mirror of
https://github.com/golang/go
synced 2024-09-15 22:20:06 +00:00
strconv: implement Ryū-like algorithm for fixed precision ftoa
This patch implements a simplified version of Ulf Adams, "Ryū: Fast Float-to-String Conversion" (doi:10.1145/3192366.3192369) for formatting floating-point numbers with a fixed number of decimal digits. It uses the same principles but does not need to handle the complex task of finding a shortest representation. This allows to handle a few more cases than Grisu3, notably formatting with up to 18 significant digits. name old time/op new time/op delta AppendFloat/32Fixed8Hard-4 72.0ns ± 2% 56.0ns ± 2% -22.28% (p=0.000 n=10+10) AppendFloat/32Fixed9Hard-4 74.8ns ± 0% 64.2ns ± 2% -14.16% (p=0.000 n=8+10) AppendFloat/64Fixed1-4 60.4ns ± 1% 54.2ns ± 1% -10.31% (p=0.000 n=10+9) AppendFloat/64Fixed2-4 66.3ns ± 1% 53.3ns ± 1% -19.54% (p=0.000 n=10+9) AppendFloat/64Fixed3-4 61.0ns ± 1% 55.0ns ± 2% -9.80% (p=0.000 n=9+10) AppendFloat/64Fixed4-4 66.9ns ± 0% 52.0ns ± 2% -22.20% (p=0.000 n=8+10) AppendFloat/64Fixed12-4 95.5ns ± 1% 76.2ns ± 3% -20.19% (p=0.000 n=10+9) AppendFloat/64Fixed16-4 1.62µs ± 0% 0.07µs ± 2% -95.69% (p=0.000 n=10+10) AppendFloat/64Fixed12Hard-4 1.27µs ± 1% 0.07µs ± 1% -94.83% (p=0.000 n=9+9) AppendFloat/64Fixed17Hard-4 3.68µs ± 1% 0.08µs ± 2% -97.86% (p=0.000 n=10+9) AppendFloat/64Fixed18Hard-4 3.67µs ± 0% 3.72µs ± 1% +1.44% (p=0.000 n=9+10) Updates #15672 Change-Id: I160963e141dd48287ad8cf57bcc3c686277788e8 Reviewed-on: https://go-review.googlesource.com/c/go/+/170079 Reviewed-by: Emmanuel Odeke <emmanuel@orijtech.com> Trust: Emmanuel Odeke <emmanuel@orijtech.com> Trust: Nigel Tao <nigeltao@golang.org> Trust: Robert Griesemer <gri@golang.org> Run-TryBot: Emmanuel Odeke <emmanuel@orijtech.com> TryBot-Result: Go Bot <gobot@golang.org>
This commit is contained in:
Rémy Oudompheng
Emmanuel Odeke
parent
8f4c5068e0
commit
0184b445c0
|
|
@ -143,12 +143,15 @@ func genericFtoa(dst []byte, val float64, fmt byte, prec, bitSize int) []byte {
|
|||
}
|
||||
digits = prec
|
||||
}
|
||||
if digits <= 15 {
|
||||
// try fast algorithm when the number of digits is reasonable.
