math/gfreduce.[ch]: Fix out-of-bounds memory access.

[u/mdw/catacomb] / math / mpmul.h

/* -*-c-*-
 *
 * Multiply many small numbers together
 *
 * (c) 2000 Straylight/Edgeware
 */

/*----- Licensing notice --------------------------------------------------*
 *
 * This file is part of Catacomb.
 *
 * Catacomb is free software; you can redistribute it and/or modify
 * it under the terms of the GNU Library General Public License as
 * published by the Free Software Foundation; either version 2 of the
 * License, or (at your option) any later version.
 *
 * Catacomb is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU Library General Public License for more details.
 *
 * You should have received a copy of the GNU Library General Public
 * License along with Catacomb; if not, write to the Free
 * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
 * MA 02111-1307, USA.
 */

#ifndef CATACOMB_MPMUL_H
#define CATACOMB_MPMUL_H

#ifdef __cplusplus
  extern "C" {
#endif

/*----- Header files ------------------------------------------------------*/

#ifndef CATACOMB_MP_H
#  include "mp.h"
#endif

/*----- Magic numbers -----------------------------------------------------*/

/* --- How the algorithm works --- *
 *
 * Multiplication on large integers is least wasteful when the numbers
 * multiplied are approximately the same size.  When a new multiplier is
 * added to the system, we push it onto a stack.  Then we `reduce' the stack:
 * while the value on the top of the stack is not shorter than the value
 * below it, replace the top two elements by their product.
 *
 * Let %$b$% be the radix of our multiprecision integers, and let %$Z$% be
 * the maximum number of digits.  Then the largest integer we can represent
 * is %$M - 1 = b^Z - 1$%.  We could assume that all of the integers we're
 * given are about the same size.  This would give us the same upper bound as
 * that derived in `mptext.c'.
 *
 * However, we're in less control over our inputs.  In particular, if a
 * sequence of integers with strictly decreasing lengths is input then we're
 * sunk.  Suppose that the stack contains, from top to bottom, %$b^i$%,
 * %$b^{i+1}$%, ..., %$b^n$%.  The final product will therefore be
 * %$p = b^{(n+i)(n-i+1)/2}$%.  We must now find the maximum stack depth
 * %$d = n - i$% such that %$p > M$%.
 *
 * Taking logs of both sides gives that %$(d + 2 i)(d + 1) > 2 Z$%.  We can
 * maximize %$d$% by taking %$i = 0$%, which gives that %$d^2 + d > 2 Z$%, so
 * %$d$% must be approximately %$(\sqrt{8 Z + 1} - 1)/2$%, which is
 * uncomfortably large.
 *
 * We compromise by choosing double the `mptext' bound and imposing high- and
 * low-water marks for forced reduction.
 */

#define MPMUL_DEPTH (2 * (CHAR_BIT * sizeof(size_t) + 10))

/*----- Data structures ---------------------------------------------------*/

typedef struct mpmul {
  size_t i;
  mp *v[MPMUL_DEPTH];
} mpmul;

#define MPMUL_INIT { 0 }

/*----- Functions provided ------------------------------------------------*/

/* --- @mpmul_init@ --- *
 *
 * Arguments:	@mpmul *b@ = pointer to multiplier context to initialize
 *
 * Returns:	---
 *
 * Use:		Initializes a big multiplier context for use.
 */

extern void mpmul_init(mpmul */*b*/);

/* --- @mpmul_add@ --- *
 *
 * Arguments:	@mpmul *b@ = pointer to multiplier context
 *		@mp *x@ = the next factor to multiply in
 *
 * Returns:	---
 *
 * Use:		Contributes another factor to the mix.  It's important that
 *		the integer lasts at least as long as the multiplication
 *		context; this sort of rules out @mp_build@ integers.
 */

extern void mpmul_add(mpmul */*b*/, mp */*x*/);

/* --- @mpmul_done@ --- *
 *
 * Arguments:	@mpmul *b@ = pointer to big multiplication context
 *
 * Returns:	The product of all the numbers contributed.
 *
 * Use:		Returns a (large) product of numbers.  The context is
 *		deallocated.
 */

extern mp *mpmul_done(mpmul */*b*/);

/* --- @mp_factorial@ --- *
 *
 * Arguments:	@unsigned long i@ = number whose factorial should be
 *			computed.
 *
 * Returns:	The requested factorial.
 */

extern mp *mp_factorial(unsigned long /*i*/);

/*----- That's all, folks -------------------------------------------------*/

#ifdef __cplusplus
  }
#endif

#endif