math/big: always round after the sign is set

Some rounding modes are affected by the sign of the value to
be rounded. Make sure the sign is set before round is called.
Added tests (that failed before the fix).

Change-Id: Idd09b8fcbab89894fede0b9bc922cda5ddc87930
Reviewed-on: https://go-review.googlesource.com/4876Reviewed-by: Rob Pike <r@golang.org>

src/math/big/float.go

@@ -298,6 +298,10 @@ func validate(args ...*Float) {
 // sbit must be 0 or 1 and summarizes any "sticky bit" information one might
 // have before calling round. z's mantissa must be normalized (with the msb set)
 // or empty.
+//
+// CAUTION: The rounding modes ToNegativeInf, ToPositiveInf are affected by the
+// sign of z. For correct rounding, the sign of z must be set correctly before
+// calling round.
 func (z *Float) round(sbit uint) {
 	if debugFloat {
 		validate(z)
@@ -1076,7 +1080,7 @@ func (z *Float) Add(x, y *Float) *Float {
 	}
 
 	// x, y != 0
-	neg := x.neg
+	z.neg = x.neg
 	if x.neg == y.neg {
 		// x + y == x + y
 		// (-x) + (-y) == -(x + y)
@@ -1087,11 +1091,10 @@ func (z *Float) Add(x, y *Float) *Float {
 		if x.ucmp(y) >= 0 {
 			z.usub(x, y)
 		} else {
-			neg = !neg
+			z.neg = !z.neg
 			z.usub(y, x)
 		}
 	}
-	z.neg = neg
 	return z
 }
 
@@ -1116,7 +1119,7 @@ func (z *Float) Sub(x, y *Float) *Float {
 	}
 
 	// x, y != 0
-	neg := x.neg
+	z.neg = x.neg
 	if x.neg != y.neg {
 		// x - (-y) == x + y
 		// (-x) - y == -(x + y)
@@ -1127,11 +1130,10 @@ func (z *Float) Sub(x, y *Float) *Float {
 		if x.ucmp(y) >= 0 {
 			z.usub(x, y)
 		} else {
-			neg = !neg
+			z.neg = !z.neg
 			z.usub(y, x)
 		}
 	}
-	z.neg = neg
 	return z
 }
 
@@ -1158,8 +1160,8 @@ func (z *Float) Mul(x, y *Float) *Float {
 	}
 
 	// x, y != 0
-	z.umul(x, y)
 	z.neg = x.neg != y.neg
+	z.umul(x, y)
 	return z
 }
 

src/math/big/float_test.go

@@ -1077,6 +1077,58 @@ func TestFloatQuoSmoke(t *testing.T) {
 	}
 }
 
+// For rounding modes ToNegativeInf and ToPositiveInf, rounding is affected
+// by the sign of the value to be rounded. Test that rounding happens after
+// the sign of a result has been set.
+// This test uses specific values that are known to fail if rounding is
+// "factored" out before setting the result sign.
+func TestFloatArithmeticRounding(t *testing.T) {
+	for _, test := range []struct {
+		mode       RoundingMode
+		prec       uint
+		x, y, want int64
+		op         byte
+	}{
+		{ToZero, 3, -0x8, -0x1, -0x8, '+'},
+		{AwayFromZero, 3, -0x8, -0x1, -0xa, '+'},
+		{ToNegativeInf, 3, -0x8, -0x1, -0xa, '+'},
+
+		{ToZero, 3, -0x8, 0x1, -0x8, '-'},
+		{AwayFromZero, 3, -0x8, 0x1, -0xa, '-'},
+		{ToNegativeInf, 3, -0x8, 0x1, -0xa, '-'},
+
+		{ToZero, 3, -0x9, 0x1, -0x8, '*'},
+		{AwayFromZero, 3, -0x9, 0x1, -0xa, '*'},
+		{ToNegativeInf, 3, -0x9, 0x1, -0xa, '*'},
+
+		{ToZero, 3, -0x9, 0x1, -0x8, '/'},
+		{AwayFromZero, 3, -0x9, 0x1, -0xa, '/'},
+		{ToNegativeInf, 3, -0x9, 0x1, -0xa, '/'},
+	} {
+		var x, y, z Float
+		x.SetInt64(test.x)
+		y.SetInt64(test.y)
+		z.SetPrec(test.prec).SetMode(test.mode)
+		switch test.op {
+		case '+':
+			z.Add(&x, &y)
+		case '-':
+			z.Sub(&x, &y)
+		case '*':
+			z.Mul(&x, &y)
+		case '/':
+			z.Quo(&x, &y)
+		default:
+			panic("unreachable")
+		}
+		if got, acc := z.Int64(); got != test.want || acc != Exact {
+			t.Errorf("%s, %d bits: %d %c %d = %d (%s); want %d (Exact)",
+				test.mode, test.prec, test.x, test.op, test.y, got, acc, test.want,
+			)
+		}
+	}
+}
+
 func TestFloatCmp(t *testing.T) {
 	// TODO(gri) implement this
 }