|
||||
var buf [24]byte
|
||||
var buf [24]byte
|
||||
if bitSize == 32 && digits <= 9 {
|
||||
digs.d = buf[:]
|
||||
f := extFloat{mant, exp - int(flt.mantbits), neg}
|
||||
ok = f.FixedDecimal(&digs, digits)
|
||||
ryuFtoaFixed32(&digs, uint32(mant), exp-int(flt.mantbits), digits)
|
||||
ok = true
|
||||
} else if digits <= 18 {
|
||||
digs.d = buf[:]
|
||||
ryuFtoaFixed64(&digs, mant, exp-int(flt.mantbits), digits)
|
||||
ok = true
|
||||
}
|
||||
}
|
||||
if !ok {
|
||||
|
|
|
|||
|
|
@ -77,6 +77,14 @@ var ftoatests = []ftoaTest{
|
|||
{1.2345e6, 'f', 5, "1234500.00000"},
|
||||
{1.2345e6, 'g', 5, "1.2345e+06"},
|
||||
|
||||
// Round to even
|
||||
{1.2345e6, 'e', 3, "1.234e+06"},
|
||||
{1.2355e6, 'e', 3, "1.236e+06"},
|
||||
{1.2345, 'f', 3, "1.234"},
|
||||
{1.2355, 'f', 3, "1.236"},
|
||||
{1234567890123456.5, 'e', 15, "1.234567890123456e+15"},
|
||||
{1234567890123457.5, 'e', 15, "1.234567890123458e+15"},
|
||||
|
||||
{1e23, 'e', 17, "9.99999999999999916e+22"},
|
||||
{1e23, 'f', 17, "99999999999999991611392.00000000000000000"},
|
||||
{1e23, 'g', 17, "9.9999999999999992e+22"},
|
||||
|
|
@ -241,11 +249,19 @@ var ftoaBenches = []struct {
|
|||
{"32Point", 339.7784, 'g', -1, 32},
|
||||
{"32Exp", -5.09e25, 'g', -1, 32},
|
||||
{"32NegExp", -5.11e-25, 'g', -1, 32},
|
||||
{"32Fixed8Hard", math.Ldexp(15961084, -125), 'e', 8, 32},
|
||||
{"32Fixed9Hard", math.Ldexp(14855922, -83), 'e', 9, 32},
|
||||
|
||||
{"64Fixed1", 123456, 'e', 3, 64},
|
||||
{"64Fixed2", 123.456, 'e', 3, 64},
|
||||
{"64Fixed3", 1.23456e+78, 'e', 3, 64},
|
||||
{"64Fixed4", 1.23456e-78, 'e', 3, 64},
|
||||
{"64Fixed12", 1.23456e-78, 'e', 12, 64},
|
||||
{"64Fixed16", 1.23456e-78, 'e', 16, 64},
|
||||
// From testdata/testfp.txt
|
||||
{"64Fixed12Hard", math.Ldexp(6965949469487146, -249), 'e', 12, 64},
|
||||
{"64Fixed17Hard", math.Ldexp(8887055249355788, 665), 'e', 17, 64},
|
||||
{"64Fixed18Hard", math.Ldexp(6994187472632449, 690), 'e', 18, 64},
|
||||
|
||||
// Trigger slow path (see issue #15672).
|
||||
{"Slowpath64", 622666234635.3213e-320, 'e', -1, 64},
|
||||
|
|
|
|||
311
src/strconv/ftoaryu.go
Normal file
311
src/strconv/ftoaryu.go
Normal file
|
|
@ -0,0 +1,311 @@
|
|||
// Copyright 2021 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
|
||||
|
||||
import (
|
||||
"math/bits"
|
||||
)
|
||||
|
||||
// binary to decimal conversion using the Ryū algorithm.
|
||||
//
|
||||
// See Ulf Adams, "Ryū: Fast Float-to-String Conversion" (doi:10.1145/3192366.3192369)
|
||||
//
|
||||
// Fixed precision formatting is a variant of the original paper's
|
||||
// algorithm, where a single multiplication by 10^k is required,
|
||||
// sharing the same rounding guarantees.
|
||||
|
||||
// ryuFtoaFixed32 formats mant*(2^exp) with prec decimal digits.
|
||||
func ryuFtoaFixed32(d *decimalSlice, mant uint32, exp int, prec int) {
|
||||
if prec < 0 {
|
||||
panic("ryuFtoaFixed32 called with negative prec")
|
||||
}
|
||||
if prec > 9 {
|
||||
panic("ryuFtoaFixed32 called with prec > 9")
|
||||
}
|
||||
// Zero input.
