Thanks for the advice.
This is the piece of code where I use that function:
// compute hat(Du)
pf := float64(p)
for j := 0; j < N; j++ {
ikp := ImagPowN(p) * complex(math.Pow(K[j], pf), 0)
DuHat[j] = ikp * S[j] * A[j]
}
where p is an integer (unbounded), K[j] is a real number from -Inf to +Inf
and S[j] and A[j] are complex (unbounded too)
By using the ImagPowN(p) function, the code is much faster now...
Cheers.
D
On Friday, August 4, 2017 at 10:54:14 AM UTC+10, Michael Jones wrote:
>
> 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 <dorival...@gmail.com
> <javascript:>> 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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>
>
>
> --
> Michael T. Jones
> michae...@gmail.com <javascript:>
>
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