math/mpreduce.h: Missing include files.

[u/mdw/catacomb] / math / mptext-len.c

/* -*-c-*-
 *
 * Work out length of a number's string representation
 *
 * (c) 2002 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.
 */

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

#include "mp.h"
#include "mptext.h"

/*----- Main code ---------------------------------------------------------*/

/* --- @mptext_len@ --- *
 *
 * Arguments:	@mp *x@ = number to work on
 *		@int r@ = radix the number will be expressed in
 *
 * Returns:	The number of digits needed to represent the number in the
 *		given base.  This will not include space for a leading sign
 *		(use @MP_NEGP@ to check that, or just add one on for luck);
 *		neither will it add space for a terminating null.  In general
 *		the answer will be an overestimate.
 */

size_t mptext_len(mp *x, int r)
{
  unsigned long b = mp_bits(x);
  int s, ss = 2;
  size_t n;
  unsigned d = 0;

  /* --- Huh? --- *
   *
   * The number of digits is at most %$\lceil b \log 2/\log r \rceil$%.  We
   * produce an underestimate of %$\log_2 r = \log r/\log 2$% and divide by
   * that.  How?  By linear interpolation between known points on the curve.
   * The known points are precisely the powers of 2, so we can find a pair
   * efficiently by doubling up.  The log curve is convex, so linear
   * interpolation between points on the curve is always an underestimate.
   *
   * The integer maths here is a bit weird, so here's how it works.  If
   * %$s = 2^d$% is the power of 2 below %$r$% then we want to compute
   * %$\lceil b/(d + (r - s)/s) \rceil = \lceil (b s)/(s(d - 1) + r \rceil$%
   * which is %$\lfloor (r + s (b + d - 1) - 1)/(r + s(d - 1)) \rfloor$%.
   * Gluing the whole computation together like this makes the code hard to
   * read, but means that there are fewer possibilities for rounding errors
   * and thus we get a tighter bound.
   */

  /* --- Find the right pair of points --- */

  if (r < 0) r = -r;
  do {
    s = ss;
    d++;
    if (r == s) {
      n = (b + (d - 1))/d;
      goto done;
    }
    ss = s << 1;
  } while (ss <= r);

  /* --- Do the interpolation --- */

  n = (r + s*(b + d - 1) - 1)/(r + s*(d - 1));

  /* --- Fixups --- */

done:
  if (!n)
    n = 1;
  return (n);
}

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