libgo/go/strconv/atof.go - gofrontend - 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

 // decimal to binary floating point conversion.
 // Algorithm:
 //   1) Store input in multiprecision decimal.
 //   2) Multiply/divide decimal by powers of two until in range [0.5, 1)
 //   3) Multiply by 2^precision and round to get mantissa.

 import "math"
 import "runtime"

 var optimize = true // set to false to force slow-path conversions for testing

 // commonPrefixLenIgnoreCase returns the length of the common
 // prefix of s and prefix, with the character case of s ignored.
 // The prefix argument must be all lower-case.
 func commonPrefixLenIgnoreCase(s, prefix string) int {
 	n := len(prefix)
 	if n > len(s) {
 		n = len(s)
 	}
 	for i := 0; i < n; i++ {
 		c := s[i]
 		if 'A' <= c && c <= 'Z' {
 			c += 'a' - 'A'
 		}
 		if c != prefix[i] {
 			return i
 		}
 	}
 	return n
 }

 // special returns the floating-point value for the special,
 // possibly signed floating-point representations inf, infinity,
 // and NaN. The result is ok if a prefix of s contains one
 // of these representations and n is the length of that prefix.
 // The character case is ignored.
 func special(s string) (f float64, n int, ok bool) {
 	if len(s) == 0 {
 		return 0, 0, false
 	}
 	sign := 1
 	nsign := 0
 	switch s[0] {
 	case '+', '-':
 		if s[0] == '-' {
 			sign = -1
 		}
 		nsign = 1
 		s = s[1:]
 		fallthrough
 	case 'i', 'I':
 		n := commonPrefixLenIgnoreCase(s, "infinity")
 		// Anything longer than "inf" is ok, but if we
 		// don't have "infinity", only consume "inf".
 		if 3 < n && n < 8 {
 			n = 3
 		}
 		if n == 3 || n == 8 {
 			return math.Inf(sign), nsign + n, true
 		}
 	case 'n', 'N':
 		if commonPrefixLenIgnoreCase(s, "nan") == 3 {
 			return math.NaN(), 3, true
 		}
 	}
 	return 0, 0, false
 }

 func (b *decimal) set(s string) (ok bool) {
 	i := 0
 	b.neg = false
 	b.trunc = false

 	// optional sign
 	if i >= len(s) {
 		return
 	}
 	switch {
 	case s[i] == '+':
 		i++
 	case s[i] == '-':
 		b.neg = true
 		i++
 	}

 	// digits
 	sawdot := false
 	sawdigits := false
 	for ; i < len(s); i++ {
 		switch {
 		case s[i] == '_':
 			// readFloat already checked underscores
 			continue
 		case s[i] == '.':
 			if sawdot {
 				return
 			}
 			sawdot = true
 			b.dp = b.nd
 			continue

 		case '0' <= s[i] && s[i] <= '9':
 			sawdigits = true
 			if s[i] == '0' && b.nd == 0 { // ignore leading zeros
 				b.dp--
 				continue
 			}
 			if b.nd < len(b.d) {
 				b.d[b.nd] = s[i]
 				b.nd++
 			} else if s[i] != '0' {
 				b.trunc = true
 			}
 			continue
 		}
 		break
 	}
 	if !sawdigits {
 		return
 	}
 	if !sawdot {
 		b.dp = b.nd
 	}

 	// optional exponent moves decimal point.
 	// if we read a very large, very long number,
 	// just be sure to move the decimal point by
 	// a lot (say, 100000).  it doesn't matter if it's
 	// not the exact number.
 	if i < len(s) && lower(s[i]) == 'e' {
 		i++
 		if i >= len(s) {
 			return
 		}
 		esign := 1
 		if s[i] == '+' {
 			i++
 		} else if s[i] == '-' {
 			i++
 			esign = -1
 		}
 		if i >= len(s) || s[i] < '0' || s[i] > '9' {
 			return
 		}
 		e := 0
 		for ; i < len(s) && ('0' <= s[i] && s[i] <= '9' || s[i] == '_'); i++ {
 			if s[i] == '_' {
 				// readFloat already checked underscores
 				continue
 			}
 			if e < 10000 {
 				e = e*10 + int(s[i]) - '0'
 			}
 		}
 		b.dp += e * esign
 	}

 	if i != len(s) {
 		return
 	}

 	ok = true
 	return
 }

 // readFloat reads a decimal or hexadecimal mantissa and exponent from a float
 // string representation in s; the number may be followed by other characters.
 // readFloat reports the number of bytes consumed (i), and whether the number
 // is valid (ok).
 func readFloat(s string) (mantissa uint64, exp int, neg, trunc, hex bool, i int, ok bool) {
 	underscores := false

 	// optional sign
 	if i >= len(s) {
 		return
 	}
 	switch {
 	case s[i] == '+':
 		i++
 	case s[i] == '-':
 		neg = true
 		i++
 	}

