[REFACTOR] Add Types to IterVar, Isolate Operator (#62)

* [IterVar/REFACTOR] Add types to IterVar

* [ARITH/REFACTOR] Move IntSet to include

* [REFACTOR/OP] Move Op detail to seperate folder.

* fix test

src/arithmetic/int_set.h → include/tvm/arithmetic.h

 /*!
  *  Copyright (c) 2016 by Contributors
- * \file int_set.h
- * \brief Abstraction for all integer set operations.
+ * \file arithmetic.h
+ * \brief Algebra and set operations.
  */
-#ifndef TVM_ARITHMETIC_INT_SET_H_
-#define TVM_ARITHMETIC_INT_SET_H_
+#ifndef TVM_ARITHMETIC_H_
+#define TVM_ARITHMETIC_H_
 
-#include <tvm/expr.h>
-#include <tvm/schedule.h>
 #include <vector>
+#include <unordered_map>
+#include <memory>
+#include "./expr.h"
 
 namespace tvm {
+/*! \brief namespace of arithmetic */
 namespace arith {
-
+/*!
+ * \brief Sign of an expression or set.
+ */
 enum SignType {
   kPositive,
   kNegative,
@@ -102,6 +106,41 @@ class IntSet : public NodeRef {
 };
 
 /*!
+ * \brief Range of a linear integer function.
+ *  Use to do specify the possible index values.
+ *
+ *  set = { base + coeff * x | x in Z }
+ *
+ *  When coeff != 0, it can also be written as
+ *  set = { n | n % coeff == base }
+ *
+ *  This is useful to decide if the index is dividable by certain value.
+ *  For example, if index = 0 + 4 x, then we know it can be divided by 4.
+ */
+struct ModularEntry {
+  /*! \brief The base */
+  int base;
+  /*! \brief linear co-efficient */
+  int coeff;
+
+  /*! \return entry represent everything */
+  static ModularEntry everything() {
+    // always safe to set 0 + x, so it can be everything.
+    ModularEntry e;
+    e.base = 0; e.coeff = 1;
+    return e;
+  }
+  /*!
+   * \brief Add two modular entries together to get a new modular entry.
+   * \param a The left operand.
+   * \param b The right operand.
+   * \return The combined modular entry.
+   */
+  static ModularEntry Add(const ModularEntry& a,
+                          const ModularEntry& b);
+};
+
+/*!
  * \brief Base class of all IntSet containers.
  */
 struct IntSetNode : public Node {
@@ -109,9 +148,6 @@ struct IntSetNode : public Node {
   TVM_DECLARE_BASE_NODE_INFO(IntSetNode, Node);
 };
 
-using ExprIntSetMap = std::unordered_map<Expr, IntSet,
-      Halide::ExprHash, Halide::ExprEqual>;
-
 /*!
  * \brief Find an symbolic integer set that contains all possible values of
  *  e given the domain of each iteration variables.
@@ -122,6 +158,13 @@ using ExprIntSetMap = std::unordered_map<Expr, IntSet,
  */
 IntSet EvalSet(Expr e,
                const Map<IterVar, IntSet>& dom_map);
+/*!
+ * \brief Same as EvalSet, but takes unordered_map
+ *
+ * \param e The expression to be evaluated.
+ * \param dom_map The domain of each variable.
+ * \return An integer set that can cover all the possible values of e.
+ */
 IntSet EvalSet(Expr e,
                const std::unordered_map<const Variable*, IntSet>& dom_map);
 
@@ -135,11 +178,18 @@ IntSet EvalSet(Expr e,
  */
 IntSet EvalSet(Range r,
                const Map<IterVar, IntSet>& dom_map);
+/*!
+ * \brief Same as EvalSet, but takes unordered_map
+ *
+ * \param r The range to be evaluated.
+ * \param dom_map The domain of each variable.
+ * \return An integer set that can cover all the possible values of e.
+ */
 IntSet EvalSet(Range r,
                const std::unordered_map<const Variable*, IntSet>& dom_map);
 
-
-
+/*! \brief Map from Expr to IntSet */
+using ExprIntSetMap = std::unordered_map<Expr, IntSet, ExprHash, ExprEqual>;
 /*!
  * \brief Find the integer set of every sub-expression, given the
  *  domain of each iteration variables.
@@ -148,7 +198,8 @@ IntSet EvalSet(Range r,
  * \param dom_map The domain of each variable.
  * \return the map from the expression to its possible value.
  */
-ExprIntSetMap EvalSetForEachSubExpr(Expr r,
+ExprIntSetMap EvalSetForEachSubExpr(
+    Expr e,
     const std::unordered_map<const Variable*, IntSet>& dom_map);
 
 /*!
@@ -165,11 +216,6 @@ IntSet Union(const Array<IntSet>& sets);
  */
 IntSet Intersect(const Array<IntSet>& sets);
 
-// implementation
-inline const IntSetNode* IntSet::operator->() const {
-  return static_cast<const IntSetNode*>(node_.get());
-}
-
 /*!
  * \brief Deduce the bound of the target variable in a expression,
  *  give the domain of each variables. Return undefined IntSet to
@@ -178,18 +224,49 @@ inline const IntSetNode* IntSet::operator->() const {
  * \param v The target variable to be deduced.
  * \param cond The conditional expression.
  * \param hint_map The domain of variable, used to help deduce.
- * \param relax The domain of each variable, used to relax the domain.
+ * \param relax_map The domain of each variable, used to relax the domain,
+ *        The deduce bound mush implies e for all value in relax_map
  * \return An integer set that can cover all the possible values.
  */
 IntSet DeduceBound(Expr v, Expr cond,
                    const Map<Var, IntSet>& hint_map,
                    const Map<Var, IntSet>& relax_map);
-IntSet DeduceBound(Expr v, Expr e,
+/*!
+ * \brief Same as DeduceBound with  unordered_map signature.
+ *
+ * \param v The target variable to be deduced.
+ * \param cond The conditional expression.
+ * \param hint_map The domain of variable, used to help deduce.
+ * \param relax_map The domain of each variable, used to relax the domain,
+ *        The deduce bound mush implies e for all value in relax_map
+ * \return An integer set that can cover all the possible values.
+ */
+IntSet DeduceBound(Expr v, Expr cond,
                    const std::unordered_map<const Variable*, IntSet>& hint_map,
                    const std::unordered_map<const Variable*, IntSet>& relax_map);
 
+/*!
+ * \brief Evaluate the expression with modular analysis
+ * \param e The expression to be evaluated.
+ * \param mod_map Map of modular statistics of known variables.
+ * \return The ModularEntry covering all possible value of e.
+ */
+ModularEntry EvalModular(
+    const Expr& e,
+    const std::unordered_map<const Variable*, ModularEntry>& mod_map);
 
+/*!
+ * \brief Same as EvalModular, used by front-end.
+ * \param e The expression to be evaluated.
+ * \param mod_map Map of modular statistics of known variables.
+ * \return A ModularSet covering all possible value of e.
+ */
+IntSet EvalModular(const Expr& e,
+                   const Map<Var, IntSet>& mod_map);
+// implementation
+inline const IntSetNode* IntSet::operator->() const {
+  return static_cast<const IntSetNode*>(node_.get());
+}
 }  // namespace arith
 }  // namespace tvm
-
-#endif  // TVM_ARITHMETIC_INT_SET_H_
+#endif  // TVM_ARITHMETIC_H_

include/tvm/expr.h

@@ -22,6 +22,8 @@ using Halide::Bool;
 using Halide::Int;
 using Halide::UInt;
 using Halide::Handle;
+using Halide::ExprHash;
+using Halide::ExprEqual;
 
 using Halide::Expr;
 using Halide::VarExpr;
@@ -57,7 +59,14 @@ class Var : public Halide::VarExpr {
                Type t = Int(32)) : VarExpr(name_hint, t) {}
   explicit Var(std::shared_ptr<Node> n) : VarExpr(n) {}
   explicit Var(VarExpr v) : VarExpr(v) {}
-
+  /*!
+   * \brief Make a new copy of var with same type, append suffix
+   * \param suffix The suffix to be appended.
+   * \return the new Var copy
+   */
+  Var copy_with_suffix(const std::string& suffix) const {
+    return Var((*this)->name_hint + suffix, (*this)->type);
+  }
   /*! \brief type indicate the container type */
   using ContainerType = Variable;
 };
@@ -91,6 +100,72 @@ class Range : public Halide::IR::Range {
 };
 
 /*!
+ * \brief Type of iteration variable.
+ *  Each IterVar have a specific type.
+ *
+ *  The type of iter var can be overriden via
+ *  stage.iter_var_attrs given they are compatible.
+ */
+enum IterVarType : int {
+  /*!
+   * \brief Data parallel iteration.
+   *  This normally corresponds to axis of Tensor.
+   *  Allow all IterVar manipulations.
+   *
+   * \note This does not mean the loop
+   *  have to be executed in parallel fashion.
+   */
+  kDataPar = 0,
+  /*!
+   * \brief The IterVar itself is a thread-index
+   *  of a fixed thread launching group.
+   *  Note that this is already assumed to be paralellized.
+   *
+   *  Disallow: split/fuse/vectorize/parallel
+   */
+  kThreadIndex = 1,
+  /*!
+   * \brief Communicative reduction.
+   *  Cannot be directly parallelized.
+   *
+   *  Disallow: parallel/vectorize
+   */
+  kCommReduce = 2,
+  /*!
+   * \brief Serial loops with loop carry dependency,
+   *  the iteration must execute in order.
+   *  Cannot be re-ordered.
+   *
+   *  Disallow: reorder/parallel/vectorize
+   */
+  kOrdered = 3,
+  /*!
+   * \brief IterVar is opaque,
+   *
+   *  May not corresponds to any generated loop
+   *  Disallow all IterVar manipulations and compute_at
+   *
+   * \note This is usually used to implement composite op
+   *  or external op, where the
+   */
+  kOpaque = 4,
+  // The following are possible additional
+  // types that are provided during schedule
+  /*!
+   * \brief The execution is unrolled.
+   */
+  kUnrolled = 5,
+  /*!
+   * \brief The loop is vectorized.
+   */
+  kVectorized = 6,
+  /*!
+   * \brief The loop is parallelized.
+   */
+  kParallelized = 7
+};
+
+/*!
  * \brief Iteration Variable,
  *  represents an iteration over an integer interval.
  */
@@ -101,13 +176,6 @@ class IterVar : public NodeRef {
   // construct from shared ptr.
   explicit IterVar(std::shared_ptr<Node> n) : NodeRef(n) {}
   /*!
-   * \brief construction of iteration variable.
-   * \param dom The iteration domain.
-   * \param var_name The name of iteration variable.
-   * \param thread_tag The additional tag to indicate whether the var is binded to fixed-thread.
-   */
-  explicit IterVar(Range dom, std::string var_name = "i", std::string thread_tag = "");
-  /*!
    * \brief access the internal node container
    * \return the pointer to the internal node container
    */
@@ -120,6 +188,22 @@ class IterVar : public NodeRef {
   using ContainerType = IterVarNode;
 };
 
+/*!
+ * \brief Create a new IterVar that represents an axis in thread.
+ *
+ * \param dom Optional, domain of the thread axis.
+ * \param tag The thread tag of the axis.
+ */
+IterVar thread_axis(Range dom, std::string tag);
+
+/*!
+ * \brief Create a new IterVar for reduction operations.
+ *
+ * \param dom The domain of the reduction axis.
+ * \param name The name of the reduction axis.
+ */
+IterVar reduce_axis(Range dom, std::string name = "rv");
+
 using Domain = Array<Range>;
 
 // functions
@@ -168,6 +252,8 @@ class IterVarNode : public Node {
   Range dom;
   /*! \brief The looping variable */
   Var var;
+  /*! \brief The type of the IterVar */
+  IterVarType iter_type;
   /*!
    * \brief additional tag on the iteration variable,
    *  set this if this is binded already to a known thread tag.
@@ -177,10 +263,13 @@ class IterVarNode : public Node {
   void VisitAttrs(AttrVisitor* v) final {
     v->Visit("dom", &dom);
     v->Visit("var", &var);
+    v->Visit("iter_type", &iter_type);
     v->Visit("thread_tag", &thread_tag);
   }
 
-  static IterVar make(Range dom, Var var, std::string thread_tag);
+  static IterVar make(Range dom, Var var,
+                      IterVarType iter_type,
+                      std::string thread_tag = "");
 
   static constexpr const char* _type_key = "IterVar";
   TVM_DECLARE_NODE_TYPE_INFO(IterVarNode, Node);
@@ -195,6 +284,20 @@ inline IterVar::operator Expr() const {
   return (*this)->var;
 }
 
+inline const char* IterVarType2String(IterVarType t) {
+  switch (t) {
+    case kDataPar: return "DataPar";
+    case kThreadIndex: return "ThreadIndex";
+    case kCommReduce: return "CommRedude";
+    case kOrdered: return "Ordered";
+    case kOpaque: return "Opaque";
+    case kUnrolled: return "Unrolled";
+    case kVectorized: return "Vectorized";
+    case kParallelized: return "Parallelized";
+  }
+  return "Unknown";
+}
+
 }  // namespace tvm
 
 namespace std {

include/tvm/ir.h

@@ -32,15 +32,23 @@ struct Reduce : public ExprNode<Reduce> {
   Expr source;
   /*! \brief The reduction axis */
   Array<IterVar> axis;
+  /*!
+   * \brief Predicate on the reduction
+   *  Only add the body to reduction if condition is true.
+   */
+  Expr condition;
 
   /*! \brief construct expr from op and rdom */
-  static Expr make(std::string op, Expr src, Array<IterVar> rdom);
+  static Expr make(std::string op, Expr src,
+                   Array<IterVar> rdom,
+                   Expr condition = make_const(Bool(1), true));
 
   void VisitAttrs(AttrVisitor* v) final {
     v->Visit("dtype", &type);
     v->Visit("op", &op);
     v->Visit("source", &source);
     v->Visit("axis", &axis);
+    v->Visit("condition", &condition);
   }
   static const IRNodeType _type_info = IRNodeType::ExtensionExpr;
   static constexpr const char* _type_key = "Reduce";
@@ -86,6 +94,12 @@ constexpr const char* storage_scope = "storage_scope";
  * \brief Mark storage scope of realizations
  */
 constexpr const char* realize_scope = "realize_scope";
+/*! \brief Mark of loop scope */
+constexpr const char* loop_scope = "loop_scope";
+/*! \brief Mark of scan update scope */
+constexpr const char* scan_update_scope = "scan_update_scope";
+/*! \brief Mark of scan init scope */
+constexpr const char* scan_init_scope = "scan_init_scope";
 }  // namespace attr
 
 /*! \brief namespace of TVM Intrinsic functions */

include/tvm/ir_visitor.h

@@ -61,8 +61,8 @@ namespace ir {
  * // These traps may not happen if we program carefully
  * // But it is recommended to use ExprFunctor, which allows direct
  * // return the value, this helps us to avoid such problems.
- * \encode
  *
+ * \endcode
  */
 class IRVisitor {
  public:

include/tvm/operation.h

@@ -7,11 +7,136 @@
 #define TVM_OPERATION_H_
 
 #include <string>
+#include <vector>
+#include <unordered_map>
 #include "./expr.h"
 #include "./tensor.h"
+#include "./schedule.h"
+#include "./arithmetic.h"
 
 namespace tvm {
 
+using arith::IntSet;
+
+/*!
+ * \brief Temporary data structure to store union
+ *  of bounds of each axis of Tensor.
+ */
+struct TensorDom {
+  // constructor
+  explicit TensorDom(int ndim)
+      : data(ndim) {}
+  /*! \brief The domain data */
+  std::vector<std::vector<IntSet> > data;
+};
+
+/*!
+ * \brief The map beteen tensor and operation it feeds to.
+ */
+using FeedGraph = std::unordered_map<Tensor, std::vector<Operation> >;
+
+/*! \brief The graph context used during bound inference. */
+struct GraphContext {
+  /*! \brief The feed graph */
+  FeedGraph feed_graph;
+};
+
+/*!
+ * \brief Base class of all operation nodes
+ */
+class OperationNode : public FunctionBaseNode {
+ public:
+  /*! \brief optional name of the operation */
+  std::string name;
+  /*! \return name of the operation */
+  const std::string& func_name() const final {
+    return name;
+  }
+  /*!
+   * \return The list of iteration variable at root
+   * \note root_iter_vars dedides the shape of the outputs.
+   */
+  virtual Array<IterVar> root_iter_vars() const = 0;
+  /*!
+   * \brief Get data type. i-th output tensor.
+   * \param i The output index.
+   * \return type of i-th output.
+   */
+  virtual Type output_dtype(size_t i) const = 0;
+  /*!
+   * \brief Get shape of i-th output tensor.
+   * \param i The output index.
+   * \return shape of i-th output.
+   */
+  virtual Array<Expr> output_shape(size_t i) const = 0;
+  /*!
+   * \brief List all the input Tensors.
+   * \return List if input tensors.
+   */
+  virtual Array<Tensor> InputTensors() const = 0;
+  /*!
+   * \brief Replace the input of the operation by pattern specified by rmap.
+   *
+   * \param self The reference to self.
+   * \param rmap The replacement map.
+   * \return self if nothing is replaced, otherwise return replaced op.
+   */
+  virtual Operation ReplaceInputs(
+      const Operation& self,
+      const std::unordered_map<Tensor, Tensor>& rmap) const = 0;
+  /*!
+   * \brief Propagate the bounds to inputs
+   * \param self The reference to self.
+   * \param dom_map the domain map of Variables(corresponds to root_iter_vars)
+   * \param out_dom_map The output domain.
+   *  The function is only asked to fill the bounds for Tensors that
+   *  is already in the out_dom_map
+   */
+  virtual void PropBoundToInputs(
+      const Operation& self,
+      const std::unordered_map<const Variable*, IntSet>& dom_map,
+      std::unordered_map<Tensor, TensorDom>* out_dom_map) const = 0;
+  /*!
+   * \brief Gather the bound from output tensor.
+   *  Set the range of each root_iter_vars in the op to out_dom_map
+   *
+   * \param self The reference to self.
+   * \param graph_ctx The global graph context information.
+   * \param tensor_dom Domain map of Tensor->access set of each dimension.
+   * \param out_dom_map The output domain map of each IterVar to be setted.
+   */
+  virtual void GatherBound(
+      const Operation& self,
+      const GraphContext& graph_ctx,
+      const std::unordered_map<Tensor, TensorDom>& tensor_dom,
+      std::unordered_map<IterVar, Range>* out_dom_map) const = 0;
+  /*!
+   * \brief Build the Realize statement that realizes
+   *   the op's output tensors.
+   * \param self The reference to self.
+   * \param realize_map The realization domain map of the operators.
+   * \param body The body that is going to get
+   * \return A realization statement that wraps body.
+   */
+  virtual Stmt BuildRealize(
+      const Operation& self,
+      const std::unordered_map<IterVar, Range>& realize_map,
+      const Stmt& body) const = 0;
+  /*!
+   * \brief Build the statement that provide the output tensors.
+   * \param stage The schedule stage of the op.
+   * \param dom_map The domain map of all iteration domains.
+   * \return A statement that add production and wraps consumer.
+   */
+  virtual Stmt BuildProvide(
+      const Stage& stage,
+      const std::unordered_map<IterVar, Range>& dom_map) const = 0;
+
+  static constexpr const char* _type_key = "Operation";
+
+  TVM_DECLARE_BASE_NODE_INFO(OperationNode, Node);
+};
+
 /*!
  * \brief A placeholder op represents an input placeholder.
  */
@@ -21,13 +146,31 @@ class PlaceholderOpNode : public OperationNode {
   Array<Expr> shape;
   /*! \brief The data type of the input. */
   Type dtype;
-
-  int num_outputs() const final {
-    return 1;
-  }
+  // override behavior.
+  int num_outputs() const final;
   Array<IterVar> root_iter_vars() const final;
   Type output_dtype(size_t i) const final;
   Array<Expr> output_shape(size_t i) const final;
+  Array<Tensor> InputTensors() const final;
+  Operation ReplaceInputs(
+      const Operation& self,
+      const std::unordered_map<Tensor, Tensor>& rmap) const final;
+  void PropBoundToInputs(
+      const Operation& self,
+      const std::unordered_map<const Variable*, IntSet>& dom_map,
+      std::unordered_map<Tensor, TensorDom>* out_dom_map) const final;
+  void GatherBound(
+      const Operation& self,
+      const GraphContext& graph_ctx,
+      const std::unordered_map<Tensor, TensorDom>& tensor_dom,
+      std::unordered_map<IterVar, Range>* out_dom_map) const final;
+  Stmt BuildRealize(
+      const Operation& self,
+      const std::unordered_map<IterVar, Range>& realize_map,
+      const Stmt& body) const final;
+  Stmt BuildProvide(
+      const Stage& stage,
+      const std::unordered_map<IterVar, Range>& dom_map) const final;
 
