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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.
// Binary to decimal floating point conversion.
// Algorithm:
// 1) store mantissa in multiprecision decimal
// 2) shift decimal by exponent
// 3) read digits out & format
package strconv
import "math"
// TODO: move elsewhere?
type floatInfo struct {
mantbits uint
expbits uint
bias int
}
var float32info = floatInfo{23, 8, -127}
var float64info = floatInfo{52, 11, -1023}
func floatsize() int {
// Figure out whether float is float32 or float64.
// 1e-35 is representable in both, but 1e-70
// is too small for a float32.
var f float = 1e-35
if f*f == 0 {
return 32
}
return 64
}
// Floatsize gives the size of the float type, either 32 or 64.
var FloatSize = floatsize()
// Ftoa32 converts the 32-bit floating-point number f to a string,
// according to the format fmt and precision prec.
//
// The format fmt is one of
// 'b' (-ddddp±ddd, a binary exponent),
// 'e' (-d.dddde±dd, a decimal exponent),
// 'f' (-ddd.dddd, no exponent), or
// 'g' ('e' for large exponents, 'f' otherwise).
//
// The precision prec controls the number of digits
// (excluding the exponent) printed by the 'e', 'f', and 'g' formats.
// For 'e' and 'f' it is the number of digits after the decimal point.
// For 'g' it is the total number of digits.
// The special precision -1 uses the smallest number of digits
// necessary such that Atof32 will return f exactly.
//
// Ftoa32(f) is not the same as Ftoa64(float32(f)),
// because correct rounding and the number of digits
// needed to identify f depend on the precision of the representation.
func Ftoa32(f float32, fmt byte, prec int) string {
return genericFtoa(uint64(math.Float32bits(f)), fmt, prec, &float32info)
}
// Ftoa64 is like Ftoa32 but converts a 64-bit floating-point number.
func Ftoa64(f float64, fmt byte, prec int) string {
return genericFtoa(math.Float64bits(f), fmt, prec, &float64info)
}
// Ftoa behaves as Ftoa32 or Ftoa64, depending on the size of the float type.
func Ftoa(f float, fmt byte, prec int) string {
if FloatSize == 32 {
return Ftoa32(float32(f), fmt, prec)
}
return Ftoa64(float64(f), fmt, prec)
}
func genericFtoa(bits uint64, fmt byte, prec int, flt *floatInfo) string {
neg := bits>>flt.expbits>>flt.mantbits != 0
exp := int(bits>>flt.mantbits) & (1<<flt.expbits - 1)
mant := bits & (uint64(1)<<flt.mantbits - 1)
switch exp {
case 1<<flt.expbits - 1:
// Inf, NaN
if mant != 0 {
return "NaN"
}
if neg {
return "-Inf"
}
return "+Inf"
case 0:
// denormalized
exp++
default:
// add implicit top bit
mant |= uint64(1) << flt.mantbits
}
exp += flt.bias
// Pick off easy binary format.
if fmt == 'b' {
return fmtB(neg, mant, exp, flt)
}
// Create exact decimal representation.
// The shift is exp - flt.mantbits because mant is a 1-bit integer
// followed by a flt.mantbits fraction, and we are treating it as
// a 1+flt.mantbits-bit integer.
d := newDecimal(mant).Shift(exp - int(flt.mantbits))
// Round appropriately.
// Negative precision means "only as much as needed to be exact."
shortest := false
if prec < 0 {
shortest = true
roundShortest(d, mant, exp, flt)
switch fmt {
case 'e', 'E':
prec = d.nd - 1
case 'f':
prec = max(d.nd-d.dp, 0)
case 'g', 'G':
prec = d.nd
}
} else {
switch fmt {
case 'e', 'E':
d.Round(prec + 1)
case 'f':
d.Round(d.dp + prec)
case 'g', 'G':
if prec == 0 {
prec = 1
}
d.Round(prec)
}
}
switch fmt {
case 'e', 'E':
return fmtE(neg, d, prec, fmt)
case 'f':
return fmtF(neg, d, prec)
case 'g', 'G':
// trailing zeros are removed.
if prec > d.nd {
prec = d.nd
}
// %e is used if the exponent from the conversion
// is less than -4 or greater than or equal to the precision.
// if precision was the shortest possible, use precision 6 for this decision.
eprec := prec
if shortest {
eprec = 6
}
exp := d.dp - 1
if exp < -4 || exp >= eprec {
return fmtE(neg, d, prec-1, fmt+'e'-'g')
}
return fmtF(neg, d, max(prec-d.dp, 0))
}
return "%" + string(fmt)
}
// Round d (= mant * 2^exp) to the shortest number of digits
// that will let the original floating point value be precisely
// reconstructed. Size is original floating point size (64 or 32).
func roundShortest(d *decimal, mant uint64, exp int, flt *floatInfo) {
// If mantissa is zero, the number is zero; stop now.
if mant == 0 {
d.nd = 0
return
}
// TODO(rsc): Unless exp == minexp, if the number of digits in d
// is less than 17, it seems likely that it would be
// the shortest possible number already. So maybe we can
// bail out without doing the extra multiprecision math here.
// Compute upper and lower such that any decimal number
// between upper and lower (possibly inclusive)
// will round to the original floating point number.
