[ARITH][IR] Introduce FloorDiv/Mod (#3479)

* [ARITH][IR] Introduce FloorDiv/Mod

* Address review comments

* address review comments, fix div sub rule

include/tvm/expr_operator.h

@@ -332,6 +332,26 @@ TVM_DLL Expr operator||(Expr a, Expr b);
  */
 TVM_DLL Expr operator!(Expr a);
 /*!
+ * \brief compute floor(a / b)
+ *
+ * \param a left operand
+ * \param b right operand
+ * \return The result expression.
+ * \note this function does eager constant folding for
+ *       index types(int32, int64) when possible.
+ */
+TVM_DLL Expr floordiv(Expr a, Expr b);
+/*!
+ * \brief compute the remainder of floordiv
+ *
+ * \param a left operand
+ * \param b right operand
+ * \return The result expression.
+ * \note this function does eager constant folding for
+ *       index types(int32, int64) when possible.
+ */
+TVM_DLL Expr floormod(Expr a, Expr b);
+/*!
  * \brief take maximum of two values
  *
  * \param a left operand

include/tvm/ir.h

@@ -178,6 +178,18 @@ class Mod : public BinaryOpNode<Mod> {
   static constexpr const char* _type_key = "Mod";
 };
 
+/*! \brief Floor division, floor(a/b) */
+class FloorDiv : public BinaryOpNode<FloorDiv> {
+ public:
+  static constexpr const char* _type_key = "FloorDiv";
+};
+
+/*! \brief The remainder of the floordiv */
+class FloorMod : public BinaryOpNode<FloorMod> {
+ public:
+  static constexpr const char* _type_key = "FloorMod";
+};
+
 /*! \brief min(a, b) */
 class Min : public BinaryOpNode<Min> {
  public:

include/tvm/ir_functor_ext.h

@@ -140,6 +140,8 @@ class ExprFunctor<R(const Expr& n, Args...)> {
   virtual R VisitExpr_(const Mul* op, Args... args) EXPR_FUNCTOR_DEFAULT;
   virtual R VisitExpr_(const Div* op, Args... args) EXPR_FUNCTOR_DEFAULT;
   virtual R VisitExpr_(const Mod* op, Args... args) EXPR_FUNCTOR_DEFAULT;
+  virtual R VisitExpr_(const FloorDiv* op, Args... args) EXPR_FUNCTOR_DEFAULT;
+  virtual R VisitExpr_(const FloorMod* op, Args... args) EXPR_FUNCTOR_DEFAULT;
   virtual R VisitExpr_(const Min* op, Args... args) EXPR_FUNCTOR_DEFAULT;
   virtual R VisitExpr_(const Max* op, Args... args) EXPR_FUNCTOR_DEFAULT;
   virtual R VisitExpr_(const EQ* op, Args... args) EXPR_FUNCTOR_DEFAULT;
@@ -180,6 +182,8 @@ class ExprFunctor<R(const Expr& n, Args...)> {
     IR_EXPR_FUNCTOR_DISPATCH(Mul);
     IR_EXPR_FUNCTOR_DISPATCH(Div);
     IR_EXPR_FUNCTOR_DISPATCH(Mod);
+    IR_EXPR_FUNCTOR_DISPATCH(FloorDiv);
+    IR_EXPR_FUNCTOR_DISPATCH(FloorMod);
     IR_EXPR_FUNCTOR_DISPATCH(Min);
     IR_EXPR_FUNCTOR_DISPATCH(Max);
     IR_EXPR_FUNCTOR_DISPATCH(EQ);

include/tvm/ir_mutator.h

@@ -98,6 +98,8 @@ class TVM_DLL IRMutator {
   virtual Expr Mutate_(const Mul* op, const Expr& e);
   virtual Expr Mutate_(const Div* op, const Expr& e);
   virtual Expr Mutate_(const Mod* op, const Expr& e);
+  virtual Expr Mutate_(const FloorDiv* op, const Expr& e);
+  virtual Expr Mutate_(const FloorMod* op, const Expr& e);
   virtual Expr Mutate_(const Min* op, const Expr& e);
   virtual Expr Mutate_(const Max* op, const Expr& e);
   virtual Expr Mutate_(const EQ* op, const Expr& e);

include/tvm/ir_visitor.h

@@ -114,6 +114,8 @@ class TVM_DLL IRVisitor {
   virtual void Visit_(const Mul* op);
   virtual void Visit_(const Div* op);
   virtual void Visit_(const Mod* op);
+  virtual void Visit_(const FloorDiv* op);
+  virtual void Visit_(const FloorMod* op);
   virtual void Visit_(const Min* op);
   virtual void Visit_(const Max* op);
   virtual void Visit_(const EQ* op);

python/tvm/api.py

@@ -888,7 +888,46 @@ def comm_reducer(fcombine, fidentity, name="reduce"):
     return reducer
 
