Well, if you are relying on exact results from floating point arithmetic you're in trouble no matter what you do. I would just ignore the slight error and when finally printing the results do some rounding. Trying to fudge things is just going to bite you somewhere else. (BTW, I much prefer the name "floating point" to "real". I think the latter should be reserved for when you actually have real numbers.) -- Lennart Matthias Fischmann wrote:
hi,
I think this is the well-known issue of using real numbers in decimal representation on a machine that thinks binary, but I don't know what to do with it, and some of you maybe do.
I want to shift+stretch a list of doubles into a given interval. example:
| x1 = [2, 3, 4, 5, 10] | y1 = normInterval x1 0 1 | => y1 = [0.0,0.125,0.25,0.375,1.0]
The function that does this looks something like this:
| normInterval :: [Double] -> Double -> Double -> [Double] | normInterval ps lower upper = map (\ x -> (x - oldLower) * stretch + lower) ps | where | oldLower = head ps | oldUpper = last ps | stretch = (upper - lower) / (oldUpper - oldLower)
However, with bigger numbers I get rounding errors:
| x2 = [0.0,1.9569471624266144e-3,5.870841487279843e-3,1.5655577299412915e-2,3.913894324853229e-2,9.393346379647749e-2,0.2191780821917808,0.5009784735812133,1.1272015655577299,2.504892367906066] | y2 = normInterval x2 0 1 | => y2 = [0.0,7.8125e-4,2.3437500000000003e-3,6.25e-3,1.5625000000000003e-2,3.7500000000000006e-2,8.750000000000001e-2,0.2,0.45000000000000007,0.9999999999999999]
The solution that pops to my mind is very simple:
| normInterval :: [Double] -> Double -> Double -> [Double] | normInterval ps lower upper = repair (map (\ x -> (x - oldLower) * stretch + lower) ps) | where | oldLower = head ps | oldUpper = last ps | stretch = (upper - lower) / (oldUpper - oldLower) | | -- fix rounding error: | repair [i] = [upper] | repair (h:t) = h : repair t
It works, but it's ugly. Is there a better way to do this?
Thanks, Matthias
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