|
||||
if mant == 0 {
|
||||
d.nd, d.dp = 0, 0
|
||||
return
|
||||
}
|
||||
// Renormalize to a 25-bit mantissa.
|
||||
e2 := exp
|
||||
if b := bits.Len32(mant); b < 25 {
|
||||
mant <<= uint(25 - b)
|
||||
e2 += int(b) - 25
|
||||
}
|
||||
// Choose an exponent such that rounded mant*(2^e2)*(10^q) has
|
||||
// at least prec decimal digits, i.e
|
||||
// mant*(2^e2)*(10^q) >= 10^(prec-1)
|
||||
// Because mant >= 2^24, it is enough to choose:
|
||||
// 2^(e2+24) >= 10^(-q+prec-1)
|
||||
// or q = -mulByLog2Log10(e2+24) + prec - 1
|
||||
q := -mulByLog2Log10(e2+24) + prec - 1
|
||||
|
||||
// Now compute mant*(2^e2)*(10^q).
|
||||
// Is it an exact computation?
|
||||
// Only small positive powers of 10 are exact (5^28 has 66 bits).
|
||||
exact := q <= 27 && q >= 0
|
||||
|
||||
di, dexp2, d0 := mult64bitPow10(mant, e2, q)
|
||||
if dexp2 >= 0 {
|
||||
panic("not enough significant bits after mult64bitPow10")
|
||||
}
|
||||
// As a special case, computation might still be exact, if exponent
|
||||
// was negative and if it amounts to computing an exact division.
|
||||
// In that case, we ignore all lower bits.
|
||||
// Note that division by 10^11 cannot be exact as 5^11 has 26 bits.
|
||||
if q < 0 && q >= -10 && divisibleByPower5(uint64(mant), -q) {
|
||||
exact = true
|
||||
d0 = true
|
||||
}
|
||||
// Remove extra lower bits and keep rounding info.
|
||||
extra := uint(-dexp2)
|
||||
extraMask := uint32(1<<extra - 1)
|
||||
|
||||
di, dfrac := di>>extra, di&extraMask
|
||||
roundUp := false
|
||||
if exact {
|
||||
// If we computed an exact product, d + 1/2
|
||||
// should round to d+1 if 'd' is odd.
|
||||
roundUp = dfrac > 1<<(extra-1) ||
|
||||
(dfrac == 1<<(extra-1) && !d0) ||
|
||||
(dfrac == 1<<(extra-1) && d0 && di&1 == 1)
|
||||
} else {
|
||||
// otherwise, d+1/2 always rounds up because
|
||||
// we truncated below.
|
||||
roundUp = dfrac>>(extra-1) == 1
|
||||
}
|
||||
if dfrac != 0 {
|
||||
d0 = false
|
||||
}
|
||||
// Proceed to the requested number of digits
|
||||
formatDecimal(d, uint64(di), !d0, roundUp, prec)
|
||||
// Adjust exponent
|
||||
d.dp -= q
|
||||
}
|
||||
|
||||
// ryuFtoaFixed64 formats mant*(2^exp) with prec decimal digits.
|
||||
func ryuFtoaFixed64(d *decimalSlice, mant uint64, exp int, prec int) {
|
||||
if prec > 18 {
|
||||
panic("ryuFtoaFixed64 called with prec > 18")
|
||||
}
|
||||
// Zero input.
|
||||
if mant == 0 {
|
||||
d.nd, d.dp = 0, 0
|
||||
return
|
||||
}
|
||||
// Renormalize to a 55-bit mantissa.
