0, "wrong q8_0 block size/padding");
+static_assert(sizeof(block_q8_0) == 2*sizeof(float) + QK8_0, "wrong q8_0 block size/padding");
 
 
 // reference implementation for deterministic creation of model files
@@ -1299,12 +1300,38 @@ static void quantize_row_q8_0_reference(const float * restrict x, block_q8_0 * r
 
         y[i].d = d;
 
+        int sum = 0;
         for (int l = 0; l < QK8_0; ++l) {
             const float v = x[i*QK8_0 + l]*id;
             y[i].qs[l] = roundf(v);
-        }
-    }
+            sum += y[i].qs[l];
+        }
+        y[i].s = d * sum;
+    }
+}
+
+#ifdef __AVX2__
+// There is no better way of doing this?
+// I guess not, AVX is not very good at horizontal sums.
+// The commented solution for a hotrizontal sum was suggested by @pubby as being slightly
+// faster than the solution below. As I don't have an AVX2 system handt right now to test,
+// keeping the original.
+// TODO: Please try and if it does make a differece, uncomment and remove the implementation below.
+//static inline float horizontal_sum(__m256i a) {
+//    __m256i b = _mm256_castps_si256(_mm256_movehdup_ps(_mm256_castsi256_ps(a)));
+//    __m256i sum = _mm256_add_epi32(a, b);
+//    __m256i hi = _mm256_unpackhi_epi64(sum, sum);
+//    sum = _mm256_add_epi32(sum, hi);
+//    return _mm256_cvtsi256_si32(sum) + _mm256_extract_epi32(sum, 4);
+//}
+static inline float horizontal_sum(__m256i a) {
+    __m128i sum128 = _mm_add_epi32(_mm256_castsi256_si128(a), _mm256_extracti128_si256(a, 1));
+    __m128i hi64 = _mm_unpackhi_epi64(sum128, sum128);
+    __m128i sum64 = _mm_add_epi32(hi64, sum128);
+    __m128i hi32  = _mm_shuffle_epi32(sum64, _MM_SHUFFLE(2, 3, 0, 1));
+    return _mm_cvtsi128_si32(_mm_add_epi32(sum64, hi32));
 }
+#endif
 
 static void quantize_row_q8_0(const float * restrict x, void * restrict vy, int k) {
     assert(k % QK8_0 == 0);
@@ -1332,6 +1359,8 @@ static void quantize_row_q8_0(const float * restrict x, void * restrict vy, int
 
         y[i].d = d;
 
+        int32x4_t accv = vdupq_n_s32(0);
+
         for (int l = 0; l < 8; l++) {
             const float32x4_t v  = vmulq_n_f32(srcv[l], id);
             const int32x4_t   vi = vcvtnq_s32_f32(v);
@@ -1340,7 +1369,11 @@ static void quantize_row_q8_0(const float * restrict x, void * restrict vy, int
             y[i].qs[4*l + 1] = vgetq_lane_s32(vi, 1);
             y[i].qs[4*l + 2] = vgetq_lane_s32(vi, 2);
             y[i].qs[4*l + 3] = vgetq_lane_s32(vi, 3);
+
+            accv = vaddq_s32(accv, vi);
         }
+        int32_t sum = vaddvq_s32(accv);
+        y[i].s = d * sum;
     }
 #elif defined(__AVX2__) || defined(__AVX__)
     for (int i = 0; i < nb; i++) {
@@ -1388,6 +1421,10 @@ static void quantize_row_q8_0(const float * restrict x, void * restrict vy, int
         __m256i i3 = _mm256_cvtps_epi32( v3 );
 
 #if defined(__AVX2__)
+
+        // Compute the sum of the quants and set y[i].s
+        y[i].s = d * horizontal_sum(_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
@@ -1430,6 +1467,14 @@ static void quantize_row_q8_0(const float * restrict x, void * restrict vy, int
     // scalar
     quantize_row_q8_0_reference(x, y, k);
 #endif
+#if defined __AVX__
+    // TODO: vectorize this
+    for (int i=0; i<nb; ++i) {
+        int sum = 0;
+        for (int l=0; l<QK8_0; ++l) sum += y[i].qs[l];
+        y[i].s = y[i].d * sum;
+    }
+#endif
 }
 
 static void dequantize_row_q4_0(const void * restrict vx, float * restrict y, int k) {
@@ -2372,14 +2417,17 @@ static void ggml_vec_dot_q4_0_q8_0(const int n, float * restrict s, const void *
     float32x4_t sumv0 = vdupq_n_f32(0.0f);
     float32x4_t sumv1 = vdupq_n_f32(0.0f);
 
