[Haskell-cafe] Data.Complex.magnitude slow?
stefan kersten
sk at k-hornz.de
Thu Jul 17 15:21:32 EDT 2008
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 ...
<sk>
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