402 lines
13 KiB
Fortran
402 lines
13 KiB
Fortran
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!
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!=======================================================================
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!
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MODULE ACCURACY_REAL
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!
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INTEGER, PARAMETER :: SP = SELECTED_REAL_KIND(6, 37) ! single precision
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INTEGER, PARAMETER :: DP = SELECTED_REAL_KIND(15, 307) ! double precision
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INTEGER, PARAMETER :: QP = SELECTED_REAL_KIND(33, 4931) ! quadruple precision
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!
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INTEGER, PARAMETER :: WP = DP ! selected value for code
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!
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END MODULE ACCURACY_REAL
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!
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!=======================================================================
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!
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MODULE ACCURACY_INTEGER
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!
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INTEGER, PARAMETER :: I1 = SELECTED_INT_KIND(8) ! default precision
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INTEGER, PARAMETER :: I2 = SELECTED_INT_KIND(16) ! single precision
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INTEGER, PARAMETER :: I4 = SELECTED_INT_KIND(32) ! double precision
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INTEGER, PARAMETER :: I8 = SELECTED_INT_KIND(64) ! quadruple precision
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!
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INTEGER, PARAMETER :: IW = I1 ! selected value for code
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!
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END MODULE ACCURACY_INTEGER
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!
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!=======================================================================
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!
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MODULE MINMAX_VALUES
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!
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USE ACCURACY_REAL
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USE ACCURACY_INTEGER
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!
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INTEGER (IW) :: III
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!
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REAL (WP) :: XXX
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!
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INTEGER (IW), PARAMETER :: INT_MAX = HUGE(III) ! maximal value of integer
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!
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REAL (WP), PARAMETER :: LN2 = 0.6931471805599453094172321214581765681D0 ! ln(2)
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REAL (WP), PARAMETER :: MAX_2XP = MAXEXPONENT(XXX) ! max value of y so that 2^x is defined
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REAL (WP), PARAMETER :: MIN_2XP = MINEXPONENT(XXX) ! max value of y so that 2^-x is defined
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REAL (WP), PARAMETER :: REL_MIN = TINY(XXX) ! minimum value of real number
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REAL (WP), PARAMETER :: REL_MAX = HUGE(XXX) ! maximum value of real number
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REAL (WP), PARAMETER :: EPS_MIN = EPSILON(XXX) ! smallest value real such that x + epsilon /= x and x = 1
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REAL (WP), PARAMETER :: DGT_SIG = DIGITS(XXX) ! number of significant digits
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!
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CONTAINS
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!
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!=======================================================================
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!
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SUBROUTINE MINMAX_EXP(MAX_EXP,MIN_EXP)
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!
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! This module computes the maximal and minimal exponent
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! so that e^x is defined
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!
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IMPLICIT NONE
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!
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REAL (WP), INTENT(OUT) :: MAX_EXP,MIN_EXP
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!
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REAL (WP), PARAMETER :: LN2 = 0.6931471805599453094172321214581765681D0 ! ln(2)
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!
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MAX_EXP = INT(MAXEXPONENT(XXX) * LN2) ! max value of y so that e^x is defined
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MIN_EXP = INT(MINEXPONENT(XXX) * LN2) ! max value of y so that e^-x is defined
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!
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END SUBROUTINE MINMAX_EXP
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!
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END MODULE MINMAX_VALUES
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!
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!=======================================================================
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!
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MODULE MACHINE_ACCURACY
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!
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! This module provides the AMOS legacy routines for machine accuracy:
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!
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! * FUNCTION D1MACH(I) --> double precision reals
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!
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! * FUNCTION I1MACH(I) --> integers
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!
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! * FUNCTION R1MACH(I) --> single precision reals
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!
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!
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USE ACCURACY_REAL
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USE ACCURACY_INTEGER
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!
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CONTAINS
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!
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!=======================================================================
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!
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FUNCTION D1MACH(I)
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!
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IMPLICIT NONE
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!
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INTEGER (IW) :: I
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!
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REAL (WP) :: D1MACH
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REAL (WP) :: B,X
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!
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!***BEGIN PROLOGUE D1MACH
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!***PURPOSE Return floating point machine dependent constants.