 	// digits
 	base := uint64(10)
 	maxMantDigits := 19 // 10^19 fits in uint64
 	expChar := byte('e')
 	if i+2 < len(s) && s[i] == '0' && lower(s[i+1]) == 'x' {
 		base = 16
 		maxMantDigits = 16 // 16^16 fits in uint64
 		i += 2
 		expChar = 'p'
 		hex = true
 	}
 	sawdot := false
 	sawdigits := false
 	nd := 0
 	ndMant := 0
 	dp := 0
 loop:
 	for ; i < len(s); i++ {
 		switch c := s[i]; true {
 		case c == '_':
 			underscores = true
 			continue

 		case c == '.':
 			if sawdot {
 				break loop
 			}
 			sawdot = true
 			dp = nd
 			continue

 		case '0' <= c && c <= '9':
 			sawdigits = true
 			if c == '0' && nd == 0 { // ignore leading zeros
 				dp--
 				continue
 			}
 			nd++
 			if ndMant < maxMantDigits {
 				mantissa *= base
 				mantissa += uint64(c - '0')
 				ndMant++
 			} else if c != '0' {
 				trunc = true
 			}
 			continue

 		case base == 16 && 'a' <= lower(c) && lower(c) <= 'f':
 			sawdigits = true
 			nd++
 			if ndMant < maxMantDigits {
 				mantissa *= 16
 				mantissa += uint64(lower(c) - 'a' + 10)
 				ndMant++
 			} else {
 				trunc = true
 			}
 			continue
 		}
 		break
 	}
 	if !sawdigits {
 		return
 	}
 	if !sawdot {
 		dp = nd
 	}

 	if base == 16 {
 		dp *= 4
 		ndMant *= 4
 	}

 	// optional exponent moves decimal point.
 	// if we read a very large, very long number,
 	// just be sure to move the decimal point by
 	// a lot (say, 100000).  it doesn't matter if it's
 	// not the exact number.
 	if i < len(s) && lower(s[i]) == expChar {
 		i++
 		if i >= len(s) {
 			return
 		}
 		esign := 1
 		if s[i] == '+' {
 			i++
 		} else if s[i] == '-' {
 			i++
 			esign = -1
 		}
 		if i >= len(s) || s[i] < '0' || s[i] > '9' {
 			return
 		}
 		e := 0
 		for ; i < len(s) && ('0' <= s[i] && s[i] <= '9' || s[i] == '_'); i++ {
 			if s[i] == '_' {
 				underscores = true
 				continue
 			}
 			if e < 10000 {
 				e = e*10 + int(s[i]) - '0'
 			}
 		}
 		dp += e * esign
 	} else if base == 16 {
 		// Must have exponent.
 		return
 	}

 	if mantissa != 0 {
 		exp = dp - ndMant
 	}

 	if underscores && !underscoreOK(s[:i]) {
 		return
 	}

 	ok = true
 	return
 }

 // decimal power of ten to binary power of two.
 var powtab = []int{1, 3, 6, 9, 13, 16, 19, 23, 26}

 func (d *decimal) floatBits(flt *floatInfo) (b uint64, overflow bool) {
 	var exp int
 	var mant uint64

 	// Zero is always a special case.
 	if d.nd == 0 {
 		mant = 0
 		exp = flt.bias
 		goto out
 	}

 	// Obvious overflow/underflow.
 	// These bounds are for 64-bit floats.
 	// Will have to change if we want to support 80-bit floats in the future.
 	if d.dp > 310 {
 		goto overflow
 	}
 	if d.dp < -330 {
 		// zero
 		mant = 0
 		exp = flt.bias
 		goto out
 	}

 	// Scale by powers of two until in range [0.5, 1.0)
 	exp = 0
 	for d.dp > 0 {
 		var n int
 		if d.dp >= len(powtab) {
 			n = 27
 		} else {
 			n = powtab[d.dp]
 		}
 		d.Shift(-n)
 		exp += n
 	}
 	for d.dp < 0 || d.dp == 0 && d.d[0] < '5' {
 		var n int
 		if -d.dp >= len(powtab) {
 			n = 27
 		} else {
 			n = powtab[-d.dp]
 		}
 		d.Shift(n)
 		exp -= n
 	}

 	// Our range is [0.5,1) but floating point range is [1,2).
 	exp--

 	// Minimum representable exponent is flt.bias+1.
 	// If the exponent is smaller, move it up and
 	// adjust d accordingly.
 	if exp < flt.bias+1 {
 		n := flt.bias + 1 - exp
 		d.Shift(-n)
 		exp += n
 	}

 	if exp-flt.bias >= 1<<flt.expbits-1 {
 		goto overflow
 	}

 	// Extract 1+flt.mantbits bits.
 	d.Shift(int(1 + flt.mantbits))
 	mant = d.RoundedInteger()

