strconv: extend Grisu3 algorithm to float32.

Also improve extfloat.Normalize to obtain a modest performance
gain in parsing, and add a shortcut path for exact integers.

benchmark                              old ns/op    new ns/op    delta
BenchmarkAtof64Decimal                        73           73   -0.54%
BenchmarkAtof64Float                          91           91   -0.54%
BenchmarkAtof64FloatExp                      198          180   -9.09%
BenchmarkAtof64Big                           307          308   +0.33%

BenchmarkAtof32Decimal                        72           72   +0.42%
BenchmarkAtof32Float                          83           83   -0.72%
BenchmarkAtof32FloatExp                      212          186  -12.26%
BenchmarkAtof32Random                        262          250   -4.58%

BenchmarkAppendFloatDecimal                  474          305  -35.65%
BenchmarkAppendFloat                         497          489   -1.61%
BenchmarkAppendFloatExp                      493          483   -2.03%
BenchmarkAppendFloatNegExp                   481          481   +0.00%
BenchmarkAppendFloatBig                      667          652   -2.25%

BenchmarkAppendFloat32Integer                338          307   -9.17%
BenchmarkAppendFloat32ExactFraction          364          439  +20.60%
BenchmarkAppendFloat32Point                 1299          490  -62.28%
BenchmarkAppendFloat32Exp                   2593          489  -81.14%
BenchmarkAppendFloat32NegExp                5116          481  -90.60%

R=rsc, r
CC=golang-dev, remy
https://golang.org/cl/6303087

src/pkg/strconv/decimal.go

@@ -79,7 +79,7 @@ func trim(a *decimal) {
 
 // Assign v to a.
 func (a *decimal) Assign(v uint64) {
-	var buf [50]byte
+	var buf [24]byte
 
 	// Write reversed decimal in buf.
 	n := 0

src/pkg/strconv/extfloat.go

@@ -190,29 +190,24 @@ func (f *extFloat) Assign(x float64) {
 	f.exp -= 64
 }
 
-// AssignComputeBounds sets f to the value of x and returns
+// AssignComputeBounds sets f to the floating point value
+// defined by mant, exp and precision given by flt. It returns
 // lower, upper such that any number in the closed interval
-// [lower, upper] is converted back to x.
+// [lower, upper] is converted back to the same floating point number.
-func (f *extFloat) AssignComputeBounds(x float64) (lower, upper extFloat) {
+func (f *extFloat) AssignComputeBounds(mant uint64, exp int, neg bool, flt *floatInfo) (lower, upper extFloat) {
-	// Special cases.
+	f.mant = mant
-	bits := math.Float64bits(x)
+	f.exp = exp - int(flt.mantbits)
-	flt := &float64info
-	neg := bits>>(flt.expbits+flt.mantbits) != 0
-	expBiased := int(bits>>flt.mantbits) & (1<<flt.expbits - 1)
-	mant := bits & (uint64(1)<<flt.mantbits - 1)
-
-	if expBiased == 0 {
-		// denormalized.
-		f.mant = mant
-		f.exp = 1 + flt.bias - int(flt.mantbits)
-	} else {
-		f.mant = mant | 1<<flt.mantbits
-		f.exp = expBiased + flt.bias - int(flt.mantbits)
-	}
 	f.neg = neg
+	if f.exp <= 0 && mant == (mant>>uint(-f.exp))<<uint(-f.exp) {
+		// An exact integer
+		f.mant >>= uint(-f.exp)
+		f.exp = 0
+		return *f, *f
+	}
+	expBiased := exp - flt.bias
 
 	upper = extFloat{mant: 2*f.mant + 1, exp: f.exp - 1, neg: f.neg}
-	if mant != 0 || expBiased == 1 {
+	if mant != 1<<flt.mantbits || expBiased == 1 {
 		lower = extFloat{mant: 2*f.mant - 1, exp: f.exp - 1, neg: f.neg}
 	} else {
 		lower = extFloat{mant: 4*f.mant - 1, exp: f.exp - 2, neg: f.neg}
@@ -222,20 +217,38 @@ func (f *extFloat) AssignComputeBounds(x float64) (lower, upper extFloat) {
 
 // Normalize normalizes f so that the highest bit of the mantissa is
 // set, and returns the number by which the mantissa was left-shifted.
-func (f *extFloat) Normalize() uint {
+func (f *extFloat) Normalize() (shift uint) {
-	if f.mant == 0 {
+	mant, exp := f.mant, f.exp
+	if mant == 0 {
 		return 0
 	}
-	exp_before := f.exp
+	if mant>>(64-32) == 0 {
-	for f.mant < (1 << 55) {
+		mant <<= 32
-		f.mant <<= 8
+		exp -= 32
-		f.exp -= 8
 	}
-	for f.mant < (1 << 63) {
+	if mant>>(64-16) == 0 {
-		f.mant <<= 1
+		mant <<= 16
-		f.exp -= 1
+		exp -= 16
 	}
-	return uint(exp_before - f.exp)
+	if mant>>(64-8) == 0 {
+		mant <<= 8
+		exp -= 8
+	}
+	if mant>>(64-4) == 0 {
+		mant <<= 4
+		exp -= 4
+	}
+	if mant>>(64-2) == 0 {
+		mant <<= 2
+		exp -= 2
+	}
+	if mant>>(64-1) == 0 {
+		mant <<= 1
+		exp -= 1
+	}
+	shift = uint(f.exp - exp)
+	f.mant, f.exp = mant, exp
+	return
 }
 
