80 lines
2.4 KiB
C
80 lines
2.4 KiB
C
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/*=============================================================================
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This file is part of FLINT.
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FLINT is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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FLINT is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with FLINT; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2011 William Hart
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******************************************************************************/
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#define ulong ulongxx /* interferes with system includes */
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#include <math.h>
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#undef ulong
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#include <gmp.h>
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#include "flint.h"
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#include "ulong_extras.h"
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mp_limb_t n_factor_lehman(mp_limb_t n)
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{
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double limit;
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mp_limb_t cuberoot, k;
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n_factor_t factors;
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slong bound;
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#if FLINT64 /* cannot compute enough primes */
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if (n > UWORD(10000000000000000)) return n;
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#endif
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if ((n & 1) == 0) return 2;
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limit = pow(n, 1.0/3.0);
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cuberoot = (mp_limb_t) ceil(limit);
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bound = n_prime_pi(cuberoot);
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n_factor_init(&factors);
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if (n_factor_trial_range(&factors, n, 0, bound) != n)
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return factors.p[0];
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if ((factors.p[0] = n_factor_one_line(n, FLINT_FACTOR_ONE_LINE_ITERS)))
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if (factors.p[0] != n)
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return factors.p[0];
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for (k = 1; k <= cuberoot + 1; k++)
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{
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double low = 2.0*sqrt((double) k)*sqrt((double) n);
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mp_limb_t x = (mp_limb_t) ceil(low - 0.0001);
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mp_limb_t end = (mp_limb_t) floor(0.0001 + low + pow(n, 1.0/6.0)/((double) 4.0*sqrt((double) k)));
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mp_limb_t sub = k*n*4;
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for ( ; x <= end; x++)
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{
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mp_limb_t p, sq = x*x - sub;
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if (n_is_square(sq))
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{
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sq = sqrt((double) sq);
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p = n_gcd(n, x - sq);
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if (p != 1)
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return p;
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}
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}
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}
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return n;
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}
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