Mercurial > octave
view libinterp/corefcn/__isprimelarge__.cc @ 31237:e3016248ca5d
uifigure.m: Call set () only if varargin is not empty (bug #63088)
* uifigure.m: Call set () only if varargin is not empty.
author | John Donoghue <john.donoghue@ieee.org> |
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date | Wed, 21 Sep 2022 09:55:32 -0400 |
parents | 5f015f2829b7 |
children | 068342cc93b8 |
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//////////////////////////////////////////////////////////////////////// // // Copyright (C) 2021-2022 The Octave Project Developers // // See the file COPYRIGHT.md in the top-level directory of this // distribution or <https://octave.org/copyright/>. // // This file is part of Octave. // // Octave is free software: you can redistribute it and/or modify it // under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // Octave is distributed in the hope that it will be useful, but // WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with Octave; see the file COPYING. If not, see // <https://www.gnu.org/licenses/>. // //////////////////////////////////////////////////////////////////////// #if defined (HAVE_CONFIG_H) # include "config.h" #endif #include "defun.h" #include "error.h" #include "ovl.h" OCTAVE_NAMESPACE_BEGIN // This function implements the Schrage technique for modular multiplication. // The returned value is equivalent to "mod (a*b, modulus)" // but calculated without overflow. uint64_t safemultiply (uint64_t a, uint64_t b, uint64_t modulus) { if (! a || ! b) return 0; else if (b == 1) return a; else if (a == 1) return b; else if (a > b) { uint64_t tmp = a; a = b; b = tmp; } uint64_t q = modulus / a; uint64_t r = modulus - q * a; uint64_t term1 = a * (b % q); uint64_t term2 = (r < q) ? r * (b / q) : safemultiply (r, b / q, modulus); return (term1 > term2) ? (term1 - term2) : (term1 + modulus - term2); } // This function returns "mod (a^b, modulus)" // but calculated without overflow. uint64_t safepower (uint64_t a, uint64_t b, uint64_t modulus) { uint64_t retval = 1; while (b > 0) { if (b & 1) retval = safemultiply (retval, a, modulus); b >>= 1; a = safemultiply (a, a, modulus); } return retval; } // This function implements a single round of Miller-Rabin primality testing. // Returns false if composite, true if pseudoprime for this divisor. bool millerrabin (uint64_t div, uint64_t d, uint64_t r, uint64_t n) { uint64_t x = safepower (div, d, n); if (x == 1 || x == n-1) return true; for (uint64_t j = 1; j < r; j++) { x = safemultiply (x, x, n); if (x == n-1) return true; } return false; } // This function uses the Miller-Rabin test to find out whether the input is // prime or composite. The input is required to be a scalar 64-bit integer. bool isprimescalar (uint64_t n) { // Fast return for even numbers. // n==2 is excluded by the time this function is called. if (! (n & 1)) return false; // n is now odd. Rewrite n as d * 2^r + 1, where d is odd. uint64_t d = n-1; uint64_t r = 0; while (! (d & 1)) { d >>= 1; r++; } // Miller-Rabin test with the first 12 primes. // If the number passes all 12 tests, then it is prime. // If it fails any, then it is composite. // The first 12 primes suffice to test all 64-bit integers. return millerrabin ( 2, d, r, n) && millerrabin ( 3, d, r, n) && millerrabin ( 5, d, r, n) && millerrabin ( 7, d, r, n) && millerrabin (11, d, r, n) && millerrabin (13, d, r, n) && millerrabin (17, d, r, n) && millerrabin (19, d, r, n) && millerrabin (23, d, r, n) && millerrabin (29, d, r, n) && millerrabin (31, d, r, n) && millerrabin (37, d, r, n); /* Mathematical references for the curious as to why we need only the 12 smallest primes for testing all 64-bit numbers: (1) https://oeis.org/A014233 Comment: a(12) > 2^64. Hence the primality of numbers < 2^64 can be determined by asserting strong pseudoprimality to all prime bases <= 37 (=prime(12)). Testing to prime bases <=31 does not suffice, as a(11) < 2^64 and a(11) is a strong pseudoprime to all prime bases <= 31 (=prime(11)). - Joerg Arndt, Jul 04 2012 (2) https://arxiv.org/abs/1509.00864 Strong Pseudoprimes to Twelve Prime Bases Jonathan P. Sorenson, Jonathan Webster In addition, a source listed here: https://miller-rabin.appspot.com/ reports that all 64-bit numbers can be covered with only 7 divisors, namely 2, 325, 9375, 28178, 450775, 9780504, and 1795265022. There was no peer-reviewed article to back it up though, so this code uses the 12 primes <= 37. */ } DEFUN (__isprimelarge__, args, , doc: /* -*- texinfo -*- @deftypefn {} {@var{x} =} __isprimelarge__ (@var{n}) Use the Miller-Rabin test to find out whether the elements of N are prime or composite. The input N is required to be a vector or array of 64-bit integers. You should call isprime(N) instead of directly calling this function. @seealso{isprime, factor} @end deftypefn */) { int nargin = args.length (); if (nargin != 1) print_usage (); // This function is intended for internal use by isprime.m, // so the following error handling should not be necessary. But it is // probably good practice for any curious users calling it directly. uint64NDArray vec = args(0).xuint64_array_value ("__isprimelarge__: unable to convert input. Call isprime() instead."); boolNDArray retval (vec.dims(), false); for (octave_idx_type i = vec.numel() - 1; i >= 0; i--) retval(i) = isprimescalar (vec(i)); // Note: If vec(i) <= 37, this function could go into an infinite loop. // That situation does not arise when calling this from isprime.m // but it could arise if the user calls this function directly with low input // or negative input. // But it turns out that adding this validation: // "if (vec(i) <= 37) then raise an error else call isprimescalar (vec(i))" // slows this function down by over 20% for some inputs, // so it is better to leave all the input validation in isprime.m // and not add it here. The function DOCSTRING now explicitly says: // "You should call isprime(N) instead of directly calling this function." return ovl (retval); } /* %!assert (__isprimelarge__ (41:50), logical ([1 0 1 0 0 0 1 0 0 0])) %!assert (__isprimelarge__ (uint64 (12345)), false) %!assert (__isprimelarge__ (uint64 (2147483647)), true) %!assert (__isprimelarge__ (uint64 (2305843009213693951)), true) %!assert (__isprimelarge__ (uint64 (18446744073709551557)), true) %!assert (__isprimelarge__ ([uint64(12345), uint64(2147483647), ... %! uint64(2305843009213693951), ... %! uint64(18446744073709551557)]), %! logical ([0 1 1 1])) %!error <unable to convert input> (__isprimelarge__ ({'foo'; 'bar'})) */ OCTAVE_NAMESPACE_END