This is a set of branch-free, table-free implementations of the math functions in <math.h>.

All of the code is "public domain"¹ - if you like, you can copy out the sin implementation if that's all you need.

These functions differ slightly from the C standard library by design - to stay fast, they don't do range checking by default, or follow C's precision requirements. Think of these routines more as "decent approximations", for when you know the particular input domain and you have leeway with the output. Video games are a good use case.

These functions stick to the C API, but the library doesn't implement all of math.h - notable exclusions are machine-related functions (e.g. fma, nextafter), precision-related functions (e.g. expm1), complex numbers, and tgamma/lgamma. The standard elementary functions that you would expect are included, as well as hyperbolic trig.

The library uses a select few functions, fully implemented from scratch, in order to derive the implementation of others via identities. For example, cos(x) is implemented as sin(x + π/2), and tan(x) is implemented as sin(x)/cos(x). This simplifies many of the routines, since the potential precision loss from this approach is negligible within the given bounds of the library.

• atan2 is highly discontinuous, so a truly branch-free implementation of this routine is likely impossible.

I want this library to be easy to use, so no attribution is necessary.

¹Actual public domain dedications are of unclear legality worldwide, so an equivalent permissive license (no-clause BSD) is used, available at the bottom of the file.

Algorithm credit:

• The sin algorithm was invented by Nicolas Capens (@c0d1f1ed) on a now-defunct programming forum..
• round, sqrt, rsqrt, and log are publicly available algorithms.
• The rest are new, to my knowledge.