diff --git a/src/math/big/float.go b/src/math/big/float.go
index dff40545d5..b13fea6a6a 100644
--- a/src/math/big/float.go
+++ b/src/math/big/float.go
@@ -381,14 +381,11 @@ func (x *Float) validate() {
 func (z *Float) round(sbit uint) {
 	if debugFloat {
 		z.validate()
-		if z.form > finite {
-			panic(fmt.Sprintf("round called for non-finite value %s", z))
-		}
 	}
-	// z.form <= finite
 
 	z.acc = Exact
-	if z.form == zero {
+	if z.form != finite {
+		// ±0 or ±Inf => nothing left to do
 		return
 	}
 	// z.form == finite && len(z.mant) > 0
diff --git a/src/math/big/float_test.go b/src/math/big/float_test.go
index 23abe18baa..d3b214b631 100644
--- a/src/math/big/float_test.go
+++ b/src/math/big/float_test.go
@@ -92,24 +92,11 @@ func TestFloatZeroValue(t *testing.T) {
 }
 
 func makeFloat(s string) *Float {
-	var x Float
-
-	switch s {
-	case "0":
-		return &x
-	case "-0":
-		return x.Neg(&x)
-	case "Inf", "+Inf":
-		return x.SetInf(false)
-	case "-Inf":
-		return x.SetInf(true)
+	x, _, err := ParseFloat(s, 0, 1000, ToNearestEven)
+	if err != nil {
+		panic(err)
 	}
-
-	x.SetPrec(1000)
-	if _, ok := x.SetString(s); !ok {
-		panic(fmt.Sprintf("%q is not a valid float", s))
-	}
-	return &x
+	return x
 }
 
 func TestFloatSetPrec(t *testing.T) {
diff --git a/src/math/big/floatconv.go b/src/math/big/floatconv.go
index dc62b450db..4a070ca64d 100644
--- a/src/math/big/floatconv.go
+++ b/src/math/big/floatconv.go
@@ -14,60 +14,19 @@ import (
 
 // SetString sets z to the value of s and returns z and a boolean indicating
 // success. s must be a floating-point number of the same format as accepted
-// by Scan, with number prefixes permitted.
+// by Parse, with base argument 0.
 func (z *Float) SetString(s string) (*Float, bool) {
-	r := strings.NewReader(s)
-
-	f, _, err := z.Scan(r, 0)
-	if err != nil {
-		return nil, false
+	if f, _, err := z.Parse(s, 0); err == nil {
+		return f, true
 	}
-
-	// there should be no unread characters left
-	if _, err = r.ReadByte(); err != io.EOF {
-		return nil, false
-	}
-
-	return f, true
+	return nil, false
 }
 
-// Scan scans the number corresponding to the longest possible prefix
-// of r representing a floating-point number with a mantissa in the
-// given conversion base (the exponent is always a decimal number).
-// It sets z to the (possibly rounded) value of the corresponding
-// floating-point number, and returns z, the actual base b, and an
-// error err, if any. If z's precision is 0, it is changed to 64
-// before rounding takes effect. The number must be of the form:
-//
-//	number   = [ sign ] [ prefix ] mantissa [ exponent ] .
-//	sign     = "+" | "-" .
-//      prefix   = "0" ( "x" | "X" | "b" | "B" ) .
-//	mantissa = digits | digits "." [ digits ] | "." digits .
-//	exponent = ( "E" | "e" | "p" ) [ sign ] digits .
-//	digits   = digit { digit } .
-//	digit    = "0" ... "9" | "a" ... "z" | "A" ... "Z" .
-//
-// The base argument must be 0, 2, 10, or 16. Providing an invalid base
-// argument will lead to a run-time panic.
-//
-// For base 0, the number prefix determines the actual base: A prefix of
-// "0x" or "0X" selects base 16, and a "0b" or "0B" prefix selects
-// base 2; otherwise, the actual base is 10 and no prefix is accepted.
-// The octal prefix "0" is not supported (a leading "0" is simply
-// considered a "0").
-//
-// A "p" exponent indicates a binary (rather then decimal) exponent;
-// for instance "0x1.fffffffffffffp1023" (using base 0) represents the
-// maximum float64 value. For hexadecimal mantissae, the exponent must
-// be binary, if present (an "e" or "E" exponent indicator cannot be
-// distinguished from a mantissa digit).
-//
-// The returned *Float f is nil and the value of z is valid but not
-// defined if an error is reported.
-//
-// BUG(gri) The Float.Scan signature conflicts with Scan(s fmt.ScanState, ch rune) error.
-//          (https://github.com/golang/go/issues/10938)
-func (z *Float) Scan(r io.ByteScanner, base int) (f *Float, b int, err error) {
+// scan is like Parse but reads the longest possible prefix representing a valid
+// floating point number from an io.ByteScanner rather than a string. It serves
+// as the implementation of Parse. It does not recognize ±Inf and does not expect
+// EOF at the end.
+func (z *Float) scan(r io.ByteScanner, base int) (f *Float, b int, err error) {
 	prec := z.prec
 	if prec == 0 {
 		prec = 64
@@ -211,14 +170,55 @@ func (z *Float) pow10(n int64) *Float {
 	return z
 }
 
