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 nonnegative 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 ⛓
Generate and return the factorial of the input positive integer.
This module contains procedures and generic interfaces for the Factorial function.
 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.
 See also
 getFactorial
Example usage ⛓
12 type(display_type) :: disp
16 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
17 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
18 call disp%show(
"! Compute the factorial of a scalar or array of integers.")
19 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
20 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
24 call disp%show(
"getFactorial(5_IKS)")
29 call disp%show(
"getFactorial(5_IKD)")
34 call disp%show(
"getFactorial(int([(i, i = 1,13,2)],IKS))")
39 call disp%show(
"getFactorial(int([(i, i = 1,20,2)],IKD))")
This is a generic method of the derived type display_type with pass attribute.
This is a generic method of the derived type display_type with pass attribute.
This module contains classes and procedures for input/output (IO) or generic display operations on st...
type(display_type) disp
This is a scalar module variable an object of type display_type for general display.
This module defines the relevant Fortran kind typeparameters frequently used in the ParaMonte librar...
integer, parameter LK
The default logical kind in the ParaMonte library: kind(.true.) in Fortran, kind(....
integer, parameter IKS
The singleprecision integer kind in Fortran mode. On most platforms, this is a 32bit integer kind.
integer, parameter IK
The default integer kind in the ParaMonte library: int32 in Fortran, c_int32_t in CFortran Interoper...
integer, parameter IKD
The double precision integer kind in Fortran mode. On most platforms, this is a 64bit integer kind.
integer, parameter SK
The default character kind in the ParaMonte library: kind("a") in Fortran, c_char in CFortran Intero...
Generate and return an object of type display_type.
Example Unix compile command via Intel ifort
compiler ⛓
3ifort fpp standardsemantics O3 Wl,rpath,../../../lib I../../../inc main.F90 ../../../lib/libparamonte* o main.exe
Example Windows Batch compile command via Intel ifort
compiler ⛓
2set PATH=..\..\..\lib;%PATH%
3ifort /fpp /standardsemantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte*.lib /exe:main.exe
Example Unix / MinGW compile command via GNU gfortran
compiler ⛓
3gfortran cpp ffreelinelengthnone O3 Wl,rpath,../../../lib I../../../inc main.F90 ../../../lib/libparamonte* o main.exe
Example output ⛓
18+1,
+6,
+120,
+5040,
+362880,
+39916800,
+1932053504
22+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.

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.

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.