Mercurial > octave
view libinterp/corefcn/__isprimelarge__.cc @ 31605:e88a07dec498 stable
maint: Use macros to begin/end C++ namespaces.
* oct-conf-post-public.in.h: Define two macros (OCTAVE_BEGIN_NAMESPACE,
OCTAVE_END_NAMESPACE) that can be used to start/end a namespace.
* mk-opts.pl, build-env.h, build-env.in.cc, __betainc__.cc, __contourc__.cc,
__dsearchn__.cc, __eigs__.cc, __expint__.cc, __ftp__.cc, __gammainc__.cc,
__ichol__.cc, __ilu__.cc, __isprimelarge__.cc, __lin_interpn__.cc,
__magick_read__.cc, __pchip_deriv__.cc, __qp__.cc, amd.cc, auto-shlib.cc,
auto-shlib.h, balance.cc, base-text-renderer.cc, base-text-renderer.h,
besselj.cc, bitfcns.cc, bsxfun.cc, c-file-ptr-stream.cc, c-file-ptr-stream.h,
call-stack.cc, call-stack.h, ccolamd.cc, cellfun.cc, chol.cc, colamd.cc,
colloc.cc, conv2.cc, daspk.cc, dasrt.cc, dassl.cc, data.cc, data.h, debug.cc,
defaults.cc, defaults.h, defun-int.h, defun.cc, det.cc, dirfns.cc, display.cc,
display.h, dlmread.cc, dmperm.cc, dot.cc, dynamic-ld.cc, dynamic-ld.h, eig.cc,
ellipj.cc, environment.cc, environment.h, error.cc, error.h, errwarn.h,
event-manager.cc, event-manager.h, event-queue.cc, event-queue.h, fcn-info.cc,
fcn-info.h, fft.cc, fft2.cc, fftn.cc, file-io.cc, filter.cc, find.cc,
ft-text-renderer.cc, ft-text-renderer.h, gcd.cc, getgrent.cc, getpwent.cc,
getrusage.cc, givens.cc, gl-render.cc, gl-render.h, gl2ps-print.cc,
gl2ps-print.h, graphics-toolkit.cc, graphics-toolkit.h, graphics.cc,
graphics.in.h, gsvd.cc, gtk-manager.cc, gtk-manager.h, hash.cc, help.cc,
help.h, hess.cc, hex2num.cc, hook-fcn.cc, hook-fcn.h, input.cc, input.h,
interpreter-private.cc, interpreter-private.h, interpreter.cc, interpreter.h,
inv.cc, jsondecode.cc, jsonencode.cc, kron.cc, latex-text-renderer.cc,
latex-text-renderer.h, load-path.cc, load-path.h, load-save.cc, load-save.h,
lookup.cc, ls-ascii-helper.cc, ls-ascii-helper.h, ls-oct-text.cc, ls-utils.cc,
ls-utils.h, lsode.cc, lu.cc, mappers.cc, matrix_type.cc, max.cc, mex-private.h,
mex.cc, mgorth.cc, nproc.cc, oct-fstrm.cc, oct-fstrm.h, oct-hdf5-types.cc,
oct-hdf5-types.h, oct-hist.cc, oct-hist.h, oct-iostrm.cc, oct-iostrm.h,
oct-opengl.h, oct-prcstrm.cc, oct-prcstrm.h, oct-procbuf.cc, oct-procbuf.h,
oct-process.cc, oct-process.h, oct-stdstrm.h, oct-stream.cc, oct-stream.h,
oct-strstrm.cc, oct-strstrm.h, oct-tex-lexer.in.ll, oct-tex-parser.yy,
ordqz.cc, ordschur.cc, pager.cc, pager.h, pinv.cc, pow2.cc, pr-flt-fmt.cc,
pr-output.cc, procstream.cc, procstream.h, psi.cc, qr.cc, quad.cc, quadcc.cc,
qz.cc, rand.cc, rcond.cc, regexp.cc, schur.cc, settings.cc, settings.h,
