Example Code (Cache Optimization)#
A simple timing helper class (
StopWatch.hpp)#1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 | #pragma once
#include <chrono>
class StopWatch
{
private:
using clock_type = std::chrono::system_clock;
using time_type = std::chrono::time_point<clock_type>;
public:
/// A singleton.
static StopWatch & me()
{
static StopWatch instance;
return instance;
}
StopWatch() : m_start(clock_type::now()), m_stop(m_start) {}
StopWatch(StopWatch const & ) = default;
StopWatch(StopWatch &&) = default;
StopWatch & operator=(StopWatch const & ) = default;
StopWatch & operator=(StopWatch &&) = default;
~StopWatch() = default;
/**
* Return seconds between laps.
*/
double lap()
{
m_start = m_stop;
m_stop = clock_type::now();
return std::chrono::duration<double>(m_stop - m_start).count();
}
/**
* Return seconds between end and start.
*/
double duration() const { return std::chrono::duration<double>(m_stop - m_start).count(); }
/**
* Return resolution in second.
*/
static constexpr double resolution()
{
return double(clock_type::period::num) / double(clock_type::period::den);
}
private:
time_type m_start;
time_type m_stop;
}; /* end struct StopWatch */
|
Example code for skipped access (
01_skip_access.cpp)#1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 | #include "StopWatch.hpp"
#include <cstddef>
#include <iostream>
int main(int argc, char ** argv)
{
constexpr const size_t nelem = 128 * 1024 * 1024;
int * arr = new int[nelem];
double elapsed;
StopWatch sw;
// Sequential; accessing all data every 4 bytes.
for (size_t i=0; i<nelem; ++i) { arr[i] = i; }
sw.lap();
for (size_t i=0; i<nelem; ++i) { arr[i] *= 3; }
elapsed = sw.lap();
std::cout << "Sequential takes: " << elapsed << " sec" << std::endl;
std::cout << std::endl;
// Skipping 2; accessing 4 bytes every 8 bytes.
for (size_t i=0; i<nelem; ++i) { arr[i] = i; }
sw.lap();
for (size_t i=0; i<nelem; i+=2) { arr[i] *= 3; }
elapsed = sw.lap();
std::cout << "Skipping 2 takes: " << elapsed << " sec" << std::endl;
// Skipping 4; accessing 4 bytes every 16 bytes.
for (size_t i=0; i<nelem; ++i) { arr[i] = i; }
sw.lap();
for (size_t i=0; i<nelem; i+=4) { arr[i] *= 3; }
elapsed = sw.lap();
std::cout << "Skipping 4 takes: " << elapsed << " sec" << std::endl;
// Skipping 8; accessing 4 bytes every 32 bytes.
for (size_t i=0; i<nelem; ++i) { arr[i] = i; }
sw.lap();
for (size_t i=0; i<nelem; i+=8) { arr[i] *= 3; }
elapsed = sw.lap();
std::cout << "Skipping 8 takes: " << elapsed << " sec" << std::endl;
// Skipping 16; accessing 4 bytes every 64 bytes.
for (size_t i=0; i<nelem; ++i) { arr[i] = i; }
sw.lap();
for (size_t i=0; i<nelem; i+=16) { arr[i] *= 3; }
elapsed = sw.lap();
std::cout << "Skipping 16 takes: " << elapsed << " sec" << std::endl;
std::cout << std::endl;
// Skipping 32; accessing 4 bytes every 128 bytes.
for (size_t i=0; i<nelem; ++i) { arr[i] = i; }
sw.lap();
for (size_t i=0; i<nelem; i+=32) { arr[i] *= 3; }
elapsed = sw.lap();
std::cout << "Skipping 32 takes: " << elapsed << " sec" << std::endl;
// Skipping 64; accessing 4 bytes every 256 bytes.
for (size_t i=0; i<nelem; ++i) { arr[i] = i; }
sw.lap();
for (size_t i=0; i<nelem; i+=64) { arr[i] *= 3; }
elapsed = sw.lap();
std::cout << "Skipping 64 takes: " << elapsed << " sec" << std::endl;
// Skipping 128; accessing 4 bytes every 512 bytes.
