I had always thought expression templates at the very least needed the optimizer to inline/flatten the tree of function calls that are built up. For instance, for something like x + y * z I'd expect an expression template type like sum<vector, product<vector, vector>> where sum would effectively have:
That would require the optimizer to inline the latter into the former to end up with a single expression, though. Is there a different way to express this that doesn't rely on the optimizer for inlining?
Expression templates do not rely on optimizer since you're not dealing with the computations directly but rather expressions (nodes) through which you are deferring the computation part until the very last moment (when you have a fully built an expression of expressions, basically almost an AST). This guarantees that you get zero cost when you really need it. What you're describing is something keen of copy elision and function folding though inlining which is pretty much basics in any c++ compiler and happens automatically without special care.
> since you're not dealing with the computations directly but rather expressions (nodes) through which you are deferring the computation part until the very last moment (when you have a fully built an expression of expressions, basically almost an AST).
Right, I understand that. What is not exactly clear to me is how you get from the tree of deferred expressions to the "flat" optimized expression without involving the optimizer.
Take something like the above example for instance - w = x + y * z for vectors w/x/y/z. How do you get from that to effectively
for (size_t i = 0; i < w.size(); ++i) {
w[i] = x[i] + y[i] * z[i];
}
The example is false because that's not how you would write an expression template for given computation so the question being how is it that the optimizer is not involved is also not quite set in the correct context so I can't give you an answer for that. Of course that the optimizer is generally going to be involved, as it is for all the code and not the expression templates, but expression templates do not require the optimizer in the way you're trying to suggest. Expression templates do not rely on O1, O2 or O3 levels being set - they work the same way in O0 too and that may be the hint you were looking for.
> The example is false because that's not how you would write an expression template for given computation
OK, so how would you write an expression template for the given computation, then?
> Expression templates do not rely on O1, O2 or O3 levels being set - they work the same way in O0 too and that may be the hint you were looking for.
This claim confuses me given how expression templates seem to work in practice?
For example, consider Todd Veldhuizen's 1994 paper introducing expression templates [0]. If you take the examples linked at the top of the page and plug them into Godbolt (with slight modifications to isolate the actual work of interest) you can see that with -O0 you get calls to overloaded operators instead of the nice flattened/unrolled/optimized operations you get with -O1.
You see something similar with Eigen [2] - you get function calls to "raw" expression template internals with -O0, and you need to enable the optimizer to get unrolled/flattened/etc. operations.
Similar thing yet again with Blaze [3].
At least to me, it looks like expression templates produce quite different outputs when the optimizer is enabled vs. disabled, and the -O0 outputs very much don't resemble the manually-unrolled/flattened-like output one might expect (and arguably gets with optimizations enabled). Did all of these get expression templates wrong as well?
Look, I have just completed work on some high performance serialization library which avoids computing heavy expressions and temporary allocations all by using expression templates and no, optimization levels are not needed. The code works as advertised at O0 - that's the whole deal around it. If you have a genuine question you should ask one but please do not disguise so that it only goes to prove your point. I am not that naive. All I can say is that your understanding of expression templates is not complete and therefore you draw incorrect conclusions. Silly example you provided shows that you don't understand how expression template code looks like and yet you're trying to prove your point all over and over again. Also, most of the time I am writing my comments on my mobile so I understand that my responses sometime appear too blunt but in any case I will obviously not going to write, run or check the code as if I had been on my work. My comments here is not work, and I am not here to win arguments, but most of the time learn from other people's experiences, and sometimes dispute conclusions based on those experiences too. If you don't believe me, or you believe expression templates work differently, then so be it.
> If you have a genuine question you should ask one but please do not disguise so that it only goes to prove your point.
I think my question is pretty simple: "How does an optimizer-independent expression template implementation work?" Evidently the resources I've found so far describe "optimizer-dependent expression templates", and apparently none of the "expression template" implementations I've had reason to look at disabused me of that notion.
> My comments here is not work, and I am not here to win arguments, but most of the time learn from other people's experiences, and sometimes dispute conclusions based on those experiences too.
Sure, and I like to learn as well from the more knowledgeable/experienced folk here, but as much as I want to do so here I'm finding it difficult since there's precious little for me to go off of beyond basically just being told I'm wrong.
> If you don't believe me, or you believe expression templates work differently, then so be it.
I want to understand how you understand expression templates, but between the above and not being able to find useful examples of your description of expression templates I'm at a bit of a loss.
Expression templates do AST manipulation of expressions at compile time. Let's say you have a complex matrix expression that naively maps to multiple BLAS operations but can be reduced to a single BLAS call. With expression templates you can translate one to the other, this is a static manipulation that does not depend on compiler level. What does depend on the compiler is whether the incidental trivial function calls to operators gets optimized away or not. But, especially with large matrices, the BLAS call will dominate anyway, so the optimization level shouldn't matter.
Of course in many cases the optimization level does matter: if you are optimizing small vector operators to simd inlining will still be important.
> With expression templates you can translate one to the other, this is a static manipulation that does not depend on compiler level.
How does that work on an implementation level? First thing that comes to mind is specialization, but I wouldn't be surprised if it were something else.
> What does depend on the compiler is whether the incidental trivial function calls to operators gets optimized away or not.
> Of course in many cases the optimization level does matter: if you are optimizing small vector operators to simd inlining will still be important.
Perhaps this is the source of my confusion; my uses of expression templates so far have generally been "simpler" ones which rely on the optimizer to unravel things. I haven't been exposed much to the kind of matrix/BLAS-related scenarios you describe.
Partial specialization specifically. Match some patterns and covert it to something else. For example:
struct F { double x; };
enum Op { Add, Mul };
auto eval(F x) { return x.x; }
template<class L, class R, Op op> struct Expr;
template<class L, class R> struct Expr<L,R,Add>{ L l; R r;
friend auto eval(Expr self) { return eval(self.l) + eval(self.r); } };
template<class L, class R> struct Expr<L,R,Mul>{ L l; R r;
friend auto eval(Expr self) { return eval(self.l) * eval(self.r); } };
template<class L, class R, class R2> struct Expr<Expr<L, R, Mul>, R2, Add>{ Expr<L,R, Mul> l; R2 r;
friend auto eval(Expr self) { return fma(eval(self.l.l), eval(self.l.r), eval(self.r));}};
template<class L, class R>
auto operator +(L l, R r) { return Expr<L, R, Add>{l, r}; }
template<class L, class R>
auto operator *(L l, R r) { return Expr<L, R, Mul>{l, r}; }
double optimized(F x, F y, F z) { return eval(x * y + z); }
double non_optimized(F x, F y, F z) { return eval(x + y * z); }
Optimized always generates a call to fma, non-optimized does not. Use -O1 to see the difference (will inline trivial functions, but will not do other optimizations). -O0 also generates the fma, but it is lost in the noise.
The magic happens by specifically matching the pattern Expr<Expr<L, R, Mul>, R2, Add>; try to add a rule to optimize x+y*z as well.
Hrm, OK, that makes sense. Thanks for taking the time to explain! Guessing optimizing x+y*z would entail something similar to the third eval() definition but with Expr<L, Expr<L2, R2, Mul>, Add> instead.
I think at this point I can see how my initial assertion was wrong - specialization isn't fully orthogonal to expression templates, as the former is needed for some of the latter's use cases.
Does make me wonder how far one could get with rustc's internal specialization attributes...
