Hi Roberto,
basicall, what I need Z-polytopes for is a problem like the following:
Assume we have a certain loop-nest with some statements that access a certain array:
for(i=0; i<n; i++) { for(j=0; j<n; j++) { A[2*i][2*j] = ... A[i][i] = ... } }
(in general, array accesses can be arbitrary affine functions of loop variables and structural parameters)
What I want to analyze is the array elements that are accessed by this program. I want to count the number of array elements that are needed during this computation. Unfortunately, the resulting sets are not always convex polytopes, e.g. in this case, the first array access function yields a set of points with only even numbers for coordinate entries.
So I have to use Z-polytopes to describe this set and count the number of points it contains. For this purpose, I have to calculate a disjoint union of the two Z-polytopes resulting from mapping each array access function (2i,2j) and (i,i) on the index space of each statement. Then, I can use the Barvinok algorithm to count the number of elements for each set in the resulting (disjoint) union.
I have implemented this method using the PolyLib, but unfortunately there seem to be fundamental problems with the implementation of Z-polytopes. So I was hoping that I could use PPL to achieve something equivalent.
I hope this will clear up a few of the misunderstandings? But feel free to ask further questions.
I also intend to follow the graphite telephone conference call this Wednesday at 3pm.
greetings, Michael Classen
On Fri, Jul 10, 2009 at 6:05 PM, Roberto Bagnarabagnara@cs.unipr.it wrote:
Michael Classen wrote:
Hello Roberto,
this is basically what I was referring to:
Hi Michael,
thanks for clarifying. I need to understand more about what you mean by:
I basically just want to know if I can get correct integer results when using this combination of datatypes. I want to use operations like union, intersection, projection, basically most standard operations you want to use on polytopes.
What do you mean by "correct integer results"?
What I am worried about is that you may believe the PPL supports the computation of the integer hull of a convex rational polyhedron (i.e., the smallest polyhedron containing only the integer points of the given rational polyhedron). The PPL does not provide an algorithm to solve this (difficult!) problem.
What the PPL provides is:
- the C_Polyhedron class that you know;
- the Grid class that is able, in particular, to express
the integer lattice; 3) a generic Partially_Reduced_Product class that allows to combine two domains, given a reduction procedure that propagates _some_ information from one to the other. I am wondering if this is the same notion of "combination" you use above.
In point (3) the key words are "partially" and "some". If _all_ the information was propagated from the Grid component to the C_Polyhedron component, we would be able to compute the integer hull, but this is not the case.
Going back to the expression "correct integer results", a Partially_Reduced_Product among a C_Polyhedron and a Grid encoding the integer lattice provides (as far as we know) correct, but possibly (and often) imprecise results. Cheers,
Roberto
-- Prof. Roberto Bagnara Computer Science Group Department of Mathematics, University of Parma, Italy http://www.cs.unipr.it/~bagnara/ mailto:bagnara@cs.unipr.it