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/**
*
* @file flops.h
*
* File provided by Univ. of Tennessee,
*
* @version 1.0.0
* @author Mathieu Faverge
* @date January 2025
*
**/
/*
* This file provide the flops formula for all Level 3 BLAS and some
* Lapack routines. Each macro uses the same size parameters as the
* function associated and provide one formula for additions and one
* for multiplications. Example to use these macros:
*
* FLOPS_ZGEMM( m, n, k )
*
* All the formula are reported in the LAPACK Lawn 41:
* http://www.netlib.org/lapack/lawns/lawn41.ps
*/
#ifndef MAGMA_FLOPS_H
#define MAGMA_FLOPS_H
/***************************************************************************//**
Generic formula coming from LAWN 41
*******************************************************************************/
/*
* Level 1 BLAS
*/
#define FMULS_AXPY(n_) (n_)
#define FADDS_AXPY(n_) (n_)
/*
* Level 2 BLAS
*/
#define FMULS_GEMV(m_, n_) ((m_) * (n_) + 2. * (m_))
#define FADDS_GEMV(m_, n_) ((m_) * (n_) )
#define FMULS_SYMV(n_) FMULS_GEMV( (n_), (n_) )
#define FADDS_SYMV(n_) FADDS_GEMV( (n_), (n_) )
#define FMULS_HEMV FMULS_SYMV
#define FADDS_HEMV FADDS_SYMV
/*
* Level 3 BLAS
*/
#define FMULS_GEMM(m_, n_, k_) ((m_) * (n_) * (k_))
#define FADDS_GEMM(m_, n_, k_) ((m_) * (n_) * (k_))
#define FMULS_SYMM(side_, m_, n_) ( ( (side_) == MagmaLeft ) ? FMULS_GEMM((m_), (m_), (n_)) : FMULS_GEMM((m_), (n_), (n_)) )
#define FADDS_SYMM(side_, m_, n_) ( ( (side_) == MagmaLeft ) ? FADDS_GEMM((m_), (m_), (n_)) : FADDS_GEMM((m_), (n_), (n_)) )
#define FMULS_HEMM FMULS_SYMM
#define FADDS_HEMM FADDS_SYMM
#define FMULS_SYRK(k_, n_) (0.5 * (k_) * (n_) * ((n_)+1))
#define FADDS_SYRK(k_, n_) (0.5 * (k_) * (n_) * ((n_)+1))
#define FMULS_HERK FMULS_SYRK
#define FADDS_HERK FADDS_SYRK
#define FMULS_SYR2K(k_, n_) ((k_) * (n_) * (n_) )
#define FADDS_SYR2K(k_, n_) ((k_) * (n_) * (n_) + (n_))
#define FMULS_HER2K FMULS_SYR2K
#define FADDS_HER2K FADDS_SYR2K
#define FMULS_TRMM_2(m_, n_) (0.5 * (n_) * (m_) * ((m_)+1))
#define FADDS_TRMM_2(m_, n_) (0.5 * (n_) * (m_) * ((m_)-1))
#define FMULS_TRMM(side_, m_, n_) ( ( (side_) == MagmaLeft ) ? FMULS_TRMM_2((m_), (n_)) : FMULS_TRMM_2((n_), (m_)) )
#define FADDS_TRMM(side_, m_, n_) ( ( (side_) == MagmaLeft ) ? FADDS_TRMM_2((m_), (n_)) : FADDS_TRMM_2((n_), (m_)) )
#define FMULS_TRSM FMULS_TRMM
#define FADDS_TRSM FADDS_TRMM
/*
* Lapack
*/
#define FMULS_GETRF(m_, n_) ( ((m_) < (n_)) \
? (0.5 * (m_) * ((m_) * ((n_) - (1./3.) * (m_) - 1. ) + (n_)) + (2. / 3.) * (m_)) \
: (0.5 * (n_) * ((n_) * ((m_) - (1./3.) * (n_) - 1. ) + (m_)) + (2. / 3.) * (n_)) )
#define FADDS_GETRF(m_, n_) ( ((m_) < (n_)) \
? (0.5 * (m_) * ((m_) * ((n_) - (1./3.) * (m_) ) - (n_)) + (1. / 6.) * (m_)) \
: (0.5 * (n_) * ((n_) * ((m_) - (1./3.) * (n_) ) - (m_)) + (1. / 6.) * (n_)) )
#define FMULS_GETRI(n_) ( (n_) * ((5. / 6.) + (n_) * ((2. / 3.) * (n_) + 0.5)) )
#define FADDS_GETRI(n_) ( (n_) * ((5. / 6.) + (n_) * ((2. / 3.) * (n_) - 1.5)) )
#define FMULS_GETRS(n_, nrhs_) ((nrhs_) * (n_) * (n_) )
#define FADDS_GETRS(n_, nrhs_) ((nrhs_) * (n_) * ((n_) - 1 ))
#define FMULS_POTRF(n_) ((n_) * (((1. / 6.) * (n_) + 0.5) * (n_) + (1. / 3.)))
#define FADDS_POTRF(n_) ((n_) * (((1. / 6.) * (n_) ) * (n_) - (1. / 6.)))
