std.math performance (SSE vs. real)

[Andrei Alexandrescu via Digitalmars-d]

On 6/28/14, 5:33 PM, Walter Bright wrote:
> On 6/28/2014 7:01 AM, Andrei Alexandrescu wrote:
>> On 6/28/14, 3:42 AM, Walter Bright wrote:
>>> Inverting matrices is commonplace for solving N equations with N
>>> unknowns.
>>
>> Actually nobody does that.
>
> I did that at Boeing when doing analysis of the movement of the control
> linkages. The traditional way it had been done before was using paper
> and pencil with drafting tools - I showed how it could be done with
> matrix math.

Pen on paper is a low baseline. The classic way to solve linear 
equations with computers is to use Gaussian elimination methods adjusted 
to cancel imprecision. (There are a number of more specialized methods.)

For really large equations with sparse matrices one uses the method of 
relaxations.

>> I have an alarm go off when someone proffers a very strong conviction.
>> Very
>> strong convictions means there is no listening to any argument right
>> off the
>> bat, which locks out any reasonable discussion before it even begins.
>
> So far, everyone here has dismissed my experienced out of hand. You too,
> with "nobody does that". I don't know how anyone here can make such a
> statement. How many of us have worked in non-programming engineering
> shops, besides me?

My thesis - http://erdani.com/research/dissertation_color.pdf - and some 
of my work at Facebook, which has been patented - 
http://www.faqs.org/patents/app/20140046959 - use large matrix algebra 
intensively.

>> For better or worse modern computing units have focused on 32- and
>> 64-bit float,
>> leaving 80-bit floats neglected.
>
> Yep, for the game/graphics industry. Modern computing has also produced
> crappy trig functions with popular C compilers, because nobody using C
> cares about accurate answers (or they just assume what they're getting
> is correct - even worse).
>
>
>> I think it's time to accept that simple fact
>> and act on it, instead of claiming we're the best in the world at FP
>> math while
>> everybody else speeds by.
>
> Leaving us with a market opportunity for precision FP.
>
> I note that even the title of this thread says nothing about accuracy,
> nor did the benchmark attempt to assess if there was a difference in
> results.

All I'm saying is that our convictions should be informed by, and 
commensurate with, our expertise.


Andrei