flops.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_FLOPS_HH
#define BLAS_FLOPS_HH
 
#include "blas.hh"
 
namespace blas {
 
// =============================================================================
// Level 1 BLAS
 
// -----------------------------------------------------------------------------
inline double fmuls_asum( double n )
    { return 0; }
 
inline double fadds_asum( double n )
    { return n-1; }
 
// -----------------------------------------------------------------------------
inline double fmuls_axpy( double n )
    { return n; }
 
inline double fadds_axpy( double n )
    { return n; }
 
// -----------------------------------------------------------------------------
inline double fmuls_iamax( double n )
    { return 0; }
 
// n-1 compares, which are essentially adds (x > y is x - y > 0)
inline double fadds_iamax( double n )
    { return n-1; }
 
// -----------------------------------------------------------------------------
inline double fmuls_nrm2( double n )
    { return n; }
 
inline double fadds_nrm2( double n )
    { return n-1; }
 
// -----------------------------------------------------------------------------
inline double fmuls_dot( double n )
    { return n; }
 
inline double fadds_dot( double n )
    { return n-1; }
 
// -----------------------------------------------------------------------------
inline double fmuls_scal( double n )
    { return n; }
 
inline double fadds_scal( double n )
    { return 0; }
 
// -----------------------------------------------------------------------------
inline double fmuls_rot( double n )
    { return 4 * n; }
 
inline double fadds_rot( double n )
    { return 2 * n; }
 
// -----------------------------------------------------------------------------
inline double fmuls_rotm( double n )
    { return 2 * n; }
 
inline double fadds_rotm( double n )
    { return 2 * n; }
 
// =============================================================================
// Level 2 BLAS
// most formulas assume alpha=1, beta=0 or 1; otherwise add lower-order terms.
// i.e., this is minimum flops and bandwidth that could be consumed.
 
// -----------------------------------------------------------------------------
inline double fmuls_gemv( double m, double n )
    { return m*n; }
 
inline double fadds_gemv( double m, double n )
    { return m*n; }
 
// -----------------------------------------------------------------------------
inline double fmuls_trmv( double n )
    { return 0.5*n*(n + 1); }
 
inline double fadds_trmv( double n )
    { return 0.5*n*(n - 1); }
 
// -----------------------------------------------------------------------------
inline double fmuls_ger( double m, double n )
    { return m*n; }
 
inline double fadds_ger( double m, double n )
    { return m*n; }
 
// -----------------------------------------------------------------------------
inline double fmuls_gemm( double m, double n, double k )
    { return m*n*k; }
 
inline double fadds_gemm( double m, double n, double k )
    { return m*n*k; }
 
// -----------------------------------------------------------------------------
// Assume gbmm is band matrix A (m-by-k) and general matrix B (k-by-n).
// Usually, the bottom equation (m-kl <= k and k-ku <= m) calculates the flops,
// but some matrices are too tall or too wide and require extra care.
// This bottom equation fails because a triangle it subtracts extends beyond
// the matrix, so it should subtract a trapezoid instead.
// For the first corner (m-kl > k) case,
// think rectangle minus trapezoid minus triangle and reduce:
//        (m*k - (m-kl+m-k-kl-1)/2*k - (k-ku-1)*(k-ku)/2)*n;
//        (m*k - (m-kl)*k+(k-1)*k/2 - (k-ku-1)*(k-ku)/2)*n;
//        (kl*k + (k+1)*k/2 - (k-ku-1)*(k-ku)/2)*n;
// We are conveniently left with the geometric interpretation of
// rectangle plus triangle minus triangle.
inline double fmuls_gbmm( double m, double n, double k, double kl, double ku )
{
    if (m-kl > k)
        return (kl*k + (k+1)*k/2. - (k-ku-1)*(k-ku)/2.)*n;
    if (k-ku > m)
        return (ku*m - (m-kl-1)*(m-kl)/2. + (m+1)*m/2.)*n;
    return (m*k - (m-kl-1)*(m-kl)/2. - (k-ku-1)*(k-ku)/2.)*n;
}
 
// Assuming alpha=1, beta=1, adds are same as muls.
inline double fadds_gbmm( double m, double n, double k, double kl, double ku )
{
    return fmuls_gbmm( m, n, k, kl, ku );
}
 
// -----------------------------------------------------------------------------
inline double fmuls_hemm( blas::Side side, double m, double n )
    { return (side == blas::Side::Left ? m*m*n : m*n*n); }
 
inline double fadds_hemm( blas::Side side, double m, double n )
    { return (side == blas::Side::Left ? m*m*n : m*n*n); }
 
