This is the version of a pure imaginary real number raised to the power of
n (integer):
// ImagXpowN computes (x⋅i)ⁿ
//
// (x⋅i)¹ = x¹⋅i (x⋅i)² = -x² (x⋅i)³ = -x³ ⋅i (x⋅i)⁴ =
x⁴
// (x⋅i)⁵ = x⁵⋅i (x⋅i)⁶ = -x⁶ (x⋅i)⁷ = -x⁷ ⋅i (x⋅i)⁸ =
x⁸
// (x⋅i)⁹ = x⁹⋅i (x⋅i)¹⁰ = -x¹⁰ (x⋅i)¹¹ = -x¹¹⋅i (x⋅i)¹² =
x¹²
//
func ImagXpowN(x float64, n int) complex128 {
if n == 0 {
return 1
}
xn := math.Pow(x, float64(n))
switch n % 4 {
case 1:
return complex(0, xn)
case 2:
return complex(-xn, 0)
case 3:
return complex(0, -xn)
}
return complex(xn, 0)
}
These are the benchmark functions:
func BenchmarkImagXpowN(b *testing.B) {
x := 2.5
for i := 0; i < b.N; i++ {
for n := 0; n < 200; n++ {
ImagXpowN(x, n)
}
}
}
func BenchmarkImagXpowNcmplx(b *testing.B) {
x := 2.5
for i := 0; i < b.N; i++ {
for n := 0; n < 200; n++ {
cmplx.Pow(complex(0, x), complex(float64(n), 0))
}
}
}
With the following results:
BenchmarkImagXpowN-32 200000 10299 ns/op
BenchmarkImagXpowNcmplx-32 100000 18595 ns/op
Now it's "just" 1.8x faster.
Cheers
D
On Friday, August 4, 2017 at 10:43:41 AM UTC+10, Dorival Pedroso wrote:
>
> Hi,
>
> This is an interesting benchmark:
>
> Given this function:
> // ImagPowN computes iⁿ = (√-1)ⁿ
> //
> // i¹ = i i² = -1 i³ = -i i⁴ = 1
> // i⁵ = i i⁶ = -1 i⁷ = -i i⁸ = 1
> // i⁹ = i i¹⁰ = -1 i¹¹ = -i i¹² = 1
> //
> func ImagPowN(n int) complex128 {
> if n == 0 {
> return 1
> }
> switch n % 4 {
> case 1:
> return 1i
> case 2:
> return -1
> case 3:
> return -1i
> }
> return 1
> }
>
> And this benchmark test:
> var (
> imagpownRes complex128
> )
>
> func BenchmarkImagPowN(b *testing.B) {
> var res complex128
> for i := 0; i < b.N; i++ {
> for n := 0; n < 200; n++ {
> res = ImagPowN(n)
> }
> }
> imagpownRes = res
> }
>
> func BenchmarkImagPowNcmplx(b *testing.B) {
> var res complex128
> for i := 0; i < b.N; i++ {
> for n := 0; n < 200; n++ {
> res = cmplx.Pow(1i, complex(float64(n), 0))
> }
> }
> imagpownRes = res
> }
>
> We get this output ( go test -run=XXX -bench=. ):
> BenchmarkImagPowN-32 3000000 470 ns/op
> BenchmarkImagPowNcmplx-32 200000 10050 ns/op
>
> A 20x speed up...
>
> Cheers.
> Dorival
>
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