Numerical Libraries and Functions

When we think of how to represent fractional numbers in code, we reach for double and float, and almost never reach for anything else. There are several alternatives, including constructive real numbers that are used in calculators, and rational numbers. One alternative predates all of these, including floating point, and actually allows you to compute faster than when you use floating point numbers. That alternative is fixed point: a primitive form of decimal that does not offer any of the conveniences of float, but allows you to do decimal computations more quickly and efficiently.

Occasionally, I like to peruse uops.info. It is a great resource for micro-optimization: benchmark every x86 instruction on every architecture, and compile the results. Every time I look at this table, there is one thing that sticks out to me: the DIV instruction. On a Coffee Lake CPU, an 8-bit DIV takes a long time: 25 cycles. Cannon Lake and Ice Lake do a lot better, and so does AMD. We know that divider architecture is different between architectures, and aggregating all of the performance numbers for an 8-bit DIV, we see: