Adding a simple program to measure speed of dot products (#1041)

On my Mac, the direct Q4_1 product is marginally slower
(~69 vs ~55 us for Q4_0). The SIMD-ified ggml version
is now almost 2X slower (~121 us).

On a Ryzen 7950X CPU, the direct product for Q4_1 quantization
is faster than the AVX2 implementation (~60 vs ~62 us).

---------

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

2 files changed, 309 insertions, 0 deletions

diff --git a/pocs/vdot/CMakeLists.txt b/pocs/vdot/CMakeLists.txt
new file mode 100644
index 0000000..cbc8522
--- /dev/null
+++ b/pocs/vdot/CMakeLists.txt
@@ -0,0 +1,4 @@
+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)
diff --git a/pocs/vdot/vdot.cpp b/pocs/vdot/vdot.cpp
new file mode 100644
index 0000000..26bf50c
--- /dev/null
+++ b/pocs/vdot/vdot.cpp
@@ -0,0 +1,305 @@
+#include <cstdio>
+#include <vector>
+#include <random>
+#include <chrono>
+#include <cstdlib>
+#include <cmath>
+#include <cassert>
+#include <cstring>
+#include <array>
+
+#include <ggml.h>
+
+constexpr int kVecSize = 1 << 18;
+
+float drawFromGaussianPdf(std::mt19937& rndm) {
+    constexpr double kScale = 1./(1. + std::mt19937::max());
+    constexpr double kTwoPiTimesScale = 6.28318530717958647692*kScale;
+    static float lastX;
+    static bool haveX = false;
+    if (haveX) { haveX = false; return lastX; }
+    auto r = sqrt(-2*log(1 - kScale*rndm()));
+    auto phi = kTwoPiTimesScale * rndm();
+    lastX = r*sin(phi);
+    haveX = true;
+    return r*cos(phi);
+}
+void fillRandomGaussianFloats(std::vector<float>& values, std::mt19937& rndm, float mean = 0) {
+    for (auto& v : values) v = mean + drawFromGaussianPdf(rndm);
+}
+
+// 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
+    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");
+
+// "Scalar" dot product between the quantized vector x and float vector y
+inline double dot(int n, const block_q4_0* x, const float* y) {
+    const static float kValues[16] = {-8.f, -7.f, -6.f, -5.f, -4.f, -3.f, -2.f, -1.f, 0.f, 1.f, 2.f, 3.f, 4.f, 5.f, 6.f, 7.f};
+    constexpr uint32_t kMask1 = 0x0f0f0f0f;
+    uint32_t u1, u2;
+    auto q1 = (const uint8_t*)&u1;
+    auto q2 = (const uint8_t*)&u2;
+    double sum = 0;
+    for (int i=0; i<n; ++i) {
+        float d = x->d;
+        auto u = (const uint32_t*)x->qs;
+        float s = 0;
+        for (int k=0; k<4; ++k) {
+            u1 = u[k] & kMask1;
+            u2 = (u[k] >> 4) & kMask1;
+            s += y[0]*kValues[q1[0]] + y[1]*kValues[q2[0]] +
+                 y[2]*kValues[q1[1]] + y[3]*kValues[q2[1]] +
+                 y[4]*kValues[q1[2]] + y[5]*kValues[q2[2]] +
+                 y[6]*kValues[q1[3]] + y[7]*kValues[q2[3]];
+            y += 8;
+        }
+        sum += s*d;
+        ++x;
+    }
+    return sum;
+}
+// Alternative version of the above. Faster on my Mac (~45 us vs ~55 us per dot product),
+// but about the same on X86_64 (Ryzen 7950X CPU).
