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math: special cases for Pow

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R=rsc
CC=golang-dev
https://golang.org/cl/176064
This commit is contained in:
Charles L. Dorian 2009-12-15 20:43:12 -08:00 committed by Russ Cox
parent 3269647502
commit d5bcf7bf41
2 changed files with 202 additions and 5 deletions
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152
src/pkg/math/all_test.go
View File

@ -154,6 +154,126 @@ var tanh = []float64{
9.4936501296239700e-01,
-9.9999994291374019e-01,
}
var vfsin = []float64{
NaN(),
Inf(-1),
0,
Inf(1),
}
var vfasin = []float64{
NaN(),
-Pi,
0,
Pi,
}
var vf1 = []float64{
NaN(),
Inf(-1),
-Pi,
-1,
0,
1,
Pi,
Inf(1),
}
var vfhypot = [][2]float64{
[2]float64{Inf(-1), 1},
[2]float64{Inf(1), 1},
[2]float64{1, Inf(-1)},
[2]float64{1, Inf(1)},
[2]float64{NaN(), Inf(-1)},
[2]float64{NaN(), Inf(1)},
[2]float64{1, NaN()},
[2]float64{NaN(), 1},
}
var vf2 = [][2]float64{
[2]float64{-Pi, Pi},
[2]float64{-Pi, -Pi},
[2]float64{Inf(-1), 3},
[2]float64{Inf(-1), Pi},
[2]float64{Inf(-1), -3},
[2]float64{Inf(-1), -Pi},
[2]float64{Inf(1), Pi},
[2]float64{0, -Pi},
[2]float64{Inf(1), -Pi},
[2]float64{0, Pi},
[2]float64{-1, Inf(-1)},
[2]float64{-1, Inf(1)},
[2]float64{1, Inf(-1)},
[2]float64{1, Inf(1)},
[2]float64{-1 / 2, Inf(1)},
[2]float64{1 / 2, Inf(1)},
[2]float64{-Pi, Inf(-1)},
[2]float64{Pi, Inf(-1)},
[2]float64{-1 / 2, Inf(-1)},
[2]float64{1 / 2, Inf(-1)},
[2]float64{-Pi, Inf(1)},
[2]float64{Pi, Inf(1)},
[2]float64{NaN(), -Pi},
[2]float64{NaN(), Pi},
[2]float64{Inf(-1), NaN()},
[2]float64{-Pi, NaN()},
[2]float64{0, NaN()},
[2]float64{Pi, NaN()},
[2]float64{Inf(1), NaN()},
[2]float64{NaN(), NaN()},
[2]float64{Inf(-1), 1},
[2]float64{-Pi, 1},
[2]float64{0, 1},
[2]float64{Pi, 1},
[2]float64{Inf(1), 1},
[2]float64{NaN(), 1},
[2]float64{Inf(-1), 0},
[2]float64{-Pi, 0},
[2]float64{0, 0},
[2]float64{Pi, 0},
[2]float64{Inf(1), 0},
[2]float64{NaN(), 0},
}
var pow2 = []float64{
NaN(),
NaN(),
Inf(-1),
Inf(1),
0,
0,
Inf(1),
Inf(1),
0,
0,
NaN(),
NaN(),
NaN(),
NaN(),
0,
0,
0,
0,
Inf(1),
Inf(1),
Inf(1),
Inf(1),
NaN(),
NaN(),
NaN(),
NaN(),
NaN(),
NaN(),
NaN(),
NaN(),
Inf(-1),
-Pi,
0,
Pi,
Inf(1),
NaN(),
1,
1,
1,
1,
1,
1,
}
func tolerance(a, b, e float64) bool {
d := a - b
@ -172,6 +292,19 @@ func tolerance(a, b, e float64) bool {
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 alike(a, b float64) bool {
switch {
case IsNaN(a) && IsNaN(b):
return true
case IsInf(a, 1) && IsInf(b, 1):
return true
case IsInf(a, -1) && IsInf(b, -1):
return true
case a == b:
return true
}
return false
}
func TestAsin(t *testing.T) {
for i := 0; i < len(vf); i++ {
@ -223,6 +356,11 @@ func TestPow(t *testing.T) {
t.Errorf("Pow(10, %.17g) = %.17g, want %.17g\n", vf[i], f, pow[i])
}
}
for i := 0; i < len(vf2); i++ {
if f := Pow(vf2[i][0], vf2[i][1]); !alike(pow2[i], f) {
t.Errorf("Pow(%.17g, %.17g) = %.17g, want %.17g\n", vf2[i][0], vf2[i][1], f, pow2[i])
}
}
}
func TestSin(t *testing.T) {
@ -336,3 +474,17 @@ func TestFloatMinMax(t *testing.T) {
}
}
}
// Benchmarks
func BenchmarkPowInt(b *testing.B) {
for i := 0; i < b.N; i++ {
Pow(2, 2)
}
}
func BenchmarkPowFrac(b *testing.B) {
for i := 0; i < b.N; i++ {
Pow(2.5, 1.5)
}
}

55
src/pkg/math/pow.go
View File

@ -4,23 +4,68 @@
package math
func isOddInt(x float64) bool {
xi, xf := Modf(x)
return xf == 0 && int64(xi)&1 == 1
}
// Pow returns x**y, the base-x exponential of y.
func Pow(x, y float64) float64 {
// TODO: x or y NaN, ±Inf, maybe ±0.
// TODO: maybe ±0.
// TODO(rsc): Remove manual inlining of IsNaN, IsInf
// when compiler does it for us
switch {
case y == 0:
return 1
case y == 1:
return x
case x == 0 && y > 0:
return 0
case x == 0 && y < 0:
return Inf(1)
case y == 0.5:
return Sqrt(x)
case y == -0.5:
return 1 / Sqrt(x)
case x != x || y != y: // IsNaN(x) || IsNaN(y):
return NaN()
case x == 0:
switch {
case y < 0:
return Inf(1)
case y > 0:
return 0
}
case y > MaxFloat64 || y < -MaxFloat64: // IsInf(y, 0):
switch {
case Fabs(x) == 1:
return NaN()
case Fabs(x) < 1:
switch {
case IsInf(y, -1):
return Inf(1)
case IsInf(y, 1):
return 0
}
case Fabs(x) > 1:
switch {
case IsInf(y, -1):
return 0
case IsInf(y, 1):
return Inf(1)
}
}
case x > MaxFloat64 || x < -MaxFloat64: // IsInf(x, 0):
switch {
case y < 0:
return 0
case y > 0:
switch {
case IsInf(x, -1):
if isOddInt(y) {
return Inf(-1)
}
return Inf(1)
case IsInf(x, 1):
return Inf(1)
}
}
}
absy := y