[RFC] use templated isl types memberRange

Templated isl types require the user to specify the domain and range
universes of isl objects, allowing the compiler to check whether
it makes sense to combine pairs of objects.
This RFC only converts isPromotableToRegistersBelow and some related
functions to illustrate the effect.
The isPromotableToRegistersBelow was already applying operations
correctly, so the code itself did not require any changes.
However, one variable was reused to store different types
of intermediate result and this one had to be split up into
several variables because they now have different types.

Author: Sven Verdoolaege

tc/core/polyhedral/cuda/mapped_scop.cc

@@ -296,8 +296,8 @@ bool MappedScop::detectReductions(ScheduleTree* tree) {
   });
   // The outer (coincident) members, together with the prefix schedule,
   // need to determine a single reduction.
-  auto prefix = prefixScheduleMupa(schedule(), tree);
-  prefix = prefix.range_product(band->memberRange(0, nCoincident));
+  auto prefix = prefixScheduleMupa<Prefix>(schedule(), tree)
+      .range_product(band->memberRange<Band>(0, nCoincident));
   if (!isSingleReductionWithin(updates, prefix, scop())) {
     return false;
   }
@@ -331,7 +331,7 @@ isl::multi_union_pw_aff MappedScop::reductionMapSchedule(
   TC_CHECK_GE(nMember, reductionDim + 1);
 
   auto first = reductionDim + 1 - nMappedThreads;
-  return reductionBand->memberRange(first, nMappedThreads);
+  return reductionBand->memberRange<ReductionSchedule>(first, nMappedThreads);
 }
 
 ScheduleTree* MappedScop::separateReduction(ScheduleTree* st) {

tc/core/polyhedral/domain_types.h

@@ -1,6 +1,7 @@
 namespace tc {
 namespace polyhedral {
 
+struct Band;
 struct Prefix;
 struct Reduction;
 struct ReductionSchedule;

tc/core/polyhedral/schedule_tree_elem.h

@@ -23,6 +23,7 @@
 #include "tc/external/isl.h"
 
 #include "tc/core/check.h"
+#include "tc/core/polyhedral/domain_types.h"
 #include "tc/core/polyhedral/mapping_types.h"
 #include "tc/core/polyhedral/schedule_tree.h"
 
@@ -331,14 +332,15 @@ struct ScheduleTreeBand : public ScheduleTree {
 
   // Extract the range of "n" members starting at "first"
   // (in an anonymous space).
-  isl::multi_union_pw_aff memberRange(size_t first, size_t n) const {
+  template <typename Range>
+  isl::MultiUnionPwAff<Statement, Range> memberRange(size_t first, size_t n) const {
     auto list = mupa_.get_union_pw_aff_list();
     auto space = mupa_.get_space().params().add_unnamed_tuple_ui(n);
     auto end = first + n;
     TC_CHECK_LE(end, nMember());
     list = list.drop(end, nMember() - end);
     list = list.drop(0, first);
-    return isl::multi_union_pw_aff(space, list);
+    return isl::MultiUnionPwAff<Statement, Range>(isl::multi_union_pw_aff(space, list));
   }
 
  public: