Identifying Leap Years (2020)
David Turner explores optimizing leap year calculations for performance gains by using bitwise operations and integer bounds. He presents efficient methods, mathematical proofs, and considerations for signed integers, highlighting limitations pre-Gregorian calendar.
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David Turner discusses the optimization of leap year calculations for performance gains. He explores different methods to determine leap years without using division, focusing on bitwise operations and integer bounds. Turner presents three versions of leap year calculations, emphasizing the efficiency of bitwise operations and single multiplications. He also delves into the mathematical proofs behind these calculations, showcasing the use of coprime numbers and modular arithmetic. Turner provides constants for different integer widths and discusses considerations for signed integers. He concludes by mentioning the limitations of applying these calculations to dates before the Gregorian calendar. Turner's analysis offers insights into optimizing leap year checks for computational efficiency.
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6 commentsAs the article mentions, you need a slightly different calculation in the period between 45 BC and 1582 AD -- the rule about 400 didn't exist in the Julian calendar in force then. Before 45 BC, and in non-Roman-based calendars, it gets even more complicated with intercalary months and postponing New Year's and such.
But surely in all but the tiniest fraction of cases, you only care about years after 1582, and years that are no more than a few centuries in the future. There are only 223 leap years from 1582-2500 (I checked with ChatGPT so that number must be right!) A binary search of an ordered 223-item list would require at most 8 comparisons, and if you don't mind a little more space, you could just store all 919 of those years in a list and look up the answer directly. Wouldn't either be faster than any of these methods (and clearer)?
16bit: https://gcc.godbolt.org/z/6G38YxcGr
32bit: https://gcc.godbolt.org/z/vEzf9h1jo
I thought it's interesting how "div" is used in 16bit versions, whereas for 32bit versions the compiler optimized all of them to use only imul.
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