octave: scripts/specfun/isprime.m annotate

annotate scripts/specfun/isprime.m @ 31051:5f015f2829b7

maint: Merge stable to default

author	Arun Giridhar <arungiridhar@gmail.com>
date	Wed, 01 Jun 2022 17:20:22 -0400
parents	83f9f8bda883 3a93a77dd4cf
children	597f3ee61a48

rev	line source
27923 bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	1 ########################################################################
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	2 ##
30564 796f54d4ddbf update Octave Project Developers copyright for the new year John W. Eaton <jwe@octave.org> parents: 30400 diff changeset	3 ## Copyright (C) 2000-2022 The Octave Project Developers
27918 b442ec6dda5c use centralized file for copyright info for individual contributors John W. Eaton <jwe@octave.org> parents: 27803 diff changeset	4 ##
27923 bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	5 ## See the file COPYRIGHT.md in the top-level directory of this
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	6 ## distribution or <https://octave.org/copyright/>.
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	7 ##
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	8 ## This file is part of Octave.
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	9 ##
24534 194eb4bd202b maint: Update punctuation for GPL v3 license text. Rik <rik@octave.org> parents: 23220 diff changeset	10 ## Octave is free software: you can redistribute it and/or modify it
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	11 ## under the terms of the GNU General Public License as published by
24534 194eb4bd202b maint: Update punctuation for GPL v3 license text. Rik <rik@octave.org> parents: 23220 diff changeset	12 ## the Free Software Foundation, either version 3 of the License, or
22755 3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22323 diff changeset	13 ## (at your option) any later version.
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	14 ##
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	15 ## Octave is distributed in the hope that it will be useful, but
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	16 ## WITHOUT ANY WARRANTY; without even the implied warranty of
22755 3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22323 diff changeset	17 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22323 diff changeset	18 ## GNU General Public License for more details.
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	19 ##
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	20 ## You should have received a copy of the GNU General Public License
7016 93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 5827 diff changeset	21 ## along with Octave; see the file COPYING. If not, see
24534 194eb4bd202b maint: Update punctuation for GPL v3 license text. Rik <rik@octave.org> parents: 23220 diff changeset	22 ## <https://www.gnu.org/licenses/>.
27923 bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	23 ##
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	24 ########################################################################
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	25
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	26 ## -- texinfo --
30558 83aeaba707d8 doc: Use TF for output variable in documentation for isXXX functions in scripts/ directory. Rik <rik@octave.org> parents: 30400 diff changeset	27 ## @deftypefn {} {@var{tf} =} isprime (@var{x})
20162 2645f9ef8c88 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	28 ## Return a logical array which is true where the elements of @var{x} are prime
2645f9ef8c88 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	29 ## numbers and false where they are not.
11431 0d9640d755b1 Improve docstrings for all isXXX functions. Rik <octave@nomad.inbox5.com> parents: 10664 diff changeset	30 ##
19052 bb0c5e182c12 isprime.m: Update docstring to note that 1 is not prime. Rik <rik@octave.org> parents: 19050 diff changeset	31 ## A prime number is conventionally defined as a positive integer greater than
bb0c5e182c12 isprime.m: Update docstring to note that 1 is not prime. Rik <rik@octave.org> parents: 19050 diff changeset	32 ## 1 (e.g., 2, 3, @dots{}) which is divisible only by itself and 1. Octave
bb0c5e182c12 isprime.m: Update docstring to note that 1 is not prime. Rik <rik@octave.org> parents: 19050 diff changeset	33 ## extends this definition to include both negative integers and complex
bb0c5e182c12 isprime.m: Update docstring to note that 1 is not prime. Rik <rik@octave.org> parents: 19050 diff changeset	34 ## values. A negative integer is prime if its positive counterpart is prime.
bb0c5e182c12 isprime.m: Update docstring to note that 1 is not prime. Rik <rik@octave.org> parents: 19050 diff changeset	35 ## This is equivalent to @code{isprime (abs (x))}.
19597 db92e7e28e1f strip trailing whitespace from most source files John W. Eaton <jwe@octave.org> parents: 19052 diff changeset	36 ##
19050 2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19046 diff changeset	37 ## If @code{class (@var{x})} is complex, then primality is tested in the domain
25143 13fd0610480f doc: Use https whenever possible in @url entries. Rik <rik@octave.org> parents: 25054 diff changeset	38 ## of Gaussian integers (@url{https://en.wikipedia.org/wiki/Gaussian_integer}).