 
+def floordiv(a, b):
+    """Compute the floordiv of two expressions.
+
+    Parameters
+    ----------
+    a : Expr
+        The left hand operand
+
+    b : Expr
+        The right hand operand
+
+    Returns
+    -------
+    res : Expr
+        The result expression.
+    """
+    return _make._OpFloorDiv(a, b)
+
+
+def floormod(a, b):
+    """Compute the floormod of two expressions.
+
+    Parameters
+    ----------
+    a : Expr
+        The left hand operand
+
+    b : Expr
+        The right hand operand
+
+    Returns
+    -------
+    res : Expr
+        The result expression.
+    """
+    return _make._OpFloorMod(a, b)
+
+
 _init_api("tvm.api")
+
 #pylint: disable=unnecessary-lambda
 sum = comm_reducer(lambda x, y: x+y, lambda t: const(0, dtype=t), name="sum")
 min = comm_reducer(lambda x, y: _make._OpMin(x, y), max_value, name='min')

python/tvm/expr.py

@@ -463,6 +463,40 @@ class Mod(BinaryOpExpr):
 
 
 @register_node
+class FloorDiv(BinaryOpExpr):
+    """FloorDiv node.
+
+    Parameters
+    ----------
+    a : Expr
+        The left hand operand.
+
+    b : Expr
+        The right hand operand.
+    """
+    def __init__(self, a, b):
+        self.__init_handle_by_constructor__(
+            _make.FloorDiv, a, b)
+
+
+@register_node
+class FloorMod(BinaryOpExpr):
+    """FloorMod node.
+
+    Parameters
+    ----------
+    a : Expr
+        The left hand operand.
+
+    b : Expr
+        The right hand operand.
+    """
+    def __init__(self, a, b):
+        self.__init_handle_by_constructor__(
+            _make.FloorMod, a, b)
+
+
+@register_node
 class Min(BinaryOpExpr):
     """Min node.
 

src/api/api_ir.cc

@@ -126,6 +126,8 @@ REGISTER_MAKE(Sub);
 REGISTER_MAKE(Mul);
 REGISTER_MAKE(Div);
 REGISTER_MAKE(Mod);
+REGISTER_MAKE(FloorDiv);
+REGISTER_MAKE(FloorMod);
 REGISTER_MAKE(Min);
 REGISTER_MAKE(Max);
 REGISTER_MAKE(EQ);
@@ -192,6 +194,8 @@ REGISTER_MAKE_BINARY_OP(_OpSub, operator-);
 REGISTER_MAKE_BINARY_OP(_OpMul, operator*);
 REGISTER_MAKE_BINARY_OP(_OpDiv, operator/);
 REGISTER_MAKE_BINARY_OP(_OpMod, operator%);
+REGISTER_MAKE_BINARY_OP(_OpFloorDiv, floordiv);
+REGISTER_MAKE_BINARY_OP(_OpFloorMod, floormod);
 REGISTER_MAKE_BINARY_OP(_OpMin, min);
 REGISTER_MAKE_BINARY_OP(_OpMax, max);
 REGISTER_MAKE_BINARY_OP(_OpEQ, operator==);

src/arithmetic/const_fold.h

@@ -29,6 +29,7 @@
 #include <tvm/ir_mutator.h>
 #include <tvm/expr_operator.h>
 #include <algorithm>
+#include "int_operator.h"
 
 namespace tvm {
 namespace arith {
@@ -184,9 +185,7 @@ template<>
 inline Expr TryConstFold<ir::Mod>(Expr a, Expr b) {
   TVM_INDEX_CONST_PROPAGATION({
       const Type& rtype = a.type();
-      // due to division and mod can have different modes
-      // only constant fold positive number where rule is fixed.
-      if (pa && pb && pa->value >= 0 && pb->value > 0) {
+      if (pa && pb) {
         return IntImm::make(rtype, pa->value % pb->value);
       }
       if (pa) {
@@ -201,6 +200,51 @@ inline Expr TryConstFold<ir::Mod>(Expr a, Expr b) {
 }
 
 template<>
+inline Expr TryConstFold<ir::FloorDiv>(Expr a, Expr b) {
+  TVM_ARITH_CONST_PROPAGATION({
+      const Type& rtype = a.type();
+      if (pa && pb) {
+        CHECK_NE(pb->value, 0) << "Divide by zero";
+        return IntImm::make(rtype, arith::floordiv(pa->value, pb->value));
+      }
+      if (pa) {
+        if (pa->value == 0) return a;
+      }
+      if (pb) {
+        if (pb->value == 1) return a;
+        CHECK_NE(pb->value, 0) << "Divide by zero";
+      }
+      if (fa && fb && fb->value != 0) {
+        return FloatImm::make(rtype, std::floor(fa->value / fb->value));
+      }
+      if (fa && fa->value == 0) return a;
+      if (fb) {
+        if (fb->value == 1) return a;
+        CHECK_NE(fb->value, 0) << "Divide by zero";
+      }
+    });
+  return Expr();
+}
+
+template<>
+inline Expr TryConstFold<ir::FloorMod>(Expr a, Expr b) {
+  TVM_INDEX_CONST_PROPAGATION({
+      const Type& rtype = a.type();
+      if (pa && pb) {
+        return IntImm::make(rtype, arith::floormod(pa->value, pb->value));
+      }
+      if (pa) {
+        if (pa->value == 0) return a;
+      }
+      if (pb) {
+        if (pb->value == 1) return make_zero(rtype);
+        CHECK_NE(pb->value, 0) << "Divide by zero";
+      }
+    });
+  return Expr();
+}
+
+template<>
 inline Expr TryConstFold<ir::Min>(Expr a, Expr b) {
   TVM_ARITH_CONST_PROPAGATION({
       const Type& rtype = a.type();

src/arithmetic/const_int_bound.cc

@@ -24,7 +24,7 @@
 #include <tvm/arithmetic.h>
 #include <tvm/ir_functor_ext.h>
 #include <algorithm>
-#include "int_op_overflow.h"
+#include "int_operator.h"
 #include "pattern_match.h"
 
 namespace tvm {
@@ -215,6 +215,37 @@ class ConstIntBoundAnalyzer::Impl :
     }
   }
 