   void VisitAttrs(AttrVisitor* v) final {
     v->Visit("name", &name);
@@ -55,13 +198,31 @@ class ComputeOpNode : public OperationNode {
   Expr body;
   /*! \brief constructor */
   ComputeOpNode() {}
-
-  int num_outputs() const final {
-    return 1;
-  }
+  // override functions
+  int num_outputs() const final;
   Array<IterVar> root_iter_vars() const final;
   Type output_dtype(size_t i) const final;
   Array<Expr> output_shape(size_t i) const final;
+  Array<Tensor> InputTensors() const final;
+  Operation ReplaceInputs(
+      const Operation& self,
+      const std::unordered_map<Tensor, Tensor>& rmap) const final;
+  void PropBoundToInputs(
+      const Operation& self,
+      const std::unordered_map<const Variable*, IntSet>& dom_map,
+      std::unordered_map<Tensor, TensorDom>* out_dom_map) const final;
+  void GatherBound(
+      const Operation& self,
+      const GraphContext& graph_ctx,
+      const std::unordered_map<Tensor, TensorDom>& tensor_dom,
+      std::unordered_map<IterVar, Range>* out_dom_map) const final;
+  Stmt BuildRealize(
+      const Operation& self,
+      const std::unordered_map<IterVar, Range>& realize_map,
+      const Stmt& body) const final;
+  Stmt BuildProvide(
+      const Stage& stage,
+      const std::unordered_map<IterVar, Range>& dom_map) const final;
 
   void VisitAttrs(AttrVisitor* v) final {
     v->Visit("name", &name);
@@ -107,6 +268,26 @@ class ScanOpNode : public OperationNode {
   Array<IterVar> root_iter_vars() const final;
   Type output_dtype(size_t i) const final;
   Array<Expr> output_shape(size_t i) const final;
+  Array<Tensor> InputTensors() const final;
+  Operation ReplaceInputs(
+      const Operation& self,
+      const std::unordered_map<Tensor, Tensor>& rmap) const final;
+  void PropBoundToInputs(
+      const Operation& self,
+      const std::unordered_map<const Variable*, IntSet>& dom_map,
+      std::unordered_map<Tensor, TensorDom>* out_dom_map) const final;
+  void GatherBound(
+      const Operation& self,
+      const GraphContext& graph_ctx,
+      const std::unordered_map<Tensor, TensorDom>& tensor_dom,
+      std::unordered_map<IterVar, Range>* out_dom_map) const final;
+  Stmt BuildRealize(
+      const Operation& self,
+      const std::unordered_map<IterVar, Range>& realize_map,
+      const Stmt& body) const final;
+  Stmt BuildProvide(
+      const Stage& stage,
+      const std::unordered_map<IterVar, Range>& dom_map) const final;
 
   void VisitAttrs(AttrVisitor* v) final {
     v->Visit("name", &name);
@@ -188,19 +369,9 @@ inline Tensor compute(Array<Expr> shape,
   return compute(shape, fc, name);
 }
 
+// inline function.
+inline const OperationNode* Operation::operator->() const {
+  return static_cast<const OperationNode*>(node_.get());
+}
 }  // namespace tvm
-
-
-namespace std {
-template <>
-struct hash<::tvm::Tensor> {
-  std::size_t operator()(const ::tvm::Tensor& k) const {
-    if (k.defined() && k->op.defined()) {
-      return k->op.hash();
-    } else{
-      return k.hash();
-    }
-  }
-};
-}  // namespace std
 #endif  // TVM_OPERATION_H_

include/tvm/schedule.h

@@ -8,7 +8,7 @@
 
 #include <string>
 #include "./base.h"
-#include "./operation.h"
+#include "./tensor.h"
 
 namespace tvm {
 
@@ -31,13 +31,6 @@ enum AttachType : int {
   kScanUpdate = 5
 };
 
-/*! \brief IterVar type */
-enum IterVarType : int {
-  kUnrolled = 1,
-  kVectorized = 2,
-  kParallel = 3
-};
-
 /*! \brief Stage, contains scheduling for a stage of computation. */
 class Stage : public NodeRef {
  public:

include/tvm/tensor.h

@@ -14,6 +14,7 @@
 
 #include "./base.h"
 #include "./expr.h"
+#include "./arithmetic.h"
 
 namespace tvm {
 
@@ -156,34 +157,8 @@ class TensorNode : public Node {
   TVM_DECLARE_NODE_TYPE_INFO(TensorNode, Node);
 };
 
-/*!
- * \brief base class of operation node.
- */
-class OperationNode : public FunctionBaseNode {
- public:
-  /*! \brief optional name of the operation */
-  std::string name;
-  /*! \return name of the operation */
-  const std::string& func_name() const final {
-    return name;
-  }
-  /*! \return the list of iteration variable at root */
-  virtual Array<IterVar> root_iter_vars() const = 0;
-  /*! \return type of i-th output */
-  virtual Type output_dtype(size_t i) const = 0;
-  /*! \return shape of i-th output */
-  virtual Array<Expr> output_shape(size_t i) const = 0;
-
-  static constexpr const char* _type_key = "Operation";
-
-  TVM_DECLARE_BASE_NODE_INFO(OperationNode, Node);
-};
 
 // Implementations of inline functions
-inline const OperationNode* Operation::operator->() const {
-  return static_cast<const OperationNode*>(node_.get());
-}
-
 inline const TensorNode* Tensor::operator->() const {
   return static_cast<const TensorNode*>(node_.get());
 }
@@ -249,5 +224,16 @@ struct hash<::tvm::Operation> {
     return k.hash();
   }
 };
-}
+
+template <>
+struct hash<::tvm::Tensor> {
+  std::size_t operator()(const ::tvm::Tensor& k) const {
+    if (k.defined() && k->op.defined()) {
+      return k->op.hash();
+    } else{
+      return k.hash();
+    }
+  }
+};
+}  // namespace std
 #endif  // TVM_TENSOR_H_

python/tvm/api.py

@@ -132,7 +132,7 @@ def compute(shape, fcompute, name="compute"):
     if ndim != len(arg_names):
         raise ValueError("fcompute do not match dimension, ndim=%d" % ndim)
 
-    dim_var = [IterVar((0, s), x) for x, s in zip(arg_names, shape)]
+    dim_var = [_IterVar((0, s), x, 0) for x, s in zip(arg_names, shape)]
     body = fcompute(*[v.var for v in dim_var])
     body = convert(body)
     op_node = _api_internal._ComputeOp(
@@ -181,7 +181,7 @@ def scan(init, update, state_placeholder, name="scan"):
         state_placeholder = [state_placeholder]
     if len(init) != len(update) or len(init) != len(state_placeholder):
         raise ValueError("init, update, state_placeholder must have same length")
-    axis = IterVar((init[0].shape[0], update[0].shape[0]), "%s.idx" % name)
+    axis = _IterVar((init[0].shape[0], update[0].shape[0]), "%s.idx" % name, 3)
     op = _api_internal._ScanOp(name, axis, init, update, state_placeholder)
     res = [op.output(i) for i in range(len(update))]
     return (res[0] if len(res) == 1 else res)
@@ -225,8 +225,8 @@ def Buffer(shape, dtype=None,
         name, ptr, shape, strides, dtype)
 
 
-def IterVar(dom=None, name=None, thread_tag=''):
-    """Create a iteration variable
+def _IterVar(dom, name, iter_type, thread_tag=''):
+    """Internal function to create IterVar
 
     Parameters
     ----------
@@ -236,6 +236,9 @@ def IterVar(dom=None, name=None, thread_tag=''):
     name : str
         The name of iteration variable.
 
+    iter_type : int
+        The type of iteration.
+
     thread_tag : str
         The thread tag of the iteration variable.
 
@@ -252,10 +255,41 @@ def IterVar(dom=None, name=None, thread_tag=''):
 
         if not isinstance(dom, _collections.Range):
             raise ValueError("dom need to be Range")
-    if name is None:
-        name = thread_tag if thread_tag else name
     name = name if name else 'iter'
-    return _api_internal._IterVar(dom, name, thread_tag)
+    var = Var(name)
+    return _api_internal._IterVar(dom, var, iter_type, thread_tag)
+
+
+def thread_axis(dom, tag, name=''):
+    """Create a new IterVar to represent thread index.
+
+    Parameters
+    ----------
+    dom : Range
+        The domain of iteration.
+
+    tag : str
+        The thread tag
+
+    name : str, optional
+        The name of the var.
+    """
+    name = name if name else tag
+    return _IterVar(dom, name, 1, tag)
+
+
+def reduce_axis(dom, name="rv"):
+    """Create a new IterVar for reduction.
+
+    Parameters
+    ----------
+    dom : Range
+        The domain of iteration.
+
+    name : str
+        The name of the variable.
+    """
+    return _IterVar(dom, name, 2)
 
 
 def sum(expr, axis):

python/tvm/collections.py

@@ -55,7 +55,14 @@ class Range(NodeBase):
 @register_node
 class IterVar(NodeBase, _expr.ExprOp):
     """Represent iteration variable."""
-    pass
+    DataPar = 0
+    ThreadIndex = 1
+    CommReduce = 2
+    Ordered = 3
+    DimInfo = 4
+    Unrolled = 5
+    Vectorized = 6
+    Parallelized = 7
 
 
 @register_node

src/README.md

-# Code organization
+# Code Organization
 
-- api API functionr registration
+Header files in include are public APIs that share across modules.
+There can be internal header files within each module that sit in src.
+
+The current code modules in src.
+- api API function registration
 - lang The definition of DSL related data structure
-- schedule The operations on the schedule graph before converting to IR.
 - arithmetic Arithmetic expression and set simplification
+- op The detail implementations about each operation(compute, scan, placeholder)
+- schedule The operations on the schedule graph before converting to IR.
 - pass The optimization pass on the IR structure
-- runtime Minimum runtime related codes.
-- codegen The code generator
+- codegen The code generator.
+- runtime Minimum runtime related codes

src/api/api_arith.cc

@@ -6,8 +6,7 @@
 #include <tvm/expr.h>
 #include <tvm/ir.h>
 #include <tvm/api_registry.h>
-#include "../arithmetic/int_set.h"
-#include "../arithmetic/modular.h"
+#include <tvm/arithmetic.h>
 
 namespace tvm {
 namespace arith {

src/api/api_lang.cc

@@ -6,6 +6,7 @@
 #include <tvm/expr.h>
 #include <tvm/ir.h>
 #include <tvm/tensor.h>
+#include <tvm/operation.h>
 #include <tvm/buffer.h>
 #include <tvm/schedule.h>
 #include <tvm/api_registry.h>
@@ -188,10 +189,12 @@ TVM_REGISTER_API(_OpGetOutput)
         static_cast<size_t>(args[1].operator int64_t()));
   });
 
-
 TVM_REGISTER_API(_IterVar)
 .set_body([](TVMArgs args,  TVMRetValue* ret) {
-    *ret = IterVar(args[0], args[1], args[2]);
+    *ret = IterVarNode::make(
+        args[0], args[1],
+        static_cast<IterVarType>(args[2].operator int()),
+        args[3]);
   });
 
 TVM_REGISTER_API(_Schedule)

src/arithmetic/bound_deducer.cc

@@ -6,10 +6,11 @@
 #include <tvm/expr.h>
 #include <tvm/ir_pass.h>
 #include <tvm/ir_visitor.h>
+#include <tvm/arithmetic.h>
 #include <tvm/api_registry.h>
+
 #include <unordered_set>
 #include <unordered_map>
-#include "./int_set.h"
 
 namespace tvm {
 namespace arith {

src/arithmetic/canonical.cc

@@ -4,7 +4,7 @@
  * \brief Canonicalize simplification.
  */
 #include <tvm/ir_mutator.h>
-#include "./int_set.h"
+#include <tvm/arithmetic.h>
 #include "./canonical.h"
 #include "./compute_expr.h"
 

src/arithmetic/int_set.cc

@@ -5,9 +5,9 @@
  */
 #include <tvm/ir.h>
 #include <tvm/ir_pass.h>
+#include <tvm/arithmetic.h>
 #include <pass/Interval.h>
 #include <unordered_map>
-#include "./int_set.h"
 #include "./compute_expr.h"
 #include "./int_set_internal.h"
 

src/arithmetic/int_set_internal.h

@@ -8,8 +8,7 @@
 
 #include <tvm/ir.h>
 #include <tvm/ir_pass.h>
-#include "./int_set.h"
-#include "./modular.h"
+#include <tvm/arithmetic.h>
 
 namespace tvm {
 namespace arith {

src/arithmetic/modular.cc

@@ -6,8 +6,8 @@
 #include <tvm/ir.h>
 #include <tvm/ir_functor_ext.h>
 #include <tvm/ir_visitor.h>
+#include <tvm/arithmetic.h>
 #include <limits>
-#include "./modular.h"
 #include "./int_set_internal.h"
 
 namespace tvm {

src/arithmetic/modular.h

-/*!
- *  Copyright (c) 2017 by Contributors
- * \file modular.h
- * \brief Modular integer set analysis
- */
-#ifndef TVM_ARITHMETIC_MODULAR_H_
-#define TVM_ARITHMETIC_MODULAR_H_
-
-#include <tvm/expr.h>
-#include "./int_set.h"
-
-namespace tvm {
-namespace arith {
-
-/*!
- * \brief Range of a linear integer function.
- *  Use to do specify the possible index values.
- *
- *  set = { base + coeff * x | x \in Z }
- *
- *  When coeff != 0, it can also be written as
- *  set = { n | n % coeff == base }
- *
- *  This is useful to decide if the index is dividable by certain value.
- *  For example, if index = 0 + 4 x, then we know it can be divided by 4.
- */
-struct ModularEntry {
-  /*! \brief The base */
-  int base;
-  /*! \brief linear co-efficient */
-  int coeff;
-
-  /*! \return entry represent everything */
-  static ModularEntry everything() {
-    // always safe to set 0 + x, so it can be everything.
-    ModularEntry e;
-    e.base = 0; e.coeff = 1;
-    return e;
-  }
-  /*!
-   * \brief Add two modular entries together to get a new modular entry.
-   * \param a The left operand.
-   * \param b The right operand.
-   * \return The combined modular entry.
-   */
-  static ModularEntry Add(const ModularEntry& a,
-                          const ModularEntry& b);
-};
-
-/*!
- * \brief Evaluate the expression with modular analysis
- * \param e The expression to be evaluated.
- * \param mod_map Map of modular statistics of known variables.
- * \return The ModularEntry covering all possible value of e.
- */
-ModularEntry EvalModular(
-    const Expr& e,
-    const std::unordered_map<const Variable*, ModularEntry>& mod_map);
-/*!
- * \brief Same as EvalModular, used by front-end.
- * \param e The expression to be evaluated.
- * \param mod_map Map of modular statistics of known variables.
- * \return A ModularSet covering all possible value of e.
- */
-IntSet EvalModular(const Expr& e,
-                   const Map<Var, IntSet>& mod_map);
-}  // namespace arith
-}  // namespace tvm
-#endif  // TVM_ARITHMETIC_MODULAR_H_

src/codegen/llvm/codegen_llvm.h

@@ -10,11 +10,11 @@
 #include <tvm/ir.h>
 #include <tvm/ir_functor_ext.h>
 #include <tvm/codegen.h>
+#include <tvm/arithmetic.h>
 #include <memory>
 #include <vector>
 #include <string>
 #include "./llvm_common.h"
-#include "../../arithmetic/modular.h"
 
 namespace tvm {
 namespace codegen {

src/lang/expr.cc

@@ -26,27 +26,36 @@ Range Range::make_with_min_extent(Expr min, Expr extent) {
   return Range(std::make_shared<Halide::IR::RangeNode>(min, extent));
 }
 
-IterVar::IterVar(Range dom, std::string var_name, std::string thread_tag)
-    : IterVar(IterVarNode::make(dom, Var(var_name, Int(32)), thread_tag)) {}
-
-IterVar IterVarNode::make(Range dom, Var var, std::string thread_tag) {
+IterVar IterVarNode::make(Range dom, Var var,
+                          IterVarType t, std::string thread_tag) {
   std::shared_ptr<IterVarNode> n = std::make_shared<IterVarNode>();
   n->dom = dom;
   n->var = var;
+  n->iter_type = t;
   n->thread_tag = thread_tag;
   return IterVar(n);
 }
 
+IterVar thread_axis(Range dom, std::string tag) {
+  return IterVarNode::make(
+      dom, Var(tag), kThreadIndex, tag);
+}
+
+IterVar reduce_axis(Range dom, std::string name) {
+  return IterVarNode::make(
+      dom, Var(name), kCommReduce);
+}
+
 Expr sum(Expr source, Array<IterVar> rdom) {
-  return ir::Reduce::make("Add", source, rdom);
+  return ir::Reduce::make("Add", source, rdom, make_const(Bool(1), true));
 }
 
