strconv: extend fast parsing algorithm to ParseFloat(s, 32)

benchmark                  old ns/op    new ns/op    delta
BenchmarkAtof32Decimal           215           73  -65.72%
BenchmarkAtof32Float             233           83  -64.21%
BenchmarkAtof32FloatExp         3351          209  -93.76%
BenchmarkAtof32Random           1939          260  -86.59%

R=rsc
CC=golang-dev, remy
https://golang.org/cl/6294071

src/pkg/strconv/atof.go

@@ -411,33 +411,35 @@ func atof64exact(mantissa uint64, exp int, neg bool) (f float64, ok bool) {
 	return
 }
 
-// If possible to convert decimal d to 32-bit float f exactly,
+// If possible to compute mantissa*10^exp to 32-bit float f exactly,
 // entirely in floating-point math, do so, avoiding the machinery above.
-func (d *decimal) atof32() (f float32, ok bool) {
-	// Exact integers are <= 10^7.
-	// Exact powers of ten are <= 10^10.
-	if d.nd > 7 {
+func atof32exact(mantissa uint64, exp int, neg bool) (f float32, ok bool) {
+	if mantissa>>float32info.mantbits != 0 {
 		return
 	}
+	f = float32(mantissa)
+	if neg {
+		f = -f
+	}
 	switch {
-	case d.dp == d.nd: // int
-		f := d.atof32int()
+	case exp == 0:
 		return f, true
-
-	case d.dp > d.nd && d.dp <= 7+10: // int * 10^k
-		f := d.atof32int()
-		k := d.dp - d.nd
+	// Exact integers are <= 10^7.
+	// Exact powers of ten are <= 10^10.
+	case exp > 0 && exp <= 7+10: // int * 10^k
 		// If exponent is big but number of digits is not,
 		// can move a few zeros into the integer part.
-		if k > 10 {
-			f *= float32pow10[k-10]
-			k = 10
+		if exp > 10 {
+			f *= float32pow10[exp-10]
+			exp = 10
 		}
-		return f * float32pow10[k], true
-
-	case d.dp < d.nd && d.nd-d.dp <= 10: // int / 10^k
-		f := d.atof32int()
-		return f / float32pow10[d.nd-d.dp], true
+		if f > 1e7 || f < -1e7 {
+			// the exponent was really too large.
+			return
+		}
+		return f * float32pow10[exp], true
+	case exp < 0 && exp >= -10: // int / 10^k
+		return f / float32pow10[-exp], true
 	}
 	return
 }
@@ -449,15 +451,32 @@ func atof32(s string) (f float32, err error) {
 		return float32(val), nil
 	}
 
+	if optimize {
+		// Parse mantissa and exponent.
+		mantissa, exp, neg, trunc, ok := readFloat(s)
+		if ok {
+			// Try pure floating-point arithmetic conversion.
+			if !trunc {
+				if f, ok := atof32exact(mantissa, exp, neg); ok {
+					return f, nil
+				}
+			}
+			// Try another fast path.
+			ext := new(extFloat)
+			if ok := ext.AssignDecimal(mantissa, exp, neg, trunc, &float32info); ok {
+				b, ovf := ext.floatBits(&float32info)
+				f = math.Float32frombits(uint32(b))
+				if ovf {
+					err = rangeError(fnParseFloat, s)
+				}
+				return f, err
+			}
+		}
+	}
 	var d decimal
 	if !d.set(s) {
 		return 0, syntaxError(fnParseFloat, s)
 	}
-	if optimize {
-		if f, ok := d.atof32(); ok {
-			return f, nil
-		}
-	}
 	b, ovf := d.floatBits(&float32info)
 	f = math.Float32frombits(uint32(b))
 	if ovf {
@@ -483,8 +502,8 @@ func atof64(s string) (f float64, err error) {
 			}
 			// Try another fast path.
 			ext := new(extFloat)
-			if ok := ext.AssignDecimal(mantissa, exp, neg, trunc); ok {
-				b, ovf := ext.floatBits()
+			if ok := ext.AssignDecimal(mantissa, exp, neg, trunc, &float64info); ok {
+				b, ovf := ext.floatBits(&float64info)
 				f = math.Float64frombits(b)
 				if ovf {
 					err = rangeError(fnParseFloat, s)

src/pkg/strconv/atof_test.go

@@ -134,6 +134,46 @@ var atoftests = []atofTest{
 	{"1.00000000000000011102230246251565404236316680908203125" + strings.Repeat("0", 10000) + "1", "1.0000000000000002", nil},
 }
 