|
||||
e2 := exp
|
||||
if b := bits.Len64(mant); b < 55 {
|
||||
mant = mant << uint(55-b)
|
||||
e2 += int(b) - 55
|
||||
}
|
||||
// Choose an exponent such that rounded mant*(2^e2)*(10^q) has
|
||||
// at least prec decimal digits, i.e
|
||||
// mant*(2^e2)*(10^q) >= 10^(prec-1)
|
||||
// Because mant >= 2^54, it is enough to choose:
|
||||
// 2^(e2+54) >= 10^(-q+prec-1)
|
||||
// or q = -mulByLog2Log10(e2+54) + prec - 1
|
||||
//
|
||||
// The minimal required exponent is -mulByLog2Log10(1025)+18 = -291
|
||||
// The maximal required exponent is mulByLog2Log10(1074)+18 = 342
|
||||
q := -mulByLog2Log10(e2+54) + prec - 1
|
||||
|
||||
// Now compute mant*(2^e2)*(10^q).
|
||||
// Is it an exact computation?
|
||||
// Only small positive powers of 10 are exact (5^55 has 128 bits).
|
||||
exact := q <= 55 && q >= 0
|
||||
|
||||
di, dexp2, d0 := mult128bitPow10(mant, e2, q)
|
||||
if dexp2 >= 0 {
|
||||
panic("not enough significant bits after mult128bitPow10")
|
||||
}
|
||||
// As a special case, computation might still be exact, if exponent
|
||||
// was negative and if it amounts to computing an exact division.
|
||||
// In that case, we ignore all lower bits.
|
||||
// Note that division by 10^23 cannot be exact as 5^23 has 54 bits.
|
||||
if q < 0 && q >= -22 && divisibleByPower5(mant, -q) {
|
||||
exact = true
|
||||
d0 = true
|
||||
}
|
||||
// Remove extra lower bits and keep rounding info.
|
||||
extra := uint(-dexp2)
|
||||
extraMask := uint64(1<<extra - 1)
|
||||
|
||||
di, dfrac := di>>extra, di&extraMask
|
||||
roundUp := false
|
||||
if exact {
|
||||
// If we computed an exact product, d + 1/2
|
||||
// should round to d+1 if 'd' is odd.
|
||||
roundUp = dfrac > 1<<(extra-1) ||
|
||||
(dfrac == 1<<(extra-1) && !d0) ||
|
||||
(dfrac == 1<<(extra-1) && d0 && di&1 == 1)
|
||||
} else {
|
||||
// otherwise, d+1/2 always rounds up because
|
||||
// we truncated below.
|
||||
roundUp = dfrac>>(extra-1) == 1
|
||||
}
|
||||
if dfrac != 0 {
|
||||
d0 = false
|
||||
}
|
||||
// Proceed to the requested number of digits
|
||||
formatDecimal(d, di, !d0, roundUp, prec)
|
||||
// Adjust exponent
|
||||
d.dp -= q
|
||||
}
|
||||
|
||||
// formatDecimal fills d with at most prec decimal digits
|
||||
// of mantissa m. The boolean trunc indicates whether m
|
||||
// is truncated compared to the original number being formatted.
