!-------------------------------------------------------------------------------------------------- !> @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 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_int integer, parameter :: pPETSCINT = kind(dummy_int) PetscScalar, private :: dummy_scalar real(pREAL), parameter, private :: pPETSCSCALAR = kind(dummy_scalar) #endif integer, parameter :: pSTRLEN = 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=pSTRLEN), dimension(0), parameter :: emptyStrArray = [character(len=pSTRLEN)::] 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)', ' real 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 prec_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 prec_selfTest() integer, allocatable, dimension(:) :: realloc_lhs_test real(pREAL), dimension(1) :: f integer(pI64), dimension(1) :: i real(pREAL), dimension(2) :: r #ifdef PETSC if (pREAL /= pPETSCSCALAR) error stop 'PETSc and DAMASK scalar datatypes do not match' #endif 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 prec_selfTest end module prec