gemm.hh

// 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 {
 
// =============================================================================
 
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