19050 2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19046 diff changeset	39 ## Some non-complex integers are prime in the ordinary sense, but not in the
2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19046 diff changeset	40 ## domain of Gaussian integers. For example, @math{5 = (1+2i)*(1-2i)} shows
2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19046 diff changeset	41 ## that 5 is not prime because it has a factor other than itself and 1.
2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19046 diff changeset	42 ## Exercise caution when testing complex and real values together in the same
2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19046 diff changeset	43 ## matrix.
2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19046 diff changeset	44 ##
2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19046 diff changeset	45 ## Examples:
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	46 ##
11431 0d9640d755b1 Improve docstrings for all isXXX functions. Rik <octave@nomad.inbox5.com> parents: 10664 diff changeset	47 ## @example
0d9640d755b1 Improve docstrings for all isXXX functions. Rik <octave@nomad.inbox5.com> parents: 10664 diff changeset	48 ## @group
0d9640d755b1 Improve docstrings for all isXXX functions. Rik <octave@nomad.inbox5.com> parents: 10664 diff changeset	49 ## isprime (1:6)
26600 f6730533820e doc: clean up doc example blocks for accuracy and consistent formatting Mike Miller <mtmiller@octave.org> parents: 26376 diff changeset	50 ## @result{} 0 1 1 0 1 0
11431 0d9640d755b1 Improve docstrings for all isXXX functions. Rik <octave@nomad.inbox5.com> parents: 10664 diff changeset	51 ## @end group
0d9640d755b1 Improve docstrings for all isXXX functions. Rik <octave@nomad.inbox5.com> parents: 10664 diff changeset	52 ## @end example
19046 89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19045 diff changeset	53 ##
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19045 diff changeset	54 ## @example
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19045 diff changeset	55 ## @group
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19045 diff changeset	56 ## isprime ([i, 2, 3, 5])
26600 f6730533820e doc: clean up doc example blocks for accuracy and consistent formatting Mike Miller <mtmiller@octave.org> parents: 26376 diff changeset	57 ## @result{} 0 0 1 0
19046 89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19045 diff changeset	58 ## @end group
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19045 diff changeset	59 ## @end example
19050 2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19046 diff changeset	60 ##
30261 a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	61 ## Programming Note: @code{isprime} is suitable for all @var{x}
a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	62 ## in the range abs(@var{x})
a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	63 ## @tex
a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	64 ## $ < 2^{64}$.
a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	65 ## @end tex
a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	66 ## @ifnottex
a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	67 ## < 2^64.
a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	68 ## @end ifnottex
19050 2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19046 diff changeset	69 ##
27803 e8823425a60b doc: Change markup for "Matlab". Markus Mützel <markus.muetzel@gmx.de> parents: 26600 diff changeset	70 ## Compatibility Note: @sc{matlab} does not extend the definition of prime
19050 2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19046 diff changeset	71 ## numbers and will produce an error if given negative or complex inputs.
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	72 ## @seealso{primes, factor, gcd, lcm}
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	73 ## @end deftypefn
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	74
30558 83aeaba707d8 doc: Use TF for output variable in documentation for isXXX functions in scripts/ directory. Rik <rik@octave.org> parents: 30400 diff changeset	75 function tf = isprime (x)
7125 f084ba47812b [project @ 2007-11-08 02:29:23 by jwe] jwe parents: 7017 diff changeset	76
28891 de5f2f9a64ff maint: Use same coding style when checking for a minimum of 1 input. Rik <rik@octave.org> parents: 27923 diff changeset	77 if (nargin < 1)
19041 0976f9fccbbd isprime.m: Verify that input is a real number (bug #43041) Rik <rik@octave.org> parents: 17744 diff changeset	78 print_usage ();
19046 89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19045 diff changeset	79 elseif (any (fix (x) != x))
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19045 diff changeset	80 error ("isprime: X contains non-integer entries");
19041 0976f9fccbbd isprime.m: Verify that input is a real number (bug #43041) Rik <rik@octave.org> parents: 17744 diff changeset	81 endif
0976f9fccbbd isprime.m: Verify that input is a real number (bug #43041) Rik <rik@octave.org> parents: 17744 diff changeset	82
19045 920a400929ca * isprime.m: Return an empty array for empty input Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19041 diff changeset	83 if (isempty (x))
30558 83aeaba707d8 doc: Use TF for output variable in documentation for isXXX functions in scripts/ directory. Rik <rik@octave.org> parents: 30400 diff changeset	84 tf = x;
19045 920a400929ca * isprime.m: Return an empty array for empty input Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19041 diff changeset	85 return;
920a400929ca * isprime.m: Return an empty array for empty input Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19041 diff changeset	86 endif
920a400929ca * isprime.m: Return an empty array for empty input Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19041 diff changeset	87
19046 89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19045 diff changeset	88 if (iscomplex (x))
30558 83aeaba707d8 doc: Use TF for output variable in documentation for isXXX functions in scripts/ directory. Rik <rik@octave.org> parents: 30400 diff changeset	89 tf = isgaussianprime (x);
19046 89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19045 diff changeset	90 return;
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19045 diff changeset	91 endif
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19045 diff changeset	92
30261 a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	93 ## Code strategy is to quickly compare entries in x with small primes
a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	94 ## using lookup(), then do direct division on larger numbers up to
a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	95 ## a threshold, then call Miller-Rabin for numbers over the threshold.
