Ignorant question:
Given the ridiculous number of transistors and so on we can use in CPUs and GPUs nowadays how feasible is a relatively huge trig lookup table burned into rom?
How do computers calculate sine?
41–50 of 167 posts
Re: How do computers calculate sine?
#42Earlier quoted context omitted.
But transcendentals like sine are not part of the strictly defined basic arithmetic; they are intentionally defined with relaxed behavior.
Even there many standard libraries provide very good precision at least within sane domain.
Yeah, that’s kind of my point. 99% consistent isn’t.
Re: How do computers calculate sine?
#43This 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.
This is not always a safe assumption (in certain scenarios floating point results being nondeterministic has the possibility to introduce bugs and security issues) and is also a kind of sad way to look at the world. The response to "I don't understand how this works" should not be to adopt an incorrect viewpoint, but to know the limitations of your understanding.
Re: How do computers calculate sine?
#44CORDIC is how it's usually done in hardware (and FPGAs). https://en.wikipedia.org/wiki/CORDIC
Why would you ever use CORDIC if you had any other option?
Re: How do computers calculate sine?
#45Ignorant question: Given the ridiculous number of transistors and so on we can use in CPUs and GPUs nowadays how feasible is a relatively huge trig lookup table burned into rom?
Seems like a terrible idea on latency grounds alone.
Re: How do computers calculate sine?
#46CORDIC 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 e…
Multiplication is pretty much needed in cordic! And is far from obsolete! It works perfectly fine, and dont have any of the problems said in the article.
Re: How do computers calculate sine?
#47CORDIC is how it's usually done in hardware (and FPGAs). https://en.wikipedia.org/wiki/CORDIC
Why would you ever use CORDIC if you had any other option?
It's great for hardware implementations, because it's simple and you get good/excellent accuracy. I wouldn't be surprised if that's still how modern x86-64 CPUs compute sin, cos, etc.
That said, last time I had to do that in software, I used Taylor series. Might not have been an optimal solution.
EDIT:
AMD's Zen 4 takes 50-200 cycles (latency) to compute sine. I think that strongly suggests AMD uses CORDIC. https://www.agner.org/optimize/instruction_tables.pdf page 130.
Same for Intel, Tiger Lake (Intel gen 11) has 60-120 cycles of latency. Page 353.
I'd guess usually ~50 cycles for Zen 4 (and ~60 for Intel) for float32, float64/float80 datatype. Denormals might also cost more cycles.
Re: How do computers calculate sine?
#48Re: How do computers calculate sine?
#49Ignorant question: Given the ridiculous number of transistors and so on we can use in CPUs and GPUs nowadays how feasible is a relatively huge trig lookup table burned into rom?
There is huge number of 64bit floats and huge portion of those are between 0..pi/2.
Re: How do computers calculate sine?
#50I blogged my adventure of implementing cosine from scratch and how others have done it: