math/big: add support for general encoding interfaces

TextMarshaller and TextUnmarshaller to ease transport of
unlimited precision rational numbers.

Fixes #7287.

Consists of encode and decode functions and two test
functions, one using JSON and one using XML. Each
verifies round trips for integers (rationals with
denominator == 1) and for fractional vaues.

LGTM=gri
R=gri, cookieo9, bradfitz, mtj
CC=golang-codereviews
https://golang.org/cl/61180043

src/pkg/math/big/rat.go

@@ -585,3 +585,16 @@ func (z *Rat) GobDecode(buf []byte) error {
 	z.b.abs = z.b.abs.setBytes(buf[i:])
 	return nil
 }
+
+// MarshalText implements the encoding.TextMarshaler interface
+func (r *Rat) MarshalText() (text []byte, err error) {
+	return []byte(r.RatString()), nil
+}
+
+// UnmarshalText implements the encoding.TextUnmarshaler interface
+func (r *Rat) UnmarshalText(text []byte) error {
+	if _, ok := r.SetString(string(text)); !ok {
+		return fmt.Errorf("math/big: cannot unmarshal %q into a *big.Rat", text)
+	}
+	return nil
+}

src/pkg/math/big/rat_test.go

@@ -7,6 +7,8 @@ package big
 import (
 	"bytes"
 	"encoding/gob"
+	"encoding/json"
+	"encoding/xml"
 	"fmt"
 	"math"
 	"strconv"
@@ -433,6 +435,69 @@ func TestGobEncodingNilRatInSlice(t *testing.T) {
 	}
 }
 
+var ratNums = []string{
+	"-141592653589793238462643383279502884197169399375105820974944592307816406286",
+	"-1415926535897932384626433832795028841971",
+	"-141592653589793",
+	"-1",
+	"0",
+	"1",
+	"141592653589793",
+	"1415926535897932384626433832795028841971",
+	"141592653589793238462643383279502884197169399375105820974944592307816406286",
+}
+
+var ratDenoms = []string{
+	"1",
+	"718281828459045",
+	"7182818284590452353602874713526624977572",
+	"718281828459045235360287471352662497757247093699959574966967627724076630353",
+}
+
+func TestRatJSONEncoding(t *testing.T) {
+	for _, num := range ratNums {
+		for _, denom := range ratDenoms {
+			var tx Rat
+			tx.SetString(num + "/" + denom)
+			b, err := json.Marshal(&tx)
+			if err != nil {
+				t.Errorf("marshaling of %s failed: %s", &tx, err)
+				continue
+			}
+			var rx Rat
+			if err := json.Unmarshal(b, &rx); err != nil {
+				t.Errorf("unmarshaling of %s failed: %s", &tx, err)
+				continue
+			}
+			if rx.Cmp(&tx) != 0 {
+				t.Errorf("JSON encoding of %s failed: got %s want %s", &tx, &rx, &tx)
+			}
+		}
+	}
+}
+
+func TestRatXMLEncoding(t *testing.T) {
+	for _, num := range ratNums {
+		for _, denom := range ratDenoms {
+			var tx Rat
+			tx.SetString(num + "/" + denom)
+			b, err := xml.Marshal(&tx)
+			if err != nil {
+				t.Errorf("marshaling of %s failed: %s", &tx, err)
+				continue
+			}
+			var rx Rat
+			if err := xml.Unmarshal(b, &rx); err != nil {
+				t.Errorf("unmarshaling of %s failed: %s", &tx, err)
+				continue
+			}
+			if rx.Cmp(&tx) != 0 {
+				t.Errorf("XML encoding of %s failed: got %s want %s", &tx, &rx, &tx)
+			}
+		}
+	}
+}
+
 func TestIssue2379(t *testing.T) {
 	// 1) no aliasing
 	q := NewRat(3, 2)