1 /* mpz_nextprime(p,t) - compute the next prime > t and store that in p. 2 3 Copyright 1999, 2000, 2001, 2008, 2009 Free Software Foundation, Inc. 4 5 Contributed to the GNU project by Niels M�ller and Torbj�rn 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 int cnt; 47 mp_size_t pn; 48 unsigned long nbits; 49 unsigned incr; 50 TMP_SDECL; 51 52 /* First handle tiny numbers */ 53 if (mpz_cmp_ui (n, 2) < 0) 54 { 55 mpz_set_ui (p, 2); 56 return; 57 } 58 mpz_add_ui (p, n, 1); 59 mpz_setbit (p, 0); 60 61 if (mpz_cmp_ui (p, 7) <= 0) 62 return; 63 64 pn = SIZ(p); 65 count_leading_zeros (cnt, PTR(p)[pn - 1]); 66 nbits = pn * GMP_NUMB_BITS - (cnt - GMP_NAIL_BITS); 67 if (nbits / 2 >= NUMBER_OF_PRIMES) 68 prime_limit = NUMBER_OF_PRIMES - 1; 69 else 70 prime_limit = nbits / 2; 71 72 TMP_SMARK; 73 74 /* Compute residues modulo small odd primes */ 75 moduli = TMP_SALLOC_TYPE (prime_limit * sizeof moduli[0], unsigned short); 76 77 for (;;) 78 { 79 /* FIXME: Compute lazily? */ 80 prime = 3; 81 for (i = 0; i < prime_limit; i++) 82 { 83 moduli[i] = mpz_fdiv_ui (p, prime); 84 prime += primegap[i]; 85 } 86 87 #define INCR_LIMIT 0x10000 /* deep science */ 88 89 for (difference = incr = 0; incr < INCR_LIMIT; difference += 2) 90 { 91 /* First check residues */ 92 prime = 3; 93 for (i = 0; i < prime_limit; i++) 94 { 95 unsigned r; 96 /* FIXME: Reduce moduli + incr and store back, to allow for 97 division-free reductions. Alternatively, table primes[]'s 98 inverses (mod 2^16). */ 99 r = (moduli[i] + incr) % prime; 100 prime += primegap[i]; 101 102 if (r == 0) 103 goto next; 104 } 105 106 mpz_add_ui (p, p, difference); 107 difference = 0; 108 109 /* Miller-Rabin test */ 110 if (mpz_millerrabin (p, 10)) 111 goto done; 112 next:; 113 incr += 2; 114 } 115 mpz_add_ui (p, p, difference); 116 difference = 0; 117 } 118 done: 119 TMP_SFREE; 120 } 121