src/strconv/atof_test.go - go - Git at Google

 // Copyright 2009 The Go Authors. All rights reserved.
 // Use of this source code is governed by a BSD-style
 // license that can be found in the LICENSE file.

 package strconv_test

 import (
 	"math"
 	"math/rand"
 	"reflect"
 	. "strconv"
 	"strings"
 	"testing"
 	"time"
 )

 type atofTest struct {
 	in  string
 	out string
 	err error
 }

 var atoftests = []atofTest{
 	{"", "0", ErrSyntax},
 	{"1", "1", nil},
 	{"+1", "1", nil},
 	{"1x", "0", ErrSyntax},
 	{"1.1.", "0", ErrSyntax},
 	{"1e23", "1e+23", nil},
 	{"1E23", "1e+23", nil},
 	{"100000000000000000000000", "1e+23", nil},
 	{"1e-100", "1e-100", nil},
 	{"123456700", "1.234567e+08", nil},
 	{"99999999999999974834176", "9.999999999999997e+22", nil},
 	{"100000000000000000000001", "1.0000000000000001e+23", nil},
 	{"100000000000000008388608", "1.0000000000000001e+23", nil},
 	{"100000000000000016777215", "1.0000000000000001e+23", nil},
 	{"100000000000000016777216", "1.0000000000000003e+23", nil},
 	{"-1", "-1", nil},
 	{"-0.1", "-0.1", nil},
 	{"-0", "-0", nil},
 	{"1e-20", "1e-20", nil},
 	{"625e-3", "0.625", nil},

 	// zeros
 	{"0", "0", nil},
 	{"0e0", "0", nil},
 	{"-0e0", "-0", nil},
 	{"+0e0", "0", nil},
 	{"0e-0", "0", nil},
 	{"-0e-0", "-0", nil},
 	{"+0e-0", "0", nil},
 	{"0e+0", "0", nil},
 	{"-0e+0", "-0", nil},
 	{"+0e+0", "0", nil},
 	{"0e+01234567890123456789", "0", nil},
 	{"0.00e-01234567890123456789", "0", nil},
 	{"-0e+01234567890123456789", "-0", nil},
 	{"-0.00e-01234567890123456789", "-0", nil},
 	{"0e291", "0", nil}, // issue 15364
 	{"0e292", "0", nil}, // issue 15364
 	{"0e347", "0", nil}, // issue 15364
 	{"0e348", "0", nil}, // issue 15364
 	{"-0e291", "-0", nil},
 	{"-0e292", "-0", nil},
 	{"-0e347", "-0", nil},
 	{"-0e348", "-0", nil},

 	// NaNs
 	{"nan", "NaN", nil},
 	{"NaN", "NaN", nil},
 	{"NAN", "NaN", nil},

 	// Infs
 	{"inf", "+Inf", nil},
 	{"-Inf", "-Inf", nil},
 	{"+INF", "+Inf", nil},
 	{"-Infinity", "-Inf", nil},
 	{"+INFINITY", "+Inf", nil},
 	{"Infinity", "+Inf", nil},

 	// largest float64
 	{"1.7976931348623157e308", "1.7976931348623157e+308", nil},
 	{"-1.7976931348623157e308", "-1.7976931348623157e+308", nil},
 	// next float64 - too large
 	{"1.7976931348623159e308", "+Inf", ErrRange},
 	{"-1.7976931348623159e308", "-Inf", ErrRange},
 	// the border is ...158079
 	// borderline - okay
 	{"1.7976931348623158e308", "1.7976931348623157e+308", nil},
 	{"-1.7976931348623158e308", "-1.7976931348623157e+308", nil},
 	// borderline - too large
 	{"1.797693134862315808e308", "+Inf", ErrRange},
 	{"-1.797693134862315808e308", "-Inf", ErrRange},

 	// a little too large
 	{"1e308", "1e+308", nil},
 	{"2e308", "+Inf", ErrRange},
 	{"1e309", "+Inf", ErrRange},

