From ab9fc001a865ff5c9e08e84298be9bcb9cc61e1b Mon Sep 17 00:00:00 2001
From: mdw <mdw>
Date: Wed, 22 Dec 1999 15:55:33 +0000
Subject: [PATCH] Modify `mprand' slightly.  Add `mprand_range'.

---
 mprand.c | 62 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++---
 1 file changed, 59 insertions(+), 3 deletions(-)

diff --git a/mprand.c b/mprand.c
index 41c2b39..bf8af69 100644
--- a/mprand.c
+++ b/mprand.c
@@ -1,6 +1,6 @@
 /* -*-c-*-
  *
- * $Id: mprand.c,v 1.1 1999/12/10 23:23:05 mdw Exp $
+ * $Id: mprand.c,v 1.2 1999/12/22 15:55:33 mdw Exp $
  *
  * Generate a random multiprecision integer
  *
@@ -30,6 +30,9 @@
 /*----- Revision history --------------------------------------------------* 
  *
  * $Log: mprand.c,v $
+ * Revision 1.2  1999/12/22 15:55:33  mdw
+ * Modify `mprand' slightly.  Add `mprand_range'.
+ *
  * Revision 1.1  1999/12/10 23:23:05  mdw
  * Support for generating random large integers.
  *
@@ -63,7 +66,7 @@
 
 mp *mprand(mp *d, unsigned b, grand *r, mpw or)
 {
-  size_t sz = (b + 7) / 8;
+  size_t sz = (b + 7) >> 3;
   octet *v = xmalloc(sz);
   unsigned m;
 
@@ -76,7 +79,7 @@ mp *mprand(mp *d, unsigned b, grand *r, mpw or)
    * This is slightly tricky.  Oh, well.
    */
 
-  b = (b - 1) % 8;
+  b = (b - 1) & 7;
   m = (1 << b);
   v[0] = (v[0] & (m - 1)) | m;
 
@@ -88,4 +91,57 @@ mp *mprand(mp *d, unsigned b, grand *r, mpw or)
   return (d);
 }
 
+/* --- @mprand_range@ --- *
+ *
+ * Arguments:	@mp *d@ = destination integer
+ *		@mp *l@ = limit for random number
+ *		@grand *r@ = random number source
+ *		@mpw or@ = mask for low-order bits
+ *
+ * Returns: 	A pseudorandom integer, unformly distributed over the
+ *		interval %$[0, l)$%.
+ *
+ * Use:		Generates a uniformly-distributed pseudorandom number in the
+ *		appropriate range.
+ */
+
+mp *mprand_range(mp *d, mp *l, grand *r, mpw or)
+{
+  size_t b = mp_bits(l);
+  size_t sz = (b + 7) >> 3;
+  octet *v = xmalloc(sz);
+  unsigned m;
+
+  /* --- The algorithm --- *
+   *
+   * Rather simpler than most.  Find the number of bits in the number %$l$%
+   * (i.e., the integer %$b$% such that %$2^{b - 1} \le l < 2^b$%), and
+   * generate pseudorandom integers with %$n$% bits (but not, unlike in the
+   * function above, with the top bit forced to 1).  If the integer is
+   * greater than or equal to %$l$%, try again.
+   *
+   * This is similar to the algorithms used in @lcrand_range@ and friends,
+   * except that I've forced the `raw' range of the random numbers such that
+   * %$l$% itself is the largest multiple of %$l$% in the range (since, by
+   * the inequality above, %$2^b \le 2l$%).  This removes the need for costly
+   * division and remainder operations.
+   *
+   * As usual, the number of iterations expected is two.
+   */
+
+  b = (b - 1) & 7;
+  m = (1 << b) - 1;
+  do {
+    r->ops->fill(r, v, sz);
+    v[0] &= m;
+    d = mp_loadb(d, v, sz);
+    d->v[0] |= or;
+  } while (MP_CMP(d, >=, l));
+
+  /* --- Done --- */
+
+  free(v);
+  return (d);
+}
+
 /*----- That's all, folks -------------------------------------------------*/
-- 
2.11.0