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# rsc/ftoa.go

Created July 1, 2011 04:34
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Floating Point to Decimal Conversion Is Easy
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 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 commented Jan 15, 2015

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