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- // 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 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)
- }
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