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Java (the most popular programming language in the world by many metrics, if you didn't know) works exactly like this.

I understand that C and Java have (sometimes) different use cases, still I feel reasonably confident that 32-bit arithmetic is going to be efficient enough on most platforms of interest (some embedded platforms might be a problem).

It's true that something like the Posix int_fast_16_t (etc) types might be useful though.

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