[Polly] Add dumpPw() and dumpExpanded() functions. NFC.

[Meinersbur]

Summary

These functions print a multi-line and sorted representation of unions of polyhedra. Each polyhedron has its own line.

Example output:
[p_0, p_1, p_2] -> {

Stmt0[0] -> [0, 0];
Stmt0[i0] -> [i0, 0] : 0 < i0 <= 5 - p_2;
Stmt1[0] -> [0, 2] : p_1 = 1 and p_0 = -1;
Stmt2[0] -> [0, 1] : p_1 >= 3 + p_0;
Stmt3[0] -> [0, 3];

}

dumpExpanded() prints each point in the sets, except if the dimension is unbounded.

Example output of { [MemRef_A[i0] -> [i1]] : (exists (e0 = floor((1 + i1)/3): i0 = 1 and 3e0 <= i1 and 3e0 >= -1 + i1 and i1 >= 15 and i1 <= 25)) or (exists (e0 = floor((i1)/3): i0 = 0 and 3e0 < i1 and 3e0 >= -2 + i1 and i1 > 0 and i1 <= 11)) }:

{

[MemRef_A[0] ->[1]];
[MemRef_A[0] ->[2]];
[MemRef_A[0] ->[4]];
[MemRef_A[0] ->[5]];
[MemRef_A[0] ->[7]];
[MemRef_A[0] ->[8]];
[MemRef_A[0] ->[10]];
[MemRef_A[0] ->[11]];
[MemRef_A[1] ->[15]];
[MemRef_A[1] ->[16]];
[MemRef_A[1] ->[18]];
[MemRef_A[1] ->[19]];
[MemRef_A[1] ->[21]];
[MemRef_A[1] ->[22]];
[MemRef_A[1] ->[24]];
[MemRef_A[1] ->[25]]

}

These functions help to understand the isl's sets while debugging Polly.

[grosser]

LGTM.

