math: fix Gamma(x) for x < -170.5 and other corner cases
Fixes #11441.
Test tables generated by
package main
import (
"bytes"
"fmt"
"log"
"os/exec"
"strconv"
"strings"
)
var inputs = []float64{
0.5,
1.5,
2.5,
3.5,
-0.5,
-1.5,
-2.5,
-3.5,
0.1,
0.01,
1e-8,
1e-16,
1e-3,
1e-16,
1e-308,
5.6e-309,
5.5e-309,
1e-309,
1e-323,
5e-324,
-0.1,
-0.01,
-1e-8,
-1e-16,
-1e-3,
-1e-16,
-1e-308,
-5.6e-309,
-5.5e-309,
-1e-300 / 1e9,
-1e-300 / 1e23,
-5e-300 / 1e24,
-0.
9999999999999999,
-1.
0000000000000002,
-1.
9999999999999998,
-2.
0000000000000004,
-100.
00000000000001,
-99.
999999999999986,
17,
171,
171.6,
171.624,
171.625,
172,
2000,
-100.5,
-160.5,
-170.5,
-171.5,
-176.5,
-177.5,
-178.5,
-179.5,
-201.0001,
-202.9999,
-1000.5,
-
1000000000.3,
-
4503599627370495.5,
-63.
349078729022985,
-127.
45117632943295,
}
func main() {
var buf bytes.Buffer
for _, v := range inputs {
fmt.Fprintf(&buf, "gamma(%.1000g)\n", v)
}
cmd := exec.Command("gp", "-q")
cmd.Stdin = &buf
out, err := cmd.CombinedOutput()
if err != nil {
log.Fatalf("gp: %v", err)
}
f := strings.Split(string(out), "\n")
if len(f) > 0 && f[len(f)-1] == "" {
f = f[:len(f)-1]
}
if len(f) != len(inputs) {
log.Fatalf("gp: wrong output count\n%s\n", out)
}
for i, g := range f {
gf, err := strconv.ParseFloat(strings.Replace(g, " E", "e", -1), 64)
if err != nil {
if strings.Contains(err.Error(), "value out of range") {
if strings.HasPrefix(g, "-") {
fmt.Printf("\t{%g, Inf(-1)},\n", inputs[i])
} else {
fmt.Printf("\t{%g, Inf(1)},\n", inputs[i])
}
continue
}
log.Fatal(err)
}
if gf == 0 && strings.HasPrefix(g, "-") {
fmt.Printf("\t{%g, Copysign(0, -1)},\n", inputs[i])
continue
}
fmt.Printf("\t{%g, %g},\n", inputs[i], gf)
}
}
Change-Id: Ie98c7751d92b8ffb40e8313f5ea10df0890e2feb
Reviewed-on: https://go-review.googlesource.com/30146
Run-TryBot: Russ Cox <rsc@golang.org>
Reviewed-by: Quentin Smith <quentin@golang.org>