[warpech]

This 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...

[retrac]

Rounding transcendentals correctly has unknown time and space complexity. [1] Sort of brushes up against the halting problem. With limited precision, the upper limit becomes calculable but it's rather large - packages that offer correct rounding on 64-bit floating point use potentially hundreds of bytes to deal with a single floating point value. Dedicated circuitry to implement it fast would be big and complicated even by today's standards.

https://en.wikipedia.org/wiki/Rounding#Table-maker's_dilemma

[lifthrasiir]

True in general, almost false for binary64. Important univariate functions have been thoroughly mapped for known hard-to-round cases, which resulted in the fact that we only need at most triple-double format to do the correct rounding. (Bivariate functions like `pow` are much harder, and not yet fully mapped as of this writing.) As a result we now have a mathematical library that almost ensures correct rounding [1], and a further optimization is currently in progress.

[1] https://core-math.gitlabpages.inria.fr/

[throwawaymaths]

unknown time and space complexity

True in general but for the basic datatypes sent through hardware regusters your processor architecture has fixed precision. So the time and space complexity is O(1)

[ImHereToVote]

We should just use analog circuit for this sort of thing where the exact precision doesn't matter.

[Arelius]

Yeah, but you'd be surprised at how frequently they appear to be the same. I once worked on a HTML5 game that that relied on deterministic simulation for networking. And it wasn't untill pretty late in development that a build of Chrome shipped on some platform that finally triggered a desync in our extensive cross-platform test suite.

We implemented a deterministic approximation, and moved on. But I learned something important about trig functions that day.

[cogman10]

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.

[bnprks]

Sadly even SSE vs. AVX is enough to often give different results, as SSE doesn't have support for fused multiply-add instructions which allow calculation of a*b + c with guaranteed correct rounding. Even though this should allow CPUs from 2013 and later to all use FMA, gcc/clang don't enable AVX by default for the x86-64 targets. And even if they did, results are only guaranteed identical if implementations have chosen the exact same polynomial approximation method and no compiler optimizations alter the instruction sequence.

Unfortunately, floating point results will probably continue to differ across platforms for the foreseeable future.

[enriquto]

> x87 is just a really weird and funky instruction set that's best left in the gutter of history

hmmm, can you use the long doubles in sse or avx? They are glorious, and as far as I see from playing with godbolt, they still require dirtying your hands with the x87 stack.

[bee_rider]

They do, however, have some intrinsics for trig functions in AVX in their compilers. Not as good as having an instruction of course.

[fulafel]

What about GPU ISAs?

[paulddraper]

> deterministic

I would use the word "consistent."

Non-determinism implies randomness.

[TylerE]

Safer to assume that floats are never deterministic.

[jacobolus]

Floats follow a clear specification which determines precisely how basic arithmetic should work. They should work the same on all popular modern platforms. (Whether specific software libraries are the same is a separate question.)

[saagarjha]

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.

[throwway120385]

It depends. If you're constrained to one chip and one platform you can characterize or you can estimate the characteristics of a float that matter in your application. In some applications like embedded that's actually totally fine, and modern embedded chips can often do floating point as fast or faster than they can emulate fixed point to work around floating point's drawbacks. On one project I worked on they originally wrote everything fixed point out of fear that floating point would introduce some deleterious effect. But in the end they rewrote parts of the project using floating point to no ill effect and great performance improvement. And there were features of the product that they had to strike because the rewrite needed to support them couldn't touch certain sensitive areas of the code that had been tested extensively in the 2 or 3 years of development. It would have been much better to evaluate the assumption that floats are bad early on in the project and make the decision based on real information. The heuristic they were applying ended up costing part of the product that was strategically important.

[aardvark179]

Floats are well defined, and it is perfectly possible to reason about how algorithms based on them should behave. Few languages specify the accuracy of things like trig functions, so relying on them can be tricky, and JavaScript is particularly bad in that respect.

[mhh__]

They're always deterministic in some sense (and as long as your OS respects the rounding mode after a context switch properly). This might sound pedantic but it determines how we think about floats — the behaviour is specified quite exactly.

[charlieyu1]

But why? We all know 0.1+0.2 won’t give 0.3 with floats but at least we should expect deterministic result for same numbers and same operations and same order, no?

[contravariant]

I don't think that's safe at all. Catastrophic cancellation would be quite a lot less catastrophic if rounding errors were random but accurate on average.

[aardvark179]

Somewhat annoyingly the ascribe standard only specifies that various math functions return an approximation but does not set any bounds on that approximation. So for many functions you could just return NaN and still be compliant.

[layer8]

Isn’t NaN the one value that can’t possibly count as an approximation, because it’s not a number and unordered? ;)

[adgjlsfhk1]

some languages (e.g. Julia) provide their own math library do that you get the same results across across operating systems.

[quickthrower2]

So you can use sin(x) for various x to tell what you are running on. Maybe even in the browser?

[Karliss]

There is a shader which uses similar idea to detect what kind of GPU you have https://www.shadertoy.com/view/slySWV

[lifthrasiir]

V8 and SpiderMonkey have converged to the same underlying library (fdlibm), partly for the interoperability, so you generally can't.