+var atof32tests = []atofTest{
+	// Exactly halfway between 1 and the next float32.
+	// Round to even (down).
+	{"1.000000059604644775390625", "1", nil},
+	// Slightly lower.
+	{"1.000000059604644775390624", "1", nil},
+	// Slightly higher.
+	{"1.000000059604644775390626", "1.0000001", nil},
+	// Slightly higher, but you have to read all the way to the end.
+	{"1.000000059604644775390625" + strings.Repeat("0", 10000) + "1", "1.0000001", nil},
+
+	// largest float32: (1<<128) * (1 - 2^-24)
+	{"340282346638528859811704183484516925440", "3.4028235e+38", nil},
+	{"-340282346638528859811704183484516925440", "-3.4028235e+38", nil},
+	// next float32 - too large
+	{"3.4028236e38", "+Inf", ErrRange},
+	{"-3.4028236e38", "-Inf", ErrRange},
+	// the border is 3.40282356779...e+38
+	// borderline - okay
+	{"3.402823567e38", "3.4028235e+38", nil},
+	{"-3.402823567e38", "-3.4028235e+38", nil},
+	// borderline - too large
+	{"3.4028235678e38", "+Inf", ErrRange},
+	{"-3.4028235678e38", "-Inf", ErrRange},
+
+	// Denormals: less than 2^-126
+	{"1e-38", "1e-38", nil},
+	{"1e-39", "1e-39", nil},
+	{"1e-40", "1e-40", nil},
+	{"1e-41", "1e-41", nil},
+	{"1e-42", "1e-42", nil},
+	{"1e-43", "1e-43", nil},
+	{"1e-44", "1e-44", nil},
+	{"6e-45", "6e-45", nil}, // 4p-149 = 5.6e-45
+	{"5e-45", "6e-45", nil},
+	// Smallest denormal
+	{"1e-45", "1e-45", nil}, // 1p-149 = 1.4e-45
+	{"2e-45", "1e-45", nil},
+}
+
 type atofSimpleTest struct {
 	x float64
 	s string
@@ -154,6 +194,12 @@ func init() {
 			test.err = &NumError{"ParseFloat", test.in, test.err}
 		}
 	}
+	for i := range atof32tests {
+		test := &atof32tests[i]
+		if test.err != nil {
+			test.err = &NumError{"ParseFloat", test.in, test.err}
+		}
+	}
 
 	// Generate random inputs for tests and benchmarks
 	rand.Seed(time.Now().UnixNano())
@@ -206,6 +252,19 @@ func testAtof(t *testing.T, opt bool) {
 			}
 		}
 	}
+	for _, test := range atof32tests {
+		out, err := ParseFloat(test.in, 32)
+		out32 := float32(out)
+		if float64(out32) != out {
+			t.Errorf("ParseFloat(%v, 32) = %v, not a float32 (closest is %v)", test.in, out, float64(out32))
+			continue
+		}
+		outs := FormatFloat(float64(out32), 'g', -1, 32)
+		if outs != test.out || !reflect.DeepEqual(err, test.err) {
+			t.Errorf("ParseFloat(%v, 32) = %v, %v want %v, %v  # %v",
+				test.in, out32, err, test.out, test.err, out)
+		}
+	}
 	SetOptimize(oldopt)
 }
 
