1 /* mpz_fac_ui(result, n) -- Set RESULT to N!.
3 Copyright (C) 1991 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 General Public License as published by
9 the Free Software Foundation; either version 2, or (at your option)
12 The GNU MP Library is distributed in the hope that it will be useful,
13 but WITHOUT ANY WARRANTY; without even the implied warranty of
14 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
15 GNU General Public License for more details.
17 You should have received a copy of the GNU General Public License
18 along with the GNU MP Library; see the file COPYING. If not, write to
19 the Free Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA. */
31 mpz_fac_ui (MP_INT *result, unsigned long int n)
33 mpz_fac_ui (result, n)
40 /* Be silly. Just multiply the numbers in ascending order. O(n**2). */
44 mpz_set_ui (result, (mp_limb) 1);
46 for (k = 2; k <= n; k++)
47 mpz_mul_ui (result, result, k);
50 /* Be smarter. Multiply groups of numbers in ascending order until the
51 product doesn't fit in a limb. Multiply these partial products in a
52 balanced binary tree fashion, to make the operand have as equal sizes
53 as possible. (When the operands have about the same size, mpn_mul
59 /* Stack of partial products, used to make the computation balanced
60 (i.e. make the sizes of the multiplication operands equal). The
61 topmost position of MP_STACK will contain a one-limb partial product,
62 the second topmost will contain a two-limb partial product, and so
63 on. MP_STACK[0] will contain a partial product with 2**t limbs.
64 To compute n! MP_STACK needs to be less than
65 log(n)**2/log(BITS_PER_MP_LIMB), so 30 is surely enough. */
66 #define MP_STACK_SIZE 30
67 MP_INT mp_stack[MP_STACK_SIZE];
69 /* TOP is an index into MP_STACK, giving the topmost element.
70 TOP_LIMIT_SO_FAR is the largets value it has taken so far. */
71 int top, top_limit_so_far;
73 /* Count of the total number of limbs put on MP_STACK so far. This
74 variable plays an essential role in making the compututation balanced.
76 unsigned int tree_cnt;
78 top = top_limit_so_far = -1;
81 for (k = 2; k <= n; k++)
83 /* Multiply the partial product in P with K. */
84 umul_ppmm (p1, p0, p, k);
86 /* Did we get overflow into the high limb, i.e. is the partial
87 product now more than one limb? */
92 if (tree_cnt % 2 == 0)
96 /* TREE_CNT is even (i.e. we have generated an even number of
97 one-limb partial products), which means that we have a
98 single-limb product on the top of MP_STACK. */
100 mpz_mul_ui (&mp_stack[top], &mp_stack[top], p);
102 /* If TREE_CNT is divisable by 4, 8,..., we have two
103 similar-sized partial products with 2, 4,... limbs at
104 the topmost two positions of MP_STACK. Multiply them
105 to form a new partial product with 4, 8,... limbs. */
106 for (i = 4; (tree_cnt & (i - 1)) == 0; i <<= 1)
108 mpz_mul (&mp_stack[top - 1],
109 &mp_stack[top], &mp_stack[top - 1]);
115 /* Put the single-limb partial product in P on the stack.
116 (The next time we get a single-limb product, we will
117 multiply the two together.) */
119 if (top > top_limit_so_far)
121 if (top > MP_STACK_SIZE)
123 /* The stack is now bigger than ever, initialize the top
125 mpz_init_set_ui (&mp_stack[top], p);
129 mpz_set_ui (&mp_stack[top], p);
132 /* We ignored the last result from umul_ppmm. Put K in P as the
133 first component of the next single-limb partial product. */
137 /* We didn't get overflow in umul_ppmm. Put p0 in P and try
138 with one more value of K. */
142 /* We have partial products in mp_stack[0..top], in descending order.
143 We also have a small partial product in p.
144 Their product is the final result. */
146 mpz_set_ui (result, p);
148 mpz_mul_ui (result, &mp_stack[top--], p);
150 mpz_mul (result, result, &mp_stack[top--]);
152 /* Free the storage allocated for MP_STACK. */
153 for (top = top_limit_so_far; top >= 0; top--)
154 mpz_clear (&mp_stack[top]);