}
}
+func fdiv(a, b float64) float64 { return a / b }
+
const (
below1e23 = 99999999999999974834176
above1e23 = 100000000000000008388608
{1, 'e', 5, "1.00000e+00"},
{1, 'f', 5, "1.00000"},
{1, 'g', 5, "1"},
- // {1, 'g', -1, "1"},
- // {20, 'g', -1, "20"},
- // {1234567.8, 'g', -1, "1.2345678e+06"},
- // {200000, 'g', -1, "200000"},
- // {2000000, 'g', -1, "2e+06"},
+ {1, 'g', -1, "1"},
+ {20, 'g', -1, "20"},
+ {1234567.8, 'g', -1, "1.2345678e+06"},
+ {200000, 'g', -1, "200000"},
+ {2000000, 'g', -1, "2e+06"},
// g conversion and zero suppression
{400, 'g', 2, "4e+02"},
{0, 'e', 5, "0.00000e+00"},
{0, 'f', 5, "0.00000"},
{0, 'g', 5, "0"},
- // {0, 'g', -1, "0"},
+ {0, 'g', -1, "0"},
{-1, 'e', 5, "-1.00000e+00"},
{-1, 'f', 5, "-1.00000"},
{-1, 'g', 5, "-1"},
- // {-1, 'g', -1, "-1"},
+ {-1, 'g', -1, "-1"},
{12, 'e', 5, "1.20000e+01"},
{12, 'f', 5, "12.00000"},
{12, 'g', 5, "12"},
- // {12, 'g', -1, "12"},
+ {12, 'g', -1, "12"},
{123456700, 'e', 5, "1.23457e+08"},
{123456700, 'f', 5, "123456700.00000"},
{123456700, 'g', 5, "1.2346e+08"},
- // {123456700, 'g', -1, "1.234567e+08"},
+ {123456700, 'g', -1, "1.234567e+08"},
{1.2345e6, 'e', 5, "1.23450e+06"},
{1.2345e6, 'f', 5, "1234500.00000"},
{1e23, 'f', 17, "99999999999999991611392.00000000000000000"},
{1e23, 'g', 17, "9.9999999999999992e+22"},
- // {1e23, 'e', -1, "1e+23"},
- // {1e23, 'f', -1, "100000000000000000000000"},
- // {1e23, 'g', -1, "1e+23"},
+ {1e23, 'e', -1, "1e+23"},
+ {1e23, 'f', -1, "100000000000000000000000"},
+ {1e23, 'g', -1, "1e+23"},
{below1e23, 'e', 17, "9.99999999999999748e+22"},
{below1e23, 'f', 17, "99999999999999974834176.00000000000000000"},
{below1e23, 'g', 17, "9.9999999999999975e+22"},
- // {below1e23, 'e', -1, "9.999999999999997e+22"},
- // {below1e23, 'f', -1, "99999999999999970000000"},
- // {below1e23, 'g', -1, "9.999999999999997e+22"},
+ {below1e23, 'e', -1, "9.999999999999997e+22"},
+ {below1e23, 'f', -1, "99999999999999970000000"},
+ {below1e23, 'g', -1, "9.999999999999997e+22"},
{above1e23, 'e', 17, "1.00000000000000008e+23"},
{above1e23, 'f', 17, "100000000000000008388608.00000000000000000"},
- // {above1e23, 'g', 17, "1.0000000000000001e+23"},
+ {above1e23, 'g', 17, "1.0000000000000001e+23"},
- // {above1e23, 'e', -1, "1.0000000000000001e+23"},
- // {above1e23, 'f', -1, "100000000000000010000000"},
- // {above1e23, 'g', -1, "1.0000000000000001e+23"},
+ {above1e23, 'e', -1, "1.0000000000000001e+23"},
+ {above1e23, 'f', -1, "100000000000000010000000"},
+ {above1e23, 'g', -1, "1.0000000000000001e+23"},
- // {fdiv(5e-304, 1e20), 'g', -1, "5e-324"},
- // {fdiv(-5e-304, 1e20), 'g', -1, "-5e-324"},
+ // TODO(gri) track down why these don't work yet
+ // {5e-304/1e20, 'g', -1, "5e-324"},
+ // {-5e-304/1e20, 'g', -1, "-5e-324"},
+ // {fdiv(5e-304, 1e20), 'g', -1, "5e-324"}, // avoid constant arithmetic
+ // {fdiv(-5e-304, 1e20), 'g', -1, "-5e-324"}, // avoid constant arithmetic
