From: Mark Wooding <mdw@distorted.org.uk>
Date: Tue, 7 Feb 2006 19:32:47 +0000 (+0000)
Subject: gcd: General tidying up.
X-Git-Url: https://git.distorted.org.uk/u/mdw/catacomb/commitdiff_plain/cf76bcbb2097c36912fae1c8a6cc77f0ce4bfafd

gcd: General tidying up.

  * Implement a GCD algorithm in calc/gfx.cal (partly to help with
    testing the Python bindings).

  * Clean up the MP and GF implementations: expunge incorrect commentary
    and redundant code.
---

diff --git a/calc/gfx.cal b/calc/gfx.cal
index 45f534b..e38f4b7 100644
--- a/calc/gfx.cal
+++ b/calc/gfx.cal
@@ -97,24 +97,36 @@ define gf_mod(x, y)
   return gf(l[[1]]);
 }
 
-define gf_inv(a, b)
+define gf_gcd(a, b)
 {
-  local g, x, y, X, Y, u, v, t, q, r;
-  x = gf(1); X = gf(0);
-  y = gf(0); Y = gf(1);
-
-  if (b == gf(0)) { g = a; } else if (a == gf(0)) { g = b; }
+  local swap = 0;
+  local g, x = 1, X = 0, y = 0, Y = 1, q, r, t;
+  if (a.x < b.x) {
+    t = a; a = b; b = t;
+    swap = 1;
+  }
+  if (b == gf(0))
+    g = a;
   else {
     while (b != gf(0)) {
-      q = gf_div(b, a); r = gf_mod(b, a);
+      q = gf_div(a, b); r = gf_mod(a, b);
       t = X * q + x; x = X; X = t;
       t = Y * q + y; y = Y; Y = t;
-      b = a; a = r;
+      a = b; b = r;
     }
     g = a;
   }
-  if (g != gf(1)) quit "not coprime in gf_inv";
-  return Y;
+  if (swap) {
+    t = x; x = y; y = t;
+  }
+  return list(g, x, y);
+}
+
+define gf_inv(a, b)
+{
+  local l = gf_gcd(b, a);
+  if (l[[0]] != gf(1)) quit "not coprime in gf_inv";
+  return l[[2]];
 }
 
 /*----- That's all, folks -------------------------------------------------*/
diff --git a/gf-gcd.c b/gf-gcd.c
index 622679a..048d29d 100644
--- a/gf-gcd.c
+++ b/gf-gcd.c
@@ -106,15 +106,7 @@ void gf_gcd(mp **gcd, mp **xx, mp **yy, mp *a, mp *b)
     return;
   }
 
-  /* --- Take a reference to the arguments --- */
-
-  a = MP_COPY(a);
-  b = MP_COPY(b);
-
-  /* --- Make sure @a@ and @b@ are not both even --- */
-
-  MP_SPLIT(a); a->f &= ~MP_NEG;
-  MP_SPLIT(b); b->f &= ~MP_NEG;
+  /* --- Main extended Euclidean algorithm --- */
 
   u = MP_COPY(a);
   v = MP_COPY(b);
@@ -124,10 +116,10 @@ void gf_gcd(mp **gcd, mp **xx, mp **yy, mp *a, mp *b)
     gf_div(&q, &u, u, v);
     if (f & f_ext) {
       t = gf_mul(MP_NEW, X, q);
-      t = gf_add(t, x, t);
+      t = gf_add(t, t, x);
       MP_DROP(x); x = X; X = t;
       t = gf_mul(MP_NEW, Y, q);
-      t = gf_add(t, y, t);
+      t = gf_add(t, t, y);
       MP_DROP(y); y = Y; Y = t;
     }
     t = u; u = v; v = t;
@@ -172,7 +164,6 @@ void gf_gcd(mp **gcd, mp **xx, mp **yy, mp *a, mp *b)
 
   MP_DROP(v);
   MP_DROP(X); MP_DROP(Y);
-  MP_DROP(a); MP_DROP(b);
 }
 
 /* -- @gf_modinv@ --- *
diff --git a/mp-gcd.c b/mp-gcd.c
index 5312400..c78181f 100644
--- a/mp-gcd.c
+++ b/mp-gcd.c
@@ -118,19 +118,19 @@ void mp_gcd(mp **gcd, mp **xx, mp **yy, mp *a, mp *b)
     return;
   }
 
-  /* --- Take a reference to the arguments --- */
+  /* --- Force the signs on the arguments and take copies --- */
 
   a = MP_COPY(a);
   b = MP_COPY(b);
 
-  /* --- Make sure @a@ and @b@ are not both even --- */
-
   MP_SPLIT(a); a->f &= ~MP_NEG;
   MP_SPLIT(b); b->f &= ~MP_NEG;
 
   u = MP_COPY(a);
   v = MP_COPY(b);
 
+  /* --- Main extended Euclidean algorithm --- */
+
   while (!MP_ZEROP(v)) {
     mp *t;
     mp_div(&q, &u, u, v);