Annotation of OpenXM_contrib/gmp/mpz/fac_ui.c, Revision 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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