for (size_t i=0; i<nelem; ++i) { arr[i] = i; }
sw.lap();
for (size_t i=0; i<nelem; i+=128) { arr[i] *= 3; }
elapsed = sw.lap();
std::cout << "Skipping 128 takes: " << elapsed << " sec" << std::endl;
// Skipping 256; accessing 4 bytes every 1024 bytes.
for (size_t i=0; i<nelem; ++i) { arr[i] = i; }
sw.lap();
for (size_t i=0; i<nelem; i+=256) { arr[i] *= 3; }
elapsed = sw.lap();
std::cout << "Skipping 256 takes: " << elapsed << " sec" << std::endl;
// Skipping 512; accessing 4 bytes every 2048 bytes.
for (size_t i=0; i<nelem; ++i) { arr[i] = i; }
sw.lap();
for (size_t i=0; i<nelem; i+=512) { arr[i] *= 3; }
elapsed = sw.lap();
std::cout << "Skipping 512 takes: " << elapsed << " sec" << std::endl;
// Skipping 1024; accessing 4 bytes every 4096 bytes.
for (size_t i=0; i<nelem; ++i) { arr[i] = i; }
sw.lap();
for (size_t i=0; i<nelem; i+=1024) { arr[i] *= 3; }
elapsed = sw.lap();
std::cout << "Skipping 1024 takes: " << elapsed << " sec" << std::endl;
delete[] arr;
}
|
Example code for data layout (
02_locality.cpp)#1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 | #include "StopWatch.hpp"
#include <cstddef>
#include <iostream>
#include <time.h>
int main(int argc, char ** argv)
{
constexpr const size_t nelem = 1024 * 1024 * 64;
// Assume row-major 2D array.
size_t ncol = 1;
size_t nrow = nelem / ncol;
double * buffer = new double[nelem];
StopWatch sw;
double elapsed;
for (size_t ncol=1; ncol<=1024 * 8; ncol *= 2)
//for (size_t ncol=1024; ncol>0; ncol /= 2)
{
// Pre-populate to cancel the effect of overcommit or delayed allocation.
for (size_t i=0; i<nelem; ++i) { buffer[i] = nelem-i; }
size_t nrow = nelem / ncol;
std::cout << "# of elements: " << nelem << " = "
<< nrow << " x " << ncol << std::endl;
// Populate flatly.
sw.lap();
for (size_t i=0; i<nelem; ++i) { buffer[i] = i; }
elapsed = sw.lap();
std::cout << "populate double flatly takes: "
<< elapsed << " sec" << std::endl;
// Populate by last index.
sw.lap();
for (size_t i=0; i<nrow; ++i) // the i-th row
{
for (size_t j=0; j<ncol; ++j) // the j-th column
{
buffer[i*ncol + j] = i*ncol + j;
}
}
double elapsed_last = elapsed = sw.lap();
std::cout << "populate double along last axis takes: "
<< elapsed << " sec" << std::endl;
// Populate by first index.
