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

   1 /* -*-c-*-
   2  *
   3  * Generate a random multiprecision integer
   4  *
   5  * (c) 1999 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 <mLib/alloc.h>
  31
  32 #include "grand.h"
  33 #include "mp.h"
  34 #include "mprand.h"
  35
  36 /*----- Main code ---------------------------------------------------------*/
  37
  38 /* --- @mprand@ --- *
  39  *
  40  * Arguments:   @mp *d@ = destination integer
  41  *              @unsigned b@ = number of bits
  42  *              @grand *r@ = pointer to random number source
  43  *              @mpw or@ = mask to OR with low-order bits
  44  *
  45  * Returns:     A random integer with the requested number of bits.
  46  *
  47  * Use:         Constructs an arbitrarily large pseudorandom integer.
  48  *              Assuming that the generator @r@ is good, the result is
  49  *              uniformly distributed in the interval %$[2^{b - 1}, 2^b)$%.
  50  *              The result is then ORred with the given @or@ value.  This
  51  *              will often be 1, to make the result odd.
  52  */
  53
  54 mp *mprand(mp *d, unsigned b, grand *r, mpw or)
  55 {
  56   size_t sz = (b + 7) >> 3;
  57   arena *a = (d && (d->f & MP_BURN)) ? arena_secure : arena_global;
  58   octet *v = x_alloc(a, sz);
  59   unsigned m;
  60
  61   /* --- Fill buffer with random data --- */
  62
  63   r->ops->fill(r, v, sz);
  64
  65   /* --- Force into the correct range --- *
  66    *
  67    * This is slightly tricky.  Oh, well.
  68    */
  69
  70   b = (b - 1) & 7;
  71   m = (1 << b);
  72   v[0] = (v[0] & (m - 1)) | m;
  73
  74   /* --- Mask, load and return --- */
  75
  76   d = mp_loadb(d, v, sz);
  77   d->v[0] |= or;
  78   memset(v, 0, sz);
  79   x_free(a, v);
  80   return (d);
  81 }
  82
  83 /* --- @mprand_range@ --- *
  84  *
  85  * Arguments:   @mp *d@ = destination integer
  86  *              @mp *l@ = limit for random number
  87  *              @grand *r@ = random number source
  88  *              @mpw or@ = mask for low-order bits
  89  *
  90  * Returns:     A pseudorandom integer, unformly distributed over the
  91  *              interval %$[0, l)$%.
  92  *
  93  * Use:         Generates a uniformly-distributed pseudorandom number in the
  94  *              appropriate range.
  95  */
  96
  97 mp *mprand_range(mp *d, mp *l, grand *r, mpw or)
  98 {
  99   size_t b = mp_bits(l);
 100   size_t sz = (b + 7) >> 3;
 101   arena *a = (d && (d->f & MP_BURN)) ? arena_secure : arena_global;
 102   octet *v = x_alloc(a, sz);
 103   unsigned m;
 104
 105   /* --- The algorithm --- *
 106    *
 107    * Rather simpler than most.  Find the number of bits in the number %$l$%
 108    * (i.e., the integer %$b$% such that %$2^{b - 1} \le l < 2^b$%), and
 109    * generate pseudorandom integers with %$n$% bits (but not, unlike in the
 110    * function above, with the top bit forced to 1).  If the integer is
 111    * greater than or equal to %$l$%, try again.
 112    *
 113    * This is similar to the algorithms used in @lcrand_range@ and friends,
 114    * except that I've forced the `raw' range of the random numbers such that
 115    * %$l$% itself is the largest multiple of %$l$% in the range (since, by
 116    * the inequality above, %$2^b \le 2l$%).  This removes the need for costly
 117    * division and remainder operations.
 118    *
 119    * As usual, the number of iterations expected is two.
 120    */
 121
 122   b = ((b - 1) & 7) + 1;
 123   m = (1 << b) - 1;
 124   do {
 125     r->ops->fill(r, v, sz);
 126     v[0] &= m;
 127     d = mp_loadb(d, v, sz);
 128     d->v[0] |= or;
 129   } while (MP_CMP(d, >=, l));
 130
 131   /* --- Done --- */
 132
 133   memset(v, 0, sz);
 134   x_free(a, v);
 135   return (d);
 136 }
 137
 138 /*----- That's all, folks -------------------------------------------------*/