 	// Rounding might have added a bit; shift down.
 	if mant == 2<<flt.mantbits {
 		mant >>= 1
 		exp++
 		if exp-flt.bias >= 1<<flt.expbits-1 {
 			goto overflow
 		}
 	}

 	// Denormalized?
 	if mant&(1<<flt.mantbits) == 0 {
 		exp = flt.bias
 	}
 	goto out

 overflow:
 	// ±Inf
 	mant = 0
 	exp = 1<<flt.expbits - 1 + flt.bias
 	overflow = true

 out:
 	// Assemble bits.
 	bits := mant & (uint64(1)<<flt.mantbits - 1)
 	bits |= uint64((exp-flt.bias)&(1<<flt.expbits-1)) << flt.mantbits
 	if d.neg {
 		bits |= 1 << flt.mantbits << flt.expbits
 	}
 	return bits, overflow
 }

 // Exact powers of 10.
 var float64pow10 = []float64{
 	1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
 	1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
 	1e20, 1e21, 1e22,
 }
 var float32pow10 = []float32{1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10}

 // If possible to convert decimal representation to 64-bit float f exactly,
 // entirely in floating-point math, do so, avoiding the expense of decimalToFloatBits.
 // Three common cases:
 //	value is exact integer
 //	value is exact integer * exact power of ten
 //	value is exact integer / exact power of ten
 // These all produce potentially inexact but correctly rounded answers.
 func atof64exact(mantissa uint64, exp int, neg bool) (f float64, ok bool) {
 	if mantissa>>float64info.mantbits != 0 {
 		return
 	}
 	// gccgo gets this wrong on 32-bit i386 when not using -msse.
 	// See TestRoundTrip in atof_test.go for a test case.
 	if runtime.GOARCH == "386" {
 		return
 	}
 	f = float64(mantissa)
 	if neg {
 		f = -f
 	}
 	switch {
 	case exp == 0:
 		// an integer.
 		return f, true
 	// Exact integers are <= 10^15.
 	// Exact powers of ten are <= 10^22.
 	case exp > 0 && exp <= 15+22: // int * 10^k
 		// If exponent is big but number of digits is not,
 		// can move a few zeros into the integer part.
 		if exp > 22 {
 			f *= float64pow10[exp-22]
 			exp = 22
 		}
 		if f > 1e15 || f < -1e15 {
 			// the exponent was really too large.
 			return
 		}
 		return f * float64pow10[exp], true
 	case exp < 0 && exp >= -22: // int / 10^k
 		return f / float64pow10[-exp], true
 	}
 	return
 }

 // 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 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 exp == 0:
 		return f, true
 	// 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 exp > 10 {
 			f *= float32pow10[exp-10]
 			exp = 10
 		}
 		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
 }

 // atofHex converts the hex floating-point string s
 // to a rounded float32 or float64 value (depending on flt==&float32info or flt==&float64info)
 // and returns it as a float64.
 // The string s has already been parsed into a mantissa, exponent, and sign (neg==true for negative).
 // If trunc is true, trailing non-zero bits have been omitted from the mantissa.
 func atofHex(s string, flt *floatInfo, mantissa uint64, exp int, neg, trunc bool) (float64, error) {
 	maxExp := 1<<flt.expbits + flt.bias - 2
 	minExp := flt.bias + 1
 	exp += int(flt.mantbits) // mantissa now implicitly divided by 2^mantbits.

 	// Shift mantissa and exponent to bring representation into float range.
 	// Eventually we want a mantissa with a leading 1-bit followed by mantbits other bits.
 	// For rounding, we need two more, where the bottom bit represents
 	// whether that bit or any later bit was non-zero.
 	// (If the mantissa has already lost non-zero bits, trunc is true,
 	// and we OR in a 1 below after shifting left appropriately.)
 	for mantissa != 0 && mantissa>>(flt.mantbits+2) == 0 {
 		mantissa <<= 1
 		exp--
 	}
 	if trunc {
 		mantissa |= 1
 	}
 	for mantissa>>(1+flt.mantbits+2) != 0 {
 		mantissa = mantissa>>1 | mantissa&1
 		exp++
 	}

 	// If exponent is too negative,
 	// denormalize in hopes of making it representable.
 	// (The -2 is for the rounding bits.)
 	for mantissa > 1 && exp < minExp-2 {
 		mantissa = mantissa>>1 | mantissa&1
 		exp++
 	}

