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