Annotation of OpenXM_contrib/gmp/mpz/fac_ui.c, Revision 1.1.1.1
1.1 maekawa 1: /* mpz_fac_ui(result, n) -- Set RESULT to N!.
2:
3: Copyright (C) 1991, 1993, 1994, 1995 Free Software Foundation, Inc.
4:
5: This file is part of the GNU MP Library.
6:
7: The GNU MP Library is free software; you can redistribute it and/or modify
8: it under the terms of the GNU Library General Public License as published by
9: the Free Software Foundation; either version 2 of the License, or (at your
10: option) any later version.
11:
12: The GNU MP Library is distributed in the hope that it will be useful, but
13: WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
14: or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Library General Public
15: License for more details.
16:
17: You should have received a copy of the GNU Library General Public License
18: along with the GNU MP Library; see the file COPYING.LIB. If not, write to
19: the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
20: MA 02111-1307, USA. */
21:
22: #ifdef DBG
23: #include <stdio.h>
24: #endif
25:
26: #include "gmp.h"
27: #include "gmp-impl.h"
28: #include "longlong.h"
29:
30: void
31: #if __STDC__
32: mpz_fac_ui (mpz_ptr result, unsigned long int n)
33: #else
34: mpz_fac_ui (result, n)
35: mpz_ptr result;
36: unsigned long int n;
37: #endif
38: {
39: #if SIMPLE_FAC
40:
41: /* Be silly. Just multiply the numbers in ascending order. O(n**2). */
42:
43: unsigned long int k;
44:
45: mpz_set_ui (result, 1L);
46:
47: for (k = 2; k <= n; k++)
48: mpz_mul_ui (result, result, k);
49: #else
50:
51: /* Be smarter. Multiply groups of numbers in ascending order until the
52: product doesn't fit in a limb. Multiply these partial product in a
53: balanced binary tree fashion, to make the operand have as equal sizes
54: as possible. When the operands have about the same size, mpn_mul
55: becomes faster. */
56:
57: unsigned long int p, k;
58: mp_limb_t p1, p0;
59:
60: /* Stack of partial products, used to make the computation balanced
61: (i.e. make the sizes of the multiplication operands equal). The
62: topmost position of MP_STACK will contain a one-limb partial product,
63: the second topmost will contain a two-limb partial product, and so
64: on. MP_STACK[0] will contain a partial product with 2**t limbs.
65: To compute n! MP_STACK needs to be less than
66: log(n)**2/log(BITS_PER_MP_LIMB), so 30 is surely enough. */
67: #define MP_STACK_SIZE 30
68: mpz_t mp_stack[MP_STACK_SIZE];
69:
70: /* TOP is an index into MP_STACK, giving the topmost element.
71: TOP_LIMIT_SO_FAR is the largets value it has taken so far. */
72: int top, top_limit_so_far;
73:
74: /* Count of the total number of limbs put on MP_STACK so far. This
75: variable plays an essential role in making the compututation balanced.
76: See below. */
77: unsigned int tree_cnt;
78:
79: top = top_limit_so_far = -1;
80: tree_cnt = 0;
81: p = 1;
82: for (k = 2; k <= n; k++)
83: {
84: /* Multiply the partial product in P with K. */
85: umul_ppmm (p1, p0, (mp_limb_t) p, (mp_limb_t) k);
86:
87: /* Did we get overflow into the high limb, i.e. is the partial
88: product now more than one limb? */
89: if (p1 != 0)
90: {
91: tree_cnt++;
92:
93: if (tree_cnt % 2 == 0)
94: {
95: mp_size_t i;
96:
97: /* TREE_CNT is even (i.e. we have generated an even number of
98: one-limb partial products), which means that we have a
99: single-limb product on the top of MP_STACK. */
100:
101: mpz_mul_ui (mp_stack[top], mp_stack[top], p);
102:
103: /* If TREE_CNT is divisable by 4, 8,..., we have two
104: similar-sized partial products with 2, 4,... limbs at
105: the topmost two positions of MP_STACK. Multiply them
106: to form a new partial product with 4, 8,... limbs. */
107: for (i = 4; (tree_cnt & (i - 1)) == 0; i <<= 1)
108: {
109: mpz_mul (mp_stack[top - 1],
110: mp_stack[top], mp_stack[top - 1]);
111: top--;
112: }
113: }
114: else
115: {
116: /* Put the single-limb partial product in P on the stack.
117: (The next time we get a single-limb product, we will
118: multiply the two together.) */
119: top++;
120: if (top > top_limit_so_far)
121: {
122: if (top > MP_STACK_SIZE)
123: abort();
124: /* The stack is now bigger than ever, initialize the top
125: element. */
126: mpz_init_set_ui (mp_stack[top], p);
127: top_limit_so_far++;
128: }
129: else
130: mpz_set_ui (mp_stack[top], p);
131: }
132:
133: /* We ignored the last result from umul_ppmm. Put K in P as the
134: first component of the next single-limb partial product. */
135: p = k;
136: }
137: else
138: /* We didn't get overflow in umul_ppmm. Put p0 in P and try
139: with one more value of K. */
140: p = p0; /* bogus if long != mp_limb_t */
141: }
142:
143: /* We have partial products in mp_stack[0..top], in descending order.
144: We also have a small partial product in p.
145: Their product is the final result. */
146: if (top < 0)
147: mpz_set_ui (result, p);
148: else
149: mpz_mul_ui (result, mp_stack[top--], p);
150: while (top >= 0)
151: mpz_mul (result, result, mp_stack[top--]);
152:
153: /* Free the storage allocated for MP_STACK. */
154: for (top = top_limit_so_far; top >= 0; top--)
155: mpz_clear (mp_stack[top]);
156: #endif
157: }
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