include/polly/Support/ISLTools.h

 /// @p Range is an isl::union_set. This is the only difference to
 /// isl::map::intersect_range and isl::union_map::interset_range.
 ///
 /// @param Map   { Domain[] -> Range[] }
 /// @param Range { Range[] }
 ///
 /// @return { Domain[] -> Range[] }
 isl::map intersectRange(isl::map Map, isl::union_set Range);
+
+/// If @p PwAff maps to a constant, return said constant. If @p Max/@p Min, it
+/// can also be a piecewise constant and it would return the minimum/maximum
+/// value. Otherwise, return NaN.
+isl::val getConstant(isl::pw_aff PwAff, bool Max, bool Min);
+
+/// Dump a description of the argument to llvm::errs().
+///
+/// In contrast to isl's dump function, there are a few differences:
+/// - Each polyhedron (pieces) is written on its own line.
+/// - Spaces are sorted by structure. E.g. maps with same domain space are
+///   grouped. Isl sorts them according to the space's hash function.
+/// - Pieces of the same space are sorted using their lower bound.
+/// - A more compact to_str representation is used instead of Isl's dump
+///   functions that try to show the internal representation.
+///
+/// The goal is to get a better understandable representation that is also
+/// useful to compare two sets. As all dump() functions, its intended use is to
+/// be called in a debugger only.
+///
+/// isl_map_dump example:
+/// [p_0, p_1, p_2] -> { Stmt0[i0] -> [o0, o1] : (o0 = i0 and o1 = 0 and i0 > 0
+/// and i0 <= 5 - p_2) or (i0 = 0 and o0 = 0 and o1 = 0); Stmt3[i0] -> [o0, o1]
+/// : (o0 = i0 and o1 = 3 and i0 > 0 and i0 <= 5 - p_2) or (i0 = 0 and o0 = 0
+/// and o1 = 3); Stmt2[i0] -> [o0, o1] : (o0 = i0 and o1 = 1 and i0 >= 3 + p_0 -
+/// p_1 and i0 > 0 and i0 <= 5 - p_2) or (o0 = i0 and o1 = 1 and i0 > 0 and i0
+/// <= 5 - p_2 and i0 < p_0 - p_1) or (i0 = 0 and o0 = 0 and o1 = 1 and p_1 >= 3
+/// + p_0) or (i0 = 0 and o0 = 0 and o1 = 1 and p_1 < p_0) or (p_0 = 0 and i0 =
+/// 2 - p_1 and o0 = 2 - p_1 and o1 = 1 and p_2 <= 3 + p_1 and p_1 <= 1) or (p_1
+/// = 1 + p_0 and i0 = 0 and o0 = 0 and o1 = 1) or (p_0 = 0 and p_1 = 2 and i0 =
+/// 0 and o0 = 0 and o1 = 1) or (p_0 = -1 and p_1 = -1 and i0 = 0 and o0 = 0 and
+/// o1 = 1); Stmt1[i0] -> [o0, o1] : (p_0 = -1 and i0 = 1 - p_1 and o0 = 1 - p_1
+/// and o1 = 2 and p_2 <= 4 + p_1 and p_1 <= 0) or (p_0 = 0 and i0 = -p_1 and o0
+/// = -p_1 and o1 = 2 and p_2 <= 5 + p_1 and p_1 < 0) or (p_0 = -1 and p_1 = 1
+/// and i0 = 0 and o0 = 0 and o1 = 2) or (p_0 = 0 and p_1 = 0 and i0 = 0 and o0
+/// = 0 and o1 = 2) }
+///
+/// dumpPw example (same set):
+/// [p_0, p_1, p_2] -> {
+///   Stmt0[0] -> [0, 0];
+///   Stmt0[i0] -> [i0, 0] : 0 < i0 <= 5 - p_2;
+///   Stmt1[0] -> [0, 2] : p_1 = 1 and p_0 = -1;