+    float sum8 = 0;
+
     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];
 
+        sum8 += x0->d * y0->s + x1->d * y1->s;
+
         const uint8x16_t m4b   = vdupq_n_u8(0xf);
-        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);
@@ -2390,12 +2438,6 @@ static void ggml_vec_dot_q4_0_q8_0(const int n, float * restrict s, const void *
         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);
@@ -2410,21 +2452,21 @@ static void ggml_vec_dot_q4_0_q8_0(const int n, float * restrict s, const void *
 
 #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_0ls), v0_0hs, v1_0hs);
-        const int32x4_t p_1 = vdotq_s32(vdotq_s32(vdupq_n_s32(0), v0_1ls, v1_1ls), v0_1hs, v1_1hs);
+        const int32x4_t p_0 = vdotq_s32(vdotq_s32(vdupq_n_s32(0), v0_0l, v1_0ls), v0_0h, v1_0hs);
+        const int32x4_t p_1 = vdotq_s32(vdotq_s32(vdupq_n_s32(0), v0_1l, v1_1ls), v0_1h, v1_1hs);
 
         sumv0 = vmlaq_n_f32(sumv0, vcvtq_f32_s32(p_0), x0->d*y0->d);
         sumv1 = vmlaq_n_f32(sumv1, vcvtq_f32_s32(p_1), x1->d*y1->d);
 #else
-        const int16x8_t pl0l = vmull_s8(vget_low_s8 (v0_0ls), vget_low_s8 (v1_0ls));
-        const int16x8_t pl0h = vmull_s8(vget_high_s8(v0_0ls), vget_high_s8(v1_0ls));
-        const int16x8_t ph0l = vmull_s8(vget_low_s8 (v0_0hs), vget_low_s8 (v1_0hs));
-        const int16x8_t ph0h = vmull_s8(vget_high_s8(v0_0hs), vget_high_s8(v1_0hs));
+        const int16x8_t pl0l = vmull_s8(vget_low_s8 (v0_0l), vget_low_s8 (v1_0ls));
+        const int16x8_t pl0h = vmull_s8(vget_high_s8(v0_0l), vget_high_s8(v1_0ls));
+        const int16x8_t ph0l = vmull_s8(vget_low_s8 (v0_0h), vget_low_s8 (v1_0hs));
+        const int16x8_t ph0h = vmull_s8(vget_high_s8(v0_0h), vget_high_s8(v1_0hs));
 
-        const int16x8_t pl1l = vmull_s8(vget_low_s8 (v0_1ls), vget_low_s8 (v1_1ls));
-        const int16x8_t pl1h = vmull_s8(vget_high_s8(v0_1ls), vget_high_s8(v1_1ls));
-        const int16x8_t ph1l = vmull_s8(vget_low_s8 (v0_1hs), vget_low_s8 (v1_1hs));
-        const int16x8_t ph1h = vmull_s8(vget_high_s8(v0_1hs), vget_high_s8(v1_1hs));
+        const int16x8_t pl1l = vmull_s8(vget_low_s8 (v0_1l), vget_low_s8 (v1_1ls));
+        const int16x8_t pl1h = vmull_s8(vget_high_s8(v0_1l), vget_high_s8(v1_1ls));
+        const int16x8_t ph1l = vmull_s8(vget_low_s8 (v0_1h), vget_low_s8 (v1_1hs));
+        const int16x8_t ph1h = vmull_s8(vget_high_s8(v0_1h), vget_high_s8(v1_1hs));
 
         const int32x4_t pl0 = vaddq_s32(vpaddlq_s16(pl0l), vpaddlq_s16(pl0h));
         const int32x4_t ph0 = vaddq_s32(vpaddlq_s16(ph0l), vpaddlq_s16(ph0h));
@@ -2436,7 +2478,7 @@ static void ggml_vec_dot_q4_0_q8_0(const int n, float * restrict s, const void *
 #endif
     }
 