+inline double dot3(int n, const block_q4_0* x, const float* y) {
+    const static std::pair<float,float> kValues[256] = {
+        {-8.f, -8.f}, {-7.f, -8.f}, {-6.f, -8.f}, {-5.f, -8.f}, {-4.f, -8.f}, {-3.f, -8.f}, {-2.f, -8.f}, {-1.f, -8.f},
+        { 0.f, -8.f}, { 1.f, -8.f}, { 2.f, -8.f}, { 3.f, -8.f}, { 4.f, -8.f}, { 5.f, -8.f}, { 6.f, -8.f}, { 7.f, -8.f},
+        {-8.f, -7.f}, {-7.f, -7.f}, {-6.f, -7.f}, {-5.f, -7.f}, {-4.f, -7.f}, {-3.f, -7.f}, {-2.f, -7.f}, {-1.f, -7.f},
+        { 0.f, -7.f}, { 1.f, -7.f}, { 2.f, -7.f}, { 3.f, -7.f}, { 4.f, -7.f}, { 5.f, -7.f}, { 6.f, -7.f}, { 7.f, -7.f},
+        {-8.f, -6.f}, {-7.f, -6.f}, {-6.f, -6.f}, {-5.f, -6.f}, {-4.f, -6.f}, {-3.f, -6.f}, {-2.f, -6.f}, {-1.f, -6.f},
+        { 0.f, -6.f}, { 1.f, -6.f}, { 2.f, -6.f}, { 3.f, -6.f}, { 4.f, -6.f}, { 5.f, -6.f}, { 6.f, -6.f}, { 7.f, -6.f},
+        {-8.f, -5.f}, {-7.f, -5.f}, {-6.f, -5.f}, {-5.f, -5.f}, {-4.f, -5.f}, {-3.f, -5.f}, {-2.f, -5.f}, {-1.f, -5.f},
+        { 0.f, -5.f}, { 1.f, -5.f}, { 2.f, -5.f}, { 3.f, -5.f}, { 4.f, -5.f}, { 5.f, -5.f}, { 6.f, -5.f}, { 7.f, -5.f},
+        {-8.f, -4.f}, {-7.f, -4.f}, {-6.f, -4.f}, {-5.f, -4.f}, {-4.f, -4.f}, {-3.f, -4.f}, {-2.f, -4.f}, {-1.f, -4.f},
+        { 0.f, -4.f}, { 1.f, -4.f}, { 2.f, -4.f}, { 3.f, -4.f}, { 4.f, -4.f}, { 5.f, -4.f}, { 6.f, -4.f}, { 7.f, -4.f},
+        {-8.f, -3.f}, {-7.f, -3.f}, {-6.f, -3.f}, {-5.f, -3.f}, {-4.f, -3.f}, {-3.f, -3.f}, {-2.f, -3.f}, {-1.f, -3.f},
+        { 0.f, -3.f}, { 1.f, -3.f}, { 2.f, -3.f}, { 3.f, -3.f}, { 4.f, -3.f}, { 5.f, -3.f}, { 6.f, -3.f}, { 7.f, -3.f},
+        {-8.f, -2.f}, {-7.f, -2.f}, {-6.f, -2.f}, {-5.f, -2.f}, {-4.f, -2.f}, {-3.f, -2.f}, {-2.f, -2.f}, {-1.f, -2.f},
+        { 0.f, -2.f}, { 1.f, -2.f}, { 2.f, -2.f}, { 3.f, -2.f}, { 4.f, -2.f}, { 5.f, -2.f}, { 6.f, -2.f}, { 7.f, -2.f},
+        {-8.f, -1.f}, {-7.f, -1.f}, {-6.f, -1.f}, {-5.f, -1.f}, {-4.f, -1.f}, {-3.f, -1.f}, {-2.f, -1.f}, {-1.f, -1.f},
+        { 0.f, -1.f}, { 1.f, -1.f}, { 2.f, -1.f}, { 3.f, -1.f}, { 4.f, -1.f}, { 5.f, -1.f}, { 6.f, -1.f}, { 7.f, -1.f},
+        {-8.f,  0.f}, {-7.f,  0.f}, {-6.f,  0.f}, {-5.f,  0.f}, {-4.f,  0.f}, {-3.f,  0.f}, {-2.f,  0.f}, {-1.f,  0.f},
+        { 0.f,  0.f}, { 1.f,  0.f}, { 2.f,  0.f}, { 3.f,  0.f}, { 4.f,  0.f}, { 5.f,  0.f}, { 6.f,  0.f}, { 7.f,  0.f},
+        {-8.f,  1.f}, {-7.f,  1.f}, {-6.f,  1.f}, {-5.f,  1.f}, {-4.f,  1.f}, {-3.f,  1.f}, {-2.f,  1.f}, {-1.f,  1.f},
+        { 0.f,  1.f}, { 1.f,  1.f}, { 2.f,  1.f}, { 3.f,  1.f}, { 4.f,  1.f}, { 5.f,  1.f}, { 6.f,  1.f}, { 7.f,  1.f},
+        {-8.f,  2.f}, {-7.f,  2.f}, {-6.f,  2.f}, {-5.f,  2.f}, {-4.f,  2.f}, {-3.f,  2.f}, {-2.f,  2.f}, {-1.f,  2.f},
