diff --git a/ecdsa.h b/ecdsa.h
index f0c837ed36..14f6b5f668 100644
--- a/ecdsa.h
+++ b/ecdsa.h
@@ -28,7 +28,7 @@ private:
 public:
     Signature(Context &ctx) : r(ctx), s(ctx) {}
 
-    bool Verify(Context &ctx, const GroupElemJac &pubkey, const Number &message) {
+    bool RecomputeR(Context &ctx, Number &r2, const GroupElemJac &pubkey, const Number &message) {
         const GroupConstants &c = GetGroupConst();
 
         if (r.IsNeg() || s.IsNeg())
@@ -39,7 +39,7 @@ public:
             return false;
 
         Context ct(ctx);
-        Number sn(ct), u1(ct), u2(ct), xrn(ct);
+        Number sn(ct), u1(ct), u2(ct);
         sn.SetModInverse(ct, s, c.order);
         // printf("s=%s 1/s=%s\n", s.ToString().c_str(), sn.ToString().c_str());
         u1.SetModMul(ct, sn, message, c.order);
@@ -50,8 +50,15 @@ public:
             return false;
         FieldElem xr; pr.GetX(xr);
         unsigned char xrb[32]; xr.GetBytes(xrb);
-        xrn.SetBytes(xrb,32); xrn.SetMod(ct,xrn,c.order);
-        return xrn.Compare(r) == 0;
+        r2.SetBytes(xrb,32); r2.SetMod(ct,r2,c.order);
+    }
+
+    bool Verify(Context &ctx, const GroupElemJac &pubkey, const Number &message) {
+        Context ct(ctx);
+        Number r2(ct);
+        if (!RecomputeR(ct, r2, pubkey, message))
+            return false;
+        return r2.Compare(r) == 0;
     }
 
     void SetRS(const Number &rin, const Number &sin) {
diff --git a/tests.cpp b/tests.cpp
index be97fec0cb..2eebbe4580 100644
--- a/tests.cpp
+++ b/tests.cpp
@@ -10,18 +10,23 @@ using namespace secp256k1;
 
 void test_ecmult() {
     Context ctx;
+    // random starting point A (on the curve)
     FieldElem ax; ax.SetHex("8b30bbe9ae2a990696b22f670709dff3727fd8bc04d3362c6c7bf458e2846004");
     FieldElem ay; ay.SetHex("a357ae915c4a65281309edf20504740f0eb3343990216b4f81063cb65f2f7e0f");
     GroupElemJac a(ax,ay);
+    // two random initial factors xn and gn
     Number xn(ctx); xn.SetHex("84cc5452f7fde1edb4d38a8ce9b1b84ccef31f146e569be9705d357a42985407");
     Number gn(ctx); gn.SetHex("a1e58d22553dcd42b23980625d4c57a96e9323d42b3152e5ca2c3990edc7c9de");
+    // two small multipliers to be applied to xn and gn in every iteration:
     Number xf(ctx); xf.SetHex("1337");
     Number gf(ctx); gf.SetHex("7113");
+    // accumulators with the resulting coefficients to A and G
     Number ae(ctx); ae.SetHex("01");
     Number ge(ctx); ge.SetHex("00");
+    // the point being computed
     GroupElemJac x = a;
     const Number &order = GetGroupConst().order;
-    for (int i=0; i<1000; i++) {
+    for (int i=0; i<20000; i++) {
         // in each iteration, compute X = xn*X + gn*G;
         ECMult(ctx, x, x, xn, gn);
         // also compute ae and ge: the actual accumulated factors for A and G
@@ -35,11 +40,10 @@ void test_ecmult() {
         gn.SetModMul(ctx, gn, gf, order);
     }
     std::string res = x.ToString();
-    assert(res == "(D37F97BBF58B4ECA238329D272C9AF0194F062B851EDF9B40F2294FA00BBFCA2,B127748E9A9F347257051588D44A1B822CA731833B2653AA3646C59A8ADAF295)");
+    assert(res == "(D6E96687F9B10D092A6F35439D86CEBEA4535D0D409F53586440BD74B933E830,B95CBCA2C77DA786539BE8FD53354D2D3B4F566AE658045407ED6015EE1B2A88)");
     // redo the computation, but directly with the resulting ae and ge coefficients:
     GroupElemJac x2; ECMult(ctx, x2, a, ae, ge);
     std::string res2 = x2.ToString();
-    printf("res=%s res2=%s\n", res.c_str(), res2.c_str());
     assert(res == res2);
 }