src/Comparisons.hs

   1 -- | Functions for comparing 'Double' values.
   2 module Comparisons (
   3   (~=),
   4   (~~=),
   5   almost_equals,
   6   kinda_equals,
   7   nearly_equals,
   8   nearly_ge,
   9   non_very_positive_entries,
  10   very_positive,
  11   )
  12 where
  13
  14 -- | epsilon is the value that will be used in all tests that require
  15 --   some measure of \"closeness.\" Increasing it will make those
  16 --   tests more tolerant.
  17 epsilon :: Double
  18 epsilon = 0.0001
  19
  20 -- | A tiny margin of error.
  21 theta :: Double
  22 theta = 0.0000000000001
  23
  24 -- | x almost equals y if x is within 'theta' of y.
  25 nearly_equals :: Double -> Double -> Bool
  26 nearly_equals x y = (abs (x - y)) < theta
  27
  28 -- | Nearly greater-than or equal-to.
  29 nearly_ge :: Double -> Double -> Bool
  30 x `nearly_ge` y = (x > y) || (x `nearly_equals` y)
  31
  32 -- | x almost equals y if x is within 'epsilon' of y.
  33 almost_equals :: Double -> Double -> Bool
  34 almost_equals x y = (abs (x - y)) < epsilon
  35
  36 infix 4 ~=
  37 (~=) :: Double -> Double -> Bool
  38 (~=) = almost_equals
  39
  40
  41 -- | Like 'almost_equals', except much more tolerant. The difference
  42 --   between the two arguments must be less than one percent of the sum
  43 --   of their magnitudes.
  44 kinda_equals :: Double -> Double -> Bool
  45 kinda_equals x y =
  46     (abs (x - y)) < threshold
  47     where
  48       threshold = ((abs x) + (abs y)) / 100.0
  49
  50 infix 4 ~~=
  51 (~~=) :: Double -> Double -> Bool
  52 (~~=) = kinda_equals
  53
  54
  55 -- | x is very positive if it is 'epsilon' greater than zero.
  56 very_positive :: Double -> Bool
  57 very_positive x =  x - epsilon > 0
  58
  59
  60 -- | Takes a list of 'Double' and returns the ones which are not very
  61 --   positive.
  62 non_very_positive_entries :: [Double] -> [Double]
  63 non_very_positive_entries = filter (not . very_positive)