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Subject: Re: [boost] [GSoC, MPL11] Community probe
From: Louis Dionne (ldionne.2_at_[hidden])
Date: 2014-05-05 10:22:10

Zach Laine <whatwasthataddress <at>> writes:


> I recently decided to completely rewrite a library for linear algebra on
> heterogeneous types using Clang 3.4, which is c++14 feature-complete
> (modulo bugs). My library previously used lots of MPL and Boost.Fusion
> code, and was largely an unreadable mess. The new version only uses MPL's
> set, but no other MPL and no Fusion code, and is quite easy to understand
> (at least by comparison). The original version took me months of spare
> time to write, including lots of time trying to wrestle MPL and Fusion into
> doing what I needed them to do. The rewrite was embarrassingly easy; it
> took me about two weeks of spare time. I threw away entire files of
> return-type-computing metaprograms. The overall line count is probably 1/4
> what it was before. My library and its needs are probably atypical with
> respect to MPL usage overall, but is probably representative of much use of
> Fusion, so keep that in mind below.

I looked at the Units-BLAS codebase (assuming that's what you were referring
to) to get a better understanding of your use case. It was very helpful in
understanding at least some of the requirements for a TMP library; thank you
for that. In what follows, I sketch out possible solutions to some of your
issues. I'm mostly thinking out loud.

> Here are the metaprogramming capabilities I needed for my Fusion-like data
> structures:
> 1) compile-time type traits, as above
> 2) simple compile-time computation, as above
> 3) purely compile-time iteration over every element of a single list of
> types
> 4) purely compile-time iteration over every pair of elements in two lists
> of types (for zip-like operations, e.g. elementwise matrix products)
> 5) runtime iteration over every element of a single tuple
> 6) runtime iteration over every pair of elements in two tuples (again, for
> zip-like operations)
> For my purposes, operations performed at each iteration in 3 through 6
> above may sometimes require the index of the iteration. Again, this is
> probably atypical.

Some kind of counting range with a zip_with constexpr function should do
the trick. Hence you could do (pseudocode):
    zip_with(your_constexpr_function, range_from(0), tuple1, ..., tupleN)

where range_from(n) produces a range from n to infinity. I have been able
to implement zip_with, but I'm struggling to make it constexpr because I
need a lambda somewhere in there. The range_from(n) should be quite feasible.

> 1 is covered nicely by existing traits, and 2 is covered by ad hoc
> application-specific code (I don't see how a library helps here).

I agree.

> There are several solutions that work for at least one of 3-6:
> - Compile-time foldl(); I did mine as constexpr, simply for readability.
> - Runtime foldl().
> - Direct expansion of a template parameter pack; example:
> template <typename MatrixLHS, typename MatrixRHS, std::size_t ...I>
> auto element_prod_impl (
> MatrixLHS lhs,
> MatrixRHS rhs,
> std::index_sequence<I...>
> ) {
> return std::make_tuple(
> (tuple_access::get<I>(lhs) * tuple_access::get<I>(rhs))...
> );
> }
> (This produces the actual result of multiplying two matrices
> element-by-element (or at least the resulting matrix's internal tuple
> storage). I'm not really doing any metaprogramming here at all, and that's
> sort of the point. Any MPL successor should be as easy to use as the above
> was to write, or I'll always write the above instead. A library might help
> here, since I had to write similar functions to do elementwise division,
> addition, etc., but if a library solution has more syntactic weight than
> the function above, I won't be inclined to use it.)

I think direct expansion of parameter packs would not be required in this
case if we had a zip_with operation:
    zip_with(std::multiplies<>{}, lhs, rhs)

However, there are other similar functions in your codebase that perform
operations that are not covered by the standard function objects. For this,
it would be _very_ useful to have constexpr lambdas.

> - Ad hoc metafunctions and constexpr functions that iterate on type-lists.
> - Ad hoc metafunctions and constexpr functions that iterate over the values
> [1..N).
> - Ad hoc metafunctions and constexpr functions that iterate over [1..N)
> indices into a larger or smaller range of values.

I'm sorry, but I don't understand the last one. Do you mean iteration
through a slice [1, N) of another sequence?

> I was unable to find much in common between my individual ad hoc
> implementations that I could lift up into library abstractions, or at least
> not without increasing the volume of code more than it was worth to me. I
> was going for simple and maintainable over abstract. Part of the lack of
> commonality was that in one case, I needed indices for each iteration, in
> another one I needed types, in another case I needed to accumulate a
> result, in another I needed to return multiple values, etc. Finding an
> abstraction that buys you more than it costs you is difficult in such
> circumstances.

I do think it is possible to find nice abstractions, but it will be worth
lifting into a separate library. I also think it will require departing
from the usual STL concepts and going into FP-world.

> So, I'm full of requirements, and no answers. :) I hope this helps, if
> only with scoping. I'll be in Aspen if you want to discuss it there too.

I'm looking forward to it.

> > It is easy to see how constexpr (and relaxed constexpr) can make the second
> > kind of computation easier to express, since that is exactly its purpose.
> > However, it is much less clear how constexpr helps us with computations of
> > the first kind. And by that I really mean that using constexpr in some way
> > to perform those computations might be more cumbersome and less efficient
> > than good old metafunctions.
> >
> >
> I've been using these to write less code, if only a bit less.
> Instead of:
> template <typename Tuple>
> struct meta;
> template <typename ...T>
> struct meta<std::tuple<T...>>
> { using type = /*...*/; };
> I've been writing:
> template <typename ...T>
> constexpr auto meta (std::tuple<T...>)
> { return /*...*/; }
> ...and calling it as decltype(meta(std::tuple</*...*/>{})). This both
> eliminates the noise coming from having a base/specialization template pair
> instead of one template, and also removes the need for a *_t template alias
> and/or typename /*...*/::type.

That's valid in most use cases, but this won't work if you want to manipulate
incomplete types, void and function types. Unless I'm mistaken, you can't
instantiate a tuple holding any of those. Since a TMP library must clearly
be able to handle the funkiest types, I don't think we can base a new TMP
library on metafunctions with that style, unless a workaround is found.
I also fear this might be slower because of possibly complex overload
resolution, but without benchmarks that's just FUD.

Like you said initially, I think your use case is representative of a C++14
Fusion-like library more than a MPL-like one. I'll have to clearly define
the boundary between those before I can claim to have explored the whole
design space for a new TMP library.


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