big: better support for string conversions

Fixes #1842.

R=r
CC=golang-dev
https://golang.org/cl/4517081

src/pkg/big/int.go

@@ -313,28 +313,30 @@ func (x *Int) String() string {
 	if x.neg {
 		s = "-"
 	}
-	return s + x.abs.string(10)
+	return s + x.abs.decimalString()
 }
 
 
-func fmtbase(ch int) int {
+func charset(ch int) string {
 	switch ch {
 	case 'b':
-		return 2
+		return lowercaseDigits[0:2]
 	case 'o':
-		return 8
+		return lowercaseDigits[0:8]
 	case 'd':
-		return 10
+		return lowercaseDigits[0:10]
 	case 'x':
-		return 16
+		return lowercaseDigits[0:16]
+	case 'X':
+		return uppercaseDigits[0:16]
 	}
-	return 10
+	return "" // unknown format
 }
 
 
 // Format is a support routine for fmt.Formatter. It accepts
-// the formats 'b' (binary), 'o' (octal), 'd' (decimal) and
-// 'x' (hexadecimal).
+// the formats 'b' (binary), 'o' (octal), 'd' (decimal), 'x'
+// (lowercase hexadecimal), and 'X' (uppercase hexadecimal).
 //
 func (x *Int) Format(s fmt.State, ch int) {
 	if x == nil {
@@ -344,7 +346,7 @@ func (x *Int) Format(s fmt.State, ch int) {
 	if x.neg {
 		fmt.Fprint(s, "-")
 	}
-	fmt.Fprint(s, x.abs.string(fmtbase(ch)))
+	fmt.Fprint(s, x.abs.string(charset(ch)))
 }
 
 

src/pkg/big/nat.go

@@ -20,6 +20,7 @@ package big
 
 import "rand"
 
+
 // An unsigned integer x of the form
 //
 //   x = x[n-1]*_B^(n-1) + x[n-2]*_B^(n-2) + ... + x[1]*_B + x[0]
@@ -668,16 +669,23 @@ func (z nat) scan(s string, base int) (nat, int, int) {
 }
 
 
-// string converts x to a string for a given base, with 2 <= base <= 16.
-// TODO(gri) in the style of the other routines, perhaps this should take
-//           a []byte buffer and return it
-func (x nat) string(base int) string {
-	if base < 2 || 16 < base {
-		panic("illegal base")
-	}
+// Character sets for string conversion.
+const (
+	lowercaseDigits = "0123456789abcdefghijklmnopqrstuvwxyz"
+	uppercaseDigits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"
+)
+
+// string converts x to a string using digits from a charset; a digit with
+// value d is represented by charset[d]. The conversion base is determined
+// by len(charset). If len(charset) < 2, the result is "<illegal base>".
+func (x nat) string(charset string) string {
+	base := len(charset)
 
-	if len(x) == 0 {
-		return "0"
+	switch {
+	case base < 2:
+		return "<illegal base>"
+	case len(x) == 0:
+		return string(charset[0])
 	}
 
 	// allocate buffer for conversion
@@ -692,13 +700,20 @@ func (x nat) string(base int) string {
 		i--
 		var r Word
 		q, r = q.divW(q, Word(base))
-		s[i] = "0123456789abcdef"[r]
+		s[i] = charset[r]
 	}
 
 	return string(s[i:])
 }
 
 
+// decimalString returns a decimal representation of x.
+// It calls x.string with the charset "0123456789".
+func (x nat) decimalString() string {
+	return x.string(lowercaseDigits[0:10])
+}
+
+
 const deBruijn32 = 0x077CB531
 
 var deBruijn32Lookup = []byte{

src/pkg/big/nat_test.go

@@ -133,7 +133,7 @@ var mulRangesN = []struct {
 
 func TestMulRangeN(t *testing.T) {
 	for i, r := range mulRangesN {
-		prod := nat(nil).mulRange(r.a, r.b).string(10)
+		prod := nat(nil).mulRange(r.a, r.b).decimalString()
 		if prod != r.prod {
 			t.Errorf("#%d: got %s; want %s", i, prod, r.prod)
 		}
@@ -167,31 +167,35 @@ func BenchmarkMul(b *testing.B) {
 }
 
 
-var tab = []struct {
-	x nat
-	b int
-	s string
+var strTests = []struct {
+	x nat    // nat value to be converted
+	c string // conversion charset
+	s string // expected result
 }{
-	{nil, 10, "0"},
-	{nat{1}, 10, "1"},
-	{nat{10}, 10, "10"},
-	{nat{1234567890}, 10, "1234567890"},
+	{nil, "01", "0"},
+	{nat{1}, "01", "1"},
+	{nat{0xc5}, "01", "11000101"},
+	{nat{03271}, lowercaseDigits[0:8], "3271"},
+	{nat{10}, lowercaseDigits[0:10], "10"},
+	{nat{1234567890}, uppercaseDigits[0:10], "1234567890"},
+	{nat{0xdeadbeef}, lowercaseDigits[0:16], "deadbeef"},
+	{nat{0xdeadbeef}, uppercaseDigits[0:16], "DEADBEEF"},
 }
 
 
 func TestString(t *testing.T) {
-	for _, a := range tab {
-		s := a.x.string(a.b)
+	for _, a := range strTests {
+		s := a.x.string(a.c)
 		if s != a.s {
 			t.Errorf("string%+v\n\tgot s = %s; want %s", a, s, a.s)
 		}
 
-		x, b, n := nat(nil).scan(a.s, a.b)
+		x, b, n := nat(nil).scan(a.s, len(a.c))
 		if x.cmp(a.x) != 0 {
 			t.Errorf("scan%+v\n\tgot z = %v; want %v", a, x, a.x)
 		}
-		if b != a.b {
-			t.Errorf("scan%+v\n\tgot b = %d; want %d", a, b, a.b)
+		if b != len(a.c) {
+			t.Errorf("scan%+v\n\tgot b = %d; want %d", a, b, len(a.c))
 		}
 		if n != len(a.s) {
 			t.Errorf("scan%+v\n\tgot n = %d; want %d", a, n, len(a.s))

src/pkg/big/rat.go

@@ -270,7 +270,7 @@ func (z *Rat) SetString(s string) (*Rat, bool) {
 
 // String returns a string representation of z in the form "a/b" (even if b == 1).
 func (z *Rat) String() string {
-	return z.a.String() + "/" + z.b.string(10)
+	return z.a.String() + "/" + z.b.decimalString()
 }
 
 
@@ -311,13 +311,13 @@ func (z *Rat) FloatString(prec int) string {
 		}
 	}
 
-	s := q.string(10)
+	s := q.decimalString()
 	if z.a.neg {
 		s = "-" + s
 	}
 
 	if prec > 0 {
-		rs := r.string(10)
+		rs := r.decimalString()
 		leadingZeros := prec - len(rs)
 		s += "." + strings.Repeat("0", leadingZeros) + rs
 	}