sw.lap();
for (size_t j=0; j<ncol; ++j) // the j-th column
{
for (size_t i=0; i<nrow; ++i) // the i-th row
{
buffer[i*ncol + j] = i*ncol + j;
}
}
double elapsed_first = elapsed = sw.lap();
std::cout << "populate double along first axis takes: "
<< elapsed << " sec" << std::endl;
std::cout << "ratio: " << elapsed_first / elapsed_last
<< std::endl << std::endl;
}
for (size_t i=0; i<nelem; ++i) { buffer[i] += i; }
delete[] buffer;
return 0;
}
|
Example code for tiled matrix-matrix multiplication
(
03_matrxi_matrix.cpp)#1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 | #include "StopWatch.hpp"
#ifdef HASMKL
#include <mkl.h>
#include <mkl_lapack.h>
#include <mkl_lapacke.h>
#else // HASMKL
#ifdef __MACH__
#include <clapack.h>
#include <Accelerate/Accelerate.h>
#endif // __MACH__
#endif // HASMKL
#include <iostream>
#include <sstream>
#include <iomanip>
#include <vector>
#include <stdexcept>
#include <functional>
struct Matrix {
public:
Matrix(size_t nrow, size_t ncol)
: m_nrow(nrow), m_ncol(ncol)
{
reset_buffer(nrow, ncol);
}
Matrix(size_t nrow, size_t ncol, std::vector<double> const & vec)
: m_nrow(nrow), m_ncol(ncol)
{
reset_buffer(nrow, ncol);
(*this) = vec;
}
Matrix & operator=(std::vector<double> const & vec)
{
if (size() != vec.size())
{
throw std::out_of_range("number of elements mismatch");
}
size_t k = 0;
for (size_t i=0; i<m_nrow; ++i)
{
for (size_t j=0; j<m_ncol; ++j)
{
(*this)(i,j) = vec[k];
++k;
}
}
return *this;
}
Matrix(Matrix const & other)
: m_nrow(other.m_nrow), m_ncol(other.m_ncol)
, m_elapsed(other.m_elapsed), m_nflo(other.m_nflo)
{
reset_buffer(other.m_nrow, other.m_ncol);
for (size_t i=0; i<m_nrow; ++i)
{
for (size_t j=0; j<m_ncol; ++j)
{
(*this)(i,j) = other(i,j);
}
}
}
Matrix & operator=(Matrix const & other)
{
if (this == &other) { return *this; }
if (m_nrow != other.m_nrow || m_ncol != other.m_ncol)
{
reset_buffer(other.m_nrow, other.m_ncol);
}
for (size_t i=0; i<m_nrow; ++i)
{
for (size_t j=0; j<m_ncol; ++j)
{
(*this)(i,j) = other(i,j);
}
}
m_elapsed = other.m_elapsed;
m_nflo = other.m_nflo;
return *this;
}
Matrix(Matrix && other)
: m_nrow(other.m_nrow), m_ncol(other.m_ncol)
, m_elapsed(other.m_elapsed), m_nflo(other.m_nflo)
{
reset_buffer(0, 0);
std::swap(m_nrow, other.m_nrow);
std::swap(m_ncol, other.m_ncol);
std::swap(m_buffer, other.m_buffer);
}
Matrix & operator=(Matrix && other)
{
if (this == &other) { return *this; }
reset_buffer(0, 0);
std::swap(m_nrow, other.m_nrow);
std::swap(m_ncol, other.m_ncol);
std::swap(m_buffer, other.m_buffer);
std::swap(m_elapsed, other.m_elapsed);
std::swap(m_nflo, other.m_nflo);
return *this;
}
~Matrix()
{
reset_buffer(0, 0);
}
double operator() (size_t row, size_t col) const { return m_buffer[index(row, col)]; }
double & operator() (size_t row, size_t col) { return m_buffer[index(row, col)]; }
double operator[] (size_t idx) const { return m_buffer[idx]; }
double & operator[] (size_t idx) { return m_buffer[idx]; }
size_t nrow() const { return m_nrow; }
size_t ncol() const { return m_ncol; }
size_t size() const { return m_nrow * m_ncol; }
double buffer(size_t i) const { return m_buffer[i]; }
std::vector<double> buffer_vector() const { return std::vector<double>(m_buffer, m_buffer+size()); }
double elapsed() const { return m_elapsed; }
double & elapsed() { return m_elapsed; }
size_t nflo() const { return m_nflo; }
size_t & nflo() { return m_nflo; }
double gflops() const { return m_nflo / m_elapsed / 1.e9; }
Matrix transpose() const;
public:
size_t index(size_t row, size_t col) const
{
return row * m_ncol + col;
}
void reset_buffer(size_t nrow, size_t ncol)
{
if (m_buffer) { delete[] m_buffer; }
const size_t nelement = nrow * ncol;
if (nelement) { m_buffer = new double[nelement]; }
else { m_buffer = nullptr; }
m_nrow = nrow;
m_ncol = ncol;
}
size_t m_nrow = 0;
size_t m_ncol = 0;
double * m_buffer = nullptr;
double m_elapsed = 0;
size_t m_nflo = 0; // number of floating-point operations.
};
Matrix Matrix::transpose() const
{
Matrix ret(nrow(), ncol());
for (size_t i=0; i<ret.nrow(); ++i)
{
for (size_t j=0; j<ret.ncol(); ++j)
{
ret(j, i) = (*this)(i, j);
}
}
return ret;
}
bool operator== (Matrix const & mat1, Matrix const & mat2)
{
if ((mat1.ncol() != mat2.ncol()) && (mat1.nrow() != mat2.ncol()))
{
return false;
}
for (size_t i=0; i<mat1.nrow(); ++i)
{
for (size_t j=0; j<mat1.ncol(); ++j)
{
if (mat1(i, j) != mat2(i, j))
{
return false;
}
}
}
return true;
}
bool operator!= (Matrix const & mat1, Matrix const & mat2)
{
return !(mat1 == mat2);
}
/*
* Throw an exception if the shapes of the two matrices don't support
* multiplication.
*/
void validate_multiplication(Matrix const & mat1, Matrix const & mat2)
{
if (mat1.ncol() != mat2.nrow())
{
throw std::out_of_range(
"the number of first matrix column "
"differs from that of second matrix row");
}
}
/*
* Get the number of floating-point operations.
*/
size_t calc_nflo(Matrix const & mat1, Matrix const & mat2)
{
return mat1.nrow() * mat1.ncol() * mat2.ncol();
}
/*
* Use MKL for the matrix matrix multiplication.
*/
Matrix multiply_mkl(Matrix const & mat1, Matrix const & mat2)
{
#if !defined(HASMKL) || defined(NOMKL)
// run with VECLIB_MAXIMUM_THREADS=1
#else // HASMKL NOMKL
mkl_set_num_threads(1);
#endif // HASMKL NOMKL
Matrix ret(mat1.nrow(), mat2.ncol());
StopWatch sw;
cblas_dgemm(
CblasRowMajor /* const CBLAS_LAYOUT Layout */
, CblasNoTrans /* const CBLAS_TRANSPOSE transa */
, CblasNoTrans /* const CBLAS_TRANSPOSE transb */
, mat1.nrow() /* const MKL_INT m */
, mat2.ncol() /* const MKL_INT n */
, mat1.ncol() /* const MKL_INT k */
, 1.0 /* const double alpha */
, mat1.m_buffer /* const double *a */
, mat1.ncol() /* const MKL_INT lda */
, mat2.m_buffer /* const double *b */
, mat2.ncol() /* const MKL_INT ldb */
, 0.0 /* const double beta */
, ret.m_buffer /* double * c */
, ret.ncol() /* const MKL_INT ldc */
);
ret.elapsed() = sw.lap();
ret.nflo() = calc_nflo(mat1, mat2);
return ret;
}
/*
* Indirect naive matrix matrix multiplication.
*/
Matrix multiply_indirect(Matrix const & mat1, Matrix const & mat2)
{
validate_multiplication(mat1, mat2);
Matrix ret(mat1.nrow(), mat2.ncol());
StopWatch sw;
for (size_t i=0; i<mat1.nrow(); ++i)
{
for (size_t k=0; k<mat2.ncol(); ++k)
{
double v = 0;
for (size_t j=0; j<mat1.ncol(); ++j)
{
v += mat1(i,j) * mat2(j,k);
}
ret(i,k) = v;
}
}
ret.elapsed() = sw.lap();
ret.nflo() = calc_nflo(mat1, mat2);
return ret;
}
/*
* Indirect naive matrix matrix multiplication but loop in a different order
* (i,j,k). It is much faster than the original order (i,k,j), because mat2
* now has a much better locality.
