Is an arithmetic shift operator useful?

Assume a language's division operator (/) rounds towards -infinity.

Other than potentially increased performance, is there any use in the language including an arithmetic shift operator (>>, say), given that x >> y would be equivalent to x / (2 ** y)?

Yes - it's useful to make it clear that you're interested in bitshifting operations; that you're thinking of a value as "a sequence of bits" rather than a magnitude.

For example, if I'm trying to represent a 32-bit integer in four bytes (and I don't have a simpler way of doing it) I might use:

bytes[0] = value & 0xff;
bytes[1] = (value >> 8) & 0xff;
bytes[2] = (value >> 16) & 0xff;
bytes[3] = (value >> 24) & 0xff;

That represents what I'm trying to do much more readably in my opinion than using the equivalent division operations.

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