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