Generate and return the factoring of the input positive integer.
The factoring of an integer number \(n\) is defined such that,
\begin{equation}
\large
n = \prod_{i=1}^{m} f_i ~,
\end{equation}
where \(m\) is the number of factors of \(n\) and \(f_i\) are the factors.
- Parameters
-
[in] | posint | : The input scalar of type integer of kind any supported by the processor (e.g., IK, IK8, IK16, IK32, or IK64) containing the positive integer (larger than 1 ) whose factoring is to be computed on return. |
- Returns
Factoring
: The output allocatable
vector of the same type and kind as the input posint
, containing the prime factors of the input integer posint
.
Possible calling interfaces ⛓
Generate and return the factoring of the input positive integer.
This module contains procedures and generic interfaces for computing the prime factors of integers.
- Warning
- The condition
1 < posint
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 input argument
posint
has the value
attribute.
-
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 integer(IK),
allocatable :: Factoring(:)
14 type(display_type) :: disp
18 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
19 call disp%show(
"! Compute the factoring of a scalar or array of integers.")
20 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
25 call disp%show(
"n = getLogUnifRand(2, huge(1))")
29 call disp%show(
"Factoring = getFactoring(n)")
33 call disp%show(
"n - product(Factoring) ! By definition, it must be zero.")
34 call disp%show( n
- product(Factoring) )
Generate and return a scalar (or array of arbitrary rank) of random value(s) from the LogUniform dist...
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 computing various statistical quantities related to t...
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 type-parameters 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 single-precision integer kind in Fortran mode. On most platforms, this is a 32-bit integer kind.
integer, parameter IK
The default integer kind in the ParaMonte library: int32 in Fortran, c_int32_t in C-Fortran Interoper...
integer, parameter IKD
The double precision integer kind in Fortran mode. On most platforms, this is a 64-bit integer kind.
integer, parameter SK
The default character kind in the ParaMonte library: kind("a") in Fortran, c_char in C-Fortran Intero...
Generate and return an object of type display_type.
Example Unix compile command via Intel ifort
compiler ⛓
3ifort -fpp -standard-semantics -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 /standard-semantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte*.lib /exe:main.exe
Example Unix / MinGW compile command via GNU gfortran
compiler ⛓
3gfortran -cpp -ffree-line-length-none -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
Example output ⛓
32+2,
+2,
+2,
+2,
+2,
+4719713
102+2,
+2,
+2,
+2,
+2,
+317,
+2693
103n
- product(Factoring)
- Test:
- test_pm_mathFactoring
- Todo:
- High Priority: The performance of the procedures under this generic interface can be improved by using more efficient algorithms and lookup tables for various ranges of input values. The following schemes could be implemented,
-
\(posint \leq 2^{16}\): Lookup table.
-
\(posint \leq 2^{70}\): Richard Brent modification of Pollard rho algorithm.
-
\(posint \leq 10^{50}\): Lenstra elliptic curve factorization.
-
\(posint \leq 10^{100}\): Quadratic Sieve.
-
\(posint \leq 10^{100}\): General Number Field Sieve.
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 127 of file pm_mathFactoring.F90.