a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	96
a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	97 x = abs (x); # handle negative entries
19046 89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19045 diff changeset	98
30261 a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	99 ## Generate prime table of suitable length up to maxp.
a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	100 ## The value of maxp needs to be at least 37,
a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	101 ## because of the method used by __isprimelarge__ below.
30400 168da23530b4 maint: strip trailing spaces from code base. Rik <rik@octave.org> parents: 30261 diff changeset	102 maxp = 37;
30261 a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	103 pr = [2 3 5 7 11 13 17 19 23 29 31 37];
30558 83aeaba707d8 doc: Use TF for output variable in documentation for isXXX functions in scripts/ directory. Rik <rik@octave.org> parents: 30400 diff changeset	104 tf = lookup (pr, x, "b"); # quick search for table matches.
19050 2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19046 diff changeset	105
31050 3a93a77dd4cf Minor performance tweaks to isprime.m and __isprimelarge__.cc Arun Giridhar <arungiridhar@gmail.com> parents: 30564 diff changeset	106 THRESHOLD = 195e8;
30261 a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	107 ## FIXME: THRESHOLD is the input value at which Miller-Rabin
a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	108 ## becomes more efficient than direct division. For smaller numbers,
a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	109 ## use direct division. For larger numbers, use Miller-Rabin.
a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	110 ##
31050 3a93a77dd4cf Minor performance tweaks to isprime.m and __isprimelarge__.cc Arun Giridhar <arungiridhar@gmail.com> parents: 30564 diff changeset	111 ## From numerical experiments in Jun 2022, this was observed:
30261 a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	112 ## THRESHOLD Division Miller-Rabin
31050 3a93a77dd4cf Minor performance tweaks to isprime.m and __isprimelarge__.cc Arun Giridhar <arungiridhar@gmail.com> parents: 30564 diff changeset	113 ## 29e9 29.8196s 26.2484s (previous value)
3a93a77dd4cf Minor performance tweaks to isprime.m and __isprimelarge__.cc Arun Giridhar <arungiridhar@gmail.com> parents: 30564 diff changeset	114 ## 20e9 26.7445s 26.0161s
3a93a77dd4cf Minor performance tweaks to isprime.m and __isprimelarge__.cc Arun Giridhar <arungiridhar@gmail.com> parents: 30564 diff changeset	115 ## 10e9 20.9330s 25.3247s
3a93a77dd4cf Minor performance tweaks to isprime.m and __isprimelarge__.cc Arun Giridhar <arungiridhar@gmail.com> parents: 30564 diff changeset	116 ## 19e9 26.5397s 26.8987s
3a93a77dd4cf Minor performance tweaks to isprime.m and __isprimelarge__.cc Arun Giridhar <arungiridhar@gmail.com> parents: 30564 diff changeset	117 ## 195e8 26.5735s 26.4749s
3a93a77dd4cf Minor performance tweaks to isprime.m and __isprimelarge__.cc Arun Giridhar <arungiridhar@gmail.com> parents: 30564 diff changeset	118 ## which is close enough, so new threshold = 195e8.
