Mercurial > octave
annotate libinterp/corefcn/__isprimelarge__.cc @ 30346:91c6288781ba
maint: Shorten some long lines in libinterp to <= 80 characters (bug #57599)
* __isprimelarge__.cc, bsxfun.cc, cellfun.cc, chol.cc, data.cc, error.h,
event-manager.h, filter.cc, find.cc, gcd.cc, gl-render.h, gl2ps-print.cc,
graphics.cc, graphics.in.h, hash.cc, help.cc, hex2num.cc, input.cc, inv.cc,
load-path.cc, load-save.cc, ls-hdf5.cc, ls-hdf5.h, ls-mat5.cc, lu.cc,
mappers.cc, matrix_type.cc, max.cc, mex.cc, mxarray.h, oct-errno.in.cc,
oct-map.cc, oct-stream.cc, oct-stream.h, pr-output.cc, psi.cc, qr.cc, rand.cc,
regexp.cc, sparse-xdiv.h, stack-frame.cc, strfind.cc, strfns.cc, sylvester.cc,
symbfact.cc, symrec.h, symscope.cc, typecast.cc, utils.cc, variables.h, xdiv.h,
xpow.h, __init_fltk__.cc, __ode15__.cc, audiodevinfo.cc, audioread.cc,
convhulln.cc, cdef-class.cc, cdef-class.h, cdef-manager.cc, cdef-method.cc,
cdef-object.cc, cdef-object.h, cdef-package.h, cdef-utils.cc, ov-base-diag.cc,
ov-base-int.cc, ov-base.h, ov-bool-mat.cc, ov-bool.cc, ov-cell.cc,
ov-ch-mat.cc, ov-class.cc, ov-class.h, ov-classdef.cc, ov-colon.h,
ov-complex.cc, ov-cx-mat.cc, ov-cx-sparse.cc, ov-dld-fcn.h, ov-fcn-handle.cc,
ov-float.cc, ov-flt-complex.cc, ov-flt-cx-diag.cc, ov-flt-cx-mat.cc,
ov-flt-re-diag.cc, ov-flt-re-mat.cc, ov-java.cc, ov-lazy-idx.cc, ov-lazy-idx.h,
ov-range.cc, ov-re-mat.cc, ov-re-mat.h, ov-re-sparse.cc, ov-scalar.cc,
ov-str-mat.cc, ov-struct.cc, ov-typeinfo.cc, ov.cc, ov.h, octave.h,
bp-table.cc, bp-table.h, lex.h, oct-lvalue.h, profiler.cc, profiler.h,
pt-binop.h, pt-colon.cc, pt-eval.cc, pt-exp.h, pt-select.h:
Shorten some long lines in libinterp to <= 80 characters.
author | Rik <rik@octave.org> |
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date | Wed, 24 Nov 2021 09:38:51 -0800 |
parents | a49c635b179d |
children | 08f6bbd3ed23 c33284f08090 |
rev | line source |
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1 //////////////////////////////////////////////////////////////////////// |
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2 // |
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3 // Copyright (C) 1994-2021 The Octave Project Developers |
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4 // |
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5 // See the file COPYRIGHT.md in the top-level directory of this |
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6 // distribution or <https://octave.org/copyright/>. |
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7 // |
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8 // This file is part of Octave. |
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9 // |
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10 // Octave is free software: you can redistribute it and/or modify it |
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11 // under the terms of the GNU General Public License as published by |
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12 // the Free Software Foundation, either version 3 of the License, or |
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13 // (at your option) any later version. |
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14 // |
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15 // Octave is distributed in the hope that it will be useful, but |
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16 // WITHOUT ANY WARRANTY; without even the implied warranty of |
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17 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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18 // GNU General Public License for more details. |
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19 // |
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20 // You should have received a copy of the GNU General Public License |
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21 // along with Octave; see the file COPYING. If not, see |
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22 // <https://www.gnu.org/licenses/>. |
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23 // |
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24 //////////////////////////////////////////////////////////////////////// |
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25 |
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26 #include "defun.h" |
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27 #include "error.h" |
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28 #include "ovl.h" |
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29 |
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30 #include <iostream> |
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31 |
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32 OCTAVE_NAMESPACE_BEGIN |
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33 |
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34 // This function implements the Schrage technique for modular multiplication. |
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35 // The returned value is equivalent to "mod (a*b, modulus)" |
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36 // but calculated without overflow. |
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37 uint64_t safemultiply (uint64_t a, uint64_t b, uint64_t modulus) |
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38 { |
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39 if (! a || ! b) |
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40 return 0; |
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41 else if (b == 1) |
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42 return a; |
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43 else if (a == 1) |
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44 return b; |
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45 else if (a > b) |
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46 { |
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47 uint64_t tmp = a; |
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48 a = b; |
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49 b = tmp; |
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50 } |
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51 |
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52 uint64_t q = modulus / a; |
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53 uint64_t r = modulus - q * a; |
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54 uint64_t term1 = a * (b % q); |
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55 uint64_t term2 = (r < q) ? r * (b / q) : safemultiply (r, b / q, modulus); |
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56 return (term1 > term2) ? (term1 - term2) : (term1 + modulus - term2); |
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57 } |
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58 |
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59 // This function returns "mod (a^b, modulus)" |
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60 // but calculated without overflow. |
