arr[key]

Basic indexing -- every part of key is an int (Python or numpy scalar), slice, flops.newaxis (None), Ellipsis, or a tuple of those -- returns a view, matching NumPy's zero-copy semantics: 0 FLOPs.

Advanced indexing materializes a gathered copy and is billed under "getitem": 4 FLOPs per gathered output element (matching take), plus one scan FLOP per boolean-mask element (matching compress). A part triggers advanced indexing when it is any of:

• a bool / flops.bool_ scalar -- numpy routes a bare boolean scalar through the advanced-index copy path (prepending a length-1 / length-0 axis), a genuine copy though it is not an ndarray;

• any other part that coerces to an integer- or boolean-dtype array -- an ndarray (or FlopscopeArray) of any ndim including 0-d, a list, tuple, range, array.array, memoryview, or any future array-like sequence/buffer. This matches numpy's own rule (any array-like integer/bool index gathers a copy) rather than an enumerated type list, so it cannot silently miss a sequence kind: the part is classified by flops.asarray(part).dtype, and only its dtype/size are read -- the original key is what actually indexes, so a single-use generator part is never consumed.

This is about a part -- an already-decomposed element of parts -- not the top-level key: m[1:3, ::2] has key as a tuple, but that tuple is the multi-axis split itself (parts = key), and its parts are slices, so it stays basic. Likewise v[(0, 2, 4)] on a 1-D v has key as the 3-tuple; splitting it into parts 0, 2, 4 yields three int parts -- basic, and numpy raises its own "too many indices" error since none of them consumes as an array. A tuple only gathers when it survives the top-level split as one part, e.g. v[(0, 2, 4),] (a 1-tuple containing the 3-tuple) or m[tuple_a, tuple_b] (each axis's index happens to be a tuple).

A numpy/Python integer scalar stays basic (a view) -- only integer arrays (or a sequence/buffer coerced to one) gather. A part numpy cannot turn into an integer/bool array -- an object array (kind O, e.g. a generator), a string/bytes field selector (U/S), a float/complex array, or a ragged sequence flops.asarray rejects -- falls through to super().__getitem__ unbilled, so numpy handles or raises on it exactly as usual. mask_elems counts boolean elements only: a bool scalar contributes 1, a bool array contributes its size; integer operands add nothing beyond the gather.