 Expr max(Expr source, Array<IterVar> rdom) {
-  return ir::Reduce::make("Max", source, rdom);
+  return ir::Reduce::make("Max", source, rdom, make_const(Bool(1), true));
 }
 
 Expr min(Expr source, Array<IterVar> rdom) {
-  return ir::Reduce::make("Min", source, rdom);
+  return ir::Reduce::make("Min", source, rdom, make_const(Bool(1), true));
 }
 
 std::ostream& operator<<(std::ostream& os, const NodeRef& n) {  // NOLINT(*)

src/lang/ir.cc

@@ -26,7 +26,11 @@ TVM_STATIC_IR_FUNCTOR(IRPrinter, vtable)
             << op->op
             << ", ";
   p->print(op->source);
-  p->stream << ", axis=" << op->axis << ")";
+  p->stream << ", axis=" << op->axis;
+  if (!is_const(op->condition, 1)) {
+    p->stream << ", condition=" << op->condition;
+  }
+  p->stream << ")";
 });
 
 }  // namespace Internal
@@ -35,7 +39,12 @@ TVM_STATIC_IR_FUNCTOR(IRPrinter, vtable)
 namespace tvm {
 namespace ir {
 
-Expr Reduce::make(std::string op, Expr source, Array<IterVar> axis) {
+Expr Reduce::make(std::string op, Expr source,
+                  Array<IterVar> axis, Expr condition) {
+  for (size_t i = 0; i < axis.size(); ++i) {
+    CHECK_EQ(axis[i]->iter_type, kCommReduce)
+        << "Can only take axis created by reduce_axis";
+  }
   auto n = std::make_shared<Reduce>();
   CHECK(source.defined());
   for (size_t i = 0; i < axis.size(); ++i) {
@@ -45,6 +54,7 @@ Expr Reduce::make(std::string op, Expr source, Array<IterVar> axis) {
   n->source = source;
   n->op = op;
   n->axis = axis;
+  n->condition = condition;
   return Expr(n);
 }
 

src/lang/operation.cc

@@ -4,209 +4,3 @@
  */
 #include <tvm/operation.h>
 #include <tvm/tensor.h>
-#include <tvm/ir.h>
-#include <tvm/ir_pass.h>
-#include <memory>
-
-namespace tvm {
-
-Tensor Operation::output(size_t i) const {
-  auto node = std::make_shared<TensorNode>();
-  node->op = *this;
-  node->value_index = 0;
-  node->dtype = (*this)->output_dtype(i);
-  node->shape = (*this)->output_shape(i);
-  return Tensor(node);
-}
-
-// PlaceholderOpNode
-TVM_STATIC_IR_FUNCTOR(IRPrinter, vtable)
-.set_dispatch<PlaceholderOpNode>([](const PlaceholderOpNode *op, IRPrinter *p) {
-    p->stream << "placeholder(" << op->name << ", " << op << ")";
-});
-
-TVM_REGISTER_NODE_TYPE(PlaceholderOpNode);
-
-Array<IterVar> PlaceholderOpNode::root_iter_vars() const {
-  return {};
-}
-
-Type PlaceholderOpNode::output_dtype(size_t i) const {
-  CHECK_EQ(i, 0U);
-  return dtype;
-}
-
-Array<Expr> PlaceholderOpNode::output_shape(size_t i) const {
-  CHECK_EQ(i, 0U);
-  return shape;
-}
-
-Operation PlaceholderOpNode::make(std::string name,
-                                  Array<Expr> shape,
-                                  Type dtype) {
-  auto n = std::make_shared<PlaceholderOpNode>();
-  n->name = name;
-  n->shape = shape;
-  n->dtype = dtype;
-  return Operation(n);
-}
-
-Tensor placeholder(Array<Expr> shape, Type dtype, std::string name) {
-  return PlaceholderOpNode::make(name, shape, dtype).output(0);
-}
-
-// ComputeOpNode
-Array<IterVar> ComputeOpNode::root_iter_vars() const {
-  if (reduce_axis.size() == 0) return axis;
-  Array<IterVar> ret = axis;
-  for (IterVar iv : reduce_axis) {
-    ret.push_back(iv);
-  }
-  return ret;
-}
-
-Type ComputeOpNode::output_dtype(size_t i) const {
-  CHECK_EQ(i, 0U);
-  return body.type();
-}
-
-Array<Expr> ComputeOpNode::output_shape(size_t i) const {
-  CHECK_EQ(i, 0U);
-  std::vector<Expr> shape;
-  for (size_t i = 0; i < axis.size(); ++i) {
-    const Range& r = axis[i]->dom;
-    shape.push_back(r->extent);
-  }
-  return Array<Expr>(shape);
-}
-
-Tensor compute(Array<Expr> shape, FCompute fcompute, std::string name) {
-  auto op_node = std::make_shared<ComputeOpNode>();
-  // compute dimension.
-  size_t ndim = shape.size();
-  std::vector<IterVar> axis;
-  std::vector<Var> args;
-  for (size_t i = 0; i < ndim; ++i) {
-    std::ostringstream os;
-    os << "ax" << i;
-    axis.emplace_back(IterVar(Range(0, shape[i]), os.str()));
-    args.push_back(axis.back()->var);
-  }
-
-  op_node->axis = Array<IterVar>(axis);
-  op_node->body = fcompute(args);
-  op_node->name = name;
-  return Operation(op_node).output(0);
-}
-
-Operation ComputeOpNode::make(std::string name,
-                              Array<IterVar> axis,
-                              Expr body) {
-  auto n = std::make_shared<ComputeOpNode>();
-  n->name = name;
-  n->axis = axis;
-  n->body = body;
-  if (n->body->is_type<ir::Reduce>()) {
-    n->reduce_axis = n->body.as<ir::Reduce>()->axis;
-  }
-  return Operation(n);
-}
-
-TVM_STATIC_IR_FUNCTOR(IRPrinter, vtable)
-.set_dispatch<ComputeOpNode>([](const ComputeOpNode *op, IRPrinter *p) {
-    p->stream << "compute(" << op->name << ", " << op << ")";
-});
-
-TVM_REGISTER_NODE_TYPE(ComputeOpNode);
-
-// Scan
-inline bool prove_equal(Expr lhs, Expr rhs) {
-  return is_zero(ir::Simplify(lhs - rhs));
-}
-
-int ScanOpNode::num_outputs() const {
-  return static_cast<int>(update.size());
-}
-Array<IterVar> ScanOpNode::root_iter_vars() const {
-  return Array<IterVar>{scan_axis};
-}
-
-Type ScanOpNode::output_dtype(size_t i) const {
-  return update[i]->dtype;
-}
-
-Array<Expr> ScanOpNode::output_shape(size_t i) const {
-  CHECK_LT(i, state_placeholder.size());
-  return state_placeholder[i]->shape;
-}
-
-Operation ScanOpNode::make(std::string name,
-                           IterVar axis,
-                           Array<Tensor> init,
-                           Array<Tensor> update,
-                           Array<Tensor> state_placeholder) {
-  auto n = std::make_shared<ScanOpNode>();
-  CHECK_EQ(init.size(), update.size());
-  CHECK_EQ(init.size(), state_placeholder.size());
-
-  for (size_t i = 0; i < init.size(); ++i) {
-    CHECK_EQ(init[i]->dtype, state_placeholder[i]->dtype);
-    CHECK_EQ(init[i]->dtype, update[i]->dtype);
-    CHECK(can_prove(init[i]->shape[0] == axis->dom->min))
-        << "init.shape[0] need to match scan_axis.dom.min";
-    CHECK(prove_equal(
-        state_placeholder[i]->shape[0], axis->dom->min + axis->dom->extent))
-        << "shate_placeholder.shape[0] need to match"
-        << " scan_axis.dom.min + scan_axis.dom.extent";
-    CHECK_EQ(state_placeholder[i].ndim(), init[i].ndim())
-        << "The dimension of init need to match state_placeholder";
-    CHECK_EQ(update[i].ndim(), state_placeholder[i].ndim())
-        << "The update.ndim need to be state_placeholder.ndim - 1";
-    for (size_t k = 0;  k < update[i].ndim(); ++k) {
-      CHECK(prove_equal(
-          update[i]->shape[k], state_placeholder[i]->shape[k]));
-      if (k != 0) {
-        // setup spatial axis
-        std::ostringstream spatial_name;
-        spatial_name << name << ".out" << i << ".i" << k;
-        n->spatial_axis_.push_back(
-            IterVar(Range::make_with_min_extent(0, update[i]->shape[k]),
-                    spatial_name.str()));
-      }
-    }
-    for (size_t k = 1;  k < init[i].ndim(); ++k) {
-      CHECK(prove_equal(
-          init[i]->shape[k], state_placeholder[i]->shape[k]));
-    }
-  }
-  n->name = name;
-  n->scan_axis = axis;
-  n->init = init;
-  n->update = update;
-  n->state_placeholder = state_placeholder;
-  return Operation(n);
-}
-
-Array<Tensor> scan(Array<Tensor> init,
-                   Array<Tensor> update,
-                   Array<Tensor> state_placeholder,
-                   std::string name) {
-  IterVar scan_axis(
-      Range::make_with_min_extent(
-          init[0]->shape[0], update[0]->shape[0] - init[0]->shape[0]),
-      name + ".idx");
-  Operation op = ScanOpNode::make(
-      name, scan_axis, init, update, state_placeholder);
-  Array<Tensor> res;
-  for (int i = 0; i < op->num_outputs(); ++i) {
-    res.push_back(op.output(i));
-  }
-  return res;
-}
-
-TVM_STATIC_IR_FUNCTOR(IRPrinter, vtable)
-.set_dispatch<ScanOpNode>([](const ScanOpNode *op, IRPrinter *p) {
-    p->stream << "scan(" << op->name << ", " << op << ")";
-});
-
-}  // namespace tvm

src/lang/tensor.cc

@@ -3,6 +3,7 @@
  * \file tensor.cc
  */
 #include <tvm/tensor.h>
+#include <tvm/operation.h>
 #include <ir/IR.h>
 #include <memory>
 
@@ -40,4 +41,13 @@ TVM_STATIC_IR_FUNCTOR(IRPrinter, vtable)
 
 TVM_REGISTER_NODE_TYPE(TensorNode);
 
+Tensor Operation::output(size_t i) const {
+  auto node = std::make_shared<TensorNode>();
+  node->op = *this;
+  node->value_index = i;
+  node->dtype = (*this)->output_dtype(i);
+  node->shape = (*this)->output_shape(i);
+  return Tensor(node);
+}
+
 }  // namespace tvm

src/op/compute_op.cc

+/*!
+ *  Copyright (c) 2017 by Contributors
+ * \brief Compute Op.
+ * \file compute_op.cc
+ */
+#include <tvm/operation.h>
+#include <tvm/arithmetic.h>
+#include <tvm/ir.h>
+#include <tvm/ir_visitor.h>
+#include <tvm/ir_pass.h>
+#include <tvm/ir_mutator.h>
+#include <unordered_set>
+#include "./make_loop.h"
+
+namespace tvm {
+
+using namespace ir;
+
+TVM_STATIC_IR_FUNCTOR(IRPrinter, vtable)
+.set_dispatch<ComputeOpNode>([](const ComputeOpNode *op, IRPrinter *p) {
+    p->stream << "compute(" << op->name << ", " << op << ")";
+});
+
+TVM_REGISTER_NODE_TYPE(ComputeOpNode);
+
+int ComputeOpNode::num_outputs() const {
+  return 1;
+}
+
+Array<IterVar> ComputeOpNode::root_iter_vars() const {
+  if (reduce_axis.size() == 0) return axis;
+  Array<IterVar> ret = axis;
+  for (IterVar iv : reduce_axis) {
+    ret.push_back(iv);
+  }
+  return ret;
+}
+
+Type ComputeOpNode::output_dtype(size_t i) const {
+  CHECK_EQ(i, 0U);
+  return body.type();
+}
+
+Array<Expr> ComputeOpNode::output_shape(size_t i) const {
+  CHECK_EQ(i, 0U);
+  std::vector<Expr> shape;
+  for (size_t i = 0; i < axis.size(); ++i) {
+    const Range& r = axis[i]->dom;
+    shape.push_back(r->extent);
+  }
+  return Array<Expr>(shape);
+}
+
+Tensor compute(Array<Expr> shape, FCompute fcompute, std::string name) {
+  auto op_node = std::make_shared<ComputeOpNode>();
+  // compute dimension.
+  size_t ndim = shape.size();
+  std::vector<IterVar> axis;
+  std::vector<Var> args;
+  for (size_t i = 0; i < ndim; ++i) {
+    std::ostringstream os;
+    os << "ax" << i;
+    axis.emplace_back(IterVarNode::make(
+        Range(0, shape[i]), Var(os.str(), shape[i].type()), kDataPar));
+    args.push_back(axis.back()->var);
+  }
+
+  op_node->axis = Array<IterVar>(axis);
+  op_node->body = fcompute(args);
+  op_node->name = name;
+  return Operation(op_node).output(0);
+}
+
+Operation ComputeOpNode::make(std::string name,
+                              Array<IterVar> axis,
+                              Expr body) {
+  auto n = std::make_shared<ComputeOpNode>();
+  n->name = name;
+  n->axis = axis;
+  n->body = body;
+  if (n->body->is_type<ir::Reduce>()) {
+    n->reduce_axis = n->body.as<ir::Reduce>()->axis;
+  }
+  return Operation(n);
+}
+
+// The schedule related logics
+Array<Tensor> ComputeOpNode::InputTensors() const {
+  Array<Tensor> ret;
+  std::unordered_set<Tensor> visited;
+  ir::PostOrderVisit(body, [&ret, &visited](const NodeRef& n) {
+      const ir::Call *call = n.as<ir::Call>();
+      if (call != nullptr && call->func.defined()) {
+        Tensor t = Operation(call->func.node_).output(call->value_index);
+        if (!visited.count(t)) {
+          ret.push_back(t);
+          visited.insert(t);
+        }
+      }
+    });
+  return ret;
+}
+
+// replacer to replace tensors
+class TensorReplacer : public ir::IRMutator {
+ public:
+  explicit TensorReplacer(const std::unordered_map<Tensor, Tensor>& vmap)
+      : vmap_(vmap) {}
+  Expr Mutate_(const ir::Call* op, const Expr& e) {
+    if (op->call_type == ir::Call::Halide) {
+      Tensor t = Operation(op->func.node_).output(op->value_index);
+      auto it = vmap_.find(t);
+      if (it != vmap_.end()) {
+        Expr ret = ir::Call::make(
+            op->type, it->second->op->name, op->args,
+            op->call_type, it->second->op, it->second->value_index);
+        found = true;
+        return IRMutator::Mutate_(ret.as<ir::Call>(), ret);
+      }
+    }
+    return IRMutator::Mutate_(op, e);
+  }
+
+  // whether it is found.
+  bool found{false};
+
+ private:
+  const std::unordered_map<Tensor, Tensor>& vmap_;
+};
+
+Operation ComputeOpNode::ReplaceInputs(
+    const Operation& self,
+    const std::unordered_map<Tensor, Tensor>& rmap) const {
+  CHECK_EQ(self.operator->(), this);
+  TensorReplacer repl(rmap);
+  Expr new_body = repl.Mutate(this->body);
+  if (repl.found) {
+    return ComputeOpNode::make(name, axis, new_body);
+  } else {
+    return self;
+  }
+}
+
+void ComputeOpNode::PropBoundToInputs(
+    const Operation& self,
+    const std::unordered_map<const Variable*, IntSet>& dom_map,
+    std::unordered_map<Tensor, TensorDom>* out_dom_map) const {
+  CHECK_EQ(self.operator->(), this);
+  auto fvisit = [&dom_map, out_dom_map](const NodeRef& n) {
+    auto *call = n.as<ir::Call>();
+    if (call != nullptr && call->func.defined()) {
+      Tensor t = Operation(call->func.node_).output(call->value_index);
+      if (t->op.defined() && out_dom_map->count(t)) {
+        TensorDom& dom = out_dom_map->at(t);
+        for (size_t i = 0; i < t.ndim(); ++i) {
+          dom.data[i].push_back(EvalSet(call->args[i], dom_map));
+        }
+      }
+    }
+  };
+  ir::PostOrderVisit(body, fvisit);
+}
+
+void ComputeOpNode::GatherBound(
+    const Operation& self,
+    const GraphContext& graph_ctx,
+    const std::unordered_map<Tensor, TensorDom>& tensor_dom,
+    std::unordered_map<IterVar, Range>* out_dom_map) const {
+  const TensorDom& tdom = tensor_dom.at(self.output(0));
+  for (size_t i = 0; i < this->axis.size(); ++i) {
+    Range r = arith::Union(tdom.data.at(i)).cover_range(this->axis[i]->dom);
+    CHECK(!out_dom_map->count(this->axis[i]));
+    (*out_dom_map)[this->axis[i]] = r;
+  }
+  for (size_t i = 0; i < this->reduce_axis.size(); ++i) {
+    CHECK(!out_dom_map->count(this->reduce_axis[i]));
+    (*out_dom_map)[this->reduce_axis[i]] = this->reduce_axis[i]->dom;
+  }
+}
+
+Stmt ComputeOpNode::BuildRealize(
+    const Operation& self,
+    const std::unordered_map<IterVar, Range>& realize_map,
+    const Stmt& realize_body) const {
+  CHECK_EQ(self.operator->(), this);
+  Tensor t = self.output(0);
+  Halide::Internal::Region bounds;
+  for (IterVar iv : this->axis) {
+    bounds.push_back(realize_map.at(iv));
+  }
+  return ir::Realize::make(t->op, t->value_index, t->dtype,
+                           bounds, const_true(), realize_body);
+}
+
+// Build a reduction body.
+void MakeReduction(const ComputeOpNode* op,
+                   const Tensor& t,
+                   Stmt* init,
+                   Stmt* provide) {
+  Stmt no_op = Evaluate::make(0);
+  std::vector<Stmt> nest;
+  Array<Expr>  args;
+  for (IterVar iv : op->axis) {
+    args.push_back(iv->var);
+  }
+  const Reduce* reduce = op->body.as<Reduce>();
+  CHECK(reduce);
+  Expr init_value, update_value;
+  if (reduce->op == "Add") {
+    init_value = make_zero(reduce->type);
+    update_value = Add::make(t(args), reduce->source);
+  } else if (reduce->op == "Max") {
+    init_value = reduce->type.min();
+    update_value = Max::make(t(args), reduce->source);
+  } else if (reduce->op == "Min") {
+    init_value = reduce->type.max();
+    update_value = Min::make(t(args), reduce->source);
+  } else {
+    LOG(FATAL) << "Unsupported reduction " << reduce->op;
+  }
+  *init = Provide::make(t->op, t->value_index, init_value, args);
+  *provide = Provide::make(t->op, t->value_index, update_value, args);
+}
+
+Stmt MakeProvide(const ComputeOpNode* op,
+                 const Tensor& t) {
+  Array<Expr> args;
+  for (IterVar iv : op->axis) {
+    args.push_back(iv->var);
+  }
+  return Provide::make(t->op, t->value_index, op->body, args);
+}
+
+// message passing to find if IterVar is related to reduction.
+void PassDownReduceFlag(const Stage& s,
+                        std::unordered_map<IterVar, int>* p_state) {
+  auto& state = *p_state;
+  for (IterVarRelation rel : s->relations) {
+    if (rel.as<SplitNode>()) {
+      const SplitNode* s = rel.as<SplitNode>();
+      int flag = state.at(s->parent);
+      state[s->outer] = flag;
+      state[s->inner] = flag;
+    } else if (rel.as<FuseNode>()) {
+      const FuseNode* s = rel.as<FuseNode>();
+      int flag_outer = state.at(s->outer);
+      int flag_inner = state.at(s->inner);
+      state[s->fused] = flag_outer | flag_inner;
+    } else if (rel.as<RebaseNode>()) {
+      const RebaseNode* s = rel.as<RebaseNode>();
+      int flag = state.at(s->parent);
+      state[s->rebased] = flag;
+    } else {
+      LOG(FATAL) << "unknown relation type";
+    }
+  }
+}
+
+Stmt Substitute(Stmt s,
+                const std::unordered_map<IterVar, Expr>& value_map) {
+  Map<Var, Expr> temp;
+  for (const auto& kv : value_map) {
+    temp.Set(kv.first->var, kv.second);
+  }
+  return ir::Substitute(s, temp);
+}
+
+Stmt ComputeOpNode::BuildProvide(
+    const Stage& stage,
+    const std::unordered_map<IterVar, Range>& dom_map) const {
+  CHECK_EQ(stage->op.operator->(), this);
+
+  Stmt init, provide;
+  if (this->reduce_axis.size() == 0) {
+    provide = MakeProvide(this, stage->op.output(0));
+  } else {
+    MakeReduction(this, stage->op.output(0), &init, &provide);
+  }
+  // make loop nest
+  std::unordered_map<IterVar, Expr> value_map;
+  auto nest = op::MakeLoopNest(
+      stage, dom_map, 0, false, std::unordered_set<IterVar>(), &value_map);
+  nest.push_back(op::MakeBoundCheck(
+      stage, dom_map, false,
+      std::unordered_set<IterVar>(), value_map));
+  provide = Substitute(provide, value_map);
+
+  if (init.defined()) {
+    // try to find the location to insert the initialization.
+    // Fuse the initialization and provide loop when possible.
+    std::unordered_map<IterVar, int> update_state;
+    for (IterVar iv : this->reduce_axis) {
+      update_state[iv] = 2;
+    }
+    for (IterVar iv : this->axis) {
+      update_state[iv] = 1;
+    }
+    // find which iter var is related to reduction and which is related to axis.
+    PassDownReduceFlag(stage, &update_state);
+    auto leaf_iter_vars = stage->leaf_iter_vars;
+    std::unordered_map<IterVar, Expr> init_value_map;
+    // first first loop that is related to reduction.
+    size_t begin_loop = leaf_iter_vars.size();
+    for (size_t i = 0; i < leaf_iter_vars.size(); ++i) {
+      auto iv = leaf_iter_vars[i];
+      int flag = update_state.at(iv);
+      if ((flag & 2) != 0) {
+        begin_loop = i; break;
+      }
+      init_value_map[iv] = value_map.at(iv);
+    }
+    // skip loops that does not relates to axis.
+    std::unordered_set<IterVar> skip_iter;
+    for (auto kv : update_state) {
+      int flag = kv.second;
+      if ((flag & 1) == 0) skip_iter.insert(kv.first);
+    }
+    auto init_nest = op::MakeLoopNest(
+        stage, dom_map, begin_loop, true,
+        skip_iter, &init_value_map);
+    init_nest.push_back(
+        op::MakeBoundCheck(stage, dom_map, true, skip_iter, init_value_map));
+    init = Substitute(init, init_value_map);
+    init  = MergeNest(init_nest, init);
+    // common nest
+    std::vector<std::vector<Stmt> > common(nest.begin(), nest.begin() + begin_loop + 1);
+    std::vector<std::vector<Stmt> > reduce(nest.begin() + begin_loop + 1, nest.end());
+    provide = MergeNest(reduce, provide);
+    return MergeNest(common, Block::make(init, provide));
+  } else {
+    return MergeNest(nest, provide);
+  }
+}
+}  // namespace tvm