sighandlers.cc, sighandlers.h, sparse-xdiv.cc, sparse-xdiv.h, sparse-xpow.cc,
sparse-xpow.h, sparse.cc, spparms.cc, sqrtm.cc, stack-frame.cc, stack-frame.h,
stream-euler.cc, strfind.cc, strfns.cc, sub2ind.cc, svd.cc, sylvester.cc,
symbfact.cc, syminfo.cc, syminfo.h, symrcm.cc, symrec.cc, symrec.h,
symscope.cc, symscope.h, symtab.cc, symtab.h, syscalls.cc, sysdep.cc, sysdep.h,
text-engine.cc, text-engine.h, text-renderer.cc, text-renderer.h, time.cc,
toplev.cc, tril.cc, tsearch.cc, typecast.cc, url-handle-manager.cc,
url-handle-manager.h, urlwrite.cc, utils.cc, utils.h, variables.cc,
variables.h, xdiv.cc, xdiv.h, xnorm.cc, xnorm.h, xpow.cc, xpow.h,
__delaunayn__.cc, __fltk_uigetfile__.cc, __glpk__.cc, __init_fltk__.cc,
__init_gnuplot__.cc, __ode15__.cc, __voronoi__.cc, audiodevinfo.cc,
audioread.cc, convhulln.cc, fftw.cc, gzip.cc, mk-build-env-features.sh,
mk-builtins.pl, cdef-class.cc, cdef-class.h, cdef-fwd.h, cdef-manager.cc,
cdef-manager.h, cdef-method.cc, cdef-method.h, cdef-object.cc, cdef-object.h,
cdef-package.cc, cdef-package.h, cdef-property.cc, cdef-property.h,
cdef-utils.cc, cdef-utils.h, ov-base.cc, ov-base.h, ov-bool-mat.cc,
ov-builtin.h, ov-cell.cc, ov-class.cc, ov-class.h, ov-classdef.cc,
ov-classdef.h, ov-complex.cc, ov-fcn-handle.cc, ov-fcn-handle.h, ov-fcn.h,
ov-java.cc, ov-java.h, ov-mex-fcn.h, ov-null-mat.cc, ov-oncleanup.cc,
ov-struct.cc, ov-typeinfo.cc, ov-typeinfo.h, ov-usr-fcn.cc, ov-usr-fcn.h,
ov.cc, ov.h, octave.cc, octave.h, mk-ops.sh, op-b-b.cc, op-b-bm.cc,
op-b-sbm.cc, op-bm-b.cc, op-bm-bm.cc, op-bm-sbm.cc, op-cdm-cdm.cc, op-cell.cc,
op-chm.cc, op-class.cc, op-cm-cm.cc, op-cm-cs.cc, op-cm-m.cc, op-cm-s.cc,
op-cm-scm.cc, op-cm-sm.cc, op-cs-cm.cc, op-cs-cs.cc, op-cs-m.cc, op-cs-s.cc,
op-cs-scm.cc, op-cs-sm.cc, op-dm-dm.cc, op-dm-scm.cc, op-dm-sm.cc,
op-dm-template.cc, op-dms-template.cc, op-fcdm-fcdm.cc, op-fcm-fcm.cc,
op-fcm-fcs.cc, op-fcm-fm.cc, op-fcm-fs.cc, op-fcn.cc, op-fcs-fcm.cc,
op-fcs-fcs.cc, op-fcs-fm.cc, op-fcs-fs.cc, op-fdm-fdm.cc, op-fm-fcm.cc,
op-fm-fcs.cc, op-fm-fm.cc, op-fm-fs.cc, op-fs-fcm.cc, op-fs-fcs.cc,
op-fs-fm.cc, op-fs-fs.cc, op-i16-i16.cc, op-i32-i32.cc, op-i64-i64.cc,
op-i8-i8.cc, op-int-concat.cc, op-m-cm.cc, op-m-cs.cc, op-m-m.cc, op-m-s.cc,
op-m-scm.cc, op-m-sm.cc, op-mi.cc, op-pm-pm.cc, op-pm-scm.cc, op-pm-sm.cc,
op-pm-template.cc, op-range.cc, op-s-cm.cc, op-s-cs.cc, op-s-m.cc, op-s-s.cc,
op-s-scm.cc, op-s-sm.cc, op-sbm-b.cc, op-sbm-bm.cc, op-sbm-sbm.cc,
op-scm-cm.cc, op-scm-cs.cc, op-scm-m.cc, op-scm-s.cc, op-scm-scm.cc,
op-scm-sm.cc, op-sm-cm.cc, op-sm-cs.cc, op-sm-m.cc, op-sm-s.cc, op-sm-scm.cc,
op-sm-sm.cc, op-str-m.cc, op-str-s.cc, op-str-str.cc, op-struct.cc,
