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 where
  12
  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   --
  18 epsilon :: Double
  19 epsilon = 0.0001
  20
  21
  22 -- | A tiny margin of error.
  23 --
  24 theta :: Double
  25 theta = 0.0000000000001
  26
  27
  28 -- | x almost equals y if x is within 'theta' of y.
  29 --
  30 --   Only used in tests.
  31 --
  32 nearly_equals :: Double -> Double -> Bool
  33 nearly_equals x y =
  34   (abs (x - y)) < theta
  35
  36
  37 -- | Nearly greater-than or equal-to.
  38 --
  39 --   Only used in tests.
  40 --
  41 nearly_ge :: Double -> Double -> Bool
  42 x `nearly_ge` y =
  43   (x > y) || (x `nearly_equals` y)
  44
  45
  46 -- | x almost equals y if x is within 'epsilon' of y.
  47 --
  48 --   Only used in tests.
  49 --
  50 almost_equals :: Double -> Double -> Bool
  51 almost_equals x y =
  52   (abs (x - y)) < epsilon
  53
  54 infix 4 ~=
  55 (~=) :: Double -> Double -> Bool
  56 (~=) = almost_equals
  57
  58
  59 -- | Like 'almost_equals', except much more tolerant. The difference
  60 --   between the two arguments must be less than one percent of the sum
  61 --   of their magnitudes.
  62 --
  63 --   Only used in tests.
  64 --
  65 kinda_equals :: Double -> Double -> Bool
  66 kinda_equals x y =
  67   (abs (x - y)) < threshold
  68   where
  69     threshold = ((abs x) + (abs y)) / 100.0
  70
  71 infix 4 ~~=
  72 (~~=) :: Double -> Double -> Bool
  73 (~~=) = kinda_equals
  74
  75
  76 -- | x is very positive if it is 'epsilon' greater than zero.
  77 --
  78 --   Only used in tests.
  79 --
  80 very_positive :: Double -> Bool
  81 very_positive x =
  82   x - epsilon > 0
  83
  84
  85 -- | Takes a list of 'Double' and returns the ones which are not very
  86 --   positive.
  87 --
  88 non_very_positive_entries :: [Double] -> [Double]
  89 non_very_positive_entries = filter (not . very_positive)