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!***LIBRARY SLATEC
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!***CATEGORY R1
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!***TYPE SINGLE PRECISION (D1MACH-S, D1MACH-D)
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!***KEYWORDS MACHINE CONSTANTS
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!***AUTHOR Fox, P. A., (Bell Labs)
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! Hall, A. D., (Bell Labs)
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! Schryer, N. L., (Bell Labs)
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!***DESCRIPTION
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!
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! D1MACH can be used to obtain machine-dependent parameters for the
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! local machine environment. It is a function subprogram with one
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! (input) argument, and can be referenced as follows:
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!
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! A = D1MACH(I)
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!
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! where I=1,...,5. The (output) value of A above is determined by
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! the (input) value of I. The results for various values of I are
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! discussed below.
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!
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! D1MACH(1) = B**(EMIN-1), the smallest positive magnitude.
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! D1MACH(2) = B**EMAX*(1 - B**(-T)), the largest magnitude.
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! D1MACH(3) = B**(-T), the smallest relative spacing.
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! D1MACH(4) = B**(1-T), the largest relative spacing.
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! D1MACH(5) = LOG10(B)
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!
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! Assume single precision numbers are represented in the T-digit,
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! base-B form
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!
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! sign (B**E)*( (X(1)/B) + ... + (X(T)/B**T) )
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!
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! where 0 .LE. X(I) .LT. B for I=1,...,T, 0 .LT. X(1), and
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! EMIN .LE. E .LE. EMAX.
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!
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! The values of B, T, EMIN and EMAX are provided in I1MACH as
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! follows:
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! I1MACH(10) = B, the base.
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! I1MACH(11) = T, the number of base-B digits.
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! I1MACH(12) = EMIN, the smallest exponent E.
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! I1MACH(13) = EMAX, the largest exponent E.
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!
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!
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!***REFERENCES P. A. Fox, A. D. Hall and N. L. Schryer, Framework for
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! a portable library, ACM Transactions on Mathematical
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! Software 4, 2 (June 1978), pp. 177-188.
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!***ROUTINES CALLED XERMSG
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!***REVISION HISTORY (YYMMDD)
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! 790101 DATE WRITTEN
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! 960329 Modified for Fortran 90 (BE after suggestions by EHG)
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!***END PROLOGUE D1MACH
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!
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X = 1.0E0_WP
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B = RADIX(X)
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!
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SELECT CASE (I)
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CASE (1)
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D1MACH = B**(MINEXPONENT(X)-1) ! the smallest positive magnitude.
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CASE (2)
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D1MACH = HUGE(X) ! the largest magnitude.
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CASE (3)
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D1MACH = B**(-DIGITS(X)) ! the smallest relative spacing.
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CASE (4)
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D1MACH = B**(1-DIGITS(X)) ! the largest relative spacing.
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CASE (5)
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D1MACH = LOG10(B)
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CASE DEFAULT
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WRITE (*,10)
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STOP
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END SELECT
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!
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! Formats:
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!
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10 FORMAT ('1ERROR 1 in D1MACH - I out of bounds')
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!
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END FUNCTION D1MACH
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!
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!=======================================================================
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!
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FUNCTION I1MACH(I)
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!
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IMPLICIT NONE
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!
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INTEGER :: I,I1MACH
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!
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REAL (SP) :: X
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!
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REAL (WP) :: XX
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!
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!***BEGIN PROLOGUE I1MACH
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!***PURPOSE Return integer machine dependent constants.
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!***LIBRARY SLATEC
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!***CATEGORY R1
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!***TYPE INTEGER (I1MACH-I)
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!***KEYWORDS MACHINE CONSTANTS
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!***AUTHOR Fox, P. A., (Bell Labs)
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! Hall, A. D., (Bell Labs)
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! Schryer, N. L., (Bell Labs)
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!***DESCRIPTION
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!
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! I1MACH can be used to obtain machine-dependent parameters for the
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! local machine environment. It is a function subprogram with one
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! (input) argument and can be referenced as follows:
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!
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! K = I1MACH(I)
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!
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! where I=1,...,16. The (output) value of K above is determined by
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! the (input) value of I. The results for various values of I are
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! discussed below.