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61 uint64_t safepower (uint64_t a, uint64_t b, uint64_t modulus) |
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62 { |
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63 uint64_t retval = 1; |
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64 while (b > 0) |
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65 { |
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66 if (b & 1) |
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67 retval = safemultiply (retval, a, modulus); |
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68 b >>= 1; |
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69 a = safemultiply (a, a, modulus); |
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70 } |
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71 return retval; |
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72 } |
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73 |
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74 // This function implements a single round of Miller-Rabin primality testing. |
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75 // Returns false if composite, true if pseudoprime for this divisor. |
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76 bool millerrabin (uint64_t div, uint64_t d, uint64_t r, uint64_t n) |
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77 { |
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78 uint64_t x = safepower (div, d, n); |
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79 if (x == 1 || x == n-1) |
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80 return true; |
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81 |
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82 for (uint64_t j = 1; j < r; j++) |
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83 { |
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84 x = safemultiply (x, x, n); |
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85 if (x == n-1) |
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86 return true; |
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87 } |
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88 return false; |
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89 } |
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90 |
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91 // This function uses the Miller-Rabin test to find out whether the input is |
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92 // prime or composite. The input is required to be a scalar 64-bit integer. |
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93 bool isprimescalar (uint64_t n) |
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94 { |
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95 // Fast return for even numbers. |
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96 // n==2 is excluded by the time this function is called. |
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97 if (! (n & 1)) |
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98 return false; |
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99 |
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100 // n is now odd. Rewrite n as d * 2^r + 1, where d is odd. |
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101 uint64_t d = n-1; |
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102 uint64_t r = 0; |
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103 while (! (d & 1)) |
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104 { |
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105 d >>= 1; |
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106 r++; |
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107 } |
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108 |
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109 // Miller-Rabin test with the first 12 primes. |
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110 // If the number passes all 12 tests, then it is prime. |
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111 // If it fails any, then it is composite. |
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112 // The first 12 primes suffice to test all 64-bit integers. |
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113 if (! millerrabin ( 2, d, r, n)) return false; |
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114 if (! millerrabin ( 3, d, r, n)) return false; |
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115 if (! millerrabin ( 5, d, r, n)) return false; |
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116 if (! millerrabin ( 7, d, r, n)) return false; |
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117 if (! millerrabin (11, d, r, n)) return false; |
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118 if (! millerrabin (13, d, r, n)) return false; |
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119 if (! millerrabin (17, d, r, n)) return false; |
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120 if (! millerrabin (19, d, r, n)) return false; |
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121 if (! millerrabin (23, d, r, n)) return false; |
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122 if (! millerrabin (29, d, r, n)) return false; |
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123 if (! millerrabin (31, d, r, n)) return false; |
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124 if (! millerrabin (37, d, r, n)) return false; |
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125 // If we are all the way here, then it is prime. |
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126 return true; |
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127 |
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128 /* |
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129 Mathematical references for the curious as to why we need only |
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130 the 12 smallest primes for testing all 64-bit numbers: |
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131 (1) https://oeis.org/A014233 |
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132 Comment: a(12) > 2^64. Hence the primality of numbers < 2^64 can be |
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133 determined by asserting strong pseudoprimality to all prime bases <= 37 |
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134 (=prime(12)). Testing to prime bases <=31 does not suffice, |
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135 as a(11) < 2^64 and a(11) is a strong pseudoprime |
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136 to all prime bases <= 31 (=prime(11)). - Joerg Arndt, Jul 04 2012 |
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137 (2) https://arxiv.org/abs/1509.00864 |
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138 Strong Pseudoprimes to Twelve Prime Bases |
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139 Jonathan P. Sorenson, Jonathan Webster |
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140 |