// -----------------------------------------------------------------------------
inline double fmuls_herk( double n, double k )
    { return 0.5*k*n*(n+1); }
 
inline double fadds_herk( double n, double k )
    { return 0.5*k*n*(n+1); }
 
// -----------------------------------------------------------------------------
inline double fmuls_her2k( double n, double k )
    { return k*n*n; }
 
inline double fadds_her2k( double n, double k )
    { return k*n*n; }
 
// -----------------------------------------------------------------------------
inline double fmuls_trmm( blas::Side side, double m, double n )
{
    if (side == blas::Side::Left)
        return 0.5*n*m*(m + 1);
    else
        return 0.5*m*n*(n + 1);
}
 
inline double fadds_trmm( blas::Side side, double m, double n )
{
    if (side == blas::Side::Left)
        return 0.5*n*m*(m - 1);
    else
        return 0.5*m*n*(n - 1);
}
 
//==============================================================================
// template class. Example:
// gflop< float >::gemm( m, n, k ) yields flops for sgemm.
// gflop< std::complex<float> >::gemm( m, n, k ) yields flops for cgemm.
//==============================================================================
template <typename T>
class Gbyte
{
public:
    // ----------------------------------------
    // Level 1 BLAS
    // read x
    static double asum( double n )
        { return 1e-9 * (n * sizeof(T)); }
 
    // read x, y; write y
    static double axpy( double n )
        { return 1e-9 * (3*n * sizeof(T)); }
 
    // read x; write y
    static double copy( double n )
        { return 1e-9 * (2*n * sizeof(T)); }
 
    // read x
    static double iamax( double n )
        { return 1e-9 * (n * sizeof(T)); }
 
    // read x
    static double nrm2( double n )
        { return 1e-9 * (n * sizeof(T)); }
 
    // read x, y
    static double dot( double n )
        { return 1e-9 * (2*n * sizeof(T)); }
 
    // read x; write x
    static double scal( double n )
        { return 1e-9 * (2*n * sizeof(T)); }
 
    // read x, y; write x, y
    static double swap( double n )
        { return 1e-9 * (4*n * sizeof(T)); }
 
    // ----------------------------------------
    // Level 2 BLAS
    // read A, x; write y
    static double gemv( double m, double n )
        { return 1e-9 * ((m*n + m + n) * sizeof(T)); }
 
    // read A triangle, x; write y
    static double hemv( double n )
        { return 1e-9 * ((0.5*(n+1)*n + 2*n) * sizeof(T)); }
 
    static double symv( double n )
        { return hemv( n ); }
 
    // read A triangle, x; write x
    static double trmv( double n )
        { return 1e-9 * ((0.5*(n+1)*n + 2*n) * sizeof(T)); }
 
    static double trsv( double n )
        { return trmv( n ); }
 
    // read A, x, y; write A
    static double ger( double m, double n )
        { return 1e-9 * ((2*m*n + m + n) * sizeof(T)); }
 
    // read A triangle, x; write A triangle
    static double her( double n )
        { return 1e-9 * (((n+1)*n + n) * sizeof(T)); }
 
    static double syr( double n )
        { return her( n ); }
 
    // read A triangle, x, y; write A triangle
    static double her2( double n )
        { return 1e-9 * (((n+1)*n + n + n) * sizeof(T)); }
 
    static double syr2( double n )
        { return her2( n ); }
 
    // read A; write B
    static double copy_2d( double m, double n )
        { return 1e-9 * (2*m*n * sizeof(T)); }
 
    // ----------------------------------------
    // Level 3 BLAS
    // read A, B, C; write C
    static double gemm( double m, double n, double k )
        { return 1e-9 * ((m*k + k*n + 2*m*n) * sizeof(T)); }
 
    static double hemm( blas::Side side, double m, double n )
    {
        // read A, B, C; write C
        double sizeA = (side == blas::Side::Left ? 0.5*m*(m+1) : 0.5*n*(n+1));
        return 1e-9 * ((sizeA + 3*m*n) * sizeof(T));
    }
 
    static double symm( blas::Side side, double m, double n )
        { return hemm( side, m, n ); }
 
    static double herk( double n, double k )
    {
        // read A, C; write C
        double sizeC = 0.5*n*(n+1);
        return 1e-9 * ((n*k + 2*sizeC) * sizeof(T));
    }
 
    static double syrk( double n, double k )
        { return herk( n, k ); }
 
    static double her2k( double n, double k )
    {
        // read A, B, C; write C
        double sizeC = 0.5*n*(n+1);
        return 1e-9 * ((2*n*k + 2*sizeC) * sizeof(T));
    }
 
    static double syr2k( double n, double k )
        { return her2k( n, k ); }
 
    static double trmm( blas::Side side, double m, double n )
    {
        // read A triangle, x; write x
        if (side == blas::Side::Left)
            return 1e-9 * ((0.5*(m+1)*m + 2*m*n) * sizeof(T));
        else
            return 1e-9 * ((0.5*(n+1)*n + 2*m*n) * sizeof(T));
    }
 
    static double trsm( blas::Side side, double m, double n )
        { return trmm( side, m, n ); }
};
 
//==============================================================================
// Traits to lookup number of operations per multiply and add.
template <typename T>
class FlopTraits
{
public:
    static constexpr double mul_ops = 1;
    static constexpr double add_ops = 1;
};
 
