Like x^r where both x and r are real numbers, in terms of the number of multiplications and additions required.
I will be very much thankful with detailed explanation or some link to literature. BR
Hello, Syed! Please, try to find something suitable in these books:
1) http://dl.acm.org/citation.cfm?id=1074233
2) http://goo.gl/2dCTfS
3) http://www.jstor.org/discover/10.2307/1994208?uid=2&uid=4&sid=21104573086077
4) http://umsl.edu/~mfrp9/misc/ia.pdf
Best regards and good luck with your research!!!
http://en.wikipedia.org/wiki/Computational_complexity_of_mathematical_operations
Computational complexity when r is an integer is O(log2 r) . The power is computed by the formula recursively as given below
x r = xr/2 . xr/2 when r is even; else x. xr/2. xr/2
For example x31 = x.x15.x15
x15 = x. x7. x7
x7 = x.x3.x3
x3= x.x.x
If r is real the complexity remained the same because r = int(r) + frac(r). Now frac(r)
Dear R. C. Mithal
Thank you very much indeed. Can it be the same as that of exponential function with real power?
BR
Yes. For complexity as r tends to infinity, the value of int (r) also tends to infinity and fract (r) is less than 1.So complexity depends on int(r).
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