// 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
func equalIgnoreCase(s1, s2 string) bool {
if len(s1) != len(s2) {
return false
}
for i := 0; i < len(s1); i++ {
c1 := s1[i]
if 'A' <= c1 && c1 <= 'Z' {
c1 += 'a' - 'A'
}
c2 := s2[i]
if 'A' <= c2 && c2 <= 'Z' {
c2 += 'a' - 'A'
}
if c1 != c2 {
return false
}
}
return true
}
func special(s string) (f float64, ok bool) {
if len(s) == 0 {
return
}
switch s[0] {
default:
return
case '+':
if equalIgnoreCase(s, "+inf") || equalIgnoreCase(s, "+infinity") {
return math.Inf(1), true
}
case '-':
if equalIgnoreCase(s, "-inf") || equalIgnoreCase(s, "-infinity") {
return math.Inf(-1), true
}
case 'n', 'N':
if equalIgnoreCase(s, "nan") {
return math.NaN(), true
}
case 'i', 'I':
if equalIgnoreCase(s, "inf") || equalIgnoreCase(s, "infinity") {
return math.Inf(1), true
}
}
return
}
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] == '_':
// underscoreOK already called
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] == '_' {
// underscoreOK already called
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 mantissa and exponent from a float
// string representation. It returns ok==false if the number could
// not fit return types or is invalid.
func readFloat(s string) (mantissa uint64, exp int, neg, trunc, hex, ok bool) {
i := 0
// 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
for ; i < len(s); i++ {
switch c := s[i]; true {
case c == '_':
// underscoreOK already called
continue
case c == '.':
if sawdot {
return
}
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] == '_' {
// underscoreOK already called
continue
}
if e < 10000 {
e = e*10 + int(s[i]) - '0'
}
}
dp += e * esign
} else if base == 16 {
// Must have exponent.
return
}
if i != len(s) {
return
}
if mantissa != 0 {
exp = dp - ndMant
}
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
}
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, err error) {
if val, ok := special(s); ok {
return float32(val), nil
}
mantissa, exp, neg, trunc, hex, ok := readFloat(s)
if hex && ok {
f, err := atofHex(s, &float32info, mantissa, exp, neg, trunc)
return float32(f), err
}
if optimize && 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
}
}
// Slow fallback.
var d decimal
if !d.set(s) {
return 0, syntaxError(fnParseFloat, s)
}
b, ovf := d.floatBits(&float32info)
f = math.Float32frombits(uint32(b))
if ovf {
err = rangeError(fnParseFloat, s)
}
return f, err
}
func atof64(s string) (f float64, err error) {
if val, ok := special(s); ok {
return val, nil
}
mantissa, exp, neg, trunc, hex, ok := readFloat(s)
if hex && ok {
return atofHex(s, &float64info, mantissa, exp, neg, trunc)
}
if optimize && ok {
// Try pure floating-point arithmetic conversion.
if !trunc {
if f, ok := atof64exact(mantissa, exp, neg); ok {
return f, nil
}
}
// Try another fast path.
ext := new(extFloat)
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)
}
return f, err
}
}
// Slow fallback.
var d decimal
if !d.set(s) {
return 0, syntaxError(fnParseFloat, s)
}
b, ovf := d.floatBits(&float64info)
f = math.Float64frombits(b)
if ovf {
err = rangeError(fnParseFloat, s)
}
return f, 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", "+Inf", and "-Inf" as their
// respective special floating point values. It ignores case when matching.
func ParseFloat(s string, bitSize int) (float64, error) {
if !underscoreOK(s) {
return 0, syntaxError(fnParseFloat, s)
}
if bitSize == 32 {
f, err := atof32(s)
return float64(f), err
}
return atof64(s)
}
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