op-ui16-ui16.cc, op-ui32-ui32.cc, op-ui64-ui64.cc, op-ui8-ui8.cc, ops.h,
anon-fcn-validator.cc, anon-fcn-validator.h, bp-table.cc, bp-table.h,
comment-list.cc, comment-list.h, filepos.h, lex.h, lex.ll, oct-lvalue.cc,
oct-lvalue.h, oct-parse.yy, parse.h, profiler.cc, profiler.h,
pt-anon-scopes.cc, pt-anon-scopes.h, pt-arg-list.cc, pt-arg-list.h,
pt-args-block.cc, pt-args-block.h, pt-array-list.cc, pt-array-list.h,
pt-assign.cc, pt-assign.h, pt-binop.cc, pt-binop.h, pt-bp.cc, pt-bp.h,
pt-cbinop.cc, pt-cbinop.h, pt-cell.cc, pt-cell.h, pt-check.cc, pt-check.h,
pt-classdef.cc, pt-classdef.h, pt-cmd.h, pt-colon.cc, pt-colon.h, pt-const.cc,
pt-const.h, pt-decl.cc, pt-decl.h, pt-eval.cc, pt-eval.h, pt-except.cc,
pt-except.h, pt-exp.cc, pt-exp.h, pt-fcn-handle.cc, pt-fcn-handle.h, pt-id.cc,
pt-id.h, pt-idx.cc, pt-idx.h, pt-jump.h, pt-loop.cc, pt-loop.h, pt-mat.cc,
pt-mat.h, pt-misc.cc, pt-misc.h, pt-pr-code.cc, pt-pr-code.h, pt-select.cc,
pt-select.h, pt-spmd.cc, pt-spmd.h, pt-stmt.cc, pt-stmt.h, pt-tm-const.cc,
pt-tm-const.h, pt-unop.cc, pt-unop.h, pt-vm-eval.cc, pt-walk.cc, pt-walk.h,
pt.cc, pt.h, token.cc, token.h, Range.cc, Range.h, idx-vector.cc, idx-vector.h,
range-fwd.h, CollocWt.cc, CollocWt.h, aepbalance.cc, aepbalance.h, chol.cc,
chol.h, gepbalance.cc, gepbalance.h, gsvd.cc, gsvd.h, hess.cc, hess.h,
lo-mappers.cc, lo-mappers.h, lo-specfun.cc, lo-specfun.h, lu.cc, lu.h,
oct-convn.cc, oct-convn.h, oct-fftw.cc, oct-fftw.h, oct-norm.cc, oct-norm.h,
oct-rand.cc, oct-rand.h, oct-spparms.cc, oct-spparms.h, qr.cc, qr.h, qrp.cc,
qrp.h, randgamma.cc, randgamma.h, randmtzig.cc, randmtzig.h, randpoisson.cc,
randpoisson.h, schur.cc, schur.h, sparse-chol.cc, sparse-chol.h, sparse-lu.cc,
sparse-lu.h, sparse-qr.cc, sparse-qr.h, svd.cc, svd.h, child-list.cc,
child-list.h, dir-ops.cc, dir-ops.h, file-ops.cc, file-ops.h, file-stat.cc,
file-stat.h, lo-sysdep.cc, lo-sysdep.h, lo-sysinfo.cc, lo-sysinfo.h,
mach-info.cc, mach-info.h, oct-env.cc, oct-env.h, oct-group.cc, oct-group.h,
oct-password.cc, oct-password.h, oct-syscalls.cc, oct-syscalls.h, oct-time.cc,
oct-time.h, oct-uname.cc, oct-uname.h, action-container.cc, action-container.h,
base-list.h, cmd-edit.cc, cmd-edit.h, cmd-hist.cc, cmd-hist.h, f77-fcn.h,
file-info.cc, file-info.h, lo-array-errwarn.cc, lo-array-errwarn.h, lo-hash.cc,
lo-hash.h, lo-ieee.h, lo-regexp.cc, lo-regexp.h, lo-utils.cc, lo-utils.h,
oct-base64.cc, oct-base64.h, oct-glob.cc, oct-glob.h, oct-inttypes.h,
oct-mutex.cc, oct-mutex.h, oct-refcount.h, oct-shlib.cc, oct-shlib.h,
oct-sparse.cc, oct-sparse.h, oct-string.h, octave-preserve-stream-state.h,
