Pow() algorithm

[s3lcuk]

hi guys
i just wanna learn Pow(x,y) function codes. In fact how can we compute
base 8 and exponent 1/3 result = 2

[MadCow108]

here's a very detailed page over the square root:
http://www.azillionmonkeys.com/qed/sqroot.html

cubic root calculation should be similar

a little shorter:
http://en.wikipedia.org/wiki/Cube_root#Numerical_methods

the pow function will probably use slower but more general methods but on the same line as the sqrt.

very simple method would be:
pow(x,y){
return exp(y*log(x));
}
but this is terribly slow and surly not used in practice :)

[Zugzwang]

very simple method would be:
pow(x,y){
return exp(y*log(x));
}


Actually, AFAIK, this is precisely the method how POW(x,y) is computed for doubles or floats on a x86 machine. As the floating point unit does not have a "pow" function (at least on a Pentium and before) but only "log" and "exp", this is how things are typically done.

[jabl]

If the exponent argument to pow() is an integer, at least g++ can replace the call to the library function pow(double, double) with the faster



TYPE
NAME (TYPE x, int m)
{
unsigned int n = m < 0 ? -m : m;
TYPE y = n % 2 ? x : 1;
while (n >>= 1)
{
x = x * x;
if (n % 2)
y = y * x;
}
return m < 0 ? 1/y : y;
}
And, if the exponent is a constant integer, it can generate an unrolled version of the above inline.

[tom66]

pow(x, y) -> exp(y * log(x))

log(x) being the natural logarithm and exp being the exponential function [e(x) = e^x]. To compute exp, use the series 1 + x + (x^2/2!) + (x^3/3!)...; usually, 10-15 terms are suitable to calculate to a reasonable degree; and for log, use the identity log(1 + x) = x + (x^2/2) + (x^3/3) + ...

I used this to extend php's bc calculator which had no support for decimal exponents.

[s3lcuk]

thank you all guys for answers
i just took an exam programming yesterday
there will be a couple of question that some well-know functions (i.w sqrt(),pow()) for programming them.

but unfortunetly there weren't any math function questions...
there were string functions instead of them :D

[xander98989]

Where can you see the implementation for the math functions? I looked through math.h, mathcalls.h, and mathdef.h but I can't find them or I can't understand what I'm looking at.

[akvino]

Actually, AFAIK, this is precisely the method how POW(x,y) is computed for doubles or floats on a x86 machine. As the floating point unit does not have a "pow" function (at least on a Pentium and before) but only "log" and "exp", this is how things are typically done.

I learned something new today:

Computation of ab where both a and b are complex
Main article: Exponentiation

Complex exponentiation ab can be defined by converting a to polar coordinates and using the identity (eln(a))b = ab: