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 9 Copyright 2009, 2010, 2012, 2013 Free Software Foundation, Inc. 10 11 This file is part of the GNU MP Library. 12 13 The GNU MP Library is free software; you can redistribute it and/or modify 14 it under the terms of either: 15 16 * the GNU Lesser General Public License as published by the Free 17 Software Foundation; either version 3 of the License, or (at your 18 option) any later version. 19 20 or 21 22 * the GNU General Public License as published by the Free Software 23 Foundation; either version 2 of the License, or (at your option) any 24 later version. 25 26 or both in parallel, as here. 27 28 The GNU MP Library is distributed in the hope that it will be useful, but 29 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 30 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License 31 for more details. 32 33 You should have received copies of the GNU General Public License and the 34 GNU Lesser General Public License along with the GNU MP Library. If not, 35 see https://www.gnu.org/licenses/. */ 36 37 /* 38 This function finds the first (smallest) factor represented in 39 trialdivtab.h. It does not stop the factoring effort just because it has 40 reached some sensible limit, such as the square root of the input number. 41 42 The caller can limit the factoring effort by passing NPRIMES. The function 43 will then divide until that limit, or perhaps a few primes more. A position 44 which only mpn_trialdiv can make sense of is returned in the WHERE 45 parameter. It can be used for restarting the factoring effort; the first 46 call should pass 0 here. 47 48 Input: 1. A non-negative number T = {tp,tn} 49 2. NPRIMES as described above, 50 3. *WHERE as described above. 51 Output: 1. *WHERE updated as described above. 52 2. Return value is non-zero if we found a factor, else zero 53 To get the actual prime factor, compute the mod B inverse 54 of the return value. 55 */ 56 57 #include "gmp-impl.h" 58 59 struct gmp_primes_dtab { 60 mp_limb_t binv; 61 mp_limb_t lim; 62 }; 63 64 struct gmp_primes_ptab { 65 mp_limb_t ppp; /* primes, multiplied together */ 66 mp_limb_t cps[7]; /* ppp values pre-computed for mpn_mod_1s_4p */ 67 gmp_uint_least32_t idx:24; /* index of first primes in dtab */ 68 gmp_uint_least32_t np :8; /* number of primes related to this entry */ 69 }; 70 71 72 static const struct gmp_primes_dtab gmp_primes_dtab[] = 73 { 74 #define WANT_dtab 75 #define P(p,inv,lim) {inv,lim} 76 #include "trialdivtab.h" 77 #undef WANT_dtab 78 #undef P 79 {0,0} 80 }; 81 82 static const struct gmp_primes_ptab gmp_primes_ptab[] = 83 { 84 #define WANT_ptab 85 #include "trialdivtab.h" 86 #undef WANT_ptab 87 }; 88 89 #define PTAB_LINES (sizeof (gmp_primes_ptab) / sizeof (gmp_primes_ptab[0])) 90 91 /* FIXME: We could optimize out one of the outer loop conditions if we 92 had a final ptab entry with a huge np field. */ 93 mp_limb_t 94 mpn_trialdiv (mp_srcptr tp, mp_size_t tn, mp_size_t nprimes, int *where) 95 { 96 mp_limb_t ppp; 97 const mp_limb_t *cps; 98 const struct gmp_primes_dtab *dp; 99 long i, j, idx, np; 100 mp_limb_t r, q; 101 102 ASSERT (tn >= 1); 103 104 for (i = *where; i < PTAB_LINES; i++) 105 { 106 ppp = gmp_primes_ptab[i].ppp; 107 cps = gmp_primes_ptab[i].cps; 108 109 r = mpn_mod_1s_4p (tp, tn, ppp << cps[1], cps); 110 111 idx = gmp_primes_ptab[i].idx; 112 np = gmp_primes_ptab[i].np; 113 114 /* Check divisibility by individual primes. */ 115 dp = &gmp_primes_dtab[idx] + np; 116 for (j = -np; j < 0; j++) 117 { 118 q = r * dp[j].binv; 119 if (q <= dp[j].lim) 120 { 121 *where = i; 122 return dp[j].binv; 123 } 124 } 125 126 nprimes -= np; 127 if (nprimes <= 0) 128 return 0; 129 } 130 return 0; 131 } 132