-module Comparisons
+-- | Functions for comparing 'Double' values.
+module Comparisons (
+ (~=),
+ (~~=),
+ almost_equals,
+ kinda_equals,
+ nearly_equals,
+ nearly_ge,
+ non_very_positive_entries,
+ very_positive )
where
+
-- | epsilon is the value that will be used in all tests that require
--- some measure of "closeness." Increasing it will make those tests
--- more tolerant.
+-- some measure of \"closeness.\" Increasing it will make those
+-- tests more tolerant.
+ --
epsilon :: Double
epsilon = 0.0001
+-- | A tiny margin of error.
+--
+theta :: Double
+theta = 0.0000000000001
+
+
+-- | x almost equals y if x is within 'theta' of y.
+--
+-- Only used in tests.
+--
+nearly_equals :: Double -> Double -> Bool
+nearly_equals x y =
+ (abs (x - y)) < theta
+
+
+-- | Nearly greater-than or equal-to.
+--
+-- Only used in tests.
+--
+nearly_ge :: Double -> Double -> Bool
+x `nearly_ge` y =
+ (x > y) || (x `nearly_equals` y)
+
+
-- | x almost equals y if x is within 'epsilon' of y.
+--
+-- Only used in tests.
+--
almost_equals :: Double -> Double -> Bool
-almost_equals x y = (abs (x - y)) < epsilon
+almost_equals x y =
+ (abs (x - y)) < epsilon
infix 4 ~=
(~=) :: Double -> Double -> Bool
(~=) = almost_equals
+-- | Like 'almost_equals', except much more tolerant. The difference
+-- between the two arguments must be less than one percent of the sum
+-- of their magnitudes.
+--
+-- Only used in tests.
+--
+kinda_equals :: Double -> Double -> Bool
+kinda_equals x y =
+ (abs (x - y)) < threshold
+ where
+ threshold = ((abs x) + (abs y)) / 100.0
+
+infix 4 ~~=
+(~~=) :: Double -> Double -> Bool
+(~~=) = kinda_equals
+
+
-- | x is very positive if it is 'epsilon' greater than zero.
+--
+-- Only used in tests.
+--
very_positive :: Double -> Bool
-very_positive x = x - epsilon > 0
+very_positive x =
+ x - epsilon > 0
--- | Takes a list of Doubles and returns the ones which are not very
+-- | Takes a list of 'Double' and returns the ones which are not very
-- positive.
+--
non_very_positive_entries :: [Double] -> [Double]
non_very_positive_entries = filter (not . very_positive)