[Haskell-cafe] Data.Complex.magnitude slow?

[Henning Thielemann]

On Thu, 17 Jul 2008, stefan kersten wrote:

> On 17.07.2008, at 17:18, Henning Thielemann wrote:
>>> i've attached an example program which seems to indicate that the 
>>> magnitude function from Data.Complex is very slow compared to a more naive 
>>> implementation (for Complex Float). on my machine (intel core2 duo, osx 
>>> 10.4) the CPU time using the library function is about 6-7 times as much 
>>> as when using the other function. any ideas what might be going on? any 
>>> flaws in my measurement code?
>> 
>> Complex.magnitude must prevent overflows, that is, if you just square 
>> 1e200::Double you get an overflow, although the end result may be also 
>> around 1e200. I guess, that to this end Complex.magnitude will separate 
>> mantissa and exponent, but this is done via Integers, I'm afraid.
>
> very enlightening, thanks! it might be possible to (almost) get the best of 
> two worlds (ported from dejagnu's libm):
>
> c_magnitude4 :: Complex Float -> Float
> c_magnitude4 (x:+y) = if x' < y'
>                       then mag y' x'
>                       else mag x' y'
>   where
>       x'      = abs x
>       y'      = abs y
>       sqr x   = x * x
>       mag a 0 = a
>       mag a b = a * sqrt (1 + sqr (b/a))
>
> is fast and doesn't overflow intermediate results but accuracy isn't so great 
> ...

Yes, that's also a possible work-around. But division is quite slow.