1 /* mpz_nextprime(p,t) - compute the next prime > t and store that in p. 2 3 Copyright 1999, 2000, 2001, 2008, 2009, 2012 Free Software Foundation, Inc. 4 5 Contributed to the GNU project by Niels M�ller and Torbjorn Granlund. 6 7 This file is part of the GNU MP Library. 8 9 The GNU MP Library is free software; you can redistribute it and/or modify 10 it under the terms of the GNU Lesser General Public License as published by 11 the Free Software Foundation; either version 3 of the License, or (at your 12 option) any later version. 13 14 The GNU MP Library is distributed in the hope that it will be useful, but 15 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 16 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public 17 License for more details. 18 19 You should have received a copy of the GNU Lesser General Public License 20 along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. */ 21 22 #include "gmp.h" 23 #include "gmp-impl.h" 24 #include "longlong.h" 25 26 static const unsigned char primegap[] = 27 { 28 2,2,4,2,4,2,4,6,2,6,4,2,4,6,6,2,6,4,2,6,4,6,8,4,2,4,2,4,14,4,6, 29 2,10,2,6,6,4,6,6,2,10,2,4,2,12,12,4,2,4,6,2,10,6,6,6,2,6,4,2,10,14,4,2, 30 4,14,6,10,2,4,6,8,6,6,4,6,8,4,8,10,2,10,2,6,4,6,8,4,2,4,12,8,4,8,4,6, 31 12,2,18,6,10,6,6,2,6,10,6,6,2,6,6,4,2,12,10,2,4,6,6,2,12,4,6,8,10,8,10,8, 32 6,6,4,8,6,4,8,4,14,10,12,2,10,2,4,2,10,14,4,2,4,14,4,2,4,20,4,8,10,8,4,6, 33 6,14,4,6,6,8,6,12 34 }; 35 36 #define NUMBER_OF_PRIMES 167 37 38 void 39 mpz_nextprime (mpz_ptr p, mpz_srcptr n) 40 { 41 unsigned short *moduli; 42 unsigned long difference; 43 int i; 44 unsigned prime_limit; 45 unsigned long prime; 46 mp_size_t pn; 47 mp_bitcnt_t nbits; 48 unsigned incr; 49 TMP_SDECL; 50 51 /* First handle tiny numbers */ 52 if (mpz_cmp_ui (n, 2) < 0) 53 { 54 mpz_set_ui (p, 2); 55 return; 56 } 57 mpz_add_ui (p, n, 1); 58 mpz_setbit (p, 0); 59 60 if (mpz_cmp_ui (p, 7) <= 0) 61 return; 62 63 pn = SIZ(p); 64 MPN_SIZEINBASE_2EXP(nbits, PTR(p), pn, 1); 65 if (nbits / 2 >= NUMBER_OF_PRIMES) 66 prime_limit = NUMBER_OF_PRIMES - 1; 67 else 68 prime_limit = nbits / 2; 69 70 TMP_SMARK; 71 72 /* Compute residues modulo small odd primes */ 73 moduli = TMP_SALLOC_TYPE (prime_limit * sizeof moduli[0], unsigned short); 74 75 for (;;) 76 { 77 /* FIXME: Compute lazily? */ 78 prime = 3; 79 for (i = 0; i < prime_limit; i++) 80 { 81 moduli[i] = mpz_fdiv_ui (p, prime); 82 prime += primegap[i]; 83 } 84 85 #define INCR_LIMIT 0x10000 /* deep science */ 86 87 for (difference = incr = 0; incr < INCR_LIMIT; difference += 2) 88 { 89 /* First check residues */ 90 prime = 3; 91 for (i = 0; i < prime_limit; i++) 92 { 93 unsigned r; 94 /* FIXME: Reduce moduli + incr and store back, to allow for 95 division-free reductions. Alternatively, table primes[]'s 96 inverses (mod 2^16). */ 97 r = (moduli[i] + incr) % prime; 98 prime += primegap[i]; 99 100 if (r == 0) 101 goto next; 102 } 103 104 mpz_add_ui (p, p, difference); 105 difference = 0; 106 107 /* Miller-Rabin test */ 108 if (mpz_millerrabin (p, 25)) 109 goto done; 110 next:; 111 incr += 2; 112 } 113 mpz_add_ui (p, p, difference); 114 difference = 0; 115 } 116 done: 117 TMP_SFREE; 118 } 119