gray/src/math.f90

! Miscellaneous mathematical functions
module math

implicit none

contains

  pure function fact(k)
    ! Factorial function k!
    ! Note: the result is a real number
    use const_and_precisions, only : wp_

    integer, intent(in) :: k
    real(wp_)           :: fact

    fact = gamma(real(1 + k, kind=wp_))
   end function fact

end module math
use the logger everywhere This converts the last remaining warnings to use the logging system. Also drops `catand` and replace it with the intrinsic `atan`, which supports complex as well as real numbers. Note: before 3eab989d the `catand` function was actually incorrent! The definition of arctan(z) can be obtained starting from the identity d/dz arctan(z) = 1/(1 + z²) = ½ [1/(1 + iz) + 1/(1 - iz)], integrating and using the definition log(z) = ∫₁^z dz/z, arctan(z) = -i/2 [log(1 + iz) - log(1 - iz)]. If log is the principal branch, log(z) = log\|z\| + i arg(z), then arctan(z) = -i/2 log(w) = 1/2 arg(w) -i/2 log\|w\| where w = (1 + iz)/(1 - iz). Finally, the real part is Re arctan(z) = 1/2 atan2(2Re(z), 1 - \|z\|²). The term -\|z\|² is missing from the `catand` definition of GRAY, but is present in the original Fortran 77 code from [SLATEC]: it has probably been lost in the translation. [SLATEC]: https://people.math.sc.edu/Burkardt/f_src/slatec/slatec.f90 2022-07-15 00:09:36 +02:00			`! Miscellaneous mathematical functions`
nocommon branch merged back into trunk 2015-11-18 17:34:33 +01:00			`module math`

use the logger everywhere This converts the last remaining warnings to use the logging system. Also drops `catand` and replace it with the intrinsic `atan`, which supports complex as well as real numbers. Note: before 3eab989d the `catand` function was actually incorrent! The definition of arctan(z) can be obtained starting from the identity d/dz arctan(z) = 1/(1 + z²) = ½ [1/(1 + iz) + 1/(1 - iz)], integrating and using the definition log(z) = ∫₁^z dz/z, arctan(z) = -i/2 [log(1 + iz) - log(1 - iz)]. If log is the principal branch, log(z) = log\|z\| + i arg(z), then arctan(z) = -i/2 log(w) = 1/2 arg(w) -i/2 log\|w\| where w = (1 + iz)/(1 - iz). Finally, the real part is Re arctan(z) = 1/2 atan2(2Re(z), 1 - \|z\|²). The term -\|z\|² is missing from the `catand` definition of GRAY, but is present in the original Fortran 77 code from [SLATEC]: it has probably been lost in the translation. [SLATEC]: https://people.math.sc.edu/Burkardt/f_src/slatec/slatec.f90 2022-07-15 00:09:36 +02:00			`implicit none`
nocommon branch merged back into trunk 2015-11-18 17:34:33 +01:00
			`contains`

use the logger everywhere This converts the last remaining warnings to use the logging system. Also drops `catand` and replace it with the intrinsic `atan`, which supports complex as well as real numbers. Note: before 3eab989d the `catand` function was actually incorrent! The definition of arctan(z) can be obtained starting from the identity d/dz arctan(z) = 1/(1 + z²) = ½ [1/(1 + iz) + 1/(1 - iz)], integrating and using the definition log(z) = ∫₁^z dz/z, arctan(z) = -i/2 [log(1 + iz) - log(1 - iz)]. If log is the principal branch, log(z) = log\|z\| + i arg(z), then arctan(z) = -i/2 log(w) = 1/2 arg(w) -i/2 log\|w\| where w = (1 + iz)/(1 - iz). Finally, the real part is Re arctan(z) = 1/2 atan2(2Re(z), 1 - \|z\|²). The term -\|z\|² is missing from the `catand` definition of GRAY, but is present in the original Fortran 77 code from [SLATEC]: it has probably been lost in the translation. [SLATEC]: https://people.math.sc.edu/Burkardt/f_src/slatec/slatec.f90 2022-07-15 00:09:36 +02:00			`pure function fact(k)`
src/math.f90: use the intrinsic gamma function - remove the `gamm` function - rewrite `fact` in terms of `gamma` 2021-12-20 18:47:28 +01:00			`! Factorial function k!`
use the logger everywhere This converts the last remaining warnings to use the logging system. Also drops `catand` and replace it with the intrinsic `atan`, which supports complex as well as real numbers. Note: before 3eab989d the `catand` function was actually incorrent! The definition of arctan(z) can be obtained starting from the identity d/dz arctan(z) = 1/(1 + z²) = ½ [1/(1 + iz) + 1/(1 - iz)], integrating and using the definition log(z) = ∫₁^z dz/z, arctan(z) = -i/2 [log(1 + iz) - log(1 - iz)]. If log is the principal branch, log(z) = log\|z\| + i arg(z), then arctan(z) = -i/2 log(w) = 1/2 arg(w) -i/2 log\|w\| where w = (1 + iz)/(1 - iz). Finally, the real part is Re arctan(z) = 1/2 atan2(2Re(z), 1 - \|z\|²). The term -\|z\|² is missing from the `catand` definition of GRAY, but is present in the original Fortran 77 code from [SLATEC]: it has probably been lost in the translation. [SLATEC]: https://people.math.sc.edu/Burkardt/f_src/slatec/slatec.f90 2022-07-15 00:09:36 +02:00			`! Note: the result is a real number`
			`use const_and_precisions, only : wp_`
src/math.f90: use the intrinsic gamma function - remove the `gamm` function - rewrite `fact` in terms of `gamma` 2021-12-20 18:47:28 +01:00
nocommon branch merged back into trunk 2015-11-18 17:34:33 +01:00			`integer, intent(in) :: k`
src/math.f90: use the intrinsic gamma function - remove the `gamm` function - rewrite `fact` in terms of `gamma` 2021-12-20 18:47:28 +01:00			`real(wp_) :: fact`
nocommon branch merged back into trunk 2015-11-18 17:34:33 +01:00
src/math.f90: use the intrinsic gamma function - remove the `gamm` function - rewrite `fact` in terms of `gamma` 2021-12-20 18:47:28 +01:00			`fact = gamma(real(1 + k, kind=wp_))`
			`end function fact`
nocommon branch merged back into trunk 2015-11-18 17:34:33 +01:00
src/math.f90: use the intrinsic gamma function - remove the `gamm` function - rewrite `fact` in terms of `gamma` 2021-12-20 18:47:28 +01:00			`end module math`