+///   Stmt1[0] -> [0, 2] : p_1 = 0 and p_0 = 0;
+///   Stmt1[1 - p_1] -> [1 - p_1, 2] : p_0 = -1 and p_1 <= 0 and p_2 <= 4 + p_1;
+///   Stmt1[-p_1] -> [-p_1, 2] : p_0 = 0 and p_1 < 0 and p_2 <= 5 + p_1;
+///   Stmt2[0] -> [0, 1] : p_1 >= 3 + p_0;
+///   Stmt2[0] -> [0, 1] : p_1 < p_0;
+///   Stmt2[0] -> [0, 1] : p_1 = 1 + p_0;
+///   Stmt2[0] -> [0, 1] : p_1 = 2 and p_0 = 0;
+///   Stmt2[0] -> [0, 1] : p_1 = -1 and p_0 = -1;
+///   Stmt2[i0] -> [i0, 1] : i0 >= 3 + p_0 - p_1 and 0 < i0 <= 5 - p_2;
+///   Stmt2[i0] -> [i0, 1] : 0 < i0 <= 5 - p_2 and i0 < p_0 - p_1;
+///   Stmt2[2 - p_1] -> [2 - p_1, 1] : p_0 = 0 and p_1 <= 1 and p_2 <= 3 + p_1;
+///   Stmt3[0] -> [0, 3];
+///   Stmt3[i0] -> [i0, 3] : 0 < i0 <= 5 - p_2
+/// }
+/// @{
+void dumpPw(const isl::set &Set);
+void dumpPw(const isl::map &Map);
+void dumpPw(const isl::union_set &USet);
+void dumpPw(const isl::union_map &UMap);
+void dumpPw(__isl_keep isl_set *Set);
+void dumpPw(__isl_keep isl_map *Map);
+void dumpPw(__isl_keep isl_union_set *USet);
+void dumpPw(__isl_keep isl_union_map *UMap);
+/// @}
+
+/// Dump all points of the argument to llvm::errs().
+///
+/// Before being printed by dumpPw(), the argument's pieces are expanded to
+/// contain only single points. If a dimension is unbounded, it keeps its
+/// representation.
+///
+/// This is useful for debugging reduced cases where parameters are set to
+/// constants to keep the example simple. Such sets can still contain
+/// existential dimensions which makes the polyhedral hard to compare.
+///
+/// Example:
+///   { [MemRef_A[i0] -> [i1]] : (exists (e0 = floor((1 + i1)/3): i0 = 1 and 3e0
+///   <= i1 and 3e0 >= -1 + i1 and i1 >= 15 and i1 <= 25)) or (exists (e0 =
+///   floor((i1)/3): i0 = 0 and 3e0 < i1 and 3e0 >= -2 + i1 and i1 > 0 and i1 <=
+///   11)) }
+///
+/// dumpExpanded:
+/// {
+///   [MemRef_A[0] ->[1]];
+///   [MemRef_A[0] ->[2]];
+///   [MemRef_A[0] ->[4]];
+///   [MemRef_A[0] ->[5]];
+///   [MemRef_A[0] ->[7]];
+///   [MemRef_A[0] ->[8]];
+///   [MemRef_A[0] ->[10]];
+///   [MemRef_A[0] ->[11]];
+///   [MemRef_A[1] ->[15]];
+///   [MemRef_A[1] ->[16]];
+///   [MemRef_A[1] ->[18]];
+///   [MemRef_A[1] ->[19]];
+///   [MemRef_A[1] ->[21]];
+///   [MemRef_A[1] ->[22]];
+///   [MemRef_A[1] ->[24]];
+///   [MemRef_A[1] ->[25]]
+/// }
+/// @{
+void dumpExpanded(const isl::set &Set);
+void dumpExpanded(const isl::map &Map);
+void dumpExpanded(const isl::union_set &USet);
+void dumpExpanded(const isl::union_map &UMap);
+void dumpExpanded(__isl_keep isl_set *Set);
+void dumpExpanded(__isl_keep isl_map *Map);
+void dumpExpanded(__isl_keep isl_union_set *USet);
+void dumpExpanded(__isl_keep isl_union_map *UMap);
+/// @}
+
 } // namespace polly
 
