diff --git a/src/math/big/float.go b/src/math/big/float.go
index 2e536e04ad..ed55e8e513 100644
--- a/src/math/big/float.go
+++ b/src/math/big/float.go
@@ -73,7 +73,7 @@ type ErrNaN struct {
 
 // NewFloat allocates and returns a new Float set to x,
 // with precision 53 and rounding mode ToNearestEven.
-// NewFloat panics with ErrNan if x is a NaN.
+// NewFloat panics with ErrNaN if x is a NaN.
 func NewFloat(x float64) *Float {
 	if math.IsNaN(x) {
 		panic(ErrNaN{"NewFloat(NaN)"})
@@ -1400,8 +1400,9 @@ func (x *Float) ucmp(y *Float) int {
 // it is changed to the larger of x's or y's precision before the operation.
 // Rounding is performed according to z's precision and rounding mode; and
 // z's accuracy reports the result error relative to the exact (not rounded)
-// result.
-// BUG(gri) Float.Add panics if an operand is Inf.
+// result. Add panics with ErrNaN if x and y are infinities with opposite
+// signs. The value of z is undefined in that case.
+//
 // BUG(gri) When rounding ToNegativeInf, the sign of Float values rounded to 0 is incorrect.
 func (z *Float) Add(x, y *Float) *Float {
 	if debugFloat {
@@ -1413,46 +1414,59 @@ func (z *Float) Add(x, y *Float) *Float {
 		z.prec = umax32(x.prec, y.prec)
 	}
 
-	// special cases
-	if x.form != finite || y.form != finite {
-		if x.form > finite || y.form > finite {
-			// TODO(gri) handle Inf separately
-			panic("Inf operand")
-		}
-		if x.form == zero {
-			z.Set(y)
-			if z.form == zero {
-				z.neg = x.neg && y.neg // -0 + -0 == -0
+	if x.form == finite && y.form == finite {
+		// x + y (commom case)
+		z.neg = x.neg
+		if x.neg == y.neg {
+			// x + y == x + y
+			// (-x) + (-y) == -(x + y)
+			z.uadd(x, y)
+		} else {
+			// x + (-y) == x - y == -(y - x)
+			// (-x) + y == y - x == -(x - y)
+			if x.ucmp(y) > 0 {
+				z.usub(x, y)
+			} else {
+				z.neg = !z.neg
+				z.usub(y, x)
 			}
-			return z
 		}
-		// y == ±0
+		return z
+	}
+
+	if x.form == inf && y.form == inf && x.neg != y.neg {
+		// +Inf + -Inf
+		// -Inf + +Inf
+		// value of z is undefined but make sure it's valid
+		z.acc = Exact
+		z.form = zero
+		z.neg = false
+		panic(ErrNaN{"addition of infinities with opposite signs"})
+	}
+
+	if x.form == zero && y.form == zero {
+		// ±0 + ±0
+		z.acc = Exact
+		z.form = zero
+		z.neg = x.neg && y.neg // -0 + -0 == -0
+		return z
+	}
+
+	if x.form == inf || y.form == zero {
+		// ±Inf + y
+		// x + ±0
 		return z.Set(x)
 	}
 
-	// x, y != 0
-	z.neg = x.neg
-	if x.neg == y.neg {
-		// x + y == x + y
-		// (-x) + (-y) == -(x + y)
-		z.uadd(x, y)
-	} else {
-		// x + (-y) == x - y == -(y - x)
-		// (-x) + y == y - x == -(x - y)
-		if x.ucmp(y) > 0 {
-			z.usub(x, y)
-		} else {
-			z.neg = !z.neg
-			z.usub(y, x)
-		}
-	}
-
-	return z
+	// ±0 + y
+	// x + ±Inf
+	return z.Set(y)
 }
 
 // Sub sets z to the rounded difference x-y and returns z.
 // Precision, rounding, and accuracy reporting are as for Add.
-// BUG(gri) Float.Sub panics if an operand is Inf.
+// Sub panics with ErrNaN if x and y are infinities with equal
+// signs. The value of z is undefined in that case.
 func (z *Float) Sub(x, y *Float) *Float {
 	if debugFloat {
 		x.validate()
@@ -1463,46 +1477,59 @@ func (z *Float) Sub(x, y *Float) *Float {
 		z.prec = umax32(x.prec, y.prec)
 	}
 