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!
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! I/O unit numbers:
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! I1MACH( 1) = the standard input unit.
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! I1MACH( 2) = the standard output unit.
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! I1MACH( 3) = the standard punch unit.
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! I1MACH( 4) = the standard error message unit.
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!
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! Words:
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! I1MACH( 5) = the number of bits per integer storage unit.
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! I1MACH( 6) = the number of characters per integer storage unit.
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!
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! Integers:
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! assume integers are represented in the S-digit, base-A form
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!
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! sign ( X(S-1)*A**(S-1) + ... + X(1)*A + X(0) )
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!
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! where 0 .LE. X(I) .LT. A for I=0,...,S-1.
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! I1MACH( 7) = A, the base.
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! I1MACH( 8) = S, the number of base-A digits.
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! I1MACH( 9) = A**S - 1, the largest magnitude.
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!
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! Floating-Point Numbers:
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! Assume floating-point numbers are represented in the T-digit,
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! base-B form
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! sign (B**E)*( (X(1)/B) + ... + (X(T)/B**T) )
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!
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! where 0 .LE. X(I) .LT. B for I=1,...,T,
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! 0 .LT. X(1), and EMIN .LE. E .LE. EMAX.
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! I1MACH(10) = B, the base.
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!
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! Single-Precision:
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! I1MACH(11) = T, the number of base-B digits.
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! I1MACH(12) = EMIN, the smallest exponent E.
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! I1MACH(13) = EMAX, the largest exponent E.
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!
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! Double-Precision:
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! I1MACH(14) = T, the number of base-B digits.
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! I1MACH(15) = EMIN, the smallest exponent E.
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! I1MACH(16) = EMAX, the largest exponent E.
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!
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! To alter this function for a particular environment, the desired
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! set of DATA statements should be activated by removing the C from
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! column 1. Also, the values of I1MACH(1) - I1MACH(4) should be
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! checked for consistency with the local operating system.
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!
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!***REFERENCES P. A. Fox, A. D. Hall and N. L. Schryer, Framework for
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! a portable library, ACM Transactions on Mathematical
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! Software 4, 2 (June 1978), pp. 177-188.
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!***ROUTINES CALLED (NONE)
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!***REVISION HISTORY (YYMMDD)
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! 750101 DATE WRITTEN
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! 960411 Modified for Fortran 90 (BE after suggestions by EHG).
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! 980727 Modified value of I1MACH(6) (BE after suggestion by EHG).
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!***END PROLOGUE I1MACH
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!
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X = 1.0
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XX = 1.0E0_WP
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SELECT CASE (I)
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CASE (1)
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I1MACH = 5 ! Input unit
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CASE (2)
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I1MACH = 6 ! Output unit
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CASE (3)
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I1MACH = 0 ! Punch unit is no longer used
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CASE (4)
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I1MACH = 0 ! Error message unit
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CASE (5)
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I1MACH = BIT_SIZE(I)
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CASE (6)
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I1MACH = 4 ! Characters per integer is hopefully no
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! longer used.
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! If it is used it has to be set manually.
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! The value 4 is correct on IEEE-machines.
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CASE (7)
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I1MACH = RADIX(1)
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CASE (8)
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I1MACH = BIT_SIZE(I) - 1
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CASE (9)
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I1MACH = HUGE(1)
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CASE (10)
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I1MACH = RADIX(X)
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CASE (11)
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I1MACH = DIGITS(X)
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CASE (12)
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I1MACH = MINEXPONENT(X)
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CASE (13)
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I1MACH = MAXEXPONENT(X)
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CASE (14)
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I1MACH = DIGITS(XX)
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CASE (15)
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I1MACH = MINEXPONENT(XX)
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CASE (16)
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I1MACH = MAXEXPONENT(XX)
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CASE DEFAULT
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WRITE (*,10)
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STOP
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END SELECT
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!
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! Formats
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!
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10 FORMAT ('Fatal in I1MACH - I out of bounds')
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!
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END FUNCTION I1MACH
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!
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!=======================================================================
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!
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FUNCTION R1MACH (I)
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!
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IMPLICIT NONE
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!
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INTEGER :: I
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!
