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bench-gemm.C
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// (c) Daniel Llorens - 2016-2017
// This library is free software; you can redistribute it and/or modify it under
// the terms of the GNU Lesser General Public License as published by the Free
// Software Foundation; either version 3 of the License, or (at your option) any
// later version.
/// @file bench-gemm.H
/// @brief Benchmark for BLAS-3 type ops
// These operations aren't really part of the ET framework, just standalone functions.
// FIXME Benchmark w/o allocation.
#include <iostream>
#include <iomanip>
#include "ra/test.H"
#include "ra/complex.H"
#include "ra/format.H"
#include "ra/big.H"
#include "ra/operators.H"
#include "ra/io.H"
#include "ra/bench.H"
using std::cout, std::endl, std::setw, std::setprecision;
using ra::Small, ra::View, ra::Unique, ra::ra_traits, ra::dim_t;
using real = double;
// -------------------
// variants of the defaults, should be slower if the default is well picked.
// -------------------
template <class A, class B, class C> inline void
gemm_block_3(ra::View<A, 2> const & a, ra::View<B, 2> const & b, ra::View<C, 2> c)
{
dim_t const m = a.size(0);
dim_t const p = a.size(1);
dim_t const n = b.size(1);
// terminal, using reduce_k, see below
if (max(m, max(p, n))<=64) {
for_each(ra::wrank<1, 1, 2>(ra::wrank<1, 0, 1>([](auto && c, auto && a, auto && b) { c += a*b; })),
c, a, b);
// split a's rows
} else if (m>=max(p, n)) {
gemm_block_3(a(ra::iota(m/2)), b, c(ra::iota(m/2)));
gemm_block_3(a(ra::iota(m-m/2, m/2)), b, c(ra::iota(m-m/2, m/2)));
// split b's columns
} else if (n>=max(m, p)) {
gemm_block_3(a, b(ra::all, ra::iota(n/2)), c(ra::all, ra::iota(n/2)));
gemm_block_3(a, b(ra::all, ra::iota(n-n/2, n/2)), c(ra::all, ra::iota(n-n/2, n/2)));
// split a's columns and b's rows
} else {
gemm_block_3(a(ra::all, ra::iota(p/2)), b(ra::iota(p/2)), c);
gemm_block_3(a(ra::all, ra::iota(p-p/2, p/2)), b(ra::iota(p-p/2, p/2)), c);
}
}
#if RA_USE_BLAS==1
extern "C" {
#include <cblas.h>
}
inline constexpr CBLAS_TRANSPOSE fliptr(CBLAS_TRANSPOSE t)
{
if (t==CblasTrans) {
return CblasNoTrans;
} else if (t==CblasNoTrans) {
return CblasTrans;
} else {
assert(0 && "BLAS doesn't support this transpose");
}
}
inline constexpr bool istr(CBLAS_TRANSPOSE t)
{
return (t==CblasTrans) || (t==CblasConjTrans);
}
template <class A> inline void
lead_and_order(A const & a, int & ld, CBLAS_ORDER & order)
{
if (a.stride(1)==1) {
order = CblasRowMajor;
ld = a.stride(0);
} else if (a.stride(0)==1) {
order = CblasColMajor;
ld = a.stride(1);
} else {
assert(0 && "not a BLAS-supported array");
}
}
inline void
gemm_blas_3(ra::View<double, 2> const & A, ra::View<double, 2> const & B, ra::View<double, 2> C)
{
CBLAS_TRANSPOSE ta = CblasNoTrans;
CBLAS_TRANSPOSE tb = CblasNoTrans;
int ldc, lda, ldb;
CBLAS_ORDER orderc, ordera, orderb;
lead_and_order(C, ldc, orderc);
lead_and_order(A, lda, ordera);
lead_and_order(B, ldb, orderb);
int K = A.size(1-istr(ta));
assert(K==B.size(istr(tb)) && "mismatched A/B");
assert(C.size(0)==A.size(istr(ta)) && "mismatched C/A");
assert(C.size(1)==B.size(1-istr(tb)) && "mismatched C/B");
if (ordera!=orderc) {
ta = fliptr(ta);
}
if (orderb!=orderc) {
tb = fliptr(tb);
}
if (C.size()>0) {
cblas_dgemm(orderc, ta, tb, C.size(0), C.size(1), K, 1., A.data(), lda, B.data(), ldb, 0, C.data(), ldc);
}
}
inline auto
gemm_blas(ra::View<double, 2> const & a, ra::View<double, 2> const & b)
{
ra::Big<decltype(a(0, 0)*b(0, 0)), 2> c({a.size(0), b.size(1)}, 0);
gemm_blas_3(a, b, c);
return c;
}
#endif // RA_USE_BLAS
int main()
{
TestRecorder tr(std::cout);
auto gemm_block = [&](auto const & a, auto const & b)
{
ra::Big<decltype(a(0, 0)*b(0, 0)), 2> c({a.size(0), b.size(1)}, 0);
gemm_block_3(a, b, c);
return c;
};
auto gemm_k = [&](auto const & a, auto const & b)
{
dim_t const M = a.size(0);
dim_t const N = b.size(1);
ra::Big<decltype(a(0, 0)*b(0, 0)), 2> c({M, N}, ra::unspecified);
for (dim_t i=0; i<M; ++i) {
for (dim_t j=0; j<N; ++j) {
c(i, j) = dot(a(i), b(ra::all, j));
}
}
return c;
};
// See test-wrank.C "outer product variants" for the logic.
