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).

See the article attached.