|
||||
func formatDecimal(d *decimalSlice, m uint64, trunc bool, roundUp bool, prec int) {
|
||||
max := uint64pow10[prec]
|
||||
trimmed := 0
|
||||
for m >= max {
|
||||
a, b := m/10, m%10
|
||||
m = a
|
||||
trimmed++
|
||||
if b > 5 {
|
||||
roundUp = true
|
||||
} else if b < 5 {
|
||||
roundUp = false
|
||||
} else { // b == 5
|
||||
// round up if there are trailing digits,
|
||||
// or if the new value of m is odd (round-to-even convention)
|
||||
roundUp = trunc || m&1 == 1
|
||||
}
|
||||
if b != 0 {
|
||||
trunc = true
|
||||
}
|
||||
}
|
||||
if roundUp {
|
||||
m++
|
||||
}
|
||||
if m >= max {
|
||||
// Happens if di was originally 99999....xx
|
||||
m /= 10
|
||||
trimmed++
|
||||
}
|
||||
// render digits (similar to formatBits)
|
||||
n := uint(prec)
|
||||
d.nd = int(prec)
|
||||
v := m
|
||||
for v >= 100 {
|
||||
var v1, v2 uint64
|
||||
if v>>32 == 0 {
|
||||
v1, v2 = uint64(uint32(v)/100), uint64(uint32(v)%100)
|
||||
} else {
|
||||
v1, v2 = v/100, v%100
|
||||
}
|
||||
n -= 2
|
||||
d.d[n+1] = smallsString[2*v2+1]
|
||||
d.d[n+0] = smallsString[2*v2+0]
|
||||
v = v1
|
||||
}
|
||||
if v > 0 {
|
||||
n--
|
||||
d.d[n] = smallsString[2*v+1]
|
||||
}
|
||||
if v >= 10 {
|
||||
n--
|
||||
d.d[n] = smallsString[2*v]
|
||||
}
|
||||
for d.d[d.nd-1] == '0' {
|
||||
d.nd--
|
||||
trimmed++
|
||||
}
|
||||
d.dp = d.nd + trimmed
|
||||
}
|
||||
|
||||
// mulByLog2Log10 returns math.Floor(x * log(2)/log(10)) for an integer x in
|
||||
// the range -1600 <= x && x <= +1600.
|
||||
//
|
||||
// The range restriction lets us work in faster integer arithmetic instead of
|
||||
// slower floating point arithmetic. Correctness is verified by unit tests.
|
||||
func mulByLog2Log10(x int) int {
|
||||
// log(2)/log(10) ≈ 0.30102999566 ≈ 78913 / 2^18
|
||||
return (x * 78913) >> 18
|
||||
}
|
||||
|
||||
// mulByLog10Log2 returns math.Floor(x * log(10)/log(2)) for an integer x in
|
||||
// the range -500 <= x && x <= +500.
|
||||
//
|
||||
// The range restriction lets us work in faster integer arithmetic instead of
|
||||
// slower floating point arithmetic. Correctness is verified by unit tests.
|
||||
func mulByLog10Log2(x int) int {
|
||||
// log(10)/log(2) ≈ 3.32192809489 ≈ 108853 / 2^15
|
||||
return (x * 108853) >> 15
|
||||
}
|
||||
|
||||
// mult64bitPow10 takes a floating-point input with a 25-bit
|
||||
// mantissa and multiplies it with 10^q. The resulting mantissa
|
||||
// is m*P >> 57 where P is a 64-bit element of the detailedPowersOfTen tables.
|
||||
// It is typically 31 or 32-bit wide.
|
||||
// The returned boolean is true if all trimmed bits were zero.
|
||||
//
|
||||
// That is:
|
||||
// m*2^e2 * round(10^q) = resM * 2^resE + ε
|
||||
// exact = ε == 0
|
||||
func mult64bitPow10(m uint32, e2, q int) (resM uint32, resE int, exact bool) {
|
||||
if q == 0 {
|
||||
return m << 7, e2 - 7, true
|
||||
}
|
||||
if q < detailedPowersOfTenMinExp10 || detailedPowersOfTenMaxExp10 < q {
|
||||
// This never happens due to the range of float32/float64 exponent
|
||||
panic("mult64bitPow10: power of 10 is out of range")
|
||||
}
|
||||
pow := detailedPowersOfTen[q-detailedPowersOfTenMinExp10][1]
|
||||
if q < 0 {
|
||||
// Inverse powers of ten must be rounded up.
|
||||
pow += 1
|
||||
}
|
||||
hi, lo := bits.Mul64(uint64(m), pow)
|
||||
e2 += mulByLog10Log2(q) - 63 + 57
|
||||
return uint32(hi<<7 | lo>>57), e2, lo<<7 == 0
|
||||
}
|
||||
|
||||
// mult128bitPow10 takes a floating-point input with a 55-bit
|
||||
// mantissa and multiplies it with 10^q. The resulting mantissa
|
||||
// is m*P >> 119 where P is a 128-bit element of the detailedPowersOfTen tables.
