1 /* mpz_fac_ui(result, n) -- Set RESULT to N!.
3 Copyright (C) 1991, 1993, 1994, 1995 Free Software Foundation, Inc.
5 This file is part of the GNU MP Library.
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.
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.
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. */
32 mpz_fac_ui (mpz_ptr result, unsigned long int n)
34 mpz_fac_ui (result, n)
41 /* Be silly. Just multiply the numbers in ascending order. O(n**2). */
45 mpz_set_ui (result, 1L);
47 for (k = 2; k <= n; k++)
48 mpz_mul_ui (result, result, k);
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
57 unsigned long int p, k;
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];
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;
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.
77 unsigned int tree_cnt;
79 top = top_limit_so_far = -1;
82 for (k = 2; k <= n; k++)
84 /* Multiply the partial product in P with K. */
85 umul_ppmm (p1, p0, (mp_limb_t) p, (mp_limb_t) k);
87 /* Did we get overflow into the high limb, i.e. is the partial
88 product now more than one limb? */
93 if (tree_cnt % 2 == 0)
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. */
101 mpz_mul_ui (mp_stack[top], mp_stack[top], p);
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)
109 mpz_mul (mp_stack[top - 1],
110 mp_stack[top], mp_stack[top - 1]);
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.) */
120 if (top > top_limit_so_far)
122 if (top > MP_STACK_SIZE)
124 /* The stack is now bigger than ever, initialize the top
126 mpz_init_set_ui (mp_stack[top], p);
130 mpz_set_ui (mp_stack[top], p);
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. */
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 */
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. */
147 mpz_set_ui (result, p);
149 mpz_mul_ui (result, mp_stack[top--], p);
151 mpz_mul (result, result, mp_stack[top--]);
153 /* Free the storage allocated for MP_STACK. */
154 for (top = top_limit_so_far; top >= 0; top--)
155 mpz_clear (mp_stack[top]);