 	// way too large
 	{"1e310", "+Inf", ErrRange},
 	{"-1e310", "-Inf", ErrRange},
 	{"1e400", "+Inf", ErrRange},
 	{"-1e400", "-Inf", ErrRange},
 	{"1e400000", "+Inf", ErrRange},
 	{"-1e400000", "-Inf", ErrRange},

 	// denormalized
 	{"1e-305", "1e-305", nil},
 	{"1e-306", "1e-306", nil},
 	{"1e-307", "1e-307", nil},
 	{"1e-308", "1e-308", nil},
 	{"1e-309", "1e-309", nil},
 	{"1e-310", "1e-310", nil},
 	{"1e-322", "1e-322", nil},
 	// smallest denormal
 	{"5e-324", "5e-324", nil},
 	{"4e-324", "5e-324", nil},
 	{"3e-324", "5e-324", nil},
 	// too small
 	{"2e-324", "0", nil},
 	// way too small
 	{"1e-350", "0", nil},
 	{"1e-400000", "0", nil},

 	// try to overflow exponent
 	{"1e-4294967296", "0", nil},
 	{"1e+4294967296", "+Inf", ErrRange},
 	{"1e-18446744073709551616", "0", nil},
 	{"1e+18446744073709551616", "+Inf", ErrRange},

 	// Parse errors
 	{"1e", "0", ErrSyntax},
 	{"1e-", "0", ErrSyntax},
 	{".e-1", "0", ErrSyntax},
 	{"1\x00.2", "0", ErrSyntax},

 	// http://www.exploringbinary.com/java-hangs-when-converting-2-2250738585072012e-308/
 	{"2.2250738585072012e-308", "2.2250738585072014e-308", nil},
 	// http://www.exploringbinary.com/php-hangs-on-numeric-value-2-2250738585072011e-308/
 	{"2.2250738585072011e-308", "2.225073858507201e-308", nil},

 	// A very large number (initially wrongly parsed by the fast algorithm).
 	{"4.630813248087435e+307", "4.630813248087435e+307", nil},

 	// A different kind of very large number.
 	{"22.222222222222222", "22.22222222222222", nil},
 	{"2." + strings.Repeat("2", 4000) + "e+1", "22.22222222222222", nil},

 	// Exactly halfway between 1 and math.Nextafter(1, 2).
 	// Round to even (down).
 	{"1.00000000000000011102230246251565404236316680908203125", "1", nil},
 	// Slightly lower; still round down.
 	{"1.00000000000000011102230246251565404236316680908203124", "1", nil},
 	// Slightly higher; round up.
 	{"1.00000000000000011102230246251565404236316680908203126", "1.0000000000000002", nil},
 	// Slightly higher, but you have to read all the way to the end.
 	{"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},

 	// 2^92 = 8388608p+69 = 4951760157141521099596496896 (4.9517602e27)
 	// is an exact power of two that needs 8 decimal digits to be correctly
 	// parsed back.
 	// The float32 before is 16777215p+68 = 4.95175986e+27
 	// The halfway is 4.951760009. A bad algorithm that thinks the previous
 	// float32 is 8388607p+69 will shorten incorrectly to 4.95176e+27.
 	{"4951760157141521099596496896", "4.9517602e+27", nil},
 }

 type atofSimpleTest struct {
 	x float64
 	s string
 }

 var (
 	atofRandomTests        []atofSimpleTest
 	benchmarksRandomBits   [1024]string
 	benchmarksRandomNormal [1024]string
 )

 func init() {
 	// The atof routines return NumErrors wrapping
 	// the error and the string. Convert the table above.
 	for i := range atoftests {
 		test := &atoftests[i]
 		if test.err != nil {
 			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())
 	if testing.Short() {
 		atofRandomTests = make([]atofSimpleTest, 100)
 	} else {
 		atofRandomTests = make([]atofSimpleTest, 10000)
 	}
 	for i := range atofRandomTests {
 		n := uint64(rand.Uint32())<<32 | uint64(rand.Uint32())
 		x := math.Float64frombits(n)
 		s := FormatFloat(x, 'g', -1, 64)
 		atofRandomTests[i] = atofSimpleTest{x, s}
 	}

