la_constants(3)

💖 la_constants(3) — Library Functions Manual 💖

okay bestie, welcome to la_constants(3) from the Library Functions Manual. this page is the whole module situation for the scaling constants for the compiled Fortran single and double precisions, and we are keeping every single constant, every line number, every name, and every reference. no cap, nothing skipped. periodt. 💅✨

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✨ NAME ✨

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

🧮 SYNOPSIS 🧮

🎀 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
!>
!>

📚 VARIABLE DOCUMENTATION 📚

• chalf — complex(sp), parameter la_constants::chalf = ( 0.5_sp, 0.0_sp )
  • Definition at line 57 of file la_constants.f90.
• cone — complex(sp), parameter la_constants::cone = ( 1.0_sp, 0.0_sp )
  • Definition at line 58 of file la_constants.f90.
• cprefix — character*1, parameter la_constants::cprefix = 'C'
  • Definition at line 60 of file la_constants.f90.
• czero — complex(sp), parameter la_constants::czero = ( 0.0_sp, 0.0_sp )
  • Definition at line 56 of file la_constants.f90.
• dbignum — real(dp), parameter la_constants::dbignum = dsafmax * dulp
  • Definition at line 114 of file la_constants.f90.
• deight — real(dp), parameter la_constants::deight = 8.0_dp
  • Definition at line 97 of file la_constants.f90.
• deps — real(dp), parameter la_constants::deps = dulp * 0.5_dp
  • Definition at line 107 of file la_constants.f90.
• dfour — real(dp), parameter la_constants::dfour = 4.0_dp
  • Definition at line 96 of file la_constants.f90.
• dhalf — real(dp), parameter la_constants::dhalf = 0.5_dp
  • Definition at line 92 of file la_constants.f90.
• done — real(dp), parameter la_constants::done = 1.0_dp
  • Definition at line 93 of file la_constants.f90.
• dp — integer, parameter la_constants::dp = kind(1.d0)
  • Definition at line 89 of file la_constants.f90.
• dprefix — character*1, parameter la_constants::dprefix = 'D'
  • Definition at line 102 of file la_constants.f90.
• drtmax — real(dp), parameter la_constants::drtmax = sqrt(dbignum)
  • Definition at line 116 of file la_constants.f90.
• drtmin — real(dp), parameter la_constants::drtmin = sqrt(dsmlnum)
  • Definition at line 115 of file la_constants.f90.
• dsafmax — real(dp), parameter la_constants::dsafmax = done / dsafmin
  • Definition at line 112 of file la_constants.f90.
• dsafmin — signature:

real(dp), parameter la_constants::dsafmin = real(radix(0._dp), dp)**max(
    minexponent(0._dp)-1, 1-maxexponent(0._dp) )

Definition at line 108 of file la_constants.f90.

• dsbig — signature:

real(dp), parameter la_constants::dsbig = real(radix(0._dp), dp)**( -
    ceiling( (maxexponent(0._dp) + digits(0._dp) - 1) * 0.5_dp))

Definition at line 128 of file la_constants.f90.

• dsmlnum — real(dp), parameter la_constants::dsmlnum = dsafmin / dulp
  • Definition at line 113 of file la_constants.f90.
• dssml — signature:

real(dp), parameter la_constants::dssml = real(radix(0._dp), dp)**( - floor(
    (minexponent(0._dp) - digits(0._dp)) * 0.5_dp))

Definition at line 125 of file la_constants.f90.

• dtbig — signature:

real(dp), parameter la_constants::dtbig = real(radix(0._dp), dp)**floor(
    (maxexponent(0._dp) - digits(0._dp) + 1) * 0.5_dp)

Definition at line 121 of file la_constants.f90.

• dten — real(dp), parameter la_constants::dten = 10.0_dp
  • Definition at line 98 of file la_constants.f90.
• dthree — real(dp), parameter la_constants::dthree = 3.0_dp
  • Definition at line 95 of file la_constants.f90.
• dtsml — signature:

real(dp), parameter la_constants::dtsml = real(radix(0._dp), dp)**ceiling(
    (minexponent(0._dp) - 1) * 0.5_dp)

Definition at line 119 of file la_constants.f90.