+  Entry VisitExpr_(const FloorDiv* op) final {
+    Entry a = VisitExpr(op->a);
+    Entry b = VisitExpr(op->b);
+    CHECK(!b.is_const(0)) << "floordiv by zero";
+    // assume no division by 0
+    if (b.min_value == 0) b.min_value = 1;
+    if (b.max_value == 0) b.max_value = -1;
+    return BinaryOpBoundry(a, b, InfAwareFloorDiv);
+  }
+
+  Entry VisitExpr_(const FloorMod* op) final {
+    Entry a = VisitExpr(op->a);
+    Entry b = VisitExpr(op->b);
+    if (b.min_value > 0) {
+      int64_t b_max_cap = InfAwareAdd(b.max_value, -1);
+      if (a.min_value >= 0) {
+        // 0 <= [a_min, a_max] < b_min
+        if (a.max_value < b.min_value) return a;
+        // other case, we can get close to 0
+        return MakeBound(0, std::min(a.max_value, b_max_cap));
+      } else {
+        return MakeBound(0, b_max_cap);
+      }
+    } else {
+      CHECK(!b.is_const(0)) << "floormod by zero";
+      // mod by negative value is rare,
+      // and we just use the simpliest rule.
+      return Everything(op->type);
+    }
+  }
+
   Entry VisitExpr_(const Min* op) final {
     Entry a = VisitExpr(op->a);
     Entry b = VisitExpr(op->b);
@@ -376,6 +407,20 @@ class ConstIntBoundAnalyzer::Impl :
     return x / y;
   }
   /*!
+   * \brief Compute floodiv(x, y), aware of inf.
+   * \param x The left operand.
+   * \param y The right operand.
+   * \return the result.
+   */
+  static int64_t InfAwareFloorDiv(int64_t x, int64_t y) {
+    CHECK_NE(y, 0);
+    if (x == kPosInf || x == kNegInf) {
+      if (y > 0) return x;
+      return -x;
+    }
+    return floordiv(x, y);
+  }
+  /*!
    * \brief Compute x / y, aware of inf.
    * \param x The left operand.
    * \param y The right operand.

src/arithmetic/int_op_overflow.h → src/arithmetic/int_operator.h

@@ -19,11 +19,11 @@
 
 /*!
  *  Copyright (c) 2019 by Contributors
- * \file int_op_overflow.h
- * \brief Utility functions to detect if an integer op will overflow.
+ * \file int_operator.h
+ * \brief Additional useful operators for integer.
  */
-#ifndef TVM_ARITHMETIC_INT_OP_OVERFLOW_H_
-#define TVM_ARITHMETIC_INT_OP_OVERFLOW_H_
+#ifndef TVM_ARITHMETIC_INT_OPERATOR_H_
+#define TVM_ARITHMETIC_INT_OPERATOR_H_
 
 #include <limits>
 
@@ -48,30 +48,30 @@ inline bool WillOverflow(int64_t x,
 }
 
 template<>
-bool WillOverflow<ir::Add>(int64_t x,
-                           int64_t y,
-                           int64_t min_value,
-                           int64_t max_value) {
+inline bool WillOverflow<ir::Add>(int64_t x,
+                                  int64_t y,
+                                  int64_t min_value,
+                                  int64_t max_value) {
   if ((y > 0) && (x > max_value - y)) return true;
   if ((y < 0) && (x < min_value - y)) return true;
   return false;
 }
 
 template<>
-bool WillOverflow<ir::Sub>(int64_t x,
-                           int64_t y,
-                           int64_t min_value,
-                           int64_t max_value) {
+inline bool WillOverflow<ir::Sub>(int64_t x,
+                                  int64_t y,
+                                  int64_t min_value,
+                                  int64_t max_value) {
   if ((y > 0) && (x < min_value + y)) return true;
   if ((y < 0) && (x > max_value + y)) return true;
   return false;
 }
 
 template<>
-bool WillOverflow<ir::Mul>(int64_t x,
-                           int64_t y,
-                           int64_t min_value,
-                           int64_t max_value) {
+inline bool WillOverflow<ir::Mul>(int64_t x,
+                                  int64_t y,
+                                  int64_t min_value,
+                                  int64_t max_value) {
   if (y == 0) return false;
   if (y > 0) {
     if (x < min_value / y)  return true;
@@ -85,13 +85,42 @@ bool WillOverflow<ir::Mul>(int64_t x,
 }
 
 template<>
-bool WillOverflow<ir::Mod>(int64_t x,
-                           int64_t y,
-                           int64_t min_value,
-                           int64_t max_value) {
+inline bool WillOverflow<ir::Mod>(int64_t x,
+                                  int64_t y,
+                                  int64_t min_value,
+                                  int64_t max_value) {
   return y == 0;
 }
 
