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strconv: faster FormatFloat for fixed number of digits.

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The performance improvement applies to the case where
prec >= 0 and fmt is 'e' or 'g'.

Additional minor optimisations are included. A small
performance impact happens in some cases due to code
refactoring.

benchmark                              old ns/op    new ns/op    delta
BenchmarkAppendFloat64Fixed1                 623          235  -62.28%
BenchmarkAppendFloat64Fixed2                1050          272  -74.10%
BenchmarkAppendFloat64Fixed3                3723          243  -93.47%
BenchmarkAppendFloat64Fixed4               10285          274  -97.34%

BenchmarkAppendFloatDecimal                  190          206   +8.42%
BenchmarkAppendFloat                         387          377   -2.58%
BenchmarkAppendFloatExp                      397          339  -14.61%
BenchmarkAppendFloatNegExp                   377          336  -10.88%
BenchmarkAppendFloatBig                      546          482  -11.72%

BenchmarkAppendFloat32Integer                188          204   +8.51%
BenchmarkAppendFloat32ExactFraction          329          298   -9.42%
BenchmarkAppendFloat32Point                  400          372   -7.00%
BenchmarkAppendFloat32Exp                    369          306  -17.07%
BenchmarkAppendFloat32NegExp                 372          305  -18.01%

R=golang-dev, rsc
CC=golang-dev, remy
https://golang.org/cl/6462049
This commit is contained in:
Rémy Oudompheng 2012-09-01 16:31:46 +02:00
parent 5a78e5ea4c
commit c1c027964e
3 changed files with 273 additions and 76 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