 	// Round using two bottom bits.
 	round := mantissa & 3
 	mantissa >>= 2
 	round |= mantissa & 1 // round to even (round up if mantissa is odd)
 	exp += 2
 	if round == 3 {
 		mantissa++
 		if mantissa == 1<<(1+flt.mantbits) {
 			mantissa >>= 1
 			exp++
 		}
 	}

 	if mantissa>>flt.mantbits == 0 { // Denormal or zero.
 		exp = flt.bias
 	}
 	var err error
 	if exp > maxExp { // infinity and range error
 		mantissa = 1 << flt.mantbits
 		exp = maxExp + 1
 		err = rangeError(fnParseFloat, s)
 	}

 	bits := mantissa & (1<<flt.mantbits - 1)
 	bits |= uint64((exp-flt.bias)&(1<<flt.expbits-1)) << flt.mantbits
 	if neg {
 		bits |= 1 << flt.mantbits << flt.expbits
 	}
 	if flt == &float32info {
 		return float64(math.Float32frombits(uint32(bits))), err
 	}
 	return math.Float64frombits(bits), err
 }

 const fnParseFloat = "ParseFloat"

 func atof32(s string) (f float32, n int, err error) {
 	if val, n, ok := special(s); ok {
 		return float32(val), n, nil
 	}

 	mantissa, exp, neg, trunc, hex, n, ok := readFloat(s)
 	if !ok {
 		return 0, n, syntaxError(fnParseFloat, s)
 	}

 	if hex {
 		f, err := atofHex(s[:n], &float32info, mantissa, exp, neg, trunc)
 		return float32(f), n, err
 	}

 	if optimize {
 		// Try pure floating-point arithmetic conversion, and if that fails,
 		// the Eisel-Lemire algorithm.
 		if !trunc {
 			if f, ok := atof32exact(mantissa, exp, neg); ok {
 				return f, n, nil
 			}
 		}
 		f, ok := eiselLemire32(mantissa, exp, neg)
 		if ok {
 			if !trunc {
 				return f, n, nil
 			}
 			// Even if the mantissa was truncated, we may
 			// have found the correct result. Confirm by
 			// converting the upper mantissa bound.
 			fUp, ok := eiselLemire32(mantissa+1, exp, neg)
 			if ok && f == fUp {
 				return f, n, nil
 			}
 		}
 	}

 	// Slow fallback.
 	var d decimal
 	if !d.set(s[:n]) {
 		return 0, n, syntaxError(fnParseFloat, s)
 	}
 	b, ovf := d.floatBits(&float32info)
 	f = math.Float32frombits(uint32(b))
 	if ovf {
 		err = rangeError(fnParseFloat, s)
 	}
 	return f, n, err
 }

 func atof64(s string) (f float64, n int, err error) {
 	if val, n, ok := special(s); ok {
 		return val, n, nil
 	}

 	mantissa, exp, neg, trunc, hex, n, ok := readFloat(s)
 	if !ok {
 		return 0, n, syntaxError(fnParseFloat, s)
 	}

 	if hex {
 		f, err := atofHex(s[:n], &float64info, mantissa, exp, neg, trunc)
 		return f, n, err
 	}

 	if optimize {
 		// Try pure floating-point arithmetic conversion, and if that fails,
 		// the Eisel-Lemire algorithm.
 		if !trunc {
 			if f, ok := atof64exact(mantissa, exp, neg); ok {
 				return f, n, nil
 			}
 		}
 		f, ok := eiselLemire64(mantissa, exp, neg)
 		if ok {
 			if !trunc {
 				return f, n, nil
 			}
 			// Even if the mantissa was truncated, we may
 			// have found the correct result. Confirm by
 			// converting the upper mantissa bound.
 			fUp, ok := eiselLemire64(mantissa+1, exp, neg)
 			if ok && f == fUp {
 				return f, n, nil
 			}
 		}
 	}

 	// Slow fallback.
 	var d decimal
 	if !d.set(s[:n]) {
 		return 0, n, syntaxError(fnParseFloat, s)
 	}
 	b, ovf := d.floatBits(&float64info)
 	f = math.Float64frombits(b)
 	if ovf {
 		err = rangeError(fnParseFloat, s)
 	}
 	return f, n, err
 }

 // ParseFloat converts the string s to a floating-point number
 // with the precision specified by bitSize: 32 for float32, or 64 for float64.
 // When bitSize=32, the result still has type float64, but it will be
 // convertible to float32 without changing its value.
 //
 // ParseFloat accepts decimal and hexadecimal floating-point number syntax.
 // If s is well-formed and near a valid floating-point number,
 // ParseFloat returns the nearest floating-point number rounded
 // using IEEE754 unbiased rounding.
 // (Parsing a hexadecimal floating-point value only rounds when
 // there are more bits in the hexadecimal representation than
 // will fit in the mantissa.)
 //
 // The errors that ParseFloat returns have concrete type *NumError
 // and include err.Num = s.
 //
 // If s is not syntactically well-formed, ParseFloat returns err.Err = ErrSyntax.
 //
 // If s is syntactically well-formed but is more than 1/2 ULP
 // away from the largest floating point number of the given size,
 // ParseFloat returns f = ±Inf, err.Err = ErrRange.
 //
 // ParseFloat recognizes the strings "NaN", and the (possibly signed) strings "Inf" and "Infinity"
 // as their respective special floating point values. It ignores case when matching.
 func ParseFloat(s string, bitSize int) (float64, error) {
 	f, n, err := parseFloatPrefix(s, bitSize)
 	if err == nil && n != len(s) {
 		return 0, syntaxError(fnParseFloat, s)
 	}
 	return f, err
 }

 func parseFloatPrefix(s string, bitSize int) (float64, int, error) {
 	if bitSize == 32 {
 		f, n, err := atof32(s)
 		return float64(f), n, err
 	}
 	return atof64(s)
 }
	// 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

