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.
+nearly_equals :: Double -> Double -> Bool
+nearly_equals x y = (abs (x - y)) < theta
+
+-- | Nearly greater-than or equal-to.
+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.
almost_equals :: 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.
+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.
very_positive :: Double -> Bool
very_positive x = x - epsilon > 0