ParaMonte Fortran 2.0.0
Parallel Monte Carlo and Machine Learning Library
See the latest version documentation.
pm_mathFactoring::getFactoring Interface Reference

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

Detailed Description

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

Factoring = getFactoring(posint)
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

1program example
2
3 use pm_kind, only: IKS, IKD
4 use pm_kind, only: SK, IK, LK
5 use pm_io, only: display_type
8
9 implicit none
10
11 integer(IK) :: i, n
12 integer(IK), allocatable :: Factoring(:)
13
14 type(display_type) :: disp
15 disp = display_type(file = "main.out.F90")
16
17 call disp%skip()
18 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
19 call disp%show("! Compute the factoring of a scalar or array of integers.")
20 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
21 call disp%skip()
22
23 do i = 1, 10
24 call disp%skip()
25 call disp%show("n = getLogUnifRand(2, huge(1))")
26 n = getLogUnifRand(2, huge(1))
27 call disp%show("n")
28 call disp%show( n )
29 call disp%show("Factoring = getFactoring(n)")
30 Factoring = getFactoring(n)
31 call disp%show("Factoring")
32 call disp%show( Factoring )
33 call disp%show("n - product(Factoring) ! By definition, it must be zero.")
34 call disp%show( n - product(Factoring) )
35 call disp%skip()
36 end do
37
38end program example
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.
Definition: pm_io.F90:11726
This is a generic method of the derived type display_type with pass attribute.
Definition: pm_io.F90:11508
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...
Definition: pm_io.F90:252
type(display_type) disp
This is a scalar module variable an object of type display_type for general display.
Definition: pm_io.F90:11393
This module defines the relevant Fortran kind type-parameters frequently used in the ParaMonte librar...
Definition: pm_kind.F90:268
integer, parameter LK
The default logical kind in the ParaMonte library: kind(.true.) in Fortran, kind(....
Definition: pm_kind.F90:541
integer, parameter IKS
The single-precision integer kind in Fortran mode. On most platforms, this is a 32-bit integer kind.
Definition: pm_kind.F90:563
integer, parameter IK
The default integer kind in the ParaMonte library: int32 in Fortran, c_int32_t in C-Fortran Interoper...
Definition: pm_kind.F90:540
integer, parameter IKD
The double precision integer kind in Fortran mode. On most platforms, this is a 64-bit integer kind.
Definition: pm_kind.F90:564
integer, parameter SK
The default character kind in the ParaMonte library: kind("a") in Fortran, c_char in C-Fortran Intero...
Definition: pm_kind.F90:539
Generate and return an object of type display_type.
Definition: pm_io.F90:10282

Example Unix compile command via Intel ifort compiler
1#!/usr/bin/env sh
2rm main.exe
3ifort -fpp -standard-semantics -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
4./main.exe

Example Windows Batch compile command via Intel ifort compiler
1del main.exe
2set PATH=..\..\..\lib;%PATH%
3ifort /fpp /standard-semantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte*.lib /exe:main.exe
4main.exe

Example Unix / MinGW compile command via GNU gfortran compiler
1#!/usr/bin/env sh
2rm main.exe
3gfortran -cpp -ffree-line-length-none -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
4./main.exe

Example output
1
2!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3! Compute the factoring of a scalar or array of integers.
4!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
5
6
7n = getLogUnifRand(2, huge(1))
8n
9+80116
10Factoring = getFactoring(n)
11Factoring
12+2, +2, +20029
13n - product(Factoring) ! By definition, it must be zero.
14+0
15
16
17n = getLogUnifRand(2, huge(1))
18n
19+39160
20Factoring = getFactoring(n)
21Factoring
22+2, +2, +2, +5, +11, +89
23n - product(Factoring) ! By definition, it must be zero.
24+0
25
26
27n = getLogUnifRand(2, huge(1))
28n
29+3
30Factoring = getFactoring(n)
31Factoring
32+3
33n - product(Factoring) ! By definition, it must be zero.
34+0
35
36
37n = getLogUnifRand(2, huge(1))
38n
39+166933
40Factoring = getFactoring(n)
41Factoring
42+13, +12841
43n - product(Factoring) ! By definition, it must be zero.
44+0
45
46
47n = getLogUnifRand(2, huge(1))
48n
49+612838528
50Factoring = getFactoring(n)
51Factoring
52+2, +2, +2, +2, +2, +2, +2, +211, +22691
53n - product(Factoring) ! By definition, it must be zero.
54+0
55
56
57n = getLogUnifRand(2, huge(1))
58n
59+673763776
60Factoring = getFactoring(n)
61Factoring
62+2, +2, +2, +2, +2, +2, +7, +1503937
63n - product(Factoring) ! By definition, it must be zero.
64+0
65
66
67n = getLogUnifRand(2, huge(1))
68n
69+272522
70Factoring = getFactoring(n)
71Factoring
72+2, +136261
73n - product(Factoring) ! By definition, it must be zero.
74+0
75
76
77n = getLogUnifRand(2, huge(1))
78n
79+183763
80Factoring = getFactoring(n)
81Factoring
82+183763
83n - product(Factoring) ! By definition, it must be zero.
84+0
85
86
87n = getLogUnifRand(2, huge(1))
88n
89+18
90Factoring = getFactoring(n)
91Factoring
92+2, +3, +3
93n - product(Factoring) ! By definition, it must be zero.
94+0
95
96
97n = getLogUnifRand(2, huge(1))
98n
99+7342
100Factoring = getFactoring(n)
101Factoring
102+2, +3671
103n - product(Factoring) ! By definition, it must be zero.
104+0
105
106
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.

  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.

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.


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