+/*!
+ * \brief Peform floor division of two integers.
+ * \param x The left operand.
+ * \param y The right operand.
+ * \return the result.
+ */
+inline int64_t floordiv(int64_t x, int64_t y) {
+  bool round_down =
+      (x >= 0 && y >= 0) ||
+      (x <= 0 && y <= 0) ||
+      (x % y == 0);
+  return round_down ? (x / y) : (x / y - 1);
+}
+
+
+/*!
+ * \brief Compute the floordiv remainder of two integers.
+ * \param x The left operand.
+ * \param y The right operand.
+ * \return the result.
+ */
+inline int64_t floormod(int64_t x, int64_t y) {
+  bool round_down =
+      (x >= 0 && y >= 0) ||
+      (x <= 0 && y <= 0) ||
+      (x % y == 0);
+  return round_down ? (x % y) : (x % y + y);
+}
+
 }  // namespace arith
 }  // namespace tvm
-#endif  // TVM_ARITHMETIC_INT_OP_OVERFLOW_H_
+#endif  // TVM_ARITHMETIC_INT_OPERATOR_H_

src/arithmetic/int_set.cc

@@ -252,6 +252,68 @@ inline IntervalSet Combine<ir::Mod>(Analyzer* analyzer,
   return IntervalSet::Everything();
 }
 
+
+template<>
+inline IntervalSet Combine<ir::FloorDiv>(Analyzer* analyzer,
+                                         IntervalSet a,
+                                         IntervalSet b) {
+  if (a->IsSinglePoint() && b->IsSinglePoint()) {
+    return IntervalSet::SinglePoint(floordiv(a->min_value, b->min_value));
+  }
+  if (a->IsEmpty()) return a;
+  if (b->IsEmpty()) return b;
+  if (b->IsSinglePoint()) {
+    if (is_zero(b->min_value)) {
+      LOG(FATAL) << "Divide by zero in CombineInterval Div";
+    }
+    if (is_one(b->min_value)) return a;
+    // no relaxation is needed in here due to set is inclusive
+    if (analyzer->CanProveGreaterEqual(b->min_value, 0)) {
+      Expr min_value = a->HasLowerBound() ? floordiv(a->min_value, b->min_value) : neg_inf();
+      Expr max_value = a->HasUpperBound() ? floordiv(a->max_value, b->min_value) : pos_inf();
+      return IntervalSet(min_value, max_value);
+    } else if (analyzer->CanProveGreaterEqual(-b->min_value, 1)) {
+      Expr min_value = a->HasUpperBound() ? floordiv(a->max_value, b->min_value) : neg_inf();
+      Expr max_value = a->HasLowerBound() ? floordiv(a->min_value, b->min_value) : pos_inf();
+      return IntervalSet(min_value, max_value);
+    } else if (a->HasUpperBound() && a->HasLowerBound()) {
+      using ir::Select;
+      Expr sign = b->min_value >= make_zero(b->min_value.type().element_of());
+      Expr e1 = floordiv(a->min_value, b->min_value);
+      Expr e2 = floordiv(a->max_value, b->min_value);
+      return IntervalSet(Select::make(sign, e1, e2), Select::make(sign, e2, e1));
+    }
+  }
+  DLOG(WARNING) << "Return Everything in CombineInterval Div";
+  return IntervalSet::Everything();
+}
+
+template<>
+inline IntervalSet Combine<ir::FloorMod>(Analyzer* analyzer,
+                                         IntervalSet a,
+                                         IntervalSet b) {
+  if (a->IsSinglePoint() && b->IsSinglePoint()) {
+    return IntervalSet::SinglePoint(floormod(a->min_value, b->min_value));
+  }
+  if (a->IsEmpty()) return a;
+  if (b->IsEmpty()) return b;
+
+  if (b->IsSinglePoint()) {
+    const Expr& divisor = b->min_value;
+    if (is_zero(divisor)) {
+      LOG(FATAL) << "Modular by zero in CombineInterval Mod";
+    }
+    if (analyzer->CanProveGreaterEqual(divisor, 0)) {
+      return IntervalSet(make_zero(divisor.type()), divisor - 1);
+    } else {
+      Expr bound = abs(divisor) - 1;
+      return IntervalSet(-bound, bound);
+    }
+  }
+  DLOG(WARNING) << "Return Everything in CombineInterval Mod";
+  return IntervalSet::Everything();
+}
+
 template<>
 inline IntervalSet Combine<ir::Max>(Analyzer* analzyer,
                                     IntervalSet a,
@@ -361,6 +423,14 @@ class IntervalSetEvaluator :
     return VisitBinaryExpr_(op);
   }
 
+  IntervalSet VisitExpr_(const FloorDiv* op) final {
+    return VisitBinaryExpr_(op);
+  }
+
+  IntervalSet VisitExpr_(const FloorMod* op) final {
+    return VisitBinaryExpr_(op);
+  }
+
   IntervalSet VisitExpr_(const Min* op) final {
     return VisitBinaryExpr_(op);
   }

src/arithmetic/modular_set.cc

@@ -179,6 +179,14 @@ class ModularSetAnalyzer::Impl :
     return Everything();
   }
 
