286 lines
8.4 KiB
C
286 lines
8.4 KiB
C
/*=============================================================================
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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 <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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/*
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Factor n = (hi, lo). Returns a factor of n.
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Assumes n is not prime and not a perfect power.
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Returns 0 if n is too large to be factored by this function.
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*/
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mp_limb_t qsieve_ll_factor(mp_limb_t hi, mp_limb_t lo)
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{
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qs_t qs_inf;
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mp_limb_t factor = 0, t;
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slong rels_found = 0;
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char * sieve;
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slong ncols, nrows, i, count;
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uint64_t * nullrows;
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uint64_t mask;
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flint_rand_t state;
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fmpz_t X, Y;
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/************************************************************************
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INITIALISATION:
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Initialise the qs_t structure.
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************************************************************************/
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#if QS_DEBUG
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flint_printf("\nStart:\n");
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#endif
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qsieve_ll_init(qs_inf, hi, lo);
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#if QS_DEBUG /* print some diagnostic information */
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{
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mpz_t _n;
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mpz_init(_n);
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flint_mpz_set_ui(_n, hi);
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mpz_mul_2exp(_n, _n, FLINT_BITS);
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flint_mpz_add_ui(_n, _n, lo);
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gmp_printf("Factoring %Zd of %wd bits\n", _n, qs_inf->bits);
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mpz_clear(_n);
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}
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#endif
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/************************************************************************
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KNUTH SCHROEPPEL:
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Try to compute a multiplier k such that there are a lot of small primes
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which are quadratic residues modulo kn. If a small factor of n is found
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during this process it is returned.
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************************************************************************/
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#if QS_DEBUG
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flint_printf("\nKnuth-Schroeppel:\n");
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#endif
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factor = qsieve_ll_knuth_schroeppel(qs_inf);
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if (factor)
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{
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#if QS_DEBUG
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flint_printf("Found small factor %wd in Knuth-Schroeppel\n", factor);
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#endif
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qsieve_ll_clear(qs_inf);
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return factor;
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}
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/* compute kn */
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fmpz_set_ui(qs_inf->kn, hi);
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fmpz_mul_2exp(qs_inf->kn, qs_inf->kn, FLINT_BITS);
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fmpz_add_ui(qs_inf->kn, qs_inf->kn, lo);
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fmpz_mul_ui(qs_inf->kn, qs_inf->kn, qs_inf->k);
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/* refine qs_inf->bits */
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qs_inf->bits = fmpz_bits(qs_inf->kn);
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if (qs_inf->bits > 2*FLINT_BITS)
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{
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qsieve_ll_clear(qs_inf);
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return 0; /* kn is too large to factor */
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}
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/************************************************************************
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COMPUTE FACTOR BASE:
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Try to compute a multiplier k such that there are a lot of small primes
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which are quadratic residues modulo kn. If a small factor of n is found
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during this process it is returned.
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************************************************************************/
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#if QS_DEBUG
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flint_printf("\nCompute factor base:\n");
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#endif
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/* compute factor base primes and associated data*/
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factor = qsieve_ll_primes_init(qs_inf);
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if (factor)
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{
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#if QS_DEBUG
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flint_printf("Found small factor %wd whilst generating factor base\n", factor);
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#endif
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qsieve_ll_clear(qs_inf);
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return factor;
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}
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/************************************************************************
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INITIALISE POLYNOMIAL DATA:
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Create space for all the polynomial information
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************************************************************************/
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#if QS_DEBUG
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flint_printf("\nInitialise poly:\n");
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#endif
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/* set (hi, lo) to kn */
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umul_ppmm(t, lo, lo, qs_inf->k);
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hi = hi*qs_inf->k + t;
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qs_inf->hi = hi;
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qs_inf->lo = lo;
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qsieve_ll_poly_init(qs_inf);
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/************************************************************************
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INITIALISE RELATION/LINAXYXYXYXY DATA:
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Create space for all the relations and matrix information
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************************************************************************/
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#if QS_DEBUG
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flint_printf("\nInitialise relations and linear algebra:\n");
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#endif
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qsieve_ll_linalg_init(qs_inf);
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/************************************************************************
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SIEVE:
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Sieve for relations
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************************************************************************/
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#if QS_DEBUG
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flint_printf("\nSieve:\n");
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#endif
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sieve = flint_malloc(qs_inf->sieve_size + sizeof(ulong));
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while (rels_found < qs_inf->num_primes + qs_inf->extra_rels)
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{
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rels_found += qsieve_ll_collect_relations(qs_inf, sieve);
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#if (QS_DEBUG & 128)
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flint_printf("%wd/%wd relations.\n", rels_found, qs_inf->num_primes + qs_inf->extra_rels);
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#endif
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}
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flint_free(sieve);
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/************************************************************************
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REDUCE MATRIX:
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Perform some light filtering on the matrix
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************************************************************************/
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ncols = qs_inf->num_primes + qs_inf->extra_rels;
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nrows = qs_inf->num_primes;
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#if QS_DEBUG
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flint_printf("Reduce matrix:\n");
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#endif
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reduce_matrix(qs_inf, &nrows, &ncols, qs_inf->matrix);
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/************************************************************************
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BLOCK LANCZOS:
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Find extra_rels nullspace vectors (if they exist)
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************************************************************************/
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#if QS_DEBUG
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flint_printf("Block lanczos:\n");
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#endif
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flint_randinit(state); /* initialise the random generator */
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do /* repeat block lanczos until it succeeds */
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{
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nullrows = block_lanczos(state, nrows, 0, ncols, qs_inf->matrix);
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} while (nullrows == NULL);
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for (i = 0, mask = 0; i < ncols; i++) /* create mask of nullspace vectors */
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mask |= nullrows[i];
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for (i = count = 0; i < 64; i++) /* count nullspace vectors found */
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{
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if (mask & ((uint64_t)(1) << i))
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count++;
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}
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flint_randclear(state); /* clean up random state */
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#if QS_DEBUG
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flint_printf("%wd nullspace vectors found\n", count);
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#endif
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/************************************************************************
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SQUARE ROOT:
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Compute the square root and take the GCD of X-Y with N
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************************************************************************/
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#if QS_DEBUG
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flint_printf("Square root:\n");
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#endif
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fmpz_fdiv_q_ui(qs_inf->kn, qs_inf->kn, qs_inf->k); /* divide kn by multiplier */
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fmpz_init(X);
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fmpz_init(Y);
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for (count = 0; count < 64; count++)
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{
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if (mask & ((uint64_t)(1) << count))
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{
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qsieve_ll_square_root(X, Y, qs_inf, nullrows, ncols, count, qs_inf->kn);
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fmpz_sub(X, X, Y);
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fmpz_gcd(X, X, qs_inf->kn);
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if (fmpz_cmp(X, qs_inf->kn) != 0 && fmpz_cmp_ui(X, 1) != 0) /* have a factor */
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{
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if (fmpz_size(X)!= 1)
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fmpz_fdiv_q(X, qs_inf->kn, X); /* take smaller of two factors */
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factor = fmpz_get_ui(X);
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break;
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}
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}
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}
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fmpz_clear(X);
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fmpz_clear(Y);
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flint_free(nullrows);
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/************************************************************************
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CLEAN UP:
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Free all used memory
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************************************************************************/
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#if QS_DEBUG
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flint_printf("\nClean up:\n");
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#endif
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qsieve_ll_clear(qs_inf);
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#if QS_DEBUG
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flint_printf("\nDone.\n");
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#endif
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return factor;
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}
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