Hi Michael, On Jul 5, 2004, at 4:52 PM, Michael Stevens wrote:
Hi Jeremy,
Thanks for chipping in on this. I don't think we have conversed before, apart from maybe a few patches I submitted for MTL. Although it would be great for everyone to work on uBLAS I think a revived MTL would also be a good thing. The design of MTL was very influential.
Thanks!
I won't comment on the other issues as I have already posted a few thoughts on these matters.
Mmmh, this open pitfalls concerning A*B*C in performance issues for non experts.
No, the right way to handle this is to have the expression template machinery identify that a temporary is needed, and create one automatically.
I wonder if you caught the discussion on this about 6 months ago. I would strongly argue that the automatic creation of temporaries in the subexpression context is a bad thing...
The roles of the expressions we declare (as in declarative programming) is twofold. a) to express the mathematical context b) to express how this should be computed. That is, to be able to express how the expression is to be evaluated. This gives us control over its numerical properties and also of the time and space complexity.
In principle, uBLAS has a one to one relationship between an expression and how it is evaluated. Simply stated this is based on an element by element evaluation of assignment. There are shortcuts in the case of sparse types but the principle holds.
An expression A+B+C can be evaluated in this manner trivially. A*B*C can also be evaluated in this manner, although the element by element rule results in an O() that is not what many users expect. To get the O() that users expect we could automagically insert temporaries. I fear this is a tar pit however. What temporary should be chosen? Each of A B or C could be a either dense, sparse, compressed, banded, symmetric or combinations therefore. The type the user expects or is "the best" is not at all clear.
Although automagically inserting temporaries in non-trivial (especially since it must all be done with template meta-programming) I do not think it is a tar pit. Here is the simply heuristic that I used for MTL 3 to decide where to put temporaries: 1. If an operation needs to read from an argument multiple times, evaluate the argument eagerly into a temporary. For example, a sparse matrix in compressed row format times the sum of two vectors: A * (x + y) In this case, the (x + y) would be evaluated into a temporary before evaluating the multiplication. 2. If an operation writes into its output in multiple passes, then perform the operation in an eager fashion. For example, the sum of a vector and the product of a sparse matrix in compressed column format and a vector. x + (A * y) In this case, the (A * y) would be evaluated into a temporary before evaluating the addition.
I think the only correct solution is to force the user to specify this type. Incidently, the no temporary evaluation should also be an option as in some cases (small sizes) it is desirable. uBLAS currently disallows this to avoid confusing the user. I should be reinstated in some form however.
All the best, Michael
-- ___________________________________ Michael Stevens Systems Engineering
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_______________________________________________ Jeremy Siek <jsiek@osl.iu.edu> http://www.osl.iu.edu/~jsiek Ph.D. Candidate, Indiana University Bloomington C++ Booster (http://www.boost.org) _______________________________________________