#define FMULS_POTRI(n_) ( (n_) * ((2. / 3.) + (n_) * ((1. / 3.) * (n_) + 1. )) )
#define FADDS_POTRI(n_) ( (n_) * ((1. / 6.) + (n_) * ((1. / 3.) * (n_) - 0.5)) )
#define FMULS_POTRS(n_, nrhs_) ((nrhs_) * (n_) * ((n_) + 1 ))
#define FADDS_POTRS(n_, nrhs_) ((nrhs_) * (n_) * ((n_) - 1 ))
//SPBTRF
//SPBTRS
//SSYTRF
//SSYTRI
//SSYTRS
#define FMULS_GEQRF(m_, n_) (((m_) > (n_)) \
? ((n_) * ((n_) * ( 0.5-(1./3.) * (n_) + (m_)) + (m_) + 23. / 6.)) \
: ((m_) * ((m_) * ( -0.5-(1./3.) * (m_) + (n_)) + 2.*(n_) + 23. / 6.)) )
#define FADDS_GEQRF(m_, n_) (((m_) > (n_)) \
? ((n_) * ((n_) * ( 0.5-(1./3.) * (n_) + (m_)) + 5. / 6.)) \
: ((m_) * ((m_) * ( -0.5-(1./3.) * (m_) + (n_)) + (n_) + 5. / 6.)) )
#define FMULS_GEQRT(m_, n_) (0.5 * (m_)*(n_))
#define FADDS_GEQRT(m_, n_) (0.5 * (m_)*(n_))
#define FMULS_GEQLF(m_, n_) FMULS_GEQRF(m_, n_)
#define FADDS_GEQLF(m_, n_) FADDS_GEQRF(m_, n_)
#define FMULS_GERQF(m_, n_) (((m_) > (n_)) \
? ((n_) * ((n_) * ( 0.5-(1./3.) * (n_) + (m_)) + (m_) + 29. / 6.)) \
: ((m_) * ((m_) * ( -0.5-(1./3.) * (m_) + (n_)) + 2.*(n_) + 29. / 6.)) )
#define FADDS_GERQF(m_, n_) (((m_) > (n_)) \
? ((n_) * ((n_) * ( -0.5-(1./3.) * (n_) + (m_)) + (m_) + 5. / 6.)) \
: ((m_) * ((m_) * ( 0.5-(1./3.) * (m_) + (n_)) + + 5. / 6.)) )
#define FMULS_GELQF(m_, n_) FMULS_GERQF(m_, n_)
#define FADDS_GELQF(m_, n_) FADDS_GERQF(m_, n_)
#define FMULS_UNGQR(m_, n_, k_) ((k_) * (2.* (m_) * (n_) + 2. * (n_) - 5./3. + (k_) * ( 2./3. * (k_) - ((m_) + (n_)) - 1.)))
#define FADDS_UNGQR(m_, n_, k_) ((k_) * (2.* (m_) * (n_) + (n_) - (m_) + 1./3. + (k_) * ( 2./3. * (k_) - ((m_) + (n_)) )))
#define FMULS_ORGQR FMULS_UNGQR
#define FADDS_ORGQR FADDS_UNGQR
#define FMULS_UNGQL FMULS_UNGQR
#define FADDS_UNGQL FADDS_UNGQR
#define FMULS_ORGQL FMULS_UNGQR
#define FADDS_ORGQL FADDS_UNGQR
#define FMULS_UNGRQ(m_, n_, k_) ((k_) * (2.* (m_) * (n_) + (m_) + (n_) - 2./3. + (k_) * ( 2./3. * (k_) - ((m_) + (n_)) - 1.)))
#define FADDS_UNGRQ(m_, n_, k_) ((k_) * (2.* (m_) * (n_) + (m_) - (n_) + 1./3. + (k_) * ( 2./3. * (k_) - ((m_) + (n_)) )))
#define FMULS_ORGRQ FMULS_UNGRQ
#define FADDS_ORGRQ FADDS_UNGRQ
#define FMULS_UNGLQ FMULS_UNGRQ
#define FADDS_UNGLQ FADDS_UNGRQ
#define FMULS_ORGLQ FMULS_UNGRQ
#define FADDS_ORGLQ FADDS_UNGRQ
#define FMULS_GEQRS(m_, n_, nrhs_) ((nrhs_) * ((n_) * ( 2.* (m_) - 0.5 * (n_) + 2.5)))
#define FADDS_GEQRS(m_, n_, nrhs_) ((nrhs_) * ((n_) * ( 2.* (m_) - 0.5 * (n_) + 0.5)))
#define FMULS_UNMQR(m_, n_, k_, side_) (( (side_) == MagmaLeft ) \
? (2.*(n_)*(m_)*(k_) - (n_)*(k_)*(k_) + 2.*(n_)*(k_)) \
: (2.*(n_)*(m_)*(k_) - (m_)*(k_)*(k_) + (m_)*(k_) + (n_)*(k_) - 0.5*(k_)*(k_) + 0.5*(k_)))
#define FADDS_UNMQR(m_, n_, k_, side_) (( ((side_)) == MagmaLeft ) \
? (2.*(n_)*(m_)*(k_) - (n_)*(k_)*(k_) + (n_)*(k_)) \
: (2.*(n_)*(m_)*(k_) - (m_)*(k_)*(k_) + (m_)*(k_)))
#define FMULS_ORMQR FMULS_UNMQR
#define FADDS_ORMQR FADDS_UNMQR
#define FMULS_UNMQL FMULS_UNMQR
#define FADDS_UNMQL FADDS_UNMQR
#define FMULS_ORMQL FMULS_UNMQR
#define FADDS_ORMQL FADDS_UNMQR
#define FMULS_UNMRQ FMULS_UNMQR
#define FADDS_UNMRQ FADDS_UNMQR
#define FMULS_ORMRQ FMULS_UNMQR
#define FADDS_ORMRQ FADDS_UNMQR
#define FMULS_UNMLQ FMULS_UNMQR
#define FADDS_UNMLQ FADDS_UNMQR
#define FMULS_ORMLQ FMULS_UNMQR
#define FADDS_ORMLQ FADDS_UNMQR
#define FMULS_TRTRI(n_) ((n_) * ((n_) * ( 1./6. * (n_) + 0.5 ) + 1./3.))
