1.1 Basically, what’s the point ?

If you want to use CLooG, this is because you want to scan or to find something inside the integral points of a set of polyhedra. There are many reasons for that. Maybe you need the generated code itself because it actually implements a very smart program transformation you found. Maybe you want to use the generated code because you know that the solution of your problem belongs to the integral points of those damned polyhedra and you don’t know which one. Maybe you just want to know if a polyhedron has integral points depending on some parameters, which is the lexicographic minimum, maximum, the third on the basis of the left etc. Probably you have your own reasons to use CLooG.

Let us illustrate a basic use of CLooG. Suppose we have a set of affine constraints that describes a part of a whatever-dimensional space, called a domain, and we want to scan it. Let us consider for instance the following set of constraints where ‘i’ and ‘j’ are the unknown (the two dimensions of the space) and ‘m’ and ‘n’ are the parameters (some symbolic constants):

2<=i<=n
2<=j<=m
j<=n+2-i

Let us also consider that we have a partial knowledge of the parameter values, called the context, expressed as affine constraints as well, for instance:

m>=2
n>=2

Note that using parameters is optional, if you are not comfortable with parameter manipulation, just replace them with any scalar value that fits m>=2 and n>=2. A graphical representation of this part of the 2-dimensional space, where the integral points are represented using heavy dots would be for instance:

The affine constraints of both the domain and the context are what we will provide to CLooG as input (in a particular shape that will be described later). The output of CLooG is a pseudo-code to scan the integral points of the input domain according to the context:

for (i=2;i<=n;i++) {
  for (j=2;j<=min(m,-i+n+2);j++) {    
    S1(i,j) ;
  }
}

If you felt such a basic example is yet interesting, there is a good chance that CLooG is appropriate for you. CLooG can do much more: scanning several polyhedra or unions of polyhedra at the same time, applying general affine transformations to the polyhedra, generate compilable code etc. Welcome to the CLooG’s user’s guide !

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