So it sounds like the special case that would be helpful is when the real
part of the complex base is 0.
On Thu, Aug 3, 2017, 18:26 Dorival Pedroso <dorival.pedr...@gmail.com>
wrote:
> 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>
>> 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
>>
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