// TODO based on this, allow a Blitz++ like notation C(i, j) = sum(A(i, k)*B(k, j), k) without using TensorIndex (no ply_index).
auto gemm_reduce_k = [&](auto const & a, auto const & b)
{
dim_t const M = a.size(0);
dim_t const N = b.size(1);
using T = decltype(a(0, 0)*b(0, 0));
ra::Big<T, 2> c({M, N}, T());
for_each(ra::wrank<1, 1, 2>(ra::wrank<1, 0, 1>([](auto && c, auto && a, auto && b) { c += a*b; })),
c, a, b);
return c;
};
#define DEFINE_GEMM_RESTRICT(NAME_K, NAME_IJ, RESTRICT) \
auto NAME_K = [&](auto const & a, auto const & b) \
{ \
dim_t const M = a.size(0); \
dim_t const N = b.size(1); \
dim_t const K = a.size(1); \
using T = decltype(a(0, 0)*b(0, 0)); \
ra::Big<T, 2> c({M, N}, T()); \
T * RESTRICT cc = c.data(); \
T const * RESTRICT aa = a.data(); \
T const * RESTRICT bb = b.data(); \
for (dim_t i=0; i<M; ++i) { \
for (dim_t j=0; j<N; ++j) { \
for (dim_t k=0; k<K; ++k) { \
cc[i*N+j] += aa[i*K+k] * bb[k*N+j]; \
} \
} \
} \
return c; \
}; \
\
auto NAME_IJ = [&](auto const & a, auto const & b) \
{ \
dim_t const M = a.size(0); \
dim_t const N = b.size(1); \
dim_t const K = a.size(1); \
using T = decltype(a(0, 0)*b(0, 0)); \
ra::Big<T, 2> c({M, N}, T()); \
T * RESTRICT cc = c.data(); \
T const * RESTRICT aa = a.data(); \
T const * RESTRICT bb = b.data(); \
for (dim_t k=0; k<K; ++k) { \
for (dim_t i=0; i<M; ++i) { \
for (dim_t j=0; j<N; ++j) { \
cc[i*N+j] += aa[i*K+k] * bb[k*N+j]; \
} \
} \
} \
return c; \
};
DEFINE_GEMM_RESTRICT(gemm_k_raw, gemm_ij_raw, /* */)
DEFINE_GEMM_RESTRICT(gemm_k_raw_restrict, gemm_ij_raw_restrict, __restrict__)
#undef DEFINE_GEMM_RESTRICT
auto bench_all = [&](int k, int m, int p, int n, int reps)
{
auto bench = [&](auto && f, char const * tag)
{
ra::Big<real, 2> a({m, p}, ra::_0-ra::_1);
ra::Big<real, 2> b({p, n}, ra::_1-2*ra::_0);
ra::Big<real, 2> ref = gemm(a, b);
ra::Big<real, 2> c;
auto bv = Benchmark().repeats(reps).runs(3).run([&]() { c = f(a, b); });
tr.info(std::setw(5), std::fixed, Benchmark::avg(bv)/(m*n*p)/1e-9, " ns [",
Benchmark::stddev(bv)/(m*n*p)/1e-9 ,"] ", tag).test_eq(ref, c);
};
tr.section(m, " (", p, ") ", n, " times ", reps);
// some variants are way too slow to check with larger arrays.
if (k>2) {
bench(gemm_k, "k");
}
if (k>1) {
bench(gemm_k_raw, "k_raw");
bench(gemm_k_raw_restrict, "k_raw_restrict");
}
if (k>0) {
bench(gemm_reduce_k, "reduce_k");
bench(gemm_ij_raw, "ij_raw");
bench(gemm_ij_raw_restrict, "ij_raw_restrict");
}
bench(gemm_block, "block");
#if RA_USE_BLAS==1
bench(gemm_blas, "blas");
#endif
bench([&](auto const & a, auto const & b) { return gemm(a, b); }, "default");
};
bench_all(3, 10, 10, 10, 10000);
bench_all(2, 100, 100, 100, 100);
bench_all(2, 500, 400, 500, 1);
bench_all(1, 10000, 10, 1000, 1);
bench_all(1, 1000, 10, 10000, 1);
bench_all(1, 100000, 10, 100, 1);
bench_all(1, 100, 10, 100000, 1);
return tr.summary();
}