src/op/make_loop.cc

+/*!
+ *  Copyright (c) 2017 by Contributors
+ * \brief Utility to make loop nest.
+ * \file make_loop.cc
+ */
+#include <tvm/ir.h>
+#include <tvm/ir_pass.h>
+#include <tvm/operation.h>
+#include "./make_loop.h"
+#include "../arithmetic/compute_expr.h"
+
+namespace tvm {
+namespace op {
+
+using namespace arith;
+using namespace ir;
+
+/*!
+ * \brief use message passing to calculate the assignment of each Var inside the loop body.
+ * \param s The schedule to be used.
+ * \param dom_map The domain map of each iteration variable's domain
+ * \param p_state The message passing state
+ *     IterVar->The assignment.
+ */
+void PassUpOffset(const Stage& s,
+                  const Map<IterVar, Range>& dom_map,
+                  std::unordered_map<IterVar, Expr>* p_state) {
+  auto& state = *p_state;
+  for (size_t i = s->relations.size(); i != 0; --i) {
+    IterVarRelation rel = s->relations[i - 1];
+    if (rel.as<SplitNode>()) {
+      const SplitNode* s = rel.as<SplitNode>();
+      Expr outer = state.at(s->outer);
+      Expr inner = state.at(s->inner);
+      Expr factor = dom_map.at(s->inner)->extent;
+      Expr parent_min = dom_map.at(s->parent)->min;
+      state[s->parent] = inner + outer * factor;
+      // add min if they exist
+      if (!is_zero(parent_min)) {
+        state[s->parent] = state[s->parent] + parent_min;
+      }
+    } else if (rel.as<FuseNode>()) {
+      const FuseNode* s = rel.as<FuseNode>();
+      Expr value = state.at(s->fused);
+      Expr factor = dom_map.at(s->inner)->extent;
+      Expr outer_min = dom_map.at(s->outer)->min;
+      Expr inner_min = dom_map.at(s->inner)->min;
+      state[s->outer] = value / factor;
+      state[s->inner] = value % factor;
+      // add min if they exist
+      if (!is_zero(outer_min)) {
+        state[s->outer] = state[s->outer] + outer_min;
+      }
+      if (!is_zero(inner_min)) {
+        state[s->inner] = state[s->inner] + inner_min;
+      }
+    } else if (rel.as<RebaseNode>()) {
+      const RebaseNode* s = rel.as<RebaseNode>();
+      Expr value = state.at(s->rebased);
+      Expr parent_min = dom_map.at(s->parent)->min;
+      // add min if they exist
+      if (!is_zero(parent_min)) {
+        state[s->parent] = value + parent_min;
+      } else {
+        state[s->parent] = value;
+      }
+    } else {
+      LOG(FATAL) << "unknown relation type";
+    }
+  }
+}
+
+std::vector<std::vector<Stmt> >
+MakeLoopNest(const Stage& stage,
+             const std::unordered_map<IterVar, Range>& dom_map,
+             size_t begin_iter_pos,
+             bool new_loop_var,
+             const std::unordered_set<IterVar>& skip_iter,
+             std::unordered_map<IterVar, Expr>* p_value_map) {
+  auto leaf_iter_vars = stage->leaf_iter_vars;
+  Stmt no_op = Evaluate::make(0);
+  // create the loop nest
+  std::vector<std::vector<Stmt> > nest;
+  nest.resize(leaf_iter_vars.size() + 1);
+  std::unordered_map<IterVar, Expr>& value_map = *p_value_map;
+
+  for (size_t i = begin_iter_pos; i < leaf_iter_vars.size(); ++i) {
+    auto iv = leaf_iter_vars[i];
+    if (skip_iter.count(iv) || iv->iter_type == kOpaque) {
+      // skip this iteration.
+      value_map[iv] = iv->var;
+      continue;
+    }
+    Range dom = dom_map.at(iv);
+    // initialize the offset and loop_level
+    Var var = iv->var;
+    if (new_loop_var) {
+      var = Var(iv->var->name_hint + ".init", iv->var.type());
+    }
+    // Mark the iter var in the IR, to remember the point
+    if (iv->thread_tag.length() == 0) {
+      ForType for_type = ForType::Serial;
+      if (stage->iter_var_attrs.count(iv)) {
+        switch (stage->iter_var_attrs[iv]->iter_type) {
+          case kUnrolled: for_type = ForType::Unrolled; break;
+          case kVectorized: for_type = ForType::Vectorized; break;
+          case kParallelized: for_type = ForType::Parallel; break;
+          default: LOG(FATAL) << "Unknown iter type"
+                              << stage->iter_var_attrs[iv]->iter_type
+                              << " in the iter_var_attrs";
+        }
+      }
+      if (is_one(dom->extent)) {
+        nest[i + 1].emplace_back(
+            LetStmt::make(var, dom->min, no_op));
+        value_map[iv] = dom->min;
+      } else if (is_zero(dom->min)) {
+        nest[i + 1].emplace_back(
+            For::make(var, 0, dom->extent,
+                      for_type, DeviceAPI::None, no_op));
+        value_map[iv] = var;
+      } else {
+        Var idx(iv->var->name_hint + ".idx", iv->var.type());
+        nest[i + 1].emplace_back(
+            For::make(idx, 0, dom->extent,
+                      for_type, DeviceAPI::None, no_op));
+        Expr new_value = dom->min + idx;
+        value_map[iv] = new_value;
+        nest[i + 1].emplace_back(
+            LetStmt::make(var, new_value, no_op));
+      }
+    } else if (iv->thread_tag == "vthread") {
+      // virtual thread
+      // Always restrict threaded IterVar to starts from 0.
+      CHECK(is_zero(dom->min));
+      CHECK(is_positive_const(dom->extent));
+      // annotate the extent of the IterVar
+      nest[i + 1].emplace_back(
+          AttrStmt::make(iv, ir::attr::virtual_thread, dom->extent, no_op));
+      value_map[iv] = var;
+    } else {
+      // Always restrict threaded IterVar to starts from 0.
+      CHECK(is_zero(dom->min));
+      // annotate the extent of the IterVar
+      nest[i + 1].emplace_back(
+          AttrStmt::make(iv, ir::attr::thread_extent, dom->extent, no_op));
+      value_map[iv] = var;
+    }
+    // annotate the extent of the IterVar
+    if (!new_loop_var) {
+      nest[i + 1].emplace_back(
+          AttrStmt::make(iv, attr::loop_scope, iv->var, no_op));
+    }
+  }
+  // message passing to get offset of root iter vars.
+  PassUpOffset(stage, dom_map, &value_map);
+  return nest;
+}
+
+
+/*!
+ * \brief message passing to find if boundary checking on IterVar is needed.
+ * \param s The stage to be used.
+ * \param p_state The message passing state
+ *     IterVar->flag
+ */
+void PassUpBoundCheck(const Stage& s,
+                      const Map<IterVar, Range>& dom_map,
+                      std::unordered_map<IterVar, bool>* p_state) {
+  auto& state = *p_state;
+  using Halide::Internal::can_prove;
+  for (size_t i = s->relations.size(); i != 0; --i) {
+    IterVarRelation rel = s->relations[i - 1];
+    if (rel.as<SplitNode>()) {
+      const SplitNode* s = rel.as<SplitNode>();
+      bool outer = state.at(s->outer);
+      bool inner = state.at(s->inner);
+      Expr factor = dom_map.at(s->inner)->extent;
+      Expr step = dom_map.at(s->outer)->extent;
+
+      if (outer || inner) {
+        state[s->parent] = true;
+      } else {
+        if (can_prove(dom_map.at(s->parent)->extent == factor * step)) {
+          state[s->parent] = false;
+        } else {
+          state[s->parent] = true;
+        }
+      }
+    } else if (rel.as<FuseNode>()) {
+      const FuseNode* s = rel.as<FuseNode>();
+      bool fused = state.at(s->fused);
+      state[s->outer] = fused;
+      state[s->inner] = fused;
+    } else if (rel.as<RebaseNode>()) {
+      const RebaseNode* s = rel.as<RebaseNode>();
+      state[s->parent] = state.at(s->rebased);
+    } else {
+      LOG(FATAL) << "unknown relation type";
+    }
+  }
+}
+
+std::vector<Stmt> MakeBoundCheck(
+    const Stage& stage,
+    const Map<IterVar, Range>& dom_map,
+    bool skip_ivar_domain,
+    const std::unordered_set<IterVar>& skip_iter,
+    const std::unordered_map<IterVar, Expr>& value_map) {
+  Stmt no_op = Evaluate::make(0);
+  std::unordered_map<IterVar, bool> bound_state;
+  for (IterVar iv : stage->leaf_iter_vars) {
+    bound_state[iv] = false;
+  }
+  PassUpBoundCheck(stage, dom_map, &bound_state);
+  // insert conditions
+  std::vector<Stmt> nest;
+  for (IterVar iv : stage->op->root_iter_vars()) {
+    if (skip_iter.count(iv) || iv->iter_type == kOpaque) continue;
+    Range dom = dom_map.at(iv);
+    if (bound_state.at(iv)) {
+      Expr condition = ComputeExpr<Sub>(value_map.at(iv), dom->min) < dom->extent;
+      nest.emplace_back(IfThenElse::make(condition, no_op));
+    }
+    CHECK(iv->dom.defined());
+    if (!skip_ivar_domain && !iv->dom.same_as(dom)) {
+      Expr condition = ComputeExpr<Sub>(value_map.at(iv), iv->dom->min) < iv->dom->extent;
+      nest.emplace_back(IfThenElse::make(condition, no_op));
+    }
+  }
+  return nest;
+}
+
+}  // namespace op
+}  // namespace tvm

src/op/make_loop.h

+/*!
+ *  Copyright (c) 2017 by Contributors
+ * \file make_loop.h
+ * \brief Utility to make loop nest from schedule stage info.
+ */
+#ifndef TVM_OP_MAKE_LOOP_H_
+#define TVM_OP_MAKE_LOOP_H_
+
+#include <tvm/expr.h>
+#include <tvm/schedule.h>
+#include <unordered_map>
+#include <unordered_set>
+#include <vector>
+#include "../pass/ir_util.h"
+
+namespace tvm {
+namespace op {
+
+using ir::MergeNest;
+
+/*!
+ * \brief Build loop nest for stage.
+ *
+ * \param stage The stage to create a loop nest.
+ * \param dom_map The range of each iter var.
+ * \param begin_iter_pos The beginning position of leaf_iter_vars to generate loop.
+ * \param new_loop_var Whether create new loop variable.
+ * \param skip_iter Whether skip certain iteration.
+ * \param p_value_map The result value of each IterVar.
+ */
+std::vector<std::vector<Stmt> >
+MakeLoopNest(const Stage& stage,
+             const std::unordered_map<IterVar, Range>& dom_map,
+             size_t begin_iter_pos,
+             bool new_loop_var,
+             const std::unordered_set<IterVar>& skip_iter,
+             std::unordered_map<IterVar, Expr>* p_value_map);
+/*!
+ * \brief Create boundary check condition for given stage.
+ *
+ * \param stage The stage to create a loop nest.
+ * \param dom_map The range of each iter var.
+ * \param skip_ivar_domain Whether we can skip check for IterVar's original domain.
+ * \param skip_iter Whether skip certain iteration.
+ * \param value_map The result value of each IterVar.
+ */
+std::vector<Stmt>
+MakeBoundCheck(const Stage& stage,
+               const Map<IterVar, Range>& dom_map,
+               bool skip_ivar_domain,
+               const std::unordered_set<IterVar>& skip_iter,
+               const std::unordered_map<IterVar, Expr>& value_map);
+}  // namespace op
+}  // namespace tvm
+#endif  // TVM_OP_MAKE_LOOP_H_

src/op/placeholder_op.cc

+/*!
+ *  Copyright (c) 2017 by Contributors
+ * \brief Placeholder op.
+ * \file placeholder_op.cc
+ */
+#include <tvm/operation.h>
+
+namespace tvm {
+
+// PlaceholderOpNode
+TVM_STATIC_IR_FUNCTOR(IRPrinter, vtable)
+.set_dispatch<PlaceholderOpNode>([](const PlaceholderOpNode *op, IRPrinter *p) {
+    p->stream << "placeholder(" << op->name << ", " << op << ")";
+});
+
+TVM_REGISTER_NODE_TYPE(PlaceholderOpNode);
+
+int PlaceholderOpNode::num_outputs() const {
+  return 1;
+}
+
+Array<IterVar> PlaceholderOpNode::root_iter_vars() const {
+  return {};
+}
+
+Type PlaceholderOpNode::output_dtype(size_t i) const {
+  CHECK_EQ(i, 0U);
+  return dtype;
+}
+
+Array<Expr> PlaceholderOpNode::output_shape(size_t i) const {
+  CHECK_EQ(i, 0U);
+  return shape;
+}
+
+
+Operation PlaceholderOpNode::make(std::string name,
+                                  Array<Expr> shape,
+                                  Type dtype) {
+  auto n = std::make_shared<PlaceholderOpNode>();
+  n->name = name;
+  n->shape = shape;
+  n->dtype = dtype;
+  return Operation(n);
+}
+
+Tensor placeholder(Array<Expr> shape, Type dtype, std::string name) {
+  return PlaceholderOpNode::make(name, shape, dtype).output(0);
+}
+
+Array<Tensor> PlaceholderOpNode::InputTensors() const {
+  return {};
+}
+
+Operation PlaceholderOpNode::ReplaceInputs(
+    const Operation& self,
+    const std::unordered_map<Tensor, Tensor>& rmap) const {
+  return self;
+}
+
+void PlaceholderOpNode::PropBoundToInputs(
+    const Operation& self,
+    const std::unordered_map<const Variable*, IntSet>& dom_map,
+    std::unordered_map<Tensor, TensorDom>* out_dom_map) const {
+}
+
+void PlaceholderOpNode::GatherBound(
+    const Operation& self,
+    const GraphContext& graph_ctx,
+    const std::unordered_map<Tensor, TensorDom>& tensor_dom,
+    std::unordered_map<IterVar, Range>* out_dom_map) const {
+}
+
+Stmt PlaceholderOpNode::BuildRealize(
+    const Operation& self,
+    const std::unordered_map<IterVar, Range>& realize_map,
+    const Stmt& body) const {
+  return body;
+}
+
+Stmt PlaceholderOpNode::BuildProvide(
+    const Stage& stage,
+    const std::unordered_map<IterVar, Range>& dom_map) const {
+  return Stmt();
+}
+}  // namespace tvm

