divmod: fix aliasing error, add tests (#180)

This change fixes a flaw in `DivMod` related to aliasing of input arguments.

ternary_test.go

@@ -21,6 +21,8 @@ var ternaryOpFuncs = []struct {
 	{"AddMod", (*Int).AddMod, bigAddMod},
 	{"MulMod", (*Int).MulMod, bigMulMod},
 	{"MulModWithReciprocal", (*Int).mulModWithReciprocalWrapper, bigMulMod},
+	{"DivModZ", divModZ, bigDivModZ},
+	{"DivModM", divModM, bigDivModM},
 }
 
 func checkTernaryOperation(t *testing.T, opName string, op opThreeArgFunc, bigOp bigThreeArgFunc, x, y, z Int) {
@@ -49,7 +51,10 @@ func checkTernaryOperation(t *testing.T, opName string, op opThreeArgFunc, bigOp
 		t.Fatalf("%v\nsecond argument had been modified: %x", operation, f2)
 	}
 	if !f3.Eq(f3orig) {
-		t.Fatalf("%v\nthird argument had been modified: %x", operation, f3)
+		if opName != "DivModZ" && opName != "DivModM" {
+			// DivMod takes m as third argument, modifies it, and returns it. That is by design.
+			t.Fatalf("%v\nthird argument had been modified: %x", operation, f3)
+		}
 	}
 	// Check if reusing args as result works correctly.
 	if have = op(f1, f1, f2orig, f3orig); have != f1 {
@@ -117,3 +122,29 @@ func (z *Int) mulModWithReciprocalWrapper(x, y, mod *Int) *Int {
 	mu := Reciprocal(mod)
 	return z.MulModWithReciprocal(x, y, mod, &mu)
 }
+
+func divModZ(z, x, y, m *Int) *Int {
+	z2, _ := z.DivMod(x, y, m)
+	return z2
+}
+
+func bigDivModZ(result, x, y, mod *big.Int) *big.Int {
+	if y.Sign() == 0 {
+		return result.SetUint64(0)
+	}
+	z2, _ := result.DivMod(x, y, mod)
+	return z2
+}
+
+func divModM(z, x, y, m *Int) *Int {
+	_, m2 := z.DivMod(x, y, m)
+	return z.Set(m2)
+}
+
+func bigDivModM(result, x, y, mod *big.Int) *big.Int {
+	if y.Sign() == 0 {
+		return result.SetUint64(0)
+	}
+	_, m2 := result.DivMod(x, y, mod)
+	return result.Set(m2)
+}

uint256.go

@@ -369,9 +369,9 @@ func umul(x, y *Int, res *[8]uint64) {
 func (z *Int) Mul(x, y *Int) *Int {
 	var (
 		carry0, carry1, carry2 uint64
-		res1, res2 uint64
-		x0, x1, x2, x3 = x[0], x[1], x[2], x[3]
-		y0, y1, y2, y3 = y[0], y[1], y[2], y[3]
+		res1, res2             uint64
+		x0, x1, x2, x3         = x[0], x[1], x[2], x[3]
+		y0, y1, y2, y3         = y[0], y[1], y[2], y[3]
 	)
 
 	carry0, z[0] = bits.Mul64(x0, y0)
@@ -610,14 +610,20 @@ func (z *Int) Mod(x, y *Int) *Int {
 // DivMod sets z to the quotient x div y and m to the modulus x mod y and returns the pair (z, m) for y != 0.
 // If y == 0, both z and m are set to 0 (OBS: differs from the big.Int)
 func (z *Int) DivMod(x, y, m *Int) (*Int, *Int) {
+	if z == m {
+		// We return both z and m as results, if they are aliased, we have to
+		// un-alias them to be able to return separate results.
+		m = new(Int).Set(m)
+	}
 	if y.IsZero() {
 		return z.Clear(), m.Clear()
 	}
 	if x.Eq(y) {
 		return z.SetOne(), m.Clear()
 	}
 	if x.Lt(y) {
-		return z.Clear(), m.Set(x)
+		m.Set(x)
+		return z.Clear(), m
 	}
 
 	// At this point:
@@ -1279,7 +1285,7 @@ func (z *Int) Sqrt(x *Int) *Int {
 			return z.SetUint64(x0)
 		}
 		for {
-			z2 = (z1 + x0 / z1) >> 1
+			z2 = (z1 + x0/z1) >> 1
 			if z2 >= z1 {
 				return z.SetUint64(z1)
 			}
@@ -1291,18 +1297,18 @@ func (z *Int) Sqrt(x *Int) *Int {
 	z2 := NewInt(0)
 
 	// Start with value known to be too large and repeat "z = ⌊(z + ⌊x/z⌋)/2⌋" until it stops getting smaller.
-	z1.Lsh(z1, uint(x.BitLen() + 1) / 2) // must be ≥ √x
+	z1.Lsh(z1, uint(x.BitLen()+1)/2) // must be ≥ √x
 
 	// We can do the first division outside the loop
-	z2.Rsh(x, uint(x.BitLen() + 1) / 2) // The first div is equal to a right shift
+	z2.Rsh(x, uint(x.BitLen()+1)/2) // The first div is equal to a right shift
 
 	for {
 		z2.Add(z2, z1)
-		
+
 		// z2 = z2.Rsh(z2, 1) -- the code below does a 1-bit rsh faster
-		z2[0] = (z2[0] >> 1) | z2[1] << 63
-		z2[1] = (z2[1] >> 1) | z2[2] << 63
-		z2[2] = (z2[2] >> 1) | z2[3] << 63
+		z2[0] = (z2[0] >> 1) | z2[1]<<63
+		z2[1] = (z2[1] >> 1) | z2[2]<<63
+		z2[2] = (z2[2] >> 1) | z2[3]<<63
 		z2[3] >>= 1
 
 		if !z2.Lt(z1) {