@@ -264,6 +323,35 @@ func TestRoundTrip(t *testing.T) {
 	}
 }
 
+// TestRoundTrip32 tries a fraction of all finite positive float32 values.
+func TestRoundTrip32(t *testing.T) {
+	step := uint32(997)
+	if testing.Short() {
+		step = 99991
+	}
+	count := 0
+	for i := uint32(0); i < 0xff<<23; i += step {
+		f := math.Float32frombits(i)
+		if i&1 == 1 {
+			f = -f // negative
+		}
+		s := FormatFloat(float64(f), 'g', -1, 32)
+
+		parsed, err := ParseFloat(s, 32)
+		parsed32 := float32(parsed)
+		switch {
+		case err != nil:
+			t.Errorf("ParseFloat(%q, 32) gave error %s", s, err)
+		case float64(parsed32) != parsed:
+			t.Errorf("ParseFloat(%q, 32) = %v, not a float32 (nearest is %v)", s, parsed, parsed32)
+		case parsed32 != f:
+			t.Errorf("ParseFloat(%q, 32) = %b (expected %b)", s, parsed32, f)
+		}
+		count++
+	}
+	t.Logf("tested %d float32's", count)
+}
+
 func BenchmarkAtof64Decimal(b *testing.B) {
 	for i := 0; i < b.N; i++ {
 		ParseFloat("33909", 64)
@@ -299,3 +387,35 @@ func BenchmarkAtof64RandomFloats(b *testing.B) {
 		ParseFloat(benchmarksRandomNormal[i%1024], 64)
 	}
 }
+
+func BenchmarkAtof32Decimal(b *testing.B) {
+	for i := 0; i < b.N; i++ {
+		ParseFloat("33909", 32)
+	}
+}
+
+func BenchmarkAtof32Float(b *testing.B) {
+	for i := 0; i < b.N; i++ {
+		ParseFloat("339.778", 32)
+	}
+}
+
+func BenchmarkAtof32FloatExp(b *testing.B) {
+	for i := 0; i < b.N; i++ {
+		ParseFloat("12.3456e32", 32)
+	}
+}
+
+var float32strings [4096]string
+
+func BenchmarkAtof32Random(b *testing.B) {
+	n := uint32(997)
+	for i := range float32strings {
+		n = (99991*n + 42) % (0xff << 23)
+		float32strings[i] = FormatFloat(float64(math.Float32frombits(n)), 'g', -1, 32)
+	}
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		ParseFloat(float32strings[i%4096], 32)
+	}
+}

src/pkg/strconv/extfloat.go

@@ -127,8 +127,7 @@ var powersOfTen = [...]extFloat{
 // floatBits returns the bits of the float64 that best approximates
 // the extFloat passed as receiver. Overflow is set to true if
 // the resulting float64 is ±Inf.
-func (f *extFloat) floatBits() (bits uint64, overflow bool) {
-	flt := &float64info
+func (f *extFloat) floatBits(flt *floatInfo) (bits uint64, overflow bool) {
 	f.Normalize()
 
 	exp := f.exp + 63
@@ -140,7 +139,7 @@ func (f *extFloat) floatBits() (bits uint64, overflow bool) {
 		exp += n
 	}
 
-	// Extract 1+flt.mantbits bits.
+	// Extract 1+flt.mantbits bits from the 64-bit mantissa.
 	mant := f.mant >> (63 - flt.mantbits)
 	if f.mant&(1<<(62-flt.mantbits)) != 0 {
 		// Round up.
@@ -266,8 +265,9 @@ var uint64pow10 = [...]uint64{
 
 // AssignDecimal sets f to an approximate value mantissa*10^exp. It
 // returns true if the value represented by f is guaranteed to be the
-// best approximation of d after being rounded to a float64. 
-func (f *extFloat) AssignDecimal(mantissa uint64, exp10 int, neg bool, trunc bool) (ok bool) {
+// best approximation of d after being rounded to a float64 or
+// float32 depending on flt.
+func (f *extFloat) AssignDecimal(mantissa uint64, exp10 int, neg bool, trunc bool, flt *floatInfo) (ok bool) {
 	const uint64digits = 19
 	const errorscale = 8
 	errors := 0 // An upper bound for error, computed in errorscale*ulp.
@@ -315,10 +315,10 @@ func (f *extFloat) AssignDecimal(mantissa uint64, exp10 int, neg bool, trunc boo
 	// The 64 bits mantissa is 1 + 52 bits for float64 + 11 extra bits.
 	//
 	// In many cases the approximation will be good enough.
-	const denormalExp = -1023 - 63
-	flt := &float64info
+	denormalExp := flt.bias - 63
 	var extrabits uint
 	if f.exp <= denormalExp {
+		// f.mant * 2^f.exp is smaller than 2^(flt.bias+1).
 		extrabits = uint(63 - flt.mantbits + 1 + uint(denormalExp-f.exp))
 	} else {
 		extrabits = uint(63 - flt.mantbits)