-    sumf = vaddvq_f32(sumv0) + vaddvq_f32(sumv1);
+    sumf = vaddvq_f32(sumv0) + vaddvq_f32(sumv1) - 8 * sum8;
 #elif defined(__AVX2__)
     // Initialize accumulator with zeros
     __m256 acc = _mm256_setzero_ps();
@@ -2569,12 +2611,16 @@ static void ggml_vec_dot_q4_1_q8_0(const int n, float * restrict s, const void *
     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_0 * restrict y0 = &y[i + 0];
         const block_q8_0 * restrict y1 = &y[i + 1];
 
+        summs += x0->m * y0->s + x1->m * y1->s;
+
         const uint8x16_t m4b = vdupq_n_u8(0xf);
 
         const uint8x16_t v0_0 = vld1q_u8(x0->qs);
@@ -2598,17 +2644,6 @@ static void ggml_vec_dot_q4_1_q8_0(const int n, float * restrict s, const void *
         const int8x16_t v1_1ls = vuzp1q_s8(v1_1l, v1_1h);
         const int8x16_t v1_1hs = vuzp2q_s8(v1_1l, v1_1h);
 
-        const int16x8_t s0i = vaddq_s16(
-                        vaddq_s16(vmovl_s8(vget_low_s8(v1_0ls)), vmovl_s8(vget_high_s8(v1_0ls))),
-                        vaddq_s16(vmovl_s8(vget_low_s8(v1_0hs)), vmovl_s8(vget_high_s8(v1_0hs))));
-
-        const int16x8_t s1i = vaddq_s16(
-                        vaddq_s16(vmovl_s8(vget_low_s8(v1_1ls)), vmovl_s8(vget_high_s8(v1_1ls))),
-                        vaddq_s16(vmovl_s8(vget_low_s8(v1_1hs)), vmovl_s8(vget_high_s8(v1_1hs))));
-
-        sumv0 = vmlaq_n_f32(sumv0, vcvtq_f32_s32(vaddl_s16(vget_low_s16(s0i), vget_high_s16(s0i))), x0->m*y0->d);
-        sumv1 = vmlaq_n_f32(sumv1, vcvtq_f32_s32(vaddl_s16(vget_low_s16(s1i), vget_high_s16(s1i))), x1->m*y1->d);
-
 #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_0ls), v0_0h, v1_0hs);
@@ -2637,24 +2672,26 @@ static void ggml_vec_dot_q4_1_q8_0(const int n, float * restrict s, const void *
 #endif
     }
 
-    sumf = vaddvq_f32(sumv0) + vaddvq_f32(sumv1);
+    sumf = vaddvq_f32(sumv0) + vaddvq_f32(sumv1) + summs;
 #elif defined(__AVX2__)
     // Initialize accumulator with zeros
     __m256 acc = _mm256_setzero_ps();
 
+    float summs = 0;
+
     // Main loop
     for (int i = 0; i < nb; ++i) {
         const float * d0 = &x[i].d;
         const float * d1 = &y[i].d;
-        const float * m0 = &x[i].m;
+        //const float * m0 = &x[i].m;
+
+        summs += x[i].m * y[i].s;
 
         const __m256 d0v = _mm256_broadcast_ss( d0 );
         const __m256 d1v = _mm256_broadcast_ss( d1 );
-        const __m256 m0v = _mm256_broadcast_ss( m0 );
 
         // Compute combined scales
         const __m256 d0d1 = _mm256_mul_ps( d0v, d1v );
-        const __m256 d1m0 = _mm256_mul_ps( d1v, m0v );
 
         // Load 16 bytes, and unpack 4 bit fields into bytes, making 32 bytes
         const __m256i bx = bytes_from_nibbles_32(x[i].qs);
@@ -2676,15 +2713,6 @@ static void ggml_vec_dot_q4_1_q8_0(const int n, float * restrict s, const void *
 
         // Accumulate d0*d1*x*y
         acc = _mm256_fmadd_ps( d0d1, xy, acc );
-
-        // Compute sum of y values
-        const __m256i y16_l = _mm256_cvtepi8_epi16( _mm256_castsi256_si128( by ) );
-        const __m256i y16_h = _mm256_cvtepi8_epi16( _mm256_extracti128_si256( by, 1 ) );
-        const __m256i ysumi = _mm256_madd_epi16( _mm256_add_epi16(y16_l, y16_h), ones );
-        const __m256 ysum = _mm256_cvtepi32_ps( ysumi );
-
-        // Accumulate d1*m0*y
-        acc = _mm256_fmadd_ps( d1m0, ysum, acc );
     }
 
