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
id_to_n(mp_limb_t id)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
n_to_bit(mp_limb_t n)97 n_to_bit (mp_limb_t n) { return ((n-5)|1)/3U; }
98
99 #if WANT_ASSERT
100 static mp_size_t
primesieve_size(mp_limb_t n)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
mpz_primorial_ui(mpz_ptr x,unsigned long n)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