-// Parse is like z.Scan(r, base), but instead of reading from an
-// io.ByteScanner, it parses the string s. An error is also returned
-// if the string contains invalid or trailing bytes not belonging to
-// the number.
+// Parse parses s which must contain a text representation of a floating-
+// point number with a mantissa in the given conversion base (the exponent
+// is always a decimal number), or a string representing an infinite value.
+//
+// It sets z to the (possibly rounded) value of the corresponding floating-
+// point value, and returns z, the actual base b, and an error err, if any.
+// If z's precision is 0, it is changed to 64 before rounding takes effect.
+// The number must be of the form:
+//
+//	number   = [ sign ] [ prefix ] mantissa [ exponent ] | infinity .
+//	sign     = "+" | "-" .
+//      prefix   = "0" ( "x" | "X" | "b" | "B" ) .
+//	mantissa = digits | digits "." [ digits ] | "." digits .
+//	exponent = ( "E" | "e" | "p" ) [ sign ] digits .
+//	digits   = digit { digit } .
+//	digit    = "0" ... "9" | "a" ... "z" | "A" ... "Z" .
+//      infinity = [ sign ] ( "inf" | "Inf" ) .
+//
+// The base argument must be 0, 2, 10, or 16. Providing an invalid base
+// argument will lead to a run-time panic.
+//
+// For base 0, the number prefix determines the actual base: A prefix of
+// "0x" or "0X" selects base 16, and a "0b" or "0B" prefix selects
+// base 2; otherwise, the actual base is 10 and no prefix is accepted.
+// The octal prefix "0" is not supported (a leading "0" is simply
+// considered a "0").
+//
+// A "p" exponent indicates a binary (rather then decimal) exponent;
+// for instance "0x1.fffffffffffffp1023" (using base 0) represents the
+// maximum float64 value. For hexadecimal mantissae, the exponent must
+// be binary, if present (an "e" or "E" exponent indicator cannot be
+// distinguished from a mantissa digit).
+//
+// The returned *Float f is nil and the value of z is valid but not
+// defined if an error is reported.
+//
 func (z *Float) Parse(s string, base int) (f *Float, b int, err error) {
-	r := strings.NewReader(s)
+	// scan doesn't handle ±Inf
+	if len(s) == 3 && (s == "Inf" || s == "inf") {
+		f = z.SetInf(false)
+		return
+	}
+	if len(s) == 4 && (s[0] == '+' || s[0] == '-') && (s[1:] == "Inf" || s[1:] == "inf") {
+		f = z.SetInf(s[0] == '-')
+		return
+	}
 
-	if f, b, err = z.Scan(r, base); err != nil {
+	r := strings.NewReader(s)
+	if f, b, err = z.scan(r, base); err != nil {
 		return
 	}
 
@@ -232,12 +232,6 @@ func (z *Float) Parse(s string, base int) (f *Float, b int, err error) {
 	return
 }
 
-// ScanFloat is like f.Scan(r, base) with f set to the given precision
-// and rounding mode.
-func ScanFloat(r io.ByteScanner, base int, prec uint, mode RoundingMode) (f *Float, b int, err error) {
-	return new(Float).SetPrec(prec).SetMode(mode).Scan(r, base)
-}
-
 // ParseFloat is like f.Parse(s, base) with f set to the given precision
 // and rounding mode.
 func ParseFloat(s string, base int, prec uint, mode RoundingMode) (f *Float, b int, err error) {
diff --git a/src/math/big/floatconv_test.go b/src/math/big/floatconv_test.go
index fffcd70ce6..656d28c975 100644
--- a/src/math/big/floatconv_test.go
+++ b/src/math/big/floatconv_test.go
@@ -11,9 +11,12 @@ import (
 )
 
 func TestFloatSetFloat64String(t *testing.T) {
+	inf := math.Inf(0)
+	nan := math.NaN()
+
 	for _, test := range []struct {
 		s string
-		x float64
+		x float64 // NaNs represent invalid inputs
 	}{
 		// basics
 		{"0", 0},
@@ -45,6 +48,25 @@ func TestFloatSetFloat64String(t *testing.T) {
 		{"1.E+10", 1e10},
 		{"+1E-10", 1e-10},
 
+		// infinities
+		{"Inf", inf},
+		{"+Inf", inf},
+		{"-Inf", -inf},
+		{"inf", inf},
+		{"+inf", inf},
+		{"-inf", -inf},
+
+		// invalid numbers
+		{"", nan},
+		{"-", nan},
+		{"0x", nan},
+		{"0e", nan},
+		{"1.2ef", nan},
+		{"2..3", nan},
+		{"123..", nan},
+		{"infinity", nan},
+		{"foobar", nan},
+
 		// misc decimal values
 		{"3.14159265", 3.14159265},
 		{"-687436.79457e-245", -687436.79457e-245},
@@ -96,8 +118,16 @@ func TestFloatSetFloat64String(t *testing.T) {
 		var x Float
 		x.SetPrec(53)
 		_, ok := x.SetString(test.s)
+		if math.IsNaN(test.x) {
+			// test.s is invalid
+			if ok {
+				t.Errorf("%s: want parse error", test.s)
+			}
+			continue
+		}
+		// test.s is valid
 		if !ok {
-			t.Errorf("%s: parse error", test.s)
+			t.Errorf("%s: got parse error", test.s)
 			continue
 		}
 		f, _ := x.Float64()