v7unix VS vectrig

This is the source for grep. It's again only 1 file, and tiny. Only uses simple calls, etc. https://github.com/v7unix/v7unix/blob/master/v7/usr/src/cmd/grep.c

This takes me back in time, to c. 1982 when I got curious about how computers calculated trig functions. Luckily I was using one of the first OSS systems (modulo AT&T lawyers): Unix V7. So I pulled up the source and took a look. You can still see it here: https://github.com/v7unix/v7unix/blob/master/v7/usr/src/libm...

It's what historic Unix did: https://github.com/v7unix/v7unix/blob/master/v7/usr/src/libc...

Why it did that? I'm not sure, but at the time C did not have 'void' functions: every function returned a value. They probably wanted to make the behavior of the stdlib functions deterministic, even if the return value was useless and undocumented.

See the V7 Unix source for sbrk here.

Thanks for explaining this. I actually wrote a SIMD implementation of trig functions years ago, using the techniques you describe.

You can check it out: https://github.com/jeremysalwen/vectrig

I compared several different methods of generating polynomials of different sizes for speed and precision (spoilers: taylor series were the worst and minimax polynomials (Remez algorithm) were the best).

Another (surprising) thing which I learned during the project was that the range reduction was just as (if not more) important to the accuracy of the implementation than the polynomial. If you think about it, you will realize that it's actually pretty difficult to quickly and accurately compute the sin of large numbers like 2^50.

I also tried to directly optimize the coefficients for the accuracy of the polynomial on the required range, but that experiment was unsuccessful.

It's all there in the repository, the implementations, notes about the different polynomials used, and the accuracy/speed statistics for the different methods.