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// Copyright (c) 2017-2023, University of Tennessee. All rights reserved.
// SPDX-License-Identifier: BSD-3-Clause
// This program is free software: you can redistribute it and/or modify it under
// the terms of the BSD 3-Clause license. See the accompanying LICENSE file.
#ifndef BLAS_GEMM_HH
#define BLAS_GEMM_HH
#include "blas/util.hh"
#include <limits>
namespace blas {
// =============================================================================
/// General matrix-matrix multiply:
/// \[
/// C = \alpha op(A) \times op(B) + \beta C,
/// \]
/// where $op(X)$ is one of
/// $op(X) = X$,
/// $op(X) = X^T$, or
/// $op(X) = X^H$,
/// alpha and beta are scalars, and A, B, and C are matrices, with
/// $op(A)$ an m-by-k matrix, $op(B)$ a k-by-n matrix, and C an m-by-n matrix.
///
/// Generic implementation for arbitrary data types.
///
/// @param[in] layout
/// Matrix storage, Layout::ColMajor or Layout::RowMajor.
///
/// @param[in] transA
/// The operation $op(A)$ to be used:
/// - Op::NoTrans: $op(A) = A$.
/// - Op::Trans: $op(A) = A^T$.
/// - Op::ConjTrans: $op(A) = A^H$.
///
/// @param[in] transB
/// The operation $op(B)$ to be used:
/// - Op::NoTrans: $op(B) = B$.
/// - Op::Trans: $op(B) = B^T$.
/// - Op::ConjTrans: $op(B) = B^H$.
///
/// @param[in] m
/// Number of rows of the matrix C and $op(A)$. m >= 0.
///
/// @param[in] n
/// Number of columns of the matrix C and $op(B)$. n >= 0.
///
/// @param[in] k
/// Number of columns of $op(A)$ and rows of $op(B)$. k >= 0.
///
/// @param[in] alpha
/// Scalar alpha. If alpha is zero, A and B are not accessed.
///
/// @param[in] A
/// - If transA = NoTrans:
/// the m-by-k matrix A, stored in an lda-by-k array [RowMajor: m-by-lda].
/// - Otherwise:
/// the k-by-m matrix A, stored in an lda-by-m array [RowMajor: k-by-lda].
///
/// @param[in] lda
/// Leading dimension of A.
/// - If transA = NoTrans: lda >= max(1, m) [RowMajor: lda >= max(1, k)].
/// - Otherwise: lda >= max(1, k) [RowMajor: lda >= max(1, m)].
///
/// @param[in] B
/// - If transB = NoTrans:
/// the k-by-n matrix B, stored in an ldb-by-n array [RowMajor: k-by-ldb].
/// - Otherwise:
/// the n-by-k matrix B, stored in an ldb-by-k array [RowMajor: n-by-ldb].
///
/// @param[in] ldb
/// Leading dimension of B.
/// - If transB = NoTrans: ldb >= max(1, k) [RowMajor: ldb >= max(1, n)].
/// - Otherwise: ldb >= max(1, n) [RowMajor: ldb >= max(1, k)].
///
/// @param[in] beta
/// Scalar beta. If beta is zero, C need not be set on input.
///
/// @param[in] C
/// The m-by-n matrix C, stored in an ldc-by-n array [RowMajor: m-by-ldc].
///
/// @param[in] ldc
/// Leading dimension of C. ldc >= max(1, m) [RowMajor: ldc >= max(1, n)].
