factorial: Fix usage message to fit in with conventions.

[u/mdw/catacomb] / mp-modsqrt.c

diff --git a/mp-modsqrt.c b/mp-modsqrt.c
index a3a6b1f..1cacacd 100644 (file)
--- a/mp-modsqrt.c
+++ b/mp-modsqrt.c
@@ -1,6 +1,6 @@
 /* -*-c-*-
  *
- * $Id: mp-modsqrt.c,v 1.1 2000/06/22 19:01:31 mdw Exp $
+ * $Id: mp-modsqrt.c,v 1.5 2004/04/08 01:36:15 mdw Exp $
  *
  * Compute square roots modulo a prime
  *
@@ -27,14 +27,6 @@
  * MA 02111-1307, USA.
  */
 
-/*----- Revision history --------------------------------------------------* 
- *
- * $Log: mp-modsqrt.c,v $
- * Revision 1.1  2000/06/22 19:01:31  mdw
- * Compute square roots in a prime field.
- *
- */
-
 /*----- Header files ------------------------------------------------------*/
 
 #include "fibrand.h"
@@ -59,6 +51,9 @@
  *             work if %$p$% is composite: you must factor the modulus, take
  *             a square root mod each factor, and recombine the results
  *             using the Chinese Remainder Theorem.
+ *
+ *             We guarantee that the square root returned is the smallest
+ *             one (i.e., the `positive' square root).
  */
 
 mp *mp_modsqrt(mp *d, mp *a, mp *p)
@@ -75,8 +70,7 @@ mp *mp_modsqrt(mp *d, mp *a, mp *p)
   /* --- Cope if %$a \not\in Q_p$% --- */
 
   if (mp_jacobi(a, p) != 1) {
-    if (d)
-      mp_drop(d);
+    mp_drop(d);
     return (0);
   }
 
@@ -94,8 +88,7 @@ mp *mp_modsqrt(mp *d, mp *a, mp *p)
 
   /* --- Find the inverse of %$a$% --- */
 
-  ainv = MP_NEW;
-  mp_gcd(0, &ainv, 0, a, p);
+  ainv = mp_modinv(MP_NEW, a, p);
   
   /* --- Split %$p - 1$% into a power of two and an odd number --- */
 
@@ -105,10 +98,13 @@ mp *mp_modsqrt(mp *d, mp *a, mp *p)
   /* --- Now to really get going --- */
 
   mpmont_create(&mm, p);
+  b = mpmont_mul(&mm, b, b, mm.r2);
   c = mpmont_expr(&mm, b, b, t);
   t = mp_add(t, t, MP_ONE);
   t = mp_lsr(t, t, 1);
-  r = mpmont_expr(&mm, t, a, t);
+  dd = mpmont_mul(&mm, MP_NEW, a, mm.r2);
+  r = mpmont_expr(&mm, t, dd, t);
+  mp_drop(dd);
   ainv = mpmont_mul(&mm, ainv, ainv, mm.r2);
 
   mone = mp_sub(MP_NEW, p, mm.r);
@@ -132,19 +128,23 @@ mp *mp_modsqrt(mp *d, mp *a, mp *p)
 
     /* --- Fiddle at the end --- */
 
-    if (MP_CMP(dd, ==, mone))
+    if (MP_EQ(dd, mone))
       r = mpmont_mul(&mm, r, r, c);
     c = mp_sqr(c, c);
     c = mpmont_reduce(&mm, c, c);
   }
 
-  /* --- Done, so tidy up --- */
+  /* --- Done, so tidy up --- *
+   *
+   * Canonify the answer.
+   */
 
   d = mpmont_reduce(&mm, d, r);
+  r = mp_sub(r, p, d);
+  if (MP_CMP(r, <, d)) { mp *tt = r; r = d; d = tt; }
   mp_drop(ainv);
   mp_drop(r); mp_drop(c);
-  if (dd)
-    mp_drop(dd);
+  mp_drop(dd);
   mp_drop(mone);
   mpmont_destroy(&mm);
 
@@ -167,13 +167,8 @@ static int verify(dstr *v)
 
   if (!r)
     ok = 0;
-  else if (MP_CMP(r, ==, rr))
+  else if (MP_EQ(r, rr))
     ok = 1;
-  else {
-    r = mp_sub(r, p, r);
-    if (MP_CMP(r, ==, rr))
-      ok = 1;
-  }
 
   if (!ok) {
     fputs("\n*** fail\n", stderr);
@@ -191,8 +186,7 @@ static int verify(dstr *v)
 
   mp_drop(a);
   mp_drop(p);
-  if (r)
-    mp_drop(r);
+  mp_drop(r);
   mp_drop(rr);
   assert(mparena_count(MPARENA_GLOBAL) == 0);
   return (ok);