Rearrange the file tree.

[u/mdw/catacomb] / mpmul.h

diff --git a/mpmul.h b/mpmul.h
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-/* -*-c-*-
- *
- * $Id: mpmul.h,v 1.2 2004/04/08 01:36:15 mdw Exp $
- *
- * 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