30261 a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	119 ##
30400 168da23530b4 maint: strip trailing spaces from code base. Rik <rik@octave.org> parents: 30261 diff changeset	120 ## The test code was this:
168da23530b4 maint: strip trailing spaces from code base. Rik <rik@octave.org> parents: 30261 diff changeset	121 ## n = THRESHOLD - (1:1e7); tic; isprime(n); toc
168da23530b4 maint: strip trailing spaces from code base. Rik <rik@octave.org> parents: 30261 diff changeset	122 ## n = THRESHOLD + (1:1e7); tic; isprime(n); toc
30261 a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	123 ##
a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	124 ## Two notes for future programmers:
a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	125 ##
a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	126 ## 1. Test and tune THRESHOLD periodically. Miller-Rabin is only CPU-limited,
a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	127 ## while factorization by division is very memory-intensive. This is
a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	128 ## plainly noticeable from the loudness of the computer fans when running
a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	129 ## the division technique! CPU speed and RAM speed scale differently over
a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	130 ## time, so test and tune THRESHOLD periodically.
a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	131 ##
a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	132 ## 2. If you make improvements elsewhere in the code that favor one over
a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	133 ## the other (not symmetric), you should also retune THRESHOLD afterwards.
a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	134 ## If the Miller-Rabin part is sped up, the optimum THRESHOLD will
a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	135 ## decrease, and if factorization is sped up, it will increase.
a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	136 ##
19050 2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19046 diff changeset	137
30261 a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	138 ## Process large entries that are still suitable for direct division
a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	139 m = x (x > maxp & x <= THRESHOLD);
a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	140 if ( ! isempty (m))
a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	141 ## Start by dividing through by the small primes until the remaining list
a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	142 ## of entries is small (and most likely prime themselves).
a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	143 pr2 = primes (sqrt (max (m)));
30558 83aeaba707d8 doc: Use TF for output variable in documentation for isXXX functions in scripts/ directory. Rik <rik@octave.org> parents: 30400 diff changeset	144 tf \|= lookup (pr2, x, "b");
30261 a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	145 for p = pr2
19041 0976f9fccbbd isprime.m: Verify that input is a real number (bug #43041) Rik <rik@octave.org> parents: 17744 diff changeset	146 m = m(rem (m, p) != 0);
19050 2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19046 diff changeset	147 if (numel (m) < numel (pr) / 10)
19041 0976f9fccbbd isprime.m: Verify that input is a real number (bug #43041) Rik <rik@octave.org> parents: 17744 diff changeset	148 break;
0976f9fccbbd isprime.m: Verify that input is a real number (bug #43041) Rik <rik@octave.org> parents: 17744 diff changeset	149 endif
0976f9fccbbd isprime.m: Verify that input is a real number (bug #43041) Rik <rik@octave.org> parents: 17744 diff changeset	150 endfor
19050 2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19046 diff changeset	151
30261 a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	152 ## Check the remaining list of possible primes against the remaining
a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	153 ## prime factors which were not tested in the for loop.
a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	154 ## This is just an optimization to use arrayfun over for loop.
a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	155 pr2 = pr2 (pr2 > p);
a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	156 mm = arrayfun (@(x) all (rem (x, pr2)), m);
19041 0976f9fccbbd isprime.m: Verify that input is a real number (bug #43041) Rik <rik@octave.org> parents: 17744 diff changeset	157 m = m(mm);
19050 2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19046 diff changeset	158
2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19046 diff changeset	159 ## Add any remaining entries, which are truly prime, to the results.
30261 a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	160 if ( ! isempty (m))
30558 83aeaba707d8 doc: Use TF for output variable in documentation for isXXX functions in scripts/ directory. Rik <rik@octave.org> parents: 30400 diff changeset	161 tf \|= lookup (sort (m), x, "b");
10664 faff5367cc05 second isprime rewrite Jaroslav Hajek <highegg@gmail.com> parents: 10657 diff changeset	162 endif
7125 f084ba47812b [project @ 2007-11-08 02:29:23 by jwe] jwe parents: 7017 diff changeset	163 endif
f084ba47812b [project @ 2007-11-08 02:29:23 by jwe] jwe parents: 7017 diff changeset	164
30261 a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	165 ## Process remaining entries (everything above THRESHOLD) with Miller-Rabin
a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	166 ii = (x(:)' > THRESHOLD);
30558 83aeaba707d8 doc: Use TF for output variable in documentation for isXXX functions in scripts/ directory. Rik <rik@octave.org> parents: 30400 diff changeset	167 tf(ii) = __isprimelarge__ (x(ii));
30261 a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	168
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	169 endfunction
9984 d1cc2e0ddf55 isprime: produce logical result John W. Eaton <jwe@octave.org> parents: 7125 diff changeset	170
30558 83aeaba707d8 doc: Use TF for output variable in documentation for isXXX functions in scripts/ directory. Rik <rik@octave.org> parents: 30400 diff changeset	171 function tf = isgaussianprime (z)
21758 ffad2baa90f7 maint: Use newlines to make code more readable. Rik <rik@octave.org> parents: 20852 diff changeset	172
19050 2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19046 diff changeset	173 ## Assume prime unless proven otherwise
30558 83aeaba707d8 doc: Use TF for output variable in documentation for isXXX functions in scripts/ directory. Rik <rik@octave.org> parents: 30400 diff changeset	174 tf = true (size (z));
19046 89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19045 diff changeset	175
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19045 diff changeset	176 x = real (z);
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19045 diff changeset	177 y = imag (z);
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19045 diff changeset	178
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19045 diff changeset	179 ## If purely real or purely imaginary, ordinary prime test for
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19045 diff changeset	180 ## that complex part if that part is 3 mod 4.
