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How to write your own Pow() function in C?

+5 votes
2,115 views

I don't want to use any library functions, Interested in How to write your own Pow(X(double),Y(double)) functions in most optimized way... can somebody help me out?

posted Jan 6, 2014 by Atiqur Rahman

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1 Answer

+1 vote

Not sure what you are looking but power for the floating point is calculated using log and exp operation. See this is what you require - 

double Pow(double x, double y) {
    return exp(log(x)*y);
}

Let me know if something different is needed.

answer Jan 6, 2014 by Salil Agrawal
exp(log(x)*y); this much i could do...now things how to calculate exp and log(x)... in most optimized way(but I don't want to use any lib. function not even log and exp)
commented Jan 6, 2014 by Atiqur Rahman
use

e^{x} = 1 + x + {x^2}{2!} + {x^3}{3!} + ... for all x
log(1-x) = - {x} - {x^2}/2 - {x^3}/3 ...   |x| < 1

Now say you want to calculate 2.5^3.5 break it to (2.5^3)*(2.5^.5) where first part is simple and for second part u need to apply exp and log operations which has power operations but power part is integer...
commented Jan 6, 2014 by Salil Agrawal
Nice explanation Salil, I don't think we have any other way...
commented Jan 6, 2014 by Amit Mishra
@Atiqur: Is your problem solved???
commented Jan 7, 2014 by Salil Agrawal
In your example, |x| > 1, it is 2.5.  How can we use log(1-x) equation?
Thanks
commented Jun 20, 2014 by anonymous
I think you have missed one point say you want to calculate 2.5^3.5 break it to (2.5^3)*(2.5^.5) now first part is easy we just need the 2.5^.5 where x = .5

I hope this should clear your doubt.
commented Jun 20, 2014 by Salil Agrawal
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How can pow() function of C output the exact value of a^b without any precision loss? 
#include <stdio.h>
#include<math.h>
int main()
{

  printf("%.0f",pow(2,1023));

  return 0;
}

Output: 89884656743115795386465259539451236680898848947115328636715040578866337902750481566354238661203768010560056939935696678829394884407208311246423715319737062188883946712432742638151109800623047059726541476042502884419075341171231440736956555270413618581675255342293149119973622969239858152417678164812112068608

Now question is how is it achieved for such a big number?

...