In the first step exanding beyond simple arithmetic, ArmMathM0 now includes
sinf(), cosf(), sincosf(), tanf(), atanf(), and atan2f().
ArmMathM0 is a ready-to-link library (GNU archive) of floating-point math for ARM Cortex-M0 and M0+ that replaces the functions provided by the compiler. Compared to the math library included with GCC, this library is both faster and smaller.
ArmMathM0 includes add, subtract, multiply, divide and square
root for both float and double. It also has float implementations for
sinf(), cosf(), sincosf(), tanf(), atanf(), and atan2f().
The plan is to build out the float functions (exp, log, etc.) before
implementing these functions for double. The higher functions in the
standard library are built on floating-point arithmetic, so those original
functions will go faster with ArmMathM0 arithmetic (roughly 2x).
ArmMathM0 has full support for Infinity and NAN, with support for denormal (tiny) numbers as a compile-time option. It is compatible with the ARM Run-time ABI, so it simply links in and satisifes compiler calls to floating-point arithmetic.
All arithmetic (including square root) provides the exact or closest representable result. This means the maximum error is 0.5 unit last place (ULP) if the exact answer is at the midpoint between two adjacent representable values.
sinf(), cosf(), sincosf() functions have an error of less than 1 ULP.
This means when the exact result is between two adjacent representable values,
it might not choose the closest one. This accuracy is valid for inputs up to ±200 radians.
tanf(), computed from sin/cos, has a max error of a little over 2 ULP in that range.
atanf(), and atan2f() have an error less than 1 ULP over all inputs.
This project was built with Microchip Studio, and the project files are included. The build folders Denormals and NoDenormals have makefiles and option settings to build their respective versions. The point of the NoDenormals build is to save on code size; there is no performance difference with normal numbers.