math/big: implement JSON un/marshaling support for Ints

Also: simplified some existing tests.

No support for Rats for now because the precision-preserving
default notation (fractions of the form a/b) is not a valid
JSON value.

Fixes #3657.

R=golang-dev, bradfitz, rsc
CC=golang-dev
https://golang.org/cl/6211079
diff --git a/src/pkg/math/big/int_test.go b/src/pkg/math/big/int_test.go
index 9700a9b..30e5591 100644
--- a/src/pkg/math/big/int_test.go
+++ b/src/pkg/math/big/int_test.go
@@ -8,6 +8,7 @@
 	"bytes"
 	"encoding/gob"
 	"encoding/hex"
+	"encoding/json"
 	"fmt"
 	"math/rand"
 	"testing"
@@ -1368,8 +1369,12 @@
 	}
 }
 
-// used by TestIntGobEncoding and TestRatGobEncoding
-var gobEncodingTests = []string{
+var encodingTests = []string{
+	"-539345864568634858364538753846587364875430589374589",
+	"-678645873",
+	"-100",
+	"-2",
+	"-1",
 	"0",
 	"1",
 	"2",
@@ -1383,26 +1388,37 @@
 	var medium bytes.Buffer
 	enc := gob.NewEncoder(&medium)
 	dec := gob.NewDecoder(&medium)
-	for i, test := range gobEncodingTests {
-		for j := 0; j < 2; j++ {
-			medium.Reset() // empty buffer for each test case (in case of failures)
-			stest := test
-			if j != 0 {
-				// negative numbers
-				stest = "-" + test
-			}
-			var tx Int
-			tx.SetString(stest, 10)
-			if err := enc.Encode(&tx); err != nil {
-				t.Errorf("#%d%c: encoding failed: %s", i, 'a'+j, err)
-			}
-			var rx Int
-			if err := dec.Decode(&rx); err != nil {
-				t.Errorf("#%d%c: decoding failed: %s", i, 'a'+j, err)
-			}
-			if rx.Cmp(&tx) != 0 {
-				t.Errorf("#%d%c: transmission failed: got %s want %s", i, 'a'+j, &rx, &tx)
-			}
+	for _, test := range encodingTests {
+		medium.Reset() // empty buffer for each test case (in case of failures)
+		var tx Int
+		tx.SetString(test, 10)
+		if err := enc.Encode(&tx); err != nil {
+			t.Errorf("encoding of %s failed: %s", &tx, err)
+		}
+		var rx Int
+		if err := dec.Decode(&rx); err != nil {
+			t.Errorf("decoding of %s failed: %s", &tx, err)
+		}
+		if rx.Cmp(&tx) != 0 {
+			t.Errorf("transmission of %s failed: got %s want %s", &tx, &rx, &tx)
+		}
+	}
+}
+
+func TestIntJSONEncoding(t *testing.T) {
+	for _, test := range encodingTests {
+		var tx Int
+		tx.SetString(test, 10)
+		b, err := json.Marshal(&tx)
+		if err != nil {
+			t.Errorf("marshaling of %s failed: %s", &tx, err)
+		}
+		var rx Int
+		if err := json.Unmarshal(b, &rx); err != nil {
+			t.Errorf("unmarshaling of %s failed: %s", &tx, err)
+		}
+		if rx.Cmp(&tx) != 0 {
+			t.Errorf("JSON encoding of %s failed: got %s want %s", &tx, &rx, &tx)
 		}
 	}
 }