makeScheduleTreeHelper: create iteration domain in parameter space first

The function makeIslAffBoundsFromExpr currently relies on the names
of the set dimensions in a space.  Even though the dependence
is very localized and it is unlikely that those names would
get dropped, it is better to not rely on them at all.
Start by collecting the constraints on the outer loop iterators
in terms of parameters and only convert them into set dimensions
at the point where the iteration domain is constructed.
This means that at least during this part of the construction,
makeIslAffBoundsFromExpr only gets called on parameter spaces.

Treating the outer loop iterators as parameters at first
makes sense because they have a fixed value at the point
where the statement is executed.
It is only at the point where the iteration domain is constructed
that the loop iterators should no longer be considered as parameters.

Since the current loop index can no longer be extracted from
the set dimension, it is obtained from the number
of outer loop iterators instead.

Author: Sven Verdoolaege

tc/core/halide2isl.cc

@@ -361,32 +361,25 @@ isl::schedule makeScheduleTreeHelper(
     IterationDomainMap* domains) {
   isl::schedule schedule;
   if (auto op = s.as<For>()) {
-    // Add one additional dimension to our set of loop variables
-    int thisLoopIdx = set.dim(isl::dim_type::set);
-    set = set.add_dims(isl::dim_type::set, 1);
-
-    // Make an id for this loop var. For set dimensions this is
-    // really just for pretty-printing.
+    // Make an id for this loop var.  It starts out as a parameter.
     isl::id id(set.get_ctx(), op->name);
-    set = set.set_dim_id(isl::dim_type::set, thisLoopIdx, id);
+    auto space = set.get_space().add_param(id);
 
-    // Construct a variable (affine function) that indexes the new dimension of
-    // this space.
-    isl::aff loopVar(
-        isl::local_space(set.get_space()), isl::dim_type::set, thisLoopIdx);
+    // Construct a variable (affine function) that references
+    // the new parameter.
+    auto loopVar = isl::aff::param_on_domain_space(space, id);
 
     // Then we add our new loop bound constraints.
-    auto lbs = halide2isl::makeIslAffBoundsFromExpr(
-        set.get_space(), op->min, false, true);
+    auto lbs =
+        halide2isl::makeIslAffBoundsFromExpr(space, op->min, false, true);
     TC_CHECK_GT(lbs.size(), 0u)
         << "could not obtain polyhedral lower bounds from " << op->min;
     for (auto lb : lbs) {
       set = set.intersect(loopVar.ge_set(lb));
     }
 
     Expr max = simplify(op->min + op->extent - 1);
-    auto ubs =
-        halide2isl::makeIslAffBoundsFromExpr(set.get_space(), max, true, false);
+    auto ubs = halide2isl::makeIslAffBoundsFromExpr(space, max, true, false);
     TC_CHECK_GT(ubs.size(), 0u)
         << "could not obtain polyhedral upper bounds from " << max;
     for (auto ub : ubs) {
@@ -407,7 +400,7 @@ isl::schedule makeScheduleTreeHelper(
     isl::multi_union_pw_aff mupa;
     body.get_domain().foreach_set([&](isl::set s) {
       isl::aff newLoopVar(
-          isl::local_space(s.get_space()), isl::dim_type::set, thisLoopIdx);
+          isl::local_space(s.get_space()), isl::dim_type::set, outer.n());
       if (mupa) {
         mupa = mupa.union_add(isl::union_pw_aff(isl::pw_aff(newLoopVar)));
       } else {
@@ -442,7 +435,7 @@ isl::schedule makeScheduleTreeHelper(
     IterationDomain iterationDomain;
     iterationDomain.tuple = isl::multi_id(tupleSpace, outer);
     domains->emplace(id, iterationDomain);
-    isl::set domain = set.set_tuple_id(id);
+    auto domain = set.unbind_params(iterationDomain.tuple);
     schedule = isl::schedule::from_domain(domain);
 
     isl::union_map newReads, newWrites;