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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" "os" ) 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) { switch { case equalIgnoreCase(s, "nan"): return math.NaN(), true case equalIgnoreCase(s, "-inf"), equalIgnoreCase(s, "-infinity"): return math.Inf(-1), true case equalIgnoreCase(s, "+inf"), equalIgnoreCase(s, "+infinity"), equalIgnoreCase(s, "inf"), equalIgnoreCase(s, "infinity"): return math.Inf(1), true } return } // TODO(rsc): Better truncation handling. func stringToDecimal(s string) (neg bool, d *decimal, trunc bool, ok bool) { i := 0 // optional sign if i >= len(s) { return } switch { case s[i] == '+': i++ case s[i] == '-': neg = true i++ } // digits b := new(decimal) 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 } b.d[b.nd] = s[i] b.nd++ 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 } d = b 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 decimalToFloatBits(neg bool, d *decimal, trunc bool, 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< 15 { return } switch { case d.dp == d.nd: // int f := decimalAtof64Int(neg, d) return f, true case d.dp > d.nd && d.dp <= 15+22: // int * 10^k f := decimalAtof64Int(neg, d) k := d.dp - d.nd // If exponent is big but number of digits is not, // can move a few zeros into the integer part. if k > 22 { f *= float64pow10[k-22] k = 22 } return f * float64pow10[k], true case d.dp < d.nd && d.nd-d.dp <= 22: // int / 10^k f := decimalAtof64Int(neg, d) return f / float64pow10[d.nd-d.dp], true } return } // If possible to convert decimal d to 32-bit float f exactly, // entirely in floating-point math, do so, avoiding the machinery above. func decimalAtof32(neg bool, d *decimal, trunc bool) (f float32, ok bool) { // Exact integers are <= 10^7. // Exact powers of ten are <= 10^10. if d.nd > 7 { return } switch { case d.dp == d.nd: // int f := decimalAtof32Int(neg, d) return f, true case d.dp > d.nd && d.dp <= 7+10: // int * 10^k f := decimalAtof32Int(neg, d) k := d.dp - d.nd // If exponent is big but number of digits is not, // can move a few zeros into the integer part. if k > 10 { f *= float32pow10[k-10] k = 10 } return f * float32pow10[k], true case d.dp < d.nd && d.nd-d.dp <= 10: // int / 10^k f := decimalAtof32Int(neg, d) return f / float32pow10[d.nd-d.dp], true } return } // Atof32 converts the string s to a 32-bit floating-point number. // // If s is well-formed and near a valid floating point number, // Atof32 returns the nearest floating point number rounded // using IEEE754 unbiased rounding. // // The errors that Atof32 returns have concrete type *NumError // and include err.Num = s. // // If s is not syntactically well-formed, Atof32 returns err.Error = os.EINVAL. // // If s is syntactically well-formed but is more than 1/2 ULP // away from the largest floating point number of the given size, // Atof32 returns f = ±Inf, err.Error = os.ERANGE. func Atof32(s string) (f float32, err os.Error) { if val, ok := special(s); ok { return float32(val), nil } neg, d, trunc, ok := stringToDecimal(s) if !ok { return 0, &NumError{s, os.EINVAL} } if optimize { if f, ok := decimalAtof32(neg, d, trunc); ok { return f, nil } } b, ovf := decimalToFloatBits(neg, d, trunc, &float32info) f = math.Float32frombits(uint32(b)) if ovf { err = &NumError{s, os.ERANGE} } return f, err } // Atof64 converts the string s to a 64-bit floating-point number. // Except for the type of its result, its definition is the same as that // of Atof32. func Atof64(s string) (f float64, err os.Error) { if val, ok := special(s); ok { return val, nil } neg, d, trunc, ok := stringToDecimal(s) if !ok { return 0, &NumError{s, os.EINVAL} } if optimize { if f, ok := decimalAtof64(neg, d, trunc); ok { return f, nil } } b, ovf := decimalToFloatBits(neg, d, trunc, &float64info) f = math.Float64frombits(b) if ovf { err = &NumError{s, os.ERANGE} } return f, err } // AtofN converts the string s to a 64-bit floating-point number, // but it rounds the result assuming that it will be stored in a value // of n bits (32 or 64). func AtofN(s string, n int) (f float64, err os.Error) { if n == 32 { f1, err1 := Atof32(s) return float64(f1), err1 } f1, err1 := Atof64(s) return f1, err1 }