fastprinter/float.go
2019-12-23 19:19:47 +08:00

279 lines
7.3 KiB
Go

// MIT License
//
// Copyright (c) 2017 José Santos <henrique_1609@me.com>
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in all
// copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
// SOFTWARE.
package fastprinter
import (
"io"
"math"
)
type floatInfo struct {
mantbits uint
expbits uint
bias int
}
var (
float64info = floatInfo{52, 11, -1023}
floatNaN = []byte("Nan")
floatNinf = []byte("-Inf")
floatPinf = []byte("+Inf")
pool_floatBuffer = newByteSliceBufferPool(800)
)
func PrintFloat(w io.Writer, f float64) (int, error) {
return PrintFloatPrecision(w, f, -1)
}
func PrintFloatPrecision(dst io.Writer, val float64, prec int) (int, error) {
var bits uint64
var flt *floatInfo
bits = math.Float64bits(val)
flt = &float64info
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:
switch {
case mant != 0:
return dst.Write(floatNaN)
case neg:
return dst.Write(floatNinf)
default:
return dst.Write(floatPinf)
}
case 0:
// denormalized
exp++
default:
// add implicit top bit
mant |= uint64(1) << flt.mantbits
}
exp += flt.bias
var digs decimalSlice
ok := false
// Negative precision means "only as much as needed to be exact."
shortest := prec < 0
if shortest {
// Try Grisu3 algorithm.
f := new(extFloat)
lower, upper := f.AssignComputeBounds(mant, exp, neg, flt)
var buf [32]byte
digs.d = buf[:]
ok = f.ShortestDecimal(&digs, &lower, &upper)
if !ok {
return bigFtoa(dst, prec, neg, mant, exp, flt)
}
// Precision for shortest representation mode.
prec = max(digs.nd-digs.dp, 0)
}
if !ok {
return bigFtoa(dst, prec, neg, mant, exp, flt)
}
return fmtF(dst, neg, digs, prec)
}
// bigFtoa uses multiprecision computations to format a float.
func bigFtoa(dst io.Writer, prec int, neg bool, mant uint64, exp int, flt *floatInfo) (int, error) {
d := new(decimal)
d.Assign(mant)
d.Shift(exp - int(flt.mantbits))
var digs decimalSlice
shortest := prec < 0
if shortest {
roundShortest(d, mant, exp, flt)
digs = decimalSlice{d: d.d[:], nd: d.nd, dp: d.dp}
prec = max(digs.nd-digs.dp, 0)
} else {
d.Round(d.dp + prec)
digs = decimalSlice{d: d.d[:], nd: d.nd, dp: d.dp}
}
return fmtF(dst, neg, digs, prec)
}
// roundShortest rounds d (= mant * 2^exp) to the shortest number of digits
// that will let the original floating point value be precisely reconstructed.
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
}
// Compute upper and lower such that any decimal number
// between upper and lower (possibly inclusive)
// will round to the original floating point number.
// We may see at once that the number is already shortest.
//
// Suppose d is not denormal, so that 2^exp <= d < 10^dp.
// The closest shorter number is at least 10^(dp-nd) away.
// The lower/upper bounds computed below are at distance
// at most 2^(exp-mantbits).
//
// So the number is already shortest if 10^(dp-nd) > 2^(exp-mantbits),
// or equivalently log2(10)*(dp-nd) > exp-mantbits.
// It is true if 332/100*(dp-nd) >= exp-mantbits (log2(10) > 3.32).
minexp := flt.bias + 1 // minimum possible exponent
if exp > minexp && 332*(d.dp-d.nd) >= 100*(exp-int(flt.mantbits)) {
// The number is already shortest.
return
}
// d = mant << (exp - mantbits)
// Next highest floating point number is mant+1 << exp-mantbits.
// Our upper bound is halfway between, mant*2+1 << exp-mantbits-1.
upper := new(decimal)
upper.Assign(mant*2 + 1)
upper.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 between, mantlo*2+1 << explo-mantbits-1.
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 := new(decimal)
lower.Assign(mantlo*2 + 1)
lower.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++ {
l := byte('0') // lower digit
if i < lower.nd {
l = lower.d[i]
}
m := d.d[i] // middle digit
u := byte('0') // upper digit
if i < upper.nd {
u = upper.d[i]
}
// Okay to round down (truncate) if lower has a different digit
// or if lower is inclusive and is exactly the result of rounding
// down (i.e., and we have reached the final digit of lower).
okdown := l != m || inclusive && 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 || m+1 < u || 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
}
}
}
type decimalSlice struct {
d []byte
nd, dp int
neg bool
}
// %f: -ddddddd.ddddd
func fmtF(dst io.Writer, neg bool, d decimalSlice, prec int) (n int, err error) {
a := pool_floatBuffer.Get().(*byteSliceBuffer)
i := 0
// sign
if neg {
a.bytes[i] = '-'
i++
}
// integer, padded with zeros as needed.
if d.dp > 0 {
m := min(d.nd, d.dp)
copy(a.bytes[i:], d.d[:m])
i += m
for ; m < d.dp; m++ {
a.bytes[i] = '0'
i++
}
} else {
a.bytes[i] = '0'
i++
}
// fraction
if prec > 0 {
a.bytes[i] = '.'
i++
for j := 0; j < prec; j++ {
ch := byte('0')
if j := d.dp + j; 0 <= j && j < d.nd {
ch = d.d[j]
}
a.bytes[i] = ch
i++
}
}
n, err = dst.Write(a.bytes[0:i])
pool_floatBuffer.Put(a)
return
}
func min(a, b int) int {
if a < b {
return a
}
return b
}
func max(a, b int) int {
if a > b {
return a
}
return b
}