IntegerInterval: add magnitude

Returns the number of integers that lie within an integer interval.

src/Data/IntegerInterval.hs

@@ -309,6 +309,16 @@ width x
         (Finite lb, Finite ub) -> ub - lb
         _ -> error "Data.IntegerInterval.width: unbounded interval"
 
+-- | Magnitude of an interval: how many integers lie within the interval.
+-- Magnitude of an unbounded interval is @undefined@.
+magnitude :: IntegerInterval -> Integer
+magnitude x
+  | null x = 0
+  | otherwise =
+      case (lowerBound x, upperBound x) of
+        (Finite lb, Finite ub) -> ub - lb + 1
+        _ -> error "Data.IntegerInterval.magnitude: unbounded interval"
+
 -- | pick up an element from the interval if the interval is not empty.
 pickup :: IntegerInterval -> Maybe Integer
 pickup x =

test/TestIntegerInterval.hs

@@ -275,6 +275,20 @@ prop_width_singleton =
   forAll arbitrary $ \x ->
     IntegerInterval.width (IntegerInterval.singleton x) == 0
 
+{--------------------------------------------------------------------
+  magnitude
+--------------------------------------------------------------------}
+
+case_magnitude_null =
+  IntegerInterval.magnitude IntegerInterval.empty @?= 0
+
+case_magnitude_positive =
+  IntegerInterval.magnitude (0 <=..< 10) @?= 10
+
+prop_magnitude_singleton =
+  forAll arbitrary $ \x ->
+    IntegerInterval.magnitude (IntegerInterval.singleton x) == 1
+
 {--------------------------------------------------------------------
   map
 --------------------------------------------------------------------}