pm_mathFactorial::getFactorial Interface Reference

Generate and return the factorial of the input positive integer. More...

Detailed Description

Generate and return the factorial of the input positive integer.

The factorial of an integer number \(n\) is defined as,

\begin{equation} \large n! = \prod_{i=1}^{n} i = \Gamma(n+1) ~. \end{equation}

Note that the factorial of a number can readily overflow the maximum integer values representable by computers. As such, getLogFactorial is a safer alternative to use.

Parameters

[in]

n

: The input scalar or array of arbitrary rank of type integer of kind any supported by the processor (e.g., IK, IK8, IK16, IK32, or IK64) containing the non-negative integer whose \(\log(n!)\) is to be computed on return.

Returns

factorial : The output scalar or array of the same shape as the input n representing the factorial of n.

Possible calling interfaces ⛓

use pm_mathFactorial, only: getFactorial
 
factorial = getFactorial(n)

Warning

The condition 0_IKG <= n must hold for the corresponding input arguments.
This condition is verified only if the library is built with the preprocessor macro CHECK_ENABLED=1.

The pure procedure(s) documented herein become impure when the ParaMonte library is compiled with preprocessor macro CHECK_ENABLED=1.
By default, these procedures are pure in release build and impure in debug and testing builds.

Remarks

The procedures under discussion are elemental.

See also

getFactorial

Example usage ⛓

program example
 
    use pm_kind, only: IKS, IKD
    use pm_kind, only: SK, IK, LK
    use pm_io, only: display_type
    use pm_mathFactorial, only: getFactorial
 
    implicit none
 
    integer(IK) :: i
 
    type(display_type) :: disp
    disp = display_type(file = "main.out.F90")
 
    call disp%skip()
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%show("! Compute the factorial of a scalar or array of integers.")
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%skip()
 
    call disp%skip()
    call disp%show("getFactorial(5_IKS)")
    call disp%show( getFactorial(5_IKS) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("getFactorial(5_IKD)")
    call disp%show( getFactorial(5_IKD) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("getFactorial(int([(i, i = 1,13,2)],IKS))")
    call disp%show( getFactorial(int([(i, i = 1,13,2)],IKS)) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("getFactorial(int([(i, i = 1,20,2)],IKD))")
    call disp%show( getFactorial(int([(i, i = 1,20,2)],IKD)) )
    call disp%skip()
 
end program example

Example Unix compile command via Intel ifort compiler ⛓

#!/usr/bin/env sh
rm main.exe
ifort -fpp -standard-semantics -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
./main.exe

Example Windows Batch compile command via Intel ifort compiler ⛓

del main.exe
set PATH=..\..\..\lib;%PATH%
ifort /fpp /standard-semantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte*.lib /exe:main.exe
main.exe

Example Unix / MinGW compile command via GNU gfortran compiler ⛓

#!/usr/bin/env sh
rm main.exe
gfortran -cpp -ffree-line-length-none -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
./main.exe

Example output ⛓

 
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
! Compute the factorial of a scalar or array of integers.
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 
getFactorial(5_IKS)
+120
 
 
getFactorial(5_IKD)
+120
 
 
getFactorial(int([(i, i = 1,13,2)],IKS))
+1, +6, +120, +5040, +362880, +39916800, +1932053504
 
 
getFactorial(int([(i, i = 1,20,2)],IKD))
+1, +6, +120, +5040, +362880, +39916800, +6227020800, +1307674368000, +355687428096000, +121645100408832000
 
 

Test:

test_pm_mathFactorial

Final Remarks ⛓

---

If you believe this algorithm or its documentation can be improved, we appreciate your contribution and help to edit this page's documentation and source file on GitHub.
For details on the naming abbreviations, see this page.
For details on the naming conventions, see this page.
This software is distributed under the MIT license with additional terms outlined below.

1. If you use any parts or concepts from this library to any extent, please acknowledge the usage by citing the relevant publications of the ParaMonte library.
   
2. If you regenerate any parts/ideas from this library in a programming environment other than those currently supported by this ParaMonte library (i.e., other than C, C++, Fortran, MATLAB, Python, R), please also ask the end users to cite this original ParaMonte library.
   

This software is available to the public under a highly permissive license.
Help us justify its continued development and maintenance by acknowledging its benefit to society, distributing it, and contributing to it.

Copyright

Computational Data Science Lab

Author:

Amir Shahmoradi, April 23, 2017, 1:36 AM, Institute for Computational Engineering and Sciences (ICES), University of Texas at Austin

Definition at line 114 of file pm_mathFactorial.F90.

---

The documentation for this interface was generated from the following file:

• src/fortran/main/pm_mathFactorial.F90