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