 	for i := range benchmarksRandomBits {
 		bits := uint64(rand.Uint32())<<32 | uint64(rand.Uint32())
 		x := math.Float64frombits(bits)
 		benchmarksRandomBits[i] = FormatFloat(x, 'g', -1, 64)
 	}

 	for i := range benchmarksRandomNormal {
 		x := rand.NormFloat64()
 		benchmarksRandomNormal[i] = FormatFloat(x, 'g', -1, 64)
 	}
 }

 func testAtof(t *testing.T, opt bool) {
 	oldopt := SetOptimize(opt)
 	for i := 0; i < len(atoftests); i++ {
 		test := &atoftests[i]
 		out, err := ParseFloat(test.in, 64)
 		outs := FormatFloat(out, 'g', -1, 64)
 		if outs != test.out || !reflect.DeepEqual(err, test.err) {
 			t.Errorf("ParseFloat(%v, 64) = %v, %v want %v, %v",
 				test.in, out, err, test.out, test.err)
 		}

 		if float64(float32(out)) == out {
 			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)
 			}
 		}
 	}
 	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)
 }

 func TestAtof(t *testing.T) { testAtof(t, true) }

 func TestAtofSlow(t *testing.T) { testAtof(t, false) }

 func TestAtofRandom(t *testing.T) {
 	for _, test := range atofRandomTests {
 		x, _ := ParseFloat(test.s, 64)
 		switch {
 		default:
 			t.Errorf("number %s badly parsed as %b (expected %b)", test.s, x, test.x)
 		case x == test.x:
 		case math.IsNaN(test.x) && math.IsNaN(x):
 		}
 	}
 	t.Logf("tested %d random numbers", len(atofRandomTests))
 }

 var roundTripCases = []struct {
 	f float64
 	s string
 }{
 	// Issue 2917.
 	// This test will break the optimized conversion if the
 	// FPU is using 80-bit registers instead of 64-bit registers,
 	// usually because the operating system initialized the
 	// thread with 80-bit precision and the Go runtime didn't
 	// fix the FP control word.
 	{8865794286000691 << 39, "4.87402195346389e+27"},
 	{8865794286000692 << 39, "4.8740219534638903e+27"},
 }

 func TestRoundTrip(t *testing.T) {
 	for _, tt := range roundTripCases {
 		old := SetOptimize(false)
 		s := FormatFloat(tt.f, 'g', -1, 64)
 		if s != tt.s {
 			t.Errorf("no-opt FormatFloat(%b) = %s, want %s", tt.f, s, tt.s)
 		}
 		f, err := ParseFloat(tt.s, 64)
 		if f != tt.f || err != nil {
 			t.Errorf("no-opt ParseFloat(%s) = %b, %v want %b, nil", tt.s, f, err, tt.f)
 		}
 		SetOptimize(true)
 		s = FormatFloat(tt.f, 'g', -1, 64)
 		if s != tt.s {
 			t.Errorf("opt FormatFloat(%b) = %s, want %s", tt.f, s, tt.s)
 		}
 		f, err = ParseFloat(tt.s, 64)
 		if f != tt.f || err != nil {
 			t.Errorf("opt ParseFloat(%s) = %b, %v want %b, nil", tt.s, f, err, tt.f)
 		}
 		SetOptimize(old)
 	}
 }

 // 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)
 	}
 }

 func BenchmarkAtof64Float(b *testing.B) {
 	for i := 0; i < b.N; i++ {
 		ParseFloat("339.7784", 64)
 	}
 }

 func BenchmarkAtof64FloatExp(b *testing.B) {
 	for i := 0; i < b.N; i++ {
 		ParseFloat("-5.09e75", 64)
 	}
 }

 func BenchmarkAtof64Big(b *testing.B) {
 	for i := 0; i < b.N; i++ {
 		ParseFloat("123456789123456789123456789", 64)
 	}
 }

 func BenchmarkAtof64RandomBits(b *testing.B) {
 	for i := 0; i < b.N; i++ {
 		ParseFloat(benchmarksRandomBits[i%1024], 64)
 	}
 }

 func BenchmarkAtof64RandomFloats(b *testing.B) {
 	for i := 0; i < b.N; i++ {
 		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)
 	}
 }
	// Copyright 2009 The Go Authors. All rights reserved.
	// Use of this source code is governed by a BSD-style
	// license that can be found in the LICENSE file.