     // Return horizontal sum of the acc vector
@@ -2693,7 +2721,7 @@ static void ggml_vec_dot_q4_1_q8_0(const int n, float * restrict s, const void *
     res = _mm_add_ps( res, _mm_movehl_ps( res, res ) );
     res = _mm_add_ss( res, _mm_movehdup_ps( res ) );
 
-    sumf = _mm_cvtss_f32( res );
+    sumf = _mm_cvtss_f32( res ) + summs;
 #else
     // scalar
     for (int i = 0; i < nb; i++) {

pocs/vdot/CMakeLists.txt

@@ -2,3 +2,8 @@ set(TARGET vdot)
 add_executable(${TARGET} vdot.cpp)
 target_link_libraries(${TARGET} PRIVATE common llama ${CMAKE_THREAD_LIBS_INIT})
 target_compile_features(${TARGET} PRIVATE cxx_std_11)
+
+set(TARGET q8dot)
+add_executable(${TARGET} q8dot.cpp)
+target_link_libraries(${TARGET} PRIVATE common llama ${CMAKE_THREAD_LIBS_INIT})
+target_compile_features(${TARGET} PRIVATE cxx_std_11)

pocs/vdot/q8dot.cpp

@@ -0,0 +1,172 @@
+#include <cstdio>
+#include <type_traits>
+#include <vector>
+#include <random>
+#include <chrono>
+#include <cstdlib>
+#include <cmath>
+#include <cassert>
+#include <cstring>
+#include <array>
+#include <type_traits>
+
+#include <ggml.h>
+
+constexpr int kVecSize = 1 << 16;
+
+// Copy-pasted from ggml.c
+#define QK4_0 32
+typedef struct {
+    float   d;          // delta
+    uint8_t qs[QK4_0 / 2];  // nibbles / quants
+} block_q4_0;
+static_assert(sizeof(block_q4_0) == sizeof(float) + QK4_0 / 2, "wrong q4_0 block size/padding");
+
+#define QK4_1 32
+typedef struct {
+    float   d;          // delta
+    float   m;          // min
+    uint8_t qs[QK4_1 / 2];  // nibbles / quants
+} block_q4_1;
+static_assert(sizeof(block_q4_1) == sizeof(float) * 2 + QK4_1 / 2, "wrong q4_1 block size/padding");
+
+// Copy-pasted from ggml.c
+#define QK8_0 32
+typedef struct {
+    float   d;          // delta
+    float   s;          // d * sum(qs[i])
+    int8_t  qs[QK8_0];  // quants
+} block_q8_0;
+static_assert(sizeof(block_q8_0) == 2*sizeof(float) + QK8_0, "wrong q8_0 block size/padding");
+
+static_assert(QK4_1 == QK8_0, "QK4_1 and QK8_0 must be the same");
+static_assert(QK4_0 == QK8_0, "QK4_0 and QK8_0 must be the same");
+
+template <typename T>
+void fillQ4blocks(std::vector<T>& blocks, std::mt19937& rndm) {
+    for (auto& b : blocks) {
+        b.d = 1;
+        for (int i=0; i<QK4_1/2; ++i) {
+            uint8_t v1 = rndm() >> 28;
+            uint8_t v2 = rndm() >> 28;
+            b.qs[i] = v1 | (v2 << 4);
+        }
+    }
+}
+
+void fillQ80blocks(std::vector<block_q8_0>& blocks, std::mt19937& rndm) {
+    for (auto& b : blocks) {
+        b.d = 1;
+        int sum = 0;
+        for (int i=0; i<QK8_0; ++i) {
+            b.qs[i] = (rndm() >> 24) - 128;
+            sum += b.qs[i];
+        }
+        b.s = b.d * sum;
+    }
+}
+
+float simpleDot(const block_q4_0& x, const block_q8_0& y) {
+    int s1 = 0; //, s2 = 0;
+    for (int i=0; i<QK4_1/2; i+=2) {
+        int v1 = x.qs[i+0] & 0xf;
+        int v2 = x.qs[i+0] >> 4;
+        int v3 = x.qs[i+1] & 0xf;
+        int v4 = x.qs[i+1] >> 4;
+        int j = 2*i;
+        s1 += v1*y.qs[j] + v2*y.qs[j+1] + v3*y.qs[j+2] + v4*y.qs[j+3];
+        //s2 += y.qs[j] + y.qs[j+1] + y.qs[j+2] + y.qs[j+3];
+    }