*/
Matrix multiply_indirect_order1(Matrix const & mat1, Matrix const & mat2)
{
validate_multiplication(mat1, mat2);
Matrix ret(mat1.nrow(), mat2.ncol());
StopWatch sw;
for (size_t i=0; i<ret.nrow(); ++i)
{
for (size_t j=0; j<ret.ncol(); ++j)
{
ret(i,j) = 0;
}
}
for (size_t i=0; i<mat1.nrow(); ++i)
{
for (size_t j=0; j<mat1.ncol(); ++j)
{
for (size_t k=0; k<mat2.ncol(); ++k)
{
ret(i,k) += mat1(i,j) * mat2(j,k);
}
}
}
ret.elapsed() = sw.lap();
ret.nflo() = calc_nflo(mat1, mat2);
return ret;
}
/*
* Direct naive matrix matrix multiplication.
*/
Matrix multiply_direct(Matrix const & mat1, Matrix const & mat2)
{
validate_multiplication(mat1, mat2);
Matrix ret(mat1.nrow(), mat2.ncol());
const size_t nrow1 = mat1.nrow();
const size_t ncol1 = mat1.ncol();
const size_t nrow2 = mat2.nrow();
const size_t ncol2 = mat2.ncol();
StopWatch sw;
for (size_t i=0; i<nrow1; ++i)
{
const size_t base1 = i * ncol1;
for (size_t k=0; k<ncol2; ++k)
{
double v = 0;
for (size_t j=0; j<ncol1; ++j)
{
v += mat1.m_buffer[base1 + j] * mat2.m_buffer[j*ncol2 + k];
}
ret.m_buffer[base1 + k] = v;
}
}
ret.elapsed() = sw.lap();
ret.nflo() = calc_nflo(mat1, mat2);
return ret;
}
template<size_t N>
struct Block
{
static constexpr const size_t NDIM = N;
double operator[] (size_t idx) const { return m_buffer[idx]; }
double & operator[] (size_t idx) { return m_buffer[idx]; }
Block<N> & operator= (double v)
{
for (size_t i=0; i<N*N; ++i) { m_buffer[i] = v; }
return *this;
}
Block<N> & operator+= (Block<N> const & other)
{
for (size_t i=0; i<N*N; ++i) { m_buffer[i] += other.m_buffer[i]; }
return *this;
}
void save(Matrix & mat, size_t it, size_t jt);
double m_buffer[N * N];
};
template<size_t N> void Block<N>::save(
Matrix & mat, size_t it, size_t jt
)
{
const size_t ncol = mat.ncol();
for (size_t i=0; i<NDIM; ++i)
{
const size_t base_s = i*NDIM;
const size_t base_t = (it*NDIM + i) * ncol + jt*NDIM;
for (size_t j=0; j<NDIM; ++j)
{
mat.m_buffer[base_t + j] = m_buffer[base_s + j];
}
}
}
template<size_t N>
struct Tiler
{
static constexpr const size_t NDIM = N;
void load(
Matrix const & mat1, size_t it1, size_t jt1
, Matrix const & mat2, size_t it2, size_t jt2
);
void multiply();
Block<N> m_mat1; // row-major
Block<N> m_mat2; // column-major
Block<N> m_ret; // row-major
};
template<size_t N> void Tiler<N>::load(
Matrix const & mat1, size_t it1, size_t jt1
, Matrix const & mat2, size_t it2, size_t jt2
)
{
const size_t ncol1 = mat1.ncol();
for (size_t i=0; i<NDIM; ++i)
{
const size_t base_t = i*NDIM;
const size_t base_s = (it1*NDIM + i) * ncol1 + jt1*NDIM;
for (size_t j=0; j<NDIM; ++j)
{
m_mat1[base_t + j] = mat1.m_buffer[base_s + j];
}
}
const size_t ncol2 = mat2.ncol();
for (size_t i=0; i<NDIM; ++i)
{
const size_t base_t = i*NDIM;
const size_t base_s = (it2*NDIM + i) * ncol2 + jt2*NDIM;
for (size_t j=0; j<NDIM; ++j)
{
m_ret[base_t + j] = mat2.m_buffer[base_s + j];
}
}
for (size_t i=0; i<NDIM; ++i)
{
const size_t base = i*NDIM;
for (size_t j=0; j<NDIM; ++j)
{
m_mat2[j*NDIM + i] = m_ret[base + j];
}
}
}
template<size_t N> void Tiler<N>::multiply()
{
for (size_t i=0; i<NDIM; ++i)
{
const size_t base1 = i*NDIM;
for (size_t k=0; k<NDIM; ++k)
{
const size_t base2 = k*NDIM;
double v = 0;
for (size_t j=0; j<NDIM; ++j)
{
v += m_mat1[base1 + j] * m_mat2[base2 + j];
}
m_ret[base1 + k] = v;
}
}
}
/*
* Tiled matrix matrix multiplication.
