Thank you, David! That was very useful! You said one thing very nicely: >> you cannot expect to be able to lift floating-point specific parts from deep within the gcc optimiser and re-use them for your own code here. I confirm that this was it that I was expecting (or rather hoping :) ). Given my pessimism drawn from the apparent misunderstanding in the communication prior, I have already started to re-implement those expression templates that are probably hidden deep within GCC. Now as you and I discussed expression templates, my reluctance with those at first is their limitation on the complexity of DAG optimizations due to only permitting transformations that are possible via meta programming (i.e., no global DAG transformations). But that is then just a practical 20-80 rule where one has to make compromises. Thank you for considering my question in detail and answering helpfully! On Tue, Aug 27, 2024 at 10:26 AM David Brown <david.brown@xxxxxxxxxxxx> wrote: > I think expression templates are what you need here. > > The "-ffast-math" optimisations are very specific to floating point > calculations, and are quite dependent on the underlying implementation > of floating point. Contrary to Segher's pessimism, "-ffast-math" is > extremely useful and gives significantly better end results in > situations where it is appropriate. But like any floating point work, > you need to understand the limitations and the suitability for the task > at hand. > > I can't see how they could be of any use to you here, other than perhaps > that the documentation for the flag might be an inspiration for the kind > of re-arrangements you want to support. As I understand it, it is the > code you are writing that will do the re-arrangements - you cannot > expect to be able to lift floating-point specific parts from deep within > the gcc optimiser and re-use them for your own code here. > > You have to decide what re-arrangement rules you will accept for your > Number type, and build up appropriate expression templates. The rules > you accept will depend entirely on what "Number" is. If it represents > ideal mathematical integers, then you get lots of possibilities. If it > represents fixed-size floating point numbers, then now re-arranging "(x > + y) - x" into "y" can give a very different result. Just like with > "-ffast-math", such a re-arrangement is fine if you are equally happy > with both results. > > David > > > > On 27/08/2024 00:04, Kai Song via Gcc-help wrote: > > I would like to add an example so as to clarify what it is that I seek > help > > on: > > > > I have a custom implementation of a class called Number. Number has > > overloaded operators that write down a program of all computations that > > Number witnesses in an original program. > > For example, when the original program reads (original code): > > z=x-(-y); > > > > Then upon execution with type Number the following program will be > produced > > (generated code) as caused through stream buffers in Number: > > tmp1 = -y; > > z = x-tmp1; > > > > This generated code is inferior to as if the original code had been > > "z=x+y;". > > Using expression templates or hoping for excellent compiler optimization > on > > the "generated code", I could try to improve the performance of the > > generated code. > > But that means equal to re-inventing the wheel, because obviously the > > compilers have exactly these algebraic optimization capabilities already > > built in. > > So I want to use these capabilities. This is what my request is all > about. > > > > Certainly the compiler has algebraic expression optimization built in, so > > what I now seek to find out is whether and how this can be leveraged > > outside the rule-scope of native c++, > > so as to improve the algebra of my original code. Of course I am aware > that > > this alters the original programs result entirely (as per the above > > example) but this is precisely what I wish for. > > > > Kind regards > > > > > > > > In response to Segher: > > > > On Mon, Aug 26, 2024 at 7:19 PM Segher Boessenkool < > > segher@xxxxxxxxxxxxxxxxxxx> wrote: > > > >> On Mon, Aug 26, 2024 at 06:00:21PM +0200, Kai Song via Gcc-help wrote: > >>> I would like to learn more how GCC implements algebraic optimization > >>> heuristic such as given in -ffast-math . > >> > >> Thank you for responding. Yet I cannot make sense of your response or > > whether if how it relates to what I asked about. > > > > > >> Oh dear. > >> > >>> In particular, I have a type Number that is used in a code > >> > >> -ffast-math means you are not dealing with numbers at all, but instead > >> with quantities somewhat akin to numbers, and you don't give two hoots > >> about what happens with them. > >> > > > > Well if it was able to "deal" with anything akin to numbers, that would > > imply I can tell it to treat a type as if it was a number. > > Clearly however, that is not the case. So you may have meant something > > else, which is impossible to identify then due to ambiguity. > > This is unfortunate because I deeply care. So if you indeed mean that > > fastmath can be applied to anything akin to numbers, > > I am looking forward to how I can use the compilers abilities in that > > regard to transform algebraic expressions with custom types. > > > > > >> > >> It replaces floating point expressions by other expressions that are > >> at best vaguely related, and almost always compute a very different > >> result. > >> > > > > Yes, so here it is besides the question; because my custom type Number, > > which is the single point of interest in the communication, is not a > > floating point type. > > > > > >> > >> If you do not care about your numbers at all, and (against better > >> judgement) prefer more speed over all quality, you can use -ffast-math. > >> > > > > Well apparently I cannot, as per my question, since the algebraic > > expressions are involving my custom class Number. > > > > > >> Or, you can admit you think arithmetic is magic. It is fine to use > >> then, too. > >> > > > > I am a mathematician. I do not know nor wonder what you seek to say. > > I do care that arithmetic expressions are concise and equivalent. > > For instance, I like when "z=x-(-y);" is replaced by "z=x+y;" where x > and y > > may be of type Number. > > > > > >> Segher > >> > > > >