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REAL (SP) :: B,X,R1MACH
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!
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!***BEGIN PROLOGUE R1MACH
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!***PURPOSE Return floating point machine dependent constants.
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!***LIBRARY SLATEC
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!***CATEGORY R1
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!***TYPE SINGLE PRECISION (R1MACH-S, D1MACH-D)
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!***KEYWORDS MACHINE CONSTANTS
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!***AUTHOR Fox, P. A., (Bell Labs)
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! Hall, A. D., (Bell Labs)
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! Schryer, N. L., (Bell Labs)
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!***DESCRIPTION
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!
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! R1MACH can be used to obtain machine-dependent parameters for the
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! local machine environment. It is a function subprogram with one
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! (input) argument, and can be referenced as follows:
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!
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! A = R1MACH(I)
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!
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! where I=1,...,5. The (output) value of A above is determined by
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! the (input) value of I. The results for various values of I are
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! discussed below.
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!
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! R1MACH(1) = B**(EMIN-1), the smallest positive magnitude.
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! R1MACH(2) = B**EMAX*(1 - B**(-T)), the largest magnitude.
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! R1MACH(3) = B**(-T), the smallest relative spacing.
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! R1MACH(4) = B**(1-T), the largest relative spacing.
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! R1MACH(5) = LOG10(B)
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!
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! Assume single precision numbers are represented in the T-digit,
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||
|
|
! base-B form
|
||
|
|
!
|
||
|
|
! sign (B**E)*( (X(1)/B) + ... + (X(T)/B**T) )
|
||
|
|
!
|
||
|
|
! where 0 .LE. X(I) .LT. B for I=1,...,T, 0 .LT. X(1), and
|
||
|
|
! EMIN .LE. E .LE. EMAX.
|
||
|
|
!
|
||
|
|
! The values of B, T, EMIN and EMAX are provided in I1MACH as
|
||
|
|
! follows:
|
||
|
|
! I1MACH(10) = B, the base.
|
||
|
|
! I1MACH(11) = T, the number of base-B digits.
|
||
|
|
! I1MACH(12) = EMIN, the smallest exponent E.
|
||
|
|
! I1MACH(13) = EMAX, the largest exponent E.
|
||
|
|
!
|
||
|
|
!
|
||
|
|
!***REFERENCES P. A. Fox, A. D. Hall and N. L. Schryer, Framework for
|
||
|
|
! a portable library, ACM Transactions on Mathematical
|
||
|
|
! Software 4, 2 (June 1978), pp. 177-188.
|
||
|
|
!***ROUTINES CALLED XERMSG
|
||
|
|
!***REVISION HISTORY (YYMMDD)
|
||
|
|
! 790101 DATE WRITTEN
|
||
|
|
! 960329 Modified for Fortran 90 (BE after suggestions by EG)
|
||
|
|
!***END PROLOGUE R1MACH
|
||
|
|
!
|
||
|
|
X = 1.0
|
||
|
|
B = RADIX(X)
|
||
|
|
!
|
||
|
|
SELECT CASE (I)
|
||
|
|
CASE (1)
|
||
|
|
R1MACH = B**(MINEXPONENT(X)-1) ! the smallest positive magnitude.
|
||
|
|
CASE (2)
|
||
|
|
R1MACH = HUGE(X) ! the largest magnitude.
|
||
|
|
CASE (3)
|
||
|
|
R1MACH = B**(-DIGITS(X)) ! the smallest relative spacing.
|
||
|
|
CASE (4)
|
||
|
|
R1MACH = B**(1-DIGITS(X)) ! the largest relative spacing.
|
||
|
|
CASE (5)
|
||
|
|
R1MACH = LOG10(B)
|
||
|
|
CASE DEFAULT
|
||
|
|
WRITE (*,10)
|
||
|
|
STOP
|
||
|
|
END SELECT
|
||
|
|
!
|
||
|
|
! Formats:
|
||
|
|
!
|
||
|
|
10 FORMAT ('1ERROR 1 IN R1MACH - I out of bounds')
|
||
|
|
!
|
||
|
|
END FUNCTION R1MACH
|
||
|
|
!
|
||
|
|
END MODULE MACHINE_ACCURACY
|