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

All of the code is public domain - 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 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.

You can re-define PT_() to decorate the function name as e.g. my_sin, or simply sin.

The outer parentheses are to prevent macro expansion in the event that PT_sin(x) is defined as a macro. Wrapper macros can be used to replace a given implementation or to the operate on the input before entering the meat of the algorithm.

One thing to note is that when functions are called in the library, they don't prevent expansion, meaning you can define a wrapper macro for PT_exp2(x) that performs range checking and that checking will propagate to PT_exp, PT_pow, etc. If you want a wrapper without this propagation behaviour, then include the library before defining the macro.

• 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.

I didn't invent all of these algorithms, but the original authors are lost to time.

• The sin algorithm was originally conceived by an anonymous user on a now-unavailable programming forum.
• The log snippet is of unknown origin, similarly to the fast inverse square root.