diff --git a/controller/ndslice.py b/controller/ndslice.py
index 7dca3d5..26e66c1 100644
--- a/controller/ndslice.py
+++ b/controller/ndslice.py
@@ -33,12 +33,32 @@ def __iter__(self):
             yield self.offset + sum(i*s for i, s in zip(loc, self.strides))
 
     def union(self, other: 'NDSlice') -> List['NDSlice']:
-        raise NotImplementedError()
+        # return a merged slice for pairs that meet regularity conditions
+        # and can be detected cheaply, otherwise just return the pair.
+        def sort(s):
+            strides, sizes = zip(*sorted(zip(s.strides, s.sizes), reverse=True))
+            return NDSlice(s.offset, list(sizes), list(strides))
+        s1, s2 = sort(self), sort(other)
+        s1, s2 = sorted([s1, s2], key=lambda s: s.offset)
+        extent = s1.sizes[0] * s1.strides[0]
+        if s1.offset + extent == s2.offset:
+            if s1.strides == s2.strides and s1.sizes[1:] == s2.sizes[1:]:
+                # congruent inner shape and strides, concatenated on long axis
+                sizes = [s1.sizes[0] + s2.sizes[0]] + s1.sizes[1:]
+                return [NDSlice(s1.offset, sizes, s1.strides)]
+        # fallback
+        return [self, other]
     
     def contains_any(self, start: int, end: int) -> bool:
         # does this slice contain any of the elements in [start, end)
         # will be used to figure out who to broadcast to.
-        raise NotImplementedError()
+        base = self.offset
+        for stride, size in sorted(zip(self.strides, self.sizes), reverse=True):
+            if end <= base or start >= base + size * stride:
+                return False
+            shift = max(0, min(size - 1, (end - base - 1) // stride))
+            base += shift * stride
+        return base >= start and base < end
     
     def index(self, value: int) -> int:
         # return index  where self[index] == value,
diff --git a/tests/controller/test_controller.py b/tests/controller/test_controller.py
index 21267a8..0c21028 100644
--- a/tests/controller/test_controller.py
+++ b/tests/controller/test_controller.py
@@ -333,6 +333,33 @@ def check(s):
         check(NDSlice(24, [4, 3, 8], [48*2, 16, 2]))
         check(NDSlice(37, [], []))
 
+        def check_contains_any(s, gen):
+            elems = set(s)
+            max_elem = max(elems)
+            span = max_elem - s.offset + 1
+            for _ in range(len(elems) * 32):
+                start = gen.randrange(s.offset - 10, max_elem + 10)
+                end = start + gen.choices(range(span), range(span, 0, -1))[0]
+                contains = s.contains_any(start, end)
+                ref = any(x in elems for x in range(start, end))
+                if contains != ref:
+                    raise RuntimeError(
+                        f"{s}.contains_any({start}, {end}) broken, false {'positive' if contains else 'negative'}"
+                    )
+
+        def check_union(s1, gen):
+            for _ in range(10):
+                s2 = fuzz(gen)
+                ref_elems = set(s1) | set(s2)
+                u = s1.union(s2)
+                elems = set()
+                for s in u:
+                    elems |= set(s)
+                if elems != ref_elems:
+                    raise RuntimeError(
+                        f"{s1}.union({s2}) broken, {'extra' if len(elems) > len(ref_elems) else 'missing'} elements"
+                    )
+
         def fuzz(gen):
             ndim = gen.choices([1, 2, 3, 4], [1, 2, 3, 4])[0]
             sizes = [gen.randrange(1, 10) for _ in range(ndim)]
@@ -354,6 +381,8 @@ def fuzz(gen):
         for _ in range(1000):
             s = fuzz(gen)
             check(s)
+            check_contains_any(s, gen)
+            check_union(s, gen)