src/op/scan_op.cc

+/*!
+ *  Copyright (c) 2017 by Contributors
+ * \brief Scan Operator.
+ * \file scan_op.cc
+ */
+#include <tvm/operation.h>
+#include <tvm/ir.h>
+#include <tvm/ir_pass.h>
+#include "./make_loop.h"
+#include "../schedule/graph.h"
+
+namespace tvm {
+
+using namespace ir;
+
+TVM_STATIC_IR_FUNCTOR(IRPrinter, vtable)
+.set_dispatch<ScanOpNode>([](const ScanOpNode *op, IRPrinter *p) {
+    p->stream << "scan(" << op->name << ", " << op << ")";
+});
+TVM_REGISTER_NODE_TYPE(ScanOpNode);
+
+inline bool prove_equal(Expr lhs, Expr rhs) {
+  return is_zero(ir::Simplify(lhs - rhs));
+}
+
+int ScanOpNode::num_outputs() const {
+  return static_cast<int>(update.size());
+}
+Array<IterVar> ScanOpNode::root_iter_vars() const {
+  Array<IterVar> ret{scan_axis};
+  for (IterVar iv : spatial_axis_) {
+    ret.push_back(iv);
+  }
+  return ret;
+}
+
+Type ScanOpNode::output_dtype(size_t i) const {
+  return update[i]->dtype;
+}
+
+Array<Expr> ScanOpNode::output_shape(size_t i) const {
+  CHECK_LT(i, state_placeholder.size());
+  return state_placeholder[i]->shape;
+}
+
+Operation ScanOpNode::make(std::string name,
+                           IterVar axis,
+                           Array<Tensor> init,
+                           Array<Tensor> update,
+                           Array<Tensor> state_placeholder) {
+  auto n = std::make_shared<ScanOpNode>();
+  CHECK_EQ(init.size(), update.size());
+  CHECK_EQ(init.size(), state_placeholder.size());
+
+  for (size_t i = 0; i < init.size(); ++i) {
+    CHECK_EQ(init[i]->dtype, state_placeholder[i]->dtype);
+    CHECK_EQ(init[i]->dtype, update[i]->dtype);
+    CHECK(can_prove(init[i]->shape[0] == axis->dom->min))
+        << "init.shape[0] need to match scan_axis.dom.min";
+    CHECK(prove_equal(
+        state_placeholder[i]->shape[0], axis->dom->min + axis->dom->extent))
+        << "shate_placeholder.shape[0] need to match"
+        << " scan_axis.dom.min + scan_axis.dom.extent";
+    CHECK_EQ(state_placeholder[i].ndim(), init[i].ndim())
+        << "The dimension of init need to match state_placeholder";
+    CHECK_EQ(update[i].ndim(), state_placeholder[i].ndim())
+        << "The update.ndim need to be state_placeholder.ndim - 1";
+    for (size_t k = 0;  k < update[i].ndim(); ++k) {
+      CHECK(prove_equal(
+          update[i]->shape[k], state_placeholder[i]->shape[k]));
+      if (k != 0) {
+        // setup spatial axis
+        std::ostringstream spatial_name;
+        spatial_name << name << ".out" << i << ".i" << k;
+        n->spatial_axis_.push_back(
+            IterVarNode::make(
+                Range::make_with_min_extent(0, update[i]->shape[k]),
+                Var(spatial_name.str()), kOpaque));
+      }
+    }
+
+    for (size_t k = 1;  k < init[i].ndim(); ++k) {
+      CHECK(prove_equal(
+          init[i]->shape[k], state_placeholder[i]->shape[k]));
+    }
+  }
+  n->name = name;
+  n->scan_axis = axis;
+  n->init = init;
+  n->update = update;
+  n->state_placeholder = state_placeholder;
+  return Operation(n);
+}
+
+Array<Tensor> scan(Array<Tensor> init,
+                   Array<Tensor> update,
+                   Array<Tensor> state_placeholder,
+                   std::string name) {
+  IterVar scan_axis =
+      IterVarNode::make(
+          Range::make_with_min_extent(
+              init[0]->shape[0], update[0]->shape[0] - init[0]->shape[0]),
+          Var(name + ".idx"), kOrdered);
+  Operation op = ScanOpNode::make(
+      name, scan_axis, init, update, state_placeholder);
+  Array<Tensor> res;
+  for (int i = 0; i < op->num_outputs(); ++i) {
+    res.push_back(op.output(i));
+  }
+  return res;
+}
+
+Array<Tensor> ScanOpNode::InputTensors() const {
+  Array<Tensor> ret;
+  for (Tensor t : init) {
+    ret.push_back(t);
+  }
+  for (Tensor t : update) {
+    ret.push_back(t);
+  }
+  return ret;
+}
+
+Operation ScanOpNode::ReplaceInputs(
+    const Operation& self,
+    const std::unordered_map<Tensor, Tensor>& rmap) const {
+  CHECK_EQ(self.operator->(), this);
+  std::shared_ptr<ScanOpNode> n = std::make_shared<ScanOpNode>(*this);
+  for (size_t i = 0; i < n->init.size(); ++i) {
+    if (rmap.count(n->init[i])) {
+      n->init.Set(i, rmap.at(n->init[i]));
+    }
+    if (rmap.count(n->update[i])) {
+      n->update.Set(i, rmap.at(n->update[i]));
+    }
+  }
+  if (!n->init.same_as(init) ||
+      !n->update.same_as(update)) {
+    return Operation(n);
+  } else {
+    return self;
+  }
+}
+
+void ScanOpNode::PropBoundToInputs(
+    const Operation& self,
+    const std::unordered_map<const Variable*, IntSet>& dom_map,
+    std::unordered_map<Tensor, TensorDom>* out_dom_map) const {
+  CHECK_EQ(self.operator->(), this);
+  for (size_t i = 0, sp_idx = 0; i < this->init.size(); ++i) {
+    TensorDom* init_dom = nullptr;
+    TensorDom* update_dom = nullptr;
+    if (out_dom_map->count(this->init[i])) {
+      init_dom = &out_dom_map->at(this->init[i]);
+    }
+    if (out_dom_map->count(this->update[i])) {
+      update_dom = &out_dom_map->at(this->update[i]);
+    }
+    // first dimension, always needed.
+    if (init_dom) {
+      init_dom->data[0].push_back(IntSet::range(
+          Range::make_with_min_extent(0, this->init[i]->shape[0])));
+    }
+    if (update_dom) {
+      update_dom->data[0].push_back(dom_map.at(this->scan_axis->var.get()));
+    }
+    // The update dimensions
+    for (size_t k = 1; k < this->update[i]->shape.size(); ++k, ++sp_idx) {
+      IterVar sp_ax = this->spatial_axis_[sp_idx];
+      if (init_dom) {
+        init_dom->data[k].push_back(dom_map.at(sp_ax->var.get()));
+      }
+      if (update_dom) {
+        update_dom->data[k].push_back(dom_map.at(sp_ax->var.get()));
+      }
+    }
+  }
+}
+
+void ScanOpNode::GatherBound(
+    const Operation& self,
+    const GraphContext& graph_ctx,
+    const std::unordered_map<Tensor, TensorDom>& tensor_dom,
+    std::unordered_map<IterVar, Range>* out_dom_map) const {
+  CHECK_EQ(self.operator->(), this);
+  using namespace schedule;
+  CHECK(!out_dom_map->count(this->scan_axis));
+  std::vector<Tensor> output(this->num_outputs());
+  for (size_t i = 0; i < output.size(); ++i) {
+    output[i] = self.output(i);
+  }
+  // Update for time axis.
+  std::vector<IntSet> time_dom;
+  for (size_t i = 0; i < output.size(); ++i) {
+    const TensorDom& d = tensor_dom.at(output[i]);
+    time_dom.insert(time_dom.end(), d.data[0].begin(), d.data[0].end());
+  }
+  CHECK(!out_dom_map->count(this->scan_axis));
+  Range sdom = this->scan_axis->dom;
+  Range r = arith::Union(time_dom).cover_range(sdom);
+  (*out_dom_map)[this->scan_axis] = Range::make_with_min_extent(
+      sdom->min, ir::Simplify(r->extent + r->min - sdom->min));
+  Array<Operation> body = ScanGetBody_(this, graph_ctx.feed_graph);
+  Map<IterVar, Expr> fix_pt = ScanFixPointAnalysis(self, body);
+  // Update for spatial axis.
+  size_t sp_idx = 0;
+  for (size_t i = 0; i < output.size(); ++i) {
+    const TensorDom& d = tensor_dom.at(output[i]);
+    for (size_t k = 1; k < this->update[i]->shape.size(); ++k, ++sp_idx) {
+      IterVar sp_ax = this->spatial_axis_[sp_idx];
+      CHECK(!out_dom_map->count(sp_ax));
+      CHECK(fix_pt.count(sp_ax));
+      if (fix_pt[sp_ax].as<ir::IntImm>()->value) {
+        // fix point, we can slice it.
+        (*out_dom_map)[sp_ax] = arith::Union(d.data[k + 1]).cover_range(sp_ax->dom);
+      } else {
+        // not a fix point, need to include everything.
+        (*out_dom_map)[sp_ax] = sp_ax->dom;
+      }
+    }
+  }
+}
+
+Stmt ScanOpNode::BuildRealize(
+    const Operation& self,
+    const std::unordered_map<IterVar, Range>& dom_map,
+    const Stmt& body) const {
+  CHECK_EQ(self.operator->(), this);
+  Range sdom = dom_map.at(this->scan_axis);
+  Range tdom = Range::make_with_min_extent(
+      0, ir::Simplify(sdom->extent + sdom->min));
+  Stmt ret = body;
+  size_t sp_idx = 0;
+  for (size_t i = 0; i < update.size(); ++i) {
+    Tensor t = self.output(i);
+    CHECK_EQ(static_cast<size_t>(t->value_index), i);
+    Halide::Internal::Region bounds;
+    bounds.push_back(tdom);
+    for (size_t k = 1; k < this->update[i]->shape.size(); ++k, ++sp_idx) {
+      IterVar sp_ax = this->spatial_axis_[sp_idx];
+      bounds.push_back(dom_map.at(sp_ax));
+    }
+    ret = ir::Realize::make(t->op, t->value_index, t->dtype,
+                            bounds, const_true(), ret);
+  }
+  return ret;
+}
+
+Stmt ScanOpNode::BuildProvide(
+    const Stage& stage,
+    const std::unordered_map<IterVar, Range>& dom_map) const {
+  CHECK_EQ(stage->op.operator->(), this);
+  Stmt provide = AttrStmt::make(
+      stage->op, attr::scan_update_scope, this->scan_axis->var,
+      Evaluate::make(0));
+  Stmt init = AttrStmt::make(
+      stage->op, attr::scan_init_scope, 0,
+      Evaluate::make(0));
+  size_t begin_scan = 0;
+  for (size_t  i = 0; i < stage->leaf_iter_vars.size(); ++i) {
+    if (stage->leaf_iter_vars[i]->iter_type == kThreadIndex) {
+      CHECK_EQ(begin_scan, i);
+      begin_scan = i + 1;
+    }
+  }
+  std::unordered_map<IterVar, Expr> vmap;
+  std::unordered_set<IterVar> empty;
+  auto nest = op::MakeLoopNest(
+      stage, dom_map, 0, false, empty, &vmap);
+  nest[begin_scan].push_back(init);
+  nest.push_back(
+      op::MakeBoundCheck(stage, dom_map, false, empty, vmap));
+  return MergeNest(nest, provide);
+}
+}  // namespace tvm

src/pass/ir_mutator.cc

@@ -44,7 +44,7 @@ inline Array<IterVar> MutateIterVarArr(Array<IterVar> rdom, IRMutator *m) {
     if (!r->extent.same_as(new_extent)) changed = true;
     new_dom[i] = IterVarNode::make(
         Range::make_with_min_extent(new_min, new_extent),
-        v->var, v->thread_tag);
+        v->var, v->iter_type, v->thread_tag);
   }
   if (!changed) {
     return rdom;
@@ -322,11 +322,13 @@ DEFINE_BIOP_EXPR_MUTATE_(Or)
 Expr IRMutator::Mutate_(const Reduce *op, const Expr& e) {
   Array<IterVar> new_axis  = MutateIterVarArr(op->axis, this);
   Expr new_source = this->Mutate(op->source);
+  Expr new_cond = this->Mutate(op->condition);
   if (op->axis.same_as(new_axis) &&
-      op->source.same_as(new_source)) {
+      op->source.same_as(new_source) &&
+      op->condition.same_as(new_cond)) {
     return e;
   } else {
-    return Reduce::make(op->op, new_source, new_axis);
+    return Reduce::make(op->op, new_source, new_axis, new_cond);
   }
 }
 

src/pass/loop_partition.cc

@@ -6,15 +6,17 @@
 #include <tvm/ir_visitor.h>
 #include <tvm/ir_mutator.h>
 #include <tvm/ir_pass.h>
+#include <tvm/arithmetic.h>
 #include <unordered_map>
 #include <unordered_set>
-#include "../arithmetic/int_set.h"
 #include "../arithmetic/int_set_internal.h"
 
 namespace tvm {
 namespace ir {
 
 using arith::IntSet;
+using arith::DeduceBound;
+using arith::Intersect;
 
 // a partition means the expr is equal to true in the interval
 struct Partition {

src/schedule/auto_inline_elem_wise.cc

@@ -3,6 +3,7 @@
  * \file auto_inline_elem_wise.cc
  */
 #include <tvm/schedule_pass.h>
+#include <tvm/operation.h>
 #include <tvm/ir_visitor.h>
 
 namespace tvm {

src/schedule/bound.cc

-
 /*!
  *  Copyright (c) 2016 by Contributors
  * \file bound.cc
@@ -8,10 +7,11 @@
 #include <tvm/ir_visitor.h>
 #include <tvm/ir_pass.h>
 #include <tvm/schedule_pass.h>
+#include <tvm/arithmetic.h>
+#include <tvm/operation.h>
 #include <unordered_map>
 #include <unordered_set>
 #include "./graph.h"
-#include "../arithmetic/int_set.h"
 #include "../runtime/thread_storage_scope.h"
 
 namespace tvm {
@@ -55,8 +55,10 @@ void PassDown(const Stage& s,
             bool match = is_zero(outer_rng->min);
             if (!prove_equal(outer_ext, outer_rng->extent)) match = false;
             CHECK(match)
+                << r->outer
                 << "IterVar is used in two places as outer scope,"
-                << " cannot prove their extents are the same";
+                << " cannot prove their extents are the same "
+                << outer_ext << " vs " << outer_rng->extent;
           }
         }
       } else {
@@ -195,162 +197,6 @@ void PassUp(const Stage& s,
   }
 }
 
-// All the itervars that are needed to output bound of op.
-// For most op, it is root_iter_vars
-// For Scan, it also contains the additional spatial axis.
-Array<IterVar> OutputRelatedIterVars(const Operation& op) {
-  if (op.as<ScanOpNode>()) {
-    const ScanOpNode* scan = op.as<ScanOpNode>();
-    Array<IterVar> ret{scan->scan_axis};
-    for (IterVar iv : scan->spatial_axis_) {
-      ret.push_back(iv);
-    }
-    return ret;
-  } else {
-    return op->root_iter_vars();
-  }
-}
-
-/*! \brief temporary data structure to store Tensor domain */
-struct TensorDom {
-  // constructor
-  explicit TensorDom(int ndim)
-      : data(ndim) {}
-  /*! \brief The domain data*/
-  std::vector<std::vector<IntSet> > data;
-};
-
-/*!
- * \brief Propagate bound to target
- * \param dom_map The domain map to be propagated
- * \param out The tensor set to be passed
- * \return The result bound
- */
-void BoundProp(const Operation& op,
-               const std::unordered_map<const Variable*, IntSet>& dom_map,
-               std::unordered_map<Tensor, TensorDom> *out) {
-  if (op.as<ComputeOpNode>()) {
-    auto fvisit = [&dom_map, out](const NodeRef& n) {
-      auto *call = n.as<ir::Call>();
-      if (call != nullptr && call->func.defined()) {
-        Tensor t = Operation(call->func.node_).output(call->value_index);
-        if (t->op.defined() && out->count(t)) {
-          TensorDom& dom = out->at(t);
-          for (size_t i = 0; i < t.ndim(); ++i) {
-            dom.data[i].push_back(EvalSet(call->args[i], dom_map));
-          }
-        }
-      }
-    };
-    ir::PostOrderVisit(op.as<ComputeOpNode>()->body, fvisit);
-  } else if (op.as<ScanOpNode>()) {
-    const ScanOpNode* scan = op.as<ScanOpNode>();
-    size_t sp_idx = 0;
-    for (size_t i = 0; i < scan->init.size(); ++i) {
-      TensorDom* init_dom = nullptr;
-      TensorDom* update_dom = nullptr;
-      if (out->count(scan->init[i])) {
-        init_dom = &out->at(scan->init[i]);
-      }
-      if (out->count(scan->update[i])) {
-        update_dom = &out->at(scan->update[i]);
-      }
-      // first dimension, always needed.
-      if (init_dom) {
-        init_dom->data[0].push_back(IntSet::range(
-            Range::make_with_min_extent(0, scan->init[i]->shape[0])));
-      }
-      if (update_dom) {
-        update_dom->data[0].push_back(dom_map.at(scan->scan_axis->var.get()));
-      }
-      // The update dimensions
-      for (size_t k = 1; k < scan->update[i]->shape.size(); ++k, ++sp_idx) {
-        IterVar sp_ax = scan->spatial_axis_[sp_idx];
-        if (init_dom) {
-          init_dom->data[k].push_back(dom_map.at(sp_ax->var.get()));
-        }
-        if (update_dom) {
-          update_dom->data[k].push_back(dom_map.at(sp_ax->var.get()));
-        }
-      }
-    }
-  } else if (op.as<PlaceholderOpNode>()) {
-    // do nothing
-  } else {
-    LOG(FATAL) << "unknown operation mode " << op->type_key();
-  }
-}
-
-
-// Given the bound of output of op
-// Pass the bound to the related axis in op.
-void GatherOpBound(const ScanOpNode* scan,
-                   const Operation& op,
-                   const FeedGraph& fg,
-                   const std::unordered_map<Tensor, TensorDom>& tmap,
-                   std::unordered_map<IterVar, Range>* rmap) {
-  CHECK(!rmap->count(scan->scan_axis));
-  std::vector<Tensor> output(op->num_outputs());
-  for (size_t i = 0; i < output.size(); ++i) {
-    output[i] = op.output(i);
-  }
-  // Update for time axis.
-  std::vector<IntSet> time_dom;
-  for (size_t i = 0; i < output.size(); ++i) {
-    const TensorDom& d = tmap.at(output[i]);
-    time_dom.insert(time_dom.end(), d.data[0].begin(), d.data[0].end());
-  }
-  CHECK(!rmap->count(scan->scan_axis));
-  Range sdom = scan->scan_axis->dom;
-  Range r = arith::Union(time_dom).cover_range(sdom);
-  (*rmap)[scan->scan_axis] = Range::make_with_min_extent(
-      sdom->min, ir::Simplify(r->extent + r->min - sdom->min));
-  Array<Operation> body = ScanGetBody_(scan, fg);
-  Map<IterVar, Expr> fix_pt = ScanFixPointAnalysis(op, body);
-  // Update for spatial axis.
-  size_t sp_idx = 0;
-  for (size_t i = 0; i < output.size(); ++i) {
-    const TensorDom& d = tmap.at(output[i]);
-    for (size_t k = 1; k < scan->update[i]->shape.size(); ++k, ++sp_idx) {
-      IterVar sp_ax = scan->spatial_axis_[sp_idx];
-      CHECK(!rmap->count(sp_ax));
-      CHECK(fix_pt.count(sp_ax));
-      if (fix_pt[sp_ax].as<ir::IntImm>()->value) {
-        // fix point, we can slice it.
-        (*rmap)[sp_ax] = arith::Union(d.data[k + 1]).cover_range(sp_ax->dom);
-      } else {
-        // not a fix point, need to include everything.
-        (*rmap)[sp_ax] = sp_ax->dom;
-      }
-    }
-  }
-}
-
-void GatherOpBound(const Operation& op,
-                   const FeedGraph& fg,
-                   const std::unordered_map<Tensor, TensorDom>& tmap,
-                   std::unordered_map<IterVar, Range>* rmap) {
-  if (op.as<ComputeOpNode>()) {
-    const ComputeOpNode* compute = op.as<ComputeOpNode>();
-    const TensorDom& tdom = tmap.at(op.output(0));
-    for (size_t i = 0; i < compute->axis.size(); ++i) {
-      Range r = arith::Union(tdom.data.at(i)).cover_range(compute->axis[i]->dom);
-      CHECK(!rmap->count(compute->axis[i]));
-      (*rmap)[compute->axis[i]] = r;
-    }
-    for (size_t i = 0; i < compute->reduce_axis.size(); ++i) {
-      CHECK(!rmap->count(compute->reduce_axis[i]));
-      (*rmap)[compute->reduce_axis[i]] = compute->reduce_axis[i]->dom;
-    }
-  } else if (op.as<ScanOpNode>()) {
-    GatherOpBound(op.as<ScanOpNode>(), op, fg, tmap, rmap);
-  } else if (op.as<PlaceholderOpNode>()) {
-    // dp nothing
-  } else {
-    LOG(FATAL) << "unknown operation mode " << op->type_key();
-  }
-}
-
 // check if scope
 inline bool ScopeRelax(const IterVar& iv, const std::string& scope) {
   using runtime::ThreadScope;
@@ -362,14 +208,14 @@ inline bool ScopeRelax(const IterVar& iv, const std::string& scope) {
 }
 