205
src/pkg/strconv/extfloat.go
View File

@ -4,8 +4,6 @@
package strconv
import "math"
// An extFloat represents an extended floating-point number, with more
// precision than a float64. It does not try to save bits: the
// number represented by the structure is mant*(2^exp), with a negative
@ -179,17 +177,6 @@ out:
return
}
// Assign sets f to the value of x.
func (f *extFloat) Assign(x float64) {
if x < 0 {
x = -x
f.neg = true
}
x, f.exp = math.Frexp(x)
f.mant = uint64(x * float64(1<<64))
f.exp -= 64
}
// AssignComputeBounds sets f to the floating point value
// defined by mant, exp and precision given by flt. It returns
// lower, upper such that any number in the closed interval
@ -354,16 +341,17 @@ func (f *extFloat) AssignDecimal(mantissa uint64, exp10 int, neg bool, trunc boo
// f by an approximate power of ten 10^-exp, and returns exp10, so
// that f*10^exp10 has the same value as the old f, up to an ulp,
// as well as the index of 10^-exp in the powersOfTen table.
// The arguments expMin and expMax constrain the final value of the
// binary exponent of f.
func (f *extFloat) frexp10(expMin, expMax int) (exp10, index int) {
// it is illegal to call this function with a too restrictive exponent range.
if expMax-expMin <= 25 {
panic("strconv: invalid exponent range")
}
func (f *extFloat) frexp10() (exp10, index int) {
// The constants expMin and expMax constrain the final value of the
// binary exponent of f. We want a small integral part in the result
// because finding digits of an integer requires divisions, whereas
// digits of the fractional part can be found by repeatedly multiplying
// by 10.
const expMin = -60
const expMax = -32
// Find power of ten such that x * 10^n has a binary exponent
// between expMin and expMax
approxExp10 := -(f.exp + 100) * 28 / 93 // log(10)/log(2) is close to 93/28.
// between expMin and expMax.
approxExp10 := ((expMin+expMax)/2 - f.exp) * 28 / 93 // log(10)/log(2) is close to 93/28.
i := (approxExp10 - firstPowerOfTen) / stepPowerOfTen
Loop:
for {
@ -385,23 +373,176 @@ Loop:
}
// frexp10Many applies a common shift by a power of ten to a, b, c.
func frexp10Many(expMin, expMax int, a, b, c *extFloat) (exp10 int) {
exp10, i := c.frexp10(expMin, expMax)
func frexp10Many(a, b, c *extFloat) (exp10 int) {
exp10, i := c.frexp10()
a.Multiply(powersOfTen[i])
b.Multiply(powersOfTen[i])
return
}
// FixedDecimal stores in d the first n significant digits
// of the decimal representation of f. It returns false
// if it cannot be sure of the answer.
func (f *extFloat) FixedDecimal(d *decimalSlice, n int) bool {
if f.mant == 0 {
d.nd = 0
d.dp = 0
d.neg = f.neg
return true
}
if n == 0 {
panic("strconv: internal error: extFloat.FixedDecimal called with n == 0")
}
// Multiply by an appropriate power of ten to have a reasonable
// number to process.
f.Normalize()
exp10, _ := f.frexp10()
shift := uint(-f.exp)
integer := uint32(f.mant >> shift)
fraction := f.mant - (uint64(integer) << shift)
ε := uint64(1) // ε is the uncertainty we have on the mantissa of f.
// Write exactly n digits to d.
needed := n // how many digits are left to write.
integerDigits := 0 // the number of decimal digits of integer.
pow10 := uint64(1) // the power of ten by which f was scaled.
for i, pow := 0, uint64(1); i < 20; i++ {
if pow > uint64(integer) {
integerDigits = i
break
}
pow *= 10
}
rest := integer
if integerDigits > needed {
// the integral part is already large, trim the last digits.
pow10 = uint64pow10[integerDigits-needed]
integer /= uint32(pow10)
rest -= integer * uint32(pow10)
} else {
rest = 0
}
// Write the digits of integer: the digits of rest are omitted.
var buf [32]byte
pos := len(buf)
for v := integer; v > 0; {
v1 := v / 10
v -= 10 * v1
pos--
buf[pos] = byte(v + '0')
v = v1
}
for i := pos; i < len(buf); i++ {
d.d[i-pos] = buf[i]
}
nd := len(buf) - pos
d.nd = nd
d.dp = integerDigits + exp10
needed -= nd
if needed > 0 {
if rest != 0 || pow10 != 1 {
panic("strconv: internal error, rest != 0 but needed > 0")
}
// Emit digits for the fractional part. Each time, 10*fraction
// fits in a uint64 without overflow.
for needed > 0 {
fraction *= 10
ε *= 10 // the uncertainty scales as we multiply by ten.
if 2*ε > 1<<shift {
// the error is so large it could modify which digit to write, abort.
return false
}
digit := fraction >> shift
d.d[nd] = byte(digit + '0')
fraction -= digit << shift
nd++
needed--
}
d.nd = nd
}
// We have written a truncation of f (a numerator / 10^d.dp). The remaining part
// can be interpreted as a small number (< 1) to be added to the last digit of the
// numerator.
//
// If rest > 0, the amount is:
// (rest<<shift | fraction) / (pow10 << shift)
// fraction being known with a ±ε uncertainty.
// The fact that n > 0 guarantees that pow10 << shift does not overflow a uint64.
//
// If rest = 0, pow10 == 1 and the amount is
// fraction / (1 << shift)
// fraction being known with a ±ε uncertainty.
//
// We pass this information to the rounding routine for adjustment.
ok := adjustLastDigitFixed(d, uint64(rest)<<shift|fraction, pow10, shift, ε)
if !ok {
return false
}
// Trim trailing zeros.
for i := d.nd - 1; i >= 0; i-- {
if d.d[i] != '0' {
d.nd = i + 1
break
}
}
return true
}
// adjustLastDigitFixed assumes d contains the representation of the integral part
// of some number, whose fractional part is num / (den << shift). The numerator
// num is only known up to an uncertainty of size ε, assumed to be less than
// (den << shift)/2.
//
// It will increase the last digit by one to account for correct rounding, typically
// when the fractional part is greater than 1/2, and will return false if ε is such
// that no correct answer can be given.
func adjustLastDigitFixed(d *decimalSlice, num, den uint64, shift uint, ε uint64) bool {
if num > den<<shift {
panic("strconv: num > den<<shift in adjustLastDigitFixed")
}
if 2*ε > den<<shift {
panic("strconv: ε > (den<<shift)/2")
}
if 2*(num+ε) < den<<shift {
return true
}
if 2*(num-ε) > den<<shift {
// increment d by 1.
i := d.nd - 1
for ; i >= 0; i-- {
if d.d[i] == '9' {
d.nd--
} else {
break
}
}
if i < 0 {
d.d[0] = '1'
d.nd = 1
d.dp++
} else {
d.d[i]++
}
return true
}
return false
}
// ShortestDecimal stores in d the shortest decimal representation of f
// which belongs to the open interval (lower, upper), where f is supposed
// to lie. It returns false whenever the result is unsure. The implementation
// uses the Grisu3 algorithm.
func (f *extFloat) ShortestDecimal(d *decimalSlice, lower, upper *extFloat) bool {
if f.mant == 0 {
d.d[0] = '0'
d.nd = 1
d.nd = 0
d.dp = 0
d.neg = f.neg
return true
}
if f.exp == 0 && *lower == *f && *lower == *upper {
// an exact integer.
@ -428,8 +569,6 @@ func (f *extFloat) ShortestDecimal(d *decimalSlice, lower, upper *extFloat) bool
d.neg = f.neg
return true
}
const minExp = -60
const maxExp = -32
upper.Normalize()
// Uniformize exponents.
if f.exp > upper.exp {
@ -441,7 +580,7 @@ func (f *extFloat) ShortestDecimal(d *decimalSlice, lower, upper *extFloat) bool
lower.exp = upper.exp
}
exp10 := frexp10Many(minExp, maxExp, lower, f, upper)
exp10 := frexp10Many(lower, f, upper)
// Take a safety margin due to rounding in frexp10Many, but we lose precision.
upper.mant++
lower.mant--
@ -459,10 +598,12 @@ func (f *extFloat) ShortestDecimal(d *decimalSlice, lower, upper *extFloat) bool
// Count integral digits: there are at most 10.
var integerDigits int
for i, pow := range uint64pow10 {
if uint64(integer) >= pow {
integerDigits = i + 1
for i, pow := 0, uint64(1); i < 20; i++ {
if pow > uint64(integer) {
integerDigits = i
break
}
pow *= 10
}
for i := 0; i < integerDigits; i++ {
pow := uint64pow10[integerDigits-i-1]

129
src/pkg/strconv/ftoa.go
View File

@ -98,47 +98,79 @@ func genericFtoa(dst []byte, val float64, fmt byte, prec, bitSize int) []byte {
return fmtB(dst, neg, mant, exp, flt)
}
// Negative precision means "only as much as needed to be exact."
shortest := prec < 0
if !optimize {
return bigFtoa(dst, prec, fmt, neg, mant, exp, flt)
}
var digs decimalSlice
ok := false
// Negative precision means "only as much as needed to be exact."
shortest := prec < 0
if shortest {
ok := false
if optimize {
// 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)
}
// 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 {
// 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 := new(decimal)
d.Assign(mant)
d.Shift(exp - int(flt.mantbits))
roundShortest(d, mant, exp, flt)
digs = decimalSlice{d: d.d[:], nd: d.nd, dp: d.dp}
return bigFtoa(dst, prec, fmt, neg, mant, exp, flt)
}
// Precision for shortest representation mode.
if prec < 0 {
switch fmt {
case 'e', 'E':
prec = digs.nd - 1
case 'f':
prec = max(digs.nd-digs.dp, 0)
case 'g', 'G':
prec = digs.nd
switch fmt {
case 'e', 'E':
prec = digs.nd - 1
case 'f':
prec = max(digs.nd-digs.dp, 0)
case 'g', 'G':
prec = digs.nd
}
} else if fmt != 'f' {
// Fixed number of digits.
digits := prec
switch fmt {
case 'e', 'E':
digits++
case 'g', 'G':
if prec == 0 {
prec = 1
}
digits = prec
}
if digits <= 15 {
// try fast algorithm when the number of digits is reasonable.
var buf [24]byte
digs.d = buf[:]
f := extFloat{mant, exp - int(flt.mantbits), neg}
ok = f.FixedDecimal(&digs, digits)
}
}
if !ok {
return bigFtoa(dst, prec, fmt, neg, mant, exp, flt)
}
return formatDigits(dst, shortest, neg, digs, prec, fmt)
}
// bigFtoa uses multiprecision computations to format a float.
func bigFtoa(dst []byte, prec int, fmt byte, neg bool, mant uint64, exp int, flt *floatInfo) []byte {
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}
// Precision for shortest representation mode.
switch fmt {
case 'e', 'E':
prec = digs.nd - 1
case 'f':
prec = max(digs.nd-digs.dp, 0)
case 'g', 'G':
prec = digs.nd
}
} else {
// Create exact decimal representation.
d := new(decimal)
d.Assign(mant)
d.Shift(exp - int(flt.mantbits))
// Round appropriately.
switch fmt {
case 'e', 'E':
@ -153,7 +185,10 @@ func genericFtoa(dst []byte, val float64, fmt byte, prec, bitSize int) []byte {
}
digs = decimalSlice{d: d.d[:], nd: d.nd, dp: d.dp}
}
return formatDigits(dst, shortest, neg, digs, prec, fmt)
}
func formatDigits(dst []byte, shortest bool, neg bool, digs decimalSlice, prec int, fmt byte) []byte {
switch fmt {
case 'e', 'E':
return fmtE(dst, neg, digs, prec, fmt)
@ -312,12 +347,15 @@ func fmtE(dst []byte, neg bool, d decimalSlice, prec int, fmt byte) []byte {
// .moredigits
if prec > 0 {
dst = append(dst, '.')
for i := 1; i <= prec; i++ {
ch = '0'
if i < d.nd {
ch = d.d[i]
}
dst = append(dst, ch)
i := 1
m := d.nd + prec + 1 - max(d.nd, prec+1)
for i < m {
dst = append(dst, d.d[i])
i++
}
for i <= prec {
dst = append(dst, '0')
i++
}
}
@ -347,13 +385,16 @@ func fmtE(dst []byte, neg bool, d decimalSlice, prec int, fmt byte) []byte {
i--
buf[i] = byte(exp + '0')
// leading zeroes
if i > len(buf)-2 {
i--
buf[i] = '0'
switch i {
case 0:
dst = append(dst, buf[0], buf[1], buf[2])
case 1:
dst = append(dst, buf[1], buf[2])
case 2:
// leading zeroes
dst = append(dst, '0', buf[2])
}
return append(dst, buf[i:]...)
return dst
}
// %f: -ddddddd.ddddd