+        { 0.f,  2.f}, { 1.f,  2.f}, { 2.f,  2.f}, { 3.f,  2.f}, { 4.f,  2.f}, { 5.f,  2.f}, { 6.f,  2.f}, { 7.f,  2.f},
+        {-8.f,  3.f}, {-7.f,  3.f}, {-6.f,  3.f}, {-5.f,  3.f}, {-4.f,  3.f}, {-3.f,  3.f}, {-2.f,  3.f}, {-1.f,  3.f},
+        { 0.f,  3.f}, { 1.f,  3.f}, { 2.f,  3.f}, { 3.f,  3.f}, { 4.f,  3.f}, { 5.f,  3.f}, { 6.f,  3.f}, { 7.f,  3.f},
+        {-8.f,  4.f}, {-7.f,  4.f}, {-6.f,  4.f}, {-5.f,  4.f}, {-4.f,  4.f}, {-3.f,  4.f}, {-2.f,  4.f}, {-1.f,  4.f},
+        { 0.f,  4.f}, { 1.f,  4.f}, { 2.f,  4.f}, { 3.f,  4.f}, { 4.f,  4.f}, { 5.f,  4.f}, { 6.f,  4.f}, { 7.f,  4.f},
+        {-8.f,  5.f}, {-7.f,  5.f}, {-6.f,  5.f}, {-5.f,  5.f}, {-4.f,  5.f}, {-3.f,  5.f}, {-2.f,  5.f}, {-1.f,  5.f},
+        { 0.f,  5.f}, { 1.f,  5.f}, { 2.f,  5.f}, { 3.f,  5.f}, { 4.f,  5.f}, { 5.f,  5.f}, { 6.f,  5.f}, { 7.f,  5.f},
+        {-8.f,  6.f}, {-7.f,  6.f}, {-6.f,  6.f}, {-5.f,  6.f}, {-4.f,  6.f}, {-3.f,  6.f}, {-2.f,  6.f}, {-1.f,  6.f},
+        { 0.f,  6.f}, { 1.f,  6.f}, { 2.f,  6.f}, { 3.f,  6.f}, { 4.f,  6.f}, { 5.f,  6.f}, { 6.f,  6.f}, { 7.f,  6.f},
+        {-8.f,  7.f}, {-7.f,  7.f}, {-6.f,  7.f}, {-5.f,  7.f}, {-4.f,  7.f}, {-3.f,  7.f}, {-2.f,  7.f}, {-1.f,  7.f},
+        { 0.f,  7.f}, { 1.f,  7.f}, { 2.f,  7.f}, { 3.f,  7.f}, { 4.f,  7.f}, { 5.f,  7.f}, { 6.f,  7.f}, { 7.f,  7.f}
+    };
+    double sum = 0;
+    for (int i=0; i<n; ++i) {
+        float d = x->d;
+        auto q = x->qs;
+        float s = 0;
+        for (int k=0; k<4; ++k) {
+            s += y[0]*kValues[q[0]].first + y[1]*kValues[q[0]].second +
+                 y[2]*kValues[q[1]].first + y[3]*kValues[q[1]].second +
+                 y[4]*kValues[q[2]].first + y[5]*kValues[q[2]].second +
+                 y[6]*kValues[q[3]].first + y[7]*kValues[q[3]].second;
+            y += 8; q += 4;
+        }
+        sum += s*d;
+        ++x;
+    }
+    return sum;
+}
+
+inline double dot41(int n, const block_q4_1* x, const float* y) {
+    const static float kValues[16] = {0.f, 1.f, 2.f, 3.f, 4.f, 5.f, 6.f, 7.f, 8.f, 9.f, 10.f, 11.f, 12.f, 13.f, 14.f, 15.f};
+    constexpr uint32_t kMask1 = 0x0f0f0f0f;
+    uint32_t u1, u2;
+    auto q1 = (const uint8_t*)&u1;
+    auto q2 = (const uint8_t*)&u2;
+    double sum = 0;
+    for (int i=0; i<n; ++i) {
+        auto u = (const uint32_t*)x->qs;
+        float s = 0, s1 = 0;
+        for (int k=0; k<4; ++k) {
+            u1 = u[k] & kMask1;
+            u2 = (u[k] >> 4) & kMask1;
+            s += y[0]*kValues[q1[0]] + y[1]*kValues[q2[0]] +
+                 y[2]*kValues[q1[1]] + y[3]*kValues[q2[1]] +
+                 y[4]*kValues[q1[2]] + y[5]*kValues[q2[2]] +
