You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
131 lines
4.9 KiB
131 lines
4.9 KiB
!> \brief \b LA_CONSTANTS is a module for the scaling constants for the compiled Fortran single and double precisions
|
|
!
|
|
! =========== DOCUMENTATION ===========
|
|
!
|
|
! Online html documentation available at
|
|
! http://www.netlib.org/lapack/explore-html/
|
|
!
|
|
! Authors:
|
|
! ========
|
|
!
|
|
!> \author Edward Anderson, Lockheed Martin
|
|
!
|
|
!> \date May 2016
|
|
!
|
|
!> \ingroup OTHERauxiliary
|
|
!
|
|
!> \par Contributors:
|
|
! ==================
|
|
!>
|
|
!> Weslley Pereira, University of Colorado Denver, USA
|
|
!> Nick Papior, Technical University of Denmark, DK
|
|
!
|
|
!> \par Further Details:
|
|
! =====================
|
|
!>
|
|
!> \verbatim
|
|
!>
|
|
!> Anderson E. (2017)
|
|
!> Algorithm 978: Safe Scaling in the Level 1 BLAS
|
|
!> ACM Trans Math Softw 44:1--28
|
|
!> https://doi.org/10.1145/3061665
|
|
!>
|
|
!> Blue, James L. (1978)
|
|
!> A Portable Fortran Program to Find the Euclidean Norm of a Vector
|
|
!> ACM Trans Math Softw 4:15--23
|
|
!> https://doi.org/10.1145/355769.355771
|
|
!>
|
|
!> \endverbatim
|
|
!
|
|
module LA_CONSTANTS
|
|
! -- LAPACK auxiliary module --
|
|
! -- LAPACK is a software package provided by Univ. of Tennessee, --
|
|
! -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
|
|
|
! Standard constants for
|
|
integer, parameter :: sp = kind(1.e0)
|
|
|
|
real(sp), parameter :: szero = 0.0_sp
|
|
real(sp), parameter :: shalf = 0.5_sp
|
|
real(sp), parameter :: sone = 1.0_sp
|
|
real(sp), parameter :: stwo = 2.0_sp
|
|
real(sp), parameter :: sthree = 3.0_sp
|
|
real(sp), parameter :: sfour = 4.0_sp
|
|
real(sp), parameter :: seight = 8.0_sp
|
|
real(sp), parameter :: sten = 10.0_sp
|
|
complex(sp), parameter :: czero = ( 0.0_sp, 0.0_sp )
|
|
complex(sp), parameter :: chalf = ( 0.5_sp, 0.0_sp )
|
|
complex(sp), parameter :: cone = ( 1.0_sp, 0.0_sp )
|
|
character*1, parameter :: sprefix = 'S'
|
|
character*1, parameter :: cprefix = 'C'
|
|
|
|
! Scaling constants
|
|
real(sp), parameter :: sulp = epsilon(0._sp)
|
|
real(sp), parameter :: seps = sulp * 0.5_sp
|
|
real(sp), parameter :: ssafmin = real(radix(0._sp),sp)**max( &
|
|
minexponent(0._sp)-1, &
|
|
1-maxexponent(0._sp) &
|
|
)
|
|
real(sp), parameter :: ssafmax = sone / ssafmin
|
|
real(sp), parameter :: ssmlnum = ssafmin / sulp
|
|
real(sp), parameter :: sbignum = ssafmax * sulp
|
|
real(sp), parameter :: srtmin = sqrt(ssmlnum)
|
|
real(sp), parameter :: srtmax = sqrt(sbignum)
|
|
|
|
! Blue's scaling constants
|
|
real(sp), parameter :: stsml = real(radix(0._sp), sp)**ceiling( &
|
|
(minexponent(0._sp) - 1) * 0.5_sp)
|
|
real(sp), parameter :: stbig = real(radix(0._sp), sp)**floor( &
|
|
(maxexponent(0._sp) - digits(0._sp) + 1) * 0.5_sp)
|
|
! ssml >= 1/s, where s was defined in https://doi.org/10.1145/355769.355771
|
|
! The correction was added in https://doi.org/10.1145/3061665 to scale denormalized numbers correctly
|
|
real(sp), parameter :: sssml = real(radix(0._sp), sp)**( - floor( &
|
|
(minexponent(0._sp) - digits(0._sp)) * 0.5_sp))
|
|
! sbig = 1/S, where S was defined in https://doi.org/10.1145/355769.355771
|
|
real(sp), parameter :: ssbig = real(radix(0._sp), sp)**( - ceiling( &
|
|
(maxexponent(0._sp) + digits(0._sp) - 1) * 0.5_sp))
|
|
|
|
! Standard constants for
|
|
integer, parameter :: dp = kind(1.d0)
|
|
|
|
real(dp), parameter :: dzero = 0.0_dp
|
|
real(dp), parameter :: dhalf = 0.5_dp
|
|
real(dp), parameter :: done = 1.0_dp
|
|
real(dp), parameter :: dtwo = 2.0_dp
|
|
real(dp), parameter :: dthree = 3.0_dp
|
|
real(dp), parameter :: dfour = 4.0_dp
|
|
real(dp), parameter :: deight = 8.0_dp
|
|
real(dp), parameter :: dten = 10.0_dp
|
|
complex(dp), parameter :: zzero = ( 0.0_dp, 0.0_dp )
|
|
complex(dp), parameter :: zhalf = ( 0.5_dp, 0.0_dp )
|
|
complex(dp), parameter :: zone = ( 1.0_dp, 0.0_dp )
|
|
character*1, parameter :: dprefix = 'D'
|
|
character*1, parameter :: zprefix = 'Z'
|
|
|
|
! Scaling constants
|
|
real(dp), parameter :: dulp = epsilon(0._dp)
|
|
real(dp), parameter :: deps = dulp * 0.5_dp
|
|
real(dp), parameter :: dsafmin = real(radix(0._dp),dp)**max( &
|
|
minexponent(0._dp)-1, &
|
|
1-maxexponent(0._dp) &
|
|
)
|
|
real(dp), parameter :: dsafmax = done / dsafmin
|
|
real(dp), parameter :: dsmlnum = dsafmin / dulp
|
|
real(dp), parameter :: dbignum = dsafmax * dulp
|
|
real(dp), parameter :: drtmin = sqrt(dsmlnum)
|
|
real(dp), parameter :: drtmax = sqrt(dbignum)
|
|
|
|
! Blue's scaling constants
|
|
real(dp), parameter :: dtsml = real(radix(0._dp), dp)**ceiling( &
|
|
(minexponent(0._dp) - 1) * 0.5_dp)
|
|
real(dp), parameter :: dtbig = real(radix(0._dp), dp)**floor( &
|
|
(maxexponent(0._dp) - digits(0._dp) + 1) * 0.5_dp)
|
|
! ssml >= 1/s, where s was defined in https://doi.org/10.1145/355769.355771
|
|
! The correction was added in https://doi.org/10.1145/3061665 to scale denormalized numbers correctly
|
|
real(dp), parameter :: dssml = real(radix(0._dp), dp)**( - floor( &
|
|
(minexponent(0._dp) - digits(0._dp)) * 0.5_dp))
|
|
! sbig = 1/S, where S was defined in https://doi.org/10.1145/355769.355771
|
|
real(dp), parameter :: dsbig = real(radix(0._dp), dp)**( - ceiling( &
|
|
(maxexponent(0._dp) + digits(0._dp) - 1) * 0.5_dp))
|
|
|
|
end module LA_CONSTANTS
|
|
|