408 lines
11 KiB
C
408 lines
11 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) 2006, 2011 William Hart
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******************************************************************************/
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#define ulong ulongxx /* interferes with system includes */
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#include <string.h>
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#include <stdlib.h>
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#include <stdio.h>
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#undef ulong
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#define ulong mp_limb_t
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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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#include "qsieve.h"
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#include "fmpz.h"
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void qsieve_ll_do_sieving(qs_t qs_inf, char * sieve)
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{
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slong num_primes = qs_inf->num_primes;
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mp_limb_t * soln1 = qs_inf->soln1;
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mp_limb_t * soln2 = qs_inf->soln2;
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prime_t * factor_base = qs_inf->factor_base;
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mp_limb_t p;
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char * end = sieve + qs_inf->sieve_size;
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register char * pos1;
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register char * pos2;
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register char * bound;
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slong size;
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slong diff;
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slong pind;
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memset(sieve, 0, qs_inf->sieve_size + sizeof(ulong));
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*end = (char) 255;
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for (pind = qs_inf->small_primes; pind < num_primes; pind++)
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{
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if (soln2[pind] == -1) continue; /* don't sieve with A factors */
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p = factor_base[pind].p;
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size = factor_base[pind].size;
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pos1 = sieve + soln1[pind];
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pos2 = sieve + soln2[pind];
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diff = pos2 - pos1;
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bound = end - 2*p;
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while (bound - pos1 > 0)
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{
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(*pos1) += size, (*(pos1 + diff)) += size, pos1 += p;
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(*pos1) += size, (*(pos1 + diff)) += size, pos1 += p;
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}
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while ((end - pos1 > 0) && (end - pos1 - diff > 0))
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{
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(*pos1) += size, (*(pos1 + diff)) += size, pos1 += p;
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}
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pos2 = pos1 + diff;
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if (end - pos2 > 0)
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{
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(*pos2) += size;
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}
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if (end - pos1 > 0)
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{
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(*pos1) += size;
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}
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}
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}
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slong qsieve_ll_evaluate_candidate(qs_t qs_inf, slong i, char * sieve)
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{
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slong bits, exp, extra_bits;
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mp_limb_t modp, prime;
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slong num_primes = qs_inf->num_primes;
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prime_t * factor_base = qs_inf->factor_base;
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fac_t * factor = qs_inf->factor;
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mp_limb_t * soln1 = qs_inf->soln1;
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mp_limb_t * soln2 = qs_inf->soln2;
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slong * small = qs_inf->small;
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mp_limb_t A = qs_inf->A;
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mp_limb_t B = qs_inf->B;
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mp_limb_t pinv;
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slong num_factors = 0;
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slong relations = 0;
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slong j;
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fmpz_t X, Y, res, p;
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fmpz_init(X);
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fmpz_init(Y);
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fmpz_init(res);
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fmpz_init(p);
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fmpz_set_ui(X, i);
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fmpz_sub_ui(X, X, qs_inf->sieve_size/2); /* X */
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#if (QS_DEBUG & 32)
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flint_printf("i = "); fmpz_print(X); flint_printf("\n");
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#endif
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fmpz_mul_ui(Y, X, A);
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if ((mp_limb_signed_t) B < 0)
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{
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fmpz_sub_ui(Y, Y, -B); /* Y = AX + B */
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fmpz_sub_ui(res, Y, -B);
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} else
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{
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fmpz_add_ui(Y, Y, B);
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fmpz_add_ui(res, Y, B);
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}
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fmpz_mul(res, res, X);
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fmpz_add(res, res, qs_inf->C); /* res = AX^2 + 2BX + C */
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bits = FLINT_ABS(fmpz_bits(res));
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bits -= BITS_ADJUST;
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extra_bits = 0;
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fmpz_set_ui(p, 2); /* divide out by powers of 2 */
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exp = fmpz_remove(res, res, p);
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#if (QS_DEBUG & 8)
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if (exp) flint_printf("2^%wd ", exp);