+  Entry VisitExpr_(const FloorDiv* op) final {
+    Entry b = VisitExpr(op->b);
+    if (b.is_const()) {
+      return DivByConst(op->a, b.base, true);
+    }
+    return Everything();
+  }
+
   Entry VisitExpr_(const Min* op) final {
     Entry a = VisitExpr(op->a);
     Entry b = VisitExpr(op->b);

src/arithmetic/pattern_match.h

@@ -6,9 +6,9 @@
  * to you under the Apache License, Version 2.0 (the
  * "License"); you may not use this file except in compliance
  * with the License.  You may obtain a copy of the License at
- * 
+ *
  *   http://www.apache.org/licenses/LICENSE-2.0
- * 
+ *
  * Unless required by applicable law or agreed to in writing,
  * software distributed under the License is distributed on an
  * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
@@ -326,6 +326,8 @@ TVM_PATTERN_BINARY_OP(operator/, ir::Div);
 TVM_PATTERN_BINARY_OP(operator%, ir::Mod);
 TVM_PATTERN_BINARY_OP(min, ir::Min);
 TVM_PATTERN_BINARY_OP(max, ir::Max);
+TVM_PATTERN_BINARY_OP(floordiv, ir::FloorDiv);
+TVM_PATTERN_BINARY_OP(floormod, ir::FloorMod);
 
 // logical expressions
 TVM_PATTERN_BINARY_OP(operator>, ir::GT);

src/arithmetic/rewrite_simplify.h

@@ -53,6 +53,8 @@ class RewriteSimplifier::Impl : public IRMutator {
   Expr Mutate_(const Mul* op, const Expr& self) override;
   Expr Mutate_(const Div* op, const Expr& self) override;
   Expr Mutate_(const Mod* op, const Expr& self) override;
+  Expr Mutate_(const FloorDiv* op, const Expr& self) override;
+  Expr Mutate_(const FloorMod* op, const Expr& self) override;
   Expr Mutate_(const Min* op, const Expr& self) override;
   Expr Mutate_(const Max* op, const Expr& self) override;
   Expr Mutate_(const EQ* op, const Expr& self) override;

src/lang/expr_operator.cc

@@ -188,6 +188,19 @@ Expr operator%(Expr a, Expr b) {
   return ir::Mod::make(a, b);
 }
 
+Expr floordiv(Expr a, Expr b) {
+  BinaryOpMatchTypes(a, b);
+  Expr ret = arith::TryConstFold<ir::FloorDiv>(a, b);
+  if (ret.defined()) return ret;
+  return ir::FloorDiv::make(a, b);
+}
+
+Expr floormod(Expr a, Expr b) {
+  BinaryOpMatchTypes(a, b);
+  Expr ret = arith::TryConstFold<ir::FloorMod>(a, b);
+  if (ret.defined()) return ret;
+  return ir::FloorMod::make(a, b);
+}
 
 Expr min(Expr a, Expr b) {
   // inf-aware simplificaiton

src/lang/ir.cc

@@ -59,14 +59,12 @@ Expr StringImm::make(std::string value) {
 Expr Cast::make(DataType t, Expr value) {
   CHECK(value.defined());
   CHECK_EQ(t.lanes(), value.type().lanes());
-
   NodePtr<Cast> node = make_node<Cast>();
   node->type = t;
   node->value = std::move(value);
   return Expr(node);
 }
 
-
 Expr And::make(Expr a, Expr b) {
   CHECK(a.defined()) << "ValueError: a is undefined";
   CHECK(b.defined()) << "ValueError: b is undefined";
@@ -700,6 +698,16 @@ TVM_STATIC_IR_FUNCTOR(IRPrinter, vtable)
 });
 
 TVM_STATIC_IR_FUNCTOR(IRPrinter, vtable)
+.set_dispatch<FloorDiv>([](const FloorDiv* op, IRPrinter *p) {
+  p->stream << "floordiv(" << op->a << ", " << op->b << ")";
+});
+
+TVM_STATIC_IR_FUNCTOR(IRPrinter, vtable)
+.set_dispatch<FloorMod>([](const FloorMod* op, IRPrinter *p) {
+  p->stream << "floormod(" << op->a << ", " << op->b << ")";
+});
+
+TVM_STATIC_IR_FUNCTOR(IRPrinter, vtable)
 .set_dispatch<And>([](const And* op, IRPrinter* p) {
     p->stream << '(';
     p->Print(op->a);
@@ -1098,7 +1106,6 @@ TVM_REGISTER_NODE_TYPE(CommReducerNode);
 TVM_REGISTER_NODE_TYPE(Reduce);
 TVM_REGISTER_NODE_TYPE(Any);
 TVM_REGISTER_NODE_TYPE(AttrStmt);
-
 TVM_REGISTER_NODE_TYPE(FloatImm);
 TVM_REGISTER_NODE_TYPE(IntImm);
 TVM_REGISTER_NODE_TYPE(UIntImm);
@@ -1110,6 +1117,8 @@ TVM_REGISTER_NODE_TYPE(Sub);
 TVM_REGISTER_NODE_TYPE(Mul);
 TVM_REGISTER_NODE_TYPE(Div);
 TVM_REGISTER_NODE_TYPE(Mod);
+TVM_REGISTER_NODE_TYPE(FloorDiv);
+TVM_REGISTER_NODE_TYPE(FloorMod);
 TVM_REGISTER_NODE_TYPE(Min);
 TVM_REGISTER_NODE_TYPE(Max);
 TVM_REGISTER_NODE_TYPE(EQ);

