ALL: Add flint

2014-05-19 00:03:37 +02:00
parent a15ef46ea6
commit d51d8e3652
3752 changed files with 446416 additions and 0 deletions
--- a/external/flint-2.4.3/fmpz_factor/factor_trial_range.c
+++ b/external/flint-2.4.3/fmpz_factor/factor_trial_range.c
@@ -0,0 +1,133 @@
+/*=============================================================================
+
+    This file is part of FLINT.
+
+    FLINT 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 2 of the License, or
+    (at your option) any later version.
+
+    FLINT 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 FLINT; if not, write to the Free Software
+    Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301 USA
+
+=============================================================================*/
+/******************************************************************************
+
+    Copyright (C) 2010 Fredrik Johansson
+
+******************************************************************************/
+
+#include <gmp.h>
+#include "flint.h"
+#include "fmpz.h"
+#include "fmpz_vec.h"
+#include "mpn_extras.h"
+#include "ulong_extras.h"
+
+int
+fmpz_factor_trial_range(fmpz_factor_t factor, const fmpz_t n, ulong start, ulong num_primes)
+{
+    ulong exp;
+    mp_limb_t p;
+    mpz_t x;
+    mp_ptr xd;
+    mp_size_t xsize;
+    slong found;
+    slong trial_start, trial_stop;
+    int ret = 1;
+
+    if (!COEFF_IS_MPZ(*n))
+    {
+        fmpz_factor_si(factor, *n);
+
+        return ret;
+    }
+
+    _fmpz_factor_set_length(factor, 0);
+
+    /* Make an mpz_t copy whose limbs will be mutated */
+    mpz_init(x);
+    fmpz_get_mpz(x, n);
+    if (x->_mp_size < 0)
+    {
+        x->_mp_size = -(x->_mp_size);
+        factor->sign = -1;
+    }
+    else
+    {
+        factor->sign = 1;
+    }
+
+    xd = x->_mp_d;
+    xsize = x->_mp_size;
+
+    /* Factor out powers of two */
+    if (start == 0)
+    {
+       xsize = flint_mpn_remove_2exp(xd, xsize, &exp);
+       if (exp != 0)
+           _fmpz_factor_append_ui(factor, UWORD(2), exp);
+    }
+
+    trial_start = FLINT_MAX(1, start);
+    trial_stop = FLINT_MIN(start + 1000, start + num_primes);
+
+    do
+    {
+        found = flint_mpn_factor_trial(xd, xsize, trial_start, trial_stop);
+
+        if (found)
+        {
+            p = n_primes_arr_readonly(found+1)[found];
+            exp = 1;
+            xsize = flint_mpn_divexact_1(xd, xsize, p);
+
+            /* Check if p^2 divides n */
+            if (flint_mpn_divisible_1_p(xd, xsize, p))
+            {
+                /* TODO: when searching for squarefree numbers
+                   (Moebius function, etc), we can abort here. */
+                xsize = flint_mpn_divexact_1(xd, xsize, p);
+                exp = 2;
+            }
+
+            /* If we're up to cubes, then maybe there are higher powers */
+            if (exp == 2 && flint_mpn_divisible_1_p(xd, xsize, p))
+            {
+                xsize = flint_mpn_divexact_1(xd, xsize, p);
+                xsize = flint_mpn_remove_power_ascending(xd, xsize, &p, 1, &exp);
+                exp += 3;
+            }
+
+            _fmpz_factor_append_ui(factor, p, exp);
+            /* flint_printf("added %wu %wu\n", p, exp); */
+
+            /* Continue using only trial division whilst it is successful.
+               This allows quickly factoring huge highly composite numbers
+               such as factorials, which can arise in some applications. */
+            trial_start = found + 1;
+            trial_stop = FLINT_MIN(trial_start + 1000, start + num_primes);
+            continue;
+        }
+        else
+        {
+            /* Insert primality test, perfect power test, other factoring
+               algorithms here... */
+            trial_start = trial_stop;
+            trial_stop = FLINT_MIN(trial_start + 1000, start + num_primes);
+        }
+    } while ((xsize > 1 || xd[0] != 1) && trial_start != trial_stop);
+
+    /* Any factor left? */
+    if (xsize > 1 || xd[0] != 1)
+        ret = 0;
+
+    mpz_clear(x);
+    return ret;
+}