DAMASK_EICMD/src/prec.f90

!--------------------------------------------------------------------------------------------------
!> @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
  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