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multiply.cpp
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multiply.cpp
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#include <immintrin.h>
#include <iostream>
#ifdef __i386
__inline__ uint64_t rdtsc() {
uint64_t x;
__asm__ volatile ("rdtsc" : "=A" (x));
return x;
}
#elif __amd64
__inline__ uint64_t rdtsc() {
uint64_t a, d;
__asm__ volatile ("rdtsc" : "=a" (a), "=d" (d));
return (d<<32) | a;
}
#endif
template<typename FP, size_t ROW, size_t COL>
struct matrix;
template<size_t ROW, size_t COL>
struct matrix<float, ROW, COL> {
alignas(64) float data[ROW*COL] = {};
float const& operator()(size_t i, size_t j) const {
return data[i*width() + j];
}
float& operator()(size_t i, size_t j) {
return data[i*width() + j];
}
constexpr size_t width() const {
return COL;
}
constexpr size_t height() const {
return ROW;
}
};
template <typename FP, size_t ROW, size_t COL>
matrix<FP, COL, ROW> transpose(const matrix<FP, ROW, COL>& m){
matrix<FP, COL, ROW> output;
for (size_t i = 0; i < m.height(); ++i)
for (size_t j = 0; j < m.width(); ++j){
output(j, i) = m(i, j);
}
return output;
}
template<typename FP, size_t ROW, size_t COL1, size_t COL2>
struct multiply_helper
{
using return_type = matrix<FP, ROW, COL2>;
using op1_type = matrix<FP, ROW, COL1>;
using op2_type = matrix<FP, COL1, COL2>;
// Fallback implementation
static return_type multiply(op1_type const& a, op2_type const& b)
{
return_type output;
for (size_t i = 0; i < ROW; ++i) {
for (size_t j = 0; j < COL2; ++j) {
for (size_t k = 0; k < COL1; ++k) {
output(i, j) += a(i, k) * b(k, j);
}
}
}
return output;
}
};
template<size_t ROW, size_t COL2>
struct multiply_helper<float, ROW, 4, COL2>
{
using return_type = matrix<float, ROW, COL2>;
using op1_type = matrix<float, ROW, 4>;
using op2_type = matrix<float, 4, COL2>;
// Implementation using SSE
static return_type multiply(op1_type const& a, op2_type const& b)
{
auto b_transposed = transpose(b);
return_type result;
for(size_t line = 0; line < a.height(); ++line)
{
__m128 cur_line = _mm_load_ps(a.data + line*a.width());
size_t done_cols = 0;
while(done_cols < b.width())
{
switch(b.width()-done_cols)
{
case 0: break; // Rien à faire mais on ne devrait jamais arriver là
case 1:
{
// SSE 128bits
__m128 col = _mm_load_ps(b_transposed.data + done_cols*b.height());
__m128 r = _mm_dp_ps(cur_line, col, 0xF1);
result(line, done_cols) = _mm_cvtss_f32(r);
++done_cols;
break;
}
case 2:
case 3:
default:
{
// SSE 256bits
__m256 line_doubled = _mm256_castps128_ps256(cur_line);
line_doubled = _mm256_insertf128_ps(line_doubled, cur_line, 1);
__m256 cols = _mm256_load_ps(b_transposed.data + done_cols*b.height());
__m256 r = _mm256_mul_ps(line_doubled, cols);
r = _mm256_hadd_ps(r, r);
r = _mm256_hadd_ps(r, r);
result(line, done_cols) = _mm256_cvtss_f32(r);
r = _mm256_permute2f128_ps(r, r, 1);
result(line, done_cols+1) = _mm256_cvtss_f32(r);
done_cols += 2;
break;
}
//default: // 4 and over
{
// SSE 512bits
done_cols += 4;
break;
}
}
}
}
return result;
}
};
template<typename FP, size_t ROW, size_t COL1, size_t COL2>
matrix<FP, ROW, COL2> multiply(matrix<FP, ROW, COL1> const& a, matrix<FP, COL1, COL2> const& b)
{
return multiply_helper<FP, ROW, COL1, COL2>::multiply(a, b);
}
template<typename FP, size_t ROW, size_t COL>
std::ostream& operator<<(std::ostream& o, matrix<FP, ROW, COL> const& m) {
for (size_t i = 0; i < m.height(); ++i) {
o << "[ ";
for (size_t j = 0; j < m.width(); ++j) {
o << m(i, j) << " ";
}
o << "]" << std::endl;
}
return o;
}
int main() {
alignas(16) float a[4] = {1, 2, 3, 4};
alignas(16) float b[4] = {1, 2, 3, 4};
__m128 sser_a = _mm_load_ps(a);
__m128 sser_b = _mm_load_ps(b);
__m128 sser_result = _mm_dp_ps(sser_a, sser_b, 0b11110001);
float final = _mm_cvtss_f32(sser_result);
std::cout << final << std::endl; // Attendu 30
matrix<float, 1, 4> c{1, 2, 3, 4};
matrix<float, 4, 3> d{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12};
auto r = multiply(c, d);
std::cout << r << std::endl;
std::cout << transpose(r) << std::endl;
}