// d = mant << (exp - mantbits)
// Next highest floating point number is mant+1 << exp-mantbits.
// Our upper bound is halfway inbetween, mant*2+1 << exp-mantbits-1.
upper := newDecimal(mant*2 + 1).Shift(exp - int(flt.mantbits) - 1)
// d = mant << (exp - mantbits)
// Next lowest floating point number is mant-1 << exp-mantbits,
// unless mant-1 drops the significant bit and exp is not the minimum exp,
// in which case the next lowest is mant*2-1 << exp-mantbits-1.
// Either way, call it mantlo << explo-mantbits.
// Our lower bound is halfway inbetween, mantlo*2+1 << explo-mantbits-1.
minexp := flt.bias + 1 // minimum possible exponent
var mantlo uint64
var explo int
if mant > 1<<flt.mantbits || exp == minexp {
mantlo = mant - 1
explo = exp
} else {
mantlo = mant*2 - 1
explo = exp - 1
}
lower := newDecimal(mantlo*2 + 1).Shift(explo - int(flt.mantbits) - 1)
// The upper and lower bounds are possible outputs only if
// the original mantissa is even, so that IEEE round-to-even
// would round to the original mantissa and not the neighbors.
inclusive := mant%2 == 0
// Now we can figure out the minimum number of digits required.
// Walk along until d has distinguished itself from upper and lower.
for i := 0; i < d.nd; i++ {
var l, m, u byte // lower, middle, upper digits
if i < lower.nd {
l = lower.d[i]
} else {
l = '0'
}
m = d.d[i]
if i < upper.nd {
u = upper.d[i]
} else {
u = '0'
}
// Okay to round down (truncate) if lower has a different digit
// or if lower is inclusive and is exactly the result of rounding down.
okdown := l != m || (inclusive && l == m && i+1 == lower.nd)
// Okay to round up if upper has a different digit and
// either upper is inclusive or upper is bigger than the result of rounding up.
okup := m != u && (inclusive || i+1 < upper.nd)
// If it's okay to do either, then round to the nearest one.
// If it's okay to do only one, do it.
switch {
case okdown && okup:
d.Round(i + 1)
return
case okdown:
d.RoundDown(i + 1)
return
case okup:
d.RoundUp(i + 1)
return
}
}
}
// %e: -d.ddddde±dd
func fmtE(neg bool, d *decimal, prec int, fmt byte) string {
buf := make([]byte, 3+max(prec, 0)+30) // "-0." + prec digits + exp
w := 0 // write index
// sign
if neg {
buf[w] = '-'
w++
}
// first digit
if d.nd == 0 {
buf[w] = '0'
} else {
buf[w] = d.d[0]
}
w++
// .moredigits
if prec > 0 {
buf[w] = '.'
w++
for i := 0; i < prec; i++ {
if 1+i < d.nd {
buf[w] = d.d[1+i]
} else {
buf[w] = '0'
}
w++
}
}
// e±
buf[w] = fmt
w++
exp := d.dp - 1
if d.nd == 0 { // special case: 0 has exponent 0
exp = 0
}
if exp < 0 {
buf[w] = '-'
exp = -exp
} else {
buf[w] = '+'
}
w++
// dddd
// count digits
n := 0
for e := exp; e > 0; e /= 10 {
n++
}
// leading zeros
for i := n; i < 2; i++ {
buf[w] = '0'
w++
}
// digits
w += n
n = 0
for e := exp; e > 0; e /= 10 {
n++
buf[w-n] = byte(e%10 + '0')
}
return string(buf[0:w])
}
// %f: -ddddddd.ddddd
func fmtF(neg bool, d *decimal, prec int) string {
buf := make([]byte, 1+max(d.dp, 1)+1+max(prec, 0))
w := 0
// sign
if neg {
buf[w] = '-'
w++
}
// integer, padded with zeros as needed.
if d.dp > 0 {
var i int
for i = 0; i < d.dp && i < d.nd; i++ {
buf[w] = d.d[i]
w++
}
for ; i < d.dp; i++ {
buf[w] = '0'
w++
}
} else {
buf[w] = '0'
w++
}
// fraction
if prec > 0 {
buf[w] = '.'
w++
for i := 0; i < prec; i++ {
if d.dp+i < 0 || d.dp+i >= d.nd {
buf[w] = '0'
} else {
buf[w] = d.d[d.dp+i]
}
w++
}
}
return string(buf[0:w])
}
// %b: -ddddddddp+ddd
func fmtB(neg bool, mant uint64, exp int, flt *floatInfo) string {
var buf [50]byte
w := len(buf)
exp -= int(flt.mantbits)
esign := byte('+')
if exp < 0 {
esign = '-'
exp = -exp
}
n := 0
for exp > 0 || n < 1 {
n++
w--
buf[w] = byte(exp%10 + '0')
exp /= 10
}
w--
buf[w] = esign
w--
buf[w] = 'p'
n = 0
for mant > 0 || n < 1 {
n++
w--
buf[w] = byte(mant%10 + '0')
mant /= 10
}
if neg {
w--
buf[w] = '-'
}
return string(buf[w:])
}
func max(a, b int) int {
if a > b {
return a
}
return b
}