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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