DIP80: phobos additions

[Manu via Digitalmars-d]

On 10 June 2015 at 02:40, Ilya Yaroshenko via Digitalmars-d
<digitalmars-d at puremagic.com> wrote:
> On Tuesday, 9 June 2015 at 16:18:06 UTC, Manu wrote:
>>
>> On 10 June 2015 at 01:26, Ilya Yaroshenko via Digitalmars-d
>> <digitalmars-d at puremagic.com> wrote:
>>>
>>>
>>>> I believe that Phobos must support some common methods of linear algebra
>>>> and general mathematics. I have no desire to join D with Fortran
>>>> libraries
>>>> :)
>>>
>>>
>>>
>>> D definitely needs BLAS API support for matrix multiplication. Best BLAS
>>> libraries are written in assembler like openBLAS. Otherwise D will have
>>> last
>>> position in corresponding math benchmarks.
>>
>>
>> A complication for linear algebra (or other mathsy things in general)
>> is the inability to detect and implement compound operations.
>> We don't declare mathematical operators to be algebraic operations,
>> which I think is a lost opportunity.
>> If we defined the properties along with their properties
>> (commutativity, transitivity, invertibility, etc), then the compiler
>> could potentially do an algebraic simplification on expressions before
>> performing codegen and optimisation.
>> There are a lot of situations where the optimiser can't simplify
>> expressions because it runs into an arbitrary function call, and I've
>> never seen an optimiser that understands exp/log/roots, etc, to the
>> point where it can reduce those expressions properly. To compete with
>> maths benchmarks, we need some means to simplify expressions properly.
>
>
> Simplified expressions would [NOT] help because
> 1. On matrix (hight) level optimisation can be done very well by programer
> (algorithms with matrixes in terms of count of matrix multiplications are
> small).

Perhaps you've never worked with incompetent programmers (in my
experience, >50% of the professional workforce).
Programmers, on average, don't know maths. They literally have no idea
how to simplify an algebraic expression.
I think there are about 3-4 (being generous!) people in my office (of
30-40) that could do it properly, and without spending heaps of time
on it.

> 2. Low level optimisation requires specific CPU/Cache optimisation. Modern
> implementations are optimised for all cache levels. See work by KAZUSHIGE
> GOTO
> http://www.cs.utexas.edu/users/pingali/CS378/2008sp/papers/gotoPaper.pdf

Low-level optimisation is a sliding scale, not a binary position.
Reaching 'optimal' state definitely requires careful consideration of
all the details you refer to, but there are a lot of improvements that
can be gained from quickly written code without full low-level
optimisation. A lot of basic low-level optimisations (like just using
appropriate opcodes, or eliding redundant operations; ie, squares
followed by sqrt) can't be applied without first simplifying
expressions.