src/pass/ir_deep_compare.cc

@@ -302,6 +302,8 @@ class IRDeepCompare :
   DEFINE_BIOP_EXPR_CMP_(Mul)
   DEFINE_BIOP_EXPR_CMP_(Div)
   DEFINE_BIOP_EXPR_CMP_(Mod)
+  DEFINE_BIOP_EXPR_CMP_(FloorDiv)
+  DEFINE_BIOP_EXPR_CMP_(FloorMod)
   DEFINE_BIOP_EXPR_CMP_(Min)
   DEFINE_BIOP_EXPR_CMP_(Max)
   DEFINE_BIOP_EXPR_CMP_(EQ)

src/pass/ir_mutator.cc

@@ -401,6 +401,8 @@ DEFINE_BIOP_EXPR_MUTATE_(Sub)
 DEFINE_BIOP_EXPR_MUTATE_(Mul)
 DEFINE_BIOP_EXPR_MUTATE_(Div)
 DEFINE_BIOP_EXPR_MUTATE_(Mod)
+DEFINE_BIOP_EXPR_MUTATE_(FloorDiv)
+DEFINE_BIOP_EXPR_MUTATE_(FloorMod)
 DEFINE_BIOP_EXPR_MUTATE_(Min)
 DEFINE_BIOP_EXPR_MUTATE_(Max)
 DEFINE_BIOP_EXPR_MUTATE_(EQ)
@@ -506,6 +508,8 @@ TVM_STATIC_IR_FUNCTOR(IRMutator, vtable_expr)
 .DISPATCH_TO_MUTATE_EXPR(Mul)
 .DISPATCH_TO_MUTATE_EXPR(Div)
 .DISPATCH_TO_MUTATE_EXPR(Mod)
+.DISPATCH_TO_MUTATE_EXPR(FloorDiv)
+.DISPATCH_TO_MUTATE_EXPR(FloorMod)
 .DISPATCH_TO_MUTATE_EXPR(Min)
 .DISPATCH_TO_MUTATE_EXPR(Max)
 .DISPATCH_TO_MUTATE_EXPR(EQ)

src/pass/ir_visitor.cc

@@ -6,9 +6,9 @@
  * to you under the Apache License, Version 2.0 (the
  * "License"); you may not use this file except in compliance
  * with the License.  You may obtain a copy of the License at
- * 
+ *
  *   http://www.apache.org/licenses/LICENSE-2.0
- * 
+ *
  * Unless required by applicable law or agreed to in writing,
  * software distributed under the License is distributed on an
  * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
@@ -139,6 +139,8 @@ DEFINE_BINOP_VISIT_(Sub)
 DEFINE_BINOP_VISIT_(Mul)
 DEFINE_BINOP_VISIT_(Div)
 DEFINE_BINOP_VISIT_(Mod)
+DEFINE_BINOP_VISIT_(FloorDiv)
+DEFINE_BINOP_VISIT_(FloorMod)
 DEFINE_BINOP_VISIT_(Min)
 DEFINE_BINOP_VISIT_(Max)
 DEFINE_BINOP_VISIT_(EQ)
@@ -250,6 +252,8 @@ TVM_STATIC_IR_FUNCTOR(IRVisitor, vtable)
 .DISPATCH_TO_VISIT(Mul)
 .DISPATCH_TO_VISIT(Div)
 .DISPATCH_TO_VISIT(Mod)
+.DISPATCH_TO_VISIT(FloorDiv)
+.DISPATCH_TO_VISIT(FloorMod)
 .DISPATCH_TO_VISIT(Min)
 .DISPATCH_TO_VISIT(Max)
 .DISPATCH_TO_VISIT(EQ)

src/pass/vectorize_loop.cc

@@ -151,6 +151,12 @@ class Vectorizer : public IRMutator {
   Expr Mutate_(const Mod* op, const Expr &e) final {
     return BinaryVec(op, e);
   }
+  Expr Mutate_(const FloorDiv* op, const Expr &e) final {
+    return BinaryVec(op, e);
+  }
+  Expr Mutate_(const FloorMod* op, const Expr &e) final {
+    return BinaryVec(op, e);
+  }
   Expr Mutate_(const Min* op, const Expr &e) final {
     return BinaryVec(op, e);
   }