 #endif /* POLLY_ISLTOOLS_H */

lib/Support/ISLTools.cpp

 //===------ ISLTools.cpp ----------------------------------------*- C++ -*-===//
 //
 //                     The LLVM Compiler Infrastructure
 //
 // This file is distributed under the University of Illinois Open Source
 // License. See LICENSE.TXT for details.
 //
 //===----------------------------------------------------------------------===//
 //
 // Tools, utilities, helpers and extensions useful in conjunction with the
 // Integer Set Library (isl).
 //
 //===----------------------------------------------------------------------===//
 
 #include "polly/Support/ISLTools.h"
+#include "llvm/ADT/StringRef.h"
 
 using namespace polly;
 
 namespace {
 /// Create a map that shifts one dimension by an offset.
 ///
 /// Example:
 /// makeShiftDimAff({ [i0, i1] -> [o0, o1] }, 1, -2)
isl::union_map polly::applyDomainRange(isl::union_map UMap,
 
   return std::move(UMap).apply_domain(std::move(LifetedFunc));
 }
 
 isl::map polly::intersectRange(isl::map Map, isl::union_set Range) {
   isl::set RangeSet = Range.extract_set(Map.get_space().range());
   return Map.intersect_range(RangeSet);
 }
+
+isl::val polly::getConstant(isl::pw_aff PwAff, bool Max, bool Min) {
+  assert(!Max || !Min); // Cannot return min and max at the same time.
+  isl::val Result;
+  PwAff.foreach_piece([=, &Result](isl::set Set, isl::aff Aff) -> isl::stat {
+    if (Result && Result.is_nan())
+      return isl::stat::ok;
+
+    // TODO: If Min/Max, we can also determine a minimum/maximum value if
+    // Set is constant-bounded.
+    if (!Aff.is_cst()) {
+      Result = isl::val::nan(Aff.get_ctx());
+      return isl::stat::error;
+    }
+
+    isl::val ThisVal = Aff.get_constant_val();
+    if (!Result) {
+      Result = ThisVal;
+      return isl::stat::ok;
+    }
+
+    if (Result.eq(ThisVal))
+      return isl::stat::ok;
+
+    if (Max && ThisVal.gt(Result)) {
+      Result = ThisVal;
+      return isl::stat::ok;
+    }
+
+    if (Min && ThisVal.lt(Result)) {
+      Result = ThisVal;
+      return isl::stat::ok;
+    }
+
+    // Not compatible
+    Result = isl::val::nan(Aff.get_ctx());
+    return isl::stat::error;
+  });
+  return Result;
+}
+
+#if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
+static void foreachPoint(const isl::set &Set,
+                         const std::function<void(isl::point P)> &F) {
+  isl_set_foreach_point(
+      Set.keep(),
+      [](__isl_take isl_point *p, void *User) -> isl_stat {
+        auto &F = *static_cast<const std::function<void(isl::point)> *>(User);
+        F(give(p));
+        return isl_stat_ok;
+      },
+      const_cast<void *>(static_cast<const void *>(&F)));
+}
+
+static void foreachPoint(isl::basic_set BSet,
+                         const std::function<void(isl::point P)> &F) {
+  foreachPoint(give(isl_set_from_basic_set(BSet.take())), F);
+}
+
+/// Determine the sorting order of the sets @p A and @p B without considering
+/// the space structure.
+///
+/// Ordering is based on the lower bounds of the set's dimensions. First
+/// dimensions are considered first.
+static int flatCompare(const isl::basic_set &A, const isl::basic_set &B) {
+  int ALen = A.dim(isl::dim::set);
+  int BLen = B.dim(isl::dim::set);
+  int Len = std::min(ALen, BLen);
+
+  for (int i = 0; i < Len; i += 1) {
+    isl::basic_set ADim =
+        A.project_out(isl::dim::param, 0, A.dim(isl::dim::param))
+            .project_out(isl::dim::set, i + 1, ALen - i - 1)
+            .project_out(isl::dim::set, 0, i);
+    isl::basic_set BDim =
+        B.project_out(isl::dim::param, 0, B.dim(isl::dim::param))
+            .project_out(isl::dim::set, i + 1, BLen - i - 1)
+            .project_out(isl::dim::set, 0, i);
+
+    isl::basic_set AHull = isl::set(ADim).convex_hull();
+    isl::basic_set BHull = isl::set(BDim).convex_hull();
+
+    bool ALowerBounded =
+        bool(isl::set(AHull).dim_has_any_lower_bound(isl::dim::set, 0));
+    bool BLowerBounded =
+        bool(isl::set(BHull).dim_has_any_lower_bound(isl::dim::set, 0));
+
