[ARITH] DeduceBound (#40)

* [PYTHON/API] Add compare and logic build-in op for Expr

* remove 'and', 'or'

* add deducer

* [WIP] bound_deducer.cc

* move IntervalSet and StrideSet into int_set_internal.h

* add multiple failure for VariablePathFinder, add EvalSign

* consider round in deduce, add success flag

* remove Visit_(Div)

* add comment, update HalideIR

* expose intset to python

* check the sign of every expr

* set return type as ExprSignType

* fine tune

* add min & max python api for interval set

* support for conditional expr

* refactor test

* add checker for BoundDeducer

* add python check test

* fix

* fix

* change range to interval; remove converter

* remove converter declaration

* remove int_set_internal.h

python/tvm/__init__.py

@@ -4,6 +4,7 @@
 from ._ctypes._node import register_node
 
 from . import tensor
+from . import arith
 from . import expr
 from . import stmt
 from . import make

python/tvm/_ctypes/_function.py

@@ -244,6 +244,7 @@ def _init_api_functions(root_namespace):
     module_internal = sys.modules["%s._api_internal" % root_namespace]
     namespace_match = {
         "_make_": sys.modules["%s.make" % root_namespace],
+        "_arith_": sys.modules["%s.arith" % root_namespace],
         "_pass_": sys.modules["%s.ir_pass" % root_namespace],
         "_codegen_": sys.modules["%s.codegen" % root_namespace],
         "_schedule_": sys.modules["%s.schedule" % root_namespace]

python/tvm/arith.py

@@ -0,0 +1,33 @@
+# pylint: disable=protected-access, no-member
+"""Arithmetic data structure and utility"""
+from __future__ import absolute_import as _abs
+from ._ctypes._node import NodeBase, register_node
+from . import _api_internal
+
+@register_node
+class IntSet(NodeBase):
+    """Represent a set of integer in one dimension."""
+    def is_nothing(self):
+        """Whether the set represent nothing"""
+        return _api_internal._IntSetIsNothing(self)
+
+    def is_everything(self):
+        """Whether the set represent everything"""
+        return _api_internal._IntSetIsEverything(self)
+
+@register_node
+class IntervalSet(IntSet):
+    """Represent set of continuous interval"""
+    def min(self):
+        """get the minimum value"""
+        return _api_internal._IntervalSetGetMin(self)
+
+    def max(self):
+        """get the maximum value"""
+        return _api_internal._IntervalSetGetMax(self)
+
+@register_node
+class StrideSet(IntSet):
+    """Represent set of strided integers"""
+    pass
+

src/api/api_arith.cc

@@ -0,0 +1,50 @@
+/*!
+ *  Copyright (c) 2016 by Contributors
+ *  Implementation of API functions related to arith
+ * \file api_arith.cc
+ */
+#include <tvm/expr.h>
+#include <tvm/ir.h>
+#include <tvm/api_registry.h>
+#include "../arithmetic/int_set.h"
+
+namespace tvm {
+namespace arith {
+
+TVM_REGISTER_API(_arith_intset_single_point)
+.set_body([](TVMArgs args, TVMRetValue *ret) {
+    *ret = IntSet::single_point(args[0]);
+  });
+
+TVM_REGISTER_API(_arith_intset_interval)
+.set_body([](TVMArgs args, TVMRetValue *ret) {
+    *ret = IntSet::interval(args[0], args[1]);
+  });
+
+TVM_REGISTER_API(_arith_DeduceBound)
+.set_body([](TVMArgs args, TVMRetValue *ret) {
+    *ret = DeduceBound(args[0], args[1], args[2]);
+  });
+
+TVM_REGISTER_API(_IntervalSetGetMin)
+.set_body([](TVMArgs args, TVMRetValue *ret) {
+    *ret = args[0].operator IntSet().min();
+  });
+
+TVM_REGISTER_API(_IntervalSetGetMax)
+.set_body([](TVMArgs args, TVMRetValue *ret) {
+    *ret = args[0].operator IntSet().max();
+  });
+
+TVM_REGISTER_API(_IntSetIsNothing)
+.set_body([](TVMArgs args, TVMRetValue *ret) {
+    *ret = args[0].operator IntSet().is_nothing();
+  });
+
+TVM_REGISTER_API(_IntSetIsEverything)
+.set_body([](TVMArgs args, TVMRetValue *ret) {
+    *ret = args[0].operator IntSet().is_everything();
+  });
+
+}  // namespace arith
+}  // namespace tvm