#define FADDS_TRTRI(n_) ((n_) * ((n_) * ( 1./6. * (n_) - 0.5 ) + 1./3.))
#define FMULS_GEHRD(n_) ( (n_) * ((n_) * (5./3. *(n_) + 0.5) - 7./6.) - 13. )
#define FADDS_GEHRD(n_) ( (n_) * ((n_) * (5./3. *(n_) - 1. ) - 2./3.) - 8. )
#define FMULS_SYTRD(n_) ( (n_) * ( (n_) * ( 2./3. * (n_) + 2.5 ) - 1./6. ) - 15.)
#define FADDS_SYTRD(n_) ( (n_) * ( (n_) * ( 2./3. * (n_) + 1. ) - 8./3. ) - 4.)
#define FMULS_HETRD FMULS_SYTRD
#define FADDS_HETRD FADDS_SYTRD
#define FMULS_GEBRD(m_, n_) ( ((m_) >= (n_)) \
? ((n_) * ((n_) * (2. * (m_) - 2./3. * (n_) + 2. ) + 20./3.)) \
: ((m_) * ((m_) * (2. * (n_) - 2./3. * (m_) + 2. ) + 20./3.)) )
#define FADDS_GEBRD(m_, n_) ( ((m_) >= (n_)) \
? ((n_) * ((n_) * (2. * (m_) - 2./3. * (n_) + 1. ) - (m_) + 5./3.)) \
: ((m_) * ((m_) * (2. * (n_) - 2./3. * (m_) + 1. ) - (n_) + 5./3.)) )
#define FMULS_LARFG(n_) (2*n_)
#define FADDS_LARFG(n_) ( n_)
/***************************************************************************//**
Users functions
*******************************************************************************/
/*
* Level 1 BLAS
*/
#define FLOPS_ZAXPY(n_) (6. * FMULS_AXPY((double)(n_)) + 2.0 * FADDS_AXPY((double)(n_)) )
#define FLOPS_CAXPY(n_) (6. * FMULS_AXPY((double)(n_)) + 2.0 * FADDS_AXPY((double)(n_)) )
#define FLOPS_DAXPY(n_) ( FMULS_AXPY((double)(n_)) + FADDS_AXPY((double)(n_)) )
#define FLOPS_SAXPY(n_) ( FMULS_AXPY((double)(n_)) + FADDS_AXPY((double)(n_)) )
/*
* Level 2 BLAS
*/
#define FLOPS_ZGEMV(m_, n_) (6. * FMULS_GEMV((double)(m_), (double)(n_)) + 2.0 * FADDS_GEMV((double)(m_), (double)(n_)) )
#define FLOPS_CGEMV(m_, n_) (6. * FMULS_GEMV((double)(m_), (double)(n_)) + 2.0 * FADDS_GEMV((double)(m_), (double)(n_)) )
#define FLOPS_DGEMV(m_, n_) ( FMULS_GEMV((double)(m_), (double)(n_)) + FADDS_GEMV((double)(m_), (double)(n_)) )
#define FLOPS_SGEMV(m_, n_) ( FMULS_GEMV((double)(m_), (double)(n_)) + FADDS_GEMV((double)(m_), (double)(n_)) )
#define FLOPS_ZHEMV(n_) (6. * FMULS_HEMV((double)(n_)) + 2.0 * FADDS_HEMV((double)(n_)) )
#define FLOPS_CHEMV(n_) (6. * FMULS_HEMV((double)(n_)) + 2.0 * FADDS_HEMV((double)(n_)) )
#define FLOPS_ZSYMV(n_) (6. * FMULS_SYMV((double)(n_)) + 2.0 * FADDS_SYMV((double)(n_)) )
#define FLOPS_CSYMV(n_) (6. * FMULS_SYMV((double)(n_)) + 2.0 * FADDS_SYMV((double)(n_)) )
#define FLOPS_DSYMV(n_) ( FMULS_SYMV((double)(n_)) + FADDS_SYMV((double)(n_)) )
#define FLOPS_SSYMV(n_) ( FMULS_SYMV((double)(n_)) + FADDS_SYMV((double)(n_)) )
/*
* Level 3 BLAS
*/
#define FLOPS_ZGEMM(m_, n_, k_) (6. * FMULS_GEMM((double)(m_), (double)(n_), (double)(k_)) + 2.0 * FADDS_GEMM((double)(m_), (double)(n_), (double)(k_)) )
#define FLOPS_CGEMM(m_, n_, k_) (6. * FMULS_GEMM((double)(m_), (double)(n_), (double)(k_)) + 2.0 * FADDS_GEMM((double)(m_), (double)(n_), (double)(k_)) )
#define FLOPS_DGEMM(m_, n_, k_) ( FMULS_GEMM((double)(m_), (double)(n_), (double)(k_)) + FADDS_GEMM((double)(m_), (double)(n_), (double)(k_)) )
#define FLOPS_SGEMM(m_, n_, k_) ( FMULS_GEMM((double)(m_), (double)(n_), (double)(k_)) + FADDS_GEMM((double)(m_), (double)(n_), (double)(k_)) )
#define FLOPS_ZHEMM(side_, m_, n_) (6. * FMULS_HEMM(side_, (double)(m_), (double)(n_)) + 2.0 * FADDS_HEMM(side_, (double)(m_), (double)(n_)) )
#define FLOPS_CHEMM(side_, m_, n_) (6. * FMULS_HEMM(side_, (double)(m_), (double)(n_)) + 2.0 * FADDS_HEMM(side_, (double)(m_), (double)(n_)) )
#define FLOPS_ZSYMM(side_, m_, n_) (6. * FMULS_SYMM(side_, (double)(m_), (double)(n_)) + 2.0 * FADDS_SYMM(side_, (double)(m_), (double)(n_)) )
#define FLOPS_CSYMM(side_, m_, n_) (6. * FMULS_SYMM(side_, (double)(m_), (double)(n_)) + 2.0 * FADDS_SYMM(side_, (double)(m_), (double)(n_)) )
#define FLOPS_DSYMM(side_, m_, n_) ( FMULS_SYMM(side_, (double)(m_), (double)(n_)) + FADDS_SYMM(side_, (double)(m_), (double)(n_)) )
#define FLOPS_SSYMM(side_, m_, n_) ( FMULS_SYMM(side_, (double)(m_), (double)(n_)) + FADDS_SYMM(side_, (double)(m_), (double)(n_)) )
#define FLOPS_ZHERK(k_, n_) (6. * FMULS_HERK((double)(k_), (double)(n_)) + 2.0 * FADDS_HERK((double)(k_), (double)(n_)) )
#define FLOPS_CHERK(k_, n_) (6. * FMULS_HERK((double)(k_), (double)(n_)) + 2.0 * FADDS_HERK((double)(k_), (double)(n_)) )
#define FLOPS_ZSYRK(k_, n_) (6. * FMULS_SYRK((double)(k_), (double)(n_)) + 2.0 * FADDS_SYRK((double)(k_), (double)(n_)) )
#define FLOPS_CSYRK(k_, n_) (6. * FMULS_SYRK((double)(k_), (double)(n_)) + 2.0 * FADDS_SYRK((double)(k_), (double)(n_)) )
#define FLOPS_DSYRK(k_, n_) ( FMULS_SYRK((double)(k_), (double)(n_)) + FADDS_SYRK((double)(k_), (double)(n_)) )
#define FLOPS_SSYRK(k_, n_) ( FMULS_SYRK((double)(k_), (double)(n_)) + FADDS_SYRK((double)(k_), (double)(n_)) )
#define FLOPS_ZHER2K(k_, n_) (6. * FMULS_HER2K((double)(k_), (double)(n_)) + 2.0 * FADDS_HER2K((double)(k_), (double)(n_)) )
#define FLOPS_CHER2K(k_, n_) (6. * FMULS_HER2K((double)(k_), (double)(n_)) + 2.0 * FADDS_HER2K((double)(k_), (double)(n_)) )
#define FLOPS_ZSYR2K(k_, n_) (6. * FMULS_SYR2K((double)(k_), (double)(n_)) + 2.0 * FADDS_SYR2K((double)(k_), (double)(n_)) )
#define FLOPS_CSYR2K(k_, n_) (6. * FMULS_SYR2K((double)(k_), (double)(n_)) + 2.0 * FADDS_SYR2K((double)(k_), (double)(n_)) )
#define FLOPS_DSYR2K(k_, n_) ( FMULS_SYR2K((double)(k_), (double)(n_)) + FADDS_SYR2K((double)(k_), (double)(n_)) )
#define FLOPS_SSYR2K(k_, n_) ( FMULS_SYR2K((double)(k_), (double)(n_)) + FADDS_SYR2K((double)(k_), (double)(n_)) )
#define FLOPS_ZTRMM(side_, m_, n_) (6. * FMULS_TRMM(side_, (double)(m_), (double)(n_)) + 2.0 * FADDS_TRMM(side_, (double)(m_), (double)(n_)) )
#define FLOPS_CTRMM(side_, m_, n_) (6. * FMULS_TRMM(side_, (double)(m_), (double)(n_)) + 2.0 * FADDS_TRMM(side_, (double)(m_), (double)(n_)) )
#define FLOPS_DTRMM(side_, m_, n_) ( FMULS_TRMM(side_, (double)(m_), (double)(n_)) + FADDS_TRMM(side_, (double)(m_), (double)(n_)) )
#define FLOPS_STRMM(side_, m_, n_) ( FMULS_TRMM(side_, (double)(m_), (double)(n_)) + FADDS_TRMM(side_, (double)(m_), (double)(n_)) )
#define FLOPS_ZTRSM(side_, m_, n_) (6. * FMULS_TRSM(side_, (double)(m_), (double)(n_)) + 2.0 * FADDS_TRSM(side_, (double)(m_), (double)(n_)) )
#define FLOPS_CTRSM(side_, m_, n_) (6. * FMULS_TRSM(side_, (double)(m_), (double)(n_)) + 2.0 * FADDS_TRSM(side_, (double)(m_), (double)(n_)) )
#define FLOPS_DTRSM(side_, m_, n_) ( FMULS_TRSM(side_, (double)(m_), (double)(n_)) + FADDS_TRSM(side_, (double)(m_), (double)(n_)) )
#define FLOPS_STRSM(side_, m_, n_) ( FMULS_TRSM(side_, (double)(m_), (double)(n_)) + FADDS_TRSM(side_, (double)(m_), (double)(n_)) )
/*
* Lapack
*/
