````// 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"`

`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 {`
`	case '+', '-':`
`		if s == '-' {`
`			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 < '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`
`	}`
`	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 numbers`
`// as defined by the Go syntax for [floating-point literals].`
`// 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 string "NaN", and the (possibly signed) strings "Inf" and "Infinity"`
`// as their respective special floating point values. It ignores case when matching.`
`//`
`// [floating-point literals]: https://go.dev/ref/spec#Floating-point_literals`
`func ParseFloat(s string, bitSize int) (float64, error) {`
`	f, n, err := parseFloatPrefix(s, bitSize)`
`	if n != len(s) && (err == nil || err.(*NumError).Err != ErrSyntax) {`
`		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)`
`}`
```