Merge from mainline (167278:168000).

[official-gcc/graphite-test-results.git] / libgo / go / strconv / atof.go

// 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
}


// 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
}