Invisible wrote:

> If you're that hell-bent on avoiding the square root, it can be 
> approximated as follows:
> 
>   Suppose that the most significant non-zero digit of x is in the 2^n 
> place. Let y = x / 2^(n/2). Now Sqrt(x) is approximately x / y.
> 
> Usually this estimated value is greater than the true square root (but 
> always by less than 45%). However, exact powers of 2 seem to come out 
> slightly below the true value. (By about 10^-16.) I don't know if that's 
> a glitch in my test program or what... It shouldn't be insurmountable 
> though.

One would have to be very hell-bent indeed to employ, in lieu of sqrt(), 
functions that are probably just as computationally expensive, like ln() 
and exp().  Unless you have a quick way of getting n and 2^(n/2) without 
ln() and exp(), you'll need them.

Now if you know the internal representation of your floats (or doubles), 
you can slap together a union like

union MajorKludge {
	double dvalue;
	char carray[sizeof double];
};

and get both n and 2^(n/2) using some very simple bitwise logical 
operations (as well as code whose portability will be highly suspect).

Regards,
John

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