- // {32, 'g', -1, "32"},
- // {32, 'g', 0, "3e+01"},
+ {32, 'g', -1, "32"},
+ {32, 'g', 0, "3e+01"},
- // {100, 'x', -1, "%x"},
+ {100, 'x', -1, "%x"},
- // {math.NaN(), 'g', -1, "NaN"},
- // {-math.NaN(), 'g', -1, "NaN"},
+ // {math.NaN(), 'g', -1, "NaN"}, // Float doesn't support NaNs
+ // {-math.NaN(), 'g', -1, "NaN"}, // Float doesn't support NaNs
{math.Inf(0), 'g', -1, "+Inf"},
{math.Inf(-1), 'g', -1, "-Inf"},
{-math.Inf(0), 'g', -1, "-Inf"},
{1.5, 'f', 0, "2"},
// http://www.exploringbinary.com/java-hangs-when-converting-2-2250738585072012e-308/
- // {2.2250738585072012e-308, 'g', -1, "2.2250738585072014e-308"},
+ {2.2250738585072012e-308, 'g', -1, "2.2250738585072014e-308"},
// http://www.exploringbinary.com/php-hangs-on-numeric-value-2-2250738585072011e-308/
- // {2.2250738585072011e-308, 'g', -1, "2.225073858507201e-308"},
+ {2.2250738585072011e-308, 'g', -1, "2.225073858507201e-308"},
// Issue 2625.
{383260575764816448, 'f', 0, "383260575764816448"},
- // {383260575764816448, 'g', -1, "3.8326057576481645e+17"},
+ {383260575764816448, 'g', -1, "3.8326057576481645e+17"},
} {
f := new(Float).SetFloat64(test.x)
got := f.Text(test.format, test.prec)
value interface{} // float32, float64, or string (== 512bit *Float)
want string
}{
- // TODO(gri) uncomment the disabled 'g'/'G' formats
- // below once (*Float).Text supports prec < 0
-
// from fmt/fmt_test.go
{"%+.3e", 0.0, "+0.000e+00"},
{"%+.3e", 1.0, "+1.000e+00"},
{"%f", 1234.5678e-8, "0.000012"},
{"%f", -7.0, "-7.000000"},
{"%f", -1e-9, "-0.000000"},
- // {"%g", 1234.5678e3, "1.2345678e+06"},
- // {"%g", float32(1234.5678e3), "1.2345678e+06"},
- // {"%g", 1234.5678e-8, "1.2345678e-05"},
+ {"%g", 1234.5678e3, "1.2345678e+06"},
+ {"%g", float32(1234.5678e3), "1.2345678e+06"},
+ {"%g", 1234.5678e-8, "1.2345678e-05"},
{"%g", -7.0, "-7"},
{"%g", -1e-9, "-1e-09"},
{"%g", float32(-1e-9), "-1e-09"},
{"%E", 1234.5678e-8, "1.234568E-05"},
{"%E", -7.0, "-7.000000E+00"},
{"%E", -1e-9, "-1.000000E-09"},
- // {"%G", 1234.5678e3, "1.2345678E+06"},
- // {"%G", float32(1234.5678e3), "1.2345678E+06"},
- // {"%G", 1234.5678e-8, "1.2345678E-05"},
+ {"%G", 1234.5678e3, "1.2345678E+06"},
+ {"%G", float32(1234.5678e3), "1.2345678E+06"},
+ {"%G", 1234.5678e-8, "1.2345678E-05"},
{"%G", -7.0, "-7"},
{"%G", -1e-9, "-1E-09"},
{"%G", float32(-1e-9), "-1E-09"},
{"%-20f", 1.23456789e3, "1234.567890 "},
{"%20.8f", 1.23456789e3, " 1234.56789000"},
{"%20.8f", 1.23456789e-3, " 0.00123457"},
- // {"%g", 1.23456789e3, "1234.56789"},
- // {"%g", 1.23456789e-3, "0.00123456789"},
- // {"%g", 1.23456789e20, "1.23456789e+20"},
+ {"%g", 1.23456789e3, "1234.56789"},
+ {"%g", 1.23456789e-3, "0.00123456789"},
+ {"%g", 1.23456789e20, "1.23456789e+20"},
{"%20e", math.Inf(1), " +Inf"},
{"%-20f", math.Inf(-1), "-Inf "},
// the total number of digits. A negative precision selects the smallest
// number of digits necessary to identify the value x uniquely.
