DAMASK_EICMD/src/prec.f90

282 lines
12 KiB
Fortran

!--------------------------------------------------------------------------------------------------
!> @author Franz Roters, Max-Planck-Institut für Eisenforschung GmbH
!> @author Philip Eisenlohr, Max-Planck-Institut für Eisenforschung GmbH
!> @author Christoph Kords, Max-Planck-Institut für Eisenforschung GmbH
!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
!> @author Luv Sharma, Max-Planck-Institut für Eisenforschung GmbH
!> @brief setting precision for real and int type
!--------------------------------------------------------------------------------------------------
module prec
use, intrinsic :: IEEE_arithmetic
use, intrinsic :: ISO_C_binding
#ifdef PETSC
#include <petsc/finclude/petscsys.h>
use PETScSys
#endif
implicit none(type,external)
public
! https://stevelionel.com/drfortran/2017/03/27/doctor-fortran-in-it-takes-all-kinds
integer, parameter :: pReal = IEEE_selected_real_kind(15,307) !< number with 15 significant digits, up to 1e+-307 (typically 64 bit)
integer, parameter :: pI32 = selected_int_kind(9) !< number with at least up to +-1e9 (typically 32 bit)
integer, parameter :: pI64 = selected_int_kind(18) !< number with at least up to +-1e18 (typically 64 bit)
#ifdef PETSC
PetscInt, private :: dummy
integer, parameter :: pPETSCINT = kind(dummy)
#endif
integer, parameter :: pSTRINGLEN = 256 !< default string length
integer, parameter :: pPATHLEN = 4096 !< maximum length of a path name on linux
real(pReal), parameter :: tol_math_check = 1.0e-8_pReal !< tolerance for internal math self-checks (rotation)
real(pReal), private, parameter :: PREAL_EPSILON = epsilon(0.0_pReal) !< minimum positive number such that 1.0 + EPSILON /= 1.0.
real(pReal), private, parameter :: PREAL_MIN = tiny(0.0_pReal) !< smallest normalized floating point number
integer, dimension(0), parameter :: emptyIntArray = [integer::]
real(pReal), dimension(0), parameter :: emptyRealArray = [real(pReal)::]
character(len=pStringLen), dimension(0), parameter :: emptyStringArray = [character(len=pStringLen)::]
private :: &
selfTest
contains
!--------------------------------------------------------------------------------------------------
!> @brief Report precision and do self test.
!--------------------------------------------------------------------------------------------------
subroutine prec_init()
print'(/,1x,a)', '<<<+- prec init -+>>>'
print'(/,a,i3)', ' integer size / bit: ',bit_size(0)
print'( a,i19)', ' maximum value: ',huge(0)
print'(/,a,i3)', ' float size / bit: ',storage_size(0.0_pReal)
print'( a,e10.3)', ' maximum value: ',huge(0.0_pReal)
print'( a,e10.3)', ' minimum value: ',PREAL_MIN
print'( a,e10.3)', ' epsilon value: ',PREAL_EPSILON
print'( a,i3)', ' decimal precision: ',precision(0.0_pReal)
call selfTest()
end subroutine prec_init
!--------------------------------------------------------------------------------------------------
!> @brief Test floating point numbers with double precision for equality.
! replaces "==" but for certain (relative) tolerance. Counterpart to dNeq
! https://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/
! AlmostEqualRelative
! ToDo: Use 'spacing': https://gcc.gnu.org/onlinedocs/gfortran/SPACING.html#SPACING
!--------------------------------------------------------------------------------------------------
logical elemental pure function dEq(a,b,tol)
real(pReal), intent(in) :: a,b
real(pReal), intent(in), optional :: tol
if (present(tol)) then
dEq = abs(a-b) <= tol
else
dEq = abs(a-b) <= PREAL_EPSILON * maxval(abs([a,b]))
end if
end function dEq
!--------------------------------------------------------------------------------------------------
!> @brief Test floating point numbers with double precision for inequality.