+    int BoundedCompare = BLowerBounded - ALowerBounded;
+    if (BoundedCompare != 0)
+      return BoundedCompare;
+
+    if (!ALowerBounded || !BLowerBounded)
+      continue;
+
+    isl::pw_aff AMin = isl::set(ADim).dim_min(0);
+    isl::pw_aff BMin = isl::set(BDim).dim_min(0);
+
+    isl::val AMinVal = polly::getConstant(AMin, false, true);
+    isl::val BMinVal = polly::getConstant(BMin, false, true);
+
+    int MinCompare = AMinVal.sub(BMinVal).sgn();
+    if (MinCompare != 0)
+      return MinCompare;
+  }
+
+  // If all the dimensions' lower bounds are equal or incomparable, sort based
+  // on the number of dimensions.
+  return ALen - BLen;
+}
+
+/// Compare the sets @p A and @p B according to their nested space structure. If
+/// the structure is the same, sort using the dimension lower bounds.
+static int recursiveCompare(const isl::basic_set &A, const isl::basic_set &B) {
+  isl::space ASpace = A.get_space();
+  isl::space BSpace = B.get_space();
+
+  int WrappingCompare = bool(ASpace.is_wrapping()) - bool(BSpace.is_wrapping());
+  if (WrappingCompare != 0)
+    return WrappingCompare;
+
+  if (ASpace.is_wrapping() && B.is_wrapping()) {
+    isl::basic_map AMap = A.unwrap();
+    isl::basic_map BMap = B.unwrap();
+
+    int FirstResult = recursiveCompare(AMap.domain(), BMap.domain());
+    if (FirstResult != 0)
+      return FirstResult;
+
+    return recursiveCompare(AMap.range(), BMap.range());
+  }
+
+  std::string AName = ASpace.has_tuple_name(isl::dim::set)
+                          ? ASpace.get_tuple_name(isl::dim::set)
+                          : std::string();
+  std::string BName = BSpace.has_tuple_name(isl::dim::set)
+                          ? BSpace.get_tuple_name(isl::dim::set)
+                          : std::string();
+
+  int NameCompare = AName.compare(BName);
+  if (NameCompare != 0)
+    return NameCompare;
+
+  return flatCompare(A, B);
+}
+
+/// Wrapper for recursiveCompare, convert a {-1,0,1} compare result to what
+/// std::sort expects.
+static bool orderComparer(const isl::basic_set &A, const isl::basic_set &B) {
+  return recursiveCompare(A, B) < 0;
+}
+
+/// Print a string representation of @p USet to @p OS.
+///
+/// The pieces of @p USet are printed in a sorted order. Spaces with equal or
+/// similar nesting structure are printed together. Compared to isl's own
+/// printing function the uses the structure itself as base of the sorting, not
+/// a hash of it. It ensures that e.g. maps spaces with same domain structure
+/// are printed together. Set pieces with same structure are printed in order of
+/// their lower bounds.
+///
+/// @param USet     Polyhedra to print.
+/// @param OS       Target stream.
+/// @param Simplify Whether to simplify the polyhedron before printing.
+/// @param IsMap    Whether @p USet is a wrapped map. If true, sets are
+///                 unwrapped before printing to again appear as a map.
+static void printSortedPolyhedra(isl::union_set USet, llvm::raw_ostream &OS,
+                                 bool Simplify, bool IsMap) {
+  if (!USet) {
+    OS << "<null>\n";
+    return;
+  }
+
+  if (Simplify)
+    simplify(USet);
+
+  // Get all the polyhedra.
+  std::vector<isl::basic_set> BSets;
+  USet.foreach_set([&BSets](isl::set Set) -> isl::stat {
+    Set.foreach_basic_set([&BSets](isl::basic_set BSet) -> isl::stat {
+      BSets.push_back(BSet);
+      return isl::stat::ok;
+    });
+    return isl::stat::ok;
+  });
+
+  if (BSets.empty()) {
+    OS << "{\n}\n";
+    return;
+  }
+
+  // Sort the polyhedra.
+  std::sort(BSets.begin(), BSets.end(), orderComparer);
+
+  // Print the polyhedra.
+  bool First = true;
+  for (const isl::basic_set &BSet : BSets) {
+    std::string Str;
+    if (IsMap)
+      Str = isl::map(BSet.unwrap()).to_str();
+    else
+      Str = isl::set(BSet).to_str();
+    size_t OpenPos = Str.find_first_of('{');
+    assert(OpenPos != std::string::npos);
+    size_t ClosePos = Str.find_last_of('}');
+    assert(ClosePos != std::string::npos);
+
+    if (First)
+      OS << llvm::StringRef(Str).substr(0, OpenPos + 1) << "\n ";
