Add the theta tolerance and nearly_equals, nearly_ge comparisons.

[spline3.git] / src / Comparisons.hs

diff --git a/src/Comparisons.hs b/src/Comparisons.hs
index 4bf4cebb69ece2947eb1deccf0dfa9cfda20f266..4a8144469415668327567717239844a4b1c85a22 100644 (file)
--- a/src/Comparisons.hs
+++ b/src/Comparisons.hs
@@ -3,11 +3,22 @@ module Comparisons
 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 = 0.00000000000001
+
+-- | 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
@@ -18,6 +29,20 @@ infix 4 ~=
 (~=) = 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