+                 y[6]*kValues[q1[3]] + y[7]*kValues[q2[3]];
+            s1 += y[0] + y[1] + y[2] + y[3] + y[4] + y[5] + y[6] + y[7];
+            y += 8;
+        }
+        sum += s*x->d + s1*x->m;
+        ++x;
+    }
+    return sum;
+}
+
+// Copy-pasted from ggml.c
+static void quantize_row_q8_0_reference(const float *x, block_q8_0 *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 l = 0; l < QK8_0; l++) {
+            const float v = x[i*QK8_0 + l];
+            amax = std::max(amax, fabsf(v));
+        }
+
+        const float d = amax / ((1 << 7) - 1);
+        const float id = d ? 1.0f/d : 0.0f;
+
+        y[i].d = d;
+
+        for (int l = 0; l < QK8_0; ++l) {
+            const float   v  = x[i*QK8_0 + l]*id;
+            y[i].qs[l] = roundf(v);
+        }
+    }
+}
+
+// Copy-pasted from ggml.c
+static void dot_q4_q8(const int n, float* s, const void* vx, const void* vy) {
+    const int nb = n / QK8_0;
+    const block_q4_0* x = (const block_q4_0*)vx;
+    const block_q8_0* y = (const block_q8_0*)vy;
+    float sumf = 0;
+    for (int i = 0; i < nb; i++) {
+        const float d0 = x[i].d;
+        const float d1 = y[i].d;
+
+        const uint8_t * p0 = x[i].qs;
+        const  int8_t * p1 = y[i].qs;
+
+        int sumi = 0;
+        for (int j = 0; j < QK8_0/2; j++) {
+            const uint8_t v0 = p0[j];
+
+            const int i0 = (int8_t) (v0 & 0xf) - 8;
+            const int i1 = (int8_t) (v0 >> 4)  - 8;
+
+            const int i2 = p1[2*j + 0];
+            const int i3 = p1[2*j + 1];
+
+            sumi += i0*i2 + i1*i3;
+        }
+        sumf += d0*d1*sumi;
+    }
+    *s = sumf;
+}
+
+int main(int argc, char** argv) {
+
+    int nloop = argc > 1 ? atoi(argv[1]) : 10;
+    bool scalar = argc > 2 ? atoi(argv[2]) : false;
+    bool useQ4_1 = argc > 3 ? atoi(argv[3]) : false;
+
+    if (scalar && useQ4_1) {
+        printf("It is not possible to use Q4_1 quantization and scalar implementations\n");
+        return 1;
+    }
+
+    std::mt19937 rndm(1234);
+
+    std::vector<float> x1(kVecSize), y1(kVecSize);
+    int n4 = useQ4_1 ? kVecSize / QK4_1 : kVecSize / QK4_0; n4 = 64*((n4 + 63)/64);
+    int n8 = kVecSize / QK8_0; n8 = 64*((n8 + 63)/64);
+
+    auto funcs = useQ4_1 ? ggml_internal_get_quantize_fn(GGML_TYPE_Q4_1) : ggml_internal_get_quantize_fn(GGML_TYPE_Q4_0);
+
+    std::vector<block_q4_0> q40;
+    std::vector<block_q4_1> q41;
+    if (useQ4_1) q41.resize(n4);
+    else q40.resize(n4);
+    std::vector<block_q8_0> q8(n8);
+    std::vector<int64_t> H(16, 0);
+    double sumt = 0, sumt2 = 0, maxt = 0;
+    double sumqt = 0, sumqt2 = 0, maxqt = 0;