///
/// @ingroup gemm
template <typename TA, typename TB, typename TC>
void gemm(
blas::Layout layout,
blas::Op transA,
blas::Op transB,
int64_t m, int64_t n, int64_t k,
scalar_type<TA, TB, TC> alpha,
TA const *A, int64_t lda,
TB const *B, int64_t ldb,
scalar_type<TA, TB, TC> beta,
TC *C, int64_t ldc )
{
// redirect if row major
if (layout == Layout::RowMajor) {
return gemm(
Layout::ColMajor,
transB,
transA,
n, m, k,
alpha,
B, ldb,
A, lda,
beta,
C, ldc);
}
else {
// check layout
blas_error_if_msg( layout != Layout::ColMajor,
"layout != Layout::ColMajor && layout != Layout::RowMajor" );
}
typedef blas::scalar_type<TA, TB, TC> scalar_t;
#define A(i_, j_) A[ (i_) + (j_)*lda ]
#define B(i_, j_) B[ (i_) + (j_)*ldb ]
#define C(i_, j_) C[ (i_) + (j_)*ldc ]
// constants
const scalar_t zero = 0;
const scalar_t one = 1;
// check arguments
blas_error_if( transA != Op::NoTrans &&
transA != Op::Trans &&
transA != Op::ConjTrans );
blas_error_if( transB != Op::NoTrans &&
transB != Op::Trans &&
transB != Op::ConjTrans );
blas_error_if( m < 0 );
blas_error_if( n < 0 );
blas_error_if( k < 0 );
blas_error_if( lda < ((transA != Op::NoTrans) ? k : m) );
blas_error_if( ldb < ((transB != Op::NoTrans) ? n : k) );
blas_error_if( ldc < m );
// quick return
if (m == 0 || n == 0 || k == 0)
return;
// alpha == zero
if (alpha == zero) {
if (beta == zero) {
for (int64_t j = 0; j < n; ++j) {
for (int64_t i = 0; i < m; ++i)
C(i, j) = zero;
}
}
else if (beta != one) {
for (int64_t j = 0; j < n; ++j) {
for (int64_t i = 0; i < m; ++i)
C(i, j) *= beta;
}
}
return;
}
// alpha != zero
if (transA == Op::NoTrans) {
if (transB == Op::NoTrans) {
for (int64_t j = 0; j < n; ++j) {
for (int64_t i = 0; i < m; ++i)
C(i, j) *= beta;
for (int64_t l = 0; l < k; ++l) {
scalar_t alpha_Blj = alpha*B(l, j);
for (int64_t i = 0; i < m; ++i)
C(i, j) += A(i, l)*alpha_Blj;
}
}
}
else if (transB == Op::Trans) {
for (int64_t j = 0; j < n; ++j) {
for (int64_t i = 0; i < m; ++i)
C(i, j) *= beta;
for (int64_t l = 0; l < k; ++l) {
scalar_t alpha_Bjl = alpha*B(j, l);
for (int64_t i = 0; i < m; ++i)
C(i, j) += A(i, l)*alpha_Bjl;
}
}
}
else { // transB == Op::ConjTrans
for (int64_t j = 0; j < n; ++j) {
for (int64_t i = 0; i < m; ++i)
C(i, j) *= beta;
for (int64_t l = 0; l < k; ++l) {
scalar_t alpha_Bjl = alpha*conj(B(j, l));
for (int64_t i = 0; i < m; ++i)
C(i, j) += A(i, l)*alpha_Bjl;
}
}
}
}
else if (transA == Op::Trans) {
if (transB == Op::NoTrans) {
for (int64_t j = 0; j < n; ++j) {
for (int64_t i = 0; i < m; ++i) {
scalar_t sum = zero;
for (int64_t l = 0; l < k; ++l)
sum += A(l, i)*B(l, j);
C(i, j) = alpha*sum + beta*C(i, j);
}
}
}
else if (transB == Op::Trans) {
for (int64_t j = 0; j < n; ++j) {
for (int64_t i = 0; i < m; ++i) {
scalar_t sum = zero;
for (int64_t l = 0; l < k; ++l)
sum += A(l, i)*B(j, l);
C(i, j) = alpha*sum + beta*C(i, j);
}
}
}
else { // transB == Op::ConjTrans
for (int64_t j = 0; j < n; ++j) {
for (int64_t i = 0; i < m; ++i) {
scalar_t sum = zero;
for (int64_t l = 0; l < k; ++l)
sum += A(l, i)*conj(B(j, l));
C(i, j) = alpha*sum + beta*C(i, j);
}
}
}
}
else { // transA == Op::ConjTrans
if (transB == Op::NoTrans) {
for (int64_t j = 0; j < n; ++j) {
for (int64_t i = 0; i < m; ++i) {
scalar_t sum = zero;
for (int64_t l = 0; l < k; ++l)
sum += conj(A(l, i))*B(l, j);
C(i, j) = alpha*sum + beta*C(i, j);
}
}
}
else if (transB == Op::Trans) {
for (int64_t j = 0; j < n; ++j) {
for (int64_t i = 0; i < m; ++i) {
scalar_t sum = zero;
for (int64_t l = 0; l < k; ++l)
sum += conj(A(l, i))*B(j, l);
C(i, j) = alpha*sum + beta*C(i, j);
}
}
}
else { // transB == Op::ConjTrans
for (int64_t j = 0; j < n; ++j) {
for (int64_t i = 0; i < m; ++i) {
scalar_t sum = zero;
for (int64_t l = 0; l < k; ++l)
sum += A(l, i)*B(j, l); // little improvement here
C(i, j) = alpha*conj(sum) + beta*C(i, j);
}
}
}
}
#undef A
#undef B
#undef C
}
} // namespace blas
#endif // #ifndef BLAS_GEMM_HH
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