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llama.cpp/pocs/vdot/vdot.cpp

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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>
2023-04-18 19:00:14 +00:00
#include <cstdio>
#include <vector>
#include <random>
#include <chrono>
#include <cstdlib>
#include <cmath>
#include <cassert>
#include <cstring>
#include <array>
#include <ggml.h>
ggml : move CPU backend to a separate file (#10144)
2024-11-03 18:34:08 +00:00
#include <ggml-cpu.h>
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>
2023-04-18 19:00:14 +00:00
build : fix and ignore MSVC warnings (#1889)
2023-06-16 18:23:53 +00:00
#if defined(_MSC_VER)
#pragma warning(disable: 4244 4267) // possible loss of data
#endif
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>
2023-04-18 19:00:14 +00:00
constexpr int kVecSize = 1 << 18;
check C++ code with -Wmissing-declarations (#3184)
2023-09-15 19:38:27 +00:00
static float drawFromGaussianPdf(std::mt19937& rndm) {
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>
2023-04-18 19:00:14 +00:00
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);
}
check C++ code with -Wmissing-declarations (#3184)
2023-09-15 19:38:27 +00:00
static void fillRandomGaussianFloats(std::vector<float>& values, std::mt19937& rndm, float mean = 0) {
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>
2023-04-18 19:00:14 +00:00
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);
ggml : move CPU backend to a separate file (#10144)
2024-11-03 18:34:08 +00:00
const auto * funcs_cpu = ggml_get_type_traits_cpu(useQ4_1 ? GGML_TYPE_Q4_1 : GGML_TYPE_Q4_0);
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>
2023-04-18 19:00:14 +00:00
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);
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) {
ggml : build backends as libraries (#10256) * ggml : build backends as libraries --------- Signed-off-by: Xiaodong Ye <xiaodong.ye@mthreads.com> Co-authored-by: Georgi Gerganov <ggerganov@gmail.com> Co-authored-by: R0CKSTAR <xiaodong.ye@mthreads.com>
2024-11-14 17:04:35 +00:00
funcs_cpu->from_float(x1.data(), q41.data(), kVecSize);
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>
2023-04-18 19:00:14 +00:00
} else {
ggml : build backends as libraries (#10256) * ggml : build backends as libraries --------- Signed-off-by: Xiaodong Ye <xiaodong.ye@mthreads.com> Co-authored-by: Georgi Gerganov <ggerganov@gmail.com> Co-authored-by: R0CKSTAR <xiaodong.ye@mthreads.com>
2024-11-14 17:04:35 +00:00
funcs_cpu->from_float(x1.data(), q40.data(), kVecSize);
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>
2023-04-18 19:00:14 +00:00
}
// 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 {
ggml : build backends as libraries (#10256) * ggml : build backends as libraries --------- Signed-off-by: Xiaodong Ye <xiaodong.ye@mthreads.com> Co-authored-by: Georgi Gerganov <ggerganov@gmail.com> Co-authored-by: R0CKSTAR <xiaodong.ye@mthreads.com>
2024-11-14 17:04:35 +00:00
const auto * vdot = ggml_get_type_traits_cpu(funcs_cpu->vec_dot_type);
ggml : fix BLAS with unsupported types (#9775) * ggml : do not use BLAS with types without to_float * ggml : return pointer from ggml_internal_get_type_traits to avoid unnecessary copies * ggml : rename ggml_internal_get_type_traits -> ggml_get_type_traits it's not really internal if everybody uses it
2024-10-08 12:21:43 +00:00
vdot->from_float(y1.data(), q8.data(), kVecSize);
ggml : move CPU backend to a separate file (#10144)
2024-11-03 18:34:08 +00:00
if (useQ4_1) funcs_cpu->vec_dot(kVecSize, &result, 0, q41.data(), 0, q8.data(), 0, 1);
else funcs_cpu->vec_dot(kVecSize, &result, 0, q40.data(), 0, q8.data(), 0, 1);
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>
2023-04-18 19:00:14 +00:00
}
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;
}
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