P.J. Plauger's _The Standard C Library_ provides an implementation for all functions in the (then) C standard: https://www.amazon.com/Standard-Library-P-J-Plauger/dp/01383...
How do computers calculate sine?
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Re: How do computers calculate sine?
#12This was my first use of open source, around 1978. I wondered how calculators and computers did trig functions, and was also using Unix V7. We had a large disk and kept the source on line. So I was able to find this: https://www.tuhs.org/cgi-bin/utree.pl?file=V7/usr/src/libm/s... and from there this book: https://www.biblio.com/book/computer-approximations-john-f-h...
Re: How do computers calculate sine?
#13CORDIC is how it's usually done in hardware (and FPGAs).
Re: How do computers calculate sine?
#14This made me realize that trigonometric functions are not deterministic across different CPU architectures, OS, and programming languages (floating point precision aside). E.g. I would assume that Math.sin(x) returns the same thing in NodeJS on Windows and Mac/M1, but it turns out it is necessarily so. https://stackoverflow.com/questions/74074312/standard-math-f...
some languages (e.g. Julia) provide their own math library do that you get the same results across across operating systems.
Re: How do computers calculate sine?
#15CORDIC is how it's usually done in hardware (and FPGAs). https://en.wikipedia.org/wiki/CORDIC
no it's not. cordic has awful convergence of 1 bit per iteration. pretty much everyone uses power series.
Re: How do computers calculate sine?
#16This made me realize that trigonometric functions are not deterministic across different CPU architectures, OS, and programming languages (floating point precision aside). E.g. I would assume that Math.sin(x) returns the same thing in NodeJS on Windows and Mac/M1, but it turns out it is necessarily so. https://stackoverflow.com/questions/74074312/standard-math-f...
Safer to assume that floats are never deterministic.
Re: How do computers calculate sine?
#17You might also find this video interesting:
"Finding the BEST sine function for Nintendo 64"
Re: How do computers calculate sine?
#181 - cos^2(x), obviously
instead, you could just double negate to optimize away the square root
-(-(sin(x))Re: How do computers calculate sine?
#19CORDIC is how it's usually done in hardware (and FPGAs). https://en.wikipedia.org/wiki/CORDIC
CORDIC is pretty obsolete, AFAIK. Its advantage is that its hardware requirements are absolutely tiny: two (?) accumulator registers, and hardware adders and shift-ers—I think that's all. No multiplication needed, in particular. Very convenient if you're building things from discrete transistors, like the some of those earlier scientific calculators!
(Also has a nice property, apparently, that CORDIC-like routines exist for a bunch of special functions and they're very similar to each other. Does anyone have a good resource for learning the details of those algorithms? They sound elegant).
Re: How do computers calculate sine?
#20This made me realize that trigonometric functions are not deterministic across different CPU architectures, OS, and programming languages (floating point precision aside). E.g. I would assume that Math.sin(x) returns the same thing in NodeJS on Windows and Mac/M1, but it turns out it is necessarily so. https://stackoverflow.com/questions/74074312/standard-math-f...
Well, what's fun is that (AFAIK) trigonometric functions tend not to be implemented in the newer floating point instructions, such as AVX or SSE.
So while what you say is true about the x87 implementation of those functions, for anything targeting a machine built in the last 20 years it's likely the code will run consistently regardless the architecture (barring architecture floating point bugs, which aren't terribly uncommon in the less significant bits and when overclocking comes into play).
x86 compilers won't use x87 instructions when SSE2 and later are available. x87 is just a really weird and funky instruction set that's best left in the gutter of history.