la_constants Module Reference

LA_CONSTANTS is a module for the scaling constants for the compiled Fortran single and double precisions More...

Variables
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'
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)
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)
real(sp), parameter	sssml = real(radix(0._sp), sp)**( - floor( (minexponent(0._sp) - digits(0._sp)) * 0.5_sp))
real(sp), parameter	ssbig = real(radix(0._sp), sp)**( - ceiling( (maxexponent(0._sp) + digits(0._sp) - 1) * 0.5_sp))
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'
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)
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)
real(dp), parameter	dssml = real(radix(0._dp), dp)**( - floor( (minexponent(0._dp) - digits(0._dp)) * 0.5_dp))
real(dp), parameter	dsbig = real(radix(0._dp), dp)**( - ceiling( (maxexponent(0._dp) + digits(0._dp) - 1) * 0.5_dp))

Detailed Description

LA_CONSTANTS is a module for the scaling constants for the compiled Fortran single and double precisions

Author

Edward Anderson, Lockheed Martin

Date

May 2016

Contributors:

Weslley Pereira, University of Colorado Denver, USA Nick Papior, Technical University of Denmark, DK

Further Details:

  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