|
||||
// It is typically 63 or 64-bit wide.
|
||||
// The returned boolean is true is all trimmed bits were zero.
|
||||
//
|
||||
// That is:
|
||||
// m*2^e2 * round(10^q) = resM * 2^resE + ε
|
||||
// exact = ε == 0
|
||||
func mult128bitPow10(m uint64, e2, q int) (resM uint64, resE int, exact bool) {
|
||||
if q == 0 {
|
||||
return m << 9, e2 - 9, true
|
||||
}
|
||||
if q < detailedPowersOfTenMinExp10 || detailedPowersOfTenMaxExp10 < q {
|
||||
// This never happens due to the range of float32/float64 exponent
|
||||
panic("mult128bitPow10: power of 10 is out of range")
|
||||
}
|
||||
pow := detailedPowersOfTen[q-detailedPowersOfTenMinExp10]
|
||||
if q < 0 {
|
||||
// Inverse powers of ten must be rounded up.
|
||||
pow[0] += 1
|
||||
}
|
||||
e2 += mulByLog10Log2(q) - 127 + 119
|
||||
|
||||
// long multiplication
|
||||
l1, l0 := bits.Mul64(m, pow[0])
|
||||
h1, h0 := bits.Mul64(m, pow[1])
|
||||
mid, carry := bits.Add64(l1, h0, 0)
|
||||
h1 += carry
|
||||
return h1<<9 | mid>>55, e2, mid<<9 == 0 && l0 == 0
|
||||
}
|
||||
|
||||
func divisibleByPower5(m uint64, k int) bool {
|
||||
if m == 0 {
|
||||
return true
|
||||
}
|
||||
for i := 0; i < k; i++ {
|
||||
if m%5 != 0 {
|
||||
return false
|
||||
}
|
||||
m /= 5
|
||||
}
|
||||
return true
|
||||
}
|
||||
31
src/strconv/ftoaryu_test.go
Normal file
31
src/strconv/ftoaryu_test.go
Normal file
|
|
@ -0,0 +1,31 @@
|
|||
// Copyright 2021 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_test
|
||||
|
||||
import (
|
||||
"math"
|
||||
. "strconv"
|
||||
"testing"
|
||||
)
|
||||
|
||||
func TestMulByLog2Log10(t *testing.T) {
|
||||
for x := -1600; x <= +1600; x++ {
|
||||
iMath := MulByLog2Log10(x)
|
||||
fMath := int(math.Floor(float64(x) * math.Ln2 / math.Ln10))
|
||||
if iMath != fMath {
|
||||
t.Errorf("mulByLog2Log10(%d) failed: %d vs %d\n", x, iMath, fMath)
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
func TestMulByLog10Log2(t *testing.T) {
|
||||
for x := -500; x <= +500; x++ {
|
||||
iMath := MulByLog10Log2(x)
|
||||
fMath := int(math.Floor(float64(x) * math.Ln10 / math.Ln2))
|
||||
if iMath != fMath {
|
||||
t.Errorf("mulByLog10Log2(%d) failed: %d vs %d\n", x, iMath, fMath)
|
||||
}
|
||||
}
|
||||
}
|
||||
|
|
@ -21,3 +21,11 @@ func SetOptimize(b bool) bool {
|
|||
func ParseFloatPrefix(s string, bitSize int) (float64, int, error) {
|
||||
return parseFloatPrefix(s, bitSize)
|
||||
}
|
||||
|
||||
func MulByLog2Log10(x int) int {
|
||||
return mulByLog2Log10(x)
|
||||
}
|
||||
|
||||
func MulByLog10Log2(x int) int {
|
||||
return mulByLog10Log2(x)
|
||||
}
|
||||
|
|
|
|||
Loading…
Reference in a new issue