+    else
+      OS << ";\n ";
+
+    OS << llvm::StringRef(Str).substr(OpenPos + 1, ClosePos - OpenPos - 2);
+    First = false;
+  }
+  assert(!First);
+  OS << "\n}\n";
+}
+
+static void recursiveExpand(isl::basic_set BSet, int Dim, isl::set &Expanded) {
+  int Dims = BSet.dim(isl::dim::set);
+  if (Dim >= Dims) {
+    Expanded = Expanded.unite(BSet);
+    return;
+  }
+
+  isl::basic_set DimOnly =
+      BSet.project_out(isl::dim::param, 0, BSet.dim(isl::dim::param))
+          .project_out(isl::dim::set, Dim + 1, Dims - Dim - 1)
+          .project_out(isl::dim::set, 0, Dim);
+  if (!DimOnly.is_bounded()) {
+    recursiveExpand(BSet, Dim + 1, Expanded);
+    return;
+  }
+
+  foreachPoint(DimOnly, [&, Dim](isl::point P) {
+    isl::val Val = P.get_coordinate_val(isl::dim::set, 0);
+    isl::basic_set FixBSet = BSet.fix_val(isl::dim::set, Dim, Val);
+    recursiveExpand(FixBSet, Dim + 1, Expanded);
+  });
+}
+
+/// Make each point of a set explicit.
+///
+/// "Expanding" makes each point a set contains explicit. That is, the result is
+/// a set of singleton polyhedra. Unbounded dimensions are not expanded.
+///
+/// Example:
+///   { [i] : 0 <= i < 2 }
+/// is expanded to:
+///   { [0]; [1] }
+static isl::set expand(const isl::set &Set) {
+  isl::set Expanded = isl::set::empty(Set.get_space());
+  Set.foreach_basic_set([&](isl::basic_set BSet) -> isl::stat {
+    recursiveExpand(BSet, 0, Expanded);
+    return isl::stat::ok;
+  });
+  return Expanded;
+}
+
+/// Expand all points of a union set explicit.
+///
+/// @see expand(const isl::set)
+static isl::union_set expand(const isl::union_set &USet) {
+  isl::union_set Expanded =
+      give(isl_union_set_empty(isl_union_set_get_space(USet.keep())));
+  USet.foreach_set([&](isl::set Set) -> isl::stat {
+    isl::set SetExpanded = expand(Set);
+    Expanded = Expanded.add_set(SetExpanded);
+    return isl::stat::ok;
+  });
+  return Expanded;
+}
+
+LLVM_DUMP_METHOD void polly::dumpPw(const isl::set &Set) {
+  printSortedPolyhedra(Set, llvm::errs(), true, false);
+}
+
+LLVM_DUMP_METHOD void polly::dumpPw(const isl::map &Map) {
+  printSortedPolyhedra(Map.wrap(), llvm::errs(), true, true);
+}
+
+LLVM_DUMP_METHOD void polly::dumpPw(const isl::union_set &USet) {
+  printSortedPolyhedra(USet, llvm::errs(), true, false);
+}
+
+LLVM_DUMP_METHOD void polly::dumpPw(const isl::union_map &UMap) {
+  printSortedPolyhedra(UMap.wrap(), llvm::errs(), true, true);
+}
+
+LLVM_DUMP_METHOD void polly::dumpPw(__isl_keep isl_set *Set) {
+  dumpPw(isl::manage(isl_set_copy(Set)));
+}
+
+LLVM_DUMP_METHOD void polly::dumpPw(__isl_keep isl_map *Map) {
+  dumpPw(isl::manage(isl_map_copy(Map)));
+}
+
+LLVM_DUMP_METHOD void polly::dumpPw(__isl_keep isl_union_set *USet) {
+  dumpPw(isl::manage(isl_union_set_copy(USet)));
+}
+
+LLVM_DUMP_METHOD void polly::dumpPw(__isl_keep isl_union_map *UMap) {
+  dumpPw(isl::manage(isl_union_map_copy(UMap)));
+}
+
+LLVM_DUMP_METHOD void polly::dumpExpanded(const isl::set &Set) {
+  printSortedPolyhedra(expand(Set), llvm::errs(), false, false);
+}
+
+LLVM_DUMP_METHOD void polly::dumpExpanded(const isl::map &Map) {
+  printSortedPolyhedra(expand(Map.wrap()), llvm::errs(), false, true);
+}
+
+LLVM_DUMP_METHOD void polly::dumpExpanded(const isl::union_set &USet) {
+  printSortedPolyhedra(expand(USet), llvm::errs(), false, false);
+}
+
+LLVM_DUMP_METHOD void polly::dumpExpanded(const isl::union_map &UMap) {
+  printSortedPolyhedra(expand(UMap.wrap()), llvm::errs(), false, true);
+}
+
+LLVM_DUMP_METHOD void polly::dumpExpanded(__isl_keep isl_set *Set) {
+  dumpExpanded(isl::manage(isl_set_copy(Set)));
+}
+
+LLVM_DUMP_METHOD void polly::dumpExpanded(__isl_keep isl_map *Map) {
+  dumpExpanded(isl::manage(isl_map_copy(Map)));
+}
+
+LLVM_DUMP_METHOD void polly::dumpExpanded(__isl_keep isl_union_set *USet) {
+  dumpExpanded(isl::manage(isl_union_set_copy(USet)));
+}
+
+LLVM_DUMP_METHOD void polly::dumpExpanded(__isl_keep isl_union_map *UMap) {
+  dumpExpanded(isl::manage(isl_union_map_copy(UMap)));
+}
+#endif