#define FLOPS_ZGETRF(m_, n_) (6. * FMULS_GETRF((double)(m_), (double)(n_)) + 2.0 * FADDS_GETRF((double)(m_), (double)(n_)) )
#define FLOPS_CGETRF(m_, n_) (6. * FMULS_GETRF((double)(m_), (double)(n_)) + 2.0 * FADDS_GETRF((double)(m_), (double)(n_)) )
#define FLOPS_DGETRF(m_, n_) ( FMULS_GETRF((double)(m_), (double)(n_)) + FADDS_GETRF((double)(m_), (double)(n_)) )
#define FLOPS_SGETRF(m_, n_) ( FMULS_GETRF((double)(m_), (double)(n_)) + FADDS_GETRF((double)(m_), (double)(n_)) )
#define FLOPS_ZGETRI(n_) (6. * FMULS_GETRI((double)(n_)) + 2.0 * FADDS_GETRI((double)(n_)) )
#define FLOPS_CGETRI(n_) (6. * FMULS_GETRI((double)(n_)) + 2.0 * FADDS_GETRI((double)(n_)) )
#define FLOPS_DGETRI(n_) ( FMULS_GETRI((double)(n_)) + FADDS_GETRI((double)(n_)) )
#define FLOPS_SGETRI(n_) ( FMULS_GETRI((double)(n_)) + FADDS_GETRI((double)(n_)) )
#define FLOPS_ZGETRS(n_, nrhs_) (6. * FMULS_GETRS((double)(n_), (double)(nrhs_)) + 2.0 * FADDS_GETRS((double)(n_), (double)(nrhs_)) )
#define FLOPS_CGETRS(n_, nrhs_) (6. * FMULS_GETRS((double)(n_), (double)(nrhs_)) + 2.0 * FADDS_GETRS((double)(n_), (double)(nrhs_)) )
#define FLOPS_DGETRS(n_, nrhs_) ( FMULS_GETRS((double)(n_), (double)(nrhs_)) + FADDS_GETRS((double)(n_), (double)(nrhs_)) )
#define FLOPS_SGETRS(n_, nrhs_) ( FMULS_GETRS((double)(n_), (double)(nrhs_)) + FADDS_GETRS((double)(n_), (double)(nrhs_)) )
#define FLOPS_ZPOTRF(n_) (6. * FMULS_POTRF((double)(n_)) + 2.0 * FADDS_POTRF((double)(n_)) )
#define FLOPS_CPOTRF(n_) (6. * FMULS_POTRF((double)(n_)) + 2.0 * FADDS_POTRF((double)(n_)) )
#define FLOPS_DPOTRF(n_) ( FMULS_POTRF((double)(n_)) + FADDS_POTRF((double)(n_)) )
#define FLOPS_SPOTRF(n_) ( FMULS_POTRF((double)(n_)) + FADDS_POTRF((double)(n_)) )
#define FLOPS_ZPOTRI(n_) (6. * FMULS_POTRI((double)(n_)) + 2.0 * FADDS_POTRI((double)(n_)) )
#define FLOPS_CPOTRI(n_) (6. * FMULS_POTRI((double)(n_)) + 2.0 * FADDS_POTRI((double)(n_)) )
#define FLOPS_DPOTRI(n_) ( FMULS_POTRI((double)(n_)) + FADDS_POTRI((double)(n_)) )
#define FLOPS_SPOTRI(n_) ( FMULS_POTRI((double)(n_)) + FADDS_POTRI((double)(n_)) )
#define FLOPS_ZPOTRS(n_, nrhs_) (6. * FMULS_POTRS((double)(n_), (double)(nrhs_)) + 2.0 * FADDS_POTRS((double)(n_), (double)(nrhs_)) )
#define FLOPS_CPOTRS(n_, nrhs_) (6. * FMULS_POTRS((double)(n_), (double)(nrhs_)) + 2.0 * FADDS_POTRS((double)(n_), (double)(nrhs_)) )
#define FLOPS_DPOTRS(n_, nrhs_) ( FMULS_POTRS((double)(n_), (double)(nrhs_)) + FADDS_POTRS((double)(n_), (double)(nrhs_)) )
#define FLOPS_SPOTRS(n_, nrhs_) ( FMULS_POTRS((double)(n_), (double)(nrhs_)) + FADDS_POTRS((double)(n_), (double)(nrhs_)) )
#define FLOPS_ZGEQRF(m_, n_) (6. * FMULS_GEQRF((double)(m_), (double)(n_)) + 2.0 * FADDS_GEQRF((double)(m_), (double)(n_)) )
#define FLOPS_CGEQRF(m_, n_) (6. * FMULS_GEQRF((double)(m_), (double)(n_)) + 2.0 * FADDS_GEQRF((double)(m_), (double)(n_)) )
#define FLOPS_DGEQRF(m_, n_) ( FMULS_GEQRF((double)(m_), (double)(n_)) + FADDS_GEQRF((double)(m_), (double)(n_)) )
#define FLOPS_SGEQRF(m_, n_) ( FMULS_GEQRF((double)(m_), (double)(n_)) + FADDS_GEQRF((double)(m_), (double)(n_)) )
#define FLOPS_ZGEQRT(m_, n_) (6. * FMULS_GEQRT((double)(m_), (double)(n_)) + 2.0 * FADDS_GEQRT((double)(m_), (double)(n_)) )
#define FLOPS_CGEQRT(m_, n_) (6. * FMULS_GEQRT((double)(m_), (double)(n_)) + 2.0 * FADDS_GEQRT((double)(m_), (double)(n_)) )
