But preprocessor requires all arithmetic take place in a common signed or unsigned type matching [u]intmax_t...
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What about allowing integers larger than intmax_t by not defining a corresponding INT_<size>_MAX and keeping the limit of the preprocessor to intmax_t? INT_MAX is useful because the size of an int isn't fixed. But you know the max of a uint128_t.
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Arguably, since the standard requires INTnnn_MAX to be defined if intnnn_t is, I think it's valid for the application to use the identifier intnnn_t if INTnnn_MAX is not defined... ;-)
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File this one away for adversarial C implementations.
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