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19045 diff changeset	181 xidx = y==0 & mod (x, 4) == 3;
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19045 diff changeset	182 yidx = x==0 & mod (y, 4) == 3;
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19045 diff changeset	183
30558 83aeaba707d8 doc: Use TF for output variable in documentation for isXXX functions in scripts/ directory. Rik <rik@octave.org> parents: 30400 diff changeset	184 tf(xidx) &= isprime (x(xidx));
83aeaba707d8 doc: Use TF for output variable in documentation for isXXX functions in scripts/ directory. Rik <rik@octave.org> parents: 30400 diff changeset	185 tf(yidx) &= isprime (y(yidx));
19046 89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19045 diff changeset	186
19050 2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19046 diff changeset	187 ## Otherwise, prime if x^2 + y^2 is prime
2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19046 diff changeset	188 zidx = ! (xidx \| yidx); # Skip entries that were already evaluated
2f117c4b5cb0 isprime.m: Document negative and complex inputs. Rik <rik@octave.org> parents: 19046 diff changeset	189 zabs = x(zidx).^2 + y(zidx).^2;
30558 83aeaba707d8 doc: Use TF for output variable in documentation for isXXX functions in scripts/ directory. Rik <rik@octave.org> parents: 30400 diff changeset	190 tf(zidx) &= isprime (zabs);
21758 ffad2baa90f7 maint: Use newlines to make code more readable. Rik <rik@octave.org> parents: 20852 diff changeset	191
19046 89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19045 diff changeset	192 endfunction
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19045 diff changeset	193
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19045 diff changeset	194
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	195 %!assert (isprime (3), true)
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	196 %!assert (isprime (4), false)
30261 a49c635b179d isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312). Arun Giridhar <arungiridhar@gmail.com> parents: 29359 diff changeset	197 %!assert (isprime (uint64 (18446744073709551557)), true)
19046 89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19045 diff changeset	198 %!assert (isprime (5i), false)
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19045 diff changeset	199 %!assert (isprime (7i), true)
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19045 diff changeset	200 %!assert (isprime ([1+2i, (2+3i)*(-1+2i)]), [true, false])
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19045 diff changeset	201 %!assert (isprime (-2), true)
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19045 diff changeset	202 %!assert (isprime (complex (-2)), false)
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19045 diff changeset	203 %!assert (isprime (2i), false)
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19045 diff changeset	204 %!assert (isprime ([i, 2, 3, 5]), [false, false, true, false])
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19045 diff changeset	205 %!assert (isprime (0), false)
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	206 %!assert (isprime (magic (3)), logical ([0, 0, 0; 1, 1, 1; 0, 0, 1]))
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	207
19833 9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions. Rik <rik@octave.org> parents: 19697 diff changeset	208 ## Test input validation
28896 90fea9cc9caa test: Add expected error message <Invalid call> to BIST tests for nargin. Rik <rik@octave.org> parents: 28891 diff changeset	209 %!error <Invalid call> isprime ()
19046 89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19045 diff changeset	210 %!error <X contains non-integer entries> isprime (0.5i)
89e275a4f6f6 Allow isprime to handle complex numbers (bug #43041) Jordi Gutiérrez Hermoso <jordigh@octave.org> parents: 19045 diff changeset	211 %!error <X contains non-integer entries> isprime (0.5)

Mercurial > octave

annotate scripts/specfun/isprime.m @ 31051:5f015f2829b7