1 /* mpz_primorial_ui(RESULT, N) -- Set RESULT to N# the product of primes <= N.
3 Contributed to the GNU project by Marco Bodrato.
5 Copyright 2012 Free Software Foundation, Inc.
7 This file is part of the GNU MP Library.
9 The GNU MP Library is free software; you can redistribute it and/or modify
10 it under the terms of either:
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.
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
22 or both in parallel, as here.
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
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/. */
36 /* TODO: Remove duplicated constants / macros / static functions...
39 /*************************************************************/
40 /* Section macros: common macros, for swing/fac/bin (&sieve) */
41 /*************************************************************/
43 #define FACTOR_LIST_STORE(P, PR, MAX_PR, VEC, I) \
45 if ((PR) > (MAX_PR)) { \
46 (VEC)[(I)++] = (PR); \
52 #define LOOP_ON_SIEVE_CONTINUE(prime,end,sieve) \
57 if (((sieve)[__index] & __mask) == 0) \
59 (prime) = id_to_n(__i)
61 #define LOOP_ON_SIEVE_BEGIN(prime,start,end,off,sieve) \
63 mp_limb_t __mask, __index, __max_i, __i; \
65 __i = (start)-(off); \
66 __index = __i / GMP_LIMB_BITS; \
67 __mask = CNST_LIMB(1) << (__i % GMP_LIMB_BITS); \
70 LOOP_ON_SIEVE_CONTINUE(prime,end,sieve)
72 #define LOOP_ON_SIEVE_STOP \
74 __mask = __mask << 1 | __mask >> (GMP_LIMB_BITS-1); \
75 __index += __mask & 1; \
76 } while (__i <= __max_i) \
78 #define LOOP_ON_SIEVE_END \
82 /*********************************************************/
83 /* Section sieve: sieving functions and tools for primes */
84 /*********************************************************/
88 bit_to_n (mp_limb_t bit
) { return (bit
*3+4)|1; }
91 /* id_to_n (x) = bit_to_n (x-1) = (id*3+1)|1*/
93 id_to_n (mp_limb_t id
) { return id
*3+1+(id
&1); }
95 /* n_to_bit (n) = ((n-1)&(-CNST_LIMB(2)))/3U-1 */
97 n_to_bit (mp_limb_t n
) { return ((n
-5)|1)/3U; }
101 primesieve_size (mp_limb_t n
) { return n_to_bit(n
) / GMP_LIMB_BITS
+ 1; }
104 /*********************************************************/
105 /* Section primorial: implementation */
106 /*********************************************************/
109 mpz_primorial_ui (mpz_ptr x
, unsigned long n
)
111 static const mp_limb_t table
[] = { 1, 1, 2, 6, 6 };
113 ASSERT (n
<= GMP_NUMB_MAX
);
115 if (n
< numberof (table
))
117 PTR (x
)[0] = table
[n
];
122 mp_limb_t
*sieve
, *factors
;
128 size
= 1 + n
/ GMP_NUMB_BITS
+ n
/ (2*GMP_NUMB_BITS
);
129 ASSERT (size
>= primesieve_size (n
));
130 sieve
= MPZ_NEWALLOC (x
, size
);
131 size
= (gmp_primesieve (sieve
, n
) + 1) / log_n_max (n
) + 1;
134 factors
= TMP_ALLOC_LIMBS (size
);
138 prod
= table
[numberof (table
)-1];
140 /* Store primes from 5 to n */
142 mp_limb_t prime
, max_prod
;
144 max_prod
= GMP_NUMB_MAX
/ n
;
146 LOOP_ON_SIEVE_BEGIN (prime
, n_to_bit(numberof (table
)), n_to_bit (n
), 0, sieve
);
147 FACTOR_LIST_STORE (prime
, prod
, max_prod
, factors
, j
);
154 mpz_prodlimbs (x
, factors
, j
);