	// decimal to binary floating point conversion.
	// Algorithm:
	// 1) Store input in multiprecision decimal.
	// 2) Multiply/divide decimal by powers of two until in range [0.5, 1)
	// 3) Multiply by 2^precision and round to get mantissa.

	import "math"
	import "runtime"

	var optimize = true // set to false to force slow-path conversions for testing

	// commonPrefixLenIgnoreCase returns the length of the common
	// prefix of s and prefix, with the character case of s ignored.
	// The prefix argument must be all lower-case.
	func commonPrefixLenIgnoreCase(s, prefix string) int {
	n := len(prefix)
	if n > len(s) {
	n = len(s)
	}
	for i := 0; i < n; i++ {
	c := s[i]
	if 'A' <= c && c <= 'Z' {
	c += 'a' - 'A'
	}
	if c != prefix[i] {
	return i
	}
	}
	return n
	}

	// special returns the floating-point value for the special,
	// possibly signed floating-point representations inf, infinity,
	// and NaN. The result is ok if a prefix of s contains one
	// of these representations and n is the length of that prefix.
	// The character case is ignored.
	func special(s string) (f float64, n int, ok bool) {
	if len(s) == 0 {
	return 0, 0, false
	}
	sign := 1
	nsign := 0
	switch s[0] {
	case '+', '-':
	if s[0] == '-' {
	sign = -1
	}
	nsign = 1
	s = s[1:]
	fallthrough
	case 'i', 'I':
	n := commonPrefixLenIgnoreCase(s, "infinity")
	// Anything longer than "inf" is ok, but if we
	// don't have "infinity", only consume "inf".
	if 3 < n && n < 8 {
	n = 3
	}
	if n == 3 \|\| n == 8 {
	return math.Inf(sign), nsign + n, true
	}
	case 'n', 'N':
	if commonPrefixLenIgnoreCase(s, "nan") == 3 {
	return math.NaN(), 3, true
	}
	}
	return 0, 0, false
	}

	func (b *decimal) set(s string) (ok bool) {
	i := 0
	b.neg = false
	b.trunc = false

	// optional sign
	if i >= len(s) {
	return
	}
	switch {
	case s[i] == '+':
	i++
	case s[i] == '-':
	b.neg = true
	i++
	}

	// digits
	sawdot := false
	sawdigits := false
	for ; i < len(s); i++ {
	switch {
	case s[i] == '_':
	// readFloat already checked underscores
	continue
	case s[i] == '.':
	if sawdot {
	return
	}
	sawdot = true
	b.dp = b.nd
	continue

	case '0' <= s[i] && s[i] <= '9':
	sawdigits = true
	if s[i] == '0' && b.nd == 0 { // ignore leading zeros
	b.dp--
	continue
	}
	if b.nd < len(b.d) {
	b.d[b.nd] = s[i]
	b.nd++
	} else if s[i] != '0' {
	b.trunc = true
	}
	continue
	}
	break
	}
	if !sawdigits {
	return
	}
	if !sawdot {
	b.dp = b.nd
	}

	// optional exponent moves decimal point.
	// if we read a very large, very long number,
	// just be sure to move the decimal point by
	// a lot (say, 100000). it doesn't matter if it's
	// not the exact number.
	if i < len(s) && lower(s[i]) == 'e' {
	i++
	if i >= len(s) {
	return
	}
	esign := 1
	if s[i] == '+' {
	i++
	} else if s[i] == '-' {
	i++
	esign = -1
	}
	if i >= len(s) \|\| s[i] < '0' \|\| s[i] > '9' {
	return
	}
	e := 0
	for ; i < len(s) && ('0' <= s[i] && s[i] <= '9' \|\| s[i] == '_'); i++ {
	if s[i] == '_' {
	// readFloat already checked underscores
	continue
	}
	if e < 10000 {
	e = e*10 + int(s[i]) - '0'
	}
	}
	b.dp += e * esign
	}

	if i != len(s) {
	return
	}

	ok = true
	return
	}

	// readFloat reads a decimal or hexadecimal mantissa and exponent from a float
	// string representation in s; the number may be followed by other characters.
	// readFloat reports the number of bytes consumed (i), and whether the number
	// is valid (ok).
	func readFloat(s string) (mantissa uint64, exp int, neg, trunc, hex bool, i int, ok bool) {
	underscores := false

