the complex power function is a difficult (time consuming) general
computation.
are you saying that you actually have a program that uses boolean gaussian
integers and needs to do lots of power operations?
if so, i highly recommend that you special case this for your own use.
if this is common then the power code could stop and check for Re(x) in
{-1,0,1} and Im(x) in {-1,0,1} before undertaking the general computation.
On Thu, Aug 3, 2017 at 5:43 PM, Dorival Pedroso <[email protected]>
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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