! replaces "!=" but for certain (relative) tolerance. Counterpart to dEq
! https://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/
! AlmostEqualRelative NOT
!--------------------------------------------------------------------------------------------------
logical elemental pure function dNeq(a,b,tol)
real(pReal), intent(in) :: a,b
real(pReal), intent(in), optional :: tol
dNeq = .not. dEq(a,b,tol)
end function dNeq
!--------------------------------------------------------------------------------------------------
!> @brief Test floating point number with double precision for equality to 0.
! replaces "==0" but everything not representable as a normal number is treated as 0. Counterpart to dNeq0
! https://de.mathworks.com/help/matlab/ref/realmin.html
! https://docs.oracle.com/cd/E19957-01/806-3568/ncg_math.html
!--------------------------------------------------------------------------------------------------
logical elemental pure function dEq0(a,tol)
real(pReal), intent(in) :: a
real(pReal), intent(in), optional :: tol
if (present(tol)) then
dEq0 = abs(a) <= tol
else
dEq0 = abs(a) <= PREAL_MIN * 10.0_pReal
end if
end function dEq0
!--------------------------------------------------------------------------------------------------
!> @brief Test floating point number with double precision for inequality to 0.
! replaces "!=0" but everything not representable as a normal number is treated as 0. Counterpart to dEq0
! https://de.mathworks.com/help/matlab/ref/realmin.html
! https://docs.oracle.com/cd/E19957-01/806-3568/ncg_math.html
!--------------------------------------------------------------------------------------------------
logical elemental pure function dNeq0(a,tol)
real(pReal), intent(in) :: a
real(pReal), intent(in), optional :: tol
dNeq0 = .not. dEq0(a,tol)
end function dNeq0
!--------------------------------------------------------------------------------------------------
!> @brief Test complex floating point numbers with double precision for equality.
! replaces "==" but for certain (relative) tolerance. Counterpart to cNeq
! https://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/
! probably a component wise comparison would be more accurate than the comparsion of the absolute
! value
!--------------------------------------------------------------------------------------------------
logical elemental pure function cEq(a,b,tol)
complex(pReal), intent(in) :: a,b
real(pReal), intent(in), optional :: tol
if (present(tol)) then
cEq = abs(a-b) <= tol
else
cEq = abs(a-b) <= PREAL_EPSILON * maxval(abs([a,b]))
end if
end function cEq
!--------------------------------------------------------------------------------------------------
!> @brief Test complex floating point numbers with double precision for inequality.
! replaces "!=" but for certain (relative) tolerance. Counterpart to cEq
! https://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/
! probably a component wise comparison would be more accurate than the comparsion of the absolute
! value
!--------------------------------------------------------------------------------------------------
logical elemental pure function cNeq(a,b,tol)
complex(pReal), intent(in) :: a,b
real(pReal), intent(in), optional :: tol
cNeq = .not. cEq(a,b,tol)
end function cNeq
!--------------------------------------------------------------------------------------------------
!> @brief Decode byte array (C_SIGNED_CHAR) as C_FLOAT array (4 byte float).
!--------------------------------------------------------------------------------------------------
pure function prec_bytesToC_FLOAT(bytes)
integer(C_SIGNED_CHAR), dimension(:), intent(in) :: bytes !< byte-wise representation of a C_FLOAT array
real(C_FLOAT), dimension(size(bytes,kind=pI64)/(storage_size(0._C_FLOAT,pI64)/8_pI64)) :: &
prec_bytesToC_FLOAT
prec_bytesToC_FLOAT = transfer(bytes,prec_bytesToC_FLOAT,size(prec_bytesToC_FLOAT))
end function prec_bytesToC_FLOAT
!--------------------------------------------------------------------------------------------------
!> @brief Decode byte array (C_SIGNED_CHAR) as C_DOUBLE array (8 byte float).