	// optional sign
	if i >= len(s) {
	return
	}
	switch {
	case s[i] == '+':
	i++
	case s[i] == '-':
	neg = true
	i++
	}

	// digits
	base := uint64(10)
	maxMantDigits := 19 // 10^19 fits in uint64
	expChar := byte('e')
	if i+2 < len(s) && s[i] == '0' && lower(s[i+1]) == 'x' {
	base = 16
	maxMantDigits = 16 // 16^16 fits in uint64
	i += 2
	expChar = 'p'
	hex = true
	}
	sawdot := false
	sawdigits := false
	nd := 0
	ndMant := 0
	dp := 0
	loop:
	for ; i < len(s); i++ {
	switch c := s[i]; true {
	case c == '_':
	underscores = true
	continue

	case c == '.':
	if sawdot {
	break loop
	}
	sawdot = true
	dp = nd
	continue

	case '0' <= c && c <= '9':
	sawdigits = true
	if c == '0' && nd == 0 { // ignore leading zeros
	dp--
	continue
	}
	nd++
	if ndMant < maxMantDigits {
	mantissa *= base
	mantissa += uint64(c - '0')
	ndMant++
	} else if c != '0' {
	trunc = true
	}
	continue

	case base == 16 && 'a' <= lower(c) && lower(c) <= 'f':
	sawdigits = true
	nd++
	if ndMant < maxMantDigits {
	mantissa *= 16
	mantissa += uint64(lower(c) - 'a' + 10)
	ndMant++
	} else {
	trunc = true
	}
	continue
	}
	break
	}
	if !sawdigits {
	return
	}
	if !sawdot {
	dp = nd
	}

	if base == 16 {
	dp *= 4
	ndMant *= 4
	}

	// optional exponent moves decimal point.
	// if we read a very large, very long number,
	// just be sure to move the decimal point by
	// a lot (say, 100000). it doesn't matter if it's
	// not the exact number.
	if i < len(s) && lower(s[i]) == expChar {
	i++
	if i >= len(s) {
	return
	}
	esign := 1
	if s[i] == '+' {
	i++
	} else if s[i] == '-' {
	i++
	esign = -1
	}
	if i >= len(s) \|\| s[i] < '0' \|\| s[i] > '9' {
	return
	}
	e := 0
	for ; i < len(s) && ('0' <= s[i] && s[i] <= '9' \|\| s[i] == '_'); i++ {
	if s[i] == '_' {
	underscores = true
	continue
	}
	if e < 10000 {
	e = e*10 + int(s[i]) - '0'
	}
	}
	dp += e * esign
	} else if base == 16 {
	// Must have exponent.
	return
	}

	if mantissa != 0 {
	exp = dp - ndMant
	}

	if underscores && !underscoreOK(s[:i]) {
	return
	}

	ok = true
	return
	}

	// decimal power of ten to binary power of two.
	var powtab = []int{1, 3, 6, 9, 13, 16, 19, 23, 26}

	func (d decimal) floatBits(flt floatInfo) (b uint64, overflow bool) {
	var exp int
	var mant uint64

	// Zero is always a special case.
	if d.nd == 0 {
	mant = 0
	exp = flt.bias
	goto out
	}

	// Obvious overflow/underflow.
	// These bounds are for 64-bit floats.
	// Will have to change if we want to support 80-bit floats in the future.
	if d.dp > 310 {
	goto overflow
	}
	if d.dp < -330 {
	// zero
	mant = 0
	exp = flt.bias
	goto out
	}

	// Scale by powers of two until in range [0.5, 1.0)
	exp = 0
	for d.dp > 0 {
	var n int
	if d.dp >= len(powtab) {
	n = 27
	} else {
	n = powtab[d.dp]
	}
	d.Shift(-n)
	exp += n
	}
	for d.dp < 0 \|\| d.dp == 0 && d.d[0] < '5' {
	var n int
	if -d.dp >= len(powtab) {
	n = 27
	} else {
	n = powtab[-d.dp]
	}
	d.Shift(n)
	exp -= n
	}

	// Our range is [0.5,1) but floating point range is [1,2).
	exp--

	// Minimum representable exponent is flt.bias+1.
	// If the exponent is smaller, move it up and
	// adjust d accordingly.
	if exp < flt.bias+1 {
	n := flt.bias + 1 - exp
	d.Shift(-n)
	exp += n
	}

	if exp-flt.bias >= 1<<flt.expbits-1 {
	goto overflow
	}

	// Extract 1+flt.mantbits bits.
	d.Shift(int(1 + flt.mantbits))
	mant = d.RoundedInteger()