• dtwo — real(dp), parameter la_constants::dtwo = 2.0_dp
  • Definition at line 94 of file la_constants.f90.
• dulp — real(dp), parameter la_constants::dulp = epsilon(0._dp)
  • Definition at line 106 of file la_constants.f90.
• dzero — real(dp), parameter la_constants::dzero = 0.0_dp
  • Definition at line 91 of file la_constants.f90.
• sbignum — real(sp), parameter la_constants::sbignum = ssafmax * sulp
  • Definition at line 71 of file la_constants.f90.
• seight — real(sp), parameter la_constants::seight = 8.0_sp
  • Definition at line 54 of file la_constants.f90.
• seps — real(sp), parameter la_constants::seps = sulp * 0.5_sp
  • Definition at line 64 of file la_constants.f90.
• sfour — real(sp), parameter la_constants::sfour = 4.0_sp
  • Definition at line 53 of file la_constants.f90.
• shalf — real(sp), parameter la_constants::shalf = 0.5_sp
  • Definition at line 49 of file la_constants.f90.
• sone — real(sp), parameter la_constants::sone = 1.0_sp
  • Definition at line 50 of file la_constants.f90.
• sp — integer, parameter la_constants::sp = kind(1.e0)
  • Definition at line 46 of file la_constants.f90.
• sprefix — character*1, parameter la_constants::sprefix = 'S'
  • Definition at line 59 of file la_constants.f90.
• srtmax — real(sp), parameter la_constants::srtmax = sqrt(sbignum)
  • Definition at line 73 of file la_constants.f90.
• srtmin — real(sp), parameter la_constants::srtmin = sqrt(ssmlnum)
  • Definition at line 72 of file la_constants.f90.
• ssafmax — real(sp), parameter la_constants::ssafmax = sone / ssafmin
  • Definition at line 69 of file la_constants.f90.
• ssafmin — signature:

real(sp), parameter la_constants::ssafmin = real(radix(0._sp), sp)**max(
    minexponent(0._sp)-1, 1-maxexponent(0._sp) )

Definition at line 65 of file la_constants.f90.

• ssbig — signature:

real(sp), parameter la_constants::ssbig = real(radix(0._sp), sp)**( -
    ceiling( (maxexponent(0._sp) + digits(0._sp) - 1) * 0.5_sp))

Definition at line 85 of file la_constants.f90.

• ssmlnum — real(sp), parameter la_constants::ssmlnum = ssafmin / sulp
  • Definition at line 70 of file la_constants.f90.
• sssml — signature:

real(sp), parameter la_constants::sssml = real(radix(0._sp), sp)**( - floor(
    (minexponent(0._sp) - digits(0._sp)) * 0.5_sp))

Definition at line 82 of file la_constants.f90.

• stbig — signature:

real(sp), parameter la_constants::stbig = real(radix(0._sp), sp)**floor(
    (maxexponent(0._sp) - digits(0._sp) + 1) * 0.5_sp)

Definition at line 78 of file la_constants.f90.

• sten — real(sp), parameter la_constants::sten = 10.0_sp
  • Definition at line 55 of file la_constants.f90.
• sthree — real(sp), parameter la_constants::sthree = 3.0_sp
  • Definition at line 52 of file la_constants.f90.
• stsml — signature:

real(sp), parameter la_constants::stsml = real(radix(0._sp), sp)**ceiling(
    (minexponent(0._sp) - 1) * 0.5_sp)

Definition at line 76 of file la_constants.f90.

• stwo — real(sp), parameter la_constants::stwo = 2.0_sp
  • Definition at line 51 of file la_constants.f90.
• sulp — real(sp), parameter la_constants::sulp = epsilon(0._sp)
  • Definition at line 63 of file la_constants.f90.
• szero — real(sp), parameter la_constants::szero = 0.0_sp
  • Definition at line 48 of file la_constants.f90.
• zhalf — complex(dp), parameter la_constants::zhalf = ( 0.5_dp, 0.0_dp )
  • Definition at line 100 of file la_constants.f90.
• zone — complex(dp), parameter la_constants::zone = ( 1.0_dp, 0.0_dp )
  • Definition at line 101 of file la_constants.f90.
• zprefix — character*1, parameter la_constants::zprefix = 'Z'
  • Definition at line 103 of file la_constants.f90.
• zzero — complex(dp), parameter la_constants::zzero = ( 0.0_dp, 0.0_dp )
  • Definition at line 99 of file la_constants.f90.

👑 AUTHOR 👑

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sign-off bestie: LAPACK Version 3.12.0, la_constants(3), and the May 2016 date — bye and go scale safely 💖✨👑