#define FLOPS_DGEQRT(m_, n_) ( FMULS_GEQRT((double)(m_), (double)(n_)) + FADDS_GEQRT((double)(m_), (double)(n_)) )
#define FLOPS_SGEQRT(m_, n_) ( FMULS_GEQRT((double)(m_), (double)(n_)) + FADDS_GEQRT((double)(m_), (double)(n_)) )
#define FLOPS_ZGEQLF(m_, n_) (6. * FMULS_GEQLF((double)(m_), (double)(n_)) + 2.0 * FADDS_GEQLF((double)(m_), (double)(n_)) )
#define FLOPS_CGEQLF(m_, n_) (6. * FMULS_GEQLF((double)(m_), (double)(n_)) + 2.0 * FADDS_GEQLF((double)(m_), (double)(n_)) )
#define FLOPS_DGEQLF(m_, n_) ( FMULS_GEQLF((double)(m_), (double)(n_)) + FADDS_GEQLF((double)(m_), (double)(n_)) )
#define FLOPS_SGEQLF(m_, n_) ( FMULS_GEQLF((double)(m_), (double)(n_)) + FADDS_GEQLF((double)(m_), (double)(n_)) )
#define FLOPS_ZGERQF(m_, n_) (6. * FMULS_GERQF((double)(m_), (double)(n_)) + 2.0 * FADDS_GERQF((double)(m_), (double)(n_)) )
#define FLOPS_CGERQF(m_, n_) (6. * FMULS_GERQF((double)(m_), (double)(n_)) + 2.0 * FADDS_GERQF((double)(m_), (double)(n_)) )
#define FLOPS_DGERQF(m_, n_) ( FMULS_GERQF((double)(m_), (double)(n_)) + FADDS_GERQF((double)(m_), (double)(n_)) )
#define FLOPS_SGERQF(m_, n_) ( FMULS_GERQF((double)(m_), (double)(n_)) + FADDS_GERQF((double)(m_), (double)(n_)) )
#define FLOPS_ZGELQF(m_, n_) (6. * FMULS_GELQF((double)(m_), (double)(n_)) + 2.0 * FADDS_GELQF((double)(m_), (double)(n_)) )
#define FLOPS_CGELQF(m_, n_) (6. * FMULS_GELQF((double)(m_), (double)(n_)) + 2.0 * FADDS_GELQF((double)(m_), (double)(n_)) )
#define FLOPS_DGELQF(m_, n_) ( FMULS_GELQF((double)(m_), (double)(n_)) + FADDS_GELQF((double)(m_), (double)(n_)) )
#define FLOPS_SGELQF(m_, n_) ( FMULS_GELQF((double)(m_), (double)(n_)) + FADDS_GELQF((double)(m_), (double)(n_)) )
#define FLOPS_ZUNGQR(m_, n_, k_) (6. * FMULS_UNGQR((double)(m_), (double)(n_), (double)(k_)) + 2.0 * FADDS_UNGQR((double)(m_), (double)(n_), (double)(k_)) )
#define FLOPS_CUNGQR(m_, n_, k_) (6. * FMULS_UNGQR((double)(m_), (double)(n_), (double)(k_)) + 2.0 * FADDS_UNGQR((double)(m_), (double)(n_), (double)(k_)) )
#define FLOPS_DORGQR(m_, n_, k_) ( FMULS_UNGQR((double)(m_), (double)(n_), (double)(k_)) + FADDS_UNGQR((double)(m_), (double)(n_), (double)(k_)) )
#define FLOPS_SORGQR(m_, n_, k_) ( FMULS_UNGQR((double)(m_), (double)(n_), (double)(k_)) + FADDS_UNGQR((double)(m_), (double)(n_), (double)(k_)) )
#define FLOPS_ZUNGQL(m_, n_, k_) (6. * FMULS_UNGQL((double)(m_), (double)(n_), (double)(k_)) + 2.0 * FADDS_UNGQL((double)(m_), (double)(n_), (double)(k_)) )
#define FLOPS_CUNGQL(m_, n_, k_) (6. * FMULS_UNGQL((double)(m_), (double)(n_), (double)(k_)) + 2.0 * FADDS_UNGQL((double)(m_), (double)(n_), (double)(k_)) )
#define FLOPS_DORGQL(m_, n_, k_) ( FMULS_UNGQL((double)(m_), (double)(n_), (double)(k_)) + FADDS_UNGQL((double)(m_), (double)(n_), (double)(k_)) )
#define FLOPS_SORGQL(m_, n_, k_) ( FMULS_UNGQL((double)(m_), (double)(n_), (double)(k_)) + FADDS_UNGQL((double)(m_), (double)(n_), (double)(k_)) )
#define FLOPS_ZUNGRQ(m_, n_, k_) (6. * FMULS_UNGRQ((double)(m_), (double)(n_), (double)(k_)) + 2.0 * FADDS_UNGRQ((double)(m_), (double)(n_), (double)(k_)) )
#define FLOPS_CUNGRQ(m_, n_, k_) (6. * FMULS_UNGRQ((double)(m_), (double)(n_), (double)(k_)) + 2.0 * FADDS_UNGRQ((double)(m_), (double)(n_), (double)(k_)) )