+    return y.d * x.d * s1 - 8 * x.d * y.s;
+    //return y.d * x.d * (s1 - 8 * s2);
+}
+
+float simpleDot(const block_q4_1& x, const block_q8_0& y) {
+    int s1 = 0; //, s2 = 0;
+    for (int i=0; i<QK4_1/2; i+=2) {
+        int v1 = x.qs[i+0] & 0xf;
+        int v2 = x.qs[i+0] >> 4;
+        int v3 = x.qs[i+1] & 0xf;
+        int v4 = x.qs[i+1] >> 4;
+        int j = 2*i;
+        s1 += v1*y.qs[j] + v2*y.qs[j+1] + v3*y.qs[j+2] + v4*y.qs[j+3];
+        //s2 += y.qs[j] + y.qs[j+1] + y.qs[j+2] + y.qs[j+3];
+    }
+    return y.d * x.d * s1 + y.s * x.m;
+    //return y.d * (x.d * s1 + x.m * s2);
+}
+
+struct Stat {
+    double sum = 0, sumt = 0, sumt2 = 0, maxt = 0;
+    int nloop = 0;
+    void addResult(double s, double t) {
+        sum += s;
+        sumt += t; sumt2 += t*t; maxt = std::max(maxt, t);
+        ++nloop;
+    }
+    void reportResult(const char* title) const {
+        if (nloop < 1) {
+            printf("%s(%s): no result\n",__func__,title);
+            return;
+        }
+        printf("============ %s\n",title);
+        printf("<dot> = %g\n",sum/nloop);
+        auto t = sumt/nloop, dt = sumt2/nloop - t*t;
+        if (dt > 0) dt = sqrt(dt);
+        printf("<time> = %g +/- %g us. Max. time = %g us.\n",t,dt,maxt);
+    }
+};
+
+
+int main(int argc, char** argv) {
+
+    int nloop = argc > 1 ? atoi(argv[1]) : 10;
+    int type  = argc > 2 ? atoi(argv[2]) : 1;
+
+    std::mt19937 rndm(1234);
+
+    std::vector<block_q4_1> x41;
+    std::vector<block_q4_0> x40;
+    std::vector<block_q8_0> y(kVecSize);
+    if (type == 0) x40.resize(kVecSize);
+    else {
+        x41.resize(kVecSize);
+        for (auto& b : x41) b.m = 1;
+    }
+
+    auto ggml_type = type == 0 ? GGML_TYPE_Q4_0 : GGML_TYPE_Q4_1;
+
+    auto funcs = ggml_internal_get_quantize_fn(ggml_type);
+
+    Stat simple, ggml;
+
+    for (int iloop=0; iloop<nloop; ++iloop) {
+
+        if (type == 0) fillQ4blocks(x40, rndm);
+        else fillQ4blocks(x41, rndm);
+        fillQ80blocks(y, rndm);
+
+        auto t1 = std::chrono::high_resolution_clock::now();
+        double s = 0;
+        if (type == 0) for (int i=0; i<kVecSize; ++i) s += simpleDot(x40[i], y[i]);
+        else for (int i=0; i<kVecSize; ++i) s += simpleDot(x41[i], y[i]);
+        auto t2 = std::chrono::high_resolution_clock::now();
+        auto t = 1e-3*std::chrono::duration_cast<std::chrono::nanoseconds>(t2-t1).count();
+        if (iloop > 3) simple.addResult(s, t);
+
+        t1 = std::chrono::high_resolution_clock::now();
+        float fs;
+        if (type == 0) funcs.vec_dot_q(kVecSize * QK4_1, &fs, x40.data(), y.data());
+        else funcs.vec_dot_q(kVecSize * QK4_1, &fs, x41.data(), y.data());
+        t2 = std::chrono::high_resolution_clock::now();
+        t = 1e-3*std::chrono::duration_cast<std::chrono::nanoseconds>(t2-t1).count();
+        if (iloop > 3) ggml.addResult(fs, t);
+
+    }
+
+    // Report the time (and the average of the dot products so the compiler does not come up with the idea
+    // of optimizing away the function calls after figuring that the result is not used).
+    simple.reportResult("Simple");
+    ggml.reportResult("ggml");
+    return 0;
+}