1 /* gmp_nextprime -- generate small primes reasonably efficiently for internal 2 GMP needs. 3 4 Contributed to the GNU project by Torbjorn Granlund. Miscellaneous 5 improvements by Martin Boij. 6 7 THE FUNCTIONS IN THIS FILE ARE INTERNAL WITH MUTABLE INTERFACES. IT IS ONLY 8 SAFE TO REACH THEM THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST 9 GUARANTEED THAT THEY WILL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE. 10 11 Copyright 2009 Free Software Foundation, Inc. 12 13 This file is part of the GNU MP Library. 14 15 The GNU MP Library is free software; you can redistribute it and/or modify 16 it under the terms of either: 17 18 * the GNU Lesser General Public License as published by the Free 19 Software Foundation; either version 3 of the License, or (at your 20 option) any later version. 21 22 or 23 24 * the GNU General Public License as published by the Free Software 25 Foundation; either version 2 of the License, or (at your option) any 26 later version. 27 28 or both in parallel, as here. 29 30 The GNU MP Library is distributed in the hope that it will be useful, but 31 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 32 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License 33 for more details. 34 35 You should have received copies of the GNU General Public License and the 36 GNU Lesser General Public License along with the GNU MP Library. If not, 37 see https://www.gnu.org/licenses/. */ 38 39 /* 40 Optimisation ideas: 41 42 1. Unroll the sieving loops. Should reach 1 write/cycle. That would be a 2x 43 improvement. 44 45 2. Separate sieving with primes p < SIEVESIZE and p >= SIEVESIZE. The latter 46 will need at most one write, and thus not need any inner loop. 47 48 3. For primes p >= SIEVESIZE, i.e., typically the majority of primes, we 49 perform more than one division per sieving write. That might dominate the 50 entire run time for the nextprime function. A incrementally initialised 51 remainder table of Pi(65536) = 6542 16-bit entries could replace that 52 division. 53 */ 54 55 #include "gmp-impl.h" 56 #include <string.h> /* for memset */ 57 58 59 unsigned long int 60 gmp_nextprime (gmp_primesieve_t *ps) 61 { 62 unsigned long p, d, pi; 63 unsigned char *sp; 64 static unsigned char addtab[] = 65 { 2,4,2,4,6,2,6,4,2,4,6,6,2,6,4,2,6,4,6,8,4,2,4,2,4,8,6,4,6,2,4,6,2,6,6,4, 66 2,4,6,2,6,4,2,4,2,10,2,10 }; 67 unsigned char *addp = addtab; 68 unsigned long ai; 69 70 /* Look for already sieved primes. A sentinel at the end of the sieving 71 area allows us to use a very simple loop here. */ 72 d = ps->d; 73 sp = ps->s + d; 74 while (*sp != 0) 75 sp++; 76 if (sp != ps->s + SIEVESIZE) 77 { 78 d = sp - ps->s; 79 ps->d = d + 1; 80 return ps->s0 + 2 * d; 81 } 82 83 /* Handle the number 2 separately. */ 84 if (ps->s0 < 3) 85 { 86 ps->s0 = 3 - 2 * SIEVESIZE; /* Tricky */ 87 return 2; 88 } 89 90 /* Exhausted computed primes. Resieve, then call ourselves recursively. */ 91 92 #if 0 93 for (sp = ps->s; sp < ps->s + SIEVESIZE; sp++) 94 *sp = 0; 95 #else 96 memset (ps->s, 0, SIEVESIZE); 97 #endif 98 99 ps->s0 += 2 * SIEVESIZE; 100 101 /* Update sqrt_s0 as needed. */ 102 while ((ps->sqrt_s0 + 1) * (ps->sqrt_s0 + 1) <= ps->s0 + 2 * SIEVESIZE - 1) 103 ps->sqrt_s0++; 104 105 pi = ((ps->s0 + 3) / 2) % 3; 106 if (pi > 0) 107 pi = 3 - pi; 108 if (ps->s0 + 2 * pi <= 3) 109 pi += 3; 110 sp = ps->s + pi; 111 while (sp < ps->s + SIEVESIZE) 112 { 113 *sp = 1, sp += 3; 114 } 115 116 pi = ((ps->s0 + 5) / 2) % 5; 117 if (pi > 0) 118 pi = 5 - pi; 119 if (ps->s0 + 2 * pi <= 5) 120 pi += 5; 121 sp = ps->s + pi; 122 while (sp < ps->s + SIEVESIZE) 123 { 124 *sp = 1, sp += 5; 125 } 126 127 pi = ((ps->s0 + 7) / 2) % 7; 128 if (pi > 0) 129 pi = 7 - pi; 130 if (ps->s0 + 2 * pi <= 7) 131 pi += 7; 132 sp = ps->s + pi; 133 while (sp < ps->s + SIEVESIZE) 134 { 135 *sp = 1, sp += 7; 136 } 137 138 p = 11; 139 ai = 0; 140 while (p <= ps->sqrt_s0) 141 { 142 pi = ((ps->s0 + p) / 2) % p; 143 if (pi > 0) 144 pi = p - pi; 145 if (ps->s0 + 2 * pi <= p) 146 pi += p; 147 sp = ps->s + pi; 148 while (sp < ps->s + SIEVESIZE) 149 { 150 *sp = 1, sp += p; 151 } 152 p += addp[ai]; 153 ai = (ai + 1) % 48; 154 } 155 ps->d = 0; 156 return gmp_nextprime (ps); 157 } 158 159 void 160 gmp_init_primesieve (gmp_primesieve_t *ps) 161 { 162 ps->s0 = 0; 163 ps->sqrt_s0 = 0; 164 ps->d = SIEVESIZE; 165 ps->s[SIEVESIZE] = 0; /* sentinel */ 166 } 167