Annotation of rpl/lapack/lapack/la_constants.f90, revision 1.1
1.1 ! bertrand 1: !> \brief \b LA_CONSTANTS is a module for the scaling constants for the compiled Fortran single and double precisions
! 2: !
! 3: ! =========== DOCUMENTATION ===========
! 4: !
! 5: ! Online html documentation available at
! 6: ! http://www.netlib.org/lapack/explore-html/
! 7: !
! 8: ! Authors:
! 9: ! ========
! 10: !
! 11: !> \author Edward Anderson, Lockheed Martin
! 12: !
! 13: !> \date May 2016
! 14: !
! 15: !> \ingroup OTHERauxiliary
! 16: !
! 17: !> \par Contributors:
! 18: ! ==================
! 19: !>
! 20: !> Weslley Pereira, University of Colorado Denver, USA
! 21: !> Nick Papior, Technical University of Denmark, DK
! 22: !
! 23: !> \par Further Details:
! 24: ! =====================
! 25: !>
! 26: !> \verbatim
! 27: !>
! 28: !> Anderson E. (2017)
! 29: !> Algorithm 978: Safe Scaling in the Level 1 BLAS
! 30: !> ACM Trans Math Softw 44:1--28
! 31: !> https://doi.org/10.1145/3061665
! 32: !>
! 33: !> Blue, James L. (1978)
! 34: !> A Portable Fortran Program to Find the Euclidean Norm of a Vector
! 35: !> ACM Trans Math Softw 4:15--23
! 36: !> https://doi.org/10.1145/355769.355771
! 37: !>
! 38: !> \endverbatim
! 39: !
! 40: module LA_CONSTANTS
! 41: ! -- LAPACK auxiliary module --
! 42: ! -- LAPACK is a software package provided by Univ. of Tennessee, --
! 43: ! -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 44:
! 45: ! Standard constants for
! 46: integer, parameter :: sp = kind(1.e0)
! 47:
! 48: real(sp), parameter :: szero = 0.0_sp
! 49: real(sp), parameter :: shalf = 0.5_sp
! 50: real(sp), parameter :: sone = 1.0_sp
! 51: real(sp), parameter :: stwo = 2.0_sp
! 52: real(sp), parameter :: sthree = 3.0_sp
! 53: real(sp), parameter :: sfour = 4.0_sp
! 54: real(sp), parameter :: seight = 8.0_sp
! 55: real(sp), parameter :: sten = 10.0_sp
! 56: complex(sp), parameter :: czero = ( 0.0_sp, 0.0_sp )
! 57: complex(sp), parameter :: chalf = ( 0.5_sp, 0.0_sp )
! 58: complex(sp), parameter :: cone = ( 1.0_sp, 0.0_sp )
! 59: character*1, parameter :: sprefix = 'S'
! 60: character*1, parameter :: cprefix = 'C'
! 61:
! 62: ! Scaling constants
! 63: real(sp), parameter :: sulp = epsilon(0._sp)
! 64: real(sp), parameter :: seps = sulp * 0.5_sp
! 65: real(sp), parameter :: ssafmin = real(radix(0._sp),sp)**max( &
! 66: minexponent(0._sp)-1, &
! 67: 1-maxexponent(0._sp) &
! 68: )
! 69: real(sp), parameter :: ssafmax = sone / ssafmin
! 70: real(sp), parameter :: ssmlnum = ssafmin / sulp
! 71: real(sp), parameter :: sbignum = ssafmax * sulp
! 72: real(sp), parameter :: srtmin = sqrt(ssmlnum)
! 73: real(sp), parameter :: srtmax = sqrt(sbignum)
! 74:
! 75: ! Blue's scaling constants
! 76: real(sp), parameter :: stsml = real(radix(0._sp), sp)**ceiling( &
! 77: (minexponent(0._sp) - 1) * 0.5_sp)
! 78: real(sp), parameter :: stbig = real(radix(0._sp), sp)**floor( &
! 79: (maxexponent(0._sp) - digits(0._sp) + 1) * 0.5_sp)
! 80: ! ssml >= 1/s, where s was defined in https://doi.org/10.1145/355769.355771
! 81: ! The correction was added in https://doi.org/10.1145/3061665 to scale denormalized numbers correctly
! 82: real(sp), parameter :: sssml = real(radix(0._sp), sp)**( - floor( &
! 83: (minexponent(0._sp) - digits(0._sp)) * 0.5_sp))
! 84: ! sbig = 1/S, where S was defined in https://doi.org/10.1145/355769.355771
! 85: real(sp), parameter :: ssbig = real(radix(0._sp), sp)**( - ceiling( &
! 86: (maxexponent(0._sp) + digits(0._sp) - 1) * 0.5_sp))
! 87:
! 88: ! Standard constants for
! 89: integer, parameter :: dp = kind(1.d0)
! 90:
! 91: real(dp), parameter :: dzero = 0.0_dp
! 92: real(dp), parameter :: dhalf = 0.5_dp
! 93: real(dp), parameter :: done = 1.0_dp
! 94: real(dp), parameter :: dtwo = 2.0_dp
! 95: real(dp), parameter :: dthree = 3.0_dp
! 96: real(dp), parameter :: dfour = 4.0_dp
! 97: real(dp), parameter :: deight = 8.0_dp
! 98: real(dp), parameter :: dten = 10.0_dp
! 99: complex(dp), parameter :: zzero = ( 0.0_dp, 0.0_dp )
! 100: complex(dp), parameter :: zhalf = ( 0.5_dp, 0.0_dp )
! 101: complex(dp), parameter :: zone = ( 1.0_dp, 0.0_dp )
! 102: character*1, parameter :: dprefix = 'D'
! 103: character*1, parameter :: zprefix = 'Z'
! 104:
! 105: ! Scaling constants
! 106: real(dp), parameter :: dulp = epsilon(0._dp)
! 107: real(dp), parameter :: deps = dulp * 0.5_dp
! 108: real(dp), parameter :: dsafmin = real(radix(0._dp),dp)**max( &
! 109: minexponent(0._dp)-1, &
! 110: 1-maxexponent(0._dp) &
! 111: )
! 112: real(dp), parameter :: dsafmax = done / dsafmin
! 113: real(dp), parameter :: dsmlnum = dsafmin / dulp
! 114: real(dp), parameter :: dbignum = dsafmax * dulp
! 115: real(dp), parameter :: drtmin = sqrt(dsmlnum)
! 116: real(dp), parameter :: drtmax = sqrt(dbignum)
! 117:
! 118: ! Blue's scaling constants
! 119: real(dp), parameter :: dtsml = real(radix(0._dp), dp)**ceiling( &
! 120: (minexponent(0._dp) - 1) * 0.5_dp)
! 121: real(dp), parameter :: dtbig = real(radix(0._dp), dp)**floor( &
! 122: (maxexponent(0._dp) - digits(0._dp) + 1) * 0.5_dp)
! 123: ! ssml >= 1/s, where s was defined in https://doi.org/10.1145/355769.355771
! 124: ! The correction was added in https://doi.org/10.1145/3061665 to scale denormalized numbers correctly
! 125: real(dp), parameter :: dssml = real(radix(0._dp), dp)**( - floor( &
! 126: (minexponent(0._dp) - digits(0._dp)) * 0.5_dp))
! 127: ! sbig = 1/S, where S was defined in https://doi.org/10.1145/355769.355771
! 128: real(dp), parameter :: dsbig = real(radix(0._dp), dp)**( - ceiling( &
! 129: (maxexponent(0._dp) + digits(0._dp) - 1) * 0.5_dp))
! 130:
! 131: end module LA_CONSTANTS
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