// The prec value is ignored for the 'b' or 'p' format.
-//
-// BUG(gri) Float.Text does not accept negative precisions (issue #10991).
func (x *Float) Text(format byte, prec int) string {
const extra = 10 // TODO(gri) determine a good/better value here
return string(x.Append(make([]byte, 0, prec+extra), format, prec))
// 1) convert Float to multiprecision decimal
var d decimal // == 0.0
if x.form == finite {
+ // x != 0
d.init(x.mant, int(x.exp)-x.mant.bitLen())
}
shortest := false
if prec < 0 {
shortest = true
- panic("unimplemented")
- // TODO(gri) complete this
- // roundShortest(&d, f.mant, int(f.exp))
+ roundShortest(&d, x)
// Precision for shortest representation mode.
switch fmt {
case 'e', 'E':
return append(buf, '%', fmt)
}
+func roundShortest(d *decimal, x *Float) {
+ // if the mantissa is zero, the number is zero - stop now
+ if len(d.mant) == 0 {
+ return
+ }
+
+ // Approach: All numbers in the interval [x - 1/2ulp, x + 1/2ulp]
+ // (possibly exclusive) round to x for the given precision of x.
+ // Compute the lower and upper bound in decimal form and find the
+ // the shortest decimal number d such that lower <= d <= upper.
+
+ // TODO(gri) strconv/ftoa.do describes a shortcut in some cases.
+ // See if we can use it (in adjusted form) here as well.
+
+ // 1) Compute normalized mantissa mant and exponent exp for x such
+ // that the lsb of mant corresponds to 1/2 ulp for the precision of
+ // x (i.e., for mant we want x.prec + 1 bits).
+ mant := nat(nil).set(x.mant)
+ exp := int(x.exp) - mant.bitLen()
+ s := mant.bitLen() - int(x.prec+1)
+ switch {
+ case s < 0:
+ mant = mant.shl(mant, uint(-s))
+ case s > 0:
+ mant = mant.shr(mant, uint(+s))
+ }
+ exp += s
+ // x = mant * 2**exp with lsb(mant) == 1/2 ulp of x.prec
+
+ // 2) Compute lower bound by subtracting 1/2 ulp.
+ var lower decimal
+ var tmp nat
+ lower.init(tmp.sub(mant, natOne), exp)
+
+ // 3) Compute upper bound by adding 1/2 ulp.
+ var upper decimal
+ upper.init(tmp.add(mant, natOne), exp)
+
+ // The upper and lower bounds are possible outputs only if
+ // the original mantissa is even, so that ToNearestEven rounding
+ // would round to the original mantissa and not the neighbors.
+ inclusive := mant[0]&2 == 0 // test bit 1 since original mantissa was shifted by 1
+
+ // Now we can figure out the minimum number of digits required.
+ // Walk along until d has distinguished itself from upper and lower.
+ for i, m := range d.mant {
+ l := byte('0') // lower digit
+ if i < len(lower.mant) {
+ l = lower.mant[i]
+ }
+ u := byte('0') // upper digit
+ if i < len(upper.mant) {
+ u = upper.mant[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 == len(lower.mant)
+
+ // 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 < len(upper.mant))
+
+ // 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
+ }
+ }
+}
+
// %e: d.ddddde±dd
func fmtE(buf []byte, fmt byte, prec int, d decimal) []byte {
// first digit
fallthrough
case 'g', 'G':
if !hasPrec {
- // TODO(gri) uncomment once (*Float).Text handles prec < 0
- // prec = -1 // default precision for 'g', 'G'
+ prec = -1 // default precision for 'g', 'G'
}
default:
fmt.Fprintf(s, "%%!%c(*big.Float=%s)", format, x.String())