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   1 /* -*-c-*-
   2  *
   3  * $Id: mprand.c,v 1.2 1999/12/22 15:55:33 mdw Exp $
   4  *
   5  * Generate a random multiprecision integer
   6  *
   7  * (c) 1999 Straylight/Edgeware
   8  */
   9
  10 /*----- Licensing notice --------------------------------------------------*
  11  *
  12  * This file is part of Catacomb.
  13  *
  14  * Catacomb is free software; you can redistribute it and/or modify
  15  * it under the terms of the GNU Library General Public License as
  16  * published by the Free Software Foundation; either version 2 of the
  17  * License, or (at your option) any later version.
  18  *
  19  * Catacomb is distributed in the hope that it will be useful,
  20  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  21  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  22  * GNU Library General Public License for more details.
  23  *
  24  * You should have received a copy of the GNU Library General Public
  25  * License along with Catacomb; if not, write to the Free
  26  * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
  27  * MA 02111-1307, USA.
  28  */
  29
  30 /*----- Revision history --------------------------------------------------*
  31  *
  32  * $Log: mprand.c,v $
  33  * Revision 1.2  1999/12/22 15:55:33  mdw
  34  * Modify `mprand' slightly.  Add `mprand_range'.
  35  *
  36  * Revision 1.1  1999/12/10 23:23:05  mdw
  37  * Support for generating random large integers.
  38  *
  39  */
  40
  41 /*----- Header files ------------------------------------------------------*/
  42
  43 #include <mLib/alloc.h>
  44
  45 #include "grand.h"
  46 #include "mp.h"
  47 #include "mprand.h"
  48
  49 /*----- Main code ---------------------------------------------------------*/
  50
  51 /* --- @mprand@ --- *
  52  *
  53  * Arguments:   @mp *d@ = destination integer
  54  *              @unsigned b@ = number of bits
  55  *              @grand *r@ = pointer to random number source
  56  *              @mpw or@ = mask to OR with low-order bits
  57  *
  58  * Returns:     A random integer with the requested number of bits.
  59  *
  60  * Use:         Constructs an arbitrarily large pseudorandom integer.
  61  *              Assuming that the generator @r@ is good, the result is
  62  *              uniformly distributed in the interval %$[2^{b - 1}, 2^b)$%.
  63  *              The result is then ORred with the given @or@ value.  This
  64  *              will often be 1, to make the result odd.
  65  */
  66
  67 mp *mprand(mp *d, unsigned b, grand *r, mpw or)
  68 {
  69   size_t sz = (b + 7) >> 3;
  70   octet *v = xmalloc(sz);
  71   unsigned m;
  72
  73   /* --- Fill buffer with random data --- */
  74
  75   r->ops->fill(r, v, sz);
  76
  77   /* --- Force into the correct range --- *
  78    *
  79    * This is slightly tricky.  Oh, well.
  80    */
  81
  82   b = (b - 1) & 7;
  83   m = (1 << b);
  84   v[0] = (v[0] & (m - 1)) | m;
  85
  86   /* --- Mask, load and return --- */
  87
  88   d = mp_loadb(d, v, sz);
  89   d->v[0] |= or;
  90   free(v);
  91   return (d);
  92 }
  93
  94 /* --- @mprand_range@ --- *
  95  *
  96  * Arguments:   @mp *d@ = destination integer
  97  *              @mp *l@ = limit for random number
  98  *              @grand *r@ = random number source
  99  *              @mpw or@ = mask for low-order bits
 100  *
 101  * Returns:     A pseudorandom integer, unformly distributed over the
 102  *              interval %$[0, l)$%.
 103  *
 104  * Use:         Generates a uniformly-distributed pseudorandom number in the
 105  *              appropriate range.
 106  */
 107
 108 mp *mprand_range(mp *d, mp *l, grand *r, mpw or)
 109 {
 110   size_t b = mp_bits(l);
 111   size_t sz = (b + 7) >> 3;
 112   octet *v = xmalloc(sz);
 113   unsigned m;
 114
 115   /* --- The algorithm --- *
 116    *
 117    * Rather simpler than most.  Find the number of bits in the number %$l$%
 118    * (i.e., the integer %$b$% such that %$2^{b - 1} \le l < 2^b$%), and
 119    * generate pseudorandom integers with %$n$% bits (but not, unlike in the
 120    * function above, with the top bit forced to 1).  If the integer is
 121    * greater than or equal to %$l$%, try again.
 122    *
 123    * This is similar to the algorithms used in @lcrand_range@ and friends,
 124    * except that I've forced the `raw' range of the random numbers such that
 125    * %$l$% itself is the largest multiple of %$l$% in the range (since, by
 126    * the inequality above, %$2^b \le 2l$%).  This removes the need for costly
 127    * division and remainder operations.
 128    *
 129    * As usual, the number of iterations expected is two.
 130    */
 131
 132   b = (b - 1) & 7;
 133   m = (1 << b) - 1;
 134   do {
 135     r->ops->fill(r, v, sz);
 136     v[0] &= m;
 137     d = mp_loadb(d, v, sz);
 138     d->v[0] |= or;
 139   } while (MP_CMP(d, >=, l));
 140
 141   /* --- Done --- */
 142
 143   free(v);
 144   return (d);
 145 }
 146
 147 /*----- That's all, folks -------------------------------------------------*/