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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 implements conversions to and from string representations // of basic data types. 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 // can change 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] == '.': 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) && (s[i] == 'e' || 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'; i++ { 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 sets ok to false if the number could // not fit return types or is invalid. func readFloat(s string) (mantissa uint64, exp int, neg, trunc, ok bool) { const uint64digits = 19 i := 0 // optional sign if i >= len(s) { return } switch { case s[i] == '+': i++ case s[i] == '-': neg = true i++ } // digits sawdot := false sawdigits := false nd := 0 ndMant := 0 dp := 0 for ; i < len(s); i++ { switch c := s[i]; true { 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 < uint64digits { mantissa *= 10 mantissa += uint64(c - '0') ndMant++ } else if s[i] != '0' { trunc = true } continue } break } if !sawdigits { return } if !sawdot { dp = 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) && (s[i] == 'e' || 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'; i++ { if e < 10000 { e = e*10 + int(s[i]) - '0' } } dp += e * esign } if i != len(s) { return } 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<>= 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 } const fnParseFloat = "ParseFloat" func atof32(s string) (f float32, err error) { if val, ok := special(s); ok { return float32(val), nil } if optimize { // Parse mantissa and exponent. mantissa, exp, neg, trunc, ok := readFloat(s) if 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 } } } 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 } if optimize { // Parse mantissa and exponent. mantissa, exp, neg, trunc, ok := readFloat(s) if 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 } } } 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. // // If s is well-formed and near a valid floating point number, // ParseFloat returns the nearest floating point number rounded // using IEEE754 unbiased rounding. // // 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. func ParseFloat(s string, bitSize int) (f float64, err error) { if bitSize == 32 { f1, err1 := atof32(s) return float64(f1), err1 } f1, err1 := atof64(s) return f1, err1 }