Fast estimation of number representation lengths.

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

diff --git a/mptext-len.c b/mptext-len.c
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+/* -*-c-*-
+ *
+ * $Id: mptext-len.c,v 1.1 2002/10/15 22:58:29 mdw Exp $
+ *
+ * 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.
+ */
+
+/*----- Revision history --------------------------------------------------* 
+ *
+ * $Log: mptext-len.c,v $
+ * Revision 1.1  2002/10/15 22:58:29  mdw
+ * Fast estimation of number representation lengths.
+ *
+ */
+
+/*----- 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_ISNEG@ 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 --- */
+
+  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 -------------------------------------------------*/