#define FLOPS_DORGRQ(m_, n_, k_) ( FMULS_UNGRQ((double)(m_), (double)(n_), (double)(k_)) + FADDS_UNGRQ((double)(m_), (double)(n_), (double)(k_)) )
#define FLOPS_SORGRQ(m_, n_, k_) ( FMULS_UNGRQ((double)(m_), (double)(n_), (double)(k_)) + FADDS_UNGRQ((double)(m_), (double)(n_), (double)(k_)) )
#define FLOPS_ZUNGLQ(m_, n_, k_) (6. * FMULS_UNGLQ((double)(m_), (double)(n_), (double)(k_)) + 2.0 * FADDS_UNGLQ((double)(m_), (double)(n_), (double)(k_)) )
#define FLOPS_CUNGLQ(m_, n_, k_) (6. * FMULS_UNGLQ((double)(m_), (double)(n_), (double)(k_)) + 2.0 * FADDS_UNGLQ((double)(m_), (double)(n_), (double)(k_)) )
#define FLOPS_DORGLQ(m_, n_, k_) ( FMULS_UNGLQ((double)(m_), (double)(n_), (double)(k_)) + FADDS_UNGLQ((double)(m_), (double)(n_), (double)(k_)) )
#define FLOPS_SORGLQ(m_, n_, k_) ( FMULS_UNGLQ((double)(m_), (double)(n_), (double)(k_)) + FADDS_UNGLQ((double)(m_), (double)(n_), (double)(k_)) )
#define FLOPS_ZUNMQR(m_, n_, k_, side_) (6. * FMULS_UNMQR((double)(m_), (double)(n_), (double)(k_), (side_)) + 2.0 * FADDS_UNMQR((double)(m_), (double)(n_), (double)(k_), (side_)) )
#define FLOPS_CUNMQR(m_, n_, k_, side_) (6. * FMULS_UNMQR((double)(m_), (double)(n_), (double)(k_), (side_)) + 2.0 * FADDS_UNMQR((double)(m_), (double)(n_), (double)(k_), (side_)) )
#define FLOPS_DORMQR(m_, n_, k_, side_) ( FMULS_UNMQR((double)(m_), (double)(n_), (double)(k_), (side_)) + FADDS_UNMQR((double)(m_), (double)(n_), (double)(k_), (side_)) )
#define FLOPS_SORMQR(m_, n_, k_, side_) ( FMULS_UNMQR((double)(m_), (double)(n_), (double)(k_), (side_)) + FADDS_UNMQR((double)(m_), (double)(n_), (double)(k_), (side_)) )
#define FLOPS_ZUNMQL(m_, n_, k_, side_) (6. * FMULS_UNMQL((double)(m_), (double)(n_), (double)(k_), (side_)) + 2.0 * FADDS_UNMQL((double)(m_), (double)(n_), (double)(k_), (side_)) )
#define FLOPS_CUNMQL(m_, n_, k_, side_) (6. * FMULS_UNMQL((double)(m_), (double)(n_), (double)(k_), (side_)) + 2.0 * FADDS_UNMQL((double)(m_), (double)(n_), (double)(k_), (side_)) )
#define FLOPS_DORMQL(m_, n_, k_, side_) ( FMULS_UNMQL((double)(m_), (double)(n_), (double)(k_), (side_)) + FADDS_UNMQL((double)(m_), (double)(n_), (double)(k_), (side_)) )
#define FLOPS_SORMQL(m_, n_, k_, side_) ( FMULS_UNMQL((double)(m_), (double)(n_), (double)(k_), (side_)) + FADDS_UNMQL((double)(m_), (double)(n_), (double)(k_), (side_)) )
#define FLOPS_ZUNMRQ(m_, n_, k_, side_) (6. * FMULS_UNMRQ((double)(m_), (double)(n_), (double)(k_), (side_)) + 2.0 * FADDS_UNMRQ((double)(m_), (double)(n_), (double)(k_), (side_)) )
#define FLOPS_CUNMRQ(m_, n_, k_, side_) (6. * FMULS_UNMRQ((double)(m_), (double)(n_), (double)(k_), (side_)) + 2.0 * FADDS_UNMRQ((double)(m_), (double)(n_), (double)(k_), (side_)) )
#define FLOPS_DORMRQ(m_, n_, k_, side_) ( FMULS_UNMRQ((double)(m_), (double)(n_), (double)(k_), (side_)) + FADDS_UNMRQ((double)(m_), (double)(n_), (double)(k_), (side_)) )
#define FLOPS_SORMRQ(m_, n_, k_, side_) ( FMULS_UNMRQ((double)(m_), (double)(n_), (double)(k_), (side_)) + FADDS_UNMRQ((double)(m_), (double)(n_), (double)(k_), (side_)) )
#define FLOPS_ZUNMLQ(m_, n_, k_, side_) (6. * FMULS_UNMLQ((double)(m_), (double)(n_), (double)(k_), (side_)) + 2.0 * FADDS_UNMLQ((double)(m_), (double)(n_), (double)(k_), (side_)) )