 // Multiply sets f to the product f*g: the result is correctly rounded,
@@ -390,6 +403,12 @@ func (f *extFloat) ShortestDecimal(d *decimal, lower, upper *extFloat) bool {
 		d.dp = 0
 		d.neg = f.neg
 	}
+	if f.exp == 0 && *lower == *f && *lower == *upper {
+		// an exact integer.
+		d.Assign(f.mant)
+		d.neg = f.neg
+		return true
+	}
 	const minExp = -60
 	const maxExp = -32
 	upper.Normalize()

src/pkg/strconv/ftoa.go

@@ -104,10 +104,10 @@ func genericFtoa(dst []byte, val float64, fmt byte, prec, bitSize int) []byte {
 	d := new(decimal)
 	if shortest {
 		ok := false
-		if optimize && bitSize == 64 {
+		if optimize {
 			// Try Grisu3 algorithm.
 			f := new(extFloat)
-			lower, upper := f.AssignComputeBounds(val)
+			lower, upper := f.AssignComputeBounds(mant, exp, neg, flt)
 			ok = f.ShortestDecimal(d, &lower, &upper)
 		}
 		if !ok {

src/pkg/strconv/ftoa_test.go

@@ -203,37 +203,23 @@ func BenchmarkFormatFloatBig(b *testing.B) {
 	}
 }
 
-func BenchmarkAppendFloatDecimal(b *testing.B) {
+func benchmarkAppendFloat(b *testing.B, f float64, fmt byte, prec, bitSize int) {
-	dst := make([]byte, 0, 30)
+	dst := make([]byte, 30)
 	for i := 0; i < b.N; i++ {
-		AppendFloat(dst, 33909, 'g', -1, 64)
+		AppendFloat(dst[:0], f, fmt, prec, bitSize)
-	}
-}
-
-func BenchmarkAppendFloat(b *testing.B) {
-	dst := make([]byte, 0, 30)
-	for i := 0; i < b.N; i++ {
-		AppendFloat(dst, 339.7784, 'g', -1, 64)
-	}
-}
-
-func BenchmarkAppendFloatExp(b *testing.B) {
-	dst := make([]byte, 0, 30)
-	for i := 0; i < b.N; i++ {
-		AppendFloat(dst, -5.09e75, 'g', -1, 64)
-	}
-}
-
-func BenchmarkAppendFloatNegExp(b *testing.B) {
-	dst := make([]byte, 0, 30)
-	for i := 0; i < b.N; i++ {
-		AppendFloat(dst, -5.11e-95, 'g', -1, 64)
 	}
 }
 
+func BenchmarkAppendFloatDecimal(b *testing.B) { benchmarkAppendFloat(b, 33909, 'g', -1, 64) }
+func BenchmarkAppendFloat(b *testing.B)        { benchmarkAppendFloat(b, 339.7784, 'g', -1, 64) }
+func BenchmarkAppendFloatExp(b *testing.B)     { benchmarkAppendFloat(b, -5.09e75, 'g', -1, 64) }
+func BenchmarkAppendFloatNegExp(b *testing.B)  { benchmarkAppendFloat(b, -5.11e-95, 'g', -1, 64) }
 func BenchmarkAppendFloatBig(b *testing.B) {
-	dst := make([]byte, 0, 30)
+	benchmarkAppendFloat(b, 123456789123456789123456789, 'g', -1, 64)
-	for i := 0; i < b.N; i++ {
-		AppendFloat(dst, 123456789123456789123456789, 'g', -1, 64)
-	}
 }
+
+func BenchmarkAppendFloat32Integer(b *testing.B)       { benchmarkAppendFloat(b, 33909, 'g', -1, 32) }
+func BenchmarkAppendFloat32ExactFraction(b *testing.B) { benchmarkAppendFloat(b, 3.375, 'g', -1, 32) }
+func BenchmarkAppendFloat32Point(b *testing.B)         { benchmarkAppendFloat(b, 339.7784, 'g', -1, 32) }
+func BenchmarkAppendFloat32Exp(b *testing.B)           { benchmarkAppendFloat(b, -5.09e25, 'g', -1, 32) }
+func BenchmarkAppendFloat32NegExp(b *testing.B)        { benchmarkAppendFloat(b, -5.11e-25, 'g', -1, 32) }