Source: atof.go in package strconv


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[0] {
	case '+', '-':
		if s[0] == '-' {
			sign = -1
		}
		nsign = 1
		s = s[1:]
		fallthrough
	case 'i', 'I':

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 {

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++ {

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

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
	}

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

±Inf

	mant = 0
	exp = 1<<flt.expbits - 1 + flt.bias
	overflow = true

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 {

an integer.

Exact integers are <= 10^15. Exact powers of ten are <= 10^22.

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
		}

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:

Exact integers are <= 10^7. Exact powers of ten are <= 10^10.

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
		}

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
	}

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
	}

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)