1 /* mpz_primorial_ui(RESULT, N) -- Set RESULT to N# the product of primes <= N. 2 3 Contributed to the GNU project by Marco Bodrato. 4 5 Copyright 2012, 2015, 2016 Free Software Foundation, Inc. 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 either: 11 12 * the GNU Lesser General Public License as published by the Free 13 Software Foundation; either version 3 of the License, or (at your 14 option) any later version. 15 16 or 17 18 * the GNU General Public License as published by the Free Software 19 Foundation; either version 2 of the License, or (at your option) any 20 later version. 21 22 or both in parallel, as here. 23 24 The GNU MP Library is distributed in the hope that it will be useful, but 25 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 26 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License 27 for more details. 28 29 You should have received copies of the GNU General Public License and the 30 GNU Lesser General Public License along with the GNU MP Library. If not, 31 see https://www.gnu.org/licenses/. */ 32 33 #include "gmp-impl.h" 34 35 /* TODO: Remove duplicated constants / macros / static functions... 36 */ 37 38 /*************************************************************/ 39 /* Section macros: common macros, for swing/fac/bin (&sieve) */ 40 /*************************************************************/ 41 42 #define FACTOR_LIST_STORE(P, PR, MAX_PR, VEC, I) \ 43 do { \ 44 if ((PR) > (MAX_PR)) { \ 45 (VEC)[(I)++] = (PR); \ 46 (PR) = (P); \ 47 } else \ 48 (PR) *= (P); \ 49 } while (0) 50 51 #define LOOP_ON_SIEVE_CONTINUE(prime,end,sieve) \ 52 __max_i = (end); \ 53 \ 54 do { \ 55 ++__i; \ 56 if (((sieve)[__index] & __mask) == 0) \ 57 { \ 58 mp_limb_t prime; \ 59 prime = id_to_n(__i) 60 61 #define LOOP_ON_SIEVE_BEGIN(prime,start,end,off,sieve) \ 62 do { \ 63 mp_limb_t __mask, __index, __max_i, __i; \ 64 \ 65 __i = (start)-(off); \ 66 __index = __i / GMP_LIMB_BITS; \ 67 __mask = CNST_LIMB(1) << (__i % GMP_LIMB_BITS); \ 68 __i += (off); \ 69 \ 70 LOOP_ON_SIEVE_CONTINUE(prime,end,sieve) 71 72 #define LOOP_ON_SIEVE_STOP \ 73 } \ 74 __mask = __mask << 1 | __mask >> (GMP_LIMB_BITS-1); \ 75 __index += __mask & 1; \ 76 } while (__i <= __max_i) 77 78 #define LOOP_ON_SIEVE_END \ 79 LOOP_ON_SIEVE_STOP; \ 80 } while (0) 81 82 /*********************************************************/ 83 /* Section sieve: sieving functions and tools for primes */ 84 /*********************************************************/ 85 86 #if 0 87 static mp_limb_t 88 bit_to_n (mp_limb_t bit) { return (bit*3+4)|1; } 89 #endif 90 91 /* id_to_n (x) = bit_to_n (x-1) = (id*3+1)|1*/ 92 static mp_limb_t 93 id_to_n (mp_limb_t id) { return id*3+1+(id&1); } 94 95 /* n_to_bit (n) = ((n-1)&(-CNST_LIMB(2)))/3U-1 */ 96 static mp_limb_t 97 n_to_bit (mp_limb_t n) { return ((n-5)|1)/3U; } 98 99 #if WANT_ASSERT 100 static mp_size_t 101 primesieve_size (mp_limb_t n) { return n_to_bit(n) / GMP_LIMB_BITS + 1; } 102 #endif 103 104 /*********************************************************/ 105 /* Section primorial: implementation */ 106 /*********************************************************/ 107 108 void 109 mpz_primorial_ui (mpz_ptr x, unsigned long n) 110 { 111 ASSERT (n <= GMP_NUMB_MAX); 112 113 if (n < 5) 114 { 115 MPZ_NEWALLOC (x, 1)[0] = (066211 >> (n*3)) & 7; 116 SIZ (x) = 1; 117 } 118 else 119 { 120 mp_limb_t *sieve, *factors; 121 mp_size_t size, j; 122 mp_limb_t prod; 123 TMP_DECL; 124 125 size = n / GMP_NUMB_BITS; 126 size = size + (size >> 1) + 1; 127 ASSERT (size >= primesieve_size (n)); 128 sieve = MPZ_NEWALLOC (x, size); 129 size = (gmp_primesieve (sieve, n) + 1) / log_n_max (n) + 1; 130 131 TMP_MARK; 132 factors = TMP_ALLOC_LIMBS (size); 133 134 j = 0; 135 136 prod = 6; 137 138 /* Store primes from 5 to n */ 139 { 140 mp_limb_t max_prod; 141 142 max_prod = GMP_NUMB_MAX / n; 143 144 LOOP_ON_SIEVE_BEGIN (prime, n_to_bit(5), n_to_bit (n), 0, sieve); 145 FACTOR_LIST_STORE (prime, prod, max_prod, factors, j); 146 LOOP_ON_SIEVE_END; 147 } 148 149 if (j != 0) 150 { 151 factors[j++] = prod; 152 mpz_prodlimbs (x, factors, j); 153 } 154 else 155 { 156 PTR (x)[0] = prod; 157 SIZ (x) = 1; 158 } 159 160 TMP_FREE; 161 } 162 } 163