src/Comparisons.hs

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