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Ajour de deux modules.

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