	package strconv_test

	import (
	"math"
	"math/rand"
	"reflect"
	. "strconv"
	"strings"
	"testing"
	"time"
	)

	type atofTest struct {
	in string
	out string
	err error
	}

	var atoftests = []atofTest{
	{"", "0", ErrSyntax},
	{"1", "1", nil},
	{"+1", "1", nil},
	{"1x", "0", ErrSyntax},
	{"1.1.", "0", ErrSyntax},
	{"1e23", "1e+23", nil},
	{"1E23", "1e+23", nil},
	{"100000000000000000000000", "1e+23", nil},
	{"1e-100", "1e-100", nil},
	{"123456700", "1.234567e+08", nil},
	{"99999999999999974834176", "9.999999999999997e+22", nil},
	{"100000000000000000000001", "1.0000000000000001e+23", nil},
	{"100000000000000008388608", "1.0000000000000001e+23", nil},
	{"100000000000000016777215", "1.0000000000000001e+23", nil},
	{"100000000000000016777216", "1.0000000000000003e+23", nil},
	{"-1", "-1", nil},
	{"-0.1", "-0.1", nil},
	{"-0", "-0", nil},
	{"1e-20", "1e-20", nil},
	{"625e-3", "0.625", nil},

	// zeros
	{"0", "0", nil},
	{"0e0", "0", nil},
	{"-0e0", "-0", nil},
	{"+0e0", "0", nil},
	{"0e-0", "0", nil},
	{"-0e-0", "-0", nil},
	{"+0e-0", "0", nil},
	{"0e+0", "0", nil},
	{"-0e+0", "-0", nil},
	{"+0e+0", "0", nil},
	{"0e+01234567890123456789", "0", nil},
	{"0.00e-01234567890123456789", "0", nil},
	{"-0e+01234567890123456789", "-0", nil},
	{"-0.00e-01234567890123456789", "-0", nil},
	{"0e291", "0", nil}, // issue 15364
	{"0e292", "0", nil}, // issue 15364
	{"0e347", "0", nil}, // issue 15364
	{"0e348", "0", nil}, // issue 15364
	{"-0e291", "-0", nil},
	{"-0e292", "-0", nil},
	{"-0e347", "-0", nil},
	{"-0e348", "-0", nil},

	// NaNs
	{"nan", "NaN", nil},
	{"NaN", "NaN", nil},
	{"NAN", "NaN", nil},

	// Infs
	{"inf", "+Inf", nil},
	{"-Inf", "-Inf", nil},
	{"+INF", "+Inf", nil},
	{"-Infinity", "-Inf", nil},
	{"+INFINITY", "+Inf", nil},
	{"Infinity", "+Inf", nil},

	// largest float64
	{"1.7976931348623157e308", "1.7976931348623157e+308", nil},
	{"-1.7976931348623157e308", "-1.7976931348623157e+308", nil},
	// next float64 - too large
	{"1.7976931348623159e308", "+Inf", ErrRange},
	{"-1.7976931348623159e308", "-Inf", ErrRange},
	// the border is ...158079
	// borderline - okay
	{"1.7976931348623158e308", "1.7976931348623157e+308", nil},
	{"-1.7976931348623158e308", "-1.7976931348623157e+308", nil},
	// borderline - too large
	{"1.797693134862315808e308", "+Inf", ErrRange},
	{"-1.797693134862315808e308", "-Inf", ErrRange},

	// a little too large
	{"1e308", "1e+308", nil},
	{"2e308", "+Inf", ErrRange},
	{"1e309", "+Inf", ErrRange},

