diff --git a/src/math/big/float.go b/src/math/big/float.go
index 314fd689ed..739d30f7ad 100644
--- a/src/math/big/float.go
+++ b/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
 }
 
diff --git a/src/math/big/float_test.go b/src/math/big/float_test.go
index 8ed7f0a4ad..17247b1eb2 100644
--- a/src/math/big/float_test.go
+++ b/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
 }