| // 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<<flt.expbits-1 { |
| goto overflow |
| } |
| |
| // Extract 1+flt.mantbits bits. |
| mant = d.Shift(int(1 + flt.mantbits)).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 neg { |
| bits |= 1 << flt.mantbits << flt.expbits |
| } |
| return bits, overflow |
| } |
| |
| // Compute exact floating-point integer from d's digits. |
| // Caller is responsible for avoiding overflow. |
| func decimalAtof64Int(neg bool, d *decimal) float64 { |
| f := float64(0) |
| for i := 0; i < d.nd; i++ { |
| f = f*10 + float64(d.d[i]-'0') |
| } |
| if neg { |
| f *= -1 // BUG work around 6g f = -f. |
| } |
| return f |
| } |
| |
| func decimalAtof32Int(neg bool, d *decimal) float32 { |
| f := float32(0) |
| for i := 0; i < d.nd; i++ { |
| f = f*10 + float32(d.d[i]-'0') |
| } |
| if neg { |
| f *= -1 // BUG work around 6g f = -f. |
| } |
| return f |
| } |
| |
| // 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 d 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 decimalAtof64(neg bool, d *decimal, trunc bool) (f float64, ok bool) { |
| // Exact integers are <= 10^15. |
| // Exact powers of ten are <= 10^22. |
| if d.nd > 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 |
| } |