add range_union function, stop using align internally

src/icepool/function.py

@@ -229,6 +229,14 @@ def max_outcome(*dice: 'T | icepool.Die[T]') -> T:
     converted_dice = [icepool.implicit_convert_to_die(die) for die in dice]
     return max(die.outcomes()[-1] for die in converted_dice)
 
+def range_union(*args: Iterable[int]) -> Sequence[int]:
+    """Produces a sequence of consecutive ints covering the argument sets."""
+    start = min((x for x in itertools.chain(*args)), default=None)
+    if start is None:
+        return ()
+    stop = max(x for x in itertools.chain(*args))
+    return tuple(range(start, stop+1))
+
 def sorted_union(*args: Iterable[T]) -> Sequence[T]:
     """Merge sets into a sorted sequence."""
     if not args:

src/icepool/population/base.py

@@ -487,20 +487,19 @@ def modal_quantity(self) -> int:
         """The highest quantity of any single outcome. """
         return max(self.quantities())
 
-    def kolmogorov_smirnov(self, other) -> Fraction:
+    def kolmogorov_smirnov(self, other: 'Population') -> Fraction:
         """Kolmogorov–Smirnov statistic. The maximum absolute difference between CDFs. """
-        a, b = icepool.align(self, other)
+        outcomes = icepool.sorted_union(self, other)
         return max(
-            abs(a - b)
-            for a, b in zip(a.probabilities('<='), b.probabilities('<=')))
+            abs(self.probability('<=', outcome) - other.probability('<=', outcome))
+            for outcome in outcomes)
 
-    def cramer_von_mises(self, other) -> Fraction:
+    def cramer_von_mises(self, other: 'Population') -> Fraction:
         """Cramér-von Mises statistic. The sum-of-squares difference between CDFs. """
-        a, b = icepool.align(self, other)
+        outcomes = icepool.sorted_union(self, other)
         return sum(
-            ((a - b)**2
-             for a, b in zip(a.probabilities('<='), b.probabilities('<='))),
-            start=Fraction(0, 1))
+            ((self.probability('<=', outcome) - other.probability('<=', outcome)) ** 2
+            for outcome in outcomes), start=Fraction(0, 1))
 
     def median(self):
         """The median, taking the mean in case of a tie.

src/icepool/population/keep.py

@@ -297,10 +297,11 @@ def _lowest_single(*args: 'T | icepool.Die[T]') -> 'icepool.Die[T]':
     dice = tuple(icepool.implicit_convert_to_die(arg) for arg in args)
     max_outcome = min(die.max_outcome() for die in dice)
     dice = tuple(die.clip(max_outcome=max_outcome) for die in dice)
-    dice = icepool.align(*dice)
+    outcomes = icepool.sorted_union(*dice)
     quantities_ge = tuple(
-        math.prod(t) for t in zip(*(die.quantities('>=') for die in dice)))
-    return icepool.from_cumulative(dice[0].outcomes(),
+        math.prod(die.quantity('>=', outcome) for die in dice)
+        for outcome in outcomes)
+    return icepool.from_cumulative(outcomes,
                                    quantities_ge,
                                    reverse=True)
 
@@ -314,7 +315,8 @@ def _highest_single(*args: 'T | icepool.Die[T]') -> 'icepool.Die[T]':
     dice = tuple(icepool.implicit_convert_to_die(arg) for arg in args)
     min_outcome = max(die.min_outcome() for die in dice)
     dice = tuple(die.clip(min_outcome=min_outcome) for die in dice)
-    dice = icepool.align(*dice)
+    outcomes = icepool.sorted_union(*dice)
     quantities_le = tuple(
-        math.prod(t) for t in zip(*(die.quantities('<=') for die in dice)))
-    return icepool.from_cumulative(dice[0].outcomes(), quantities_le)
+        math.prod(die.quantity('<=', outcome) for die in dice)
+        for outcome in outcomes)
+    return icepool.from_cumulative(outcomes, quantities_le)

tests/from_cumulative_test.py

@@ -27,7 +27,5 @@ def test_from_rv_norm():
                                1000000,
                                loc=die.mean(),
                                scale=die.standard_deviation())
-    die, norm_die = icepool.align(die, norm_die)
-    print(die.kolmogorov_smirnov(norm_die))
     assert die.probabilities('<=') == pytest.approx(
         norm_die.probabilities('<='), abs=1e-3)