DIP80: phobos additions

[John Colvin via Digitalmars-d]

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.

Optimising floating point is a massive pain because of precision 
concerns and IEEE-754 conformance. Just because something is 
analytically the same doesn't mean you want the optimiser to go 
ahead and make the switch for you.

Of the things that can be done, lazy operations should make it 
easier/possible for the optimiser to spot.