libdivide

Jokes aside, lookup tables are a common technique to avoid costly operations. I was recently implementing one to avoid integer division. In my case I knew that the nominator and denominator were 8 bit unsigned integers, so I've replaced the division with 2 table lookups and 6 shifts and arithmetic operations [1]. The well known `libdivide` [2] does that for arbitrary 16, 32, and 64 bit integers, and it has precomputed magic numbers and lookup tables for all 16-bit integers in the same repo. [1]: https://github.com/ashvardanian/StringZilla/blob/9f6ca3c6d3c... [2]: https://github.com/ridiculousfish/libdivide

libdivide tl;dr: > libdivide allows you to replace expensive integer divides with comparatively cheap multiplication and bitshifts. Compilers usually do this, but only when the divisor is known at compile time. libdivide allows you to take advantage of it at runtime. The result is that integer division can become faster - a lot faster. [...] divide SIMD vectors by runtime constants, [1] > libdivide.h is a header-only C/C++ library for optimizing integer division. Integer division is one of the slowest instructions on most CPUs e.g. on current x64 CPUs a 64-bit integer division has a latency of up to 90 clock cycles whereas a multiplication has a latency of only 3 clock cycles. libdivide allows you to replace expensive integer divsion instructions by a sequence of shift, add and multiply instructions that will calculate the integer divisio