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141 In addition, a source listed here: https://miller-rabin.appspot.com/ |
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142 reports that all 64-bit numbers can be covered with only 7 divisors, |
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143 namely 2, 325, 9375, 28178, 450775, 9780504, and 1795265022. |
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144 There was no peer-reviewed article to back it up though, |
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145 so this code uses the 12 primes <= 37. |
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146 */ |
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147 |
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148 } |
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149 |
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150 DEFUN (__isprimelarge__, args, , |
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151 doc: /* -*- texinfo -*- |
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152 @deftypefn {} {@var{x} =} __isprimelarge__ (@var{n}) |
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153 Use the Miller-Rabin test to find out whether the elements of N are prime or |
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154 composite. The input N is required to be a vector or array of 64-bit integers. |
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155 You should call isprime(N) instead of directly calling this function. |
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156 |
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157 @seealso{isprime, factor} |
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158 @end deftypefn */) |
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159 { |
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160 int nargin = args.length (); |
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161 if (nargin != 1) |
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162 print_usage (); |
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163 |
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164 // This function is intended for internal use by isprime.m, |
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165 // so the following error handling should not be necessary. But it is |
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166 // probably good practice for any curious users calling it directly. |
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167 uint64NDArray vec = args(0).xuint64_array_value |
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168 ("__isprimelarge__: unable to convert input. Call isprime() instead."); |
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169 |
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170 boolNDArray retval (vec.dims(), false); |
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171 |
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172 for (octave_idx_type i = vec.numel() - 1; i >= 0; i--) |
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173 retval(i) = isprimescalar (vec(i)); |
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174 // Note: If vec(i) <= 37, this function could go into an infinite loop. |
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175 // That situation does not arise when calling this from isprime.m |
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176 // but it could arise if the user calls this function directly with low input |
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177 // or negative input. |
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178 // But it turns out that adding this validation: |
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179 // "if (vec(i) <= 37) then raise an error else call isprimescalar (vec(i))" |
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180 // slows this function down by over 20% for some inputs, |
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181 // so it is better to leave all the input validation in isprime.m |
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182 // and not add it here. The function DOCSTRING now explicitly says: |
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183 // "You should call isprime(N) instead of directly calling this function." |
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184 |
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185 return ovl (retval); |
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186 } |
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187 |
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188 /* |
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189 %!assert (__isprimelarge__ (41:50), logical ([1 0 1 0 0 0 1 0 0 0])) |
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190 %!assert (__isprimelarge__ (uint64 (12345)), false) |
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191 %!assert (__isprimelarge__ (uint64 (2147483647)), true) |
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192 %!assert (__isprimelarge__ (uint64 (2305843009213693951)), true) |
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193 %!assert (__isprimelarge__ (uint64 (18446744073709551557)), true) |
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194 |
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195 %!assert (__isprimelarge__ ([uint64(12345), uint64(2147483647), ... |
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parents:
30261
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196 %! uint64(2305843009213693951), ... |
91c6288781ba
maint: Shorten some long lines in libinterp to <= 80 characters (bug #57599)
Rik <rik@octave.org>
parents:
30261
diff
changeset
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197 %! uint64(18446744073709551557)]), |
91c6288781ba
maint: Shorten some long lines in libinterp to <= 80 characters (bug #57599)
Rik <rik@octave.org>
parents:
30261
diff
changeset
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198 %! logical ([0 1 1 1])) |
30261
a49c635b179d
isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312).
Arun Giridhar <arungiridhar@gmail.com>
parents:
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199 |
a49c635b179d
isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312).
Arun Giridhar <arungiridhar@gmail.com>
parents:
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200 %!error <unable to convert input> (__isprimelarge__ ({'foo'; 'bar'})) |
a49c635b179d
isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312).
Arun Giridhar <arungiridhar@gmail.com>
parents:
diff
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201 */ |
a49c635b179d
isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312).
Arun Giridhar <arungiridhar@gmail.com>
parents:
diff
changeset
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202 |
a49c635b179d
isprime.m: Speed up for large integers using Miller-Rabin test (bug #61312).
Arun Giridhar <arungiridhar@gmail.com>
parents:
diff
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203 OCTAVE_NAMESPACE_END |