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@rsc /ftoa.go
Created Jul 1, 2011

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Floating Point to Decimal Conversion Is Easy
package main
import (
"fmt"
"math"
"strconv"
)
func ftoa(f float64, prec int) string {
fr, exp := math.Frexp(f)
v := int64(fr * (1<<53))
e := exp - 53
buf := make([]byte, 1000)
n := copy(buf, strconv.Itoa64(v))
for ; e > 0; e-- {
δ := 0
if buf[0] >= '5' {
δ = 1
}
x := byte(0)
for i := n-1; i >= 0; i-- {
x += 2*(buf[i] - '0')
x, buf[i+δ] = x/10, x%10 + '0'
}
if δ == 1 {
buf[0] = '1'
n++
}
}
dp := n
for ; e < 0; e++ {
if buf[n-1]%2 != 0 {
buf[n] = '0'
n++
}
δ, x := 0, byte(0)
if buf[0] < '2' {
δ, x = 1, buf[0] - '0'
n--
dp--
}
for i := 0; i < n; i++ {
x = x*10 + buf[i+δ] - '0'
buf[i], x = x/2 + '0', x%2
}
}
if prec > 0 {
if n > prec {
if buf[prec] > '5' || buf[prec] == '5' && (nonzero(buf[prec+1:n]) || buf[prec-1]%2 == 1) {
i := prec-1
for i >= 0 && buf[i] == '9' {
buf[i] = '0'
i--
}
if i >= 0 {
buf[i]++
} else {
buf[0] = '1'
dp++
}
}
n = prec
}
for n < prec {
buf[n] = '0'
n++
}
}
return fmt.Sprintf("%c.%se%+d", buf[0], buf[1:n], dp-1)
}
func nonzero(buf []byte) bool {
for _, c := range buf {
if c != '0' {
return true
}
}
return false
}
// Difficult boundary cases, derived from tables given in
// Vern Paxson, A Program for Testing IEEE Decimal-Binary Conversion
// ftp://ftp.ee.lbl.gov/testbase-report.ps.Z
//
var ftoaTests = []struct{
N int
F float64
A string
}{
// Table 3: Stress Inputs for Converting 53-bit Binary to Decimal, < 1/2 ULP
{0, math.Ldexp(8511030020275656, -342), "9.e-88"},
{1, math.Ldexp(5201988407066741, -824), "4.6e-233"},
{2, math.Ldexp(6406892948269899, +237), "1.41e+87"},
{3, math.Ldexp(8431154198732492, +72), "3.981e+37"},
{4, math.Ldexp(6475049196144587, +99), "4.1040e+45"},
{5, math.Ldexp(8274307542972842, +726), "2.92084e+234"},
{6, math.Ldexp(5381065484265332, -456), "2.891946e-122"},
{7, math.Ldexp(6761728585499734, -1057), "4.3787718e-303"},
{8, math.Ldexp(7976538478610756, +376), "1.22770163e+129"},
{9, math.Ldexp(5982403858958067, +377), "1.841552452e+129"},
{10, math.Ldexp(5536995190630837, +93), "5.4835744350e+43"},
{11, math.Ldexp(7225450889282194, +710), "3.89190181146e+229"},
{12, math.Ldexp(7225450889282194, +709), "1.945950905732e+229"},
{13, math.Ldexp(8703372741147379, +117), "1.4460958381605e+51"},
{14, math.Ldexp(8944262675275217, -1001), "4.17367747458531e-286"},
{15, math.Ldexp(7459803696087692, -707), "1.107950772878888e-197"},
{16, math.Ldexp(6080469016670379, -381), "1.2345501366327440e-99"},
{17, math.Ldexp(8385515147034757, +721), "9.25031711960365024e+232"},
{18, math.Ldexp(7514216811389786, -828), "4.198047150284889840e-234"},
{19, math.Ldexp(8397297803260511, -345), "1.1716315319786511046e-88"},
{20, math.Ldexp(6733459239310543, +202), "4.32810072844612493629e+76"},
{21, math.Ldexp(8091450587292794, -473), "3.317710118160031081518e-127"},
// Table 4: Stress Inputs for Converting 53-bit Binary to Decimal, > 1/2 ULP
{0, math.Ldexp(6567258882077402, +952), "3.e+302"},
{1, math.Ldexp(6712731423444934, +535), "7.6e+176"},
{2, math.Ldexp(6712731423444934, +534), "3.78e+176"},
{3, math.Ldexp(5298405411573037, -957), "4.350e-273"},
{4, math.Ldexp(5137311167659507, -144), "2.3037e-28"},
{5, math.Ldexp(6722280709661868, +363), "1.26301e+125"},
{6, math.Ldexp(5344436398034927, -169), "7.142211e-36"},
{7, math.Ldexp(8369123604277281, -853), "1.3934574e-241"},
{8, math.Ldexp(8995822108487663, -780), "1.41463449e-219"},
{9, math.Ldexp(8942832835564782, -383), "4.539277920e-100"},
{10, math.Ldexp(8942832835564782, -384), "2.2696389598e-100"},
{11, math.Ldexp(8942832835564782, -385), "1.13481947988e-100"},
{12, math.Ldexp(6965949469487146, -249), "7.700366561890e-60"},
{13, math.Ldexp(6965949469487146, -250), "3.8501832809448e-60"},
{14, math.Ldexp(6965949469487146, -251), "1.92509164047238e-60"},
{15, math.Ldexp(7487252720986826, +548), "6.898586531774201e+180"},
{16, math.Ldexp(5592117679628511, +164), "1.3076622631878654e+65"},
{17, math.Ldexp(8887055249355788, +665), "1.36052020756121240e+216"},
{18, math.Ldexp(6994187472632449, +690), "3.592810217475959676e+223"},
{19, math.Ldexp(8797576579012143, +588), "8.9125197712484551899e+192"},
{20, math.Ldexp(7363326733505337, +272), "5.58769757362301140950e+97"},
{21, math.Ldexp(8549497411294502, -448), "1.176257830728540379990e-119"},
{3, 12345000, "1.234e+7"},
}
func main() {
fmt.Printf("%s\n", ftoa(math.Pi, 50)) // 50 digits of math.Pi (not 50 digits of π)
//fmt.Printf("%s\n", ftoa(math.Nextafter(0, 1), 0))
for _, tt := range ftoaTests {
if a := ftoa(tt.F, tt.N+1); a != tt.A {
fmt.Printf("ftoa(%g, %d) = %q, want %q\n", tt.F, tt.N+1, a, tt.A)
}
}
}
@TechnotronicOz

This comment has been minimized.

TechnotronicOz commented Jan 15, 2015

Line 15 should be n := copy(buf, strconv.FormatInt(v, 10))

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