[ARITH][SCHEDULE] Update schedule to use the new analyzer (#3466)

include/tvm/arithmetic.h

@@ -516,6 +516,24 @@ class Analyzer {
    * \note Analyzer will call into sub-analyzers to get the result.
    */
   bool CanProveGreaterEqual(const Expr& expr, int64_t lower_bound);
+  /*!
+   * \brief Whether can we prove condition.
+   *
+   * \param cond The expression to be proved.
+   * \return The result.
+   *
+   * \note Analyzer will call into sub-analyzers to get the result.
+   */
+  bool CanProve(const Expr& cond);
+  /*!
+   * \brief Simplify expr.
+   *
+   * \param expr The expression to be simplified.
+   * \return The result.
+   *
+   * \note Analyzer will call into sub-analyzers to get the result.
+   */
+  Expr Simplify(const Expr& expr);
 };
 
 //-----------------------------------------------

include/tvm/expr.h

@@ -1,3 +1,4 @@
+
 /*
  * Licensed to the Apache Software Foundation (ASF) under one
  * or more contributor license agreements.  See the NOTICE file

src/arithmetic/analyzer.cc

@@ -23,6 +23,7 @@
  */
 #include <tvm/ir.h>
 #include <tvm/arithmetic.h>
+#include <tvm/expr_operator.h>
 
 namespace tvm {
 namespace arith {
@@ -49,8 +50,13 @@ void Analyzer::Bind(const VarExpr& v, const Expr& expr) {
 }
 
 void Analyzer::Bind(const VarExpr& v, const Range& range) {
+  CHECK(range.defined());
   Var var(v.node_);
   this->const_int_bound.Bind(var, range);
+  if (is_one(range->extent)) {
+    this->rewrite_simplify.Update(var, range->min);
+    this->canonical_simplify.Update(var, range->min);
+  }
   // skip modular_set
   // skip rewrite simplify
 }
@@ -82,5 +88,27 @@ bool Analyzer::CanProveGreaterEqual(const Expr& expr, int64_t lower_bound) {
   return false;
 }
 
+bool Analyzer::CanProve(const Expr& expr) {
+  if (const auto* ptr = expr.as<ir::UIntImm>()) {
+    return ptr->value != 0;
+  }
+  auto res = this->rewrite_simplify(expr);
+  if (const auto* ptr = res.as<ir::UIntImm>()) {
+    return ptr->value != 0;
+  }
+  res = this->canonical_simplify(expr);
+  if (const auto* ptr = res.as<ir::UIntImm>()) {
+    return ptr->value != 0;
+  }
+  return false;
+}
+
+Expr Analyzer::Simplify(const Expr& expr) {
+  if (is_const(expr)) return expr;
+  auto res = this->rewrite_simplify(expr);
+  res = this->canonical_simplify(res);
+  return res;
+}
+
 }  // namespace arith
 }  // namespace tvm

src/arithmetic/canonical_simplify.cc

@@ -262,6 +262,7 @@ class SumExprNode : public CanonicalExprNode {
           rhs.CopyOnWrite()->scale += lhs->scale;
           lhs.CopyOnWrite()->scale = 0;
         } else if (lhs->lower_factor == rhs->upper_factor &&
+                   rhs->scale != 0 &&
                    lhs->scale % rhs->scale == 0 &&
                    lhs->lower_factor == (lhs->scale / rhs->scale) * rhs->lower_factor) {
           // Rules used in the proof:

src/arithmetic/const_int_bound.cc

@@ -42,11 +42,23 @@ ConstIntBound::ConstIntBound(
   node_ = std::move(node);
 }
 
+inline void PrintBoundValue(std::ostream& os, int64_t val) {
+  if (val == ConstIntBound::kPosInf) {
+    os << "pos_inf";
+  } else if (val == ConstIntBound::kNegInf) {
+    os << "neg_inf";
+  } else {
+    os << val;
+  }
+}
+
 TVM_STATIC_IR_FUNCTOR(IRPrinter, vtable)
-.set_dispatch<ConstIntBoundNode>([](const ConstIntBoundNode *op, IRPrinter *p) {
-    p->stream << "ConstIntBound"
-              << "[" << op->min_value << ", "
-              << op->max_value << ']';
+.set_dispatch<ConstIntBoundNode>([](const ConstIntBoundNode* op, IRPrinter* p) {
+    p->stream << "ConstIntBound[";
+    PrintBoundValue(p->stream, op->min_value);
+    p->stream << ',';
+    PrintBoundValue(p->stream, op->max_value);
+    p->stream << ']';
   });
 