 void InferRootBound(const Stage& stage,
-                    const FeedGraph& feed_graph,
+                    const GraphContext& ctx,
                     const AttachPath& attach_path,
                     std::unordered_map<IterVar, Range>* rmap) {
   CHECK_NE(stage->attach_type, kInline)
       << "call schedule.normalize before scheduleops";
   if (stage->attach_type == kInlinedAlready) return;
   if (stage->is_output || stage->op.as<PlaceholderOpNode>()) {
-    for (auto iv :  OutputRelatedIterVars(stage->op)) {
+    for (auto iv :  stage->op->root_iter_vars()) {
       CHECK(iv->dom.defined());
       CHECK(!rmap->count(iv));
       (*rmap)[iv] = iv->dom;
@@ -390,8 +236,8 @@ void InferRootBound(const Stage& stage,
   for (int i = 0; i < stage->op->num_outputs(); ++i) {
     Tensor t = stage->op.output(i);
     tmap.emplace(t, TensorDom(static_cast<int>(t.ndim())));
-    auto it = feed_graph.find(t);
-    if (it != feed_graph.end()) {
+    auto it = ctx.feed_graph.find(t);
+    if (it != ctx.feed_graph.end()) {
       for (const Operation& op : it->second) {
         if (!parent.defined() || op != parent->op) {
           consumers.insert(op);
@@ -443,7 +289,7 @@ void InferRootBound(const Stage& stage,
     PassUp(parent, *rmap, &up_state);
 
     std::unordered_map<const Variable*, IntSet> dom_map;
-    for (auto iv : OutputRelatedIterVars(parent->op)) {
+    for (auto iv : parent->op->root_iter_vars()) {
       Range r;
       if (up_state.count(iv)) {
         r = up_state.at(iv).cover_range(iv->dom);
@@ -457,7 +303,7 @@ void InferRootBound(const Stage& stage,
       }
     }
     // prop from parent.
-    BoundProp(parent->op, dom_map, &tmap);
+    parent->op->PropBoundToInputs(parent->op, dom_map, &tmap);
   }
   // Bound prop by other consumers.
   // To explain the the general logic, consider the example:
@@ -490,13 +336,13 @@ void InferRootBound(const Stage& stage,
     CHECK(found || attach.size() == 0)
         << "Invalid Schedule, cannot find the producer " << stage->op
         << " along the loop nest specified by compute_at of consumer " << op;
-    for (auto iv : OutputRelatedIterVars(op)) {
+    for (auto iv : op->root_iter_vars()) {
       Range r = rmap->at(iv);
       dom_map[iv->var.get()] = EvalSet(r, relax_set);
     }
-    BoundProp(op, dom_map, &tmap);
+    op->PropBoundToInputs(op, dom_map, &tmap);
   }
-  GatherOpBound(stage->op, feed_graph, tmap, rmap);
+  stage->op->GatherBound(stage->op, ctx, tmap, rmap);
 }
 
 Map<IterVar, Range> InferBound(const Schedule& sch) {
@@ -504,13 +350,14 @@ Map<IterVar, Range> InferBound(const Schedule& sch) {
   for (Operation op : sch->outputs) {
     roots.push_back(sch->stage_map[op]->op);
   }
-  FeedGraph feed_graph = CreateFeedGraph(CreateReadGraph(roots));
+  GraphContext ctx;
+  ctx.feed_graph = CreateFeedGraph(CreateReadGraph(roots));
   AttachPath attach_path = CreateAttachPath(sch);
 
   std::unordered_map<IterVar, Range> ret;
   for (size_t i = sch->stages.size(); i != 0; --i) {
     const Stage& stage = sch->stages[i - 1];
-    InferRootBound(stage, feed_graph, attach_path, &ret);
+    InferRootBound(stage, ctx, attach_path, &ret);
     // pass down to get bound of all iter vars.
     PassDown(stage, &ret);
     // setup outer most threads.

src/schedule/graph.cc

@@ -5,6 +5,7 @@
  */
 #include <tvm/ir.h>
 #include <tvm/ir_visitor.h>
+#include <tvm/operation.h>
 #include <unordered_set>
 #include "./graph.h"
 
@@ -69,28 +70,7 @@ ReadGraph CreateReadGraph(const Array<Operation>& roots) {
   while (!stack.empty()) {
     Operation op = stack.back();
     stack.pop_back();
-    Array<Tensor> deps;
-    if (op.as<ComputeOpNode>()) {
-      auto fvisit = [&deps](const NodeRef& n) {
-        auto *call = n.as<ir::Call>();
-        if (call != nullptr && call->func.defined()) {
-          Operation call_op(call->func.node_);
-          deps.push_back(call_op.output(call->value_index));
-        }
-      };
-      ir::PostOrderVisit(op.as<ComputeOpNode>()->body, fvisit);
-    } else if (op.as<ScanOpNode>()) {
-      const ScanOpNode* scan = op.as<ScanOpNode>();
-      for (Tensor t : scan->init) {
-        deps.push_back(t);
-      }
-      for (Tensor t : scan->update) {
-        deps.push_back(t);
-      }
-    } else if (op.as<PlaceholderOpNode>()) {
-    } else {
-      LOG(FATAL) << "unknown Operation" << op->type_key();
-    }
+    Array<Tensor> deps = op->InputTensors();
     rmap.Set(op, deps);
     for (Tensor t : deps) {
       if (t->op.defined() && visited.count(t->op.get()) == 0) {
@@ -137,7 +117,6 @@ FeedGraph CreateFeedGraph(const ReadGraph& g) {
 
 AttachPath CreateAttachPath(Schedule sch) {
   AttachPath ret;
-
   for (Stage stage : sch->stages) {
     if (stage->attach_type == kScanUpdate) {
       const Stage& parent = stage->attach_stage;

src/schedule/graph.h

@@ -8,6 +8,7 @@
 
 #include <tvm/expr.h>
 #include <tvm/schedule.h>
+#include <tvm/operation.h>
 #include <unordered_map>
 #include <unordered_set>
 #include <vector>
@@ -21,11 +22,6 @@ namespace schedule {
 using ReadGraph = Map<Operation, Array<Tensor> >;
 
 /*!
- * \brief The map beteen tensor and operation it feeds to
- */
-using FeedGraph = std::unordered_map<Tensor, std::vector<Operation> >;
-
-/*!
  * \brief AttachPath maps op-> a list of IterVar
  */
 using AttachPath = Map<Operation, Array<IterVar> >;

src/schedule/schedule_dataflow_rewrite.cc

@@ -3,6 +3,7 @@
  * \file schedule_dataflow_rewrite.cc
  */
 #include <tvm/schedule.h>
+#include <tvm/operation.h>
 #include <tvm/ir_mutator.h>
 #include <tvm/ir_pass.h>
 #include <unordered_set>
@@ -19,35 +20,7 @@ size_t FindNodeRef(ArrayNode* array_node, const T& v) {
   return array_node->data.size();
 }
 
-using ir::TensorKey;
-
 // The replacer of cache.
-class TensorReplacer : public ir::IRMutator {
- public:
-  explicit TensorReplacer(const std::unordered_map<TensorKey, Tensor>& vmap)
-      : vmap_(vmap) {}
-  Expr Mutate_(const ir::Call* op, const Expr& e) {
-    if (op->call_type == ir::Call::Halide) {
-      ir::TensorKey key{op->func, op->value_index};
-      auto it = vmap_.find(key);
-      if (it != vmap_.end()) {
-        Expr ret = ir::Call::make(
-            op->type, it->second->op->name, op->args,
-            op->call_type, it->second->op, it->second->value_index);
-        found = true;
-        return IRMutator::Mutate_(ret.as<ir::Call>(), ret);
-      }
-    }
-    return IRMutator::Mutate_(op, e);
-  }
-
-  // whether it is found.
-  bool found{false};
-
- private:
-  const std::unordered_map<TensorKey, Tensor>& vmap_;
-};
-
 class VarReplacer : public ir::IRMutator {
  public:
   explicit VarReplacer(
@@ -66,47 +39,15 @@ class VarReplacer : public ir::IRMutator {
 // Replace data flow appears in all stages given the tensor change.
 // Also update vmap if subsequent dataflow need to be replaced.
 void ReplaceDataFlow(const Array<Stage>& stages,
-                     std::unordered_map<TensorKey, Tensor>* vmap) {
+                     std::unordered_map<Tensor, Tensor>* vmap) {
   for (Stage s : stages) {
-    if (s->op.as<ComputeOpNode>()) {
-      const ComputeOpNode* compute = s->op.as<ComputeOpNode>();
-      TensorReplacer repl(*vmap);
-      Expr body = repl.Mutate(compute->body);
-      if (repl.found) {
-        Operation op = ComputeOpNode::make(
-            compute->name, compute->axis, body);
-        (*vmap)[TensorKey{s->op, 0}] = op.output(0);
-        s->op = op;
-      }
-    } else if (s->op.as<ScanOpNode>()) {
-      const ScanOpNode* scan = s->op.as<ScanOpNode>();
-      std::shared_ptr<ScanOpNode> n =
-          std::make_shared<ScanOpNode>(*scan);
-      // copy on write semantics ganrantees correctness
-      for (size_t i = 0; i < n->init.size(); ++i) {
-        TensorKey key{n->init[i]->op, n->init[i]->value_index};
-        if (vmap->count(key)) {
-          n->init.Set(i, vmap->at(key));
-        }
-      }
-      for (size_t i = 0; i < n->update.size(); ++i) {
-        TensorKey key{n->update[i]->op, n->update[i]->value_index};
-        if (vmap->count(key)) {
-          n->update.Set(i, vmap->at(key));
-        }
-      }
-      if (!n->init.same_as(scan->init) ||
-          !n->update.same_as(scan->update)) {
-        Operation op(n);
+    Operation op = s->op->ReplaceInputs(s->op, *vmap);
+    if (!op.same_as(s->op)) {
       for (int i = 0; i < op->num_outputs(); ++i) {
-          (*vmap)[TensorKey{s->op, i}] = op.output(i);
+        (*vmap)[s->op.output(i)] = op.output(i);
       }
       s->op = op;
     }
-    } else if (s->op.as<PlaceholderOpNode>()) {
-    } else {
-      LOG(FATAL) << "unhandled problem";
-    }
   }
 }
 
@@ -124,25 +65,17 @@ Tensor Schedule::cache_read(const Tensor& tensor,
   Tensor cache = compute(tensor->shape, [&tensor](const Array<Var>& i) {
       return tensor(Array<Expr>(i.begin(), i.end()));
     }, os.str());
-  std::unordered_map<TensorKey, Tensor> vsub;
-  vsub[TensorKey{tensor->op, tensor->value_index}] = cache;
+  std::unordered_map<Tensor, Tensor> vsub;
+  vsub[tensor] = cache;
 
-  std::unordered_map<TensorKey, Tensor> vmap;
+  std::unordered_map<Tensor, Tensor> vmap;
   for (Operation op : readers) {
-    const ComputeOpNode* compute = op.as<ComputeOpNode>();
-    CHECK(compute)
-        << "cache read only take ComputeOp as readers";
     Stage s = operator[](op);
-    compute = s->op.as<ComputeOpNode>();
-
-    TensorReplacer repl(vsub);
-    Expr body = repl.Mutate(compute->body);
-    CHECK(repl.found)
+    Operation repl_op = s->op->ReplaceInputs(s->op, vsub);
+    CHECK(!repl_op.same_as(s->op))
         << "Cannot find " << tensor
-        << " in the body of specified reader " << op;
-    Operation repl_op = ComputeOpNode::make(
-        compute->name, compute->axis, body);
-    vmap[TensorKey{s->op, 0}] = repl_op.output(0);
+        << " in the inputs of " << s->op;
+    vmap[s->op.output(0)] = repl_op.output(0);
     s->op = repl_op;
   }
   ReplaceDataFlow((*this)->stages, &vmap);
@@ -172,7 +105,8 @@ Tensor Schedule::cache_write(const Tensor& tensor,
   std::unordered_map<const Variable*, Expr> vsub;
   for (IterVar iv : compute->axis) {
     args.push_back(iv->var);
-    IterVar new_iv(iv->dom, iv->var->name_hint + ".c");
+    IterVar new_iv = IterVarNode::make(
+        iv->dom, iv->var.copy_with_suffix(".c"), iv->iter_type);
     new_axis.push_back(new_iv);
     vsub[iv->var.get()] = new_iv->var;
   }
@@ -185,8 +119,8 @@ Tensor Schedule::cache_write(const Tensor& tensor,
       compute->name, compute->axis,
       cache_tensor(args));
 
-  std::unordered_map<TensorKey, Tensor> vmap;
-  vmap[TensorKey{orig_stage->op, 0}] = orig_new_op.output(0);
+  std::unordered_map<Tensor, Tensor> vmap;
+  vmap[orig_stage->op.output(0)] = orig_new_op.output(0);
   ReplaceDataFlow((*this)->stages, &vmap);
 
   // mutate orig stage
@@ -227,7 +161,8 @@ void RebaseNonZeroMinLoop(const Schedule& sch) {
       size_t idx = FindNodeRef(leaf_vars, iv);
       if (idx < leaf_vars->data.size()) {
         // insert rebase
-        IterVar rebased(Range(), iv->var->name_hint + ".rb");
+        IterVar rebased = IterVarNode::make(
+            Range(), iv->var.copy_with_suffix(".rb"), iv->iter_type);
         s->relations.push_back(RebaseNode::make(iv, rebased));
         leaf_vars->data[idx] = rebased.node_;
         rebase_map[iv] = rebased;
@@ -286,7 +221,7 @@ void InjectInline(const Schedule& sch) {
       }
     }
   }
-  std::unordered_map<TensorKey, Tensor> repl;
+  std::unordered_map<Tensor, Tensor> repl;
   // rewrite dataflow
   for (size_t i = 0; i < sch->stages.size(); ++i) {
     if (new_body[i].defined() &&
@@ -295,7 +230,7 @@ void InjectInline(const Schedule& sch) {
       CHECK(compute);
       Operation op = ComputeOpNode::make(
           compute->name, compute->axis, new_body[i]);
-      repl[TensorKey{sch->stages[i]->op, 0}] = op.output(0);
+      repl[sch->stages[i]->op.output(0)] = op.output(0);
       Stage s = sch->stages[i];
       s->op = op;
     }

src/schedule/schedule_lang.cc

@@ -3,6 +3,7 @@
  * \file schedule_lang.cc
  */
 #include <tvm/schedule.h>
+#include <tvm/operation.h>
 #include <tvm/ir_mutator.h>
 #include <unordered_set>
 #include "./graph.h"
@@ -35,16 +36,31 @@ size_t FindLeafVar(ArrayNode* all_vars, ArrayNode* leaf_vars, const IterVar& v)
   return 0;
 }
 
-void Split(StageNode* self, IterVar parent,
-           IterVar outer, IterVar inner, Expr factor) {
+void CheckSplit(StageNode* self, IterVar parent, IterVar outer) {
+  // Check if split is valid.
   if (self->attach_type == kScanUpdate) {
     CHECK(!parent.same_as(self->all_iter_vars[0]))
         << "Cannot split on axis[0] of scan update";
   }
+  if (outer.defined()) {
+    CHECK_EQ(outer->iter_type, kThreadIndex)
+        << "outer in split have to be ThreadIndex";
+    CHECK_EQ(parent->iter_type, kDataPar)
+        << "Split by by kThreadIndex requires kDataPar IterVar "
+        << " given " << IterVarType2String(parent->iter_type);
+  } else {
+    CHECK(parent->iter_type == kDataPar ||
+          parent->iter_type == kCommReduce ||
+          parent->iter_type == kOrdered)
+        << "Cannot split on " << IterVarType2String(parent->iter_type);
+  }
+}
+
+void Split(StageNode* self, IterVar parent,
+           IterVar outer, IterVar inner, Expr factor) {
   ArrayNode* all_vars = self->all_iter_vars.CopyOnWrite();
   ArrayNode* leaf_vars = self->leaf_iter_vars.CopyOnWrite();
   size_t pos = FindLeafVar(all_vars, leaf_vars, parent);
-
   self->relations.push_back(SplitNode::make(parent, outer, inner, factor));
   // add vars to all vars
   all_vars->data.push_back(outer.node_);
@@ -66,11 +82,7 @@ TVM_STATIC_IR_FUNCTOR(IRPrinter, vtable)
 