+    double sum = 0, sumq = 0, exactSum = 0;
+    for (int iloop=0; iloop<nloop; ++iloop) {
+
+        // Fill vector x with random numbers
+        fillRandomGaussianFloats(x1, rndm);
+
+        // Fill vector y with random numbers
+        fillRandomGaussianFloats(y1, rndm);
+
+        // Compute the exact dot product
+        for (int k=0; k<kVecSize; ++k) exactSum += x1[k]*y1[k];
+
+        // quantize x.
+        // Note, we do not include this in the timing as in practical application
+        // we already have the quantized model weights.
+        if (useQ4_1) {
+            funcs.quantize_row_q(x1.data(), q41.data(), kVecSize);
+        } else {
+            funcs.quantize_row_q(x1.data(), q40.data(), kVecSize);
+        }
+
+        // Now measure time the dot product needs using the "scalar" version above
+        auto t1 = std::chrono::high_resolution_clock::now();
+        if (useQ4_1) sum += dot41(kVecSize / QK4_1, q41.data(), y1.data());
+        else sum += dot(kVecSize / QK4_0, q40.data(), y1.data());
+        auto t2 = std::chrono::high_resolution_clock::now();
+        auto t = 1e-3*std::chrono::duration_cast<std::chrono::nanoseconds>(t2-t1).count();
+        sumt += t; sumt2 += t*t; maxt = std::max(maxt, t);
+
+        // And now measure the time needed to quantize y and perform the dot product with the quantized y
+        t1 = std::chrono::high_resolution_clock::now();
+        float result;
+        if (scalar) {
+            quantize_row_q8_0_reference(y1.data(), q8.data(), kVecSize);
+            dot_q4_q8(kVecSize, &result, q40.data(), q8.data());
+        }
+        else {
+            funcs.quantize_row_q_dot(y1.data(), q8.data(), kVecSize);
+            if (useQ4_1) funcs.vec_dot_q(kVecSize, &result, q41.data(), q8.data());
+            else funcs.vec_dot_q(kVecSize, &result, q40.data(), q8.data());
+        }
+        sumq += result;
+        t2 = std::chrono::high_resolution_clock::now();
+        t = 1e-3*std::chrono::duration_cast<std::chrono::nanoseconds>(t2-t1).count();
+        sumqt += t; sumqt2 += t*t; maxqt = std::max(maxqt, 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).
+    sum /= nloop; sumq /= nloop;
+    exactSum /= nloop;
+    printf("Exact result: <dot> = %g\n",exactSum);
+    printf("<dot> = %g, %g\n",sum,sumq);
+    sumt /= nloop; sumt2 /= nloop; sumt2 -= sumt*sumt;
+    if (sumt2 > 0) sumt2 = sqrt(sumt2);
+    printf("time = %g +/- %g us. maxt = %g us\n",sumt,sumt2,maxt);
+    sumqt /= nloop; sumqt2 /= nloop; sumqt2 -= sumqt*sumqt;
+    if (sumqt2 > 0) sumqt2 = sqrt(sumqt2);
+    printf("timeq = %g +/- %g us. maxt = %g us\n",sumqt,sumqt2,maxqt);
+    return 0;
+}