src/arithmetic/bound_deducer.cc

@@ -0,0 +1,229 @@
+/*!
+ *  Copyright (c) 2017 by Contributors
+ * \file bound_deducer.cc
+ * \brief Utility to deduce bound of expression
+ */
+#include <tvm/expr.h>
+#include <tvm/ir_pass.h>
+#include <tvm/ir_visitor.h>
+#include <tvm/api_registry.h>
+#include <unordered_set>
+#include <unordered_map>
+#include "./int_set.h"
+
+namespace tvm {
+namespace arith {
+
+using namespace ir;
+using Halide::Internal::Interval;
+
+// a visitor to find the path to the target variable
+// from a expression.
+class VariablePathFinder: public IRVisitor {
+ public:
+  explicit VariablePathFinder(Var target) : target_(target) {}
+
+  void Visit(const NodeRef& node) final {
+    if (visited_.count(node.get()) != 0) return;
+    visited_.insert(node.get());
+
+    if (!found_) path_.push_back(node.get());
+    if (node.same_as(target_)) found_ = true;
+    IRVisitor::Visit(node);
+    if (!found_) path_.pop_back();
+  }
+
+  std::vector<const Node*> path_;
+
+ private:
+  bool found_{false};
+  Var target_;
+  std::unordered_set<const Node*> visited_;
+};
+
+// get the path to the variable,
+// return empty vector to represent failure
+std::vector<const Node*> GetPath(Var target, Expr expr) {
+  VariablePathFinder v(target);
+  v.Visit(expr);
+  return v.path_;
+}
+
+class BoundDeduceIntputChecker;
+
+// a visitor to deduce the bound of a variable from a expression
+class BoundDeducer: public IRVisitor {
+ public:
+  friend class BoundDeduceInputChecker;
+  friend class Converter;
+  BoundDeducer(Var target, Expr expr,
+               const std::unordered_map<const Variable*, IntSet>& dom_map)
+  : target_(target), expr_(expr), dom_map_(dom_map) {}
+
+  bool Init();
+  void Deduce();
+
+  void Visit(const NodeRef& e) final {
+    if (!success) return;
+    if (e.get() == path_[iter_++]) {
+      IRVisitor::Visit(e);
+    } else {
+      success = false;
+      return;
+    }
+  }
+
+  void Visit_(const LT* op) final {
+    LOG(FATAL) << "unable to deduce due to multiple comparison operator";
+  }
+
+  void Visit_(const LE* op) final {
+    LOG(FATAL) << "unable to deduce due to multiple comparison operator";
+  }
+
+  void Visit_(const GT* op) final {
+    LOG(FATAL) << "unable to deduce due to multiple comparison operator";
+  }
+
+  void Visit_(const GE* op) final {
+    LOG(FATAL) << "unable to deduce due to multiple comparison operator";
+  }
+
+  void Visit_(const Add* op) final {
+    bool left = op->a.get() == path_[iter_];
+    result -= left ? op->b : op->a;
+    Visit(left ? op->a : op->b);
+  }
+
+  void Visit_(const Sub* op) final {
+    bool left = op->a.get() == path_[iter_];
+    if (left) {
+      result += op->b;
+    } else {
+      result -= op->a;
+      result = - result;
+      is_greater = !is_greater;
+    }
+    Visit(left ? op->a : op->b);
+  }
+
+  void Visit_(const Mul* op) final {
+    bool left = op->a.get() == path_[iter_];
+    Expr operand = left ? op->b : op->a;
+
+    SignType sign;
+    if (operand.type().is_uint()) {
+      sign = kPositive;
+    } else {
+      sign = expr_map_[operand].sign_type();
+    }
+
+    if (sign == SignType::kNegative) {
+      is_greater = !is_greater;
+    } else if (sign == SignType::kUnknown) {
+      // unable to get the sign of operand
+      success = false;
+      return;
+    }
+
+    // always use relax bound
+    result = result / operand + (is_greater ? 1 : -1);
+    Visit(left ? op->a : op->b);
+  }
+
+  Expr result;
+  bool is_greater{true};
+  bool is_equal{true};
+  bool success{true};
+
+ private:
+  Var  target_;
+  Expr expr_;
+  const std::unordered_map<const Variable*, IntSet>& dom_map_;
+  ExprIntSetMap expr_map_;
+  std::vector<const Node*> path_;
+  size_t iter_{0};
+};
+
+class BoundDeduceInputChecker: public IRVisitor {
+ public:
+  bool Check(BoundDeducer* deducer) {
+    deducer_ = deducer;
+    Visit(deducer_->expr_);
+    return target_count == 1;
+  }
+
+  void Visit(const NodeRef& e) final {
+    if (e.same_as(deducer_->target_)) ++target_count;
+    IRVisitor::Visit(e);
+  }
+
+ private:
+  BoundDeducer* deducer_;
+  size_t target_count{0};
+};
+
+bool BoundDeducer::Init() {
+  BoundDeduceInputChecker checker;
+  if (!checker.Check(this)) success = false;
+
+  if (const LT* op = expr_.as<LT>()) {
+    is_greater = false;
+    is_equal   = false;
+    expr_      = op->a;
+    result     = op->b;
+  } else if (const LE* op = expr_.as<LE>()) {
+    is_greater = false;
+    is_equal   = true;
+    expr_      = op->a;
+    result     = op->b;
+  } else if (const GT* op = expr_.as<GT>()) {
+    is_greater = true;
+    is_equal   = false;
+    expr_      = op->a;
+    result     = op->b;
+  } else if (const GE* op = expr_.as<GE>()) {
+    is_greater = true;
+    is_equal   = true;
+    expr_      = op->a;
+    result     = op->b;
+  } else {
+    success = false;
+  }
+  return success;
+}
+
+void BoundDeducer::Deduce() {
+  Init();
+  if (!success) return;
+
+  // get the path
+  path_ = GetPath(target_, expr_);
+  // get the sign of every subexpr
+  expr_map_ = EvalSetForEachSubExpr(expr_, dom_map_);
+
+  Visit(expr_);
+}
+
+// assuming e >= 0, deduce the bound of variable from it.
+// return empty set to represent deduce failure.
+IntSet DeduceBound(Var v, Expr e,
+                   const Map<Var, IntSet>& dom_map) {
+  std::unordered_map<const Variable*, IntSet> dmap;
+  for (auto kv : dom_map) {
+    dmap[kv.first.get()] = kv.second;
+  }
+  BoundDeducer d(v, e, dmap);
+  d.Deduce();
+  if (!d.success) return IntSet::nothing();
+  Expr min = Interval::neg_inf, max = Interval::pos_inf;
+  if (d.is_greater) {
+    min = d.is_equal ? d.result : d.result + 1;
+  } else {
+    max = d.is_equal ? d.result : d.result - 1;
+  }
+  return IntSet::interval(min, max);
+}
+
+}  // namespace arith
+}  // namespace tvm