	// Rounding might have added a bit; shift down.
	if mant == 2<<flt.mantbits {
	mant >>= 1
	exp++
	if exp-flt.bias >= 1<<flt.expbits-1 {
	goto overflow
	}
	}

	// Denormalized?
	if mant&(1<<flt.mantbits) == 0 {
	exp = flt.bias
	}
	goto out

	overflow:
	// ±Inf
	mant = 0
	exp = 1<<flt.expbits - 1 + flt.bias
	overflow = true

	out:
	// Assemble bits.
	bits := mant & (uint64(1)<<flt.mantbits - 1)
	bits \|= uint64((exp-flt.bias)&(1<<flt.expbits-1)) << flt.mantbits
	if d.neg {
	bits \|= 1 << flt.mantbits << flt.expbits
	}
	return bits, overflow
	}

	// Exact powers of 10.
	var float64pow10 = []float64{
	1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
	1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
	1e20, 1e21, 1e22,
	}
	var float32pow10 = []float32{1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10}

	// If possible to convert decimal representation to 64-bit float f exactly,
	// entirely in floating-point math, do so, avoiding the expense of decimalToFloatBits.
	// Three common cases:
	// value is exact integer
	// value is exact integer * exact power of ten
	// value is exact integer / exact power of ten
	// These all produce potentially inexact but correctly rounded answers.
	func atof64exact(mantissa uint64, exp int, neg bool) (f float64, ok bool) {
	if mantissa>>float64info.mantbits != 0 {
	return
	}
	// gccgo gets this wrong on 32-bit i386 when not using -msse.
	// See TestRoundTrip in atof_test.go for a test case.
	if runtime.GOARCH == "386" {
	return
	}
	f = float64(mantissa)
	if neg {
	f = -f
	}
	switch {
	case exp == 0:
	// an integer.
	return f, true
	// Exact integers are <= 10^15.
	// Exact powers of ten are <= 10^22.
	case exp > 0 && exp <= 15+22: // int * 10^k
	// If exponent is big but number of digits is not,
	// can move a few zeros into the integer part.
	if exp > 22 {
	f *= float64pow10[exp-22]
	exp = 22
	}
	if f > 1e15 \|\| f < -1e15 {
	// the exponent was really too large.
	return
	}
	return f * float64pow10[exp], true
	case exp < 0 && exp >= -22: // int / 10^k
	return f / float64pow10[-exp], true
	}
	return
	}

	// 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 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 exp == 0:
	return f, true
	// 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 exp > 10 {
	f *= float32pow10[exp-10]
	exp = 10
	}
	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
	}

	// atofHex converts the hex floating-point string s
	// to a rounded float32 or float64 value (depending on flt==&float32info or flt==&float64info)
	// and returns it as a float64.
	// The string s has already been parsed into a mantissa, exponent, and sign (neg==true for negative).
	// If trunc is true, trailing non-zero bits have been omitted from the mantissa.
	func atofHex(s string, flt *floatInfo, mantissa uint64, exp int, neg, trunc bool) (float64, error) {
	maxExp := 1<<flt.expbits + flt.bias - 2
	minExp := flt.bias + 1
	exp += int(flt.mantbits) // mantissa now implicitly divided by 2^mantbits.

	// Shift mantissa and exponent to bring representation into float range.
	// Eventually we want a mantissa with a leading 1-bit followed by mantbits other bits.
	// For rounding, we need two more, where the bottom bit represents
	// whether that bit or any later bit was non-zero.
	// (If the mantissa has already lost non-zero bits, trunc is true,
	// and we OR in a 1 below after shifting left appropriately.)
	for mantissa != 0 && mantissa>>(flt.mantbits+2) == 0 {
	mantissa <<= 1
	exp--
	}
	if trunc {
	mantissa \|= 1
	}
	for mantissa>>(1+flt.mantbits+2) != 0 {
	mantissa = mantissa>>1 \| mantissa&1
	exp++
	}

	// If exponent is too negative,
	// denormalize in hopes of making it representable.
	// (The -2 is for the rounding bits.)
	for mantissa > 1 && exp < minExp-2 {
	mantissa = mantissa>>1 \| mantissa&1
	exp++
	}

	// Round using two bottom bits.
	round := mantissa & 3
	mantissa >>= 2
	round \|= mantissa & 1 // round to even (round up if mantissa is odd)
	exp += 2
	if round == 3 {
	mantissa++
	if mantissa == 1<<(1+flt.mantbits) {
	mantissa >>= 1
	exp++
	}
	}

	if mantissa>>flt.mantbits == 0 { // Denormal or zero.
	exp = flt.bias
	}
	var err error
	if exp > maxExp { // infinity and range error
	mantissa = 1 << flt.mantbits
	exp = maxExp + 1
	err = rangeError(fnParseFloat, s)
	}