//------------------------------------------------------------------------------
// specialization for complex
// flops = 6*muls + 2*adds
template <typename T>
class FlopTraits< std::complex<T> >
{
public:
    static constexpr double mul_ops = 6;
    static constexpr double add_ops = 2;
};
 
//==============================================================================
// template class. Example:
// gflop< float >::gemm( m, n, k ) yields flops for sgemm.
// gflop< std::complex<float> >::gemm( m, n, k ) yields flops for cgemm.
//==============================================================================
template <typename T>
class Gflop
{
public:
    static constexpr double mul_ops = FlopTraits<T>::mul_ops;
    static constexpr double add_ops = FlopTraits<T>::add_ops;
 
    // ----------------------------------------
    // Level 1 BLAS
    static double asum( double n )
        { return 1e-9 * (mul_ops*fmuls_asum(n) +
                         add_ops*fadds_asum(n)); }
 
    static double axpy( double n )
        { return 1e-9 * (mul_ops*fmuls_axpy(n) +
                         add_ops*fadds_axpy(n)); }
 
    static double copy( double n )
        { return 0; }
 
    static double iamax( double n )
        { return 1e-9 * (mul_ops*fmuls_iamax(n) +
                         add_ops*fadds_iamax(n)); }
 
    static double nrm2( double n )
        { return 1e-9 * (mul_ops*fmuls_nrm2(n) +
                         add_ops*fadds_nrm2(n)); }
 
    static double dot( double n )
        { return 1e-9 * (mul_ops*fmuls_dot(n) +
                         add_ops*fadds_dot(n)); }
 
    static double scal( double n )
        { return 1e-9 * (mul_ops*fmuls_scal(n) +
                         add_ops*fadds_scal(n)); }
 
    static double swap( double n )
        { return 0; }
 
    static double rot( double n )
        { return 1e-9 * (mul_ops*fmuls_rot(n) +
                         add_ops*fadds_rot(n)); }
 
    static double rotm( double n )
        { return 1e-9 * (mul_ops*fmuls_rotm(n) +
                         add_ops*fadds_rotm(n)); }
 
    // ----------------------------------------
    // Level 2 BLAS
    static double gemv(double m, double n)
        { return 1e-9 * (mul_ops*fmuls_gemv(m, n) +
                         add_ops*fadds_gemv(m, n)); }
 
    static double symv(double n)
        { return gemv( n, n ); }
 
    static double hemv(double n)
        { return symv( n ); }
 
    static double trmv( double n )
        { return 1e-9 * (mul_ops*fmuls_trmv(n) +
                         add_ops*fadds_trmv(n)); }
 
    static double trsv( double n )
        { return trmv( n ); }
 
    static double her( double n )
        { return ger( n, n ); }
 
    static double syr( double n )
        { return her( n ); }
 
    static double ger( double m, double n )
        { return 1e-9 * (mul_ops*fmuls_ger(m, n) +
                         add_ops*fadds_ger(m, n)); }
 
    static double her2( double n )
        { return 2*ger( n, n ); }
 
    static double syr2( double n )
        { return her2( n ); }
 
    // ----------------------------------------
    // Level 3 BLAS
    static double gemm(double m, double n, double k)
        { return 1e-9 * (mul_ops*fmuls_gemm(m, n, k) +
                         add_ops*fadds_gemm(m, n, k)); }
 
    static double gbmm(double m, double n, double k, double kl, double ku)
        { return 1e-9 * (mul_ops*fmuls_gbmm(m, n, k, kl, ku) +
                         add_ops*fadds_gbmm(m, n, k, kl, ku)); }
 
    static double hemm(blas::Side side, double m, double n)
        { return 1e-9 * (mul_ops*fmuls_hemm(side, m, n) +
                         add_ops*fadds_hemm(side, m, n)); }
 
    static double hbmm(double m, double n, double kd)
        { return gbmm(m, n, m, kd, kd); }
 
    static double symm(blas::Side side, double m, double n)
        { return hemm( side, m, n ); }
 
    static double herk(double n, double k)
        { return 1e-9 * (mul_ops*fmuls_herk(n, k) +
                         add_ops*fadds_herk(n, k)); }
 
    static double syrk(double n, double k)
        { return herk( n, k ); }
 
    static double her2k(double n, double k)
        { return 1e-9 * (mul_ops*fmuls_her2k(n, k) +
                         add_ops*fadds_her2k(n, k)); }
 
    static double syr2k(double n, double k)
        { return her2k( n, k ); }
 
    static double trmm(blas::Side side, double m, double n)
        { return 1e-9 * (mul_ops*fmuls_trmm(side, m, n) +
                         add_ops*fadds_trmm(side, m, n)); }
 
    static double trsm(blas::Side side, double m, double n)
        { return trmm( side, m, n ); }
 
};
 
}  // namespace blas
 
#endif        //  #ifndef BLAS_FLOPS_HH