Cyclefrom

Cyclefrom is a software construct that produces elements from a finite sequence in cyclic order, beginning at a specified offset. It can be viewed as an iterator wrapper that, once initialized, repeatedly yields the elements of the input sequence in a circular fashion, never exhausting the sequence unless explicitly stopped. The key feature is that the starting point is defined, so the first element emitted is the one at the chosen offset, and subsequent outputs follow the sequence with wrap-around.

In its common form, cyclefrom takes two inputs: a finite sequence S with length n, and a starting index s with 0 ≤ s < n. The produced sequence is S[s], S[(s+1) mod n], S[(s+2) mod n], and so on, repeating indefinitely. Some variants allow starting from a given element value rather than an index, computing the first position of that value within S. If S is empty, cyclefrom yields no elements. If a start index is outside the valid range, many implementations wrap the index modulo n.

Implementation typically uses modular arithmetic to advance the position and a simple state variable to remember the current index. The per-element cost is constant time, and memory usage is O(1) beyond storing the input sequence.

Common use cases include round-robin scheduling, cyclic testing or sampling, and simulations where a fixed order must recur starting from a predefined point. Variants may offer finite cycling (a fixed number of outputs) or integration with existing iterator protocols for lazy evaluation.

See also: cycle, rotate, circular buffer, ring buffer, modular arithmetic, iterators.