1 /* mpz_mfac_uiui(RESULT, N, M) -- Set RESULT to N!^(M) = N(N-M)(N-2M)...
2
3 Contributed to the GNU project by Marco Bodrato.
4
5 Copyright 2012, 2013, 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 /*************************************************************/
36 /* Section macros: common macros, for swing/fac/bin (&sieve) */
37 /*************************************************************/
38
39 #define FACTOR_LIST_STORE(P, PR, MAX_PR, VEC, I) \
40 do { \
41 if ((PR) > (MAX_PR)) { \
42 (VEC)[(I)++] = (PR); \
43 (PR) = (P); \
44 } else \
45 (PR) *= (P); \
46 } while (0)
47
48 /*********************************************************/
49 /* Section oder factorials: */
50 /*********************************************************/
51
52 /* mpz_mfac_uiui (x, n, m) computes x = n!^(m) = n*(n-m)*(n-2m)*... */
53
54 void
mpz_mfac_uiui(mpz_ptr x,unsigned long n,unsigned long m)55 mpz_mfac_uiui (mpz_ptr x, unsigned long n, unsigned long m)
56 {
57 ASSERT (n <= GMP_NUMB_MAX);
58 ASSERT (m != 0);
59
60 if ((n < 3) | (n - 3 < m - 1)) { /* (n < 3 || n - 1 <= m || m == 0) */
61 MPZ_NEWALLOC (x, 1)[0] = n + (n == 0);
62 SIZ (x) = 1;
63 } else { /* 0 < m < n - 1 < GMP_NUMB_MAX */
64 mp_limb_t g, sn;
65 mpz_t t;
66
67 sn = n;
68 g = mpn_gcd_1 (&sn, 1, m);
69 if (g > 1) { n/=g; m/=g; }
70
71 if (m <= 2) { /* fac or 2fac */
72 if (m == 1) {
73 if (g > 2) {
74 mpz_init (t);
75 mpz_fac_ui (t, n);
76 sn = n;
77 } else {
78 if (g == 2)
79 mpz_2fac_ui (x, n << 1);
80 else
81 mpz_fac_ui (x, n);
82 return;
83 }
84 } else { /* m == 2 */
85 if (g > 1) {
86 mpz_init (t);
87 mpz_2fac_ui (t, n);
88 sn = n / 2 + 1;
89 } else {
90 mpz_2fac_ui (x, n);
91 return;
92 }
93 }
94 } else { /* m >= 3, gcd(n,m) = 1 */
95 mp_limb_t *factors;
96 mp_limb_t prod, max_prod;
97 mp_size_t j;
98 TMP_DECL;
99
100 sn = n / m + 1;
101
102 j = 0;
103 prod = n;
104 n -= m;
105 max_prod = GMP_NUMB_MAX / n;
106
107 if (g > 1)
108 factors = MPZ_NEWALLOC (x, sn / log_n_max (n) + 2);
109 else {
110 TMP_MARK;
111 factors = TMP_ALLOC_LIMBS (sn / log_n_max (n) + 2);
112 }
113
114 for (; n > m; n -= m)
115 FACTOR_LIST_STORE (n, prod, max_prod, factors, j);
116
117 factors[j++] = n;
118 factors[j++] = prod;
119
120 if (g > 1) {
121 mpz_init (t);
122 mpz_prodlimbs (t, factors, j);
123 } else {
124 mpz_prodlimbs (x, factors, j);
125 TMP_FREE;
126 return;
127 }
128 }
129
130 {
131 mpz_t p;
132
133 mpz_init (p);
134 mpz_ui_pow_ui (p, g, sn); /* g^sn */
135 mpz_mul (x, p, t);
136 mpz_clear (p);
137 mpz_clear (t);
138 }
139 }
140 }
141