413 lines
8.6 KiB
Go
413 lines
8.6 KiB
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.
|
|
|
|
// 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) {
|
|
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 (b *decimal) set(s string) (ok bool) {
|
|
i := 0
|
|
b.neg = 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
|
|
}
|
|
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
|
|
}
|
|
|
|
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<<flt.expbits-1 {
|
|
goto overflow
|
|
}
|
|
|
|
// Extract 1+flt.mantbits bits.
|
|
d.Shift(int(1 + flt.mantbits))
|
|
mant = d.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 d.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 (d *decimal) atof64int() float64 {
|
|
f := 0.0
|
|
for i := 0; i < d.nd; i++ {
|
|
f = f*10 + float64(d.d[i]-'0')
|
|
}
|
|
if d.neg {
|
|
f = -f
|
|
}
|
|
return f
|
|
}
|
|
|
|
func (d *decimal) atof32int() float32 {
|
|
f := float32(0)
|
|
for i := 0; i < d.nd; i++ {
|
|
f = f*10 + float32(d.d[i]-'0')
|
|
}
|
|
if d.neg {
|
|
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 (d *decimal) atof64() (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 := d.atof64int()
|
|
return f, true
|
|
|
|
case d.dp > d.nd && d.dp <= 15+22: // int * 10^k
|
|
f := d.atof64int()
|
|
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 := d.atof64int()
|
|
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 (d *decimal) atof32() (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 := d.atof32int()
|
|
return f, true
|
|
|
|
case d.dp > d.nd && d.dp <= 7+10: // int * 10^k
|
|
f := d.atof32int()
|
|
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 := d.atof32int()
|
|
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 = 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,
|
|
// Atof32 returns f = ±Inf, err.Error = ErrRange.
|
|
func Atof32(s string) (f float32, err error) {
|
|
if val, ok := special(s); ok {
|
|
return float32(val), nil
|
|
}
|
|
|
|
var d decimal
|
|
if !d.set(s) {
|
|
return 0, &NumError{s, ErrSyntax}
|
|
}
|
|
if optimize {
|
|
if f, ok := d.atof32(); ok {
|
|
return f, nil
|
|
}
|
|
}
|
|
b, ovf := d.floatBits(&float32info)
|
|
f = math.Float32frombits(uint32(b))
|
|
if ovf {
|
|
err = &NumError{s, ErrRange}
|
|
}
|
|
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 error) {
|
|
if val, ok := special(s); ok {
|
|
return val, nil
|
|
}
|
|
|
|
var d decimal
|
|
if !d.set(s) {
|
|
return 0, &NumError{s, ErrSyntax}
|
|
}
|
|
if optimize {
|
|
if f, ok := d.atof64(); ok {
|
|
return f, nil
|
|
}
|
|
}
|
|
b, ovf := d.floatBits(&float64info)
|
|
f = math.Float64frombits(b)
|
|
if ovf {
|
|
err = &NumError{s, ErrRange}
|
|
}
|
|
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 error) {
|
|
if n == 32 {
|
|
f1, err1 := Atof32(s)
|
|
return float64(f1), err1
|
|
}
|
|
f1, err1 := Atof64(s)
|
|
return f1, err1
|
|
}
|