git.distorted.org.uk Git - u/mdw/catacomb/blob - math/mptext-len.c

   1 /* -*-c-*-
   2  *
   3  * Work out length of a number's string representation
   4  *
   5  * (c) 2002 Straylight/Edgeware
   6  */
   7
   8 /*----- Licensing notice --------------------------------------------------*
   9  *
  10  * This file is part of Catacomb.
  11  *
  12  * Catacomb is free software; you can redistribute it and/or modify
  13  * it under the terms of the GNU Library General Public License as
  14  * published by the Free Software Foundation; either version 2 of the
  15  * License, or (at your option) any later version.
  16  *
  17  * Catacomb is distributed in the hope that it will be useful,
  18  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  19  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  20  * GNU Library General Public License for more details.
  21  *
  22  * You should have received a copy of the GNU Library General Public
  23  * License along with Catacomb; if not, write to the Free
  24  * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
  25  * MA 02111-1307, USA.
  26  */
  27
  28 /*----- Header files ------------------------------------------------------*/
  29
  30 #include "mp.h"
  31 #include "mptext.h"
  32
  33 /*----- Main code ---------------------------------------------------------*/
  34
  35 /* --- @mptext_len@ --- *
  36  *
  37  * Arguments:   @mp *x@ = number to work on
  38  *              @int r@ = radix the number will be expressed in
  39  *
  40  * Returns:     The number of digits needed to represent the number in the
  41  *              given base.  This will not include space for a leading sign
  42  *              (use @MP_NEGP@ to check that, or just add one on for luck);
  43  *              neither will it add space for a terminating null.  In general
  44  *              the answer will be an overestimate.
  45  */
  46
  47 size_t mptext_len(mp *x, int r)
  48 {
  49   unsigned long b = mp_bits(x);
  50   int s, ss = 2;
  51   size_t n;
  52   unsigned d = 0;
  53
  54   /* --- Huh? --- *
  55    *
  56    * The number of digits is at most %$\lceil b \log 2/\log r \rceil$%.  We
  57    * produce an underestimate of %$\log_2 r = \log r/\log 2$% and divide by
  58    * that.  How?  By linear interpolation between known points on the curve.
  59    * The known points are precisely the powers of 2, so we can find a pair
  60    * efficiently by doubling up.  The log curve is convex, so linear
  61    * interpolation between points on the curve is always an underestimate.
  62    *
  63    * The integer maths here is a bit weird, so here's how it works.  If
  64    * %$s = 2^d$% is the power of 2 below %$r$% then we want to compute
  65    * %$\lceil b/(d + (r - s)/s) \rceil = \lceil (b s)/(s(d - 1) + r \rceil$%
  66    * which is %$\lfloor (r + s (b + d - 1) - 1)/(r + s(d - 1)) \rfloor$%.
  67    * Gluing the whole computation together like this makes the code hard to
  68    * read, but means that there are fewer possibilities for rounding errors
  69    * and thus we get a tighter bound.
  70    */
  71
  72   /* --- Find the right pair of points --- */
  73
  74   if (r < 0) r = -r;
  75   do {
  76     s = ss;
  77     d++;
  78     if (r == s) {
  79       n = (b + (d - 1))/d;
  80       goto done;
  81     }
  82     ss = s << 1;
  83   } while (ss <= r);
  84
  85   /* --- Do the interpolation --- */
  86
  87   n = (r + s*(b + d - 1) - 1)/(r + s*(d - 1));
  88
  89   /* --- Fixups --- */
  90
  91 done:
  92   if (!n)
  93     n = 1;
  94   return (n);
  95 }
  96
  97 /*----- That's all, folks -------------------------------------------------*/