Make secp256k1_fe_mul_inner use the r != property

Suggested by Peter Dettman.

src/field_5x52_int128_impl.h

@@ -34,15 +34,17 @@ SECP256K1_INLINE static void secp256k1_fe_mul_inner(const uint64_t *a, const uin
      *  Note that [x 0 0 0 0 0] = [x*R].
      */
 
+    uint64_t a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], a4 = a[4];
+
     __int128 c, d;
 
-    d  = (__int128)a[0] * b[3]
-       + (__int128)a[1] * b[2]
-       + (__int128)a[2] * b[1]
-       + (__int128)a[3] * b[0];
+    d  = (__int128)a0 * b[3]
+       + (__int128)a1 * b[2]
+       + (__int128)a2 * b[1]
+       + (__int128)a3 * b[0];
     VERIFY_BITS(d, 114);
     /* [d 0 0 0] = [p3 0 0 0] */
-    c  = (__int128)a[4] * b[4];
+    c  = (__int128)a4 * b[4];
     VERIFY_BITS(c, 112);
     /* [c 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
     d += (c & M) * R; c >>= 52;
@@ -54,11 +56,11 @@ SECP256K1_INLINE static void secp256k1_fe_mul_inner(const uint64_t *a, const uin
     VERIFY_BITS(d, 63);
     /* [c 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
 
-    d += (__int128)a[0] * b[4]
-       + (__int128)a[1] * b[3]
-       + (__int128)a[2] * b[2]
-       + (__int128)a[3] * b[1]
-       + (__int128)a[4] * b[0];
+    d += (__int128)a0 * b[4]
+       + (__int128)a1 * b[3]
+       + (__int128)a2 * b[2]
+       + (__int128)a3 * b[1]
+       + (__int128)a4 * b[0];
     VERIFY_BITS(d, 115);
     /* [c 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
     d += c * R;
@@ -73,13 +75,13 @@ SECP256K1_INLINE static void secp256k1_fe_mul_inner(const uint64_t *a, const uin
     VERIFY_BITS(t4, 48);
     /* [d t4+(tx<<48) t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
 
-    c  = (__int128)a[0] * b[0];
+    c  = (__int128)a0 * b[0];
     VERIFY_BITS(c, 112);
     /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 0 p4 p3 0 0 p0] */
-    d += (__int128)a[1] * b[4]
-       + (__int128)a[2] * b[3]
-       + (__int128)a[3] * b[2]
-       + (__int128)a[4] * b[1];
+    d += (__int128)a1 * b[4]
+       + (__int128)a2 * b[3]
+       + (__int128)a3 * b[2]
+       + (__int128)a4 * b[1];
     VERIFY_BITS(d, 115);
     /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
     uint64_t u0 = d & M; d >>= 52;
@@ -93,48 +95,43 @@ SECP256K1_INLINE static void secp256k1_fe_mul_inner(const uint64_t *a, const uin
     c += (__int128)u0 * (R >> 4);
     VERIFY_BITS(c, 115);
     /* [d 0 t4 t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
-    uint64_t t0 = c & M; c >>= 52;
-    VERIFY_BITS(t0, 52);
+    r[0] = c & M; c >>= 52;
+    VERIFY_BITS(r[0], 52);
     VERIFY_BITS(c, 61);
-    /* [d 0 t4 t3 0 c t0] = [p8 0 0 p5 p4 p3 0 0 p0] */
+    /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 0 p0] */
 
-    c += (__int128)a[0] * b[1]
-       + (__int128)a[1] * b[0];
+    c += (__int128)a0 * b[1]
+       + (__int128)a1 * b[0];
     VERIFY_BITS(c, 114);
-    /* [d 0 t4 t3 0 c t0] = [p8 0 0 p5 p4 p3 0 p1 p0] */
-    d += (__int128)a[2] * b[4]
-       + (__int128)a[3] * b[3]
-       + (__int128)a[4] * b[2];
+    /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 p1 p0] */
+    d += (__int128)a2 * b[4]
+       + (__int128)a3 * b[3]
+       + (__int128)a4 * b[2];
     VERIFY_BITS(d, 114);
-    /* [d 0 t4 t3 0 c t0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
+    /* [d 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
     c += (d & M) * R; d >>= 52;
     VERIFY_BITS(c, 115);
     VERIFY_BITS(d, 62);
-    /* [d 0 0 t4 t3 0 c t0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
-    uint64_t t1 = c & M; c >>= 52;
-    VERIFY_BITS(t1, 52);
+    /* [d 0 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
+    r[1] = c & M; c >>= 52;
+    VERIFY_BITS(r[1], 52);
     VERIFY_BITS(c, 63);
-    /* [d 0 0 t4 t3 c t1 t0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
+    /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
 
-    c += (__int128)a[0] * b[2]
-       + (__int128)a[1] * b[1]
-       + (__int128)a[2] * b[0];
+    c += (__int128)a0 * b[2]
+       + (__int128)a1 * b[1]
+       + (__int128)a2 * b[0];
     VERIFY_BITS(c, 114);
-    /* [d 0 0 t4 t3 c t1 t0] = [p8 0 p6 p5 p4 p3 p2 p1 p0] */
-    d += (__int128)a[3] * b[4]
-       + (__int128)a[4] * b[3];
+    /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 p2 p1 p0] */
+    d += (__int128)a3 * b[4]
+       + (__int128)a4 * b[3];
     VERIFY_BITS(d, 114);
-    /* [d 0 0 t4 t3 c t1 t0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    /* [d 0 0 t4 t3 c t1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
     c += (d & M) * R; d >>= 52;
     VERIFY_BITS(c, 115);
     VERIFY_BITS(d, 62);
-    /* [d 0 0 0 t4 t3 c t1 t0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    /* [d 0 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
 
-    r[0] = t0;
-    VERIFY_BITS(r[0], 52);
-    /* [d 0 0 0 t4 t3 c t1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
-    r[1] = t1;
-    VERIFY_BITS(r[1], 52);
     /* [d 0 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
     r[2] = c & M; c >>= 52;
     VERIFY_BITS(r[2], 52);