DIP80: phobos additions

Ilya Yaroshenko via Digitalmars-d digitalmars-d at puremagic.com
Tue Jun 9 09:40:55 PDT 2015


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 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).
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


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