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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" 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<>= 1 exp++ if exp-flt.bias >= 1<>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.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<