!--------------------------------------------------------------------------------------------------
pure function prec_bytesToC_DOUBLE(bytes)
integer(C_SIGNED_CHAR), dimension(:), intent(in) :: bytes !< byte-wise representation of a C_DOUBLE array
real(C_DOUBLE), dimension(size(bytes,kind=pI64)/(storage_size(0._C_DOUBLE,pI64)/8_pI64)) :: &
prec_bytesToC_DOUBLE
prec_bytesToC_DOUBLE = transfer(bytes,prec_bytesToC_DOUBLE,size(prec_bytesToC_DOUBLE))
end function prec_bytesToC_DOUBLE
!--------------------------------------------------------------------------------------------------
!> @brief Decode byte array (C_SIGNED_CHAR) as C_INT32_T array (4 byte signed integer).
!--------------------------------------------------------------------------------------------------
pure function prec_bytesToC_INT32_T(bytes)
integer(C_SIGNED_CHAR), dimension(:), intent(in) :: bytes !< byte-wise representation of a C_INT32_T array
integer(C_INT32_T), dimension(size(bytes,kind=pI64)/(storage_size(0_C_INT32_T,pI64)/8_pI64)) :: &
prec_bytesToC_INT32_T
prec_bytesToC_INT32_T = transfer(bytes,prec_bytesToC_INT32_T,size(prec_bytesToC_INT32_T))
end function prec_bytesToC_INT32_T
!--------------------------------------------------------------------------------------------------
!> @brief Decode byte array (C_SIGNED_CHAR) as C_INT64_T array (8 byte signed integer).
!--------------------------------------------------------------------------------------------------
pure function prec_bytesToC_INT64_T(bytes)
integer(C_SIGNED_CHAR), dimension(:), intent(in) :: bytes !< byte-wise representation of a C_INT64_T array
integer(C_INT64_T), dimension(size(bytes,kind=pI64)/(storage_size(0_C_INT64_T,pI64)/8_pI64)) :: &
prec_bytesToC_INT64_T
prec_bytesToC_INT64_T = transfer(bytes,prec_bytesToC_INT64_T,size(prec_bytesToC_INT64_T))
end function prec_bytesToC_INT64_T
!--------------------------------------------------------------------------------------------------
!> @brief Check correctness of some prec functions.
!--------------------------------------------------------------------------------------------------
subroutine selfTest()
integer, allocatable, dimension(:) :: realloc_lhs_test
real(pReal), dimension(1) :: f
integer(pI64), dimension(1) :: i
real(pReal), dimension(2) :: r
realloc_lhs_test = [1,2]
if (any(realloc_lhs_test/=[1,2])) error stop 'LHS allocation'
call random_number(r)
r = r/minval(r)
if (.not. all(dEq(r,r+PREAL_EPSILON))) error stop 'dEq'
if (dEq(r(1),r(2)) .and. dNeq(r(1),r(2))) error stop 'dNeq'
if (.not. all(dEq0(r-(r+PREAL_MIN)))) error stop 'dEq0'
! https://www.binaryconvert.com
! https://www.rapidtables.com/convert/number/binary-to-decimal.html
f = real(prec_bytesToC_FLOAT(int([-65,+11,-102,+75],C_SIGNED_CHAR)),pReal)
if (dNeq(f(1),20191102.0_pReal,0.0_pReal)) error stop 'prec_bytesToC_FLOAT'
f = real(prec_bytesToC_DOUBLE(int([0,0,0,-32,+119,+65,+115,65],C_SIGNED_CHAR)),pReal)
if (dNeq(f(1),20191102.0_pReal,0.0_pReal)) error stop 'prec_bytesToC_DOUBLE'
i = int(prec_bytesToC_INT32_T(int([+126,+23,+52,+1],C_SIGNED_CHAR)),pI64)
if (i(1) /= 20191102_pI64) error stop 'prec_bytesToC_INT32_T'
i = int(prec_bytesToC_INT64_T(int([+126,+23,+52,+1,0,0,0,0],C_SIGNED_CHAR)),pI64)
if (i(1) /= 20191102_pI64) error stop 'prec_bytesToC_INT64_T'
end subroutine selfTest
end module prec