pathsearch.cc, pathsearch.h, quit.cc, quit.h, unwind-prot.cc, unwind-prot.h,
url-transfer.cc, url-transfer.h : Use new macros to begin/end C++ namespaces.
author | Rik <rik@octave.org> |
---|---|
date | Thu, 01 Dec 2022 14:23:45 -0800 |
parents | 23520a50d74d |
children | aac27ad79be6 |
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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_BEGIN_NAMESPACE(octave) // 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 */) { if (args.length () != 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'})) */ // This function implements a fast, private GCD function // optimized for uint64_t. No input validation by design. inline uint64_t localgcd (uint64_t a, uint64_t b) { return (a <= b) ? ( (b % a == 0) ? a : localgcd (a, b % a) ) : ( (a % b == 0) ? b : localgcd (a % b, b) ); } // This function implements a textbook version of the Pollard Rho // factorization algorithm with Brent update. // The code is short and simple, but the math behind it is complicated. uint64_t pollardrho (uint64_t n, uint64_t c = 1) { uint64_t i = 1, j = 2; // cycle index values uint64_t x = (c+1) % n; // can also be rand () % n uint64_t y = x; // other value in the chain uint64_t g = 0; // GCD while (true) { i++; // Calculate x = mod (x^2 + c, n) without overflow. x = safemultiply (x, x, n) + c; if (x >= n) x -= n; // Calculate GCD (abs (x-y), n). g = (x > y) ? localgcd (x - y, n) : (x < y) ? localgcd (y - x, n) : 0; if (i == j) // cycle detected ==> double j { y = x; j <<= 1; } if (g == n || i > 1000000) // cut losses, restart with a different c return pollardrho (n, c + 2); if (g > 1) // found GCD ==> exit loop properly { error_unless (n % g == 0); // theoretical possibility of GCD error return g; } } } DEFUN (__pollardrho__, args, , doc: /* -*- texinfo -*- @deftypefn {} {@var{x} =} __pollardrho__ (@var{n}) Private function. Use the Pollard Rho test to find a factor of @var{n}. The input @var{n} is required to be a composite 64-bit integer. Do not pass it a prime input! You should call factor(@var{n}) instead of directly calling this function. @seealso{isprime, factor} @end deftypefn */) { if (args.length () != 1) print_usage (); octave_uint64 inp = args(0).xuint64_scalar_value ("__pollardrho__: unable to convert input. Call factor() instead."); uint64_t n = inp; octave_uint64 retval = pollardrho (n); return ovl (retval); } /* %!assert (__pollardrho__ (uint64 (78567695338254293)), uint64 (443363)) %!assert (__pollardrho__ (1084978968791), uint64 (832957)) %!error <unable to convert input> (__pollardrho__ ({'foo'; 'bar'})) */ OCTAVE_END_NAMESPACE(octave)