15
src/pkg/strconv/ftoa_test.go
View File

@ -163,6 +163,7 @@ func TestFtoaRandom(t *testing.T) {
for i := 0; i < N; i++ {
bits := uint64(rand.Uint32())<<32 | uint64(rand.Uint32())
x := math.Float64frombits(bits)
shortFast := FormatFloat(x, 'g', -1, 64)
SetOptimize(false)
shortSlow := FormatFloat(x, 'g', -1, 64)
@ -170,6 +171,15 @@ func TestFtoaRandom(t *testing.T) {
if shortSlow != shortFast {
t.Errorf("%b printed as %s, want %s", x, shortFast, shortSlow)
}
prec := rand.Intn(12) + 5
shortFast = FormatFloat(x, 'e', prec, 64)
SetOptimize(false)
shortSlow = FormatFloat(x, 'e', prec, 64)
SetOptimize(true)
if shortSlow != shortFast {
t.Errorf("%b printed as %s, want %s", x, shortFast, shortSlow)
}
}
}
@ -223,3 +233,8 @@ func BenchmarkAppendFloat32ExactFraction(b *testing.B) { benchmarkAppendFloat(b,
func BenchmarkAppendFloat32Point(b *testing.B) { benchmarkAppendFloat(b, 339.7784, 'g', -1, 32) }
func BenchmarkAppendFloat32Exp(b *testing.B) { benchmarkAppendFloat(b, -5.09e25, 'g', -1, 32) }
func BenchmarkAppendFloat32NegExp(b *testing.B) { benchmarkAppendFloat(b, -5.11e-25, 'g', -1, 32) }
func BenchmarkAppendFloat64Fixed1(b *testing.B) { benchmarkAppendFloat(b, 123456, 'e', 3, 64) }
func BenchmarkAppendFloat64Fixed2(b *testing.B) { benchmarkAppendFloat(b, 123.456, 'e', 3, 64) }
func BenchmarkAppendFloat64Fixed3(b *testing.B) { benchmarkAppendFloat(b, 1.23456e+78, 'e', 3, 64) }
func BenchmarkAppendFloat64Fixed4(b *testing.B) { benchmarkAppendFloat(b, 1.23456e-78, 'e', 3, 64) }