 // internal entry for const int bound
@@ -95,7 +107,10 @@ class ConstIntBoundAnalyzer::Impl :
       auto it = var_map_.find(var);
       if (it != var_map_.end()) {
         CHECK(it->second == info)
-          << "var \'" << var << "\' already updated.";
+            << "Trying to update var \'" << var << "\'"
+            << " with a different const bound: "
+            << "original=" << ConstIntBound(it->second.min_value, it->second.max_value)
+            << ", new=" << ConstIntBound(info.min_value, info.max_value);
       }
     }
     var_map_[var] = info;

src/arithmetic/rewrite_simplify.cc

@@ -105,7 +105,14 @@ TryCompare(const Expr& x, int64_t val) {
 void RewriteSimplifier::Impl::
 Update(const Var& var, const Expr& info, bool override) {
   if (!override) {
-    CHECK(!var_map_.count(var));
+    auto it = var_map_.find(var);
+    if (it != var_map_.end()) {
+      CHECK(Equal(it->second, info))
+          << "Trying to update var \'" << var << "\'"
+          << " with a different value: "
+          << "original=" << it->second
+          << ", new=" << info;
+    }
   }
   var_map_[var] = info;
 }
@@ -199,6 +206,9 @@ Mutate_(const Add* op, const Expr& self) {
     TVM_TRY_RECURSIVE_REWRITE(x + c1 + y, (x + y) + c1);
     TVM_TRY_RECURSIVE_REWRITE(x + (c1 + y), (x + y) + c1);
     TVM_TRY_RECURSIVE_REWRITE((y % c1) + x * c1, x * c1 + (y % c1));
+
+    TVM_TRY_RECURSIVE_REWRITE(x + max(y, z), max(y, z) + x);
+    TVM_TRY_RECURSIVE_REWRITE(x + min(y, z), min(y, z) + x);
   }
 
   // condition rules.
@@ -477,6 +487,10 @@ Mutate_(const Div* op, const Expr& self) {
       }
     }
 
+    TVM_TRY_REWRITE(x / x, OneWithTypeLike(x));
+    TVM_TRY_REWRITE(x * c1 / x, c1);
+    TVM_TRY_REWRITE(c1 * x / x, c1);
+
     // Rules involving 2-operands.
     TVM_TRY_REWRITE_IF((x * c1 + y) / c2, x * (c1 / c2) + y / c2,
                        c1.Eval()->value >= 0 &&
@@ -684,6 +698,9 @@ Mutate_(const Mod* op, const Expr& self) {
       if (mod->coeff % c1val == 0 &&
           CanProveGreaterEqual(x.Eval(), 0)) {
         return (mod->base % c1).Eval();
+      } else if (mod->coeff % c1val == 0 &&
+                 mod->base % c1val == 0) {
+        return make_zero(ret.type());
       }
     }
   }

src/arithmetic/rewrite_simplify.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
@@ -121,6 +121,11 @@ class RewriteSimplifier::Impl : public IRMutator {
   PConstWithTypeLike<TA> ZeroWithTypeLike(const Pattern<TA>& pattern) {
     return PConstWithTypeLike<TA>(pattern.derived(), 0);
   }
+
+  template<typename TA>
+  PConstWithTypeLike<TA> OneWithTypeLike(const Pattern<TA>& pattern) {
+    return PConstWithTypeLike<TA>(pattern.derived(), 1);
+  }
 };
 
 

src/schedule/bound.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
@@ -213,6 +213,8 @@ Map<IterVar, Range> InferBound(const Schedule& sch) {
   // Prepare context
   GraphContext ctx;
   Array<Operation> roots;
+  arith::Analyzer analyzer;
+
   for (Operation op : sch->outputs) {
     roots.push_back(sch->stage_map[op]->op);
   }
@@ -233,16 +235,26 @@ Map<IterVar, Range> InferBound(const Schedule& sch) {
   for (size_t i = sch->stages.size(); i != 0; --i) {
     const Stage& stage = sch->stages[i - 1];
     InferRootBound(stage, ctx, &ret);
+
+    // bind bound of root iter vars.
+    for (auto iv :  stage->op->root_iter_vars()) {
+      auto it = ret.find(iv);
+      if (it != ret.end()) {
+        analyzer.Bind(iv->var, it->second);
+      }
+    }
+
     // pass down to get bound of all iter vars.
-    PassDownDomain(stage, &ret);
+    PassDownDomain(stage, &ret, &analyzer);
     for (IterVar iv : stage->env_threads) {
       CHECK(iv->dom.defined());
       ret[iv] = iv->dom;
     }
   }
   for (auto& p : ret) {
-    ret[p.first] = Range::make_by_min_extent(ir::Simplify(p.second->min),
-                                             ir::Simplify(p.second->extent));
+    ret[p.first] = Range::make_by_min_extent(
+        analyzer.Simplify(p.second->min),
+        analyzer.Simplify(p.second->extent));
   }
   return Map<IterVar, Range>(ret.begin(), ret.end());
 }

src/schedule/message_passing.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
@@ -34,24 +34,17 @@ namespace schedule {
 using namespace ir;
 using namespace arith;
 
