A leap year check in three instructions

I love these incomprehensible magic number optimizations. Every time I see one I wonder how many optimizations like this we missed back in the old days when we were writing all our inner loops in assembly?

Does anyone have a collection of these things?

We didn't miss them. In those days they weren't optimizations. Multiplications were really expensive.

Multiplications of this word length, one should clarify. It's not that multiplication was an inherently more expensive or different operation back then (assuming from context here that the "old days" of coding inner loops in assembly language pre-date even the 32-bit ALU era). Binary multiplication has not changed in millennia. Ancient Egyptians were using the same binary integer multiplication logic 5 millennia ago as ALUs do today.

It was that generally the fast hardware multiplication operations in ALUs didn't have very many bits in the register word length, so multiplications of wider words had to be done with library functions that did long multiplication in (say) base 256.

So this code in the headlined article would not be "three instructions" but three calls to internal helper library functions used by the compiler for long-word multiplication, comparison, and bitwise AND; not markedly more optimal than three internal helper function calls for the three original modulo operations, and in fact less optimal than the bit-twiddled modulo-powers-of-2 version found halfway down the headlined article, which would only need check the least significant byte and not call library functions for two of the 32-bit modulo operations.

Bonus points to anyone who remembers the helper function names in Microsoft BASIC's runtime library straight off the top of xyr head. It is probably a good thing that I finally seem to have forgotten them. (-: They all began with "B$" as I recall.