src/Misc.hs

   1 {-# LANGUAGE RebindableSyntax #-}
   2 {-# LANGUAGE ScopedTypeVariables #-}
   3
   4 -- | Stuff for which I'm too lazy to come up with a decent name.
   5 module Misc
   6 where
   7
   8 import NumericPrelude
   9 import Algebra.Field
  10 import Algebra.RealRing
  11 import Algebra.ToInteger
  12
  13 -- | Partition the interval [@a@, @b@] into @n@ subintervals, which we
  14 --   then return as a list of pairs.
  15 --
  16 --   Examples:
  17 --
  18 --   >>> partition 1 (-1) 1
  19 --   [(-1.0,1.0)]
  20 --
  21 --   >>> partition 4 (-1) 1
  22 --   [(-1.0,-0.5),(-0.5,0.0),(0.0,0.5),(0.5,1.0)]
  23 --
  24 partition :: (Algebra.Field.C a, Algebra.ToInteger.C b, Enum b)
  25           => b -- ^ The number of subintervals to use, @n@
  26           -> a -- ^ The \"left\" endpoint of the interval, @a@
  27           -> a -- ^ The \"right\" endpoint of the interval, @b@
  28           -> [(a,a)]
  29  -- Somebody asked for zero subintervals? Ok.
  30 partition 0 _ _ = []
  31 partition n a b
  32   | n < 0 = error "partition: asked for a negative number of subintervals"
  33   | otherwise =
  34     [ (xi, xj) | k <- [0..n-1],
  35                  let k' = fromIntegral k,
  36                  let xi = a + k'*h,
  37                  let xj = a + (k'+1)*h ]
  38     where
  39       coerced_n = fromIntegral $ toInteger n
  40       h = (b-a)/coerced_n
  41
  42
  43 -- | Compute the unit roundoff (machine epsilon) for this machine. We
  44 --   find the largest number epsilon such that 1+epsilon <= 1. If you
  45 --   request anything other than a Float or Double from this, expect
  46 --   to wait a while.
  47 --
  48 unit_roundoff :: forall a. (Algebra.RealRing.C a, Algebra.Field.C a) => a
  49 unit_roundoff =
  50   head [ 1/2^(k-1) | k <- [0..], 1 + 1/(2^k) <= (1::a) ]