tests/python/unittest/test_arith_canonical_simplify.py

@@ -28,21 +28,32 @@ class CanonicalChecker:
 def test_mul_sum_simplify():
     ck = CanonicalChecker()
     x, y, z = tvm.var("x"), tvm.var("y"), tvm.var("z")
+
     ck.verify(2 + (3 * x + z + y + 1) * 4 + x,
               x * 13 + z * 4 + y * 4 +6)
-    ck.verify((x + y + x + y * 3) / 2, y * 2 + x)
-    ck.verify((x + y + x + y * 3) % 2, 0)
     ck.verify(x * 3 - 4 * x + 1, 1 - x)
     ck.verify(y + x * 3 - 5 * x + 1 + y, y * 2 + 1 - x * 2)
+    # trucdiv
+    ck.verify((x + y + x + y * 3) / 2, y * 2 + x)
+    ck.verify((x + y + x + y * 3) % 2, 0)
+
+    # floordiv
+    fld = tvm.floordiv
+    flm = tvm.floormod
+    ck.verify(flm(x + x + y * 3, 2), flm(y * 3, 2))
+    ck.verify(fld(x + y + x + y * 3, 2), y * 2 + x)
+    ck.verify(flm(x + y + x + y * 3, 2), 0)
+    ck.verify(fld(x + x + y * 3, 2), fld(y * 3, 2) + x)
 
 
 def test_split_index_simplify():
     ck = CanonicalChecker()
     x, y, z = tvm.var("x"), tvm.var("y"), tvm.var("z")
-    ck.verify((x/3) *3 + x % 3, x)
-    ck.verify((x/6) * 6 + ((x/3) % 2) * 3 + x % 3, x)
 
+    # trucdiv
     # split div const
+    ck.verify((x/3) *3 + x % 3, x)
+    ck.verify((x/6) * 6 + ((x/3) % 2) * 3 + x % 3, x)
     ck.verify(((x % 16) / 2) * 2 / 4, (x % 16) / 4)
     ck.verify((x % 2) / 8, 0)
     ck.verify((x % 2) / 7, 0)
@@ -59,11 +70,29 @@ def test_split_index_simplify():
     # complex fold
     ck.verify((z * 9 + y) / 2 * 2 + (z * 9 + y) % 2, z * 9 + y)
 
+    ck.analyzer.update(x, tvm.arith.ConstIntBound(-100, 1000), True)
+    ck.analyzer.update(y, tvm.arith.ConstIntBound(-100, 1000), True)
+    ck.verify((x * 4 + y) / 2 * 2 + (x * 4 + y) % 2, x * 4 + y)
+
+    # floordiv
+    fld = tvm.floordiv
+    flm = tvm.floormod
+    ck.verify(fld(x, 3) * 3 + flm(x, 3), x)
+    ck.verify(fld(x, 6) * 6 + flm(fld(x, 3), 2) * 3 + flm(x, 3), x)
+    ck.verify(fld(fld(flm(x, 16), 2) * 2, 4), fld(flm(x, 16), 4))
+    ck.verify(fld(flm(x, 2), 8), 0)
+    ck.verify(fld(flm(x, 2), 7), 0)
+    ck.verify(fld(fld(flm(x, 16), 2) * 2, 6), fld(flm(x, 16), 6))
+
+    # cannot simplify mixed case, unless we canonicalize into one mode.
+    ck.verify((x/6) * 2 + fld(x,3) % 2, (x/6) * 2 + fld(x,3) % 2)
 
 
 def test_div_simplify():
     ck = CanonicalChecker()
     x = tvm.var("x")
+
+    # truc div
     ck.verify((16+48*x)/16, x*3 + 1)
     # (17+48*x)/16 is not simplifiable for arbitrary x because when 17+48*x<0
     # (17+48*x)/16 != 1+3*x
@@ -74,6 +103,22 @@ def test_div_simplify():
     # Trying expressions that are not simplifiable for any values of the variables
     ck.verify((17+47*x)/16, (x * 47 + 17) / 16)
 
+    # floordiv
+    fld = tvm.floordiv
+    ck.analyzer.update(x, tvm.arith.ConstIntBound(-1000, 10000), True)
+    ck.verify(fld(16+48*x, 16), x*3 + 1)
+    ck.verify(fld(17+48*x, 16), x * 3 + 1)
+    ck.verify(fld(17+47*x, 16), fld(x * 47 + 17, 16))
+
+
+def test_floormod_simplify():
+    ck = CanonicalChecker()
+    flm = tvm.floormod
+    x, y = tvm.var("x"), tvm.var("y")
+    ck.verify(flm(flm((x*4) + y  - 466036, 24528) - 24512,  16),
+              flm((x*4) + y  + 12, 16))
+
+
 
 def test_canonical_mixed():
     ck = CanonicalChecker()
@@ -86,6 +131,10 @@ def test_canonical_mixed():
     ck.verify(tvm.min(x, 1) - tvm.min(x, 1), 0)
     ck.verify(x * x - x * x, 0)
 
+    fld = tvm.floordiv
+    ck.verify(fld(x, (z*z)) - fld(x, (z*z)), 0)
+    ck.verify(fld(x, (z+z)) - fld(x, (z+z)), 0)
+
 
 def test_reduce_combiner_simplify():
     ck = CanonicalChecker()
@@ -218,11 +267,13 @@ def test_complex_cases():
 
 
 if __name__ == "__main__":
+    test_floormod_simplify()
+    test_mul_sum_simplify()
     test_simplify_if_then_else()
     test_div_simplify()
     test_reduce_simplify()
     test_reduce_combiner_simplify()
-    test_mul_sum_simplify()
+
     test_split_index_simplify()
     test_canonical_mixed()
     test_complex_cases()

tests/python/unittest/test_arith_const_int_bound.py

@@ -143,6 +143,52 @@ def test_mod_bound():
     assert bd.max_value == 9
 
 
+def test_floordiv_bound():
+    analyzer = tvm.arith.Analyzer()
+    x, y = tvm.var("x"), tvm.var("y")
+    fld = tvm.floordiv
+    analyzer.update(x, tvm.arith.ConstIntBound(-9, 4))
+    analyzer.update(y, tvm.arith.ConstIntBound(4, 10))
+    bd = analyzer.const_int_bound(fld(x, y))
+    assert bd.min_value == -9 // 4
+
+    analyzer.update(x, tvm.arith.ConstIntBound(-9, 4), override=True)
+    analyzer.update(y, tvm.arith.ConstIntBound(-2, 0), override=True)
+    bd = analyzer.const_int_bound(fld(x, y))
+    assert bd.min_value == -4
+    assert bd.max_value == 9
+
+    analyzer.update(x, tvm.arith.ConstIntBound(bd.NEG_INF, 4), override=True)
+    analyzer.update(y, tvm.arith.ConstIntBound(-2, 1), override=True)
+    bd = analyzer.const_int_bound(fld(x, y))
+    assert bd.min_value == bd.NEG_INF
+    assert bd.max_value == bd.POS_INF
+
+
+def test_floormod_bound():
+    analyzer = tvm.arith.Analyzer()
+    x, y = tvm.var("x"), tvm.var("y")
+    flm = tvm.floormod
+
+    analyzer.update(x, tvm.arith.ConstIntBound(-9, 4))
+    analyzer.update(y, tvm.arith.ConstIntBound(4, 10))
+    bd = analyzer.const_int_bound(flm(x, y))
+    assert bd.min_value == 0
+    assert bd.max_value == 9
+
+    analyzer.update(x, tvm.arith.ConstIntBound(bd.NEG_INF, bd.POS_INF), override=True)
+    analyzer.update(y, tvm.arith.ConstIntBound(4, 10), override=True)
+    bd = analyzer.const_int_bound(flm(x, y))
+    assert bd.min_value == 0
+    assert bd.max_value == 9
+
+    analyzer.update(x, tvm.arith.ConstIntBound(1, bd.POS_INF), override=True)
+    analyzer.update(y, tvm.arith.ConstIntBound(4, 10), override=True)
+    bd = analyzer.const_int_bound(flm(x, y))
+    assert bd.min_value == 0
+    assert bd.max_value == 9
+
+
 def test_min_max_bound():
     analyzer = tvm.arith.Analyzer()
     x, y = tvm.var("x"), tvm.var("y")
@@ -229,6 +275,8 @@ if __name__ == "__main__":
     test_mul_bound()
     test_div_bound()
     test_mod_bound()
+    test_floordiv_bound()
+    test_floormod_bound()
     test_min_max_bound()
     test_select_bound()
     test_shift_and_bound()

tests/python/unittest/test_arith_intset.py

@@ -64,9 +64,14 @@ def test_mul_div():
     ck.verify(x * y, {x : tvm.arith.IntervalSet(0, 10)}, (0, 10 * y))
     ck.verify(x * 2, {x : tvm.arith.IntervalSet(1, 10)}, (2, 20))
     ck.verify(x * -2, {x : tvm.arith.IntervalSet(1, 10)}, (-20, -2))
+
     ck.verify(x / y, {x : tvm.arith.IntervalSet(0, 10)}, (0, 10 / y))
     ck.verify(x / 2, {x : tvm.arith.IntervalSet(1, 10)}, (0, 5))
 
+    fld = tvm.floordiv
+    ck.verify(fld(x, y), {x : tvm.arith.IntervalSet(0, 10)}, (0, fld(10, y)))
+    ck.verify(fld(x, 2), {x : tvm.arith.IntervalSet(-1, 10)}, (-1, 5))
+
 
 def test_mod():
     ck = IntSetChecker()
@@ -75,6 +80,10 @@ def test_mod():
     ck.verify(x % y, {x : tvm.arith.IntervalSet(0, 10)}, (0, y - 1))
     ck.verify(x % 10, {x : tvm.arith.IntervalSet(1, 10)}, (0, 9))
 
+    flm = tvm.floormod
+    ck.verify(flm(x, 10), {x : tvm.arith.IntervalSet(-10, 10)}, (0, 9))
+
+
 def test_max_min():
     ck = IntSetChecker()
     x, y = tvm.var("x"), tvm.var("y")
@@ -99,4 +108,3 @@ if __name__ == "__main__":
     test_max_min()
     test_select()
     test_mod()
-

tests/python/unittest/test_arith_modular_set.py

@@ -61,6 +61,10 @@ def test_div_shift():
     m = analyzer.modular_set((x * 4 + 2) >> 1)
     assert m.coeff == 2
     assert m.base == 1
+    fld = tvm.floordiv
+    m = analyzer.modular_set(fld(x * 4 + 2, 2))
+    assert m.coeff == 2
+    assert m.base == 1
     # x is non-negative
     analyzer.update(x, tvm.arith.ConstIntBound(0, 100))
     m = analyzer.modular_set((x * 4 + 2) / 2)