	// way too large
	{"1e310", "+Inf", ErrRange},
	{"-1e310", "-Inf", ErrRange},
	{"1e400", "+Inf", ErrRange},
	{"-1e400", "-Inf", ErrRange},
	{"1e400000", "+Inf", ErrRange},
	{"-1e400000", "-Inf", ErrRange},

	// denormalized
	{"1e-305", "1e-305", nil},
	{"1e-306", "1e-306", nil},
	{"1e-307", "1e-307", nil},
	{"1e-308", "1e-308", nil},
	{"1e-309", "1e-309", nil},
	{"1e-310", "1e-310", nil},
	{"1e-322", "1e-322", nil},
	// smallest denormal
	{"5e-324", "5e-324", nil},
	{"4e-324", "5e-324", nil},
	{"3e-324", "5e-324", nil},
	// too small
	{"2e-324", "0", nil},
	// way too small
	{"1e-350", "0", nil},
	{"1e-400000", "0", nil},

	// try to overflow exponent
	{"1e-4294967296", "0", nil},
	{"1e+4294967296", "+Inf", ErrRange},
	{"1e-18446744073709551616", "0", nil},
	{"1e+18446744073709551616", "+Inf", ErrRange},

	// Parse errors
	{"1e", "0", ErrSyntax},
	{"1e-", "0", ErrSyntax},
	{".e-1", "0", ErrSyntax},
	{"1\x00.2", "0", ErrSyntax},

	// http://www.exploringbinary.com/java-hangs-when-converting-2-2250738585072012e-308/
	{"2.2250738585072012e-308", "2.2250738585072014e-308", nil},
	// http://www.exploringbinary.com/php-hangs-on-numeric-value-2-2250738585072011e-308/
	{"2.2250738585072011e-308", "2.225073858507201e-308", nil},

	// A very large number (initially wrongly parsed by the fast algorithm).
	{"4.630813248087435e+307", "4.630813248087435e+307", nil},

	// A different kind of very large number.
	{"22.222222222222222", "22.22222222222222", nil},
	{"2." + strings.Repeat("2", 4000) + "e+1", "22.22222222222222", nil},

	// Exactly halfway between 1 and math.Nextafter(1, 2).
	// Round to even (down).
	{"1.00000000000000011102230246251565404236316680908203125", "1", nil},
	// Slightly lower; still round down.
	{"1.00000000000000011102230246251565404236316680908203124", "1", nil},
	// Slightly higher; round up.
	{"1.00000000000000011102230246251565404236316680908203126", "1.0000000000000002", nil},
	// Slightly higher, but you have to read all the way to the end.
	{"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},

	// 2^92 = 8388608p+69 = 4951760157141521099596496896 (4.9517602e27)
	// is an exact power of two that needs 8 decimal digits to be correctly
	// parsed back.
	// The float32 before is 16777215p+68 = 4.95175986e+27
	// The halfway is 4.951760009. A bad algorithm that thinks the previous
	// float32 is 8388607p+69 will shorten incorrectly to 4.95176e+27.
	{"4951760157141521099596496896", "4.9517602e+27", nil},
	}

	type atofSimpleTest struct {
	x float64
	s string
	}

	var (
	atofRandomTests []atofSimpleTest
	benchmarksRandomBits [1024]string
	benchmarksRandomNormal [1024]string
	)

	func init() {
	// The atof routines return NumErrors wrapping
	// the error and the string. Convert the table above.
	for i := range atoftests {
	test := &atoftests[i]
	if test.err != nil {
	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())
	if testing.Short() {
	atofRandomTests = make([]atofSimpleTest, 100)
	} else {
	atofRandomTests = make([]atofSimpleTest, 10000)
	}
	for i := range atofRandomTests {
	n := uint64(rand.Uint32())<<32 \| uint64(rand.Uint32())
	x := math.Float64frombits(n)
	s := FormatFloat(x, 'g', -1, 64)
	atofRandomTests[i] = atofSimpleTest{x, s}
	}

