Implementation of Fixed Point numbers in C using integers. Number of bits to use for fraction part configurable at runtime.
For more information about Fixed Point arithmetic: Fixed-point arithmetic (Wikipedia)
The code implements overflow-safe operations for +, -, *, and /, following CMU SEI's INT32-C recommendations. For further details: INT32-C. Ensure that operations on signed integers do not result in overflow
lg2(), pow2() implemented using the BKM algorithm
Additional logarithm and power functions (ln, lg10, exp, pow10, and powxy,) all implemented through lg2 and pow2.
Trigonometric functions sin() and cos() implemented using the CORDIC algorithm
Square root now also implemented using CORDIC (achieving same accuracy, yet more than twice as fast compared to implementation combining lg2 and pow2!)
Behind the scenes, these functions work with longs or emulated longs, so as to avoid calculation inaccuracies that would inevitably appear if working just with the chosen number of frac bits, or just with int-size precision. Goals of this implementation are mostly flexibility (hence the configurable frac bits,) yet also configurable and even ultimate precision if desired. All tests should ideally run with no inaccuracy warnings, or as few as possible, regardless of frac bits in use.
Later:
- Finish trigonometric functions
- Include an inverse square root function (1/sqrt(x))
- Saturated mode
- Rewrite in Rust maybe?
You only need a C compiler like gcc installed. Simply clone this repo and then run the following script on its folder:
./r
That will compile with gcc locally, and will run the tester program. It should produce a long testing output, like the one in the output.*.txt file(s). At the end it will ideally show a list with the observed number of warnings for each of the frac bit configurations tested. If an error larger than the maximum allowed is found, an assert will get triggered stopping the program immediately, showing the function call that was being tested right then.
Up to now I have run and tested it successfully (zero asserts) on the CPUs listed below, using gcc v11.3.0 both without and with some -O options:
Little Endian CPUs:
- Intel Core i7-6700K
- Arm Cortex-A72 (-> Raspberry Pi 4 Model B)
Big Endian CPUs:
- (To be added when tried/receiving output from test runs)
If you try it on any CPU not listed above, specially one with an instruction set architecture different from the ones represented above, please get in touch and send me your output. I'll be glad to credit you for it here if you'd like! :) Either email me or send a PR for an output file named along the lines of output.cpu_model.txt
If you encounter any problems or errors, please don't hesitate to let me know as well, glad to also credit troubleshooting input/feedback. Just please mention compiler, compiler options used, and your hardware details.
To use these Fix Point Numbers yourself, for now you only need files fxp.c and its dependencies if strictly using ints and only ints. If allowing longs, then also file fxp_l.c. Most other files are auxiliary (to convert to and from floating points, to print out, test, etc.)