Generate and return the integer square root of an input non-negative integer.
More...
Generate and return the integer square root of an input non-negative integer.
See the documentation of pm_mathSqrt for more information on integer square root.
- 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 non-negative integer whose factoring is to be computed on return. |
- Returns
intSqrt
: 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 integer square root of an input non-negative integer.
This module contains procedures and generic interfaces for computing the square root of integers.
- Warning
- The condition
0 <= 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 computation of the integer square root using the linear search method can become extremely costly for large input
posint
values, typically larger than 10**5
.
For more information, see the relevant benchmarks.
-
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
- getLog1p
get1mexp
Example usage ⛓
13 integer(IKG) :: posint, intSqrt
15 type(display_type) :: disp
20 call disp%show(
"posint = getLogUnifRand(1, huge(1))")
24 call disp%show(
"intSqrt = getSqrt(posint, binary)")
25 intSqrt
= getSqrt(posint, binary)
26 call disp%show(
"[intSqrt, floor(sqrt(real(posint, RKD)))]")
27 call disp%show( [intSqrt,
floor(
sqrt(
real(posint,
RKD)))] )
28 call disp%show(
"call setAsserted(intSqrt == floor(sqrt(real(posint, RKD))))")
33 do posint
= huge(
0_IKG),
huge(
0_IKG)
- 10_IKG,
-1_IKG
37 call disp%show(
"intSqrt = getSqrt(posint, binary)")
38 intSqrt
= getSqrt(posint, binary)
39 call disp%show(
"[intSqrt, floor(sqrt(real(posint, RKD)))]")
40 call disp%show( [intSqrt,
floor(
sqrt(
real(posint,
RKD)))] )
41 call disp%show(
"call setAsserted(intSqrt == floor(sqrt(real(posint, RKD))))")
46 do posint
= 0_IKG,
10_IKG
50 call disp%show(
"intSqrt = getSqrt(posint, binary)")
51 intSqrt
= getSqrt(posint, binary)
52 call disp%show(
"[intSqrt, getSqrt(posint, linear), floor(sqrt(real(posint, RKD)))]")
54 call disp%show(
"call setAsserted(intSqrt == floor(sqrt(real(posint, RKD))))")
Generate and return a scalar (or array of arbitrary rank) of random value(s) from the LogUniform dist...
Verify the input assertion holds and if it does not, print the (optional) input message on stdout and...
Generate and return an object of type stop_type with the user-specified input attributes.
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 reporting and handling errors.
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 RKD
The double precision real kind in Fortran mode. On most platforms, this is an 64-bit real 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 ⛓
6[intSqrt,
floor(
sqrt(
real(posint,
RKD)))]
14intSqrt
= getSqrt(posint, binary)
15[intSqrt,
floor(
sqrt(
real(posint,
RKD)))]
23intSqrt
= getSqrt(posint, binary)
24[intSqrt,
floor(
sqrt(
real(posint,
RKD)))]
32intSqrt
= getSqrt(posint, binary)
33[intSqrt,
floor(
sqrt(
real(posint,
RKD)))]
41intSqrt
= getSqrt(posint, binary)
42[intSqrt,
floor(
sqrt(
real(posint,
RKD)))]
50intSqrt
= getSqrt(posint, binary)
51[intSqrt,
floor(
sqrt(
real(posint,
RKD)))]
59intSqrt
= getSqrt(posint, binary)
60[intSqrt,
floor(
sqrt(
real(posint,
RKD)))]
68intSqrt
= getSqrt(posint, binary)
69[intSqrt,
floor(
sqrt(
real(posint,
RKD)))]
77intSqrt
= getSqrt(posint, binary)
78[intSqrt,
floor(
sqrt(
real(posint,
RKD)))]
86intSqrt
= getSqrt(posint, binary)
87[intSqrt,
floor(
sqrt(
real(posint,
RKD)))]
94intSqrt
= getSqrt(posint, binary)
95[intSqrt,
floor(
sqrt(
real(posint,
RKD)))]
102intSqrt
= getSqrt(posint, binary)
103[intSqrt,
floor(
sqrt(
real(posint,
RKD)))]
110intSqrt
= getSqrt(posint, binary)
111[intSqrt,
floor(
sqrt(
real(posint,
RKD)))]
118intSqrt
= getSqrt(posint, binary)
119[intSqrt,
floor(
sqrt(
real(posint,
RKD)))]
126intSqrt
= getSqrt(posint, binary)
127[intSqrt,
floor(
sqrt(
real(posint,
RKD)))]
134intSqrt
= getSqrt(posint, binary)
135[intSqrt,
floor(
sqrt(
real(posint,
RKD)))]
142intSqrt
= getSqrt(posint, binary)
143[intSqrt,
floor(
sqrt(
real(posint,
RKD)))]
150intSqrt
= getSqrt(posint, binary)
151[intSqrt,
floor(
sqrt(
real(posint,
RKD)))]
158intSqrt
= getSqrt(posint, binary)
159[intSqrt,
floor(
sqrt(
real(posint,
RKD)))]
166intSqrt
= getSqrt(posint, binary)
167[intSqrt,
floor(
sqrt(
real(posint,
RKD)))]
174intSqrt
= getSqrt(posint, binary)
175[intSqrt,
floor(
sqrt(
real(posint,
RKD)))]
182intSqrt
= getSqrt(posint, binary)
183[intSqrt,
getSqrt(posint, linear),
floor(
sqrt(
real(posint,
RKD)))]
190intSqrt
= getSqrt(posint, binary)
191[intSqrt,
getSqrt(posint, linear),
floor(
sqrt(
real(posint,
RKD)))]
198intSqrt
= getSqrt(posint, binary)
199[intSqrt,
getSqrt(posint, linear),
floor(
sqrt(
real(posint,
RKD)))]
206intSqrt
= getSqrt(posint, binary)
207[intSqrt,
getSqrt(posint, linear),
floor(
sqrt(
real(posint,
RKD)))]
214intSqrt
= getSqrt(posint, binary)
215[intSqrt,
getSqrt(posint, linear),
floor(
sqrt(
real(posint,
RKD)))]
222intSqrt
= getSqrt(posint, binary)
223[intSqrt,
getSqrt(posint, linear),
floor(
sqrt(
real(posint,
RKD)))]
230intSqrt
= getSqrt(posint, binary)
231[intSqrt,
getSqrt(posint, linear),
floor(
sqrt(
real(posint,
RKD)))]
238intSqrt
= getSqrt(posint, binary)
239[intSqrt,
getSqrt(posint, linear),
floor(
sqrt(
real(posint,
RKD)))]
246intSqrt
= getSqrt(posint, binary)
247[intSqrt,
getSqrt(posint, linear),
floor(
sqrt(
real(posint,
RKD)))]
254intSqrt
= getSqrt(posint, binary)
255[intSqrt,
getSqrt(posint, linear),
floor(
sqrt(
real(posint,
RKD)))]
262intSqrt
= getSqrt(posint, binary)
263[intSqrt,
getSqrt(posint, linear),
floor(
sqrt(
real(posint,
RKD)))]
- Test:
- test_pm_mathIntSqrt
- Todo:
- Low Priority: A binary-representation calculation of the integer square root should be added in the future.
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 141 of file pm_mathSqrt.F90.