#define FLOPS_CUNMLQ(m_, n_, k_, side_) (6. * FMULS_UNMLQ((double)(m_), (double)(n_), (double)(k_), (side_)) + 2.0 * FADDS_UNMLQ((double)(m_), (double)(n_), (double)(k_), (side_)) )
#define FLOPS_DORMLQ(m_, n_, k_, side_) ( FMULS_UNMLQ((double)(m_), (double)(n_), (double)(k_), (side_)) + FADDS_UNMLQ((double)(m_), (double)(n_), (double)(k_), (side_)) )
#define FLOPS_SORMLQ(m_, n_, k_, side_) ( FMULS_UNMLQ((double)(m_), (double)(n_), (double)(k_), (side_)) + FADDS_UNMLQ((double)(m_), (double)(n_), (double)(k_), (side_)) )
#define FLOPS_ZGEQRS(m_, n_, nrhs_) (6. * FMULS_GEQRS((double)(m_), (double)(n_), (double)(nrhs_)) + 2.0 * FADDS_GEQRS((double)(m_), (double)(n_), (double)(nrhs_)) )
#define FLOPS_CGEQRS(m_, n_, nrhs_) (6. * FMULS_GEQRS((double)(m_), (double)(n_), (double)(nrhs_)) + 2.0 * FADDS_GEQRS((double)(m_), (double)(n_), (double)(nrhs_)) )
#define FLOPS_DGEQRS(m_, n_, nrhs_) ( FMULS_GEQRS((double)(m_), (double)(n_), (double)(nrhs_)) + FADDS_GEQRS((double)(m_), (double)(n_), (double)(nrhs_)) )
#define FLOPS_SGEQRS(m_, n_, nrhs_) ( FMULS_GEQRS((double)(m_), (double)(n_), (double)(nrhs_)) + FADDS_GEQRS((double)(m_), (double)(n_), (double)(nrhs_)) )
#define FLOPS_ZTRTRI(n_) (6. * FMULS_TRTRI((double)(n_)) + 2.0 * FADDS_TRTRI((double)(n_)) )
#define FLOPS_CTRTRI(n_) (6. * FMULS_TRTRI((double)(n_)) + 2.0 * FADDS_TRTRI((double)(n_)) )
#define FLOPS_DTRTRI(n_) ( FMULS_TRTRI((double)(n_)) + FADDS_TRTRI((double)(n_)) )
#define FLOPS_STRTRI(n_) ( FMULS_TRTRI((double)(n_)) + FADDS_TRTRI((double)(n_)) )
#define FLOPS_ZGEHRD(n_) (6. * FMULS_GEHRD((double)(n_)) + 2.0 * FADDS_GEHRD((double)(n_)) )
#define FLOPS_CGEHRD(n_) (6. * FMULS_GEHRD((double)(n_)) + 2.0 * FADDS_GEHRD((double)(n_)) )
#define FLOPS_DGEHRD(n_) ( FMULS_GEHRD((double)(n_)) + FADDS_GEHRD((double)(n_)) )
#define FLOPS_SGEHRD(n_) ( FMULS_GEHRD((double)(n_)) + FADDS_GEHRD((double)(n_)) )
#define FLOPS_ZHETRD(n_) (6. * FMULS_HETRD((double)(n_)) + 2.0 * FADDS_HETRD((double)(n_)) )
#define FLOPS_CHETRD(n_) (6. * FMULS_HETRD((double)(n_)) + 2.0 * FADDS_HETRD((double)(n_)) )
#define FLOPS_ZSYTRD(n_) (6. * FMULS_SYTRD((double)(n_)) + 2.0 * FADDS_SYTRD((double)(n_)) )
#define FLOPS_CSYTRD(n_) (6. * FMULS_SYTRD((double)(n_)) + 2.0 * FADDS_SYTRD((double)(n_)) )
#define FLOPS_DSYTRD(n_) ( FMULS_SYTRD((double)(n_)) + FADDS_SYTRD((double)(n_)) )
#define FLOPS_SSYTRD(n_) ( FMULS_SYTRD((double)(n_)) + FADDS_SYTRD((double)(n_)) )
#define FLOPS_ZGEBRD(m_, n_) (6. * FMULS_GEBRD((double)(m_), (double)(n_)) + 2.0 * FADDS_GEBRD((double)(m_), (double)(n_)) )
#define FLOPS_CGEBRD(m_, n_) (6. * FMULS_GEBRD((double)(m_), (double)(n_)) + 2.0 * FADDS_GEBRD((double)(m_), (double)(n_)) )
#define FLOPS_DGEBRD(m_, n_) ( FMULS_GEBRD((double)(m_), (double)(n_)) + FADDS_GEBRD((double)(m_), (double)(n_)) )
#define FLOPS_SGEBRD(m_, n_) ( FMULS_GEBRD((double)(m_), (double)(n_)) + FADDS_GEBRD((double)(m_), (double)(n_)) )
#define FLOPS_ZLARFG(n_) (6. * FMULS_LARFG((double)n_) + 2. * FADDS_LARFG((double)n_) )
#define FLOPS_CLARFG(n_) (6. * FMULS_LARFG((double)n_) + 2. * FADDS_LARFG((double)n_) )
#define FLOPS_DLARFG(n_) ( FMULS_LARFG((double)n_) + FADDS_LARFG((double)n_) )
#define FLOPS_SLARFG(n_) ( FMULS_LARFG((double)n_) + FADDS_LARFG((double)n_) )
#endif /* MAGMA_FLOPS_H */
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