Mike Fisher wrote in a message to RICHARD SKINNER:

 RS> I was wondering, in pascal, how do I return the Cube Root of a number?
 RS> I'm using BP7, I see a SQRT but I don't see anything for the cube root
 RS> and its been so long since school I just can't remember.:)

 RS> Any help would be appreciated,

 MF> The cube root of P is the antilogarithm of one-third of the
 MF> logarithm of P. 

 MF> ie. in Pascal, to calculate the Qth root of P ...

 MF>                root:=exp(ln(P)/Q);

Am I really missing something here, or does Pascal have no support for
direct exponentiation?  The Qth root of P is equal to P raised to the 1/Q
power.  Using C, it is a heck of a lot more efficient to compute a Qth root
as such:

   double P, Q, root;

   root = pow(P, 1.0 / Q);

It is perfectly legal and valid to use logarithmic calculations, but why?

   root = exp(log(P) / Q);

The direct exponentiation form uses a double precision special case
division -- taking a reciprocal -- which corresponds to a machine
instruction on the Intel math coprocessor, while the logarithmic form uses
a double precision division that is not a special case.  The direct
exponentiation form also incurs one function call, while the logarithmic
form incurs two.
 
-- Mike


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