!-------------------------------------------------------------------------------------------------- !> @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 implicit none public ! https://software.intel.com/en-us/blogs/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) #if(INT==8) integer, parameter :: pInt = pI64 #else integer, parameter :: pInt = pI32 #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) type :: group_float !< variable length datatype used for storage of state real(pReal), dimension(:), pointer :: p end type group_float ! http://stackoverflow.com/questions/3948210/can-i-have-a-pointer-to-an-item-in-an-allocatable-array type :: tState integer :: & sizeState = 0, & !< size of state sizeDotState = 0, & !< size of dot state, i.e. state(1:sizeDot) follows time evolution by dotState rates offsetDeltaState = 0, & !< index offset of delta state sizeDeltaState = 0 !< size of delta state, i.e. state(offset+1:offset+sizeDelta) follows time evolution by deltaState increments real(pReal), pointer, dimension(:), contiguous :: & atol real(pReal), pointer, dimension(:,:), contiguous :: & ! a pointer is needed here because we might point to state/doState. However, they will never point to something, but are rather allocated and, hence, contiguous state0, & state, & !< state dotState, & !< rate of state change deltaState !< increment of state change real(pReal), allocatable, dimension(:,:) :: & subState0 end type type, extends(tState) :: tPlasticState logical :: & nonlocal = .false. real(pReal), pointer, dimension(:,:) :: & slipRate !< slip rate end type type :: tSourceState type(tState), dimension(:), allocatable :: p !< tState for each active source mechanism in a phase end type 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'(/,a)', ' <<<+- prec init -+>>>' print'(a,i3)', ' Size of integer in bit: ',bit_size(0) print'(a,i19)', ' Maximum value: ',huge(0) print'(/,a,i3)', ' Size of float in 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 !-------------------------------------------------------------------------------------------------- logical elemental pure function dEq(a,b,tol) real(pReal), intent(in) :: a,b real(pReal), intent(in), optional :: tol real(pReal) :: eps if (present(tol)) then eps = tol else eps = PREAL_EPSILON * maxval(abs([a,b])) endif dEq = merge(.True.,.False.,abs(a-b) <= eps) 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 real(pReal) :: eps if (present(tol)) then eps = tol else eps = PREAL_MIN * 10.0_pReal endif dEq0 = merge(.True.,.False.,abs(a) <= eps) 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 real(pReal) :: eps if (present(tol)) then eps = tol else eps = PREAL_EPSILON * maxval(abs([a,b])) endif cEq = merge(.True.,.False.,abs(a-b) <= eps) 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(pInt), 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)),pInt) if(i(1) /= 20191102_pInt) error stop 'prec_bytesToC_INT32_T' i = int(prec_bytesToC_INT64_T(int([+126,+23,+52,+1,0,0,0,0],C_SIGNED_CHAR)),pInt) if(i(1) /= 20191102_pInt) error stop 'prec_bytesToC_INT64_T' end subroutine selfTest end module prec