Add initial support for pointers in reverse mode

This commit adds support for pointer operation in reverse mode. The technique is to maintain a corresponding derivative pointer variable, which gets updated (and stored/restored) in the exact same way as the primal pointer variable in both forward and reverse passes.
Added a workaround (with a FIXME comment) in the UsefulToStoreGlobal method to essentially bypass TBR analysis results for pointer expr.

Fixes vgvassilev#195, Fixes vgvassilev#197

include/clad/Differentiator/ArrayRef.h

@@ -22,7 +22,7 @@ template <typename T> class array_ref {
 
 public:
   /// Delete default constructor
-  array_ref() = delete;
+  array_ref() = default;
   /// Constructor to store the pointer to and size of an array supplied by the
   /// user
   CUDA_HOST_DEVICE array_ref(T* arr, std::size_t size)
@@ -33,16 +33,26 @@ template <typename T> class array_ref {
   /// Constructor for clad::array types
   CUDA_HOST_DEVICE array_ref(array<T>& a) : m_arr(a.ptr()), m_size(a.size()) {}
 
+  /// Operator for conversion from array_ref<T> to T*.
+  CUDA_HOST_DEVICE operator T*() { return m_arr; }
+
   template <typename U>
   CUDA_HOST_DEVICE array_ref<T>& operator=(const array<U>& a) {
     assert(m_size == a.size());
     for (std::size_t i = 0; i < m_size; ++i)
       m_arr[i] = a[i];
     return *this;
   }
+  template <typename U>
+  CUDA_HOST_DEVICE array_ref<T>& operator=(const array_ref<T>& a) {
+    m_arr = a.ptr();
+    m_size = a.size();
+    return *this;
+  }
   /// Returns the size of the underlying array
   CUDA_HOST_DEVICE std::size_t size() const { return m_size; }
   CUDA_HOST_DEVICE T* ptr() const { return m_arr; }
+  CUDA_HOST_DEVICE T*& ptr_ref() { return m_arr; }
   /// Returns an array_ref to a part of the underlying array starting at
   /// offset and having the specified size
   CUDA_HOST_DEVICE array_ref<T> slice(std::size_t offset, std::size_t size) {

include/clad/Differentiator/VisitorBase.h

@@ -527,6 +527,9 @@ namespace clad {
     /// Creates the expression Base.size() for the given Base expr. The Base
     /// expr must be of clad::array_ref<T> type
     clang::Expr* BuildArrayRefSizeExpr(clang::Expr* Base);
+    /// Creates the expression Base.ptr_ref() for the given Base expr. The Base
+    /// expr must be of clad::array_ref<T> type
+    clang::Expr* BuildArrayRefPtrRefExpr(clang::Expr* Base);
     /// Checks if the type is of clad::ValueAndPushforward<T,U> type
     bool isCladValueAndPushforwardType(clang::QualType QT);
     /// Creates the expression Base.slice(Args) for the given Base expr and Args
@@ -591,6 +594,40 @@ namespace clad {
     /// Cloning types is necessary since VariableArrayType
     /// store a pointer to their size expression.
     clang::QualType CloneType(clang::QualType T);
+
+    /// Computes effective derivative operands. It should be used when operands
+    /// might be of pointer types.
+    ///
+    /// In the trivial case, both operands are of non-pointer types, and the
+    /// effective derivative operands are `LDiff.getExpr_dx()` and
+    /// `RDiff.getExpr_dx()` respectively.
+    ///
+    /// Integers used in pointer arithmetic should be considered
+    /// non-differentiable entities. For example:
+    ///
+    /// ```
+    /// p + i;
+    /// ```
+    ///
+    /// Derived statement should be:
+    ///
+    /// ```
+    /// _d_p + i;
+    /// ```
+    ///
+    /// instead of:
+    ///
+    /// ```
+    /// _d_p + _d_i;
+    /// ```
+    ///
+    /// Therefore, effective derived expression of `i` is `i` instead of `_d_i`.
+    ///
+    /// This functions sets `derivedL` and `derivedR` arguments to effective
+    /// derived expressions.
+    void ComputeEffectiveDOperands(StmtDiff& LDiff, StmtDiff& RDiff,
+                                   clang::Expr*& derivedL,
+                                   clang::Expr*& derivedR);
   };
 } // end namespace clad
 

lib/Differentiator/BaseForwardModeVisitor.cpp

@@ -1346,52 +1346,6 @@ StmtDiff BaseForwardModeVisitor::VisitUnaryOperator(const UnaryOperator* UnOp) {
   }
 }
 
-/// Computes effective derivative operands. It should be used when operands
-/// might be of pointer types.
-///
-/// In the trivial case, both operands are of non-pointer types, and the
-/// effective derivative operands are `LDiff.getExpr_dx()` and
-/// `RDiff.getExpr_dx()` respectively.
-///
-/// Integers used in pointer arithmetic should be considered
-/// non-differentiable entities. For example:
-///
-/// ```
-/// p + i;
-/// ```
-///
-/// Derived statement should be:
-///
-/// ```
-/// _d_p + i;
-/// ```
-///
-/// instead of:
-///
-/// ```
-/// _d_p + _d_i;
-/// ```
-///
-/// Therefore, effective derived expression of `i` is `i` instead of `_d_i`.
-///
-/// This functions sets `derivedL` and `derivedR` arguments to effective
-/// derived expressions.
-static void ComputeEffectiveDOperands(StmtDiff& LDiff, StmtDiff& RDiff,
-                                      clang::Expr*& derivedL,
-                                      clang::Expr*& derivedR) {
-  derivedL = LDiff.getExpr_dx();
-  derivedR = RDiff.getExpr_dx();
-  if (utils::isArrayOrPointerType(LDiff.getExpr_dx()->getType()) &&
-      !utils::isArrayOrPointerType(RDiff.getExpr_dx()->getType())) {
-    derivedL = LDiff.getExpr_dx();
-    derivedR = RDiff.getExpr();
-  } else if (utils::isArrayOrPointerType(RDiff.getExpr_dx()->getType()) &&
-             !utils::isArrayOrPointerType(LDiff.getExpr_dx()->getType())) {
-    derivedL = LDiff.getExpr();
-    derivedR = RDiff.getExpr_dx();
-  }
-}
-
 StmtDiff
 BaseForwardModeVisitor::VisitBinaryOperator(const BinaryOperator* BinOp) {
   StmtDiff Ldiff = Visit(BinOp->getLHS());

lib/Differentiator/CladUtils.cpp

@@ -584,7 +584,8 @@ namespace clad {
             /// be more complex than just a DeclRefExpr.
             /// (e.g. `__real (n++ ? z1 : z2)`)
             m_Exprs.push_back(UnOp);
-          }
+          } else if (opCode == UnaryOperatorKind::UO_Deref)
+            m_Exprs.push_back(UnOp);
         }
 
         void VisitDeclRefExpr(clang::DeclRefExpr* DRE) {