 TVM_STATIC_IR_FUNCTOR(IRPrinter, vtable)
 .set_dispatch<IterVarAttrNode>([](const IterVarAttrNode *op, IRPrinter *p) {
-    switch (op->iter_type) {
-      case kUnrolled: p->stream << "unroll"; break;
-      case kVectorized: p->stream << "vectorize"; break;
-      case kParallel: p->stream << "parallel"; break;
-    }
+    p->stream << IterVarType2String(op->iter_type);
   });
 
 Stage::Stage(Operation op) {
@@ -78,7 +90,16 @@ Stage::Stage(Operation op) {
   n->op = op;
   n->origin_op = op;
   n->all_iter_vars = op->root_iter_vars();
+  // remove opaque var from leaf.
+  Array<IterVar> clean;
+  for (IterVar iv : n->all_iter_vars) {
+    if (iv->iter_type != kOpaque) clean.push_back(iv);
+  }
+  if (clean.size() == n->all_iter_vars.size()) {
     n->leaf_iter_vars = n->all_iter_vars;
+  } else {
+    n->leaf_iter_vars = clean;
+  }
   node_ = n;
 }
 
@@ -122,18 +143,22 @@ Stage& Stage::compute_root() {   // NOLINT(*)
 
 Stage& Stage::split(
     IterVar parent, IterVar* p_outer, IterVar* p_inner, Expr factor) {  // NOLINT(*)
-  // place holder for the splitted results.
-  IterVar outer(Range(), parent->var->name_hint + ".outer");
-  IterVar inner(Range(), parent->var->name_hint + ".inner");
-  *p_outer = outer; *p_inner = inner;
-
+  CheckSplit(operator->(), parent, IterVar());
+  IterVar outer = IterVarNode::make(
+      Range(), parent->var.copy_with_suffix(".outer"), parent->iter_type);
+  IterVar inner = IterVarNode::make(
+      Range(), parent->var.copy_with_suffix(".inner"), parent->iter_type);
+  *p_outer = outer;
+  *p_inner = inner;
   Split(operator->(), parent, outer, inner, factor);
   return *this;
 }
 
 Stage& Stage::split(IterVar parent, IterVar outer, IterVar* p_inner, Expr factor) { // NOLINT(*)
-  // place holder for the splitted results.
-  IterVar inner(Range(), parent->var->name_hint + ".inner");
+  CheckSplit(operator->(), parent, outer);
+  std::string name_inner = parent->var->name_hint + ".inner";
+  IterVar inner = IterVarNode::make(
+      Range(), Var(name_inner, parent->var.type()), parent->iter_type);
   *p_inner = inner;
   Split(operator->(), parent, outer, inner, factor);
 
@@ -144,11 +169,27 @@ Stage& Stage::fuse(IterVar inner, IterVar outer, IterVar* p_target) {  // NOLINT
   StageNode* self = operator->();
   if (self->attach_type == kScanUpdate) {
     CHECK(!inner.same_as(self->all_iter_vars[0]))
-        << "Cannot split on axis[0] of scan update";
+        << "Cannot fuse on axis[0] of scan update";
     CHECK(!outer.same_as(self->all_iter_vars[0]))
-        << "Cannot split on axis[0] of scan update";
+        << "Cannot fuse on axis[0] of scan update";
   }
-  IterVar fused(Range(), outer->var->name_hint + "." + inner->var->name_hint + ".fused");
+  CHECK(outer->iter_type == kDataPar ||
+        outer->iter_type == kCommReduce ||
+        outer->iter_type == kOrdered)
+      << "Cannot fuse " << IterVarType2String(outer->iter_type);
+  CHECK(inner->iter_type == kDataPar ||
+        inner->iter_type == kCommReduce ||
+        inner->iter_type == kOrdered)
+      << "Cannot fuse " << IterVarType2String(outer->iter_type);
+
+  IterVarType iter_type = outer->iter_type;
+  if (inner->iter_type > iter_type) iter_type = inner->iter_type;
+  std::string fused_name =
+      outer->var->name_hint + "." + inner->var->name_hint + ".fused";
+
+  IterVar fused = IterVarNode::make(
+      Range(), Var(fused_name, outer->var.type()), iter_type);
+
   *p_target = fused;
   ArrayNode* all_vars = self->all_iter_vars.CopyOnWrite();
   ArrayNode* leaf_vars = self->leaf_iter_vars.CopyOnWrite();
@@ -169,8 +210,13 @@ Stage& Stage::fuse(IterVar inner, IterVar outer, IterVar* p_target) {  // NOLINT
 
 Stage& Stage::reorder(const Array<IterVar>& order) {  // NOLINT(*)
   StageNode* self = operator->();
-  CHECK(!self->op.as<ScanOpNode>())
-      << "Cannot reorder axis of scan";
+  for (IterVar iv : order) {
+    CHECK(iv->iter_type == kDataPar ||
+          iv->iter_type == kCommReduce ||
+          iv->iter_type == kThreadIndex)
+        << "Cannot reorder IterVar("
+        << IterVarType2String(iv->iter_type) << ")";
+  }
   ArrayNode* all_vars = self->all_iter_vars.CopyOnWrite();
   ArrayNode* leaf_vars = self->leaf_iter_vars.CopyOnWrite();
   std::vector<size_t> pos;
@@ -248,7 +294,7 @@ Stage& Stage::unroll(IterVar var) {   // NOLINT(*)
 }
 
 Stage& Stage::parallel(IterVar var) {   // NOLINT(*)
-  SetAttr(operator->(), var, IterVarAttr(kParallel));
+  SetAttr(operator->(), var, IterVarAttr(kParallelized));
   return *this;
 }
 

src/schedule/schedule_ops.cc

@@ -6,445 +6,25 @@
 #include <tvm/ir_mutator.h>
 #include <tvm/ir_pass.h>
 #include <tvm/ir_visitor.h>
+#include <tvm/operation.h>
 #include <tvm/schedule_pass.h>
 #include <utility>
 #include <unordered_map>
 #include <unordered_set>
-#include "../pass/ir_util.h"
-#include "../arithmetic/compute_expr.h"
 #include "./graph.h"
 
 namespace tvm {
 namespace schedule {
 
-using namespace arith;
 using namespace ir;
 
-// Two private scope marks
-namespace attr {
-constexpr const char* loop_scope = "loop_scope";
-constexpr const char* scan_update_scope = "scan_update_scope";
-constexpr const char* scan_init_scope = "scan_init_scope";
-}  // namespace attr
-
-/*!
- * \brief message passing to find if IterVar is related to reduction.
- * \param s The stage to be used.
- * \param p_state The message passing state
- *     IterVar->flag
- */
-void PassDownFlag(const Stage& s,
-                   std::unordered_map<IterVar, int>* p_state) {
-  auto& state = *p_state;
-  for (IterVarRelation rel : s->relations) {
-    if (rel.as<SplitNode>()) {
-      const SplitNode* s = rel.as<SplitNode>();
-      int flag = state.at(s->parent);
-      state[s->outer] = flag;
-      state[s->inner] = flag;
-    } else if (rel.as<FuseNode>()) {
-      const FuseNode* s = rel.as<FuseNode>();
-      int flag_outer = state.at(s->outer);
-      int flag_inner = state.at(s->inner);
-      state[s->fused] = flag_outer | flag_inner;
-    } else if (rel.as<RebaseNode>()) {
-      const RebaseNode* s = rel.as<RebaseNode>();
-      int flag = state.at(s->parent);
-      state[s->rebased] = flag;
-    } else {
-      LOG(FATAL) << "unknown relation type";
-    }
-  }
-}
-
-/*!
- * \brief message passing to find if boundary checking on IterVar is needed.
- * \param s The stage to be used.
- * \param p_state The message passing state
- *     IterVar->flag
- */
-void PassUpBoundCheck(const Stage& s,
-                      const Map<IterVar, Range>& dom_map,
-                      std::unordered_map<IterVar, bool>* p_state) {
-  auto& state = *p_state;
-  using Halide::Internal::can_prove;
-  for (size_t i = s->relations.size(); i != 0; --i) {
-    IterVarRelation rel = s->relations[i - 1];
-    if (rel.as<SplitNode>()) {
-      const SplitNode* s = rel.as<SplitNode>();
-      bool outer = state.at(s->outer);
-      bool inner = state.at(s->inner);
-      Expr factor = dom_map.at(s->inner)->extent;
-      Expr step = dom_map.at(s->outer)->extent;
-
-      if (outer || inner) {
-        state[s->parent] = true;
-      } else {
-        if (can_prove(dom_map.at(s->parent)->extent == factor * step)) {
-          state[s->parent] = false;
-        } else {
-          state[s->parent] = true;
-        }
-      }
-    } else if (rel.as<FuseNode>()) {
-      const FuseNode* s = rel.as<FuseNode>();
-      bool fused = state.at(s->fused);
-      state[s->outer] = fused;
-      state[s->inner] = fused;
-    } else if (rel.as<RebaseNode>()) {
-      const RebaseNode* s = rel.as<RebaseNode>();
-      state[s->parent] = state.at(s->rebased);
-    } else {
-      LOG(FATAL) << "unknown relation type";
-    }
-  }
-}
-
-/*!
- * \brief use message passing to calculate the assignment of each Var inside the loop body.
- * \param s The schedule to be used.
- * \param dom_map The domain map of each iteration variable's domain
- * \param p_state The message passing state
- *     IterVar->The assignment.
- */
-void PassUpOffset(const Stage& s,
-                  const Map<IterVar, Range>& dom_map,
-                  std::unordered_map<IterVar, Expr>* p_state) {
-  auto& state = *p_state;
-  for (size_t i = s->relations.size(); i != 0; --i) {
-    IterVarRelation rel = s->relations[i - 1];
-    if (rel.as<SplitNode>()) {
-      const SplitNode* s = rel.as<SplitNode>();
-      Expr outer = state.at(s->outer);
-      Expr inner = state.at(s->inner);
-      Expr factor = dom_map.at(s->inner)->extent;
-      Expr parent_min = dom_map.at(s->parent)->min;
-      state[s->parent] = inner + outer * factor;
-      // add min if they exist
-      if (!is_zero(parent_min)) {
-        state[s->parent] = state[s->parent] + parent_min;
-      }
-    } else if (rel.as<FuseNode>()) {
-      const FuseNode* s = rel.as<FuseNode>();
-      Expr value = state.at(s->fused);
-      Expr factor = dom_map.at(s->inner)->extent;
-      Expr outer_min = dom_map.at(s->outer)->min;
-      Expr inner_min = dom_map.at(s->inner)->min;
-      state[s->outer] = value / factor;
-      state[s->inner] = value % factor;
-      // add min if they exist
-      if (!is_zero(outer_min)) {
-        state[s->outer] = state[s->outer] + outer_min;
-      }
-      if (!is_zero(inner_min)) {
-        state[s->inner] = state[s->inner] + inner_min;
-      }
-    } else if (rel.as<RebaseNode>()) {
-      const RebaseNode* s = rel.as<RebaseNode>();
-      Expr value = state.at(s->rebased);
-      Expr parent_min = dom_map.at(s->parent)->min;
-      // add min if they exist
-      if (!is_zero(parent_min)) {
-        state[s->parent] = value + parent_min;
-      } else {
-        state[s->parent] = value;
-      }
-    } else {
-      LOG(FATAL) << "unknown relation type";
-    }
-  }
-}
-
-std::vector<std::vector<Stmt> >
-MakeLoopNest(const Stage& sch,
-             const Map<IterVar, Range>& dom_map,
-             size_t begin_loop,
-             bool reduce_init_loop,
-             const std::unordered_map<IterVar, bool>& bound_state,
-             const std::unordered_map<IterVar, bool>& skip_iter,
-             std::unordered_map<IterVar, Expr>* p_value_map) {
-  auto leaf_iter_vars = sch->leaf_iter_vars;
-  Stmt no_op = Evaluate::make(0);
-  // create the loop nest
-  std::vector<std::vector<Stmt> > nest;
-  nest.resize(leaf_iter_vars.size() + 1);
-  std::unordered_map<IterVar, Expr>& value_map = *p_value_map;
-
-  for (size_t i = begin_loop; i < leaf_iter_vars.size(); ++i) {
-    auto iv = leaf_iter_vars[i];
-    if (skip_iter.count(iv) && skip_iter.at(iv)) {
-      // skip this iteration.
-      value_map[iv] = iv->var;
-      continue;
-    }
-    Range dom = dom_map.at(iv);
-    // initialize the offset and loop_level
-    Var var = iv->var;
-    if (reduce_init_loop) {
-      var = Var(iv->var->name_hint + ".init", iv->var.type());
-    }
-    // Mark the iter var in the IR, to remember the point
-    if (iv->thread_tag.length() == 0) {
-      ForType for_type = ForType::Serial;
-      if (sch->iter_var_attrs.count(iv)) {
-        switch (sch->iter_var_attrs[iv]->iter_type) {
-          case kUnrolled: for_type = ForType::Unrolled; break;
-          case kParallel: for_type = ForType::Parallel; break;
-          case kVectorized: for_type = ForType::Vectorized; break;
-        }
-      }
-      if (is_one(dom->extent)) {
-        nest[i + 1].emplace_back(
-            LetStmt::make(var, dom->min, no_op));
-        value_map[iv] = dom->min;
-      } else if (is_zero(dom->min)) {
-        nest[i + 1].emplace_back(
-            For::make(var, 0, dom->extent,
-                      for_type, DeviceAPI::None, no_op));
-        value_map[iv] = var;
-      } else {
-        Var idx(iv->var->name_hint + ".idx", iv->var.type());
-        nest[i + 1].emplace_back(
-            For::make(idx, 0, dom->extent,
-                      for_type, DeviceAPI::None, no_op));
-        Expr new_value = dom->min + idx;
-        value_map[iv] = new_value;
-        nest[i + 1].emplace_back(
-            LetStmt::make(var, new_value, no_op));
-      }
-    } else if (iv->thread_tag == "vthread") {
-      // virtual thread
-      // Always restrict threaded IterVar to starts from 0.
-      CHECK(is_zero(dom->min));
-      CHECK(is_positive_const(dom->extent));
-      // annotate the extent of the IterVar
-      nest[i + 1].emplace_back(
-          AttrStmt::make(iv, ir::attr::virtual_thread, dom->extent, no_op));
-      value_map[iv] = var;
-    } else {
-      // Always restrict threaded IterVar to starts from 0.
-      CHECK(is_zero(dom->min));
-      // annotate the extent of the IterVar
-      nest[i + 1].emplace_back(
-          AttrStmt::make(iv, ir::attr::thread_extent, dom->extent, no_op));
-      value_map[iv] = var;
-    }
-    if (!reduce_init_loop) {
-      // annotate the extent of the IterVar
-      nest[i + 1].emplace_back(
-          AttrStmt::make(iv, attr::loop_scope, iv->var, no_op));
-    }
-  }
-  // message passing to get offset of root iter vars.
-  PassUpOffset(sch, dom_map, &value_map);
-
-  // insert conditions
-  for (IterVar iv : sch->op->root_iter_vars()) {
-    if (skip_iter.count(iv)) continue;
-    Range dom = dom_map.at(iv);
-    if (bound_state.at(iv)) {
-      Expr condition = ComputeExpr<Sub>(value_map.at(iv), dom->min) < dom->extent;
-      nest.back().emplace_back(IfThenElse::make(condition, no_op));
-    }
-    CHECK(iv->dom.defined());
-    if (!reduce_init_loop && !iv->dom.same_as(dom)) {
-      Expr condition = ComputeExpr<Sub>(value_map.at(iv), iv->dom->min) < iv->dom->extent;
-      nest.back().emplace_back(IfThenElse::make(condition, no_op));
-    }
-  }
-  return nest;
-}
-
-Stmt Substitute(Stmt s,
-                const std::unordered_map<IterVar, Expr>& value_map) {
-  Map<Var, Expr> temp;
-  for (const auto& kv : value_map) {
-    temp.Set(kv.first->var, kv.second);
-  }
-  return ir::Substitute(s, temp);
-}
-
-Stmt MakeLoop(const Stage& s,
-              const Map<IterVar, Range>& dom_map,
-              Stmt provide,
-              Stmt init) {
-  std::unordered_map<IterVar, Expr> value_map;
-  // bound check state.
-  std::unordered_map<IterVar, bool> bound_state;
-  for (IterVar iv : s->leaf_iter_vars) {
-    bound_state[iv] = false;
-  }
-  PassUpBoundCheck(s, dom_map, &bound_state);
-  auto nest = MakeLoopNest(
-      s, dom_map, 0, false,
-      bound_state, {{}}, &value_map);
-
-  provide = Substitute(provide, value_map);
-  if (init.defined()) {
-    // try to find the location to insert the initialization.
-    // Fuse the initialization and provide loop when possible.
-    std::unordered_map<IterVar, int> update_state;
-    const ComputeOpNode* compute = s->op.as<ComputeOpNode>();
-    const ScanOpNode* scan = s->op.as<ScanOpNode>();
-    if (compute) {
-      for (IterVar iv : compute->reduce_axis) {
-        update_state[iv] = 2;
-      }
-      for (IterVar iv : compute->axis) {
-        update_state[iv] = 1;
-      }
-    } else if (scan) {
-      update_state[scan->scan_axis] = 2;
-      for (IterVar iv : s->outermost_threads) {
-        update_state[iv] = 1;
-      }
-    }
-    // find which iter var is related to reduction and which is related to axis.
-    PassDownFlag(s, &update_state);
-    auto leaf_iter_vars = s->leaf_iter_vars;
-    std::unordered_map<IterVar, Expr> init_value_map;
-    // first first loop that is related to reduction.
-    size_t begin_loop = leaf_iter_vars.size();
-    for (size_t i = 0; i < leaf_iter_vars.size(); ++i) {
-      auto iv = leaf_iter_vars[i];
-      int flag = update_state.at(iv);
-      if ((flag & 2) != 0) {
-        begin_loop = i; break;
-      }
-      init_value_map[iv] = value_map.at(iv);
-    }
-    // skip loops that does not relates to axis.
-    std::unordered_map<IterVar, bool> skip_iter;
-    for (auto kv : update_state) {
-      int flag = kv.second;
-      if ((flag & 1) == 0) skip_iter[kv.first] = true;
-    }
-    auto init_nest = MakeLoopNest(
-        s, dom_map, begin_loop, true,
-        bound_state, skip_iter, &init_value_map);
-    init = Substitute(init, init_value_map);
-    init  = MergeNest(init_nest, init);
-    // common nest
-    std::vector<std::vector<Stmt> > common(nest.begin(), nest.begin() + begin_loop + 1);
-    std::vector<std::vector<Stmt> > reduce(nest.begin() + begin_loop + 1, nest.end());
-    provide = MergeNest(reduce, provide);
-    return MergeNest(
-        common, Block::make(init, provide));
-  } else {
-    return MergeNest(nest, provide);
-  }
-}
-
-Stmt MakeProvide(const ComputeOpNode* op,
-                 const std::vector<Tensor>& tensors) {
-  Tensor t = tensors[0];
-  Array<Expr> args;
-  for (IterVar iv : op->axis) {
-    args.push_back(iv->var);
-  }
-  return Provide::make(t->op, t->value_index, op->body, args);
-}
-
-Stmt MakeRealize(const ComputeOpNode* op,
-                 const Map<IterVar, Range>& dom_map,
-                 const std::vector<Tensor>& tensors,
-                 Stmt body) {
-  Tensor t = tensors[0];
-  Halide::Internal::Region bounds;
-  for (IterVar iv : op->axis) {
-    bounds.push_back(dom_map.at(iv));
-  }
-  return Realize::make(t->op, t->value_index, t->dtype,
-                       bounds, make_const(Bool(1), true), body);
-}
-
-Stmt MakeRealize(const ScanOpNode* op,
-                 const Map<IterVar, Range>& dom_map,
-                 const std::vector<Tensor>& tensors,
-                 Stmt body) {
-  Range sdom = dom_map.at(op->scan_axis);
-  Range tdom = Range::make_with_min_extent(
-      0, ir::Simplify(sdom->extent + sdom->min));
-  size_t sp_idx = 0;
-  for (size_t i = 0; i < tensors.size(); ++i) {
-    const Tensor& t = tensors[i];
-    CHECK_EQ(static_cast<size_t>(t->value_index), i);
-    Halide::Internal::Region bounds;
-    bounds.push_back(tdom);
-    for (size_t k = 1; k < op->update[i]->shape.size(); ++k, ++sp_idx) {
-      IterVar sp_ax = op->spatial_axis_[sp_idx];
-      bounds.push_back(dom_map.at(sp_ax));
-    }
-    body = Realize::make(t->op, t->value_index, t->dtype,
-                         bounds, make_const(Bool(1), true), body);
-  }
-  return body;
-}
-
-
-void MakeReduction(const ComputeOpNode* op,
-                   const std::vector<Tensor>& tensors,
-                   Stmt* init,
-                   Stmt* provide) {
-  Stmt no_op = Evaluate::make(0);
-  Tensor t = tensors[0];
-  std::vector<Stmt> nest;
-  Array<Expr>  args;
-  for (IterVar iv : op->axis) {
-    args.push_back(iv->var);
-  }
-  const Reduce* reduce = op->body.as<Reduce>();
-  CHECK(reduce);
-  Expr init_value, update_value;
-  if (reduce->op == "Add") {
-    init_value = make_zero(reduce->type);
-    update_value = Add::make(t(args), reduce->source);
-  } else if (reduce->op == "Max") {
-    init_value = reduce->type.min();
-    update_value = Max::make(t(args), reduce->source);
-  } else if (reduce->op == "Min") {
-    init_value = reduce->type.max();
-    update_value = Min::make(t(args), reduce->source);
-  } else {
-    LOG(FATAL) << "Unsupported reduction " << reduce->op;
-  }
-  *init = Provide::make(t->op, t->value_index, init_value, args);
-  *provide = Provide::make(t->op, t->value_index, update_value, args);
-}
-
 Stmt MakePipeline(const Stage& s,
-                  const Map<IterVar, Range>& dom_map,
+                  const std::unordered_map<IterVar, Range>& dom_map,
                   Stmt consumer) {
-  std::vector<Tensor> tensors;
-  for (int i = 0; i < s->op->num_outputs(); ++i) {
-    tensors.emplace_back(s->op.output(i));
-  }
-
-  Stmt init, provide;
-
-  const ComputeOpNode* compute = s->op.as<ComputeOpNode>();
-  const ScanOpNode* scan = s->op.as<ScanOpNode>();
-  if (compute) {
-    if (compute->reduce_axis.size() == 0) {
-      provide = MakeProvide(compute, tensors);
-    } else {
-      MakeReduction(compute, tensors, &init, &provide);
-    }
-  } else if (scan) {
-    // Provide is done by the sub operations.
-    provide = AttrStmt::make(
-        s->op, attr::scan_update_scope, scan->scan_axis->var,
-        Evaluate::make(0));
-    init = AttrStmt::make(
-        s->op, attr::scan_init_scope, 0,
-        Evaluate::make(0));
-  } else {
-    LOG(FATAL) << "not supported op " << s->op->type_key();
-  }
-
-  Stmt producer = MakeLoop(s, dom_map, provide, init);
+  Stmt producer = s->op->BuildProvide(s, dom_map);
+  if (producer.defined()) {
     producer = ProducerConsumer::make(s->op, true, producer);
-
+  }
   Stmt pipeline = producer;
   // check if consumer is nop.
   bool is_no_op{false};
@@ -455,16 +35,7 @@ Stmt MakePipeline(const Stage& s,
     consumer = ProducerConsumer::make(s->op, false, consumer);
     pipeline = Block::make(producer, consumer);
   }
-
-  if (s->op.as<ComputeOpNode>()) {
-    pipeline = MakeRealize(s->op.as<ComputeOpNode>(),
-                           dom_map, tensors, pipeline);
-  } else if (s->op.as<ScanOpNode>()) {
-    pipeline = MakeRealize(s->op.as<ScanOpNode>(),
-                           dom_map, tensors, pipeline);
-  } else {
-    LOG(FATAL) << "not supported op";
-  }
+  pipeline = s->op->BuildRealize(s->op, dom_map, pipeline);
   // use attribute to mark scope of the operation.
   pipeline = AttrStmt::make(
       s->op, ir::attr::realize_scope,
@@ -477,7 +48,7 @@ Stmt MakePipeline(const Stage& s,
 class InjectAttach : public IRMutator {
  public:
   InjectAttach(const Stage& stage,
-                const Map<IterVar, Range>& dom_map)
+               const std::unordered_map<IterVar, Range>& dom_map)
       : stage_(stage), dom_map_(dom_map) {}
 