*/
template<size_t LSIZE>
Matrix multiply_tile(Matrix const & mat1, Matrix const & mat2)
{
validate_multiplication(mat1, mat2);
Matrix ret(mat1.nrow(), mat2.ncol());
constexpr const size_t tsize = LSIZE / sizeof(double);
const size_t nrow1 = mat1.nrow();
const size_t ncol1 = mat1.ncol();
const size_t nrow2 = mat2.nrow();
const size_t ncol2 = mat2.ncol();
const size_t ntrow1 = nrow1 / tsize;
const size_t ntcol1 = ncol1 / tsize;
const size_t ntrow2 = nrow2 / tsize;
const size_t ntcol2 = ncol2 / tsize;
Block<tsize> value;
Tiler<tsize> tiler;
StopWatch sw;
for (size_t it=0; it<ntrow1; ++it)
{
for (size_t kt=0; kt<ntcol2; ++kt)
{
value = 0;
for (size_t jt=0; jt<ntcol1; ++jt)
{
tiler.load(mat1, it, jt, mat2, jt, kt);
tiler.multiply();
value += tiler.m_ret;
}
value.save(ret, it, kt);
}
}
ret.elapsed() = sw.lap();
ret.nflo() = calc_nflo(mat1, mat2);
return ret;
}
void initialize(Matrix & mat)
{
for (size_t i=0; i<mat.nrow(); ++i)
{
for (size_t j=0; j<mat.ncol(); ++j)
{
if (0 == i%2)
{
mat(i, j) = j;
}
else
{
mat(i, j) = mat.ncol() - 1 - j;
}
}
}
}
template<size_t TSIZE=sizeof(double)>
Matrix time_tile(
std::string tag, Matrix const * gold
, Matrix const & mat1, Matrix const & mat2
)
{
std::function<Matrix (Matrix const &, Matrix const &)> runner;
if (sizeof(double) == TSIZE)
{
if ("mkl" == tag)
{
runner = multiply_mkl;
}
else if ("indirect" == tag)
{
runner = multiply_indirect;
}
else if ("indirect_order1" == tag)
{
runner = multiply_indirect_order1;
}
else if ("direct" == tag)
{
runner = multiply_direct;
}
else
{
throw std::runtime_error("invalid tag");
}
}
else
{
std::ostringstream t;
t << "tiled " << TSIZE;
tag = t.str();
runner = multiply_tile<TSIZE>;
}
std::cout << "Timing " << tag << ": ";
Matrix res = runner(mat1, mat2);
if (gold && (res != *gold))
{
throw std::runtime_error("answer mismatch");
}
std::cout << res.elapsed() << " second, "
<< res.nflo()/1.e9 << " Gflo, "
<< res.gflops() << " Gflops"
<< std::endl;
return res;
}
int main(int argc, char ** argv)
{
Matrix mat1(1 * 1024, 1 * 1024);
initialize(mat1);
Matrix mat2 = mat1;
Matrix mat_gold = time_tile("mkl", nullptr, mat1, mat2);
time_tile("indirect", &mat_gold, mat1, mat2);
time_tile("indirect_order1", &mat_gold, mat1, mat2);
time_tile("direct", &mat_gold, mat1, mat2);
time_tile<32>("", &mat_gold, mat1, mat2);
time_tile<64>("", &mat_gold, mat1, mat2);
time_tile<128>("", &mat_gold, mat1, mat2);
time_tile<256>("", &mat_gold, mat1, mat2);
time_tile<512>("", &mat_gold, mat1, mat2);
time_tile<1024>("", &mat_gold, mat1, mat2);
return 0;
}
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