lib/Transform/FlattenAlgo.cpp

 //===------ FlattenAlgo.cpp ------------------------------------*- C++ -*-===//
 //
 //                     The LLVM Compiler Infrastructure
 //
 // This file is distributed under the University of Illinois Open Source
 // License. See LICENSE.TXT for details.
 //
 //===----------------------------------------------------------------------===//
 //
 // Main algorithm of the FlattenSchedulePass. This is a separate file to avoid
 // the unittest for this requiring linking against LLVM.
 //
 //===----------------------------------------------------------------------===//
 
 #include "polly/FlattenAlgo.h"
 #include "polly/Support/ISLOStream.h"
+#include "polly/Support/ISLTools.h"
 #include "llvm/Support/Debug.h"
 #define DEBUG_TYPE "polly-flatten-algo"
 
 using namespace polly;
 using namespace llvm;
 
 namespace {
 

 bool isVariableDim(const isl::union_map &UMap) {
   return UMap.foreach_map([](isl::map Map) -> isl::stat {
     if (isVariableDim(Map))
       return isl::stat::error;
     return isl::stat::ok;
   }) == isl::stat::ok;
 }
 
-/// If @p PwAff maps to a constant, return said constant. If @p Max/@p Min, it
-/// can also be a piecewise constant and it would return the minimum/maximum
-/// value. Otherwise, return NaN.
-isl::val getConstant(isl::pw_aff PwAff, bool Max, bool Min) {
-  assert(!Max || !Min);
-  isl::val Result;
-  PwAff.foreach_piece([=, &Result](isl::set Set, isl::aff Aff) -> isl::stat {
-    if (Result && Result.is_nan())
-      return isl::stat::ok;
-
-    // TODO: If Min/Max, we can also determine a minimum/maximum value if
-    // Set is constant-bounded.
-    if (!Aff.is_cst()) {
-      Result = isl::val::nan(Aff.get_ctx());
-      return isl::stat::error;
-    }
-
-    auto ThisVal = Aff.get_constant_val();
-    if (!Result) {
-      Result = ThisVal;
-      return isl::stat::ok;
-    }
-
-    if (Result.eq(ThisVal))
-      return isl::stat::ok;
-
-    if (Max && ThisVal.gt(Result)) {
-      Result = ThisVal;
-      return isl::stat::ok;
-    }
-
-    if (Min && ThisVal.lt(Result)) {
-      Result = ThisVal;
-      return isl::stat::ok;
-    }
-
-    // Not compatible
-    Result = isl::val::nan(Aff.get_ctx());
-    return isl::stat::error;
-  });
-  return Result;
-}
-
 /// Compute @p UPwAff - @p Val.
 isl::union_pw_aff subtract(isl::union_pw_aff UPwAff, isl::val Val) {
   if (Val.is_zero())
     return UPwAff;
 
   auto Result = isl::union_pw_aff::empty(UPwAff.get_space());
   UPwAff.foreach_pw_aff([=, &Result](isl::pw_aff PwAff) -> isl::stat {
     auto ValAff =