[Haskell-cafe] [Solved] rounding errors with real numbers.

26 Feb 2006

      On Sun, Feb 26, 2006 at 01:00:54PM +0000, Chris Kuklewicz wrote:
...
To: Matthias Fischmann 
Cc: haskell-cafe@haskell.org
From: Chris Kuklewicz 
Date: Sun, 26 Feb 2006 13:00:54 +0000
Subject: Re: [Haskell-cafe] rounding errors with real numbers.
Your solution works, but is slightly wasteful with (repair) traversing
the whole list again.  Here is a slightly more efficient expression:
-- Precondition: The first parameter (xs) is sorted (ascending) :
--                 assert (all (zipWith (<=) (xs, tail xs)))
--               low' < high'
--               low  < high
normInterval :: [Double] -> Double -> Double -> [Double]
normInterval xs low high = let low' = head xs; high' = last xs;
                               scale = (high-low)/(high'-low')
                               middle = init (tail xs)
                           in (low : [scale*(x-low')+low) | x <-middle])++[high]
hi chris,

i like this code better, too.  slightly better still, because of fewer
typos:

normInterval :: [Double] -> Double -> Double -> [Double]
normInterval ps lower upper = assert check ([lower] ++ [ stretch * (p - oldLower) + lower | p <- middle ] ++ [upper])
    where
    check = lower < upper && oldLower < oldUpper && (and (zipWith (<=) ps (tail ps)))
    oldLower = head ps
    oldUpper = last ps
    stretch = (upper - lower) / (oldUpper - oldLower)
    middle = init (tail ps)

but then i'll just take this as the best solution.

thanks,
matthias