John VanSickle wrote:
> 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), 

Indeed, the *only* reason you would ever use a construction like this is 
because it's very fast and efficient to get at these numbers using the 
binary representation of a float.

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

Post a reply to this message