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#endif
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extra_bits += exp;
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small[1] = exp;
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if (factor_base[0].p != 1) /* divide out powers of the multiplier */
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{
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fmpz_set_ui(p, factor_base[0].p);
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exp = fmpz_remove(res, res, p);
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if (exp) extra_bits += exp*qs_inf->factor_base[0].size;
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small[0] = exp;
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#if (QS_DEBUG & 8)
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if (exp) flint_printf("%d^%wd ", factor_base[0].p, exp);
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#endif
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} else small[0] = 0;
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for (j = 2; j < qs_inf->small_primes; j++) /* pull out small primes */
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{
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prime = factor_base[j].p;
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pinv = factor_base[j].pinv;
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modp = n_mod2_preinv(i, prime, pinv);
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if ((modp == soln1[j]) || (modp == soln2[j]))
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{
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fmpz_set_ui(p, prime);
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exp = fmpz_remove(res, res, p);
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if (exp) extra_bits += qs_inf->factor_base[j].size;
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small[j] = exp;
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#if (QS_DEBUG & 8)
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if (exp)
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{
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fmpz_print(p);
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flint_printf("^%wd ", exp);
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}
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#endif
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} else small[j] = 0;
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}
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if (extra_bits + sieve[i] > bits)
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{
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sieve[i] += extra_bits;
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/* pull out remaining primes */
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for (j = qs_inf->small_primes; j < num_primes && extra_bits < sieve[i]; j++)
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{
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prime = factor_base[j].p;
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pinv = factor_base[j].pinv;
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modp = n_mod2_preinv(i, prime, pinv);
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if (soln2[j] != -1)
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{
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if ((modp == soln1[j]) || (modp == soln2[j]))
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{
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fmpz_set_ui(p, prime);
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exp = fmpz_remove(res, res, p);
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#if (QS_DEBUG & 8)
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if (exp)
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{
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fmpz_print(p);
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flint_printf("^%wd ", exp);
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}
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#endif
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if (exp)
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{
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extra_bits += qs_inf->factor_base[j].size;
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factor[num_factors].ind = j;
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factor[num_factors++].exp = exp;
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}
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}
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} else
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{
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fmpz_set_ui(p, prime);
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exp = fmpz_remove(res, res, p);
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factor[num_factors].ind = j;
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factor[num_factors++].exp = exp + 1;
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#if (QS_DEBUG & 8)
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if (exp)
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{
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fmpz_print(p);
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flint_printf("^%wd ", exp);
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}
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#endif
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}
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}
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if (fmpz_cmp_ui(res, 1) == 0 || fmpz_cmp_si(res, -1) == 0) /* We've found a relation */
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{
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mp_limb_t * A_ind = qs_inf->A_ind;
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slong i;
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for (i = 0; i < qs_inf->s; i++) /* Commit any outstanding A factors */
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{
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if (A_ind[i] >= j)
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{
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factor[num_factors].ind = A_ind[i];
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factor[num_factors++].exp = 1;
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}
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}
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qs_inf->num_factors = num_factors;
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relations += qsieve_ll_insert_relation(qs_inf, Y); /* Insert the relation in the matrix */
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if (qs_inf->num_relations >= qs_inf->buffer_size)
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{
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flint_printf("Error: too many duplicate relations!\n");
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flint_printf("s = %wd, bits = %wd\n", qs_inf->s, qs_inf->bits);
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abort();
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}
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goto cleanup;
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}
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}
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#if (QS_DEBUG & 8)
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flint_printf("\n");
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#endif
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cleanup:
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fmpz_clear(X);
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fmpz_clear(Y);
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fmpz_clear(res);
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fmpz_clear(p);
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return relations;
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}
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slong qsieve_ll_evaluate_sieve(qs_t qs_inf, char * sieve)
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{
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slong i = 0, j = 0;
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ulong * sieve2 = (ulong *) sieve;
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char bits = qs_inf->sieve_bits;
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slong rels = 0;
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#if (QS_DEBUG & 16)
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slong stats_limit;
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for (i = 0; i < 256; i++)
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qs_inf->sieve_tally[i] = 0;
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#endif
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#if (QS_DEBUG & 4)
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flint_printf("%wdX^2+2*%wdX+", qs_inf->A, qs_inf->B);
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fmpz_print(qs_inf->C); flint_printf("\n");
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#endif
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while (j < qs_inf->sieve_size/sizeof(ulong))
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{
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#if FLINT64
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while ((sieve2[j] & UWORD(0xE0E0E0E0E0E0E0E0)) == 0)
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#else
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while ((sieve2[j] & UWORD(0xE0E0E0E0)) == 0)
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#endif
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{
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#if (QS_DEBUG & 16)
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for (i = j*sizeof(ulong); i < (j+1)*sizeof(ulong) && i < qs_inf->sieve_size; i++)
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qs_inf->sieve_tally[(int)sieve[i]]++;
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#endif
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j++;
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}
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i = j*sizeof(ulong);
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while (i < (j+1)*sizeof(ulong) && i < qs_inf->sieve_size)
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{
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#if (QS_DEBUG & 16)
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qs_inf->sieve_tally[(int)sieve[i]]++;
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#endif
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if (sieve[i] > bits)
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rels += qsieve_ll_evaluate_candidate(qs_inf, i, sieve);
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i++;
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}
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j++;
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}
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#if (QS_DEBUG & 16)
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for (stats_limit = 255; stats_limit >= 0; stats_limit--)
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if (qs_inf->sieve_tally[stats_limit] != 0)
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break;
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for (i = 0; i <= stats_limit; i++)
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{
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if ((i % 16) == 0)
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flint_printf("|%wd:", i);
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flint_printf(" %wd", qs_inf->sieve_tally[i]);
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}
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flint_printf("|\n");
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flint_printf("Total of %wd relations for this sieve interval\n", rels);
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#endif
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return rels;
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}
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void qsieve_ll_update_offsets(int poly_add, mp_limb_t * poly_corr, qs_t qs_inf)
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{
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slong num_primes = qs_inf->num_primes;
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mp_limb_t * soln1 = qs_inf->soln1;
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mp_limb_t * soln2 = qs_inf->soln2;
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prime_t * factor_base = qs_inf->factor_base;
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mp_limb_t p, correction;
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slong pind;
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for (pind = 2; pind < num_primes; pind++)
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{
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p = factor_base[pind].p;
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correction = (poly_add ? p - poly_corr[pind] : poly_corr[pind]);
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soln1[pind] += correction;
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if (soln1[pind] >= p) soln1[pind] -= p;
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if (soln2[pind] == -1) continue;
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soln2[pind] += correction;
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if (soln2[pind] >= p) soln2[pind] -= p;
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}
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}
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slong qsieve_ll_collect_relations(qs_t qs_inf, char * sieve)
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{
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slong s = qs_inf->s;
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mp_limb_t ** A_inv2B = qs_inf->A_inv2B;
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mp_limb_t * poly_corr;
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slong relations = 0;
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slong poly_index, j;
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|
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int poly_add;
|
||
|
|
|
||
|
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qsieve_ll_compute_poly_data(qs_inf);
|
||
|
|
|
||
|
|
for (poly_index = 1; poly_index < (1<<(s - 1)); poly_index++)
|
||
|
|
{
|
||
|
|
for (j = 0; j < s; j++)
|
||
|
|
if (((poly_index >> j) & UWORD(1)) != UWORD(0)) break;
|
||
|
|
|
||
|
|
poly_add = ((poly_index >> j) & 2);
|
||
|
|
|
||
|
|
poly_corr = A_inv2B[j];
|
||
|
|
|
||
|
|
qsieve_ll_do_sieving(qs_inf, sieve);
|
||
|
|
|
||
|
|
relations += qsieve_ll_evaluate_sieve(qs_inf, sieve);
|
||
|
|
|
||
|
|
qsieve_ll_update_offsets(poly_add, poly_corr, qs_inf);
|
||
|
|
|
||
|
|
if (poly_add) qs_inf->B += (2*qs_inf->B_terms[j]);
|
||
|
|
else qs_inf->B -= (2*qs_inf->B_terms[j]);
|
||
|
|
|
||
|
|
qsieve_ll_compute_C(qs_inf);
|
||
|
|
|
||
|
|
qsieve_ll_compute_A_factor_offsets(qs_inf);
|
||
|
|
|
||
|
|
if (qs_inf->columns >= qs_inf->num_primes + qs_inf->extra_rels)
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
|
||
|
|
if (qs_inf->columns < qs_inf->num_primes + qs_inf->extra_rels)
|
||
|
|
{
|
||
|
|
qsieve_ll_do_sieving(qs_inf, sieve);
|
||
|
|
|
||
|
|
relations += qsieve_ll_evaluate_sieve(qs_inf, sieve);
|
||
|
|
|
||
|
|
relations += qsieve_ll_merge_relations(qs_inf);
|
||
|
|
}
|
||
|
|
|
||
|
|
return relations;
|
||
|
|
}
|