1/* mpn_trialdiv -- find small factors of an mpn number using trial division.
2
3   Contributed to the GNU project by Torbjorn Granlund.
4
5   THE FUNCTION IN THIS FILE IS INTERNAL WITH A MUTABLE INTERFACE.  IT IS ONLY
6   SAFE TO REACH IT THROUGH DOCUMENTED INTERFACES.  IN FACT, IT IS ALMOST
7   GUARANTEED THAT IT WILL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.
8
9Copyright 2009 Free Software Foundation, Inc.
10
11This file is part of the GNU MP Library.
12
13The GNU MP Library is free software; you can redistribute it and/or modify
14it under the terms of the GNU Lesser General Public License as published by
15the Free Software Foundation; either version 3 of the License, or (at your
16option) any later version.
17
18The GNU MP Library is distributed in the hope that it will be useful, but
19WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
20or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
21License for more details.
22
23You should have received a copy of the GNU Lesser General Public License
24along with the GNU MP Library.	If not, see http://www.gnu.org/licenses/.  */
25
26/*
27   Fast, division-free trial division for GMP.
28
29   This function will find the first (smallest) factor represented in
30   trialdivtab.h.  It does not stop the factoring effort just because it has
31   reached some sensible limit, such as the square root of the input number.
32
33   The caller can limit the factoring effort by passing NPRIMES.  The function
34   well then divide to *at least* that limit.  A position which only
35   mpn_trialdiv can make sense of is returned in the WHERE parameter.  It can
36   be used for restarting the factoring effort; the first call should pass 0
37   here.
38*/
39
40#include "gmp.h"
41#include "gmp-impl.h"
42
43struct gmp_primes_dtab {
44  mp_limb_t binv;
45  mp_limb_t lim;
46};
47
48struct gmp_primes_ptab {
49  mp_limb_t ppp;	/* primes, multiplied together */
50  mp_limb_t cps[7];	/* ppp values pre-computed for mpn_mod_1s_4p */
51  unsigned int idx:24;	/* index of  first primes in dtab */
52  unsigned int np :8;	/* number of primes related to this entry */
53};
54
55#define P(p,inv,lim) {inv,lim}
56
57#include "trialdivtab.h"
58
59#define PTAB_LINES (sizeof (gmp_primes_ptab) / sizeof (gmp_primes_ptab[0]))
60
61/* Attempt to find a factor of T using trial division.
62   Input: A non-negative number T.
63   Output: non-zero if we found a factor, zero otherwise.  To get the actual
64   prime factor, compute the mod B inverse of the return value.  */
65/* FIXME: We could optimize out one of the outer loop conditions if we
66   had a final ptab entry with a huge nd field.  */
67mp_limb_t
68mpn_trialdiv (mp_srcptr tp, mp_size_t tn, mp_size_t nprimes, int *where)
69{
70  mp_limb_t ppp;
71  mp_limb_t *cps;
72  struct gmp_primes_dtab *dp;
73  long i, j, idx, np;
74  mp_limb_t r, q;
75
76  ASSERT (tn >= 1);
77
78  for (i = *where; i < PTAB_LINES; i++)
79    {
80      ppp = gmp_primes_ptab[i].ppp;
81      cps = gmp_primes_ptab[i].cps;
82
83#if __GNU_MP_VERSION == 4 && __GNU_MP_VERSION_MINOR < 4
84      if (tn < 4)
85	r = mpn_mod_1 (tp, tn, ppp); /* FIXME */
86      else
87#endif
88	r = mpn_mod_1s_4p (tp, tn, ppp << cps[1], cps);
89
90      idx = gmp_primes_ptab[i].idx;
91      np = gmp_primes_ptab[i].np;
92
93      /* Check divisibility by individual primes.  */
94      dp = &gmp_primes_dtab[idx] + np;
95      for (j = -np; j < 0; j++)
96	{
97	  q = r * dp[j].binv;
98	  if (q <= dp[j].lim)
99	    {
100	      *where = i;
101	      return dp[j].binv;
102	    }
103	}
104
105      nprimes -= np;
106      if (nprimes <= 0)
107	return 0;
108    }
109  return 0;
110}
111