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