	for i := range benchmarksRandomBits {
	bits := uint64(rand.Uint32())<<32 \| uint64(rand.Uint32())
	x := math.Float64frombits(bits)
	benchmarksRandomBits[i] = FormatFloat(x, 'g', -1, 64)
	}

	for i := range benchmarksRandomNormal {
	x := rand.NormFloat64()
	benchmarksRandomNormal[i] = FormatFloat(x, 'g', -1, 64)
	}
	}

	func testAtof(t *testing.T, opt bool) {
	oldopt := SetOptimize(opt)
	for i := 0; i < len(atoftests); i++ {
	test := &atoftests[i]
	out, err := ParseFloat(test.in, 64)
	outs := FormatFloat(out, 'g', -1, 64)
	if outs != test.out \|\| !reflect.DeepEqual(err, test.err) {
	t.Errorf("ParseFloat(%v, 64) = %v, %v want %v, %v",
	test.in, out, err, test.out, test.err)
	}

	if float64(float32(out)) == out {
	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)
	}
	}
	}
	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)
	}

	func TestAtof(t *testing.T) { testAtof(t, true) }

	func TestAtofSlow(t *testing.T) { testAtof(t, false) }

	func TestAtofRandom(t *testing.T) {
	for _, test := range atofRandomTests {
	x, _ := ParseFloat(test.s, 64)
	switch {
	default:
	t.Errorf("number %s badly parsed as %b (expected %b)", test.s, x, test.x)
	case x == test.x:
	case math.IsNaN(test.x) && math.IsNaN(x):
	}
	}
	t.Logf("tested %d random numbers", len(atofRandomTests))
	}

	var roundTripCases = []struct {
	f float64
	s string
	}{
	// Issue 2917.
	// This test will break the optimized conversion if the
	// FPU is using 80-bit registers instead of 64-bit registers,
	// usually because the operating system initialized the
	// thread with 80-bit precision and the Go runtime didn't
	// fix the FP control word.
	{8865794286000691 << 39, "4.87402195346389e+27"},
	{8865794286000692 << 39, "4.8740219534638903e+27"},
	}

	func TestRoundTrip(t *testing.T) {
	for _, tt := range roundTripCases {
	old := SetOptimize(false)
	s := FormatFloat(tt.f, 'g', -1, 64)
	if s != tt.s {
	t.Errorf("no-opt FormatFloat(%b) = %s, want %s", tt.f, s, tt.s)
	}
	f, err := ParseFloat(tt.s, 64)
	if f != tt.f \|\| err != nil {
	t.Errorf("no-opt ParseFloat(%s) = %b, %v want %b, nil", tt.s, f, err, tt.f)
	}
	SetOptimize(true)
	s = FormatFloat(tt.f, 'g', -1, 64)
	if s != tt.s {
	t.Errorf("opt FormatFloat(%b) = %s, want %s", tt.f, s, tt.s)
	}
	f, err = ParseFloat(tt.s, 64)
	if f != tt.f \|\| err != nil {
	t.Errorf("opt ParseFloat(%s) = %b, %v want %b, nil", tt.s, f, err, tt.f)
	}
	SetOptimize(old)
	}
	}

	// 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)
	}
	}

	func BenchmarkAtof64Float(b *testing.B) {
	for i := 0; i < b.N; i++ {
	ParseFloat("339.7784", 64)
	}
	}

	func BenchmarkAtof64FloatExp(b *testing.B) {
	for i := 0; i < b.N; i++ {
	ParseFloat("-5.09e75", 64)
	}
	}

	func BenchmarkAtof64Big(b *testing.B) {
	for i := 0; i < b.N; i++ {
	ParseFloat("123456789123456789123456789", 64)
	}
	}

	func BenchmarkAtof64RandomBits(b *testing.B) {
	for i := 0; i < b.N; i++ {
	ParseFloat(benchmarksRandomBits[i%1024], 64)
	}
	}

	func BenchmarkAtof64RandomFloats(b *testing.B) {
	for i := 0; i < b.N; i++ {
	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)
	}
	}