   Stmt Mutate(Stmt stmt) final {
@@ -515,7 +86,7 @@ class InjectAttach : public IRMutator {
   // the operations to be carried
   const Stage& stage_;
   // domain map
-  const Map<IterVar, Range>& dom_map_;
+  const std::unordered_map<IterVar, Range>& dom_map_;
   // internal stack about realization scope.
   std::vector<const Node*> producer_;
 };
@@ -525,7 +96,7 @@ class InjectScanStep : public IRMutator {
  public:
   InjectScanStep(const Stage& stage,
                  const Operation& scan_op,
-                 const Map<IterVar, Range>& dom_map,
+                 const std::unordered_map<IterVar, Range>& dom_map,
                  bool is_init)
       : stage_(stage), scan_op_(scan_op),
         dom_map_(dom_map), is_init_(is_init) {}
@@ -556,23 +127,11 @@ class InjectScanStep : public IRMutator {
   const Stage& stage_;
   const Operation& scan_op_;
   // domain map
-  const Map<IterVar, Range>& dom_map_;
+  const std::unordered_map<IterVar, Range>& dom_map_;
   // whether it is init.
   bool is_init_;
 };
 
-Stmt InjectInline(const Operation op, Stmt body) {
-  CHECK(body.defined());
-
-  const ComputeOpNode* compute = op.as<ComputeOpNode>();
-  CHECK(compute != nullptr)
-      << "can only inline compute op";
-  Array<Var> args;
-  for (auto iv : compute->axis) {
-    args.push_back(iv->var);
-  }
-  return Inline(body, op, args, compute->body);
-}
 
 // Postprocessing of schedule op
 // Replace the init and update's expression by scan's buffer.
@@ -719,7 +278,7 @@ class SchedulePostProc : public IRMutator {
 };
 
 Stmt ScheduleOps(
-    Schedule sch, Map<IterVar, Range> dom_map) {
+    Schedule sch, Map<IterVar, Range> dom_map_) {
   Stmt body = Stmt();
   // scan init and scan updates
   std::unordered_map<Operation, std::pair<Operation, bool> > scan_attach;
@@ -743,6 +302,10 @@ Stmt ScheduleOps(
       }
     }
   }
+  std::unordered_map<IterVar, Range> dom_map;
+  for (auto kv : dom_map_) {
+    dom_map[kv.first] = kv.second;
+  }
 
   // reverse the post DFS order.
   for (size_t i = sch->stages.size(); i != 0; --i) {

tests/cpp/tensor_test.cc

@@ -22,7 +22,7 @@ TEST(Tensor, Reduce) {
   Var m("m"), n("n"), l("l");
   Tensor A = placeholder({m, l}, Float(32), "A");
   Tensor B = placeholder({n, l}, Float(32), "B");
-  IterVar rv(Range{0, l}, "k");
+  IterVar rv = reduce_axis(Range{0, l}, "k");
 
   auto C = compute({m, n}, [&](Var i, Var j) {
       return sum(max(1 + A[i][rv] + 1, B[j][rv]), {rv});

tests/python/integration/test_dot.py

@@ -29,7 +29,7 @@ def test_dot():
     n = tvm.Var('n')
     A = tvm.placeholder((n,), name='A')
     B = tvm.placeholder((n,), name='B')
-    k = tvm.IterVar((0, n), name='k')
+    k = tvm.reduce_axis((0, n), 'k')
     C = tvm.compute((1,), lambda _: tvm.sum(A[k] * B[k], axis=k), name='C')
     s = tvm.Schedule(C.op)
     fapi = lower(s, [A, B, C])

tests/python/integration/test_ewise.py

@@ -11,8 +11,8 @@ def test_add():
     s = tvm.Schedule(C.op)
     # create iter var and assign them tags.
     num_thread = 256
-    block_x = tvm.IterVar(thread_tag="blockIdx.x")
-    thread_x = tvm.IterVar((0, num_thread), thread_tag="threadIdx.x")
+    block_x = tvm.thread_axis(None, "blockIdx.x")
+    thread_x = tvm.thread_axis((0, num_thread), "threadIdx.x")
     _, x = s[C].split(C.op.axis[0], factor=num_thread*4, outer=block_x)
     _, x = s[C].split(x, outer=thread_x)
     _, x = s[C].split(x, factor=4)

tests/python/integration/test_gemm.py

@@ -11,7 +11,7 @@ def test_gemm():
     l = n
     A = tvm.placeholder((n, l), name='A')
     B = tvm.placeholder((m, l), name='B')
-    k = tvm.IterVar((0, l), name='k')
+    k = tvm.reduce_axis((0, l), name='k')
     C = tvm.compute(
         (n, m),
         lambda ii, jj: tvm.sum(A[ii, k] * B[jj, k], axis=k),
@@ -22,10 +22,10 @@ def test_gemm():
     scale = 8
     num_thread = 8
     block_factor = scale * num_thread
-    block_x = tvm.IterVar(thread_tag="blockIdx.x")
-    thread_x = tvm.IterVar((0, num_thread), thread_tag="threadIdx.x")
-    block_y = tvm.IterVar(thread_tag="blockIdx.y")
-    thread_y = tvm.IterVar((0, num_thread), thread_tag="threadIdx.y")
+    block_x = tvm.thread_axis(None, "blockIdx.x")
+    thread_x = tvm.thread_axis((0, num_thread), "threadIdx.x")
+    block_y = tvm.thread_axis(None, "blockIdx.y")
+    thread_y = tvm.thread_axis((0, num_thread), "threadIdx.y")
 
     CC = s.cache_write(C, "local")
     AA = s.cache_read(A, "shared", [CC])

tests/python/integration/test_reduce.py

@@ -6,14 +6,14 @@ def test_sum():
     n = tvm.Var('n')
     m = tvm.Var('m')
     A = tvm.placeholder((n, m), name='A')
-    k = tvm.IterVar((0, m))
+    k = tvm.reduce_axis((0, m))
     B = tvm.compute((n,), lambda i: tvm.sum(A[i, k], axis=k), name='B')
     # schedule
     s = tvm.Schedule(B.op)
     # create iter var and assign them tags.
     num_thread = 1
-    block_x = tvm.IterVar(thread_tag="blockIdx.x")
-    thread_x = tvm.IterVar((0, num_thread), thread_tag="threadIdx.x")
+    block_x = tvm.thread_axis(None, "blockIdx.x")
+    thread_x = tvm.thread_axis((0, num_thread), "threadIdx.x")
     _, x = s[B].split(B.op.axis[0], factor=num_thread, outer=block_x)
     _, x = s[B].split(x, outer=thread_x)
 

tests/python/integration/test_scan.py

@@ -4,7 +4,6 @@ import numpy as np
 def test_scan():
     m = tvm.Var("m")
     n = tvm.Var("n")
-    t = tvm.IterVar((1, m), name="t")
     X = tvm.placeholder((m, n), name="X")
     s_state = tvm.placeholder((m, n))
     s_init = tvm.compute((1, n), lambda _, i: X[0, i])
@@ -14,8 +13,8 @@ def test_scan():
     # schedule
     s = tvm.Schedule(res.op)
     num_thread = 256
-    block_x = tvm.IterVar(thread_tag="blockIdx.x")
-    thread_x = tvm.IterVar((0, num_thread), thread_tag="threadIdx.x")
+    block_x = tvm.thread_axis(None, "blockIdx.x")
+    thread_x = tvm.thread_axis((0, num_thread), "threadIdx.x")
     _, x = s[s_init].split(s_init.op.axis[1], factor=num_thread, outer=block_x)
     _, x = s[s_init].split(x, outer=thread_x)
     _, x = s[s_update].split(s_update.op.axis[1], factor=num_thread, outer=block_x)

tests/python/unittest/test_codegen_device.py

@@ -11,8 +11,8 @@ def test_add_pipeline():
 
     # GPU schedule have to split by gridIdx and threadIdx
     num_thread = 256
-    grid_x = tvm.IterVar(thread_tag="blockIdx.x")
-    thread_x = tvm.IterVar((0, num_thread), thread_tag="threadIdx.x")
+    grid_x = tvm.thread_axis(None, "blockIdx.x")
+    thread_x = tvm.thread_axis((0, num_thread), "threadIdx.x")
     _, x = s[C].split(C.op.axis[0], factor=num_thread, outer=grid_x)
     _, x = s[C].split(x, outer=thread_x)
 

tests/python/unittest/test_codegen_llvm.py

@@ -8,7 +8,10 @@ def test_llvm_add_pipeline():
     B = tvm.placeholder((n,), name='B')
     C = tvm.compute(A.shape, lambda *i: A(*i) + B(*i), name='C')
     s = tvm.Schedule(C.op)
+    print(s[C])
+    print("a?")
     xo, xi = s[C].split(C.op.axis[0], factor=4)
+    print("a?")
     s[C].parallel(xo)
     s[C].vectorize(xi)
     def check_llvm():
@@ -83,6 +86,9 @@ def test_llvm_madd_pipeline():
 
 
 if __name__ == "__main__":
+    print("a")
     test_llvm_add_pipeline()
+    print("a")
     test_llvm_flip_pipeline()
+    print("a")
     test_llvm_madd_pipeline()

tests/python/unittest/test_lang_schedule.py

@@ -86,8 +86,8 @@ def test_vectorize():
     xo, yo, xi, yi = s[T].tile(T.op.axis[0], T.op.axis[1], x_factor=10, y_factor=5)
     s[T].vectorize(yi)
     s[T].unroll(xi)
-    UNROLL = 1
-    VECTORIZE = 2
+    UNROLL = tvm.collections.IterVar.Unrolled
+    VECTORIZE = tvm.collections.IterVar.Vectorized
     assert s[T].iter_var_attrs[xi].iter_type == UNROLL
     assert s[T].iter_var_attrs[yi].iter_type == VECTORIZE
 

tests/python/unittest/test_lang_tensor.py

@@ -25,7 +25,7 @@ def test_tensor_reduce():
     A = tvm.placeholder((m, l), name='A')
     B = tvm.placeholder((n, l), name='B')
     T = tvm.compute((m, n, l), lambda i, j, k: A[i, k] * B[j, k])
-    rv = tvm.IterVar((0, A.shape[1]), name="k")
+    rv = tvm.reduce_axis((0, A.shape[1]), "k")
     C = tvm.compute((m, n), lambda i, j: tvm.sum(T(i, j, rv+1), axis=rv))
     # json load save
     C_json = tvm.save_json(C)
@@ -37,7 +37,6 @@ def test_tensor_reduce():
 def test_tensor_scan():
     m = tvm.Var("m")
     n = tvm.Var("n")
-    t = tvm.IterVar((1, m), "t")
     x = tvm.placeholder((m, n))
     s = tvm.placeholder((m, n))
     res = tvm.scan(tvm.compute((1, n), lambda _, i: x[0, i]),

tests/python/unittest/test_pass_storage_sync.py

@@ -9,7 +9,7 @@ def test_storage_sync():
     A2 = tvm.compute((m, l), lambda i, j: A1[i, j] + 3, name='A2')
 
     s = tvm.Schedule(A2.op)
-    block_x = tvm.IterVar(thread_tag="blockIdx.x")
+    block_x = tvm.thread_axis(None, "blockIdx.x")
     xo, xi = s[A2].split(A2.op.axis[0], factor=8, outer=block_x)
     s[A1].compute_at(s[A2], xo)
     s[A1].set_scope("shared")

tests/python/unittest/test_pass_virtual_thread.py

@@ -7,8 +7,7 @@ def test_virtual_thread():
     A2 = tvm.compute((m,), lambda i: A1[i] + 3, name='A2')
 
     s = tvm.Schedule(A2.op)
-
-    vx = tvm.IterVar((0, 2), "vx", thread_tag="vthread")
+    vx = tvm.thread_axis((0, 2), "vthread", name="vx")
     xo, xi = s[A2].split(A2.op.axis[0], outer=vx)
     xo, xi = s[A2].split(xi, 8)
     s[A1].compute_at(s[A2], xo)

tests/python/unittest/test_schedule_bound_inference.py

@@ -38,7 +38,7 @@ def test_bound3():
     s = tvm.Schedule(A2.op)
 
     s[A1].set_scope("shared")
-    thread_x = tvm.IterVar((0, 16), thread_tag="threadIdx.x")
+    thread_x = tvm.thread_axis((0, 16), "threadIdx.x")
     xo, xi = s[A2].split(A2.op.axis[0], 32)
     xi0, xi1 = s[A2].split(xi, outer=thread_x)
     yo, yi = s[A2].split(A2.op.axis[1], 16)