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.h" 56 #include "gmp-impl.h" 57 #include <string.h> /* for memset */ 58 59 60 unsigned long int 61 gmp_nextprime (gmp_primesieve_t *ps) 62 { 63 unsigned long p, d, pi; 64 unsigned char *sp; 65 static unsigned char addtab[] = 66 { 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, 67 2,4,6,2,6,4,2,4,2,10,2,10 }; 68 unsigned char *addp = addtab; 69 unsigned long ai; 70 71 /* Look for already sieved primes. A sentinel at the end of the sieving 72 area allows us to use a very simple loop here. */ 73 d = ps->d; 74 sp = ps->s + d; 75 while (*sp != 0) 76 sp++; 77 if (sp != ps->s + SIEVESIZE) 78 { 79 d = sp - ps->s; 80 ps->d = d + 1; 81 return ps->s0 + 2 * d; 82 } 83 84 /* Handle the number 2 separately. */ 85 if (ps->s0 < 3) 86 { 87 ps->s0 = 3 - 2 * SIEVESIZE; /* Tricky */ 88 return 2; 89 } 90 91 /* Exhausted computed primes. Resieve, then call ourselves recursively. */ 92 93 #if 0 94 for (sp = ps->s; sp < ps->s + SIEVESIZE; sp++) 95 *sp = 0; 96 #else 97 memset (ps->s, 0, SIEVESIZE); 98 #endif 99 100 ps->s0 += 2 * SIEVESIZE; 101 102 /* Update sqrt_s0 as needed. */ 103 while ((ps->sqrt_s0 + 1) * (ps->sqrt_s0 + 1) <= ps->s0 + 2 * SIEVESIZE - 1) 104 ps->sqrt_s0++; 105 106 pi = ((ps->s0 + 3) / 2) % 3; 107 if (pi > 0) 108 pi = 3 - pi; 109 if (ps->s0 + 2 * pi <= 3) 110 pi += 3; 111 sp = ps->s + pi; 112 while (sp < ps->s + SIEVESIZE) 113 { 114 *sp = 1, sp += 3; 115 } 116 117 pi = ((ps->s0 + 5) / 2) % 5; 118 if (pi > 0) 119 pi = 5 - pi; 120 if (ps->s0 + 2 * pi <= 5) 121 pi += 5; 122 sp = ps->s + pi; 123 while (sp < ps->s + SIEVESIZE) 124 { 125 *sp = 1, sp += 5; 126 } 127 128 pi = ((ps->s0 + 7) / 2) % 7; 129 if (pi > 0) 130 pi = 7 - pi; 131 if (ps->s0 + 2 * pi <= 7) 132 pi += 7; 133 sp = ps->s + pi; 134 while (sp < ps->s + SIEVESIZE) 135 { 136 *sp = 1, sp += 7; 137 } 138 139 p = 11; 140 ai = 0; 141 while (p <= ps->sqrt_s0) 142 { 143 pi = ((ps->s0 + p) / 2) % p; 144 if (pi > 0) 145 pi = p - pi; 146 if (ps->s0 + 2 * pi <= p) 147 pi += p; 148 sp = ps->s + pi; 149 while (sp < ps->s + SIEVESIZE) 150 { 151 *sp = 1, sp += p; 152 } 153 p += addp[ai]; 154 ai = (ai + 1) % 48; 155 } 156 ps->d = 0; 157 return gmp_nextprime (ps); 158 } 159 160 void 161 gmp_init_primesieve (gmp_primesieve_t *ps) 162 { 163 ps->s0 = 0; 164 ps->sqrt_s0 = 0; 165 ps->d = SIEVESIZE; 166 ps->s[SIEVESIZE] = 0; /* sentinel */ 167 } 168