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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. // 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. // The strconv package implements conversions to and from // string representations of basic data types. package strconv import ( "math"; "os"; ) var optimize = true // can change for testing // 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' { 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) { 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) { 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 } // Atof is like Atof32 or Atof64, depending on the size of float. func Atof(s string) (f float, err os.Error) { if FloatSize == 32 { f1, err1 := Atof32(s); return float(f1), err1; } f1, err1 := Atof64(s); return float(f1), err1; }