-	// special cases
-	if x.form != finite || y.form != finite {
-		if x.form > finite || y.form > finite {
-			// TODO(gri) handle Inf separately
-			panic("Inf operand")
-		}
-		if x.form == zero {
-			z.Neg(y)
-			if z.form == zero {
-				z.neg = x.neg && !y.neg // -0 - 0 == -0
+	if x.form == finite && y.form == finite {
+		// x - y (common case)
+		z.neg = x.neg
+		if x.neg != y.neg {
+			// x - (-y) == x + y
+			// (-x) - y == -(x + y)
+			z.uadd(x, y)
+		} else {
+			// x - y == x - y == -(y - x)
+			// (-x) - (-y) == y - x == -(x - y)
+			if x.ucmp(y) > 0 {
+				z.usub(x, y)
+			} else {
+				z.neg = !z.neg
+				z.usub(y, x)
 			}
-			return z
 		}
-		// y == ±0
+		return z
+	}
+
+	if x.form == inf && y.form == inf && x.neg == y.neg {
+		// +Inf - +Inf
+		// -Inf - -Inf
+		// value of z is undefined but make sure it's valid
+		z.acc = Exact
+		z.form = zero
+		z.neg = false
+		panic(ErrNaN{"subtraction of infinities with equal signs"})
+	}
+
+	if x.form == zero && y.form == zero {
+		// ±0 - ±0
+		z.acc = Exact
+		z.form = zero
+		z.neg = x.neg && !y.neg // -0 - +0 == -0
+		return z
+	}
+
+	if x.form == inf || y.form == zero {
+		// ±Inf - y
+		// x - ±0
 		return z.Set(x)
 	}
 
-	// x, y != 0
-	z.neg = x.neg
-	if x.neg != y.neg {
-		// x - (-y) == x + y
-		// (-x) - y == -(x + y)
-		z.uadd(x, y)
-	} else {
-		// x - y == x - y == -(y - x)
-		// (-x) - (-y) == y - x == -(x - y)
-		if x.ucmp(y) > 0 {
-			z.usub(x, y)
-		} else {
-			z.neg = !z.neg
-			z.usub(y, x)
-		}
-	}
-
-	return z
+	// ±0 - y
+	// x - ±Inf
+	return z.Neg(y)
 }
 
 // Mul sets z to the rounded product x*y and returns z.
 // Precision, rounding, and accuracy reporting are as for Add.
-// BUG(gri) Float.Mul panics if an operand is Inf.
+// Mul panics with ErrNaN if one operand is zero and the other
+// operand an infinity. The value of z is undefined in that case.
 func (z *Float) Mul(x, y *Float) *Float {
 	if debugFloat {
 		x.validate()
@@ -1515,28 +1542,39 @@ func (z *Float) Mul(x, y *Float) *Float {
 
 	z.neg = x.neg != y.neg
 
-	// special cases
-	if x.form != finite || y.form != finite {
-		if x.form > finite || y.form > finite {
-			// TODO(gri) handle Inf separately
-			panic("Inf operand")
-		}
-		// x == ±0 || y == ±0
-		z.acc = Exact
-		z.form = zero
+	if x.form == finite && y.form == finite {
+		// x * y (common case)
+		z.umul(x, y)
 		return z
 	}
 
-	// x, y != 0
-	z.umul(x, y)
+	z.acc = Exact
+	if x.form == zero && y.form == inf || x.form == inf && y.form == zero {
+		// ±0 * ±Inf
+		// ±Inf * ±0
+		// value of z is undefined but make sure it's valid
+		z.form = zero
+		z.neg = false
+		panic(ErrNaN{"multiplication of zero with infinity"})
+	}
 
+	if x.form == inf || y.form == inf {
+		// ±Inf * y
+		// x * ±Inf
+		z.form = inf
+		return z
+	}
+
+	// ±0 * y
+	// x * ±0
+	z.form = zero
 	return z
 }
 
 // Quo sets z to the rounded quotient x/y and returns z.
 // Precision, rounding, and accuracy reporting are as for Add.
-// Quo panics is both operands are 0.
-// BUG(gri) Float.Quo panics if an operand is Inf.
+// Quo panics with ErrNaN if both operands are zero or infinities.
+// The value of z is undefined in that case.
 func (z *Float) Quo(x, y *Float) *Float {
 	if debugFloat {
 		x.validate()
@@ -1549,29 +1587,32 @@ func (z *Float) Quo(x, y *Float) *Float {
 
 	z.neg = x.neg != y.neg
 
-	// special cases
-	z.acc = Exact
-	if x.form != finite || y.form != finite {
-		if x.form > finite || y.form > finite {
-			// TODO(gri) handle Inf separately
-			panic("Inf operand")
-		}
-		// x == ±0 || y == ±0
-		if x.form == zero {
-			if y.form == zero {
-				panic("0/0")
-			}
-			z.form = zero
-			return z
-		}
-		// y == ±0
-		z.form = inf
+	if x.form == finite && y.form == finite {
+		// x / y (common case)
+		z.uquo(x, y)
 		return z
 	}
 
-	// x, y != 0
-	z.uquo(x, y)
+	z.acc = Exact
+	if x.form == zero && y.form == zero || x.form == inf && y.form == inf {
+		// ±0 / ±0
+		// ±Inf / ±Inf
+		// value of z is undefined but make sure it's valid
+		z.form = zero
+		z.neg = false
+		panic(ErrNaN{"division of zero by zero or infinity by infinity"})
+	}
 
+	if x.form == zero || y.form == inf {
+		// ±0 / y
+		// x / ±Inf
+		z.form = zero
+		return z
+	}
+
+	// x / ±0
+	// ±Inf / y
+	z.form = inf
 	return z
 }
 
diff --git a/src/math/big/float_test.go b/src/math/big/float_test.go
index b3f1a60474..2a48ec4465 100644
--- a/src/math/big/float_test.go
+++ b/src/math/big/float_test.go
@@ -1438,7 +1438,7 @@ func TestFloatQuoSmoke(t *testing.T) {
 
 // TestFloatArithmeticSpecialValues tests that Float operations produce the
 // correct results for combinations of zero (±0), finite (±1 and ±2.71828),
-// and non-finite (±Inf) operands.
+// and infinite (±Inf) operands.
 func TestFloatArithmeticSpecialValues(t *testing.T) {
 	zero := 0.0
 	args := []float64{math.Inf(-1), -2.71828, -1, -zero, zero, 1, 2.71828, math.Inf(1)}
@@ -1456,38 +1456,53 @@ func TestFloatArithmeticSpecialValues(t *testing.T) {
 				t.Errorf("Float(%g) == %g (%s)", x, got, acc)
 			}
 			for _, y := range args {
-				// At the moment an Inf operand always leads to a panic (known bug).
-				// TODO(gri) remove this once the bug is fixed.
-				if math.IsInf(x, 0) || math.IsInf(y, 0) {
-					continue
-				}
 				yy.SetFloat64(y)
-				var op string
-				var z float64
+				var (
+					op string
+					z  float64
+					f  func(z, x, y *Float) *Float
+				)
 				switch i {
 				case 0:
 					op = "+"
 					z = x + y
-					got.Add(xx, yy)
+					f = (*Float).Add
 				case 1:
 					op = "-"
 					z = x - y
-					got.Sub(xx, yy)
+					f = (*Float).Sub
 				case 2:
 					op = "*"
 					z = x * y
-					got.Mul(xx, yy)
+					f = (*Float).Mul
 				case 3:
-					if x == 0 && y == 0 {
-						// TODO(gri) check for ErrNaN
-						continue // 0/0 panics with ErrNaN
-					}
 					op = "/"
 					z = x / y
-					got.Quo(xx, yy)
+					f = (*Float).Quo
 				default:
 					panic("unreachable")
 				}
+				var errnan bool // set if execution of f panicked with ErrNaN
+				// protect execution of f
+				func() {
+					defer func() {
+						if p := recover(); p != nil {
+							_ = p.(ErrNaN) // re-panic if not ErrNaN
+							errnan = true
+						}
+					}()
+					f(got, xx, yy)
+				}()
+				if math.IsNaN(z) {
+					if !errnan {
+						t.Errorf("%5g %s %5g = %5s; want ErrNaN panic", x, op, y, got)
+					}
+					continue
+				}
+				if errnan {
+					t.Errorf("%5g %s %5g panicked with ErrNan; want %5s", x, op, y, want)
+					continue
+				}
 				want.SetFloat64(z)
 				if !alike(got, want) {
 					t.Errorf("%5g %s %5g = %5s; want %5s", x, op, y, got, want)
@@ -1614,7 +1629,7 @@ func TestFloatArithmeticRounding(t *testing.T) {
 }
 
 // TestFloatCmpSpecialValues tests that Cmp produces the correct results for
-// combinations of zero (±0), finite (±1 and ±2.71828), and non-finite (±Inf)
+// combinations of zero (±0), finite (±1 and ±2.71828), and infinite (±Inf)
 // operands.
 func TestFloatCmpSpecialValues(t *testing.T) {
 	zero := 0.0