math/mp-jacobi.c: Improve the presentation.

[u/mdw/catacomb] / math / mp-jacobi.c

diff --git a/math/mp-jacobi.c b/math/mp-jacobi.c
index 1a2835b..e318ce3 100644 (file)
--- a/math/mp-jacobi.c
+++ b/math/mp-jacobi.c
@@ -55,7 +55,7 @@
  *               * %$\jacobi{a}{-1} = 1$% if @a@ is negative, or 1 if
  *                 positive;
  *               * %$\jacobi{a}{0} = 0$%;
- *               * %$\jacobi{a}{2}$ is 0 if @a@ is even, 1 if @a@ is
+ *               * %$\jacobi{a}{2}$ is 0 if @a@ is even, 1 if @a@ is
  *                 congruent to 1 or 7 (mod 8), or %$-1$% otherwise.
  *
  *             If %$n$% is positive and odd, then this is the Jacobi
@@ -130,7 +130,7 @@ int mp_jacobi(mp *a, mp *n)
       goto done;
     }
 
-    /* --- Main case with powers of two --- */
+    /* --- Strip out powers of two from %$a$% --- */
 
     a = mp_odd(a, a, &e);
     nn = n->v[0] & 7;
@@ -138,11 +138,11 @@ int mp_jacobi(mp *a, mp *n)
       s = -s;
     if (MP_LEN(a) == 1 && a->v[0] == 1)
       goto done;
-    if ((nn & 3) == 3 && (a->v[0] & 3) == 3)
-      s = -s;
 
-    /* --- Reduce and swap --- */
+    /* --- Reduce and swap, applying quadratic residuosity --- */
 
+    if ((nn & 3) == 3 && (a->v[0] & 3) == 3)
+      s = -s;
     mp_div(0, &n, n, a);
     { mp *t = n; n = a; a = t; }
   }