On Thu, Jul 17, 2008 at 05:18:01PM +0200, Henning Thielemann wrote:
On Thu, 17 Jul 2008, stefan kersten 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.
Here's the code: {-# SPECIALISE magnitude :: Complex Double -> Double #-} magnitude :: (RealFloat a) => Complex a -> a magnitude (x:+y) = scaleFloat k (sqrt ((scaleFloat mk x)^(2::Int) + (scaleFloat mk y)^(2::Int))) where k = max (exponent x) (exponent y) mk = - k So the slowdown may be due to the scaling, presumably to prevent overflow as you say. However, the e^(2 :: Int) may also be causing a slowdown, as (^) is lazy in its first argument; I'm not sure if there is a rule that will rewrite that to e*e. Stefan, perhaps you can try timing with the above code, and also with: {-# SPECIALISE magnitude :: Complex Double -> Double #-} magnitude :: (RealFloat a) => Complex a -> a magnitude (x:+y) = scaleFloat k (sqrt (sqr (scaleFloat mk x) + sqr (scaleFloat mk y))) where k = max (exponent x) (exponent y) mk = - k sqr x = x * x and let us know what the results are? Thanks Ian