-// result = ceil((a / b)), both a and b are positive integer
-inline Expr DivCeil(Expr a, Expr b) {
-  return ir::Simplify((a + b - 1) / b);
-}
-
-inline bool prove_equal(Expr lhs, Expr rhs) {
-  return is_zero(ir::Simplify(lhs - rhs));
-}
-
 void Update(std::unordered_map<IterVar, Range>* p_state,
             const IterVar& iv,
-            Range r) {
+            Range r,
+            Analyzer* analyzer) {
   auto it = p_state->find(iv);
   if (it == p_state->end()) {
     (*p_state)[iv] = r;
+    analyzer->Bind(iv->var, r);
   } else {
-    bool match = is_zero(it->second->min);
-    if (!prove_equal(r->extent, it->second->extent)) match = false;
+    bool match = is_zero(it->second->min) &&
+        analyzer->CanProve(r->extent - it->second->extent == 0);
     CHECK(match)
         << iv
         << " domain already inferred,"
@@ -62,7 +55,12 @@ void Update(std::unordered_map<IterVar, Range>* p_state,
 
 void PassDownDomain(const Stage& stage,
                     std::unordered_map<IterVar, Range>* p_state,
+                    arith::Analyzer* actx,
                     bool allow_missing) {
+  auto ceil_div = [actx](Expr a, Expr b) {
+    return actx->Simplify((a + (b - 1)) / b);
+  };
+
   auto& state = *p_state;
   // forwar iteration on relations
   for (IterVarRelation rel : stage->relations) {
@@ -74,15 +72,16 @@ void PassDownDomain(const Stage& stage,
       CHECK(!state.count(r->inner));
       const Range& range_parent = state.at(r->parent);
       if (r->factor.defined()) {
-        Update(p_state, r->inner, Range::make_by_min_extent(0, r->factor));
+        Update(p_state, r->inner,
+               Range::make_by_min_extent(0, r->factor), actx);
         Update(p_state, r->outer,
                Range::make_by_min_extent(
-                   0, DivCeil(range_parent->extent, r->factor)));
+                   0, ceil_div(range_parent->extent, r->factor)), actx);
       } else {
-        Update(p_state, r->outer, Range::make_by_min_extent(0, r->nparts));
+        Update(p_state, r->outer, Range::make_by_min_extent(0, r->nparts), actx);
         Update(p_state, r->inner,
                Range::make_by_min_extent(
-                   0, DivCeil(range_parent->extent, r->nparts)));
+                   0, ceil_div(range_parent->extent, r->nparts)), actx);
       }
     } else if (const FuseNode* r = rel.as<FuseNode>()) {
       if (!state.count(r->outer) || !state.count(r->inner)) {
@@ -100,9 +99,9 @@ void PassDownDomain(const Stage& stage,
       }
       Update(p_state, r->rebased,
              Range::make_by_min_extent(
-                 0, state.at(r->parent)->extent));
+                 0, state.at(r->parent)->extent), actx);
     } else if (const SingletonNode* s = rel.as<SingletonNode>()) {
-      Update(p_state, s->iter, Range::make_by_min_extent(0, 1));
+      Update(p_state, s->iter, Range::make_by_min_extent(0, 1), actx);
     } else {
       LOG(FATAL) << "unknown relation type";
     }
@@ -111,7 +110,7 @@ void PassDownDomain(const Stage& stage,
   for (auto kv : stage->iter_var_attrs) {
     if (kv.second->bind_thread.defined()) {
       CHECK(state.count(kv.first));
-      Update(p_state, kv.second->bind_thread, state.at(kv.first));
+      Update(p_state, kv.second->bind_thread, state.at(kv.first), actx);
     }
   }
 }

src/schedule/message_passing.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
@@ -43,11 +43,13 @@ namespace schedule {
  *
  * \param stage The stage to operate on.
  * \param p_state The state of the message passing.
+ * \param analyzer Analyzer context, storing information about bounds in p_state.
  * \param allow_missing Whether allow missing value.
  */
 void PassDownDomain(
     const Stage& stage,
     std::unordered_map<IterVar, Range>* p_state,
+    arith::Analyzer* analyzer,
     bool allow_missing = false);
 
 /*!