math: add J0 and Y0 (Bessel functions)
R=rsc
CC=golang-dev
https://golang.org/cl/661044
diff --git a/src/pkg/math/all_test.go b/src/pkg/math/all_test.go
index b28a1f4..4b0aec6 100644
--- a/src/pkg/math/all_test.go
+++ b/src/pkg/math/all_test.go
@@ -298,6 +298,18 @@
9.3834586598354592860187267089e-01,
-2.093995902923148389186189429e-05,
}
+var j0 = []float64{
+ -1.8444682230601672018219338e-01,
+ 2.27353668906331975435892e-01,
+ 9.809259936157051116270273e-01,
+ -1.741170131426226587841181e-01,
+ -2.1389448451144143352039069e-01,
+ -2.340905848928038763337414e-01,
+ -1.0029099691890912094586326e-01,
+ -1.5466726714884328135358907e-01,
+ 3.252650187653420388714693e-01,
+ -8.72218484409407250005360235e-03,
+}
var lgamma = []fi{
fi{3.146492141244545774319734e+00, 1},
fi{8.003414490659126375852113e+00, 1},
@@ -490,6 +502,18 @@
1.0000000000000000e+00,
-8.0000000000000000e+00,
}
+var y0 = []float64{
+ -3.053399153780788357534855e-01,
+ 1.7437227649515231515503649e-01,
+ -8.6221781263678836910392572e-01,
+ -3.100664880987498407872839e-01,
+ 1.422200649300982280645377e-01,
+ 4.000004067997901144239363e-01,
+ -3.3340749753099352392332536e-01,
+ 4.5399790746668954555205502e-01,
+ 4.8290004112497761007536522e-01,
+ 2.7036697826604756229601611e-01,
+}
// arguments and expected results for special cases
var vfacoshSC = []float64{
@@ -811,6 +835,19 @@
MaxInt32,
}
+var vfj0SC = []float64{
+ Inf(-1),
+ 0,
+ Inf(1),
+ NaN(),
+}
+var j0SC = []float64{
+ 0,
+ 1,
+ 0,
+ NaN(),
+}
+
var vflgammaSC = []float64{
Inf(-1),
-3,
@@ -993,6 +1030,19 @@
NaN(),
}
+var vfy0SC = []float64{
+ Inf(-1),
+ 0,
+ Inf(1),
+ NaN(),
+}
+var y0SC = []float64{
+ NaN(),
+ Inf(-1),
+ 0,
+ NaN(),
+}
+
func tolerance(a, b, e float64) bool {
d := a - b
if d < 0 {
@@ -1010,6 +1060,7 @@
func kindaclose(a, b float64) bool { return tolerance(a, b, 1e-8) }
func close(a, b float64) bool { return tolerance(a, b, 1e-14) }
func veryclose(a, b float64) bool { return tolerance(a, b, 4e-16) }
+func soclose(a, b, e float64) bool { return tolerance(a, b, e) }
func alike(a, b float64) bool {
switch {
case IsNaN(a) && IsNaN(b):
@@ -1345,6 +1396,19 @@
}
}
+func TestJ0(t *testing.T) {
+ for i := 0; i < len(vf); i++ {
+ if f := J0(vf[i]); !soclose(j0[i], f, 4e-14) {
+ t.Errorf("J0(%g) = %g, want %g\n", vf[i], f, j0[i])
+ }
+ }
+ for i := 0; i < len(vfj0SC); i++ {
+ if f := J0(vfj0SC[i]); !alike(j0SC[i], f) {
+ t.Errorf("J0(%g) = %g, want %g\n", vfj0SC[i], f, j0SC[i])
+ }
+ }
+}
+
func TestLdexp(t *testing.T) {
for i := 0; i < len(vf); i++ {
if f := Ldexp(frexp[i].f, frexp[i].i); !veryclose(vf[i], f) {
@@ -1576,6 +1640,20 @@
}
}
+func TestY0(t *testing.T) {
+ for i := 0; i < len(vf); i++ {
+ a := Fabs(vf[i])
+ if f := Y0(a); !close(y0[i], f) {
+ t.Errorf("Y0(%g) = %g, want %g\n", a, f, y0[i])
+ }
+ }
+ for i := 0; i < len(vfy0SC); i++ {
+ if f := Y0(vfy0SC[i]); !alike(y0SC[i], f) {
+ t.Errorf("Y0(%g) = %g, want %g\n", vfy0SC[i], f, y0SC[i])
+ }
+ }
+}
+
// Check that math functions of high angle values
// return similar results to low angle values
func TestLargeCos(t *testing.T) {
@@ -1812,6 +1890,12 @@
}
}
+func BenchmarkJ0(b *testing.B) {
+ for i := 0; i < b.N; i++ {
+ J0(2.5)
+ }
+}
+
func BenchmarkLdexp(b *testing.B) {
for i := 0; i < b.N; i++ {
Ldexp(.5, 2)
@@ -1930,3 +2014,9 @@
Trunc(.5)
}
}
+
+func BenchmarkY0(b *testing.B) {
+ for i := 0; i < b.N; i++ {
+ Y0(2.5)
+ }
+}