	bits := mantissa & (1<<flt.mantbits - 1)
	bits \|= uint64((exp-flt.bias)&(1<<flt.expbits-1)) << flt.mantbits
	if neg {
	bits \|= 1 << flt.mantbits << flt.expbits
	}
	if flt == &float32info {
	return float64(math.Float32frombits(uint32(bits))), err
	}
	return math.Float64frombits(bits), err
	}

	const fnParseFloat = "ParseFloat"

	func atof32(s string) (f float32, n int, err error) {
	if val, n, ok := special(s); ok {
	return float32(val), n, nil
	}

	mantissa, exp, neg, trunc, hex, n, ok := readFloat(s)
	if !ok {
	return 0, n, syntaxError(fnParseFloat, s)
	}

	if hex {
	f, err := atofHex(s[:n], &float32info, mantissa, exp, neg, trunc)
	return float32(f), n, err
	}

	if optimize {
	// Try pure floating-point arithmetic conversion, and if that fails,
	// the Eisel-Lemire algorithm.
	if !trunc {
	if f, ok := atof32exact(mantissa, exp, neg); ok {
	return f, n, nil
	}
	}
	f, ok := eiselLemire32(mantissa, exp, neg)
	if ok {
	if !trunc {
	return f, n, nil
	}
	// Even if the mantissa was truncated, we may
	// have found the correct result. Confirm by
	// converting the upper mantissa bound.
	fUp, ok := eiselLemire32(mantissa+1, exp, neg)
	if ok && f == fUp {
	return f, n, nil
	}
	}
	}

	// Slow fallback.
	var d decimal
	if !d.set(s[:n]) {
	return 0, n, syntaxError(fnParseFloat, s)
	}
	b, ovf := d.floatBits(&float32info)
	f = math.Float32frombits(uint32(b))
	if ovf {
	err = rangeError(fnParseFloat, s)
	}
	return f, n, err
	}

	func atof64(s string) (f float64, n int, err error) {
	if val, n, ok := special(s); ok {
	return val, n, nil
	}

	mantissa, exp, neg, trunc, hex, n, ok := readFloat(s)
	if !ok {
	return 0, n, syntaxError(fnParseFloat, s)
	}

	if hex {
	f, err := atofHex(s[:n], &float64info, mantissa, exp, neg, trunc)
	return f, n, err
	}

	if optimize {
	// Try pure floating-point arithmetic conversion, and if that fails,
	// the Eisel-Lemire algorithm.
	if !trunc {
	if f, ok := atof64exact(mantissa, exp, neg); ok {
	return f, n, nil
	}
	}
	f, ok := eiselLemire64(mantissa, exp, neg)
	if ok {
	if !trunc {
	return f, n, nil
	}
	// Even if the mantissa was truncated, we may
	// have found the correct result. Confirm by
	// converting the upper mantissa bound.
	fUp, ok := eiselLemire64(mantissa+1, exp, neg)
	if ok && f == fUp {
	return f, n, nil
	}
	}
	}

	// Slow fallback.
	var d decimal
	if !d.set(s[:n]) {
	return 0, n, syntaxError(fnParseFloat, s)
	}
	b, ovf := d.floatBits(&float64info)
	f = math.Float64frombits(b)
	if ovf {
	err = rangeError(fnParseFloat, s)
	}
	return f, n, err
	}

	// ParseFloat converts the string s to a floating-point number
	// with the precision specified by bitSize: 32 for float32, or 64 for float64.
	// When bitSize=32, the result still has type float64, but it will be
	// convertible to float32 without changing its value.
	//
	// ParseFloat accepts decimal and hexadecimal floating-point number syntax.
	// If s is well-formed and near a valid floating-point number,
	// ParseFloat returns the nearest floating-point number rounded
	// using IEEE754 unbiased rounding.
	// (Parsing a hexadecimal floating-point value only rounds when
	// there are more bits in the hexadecimal representation than
	// will fit in the mantissa.)
	//
	// The errors that ParseFloat returns have concrete type *NumError
	// and include err.Num = s.
	//
	// If s is not syntactically well-formed, ParseFloat returns err.Err = ErrSyntax.
	//
	// If s is syntactically well-formed but is more than 1/2 ULP
	// away from the largest floating point number of the given size,
	// ParseFloat returns f = ±Inf, err.Err = ErrRange.
	//
	// ParseFloat recognizes the strings "NaN", and the (possibly signed) strings "Inf" and "Infinity"
	// as their respective special floating point values. It ignores case when matching.
	func ParseFloat(s string, bitSize int) (float64, error) {
	f, n, err := parseFloatPrefix(s, bitSize)
	if err == nil && n != len(s) {
	return 0, syntaxError(fnParseFloat, s)
	}
	return f, err
	}

	func parseFloatPrefix(s string, bitSize int) (float64, int, error) {
	if bitSize == 32 {
	f, n, err := atof32(s)
	return float64(f), n, err
	}
	return atof64(s)
	}