/* * Licensed to the Apache Software Foundation (ASF) under one * or more contributor license agreements. See the NOTICE file * distributed with this work for additional information * regarding copyright ownership. The ASF licenses this file * 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 * KIND, either express or implied. See the License for the * specific language governing permissions and limitations * under the License. */ /*! * \file rewrite_simplify.cc * \brief Rewrite-rule based simplification. */ // Acknowledgement: Most rewrite-rules are from Halide. #include <tvm/arith/analyzer.h> #include <tvm/tir/op.h> #include <algorithm> #include "const_fold.h" #include "pattern_match.h" #include "rewrite_simplify.h" namespace tvm { namespace arith { using namespace tir; // macro for doing simple rewrite #define TVM_TRY_REWRITE(SrcExpr, ResExpr) \ if ((SrcExpr).Match(ret)) { \ return (ResExpr).Eval(); \ } // macro for rewrite + recursively rewrite ResExpr #define TVM_TRY_RECURSIVE_REWRITE(SrcExpr, ResExpr) \ if ((SrcExpr).Match(ret)) { \ return RecursiveRewrite((ResExpr).Eval()); \ } // macro rewrite only if CondExor is true after match. #define TVM_TRY_REWRITE_IF(SrcExpr, ResExpr, CondExpr) \ if ((SrcExpr).Match(ret) && (CondExpr)) { \ return (ResExpr).Eval(); \ } // macro rewrite + recursive_rewrite only if CondExor is true after match. #define TVM_TRY_RECURSIVE_REWRITE_IF(SrcExpr, ResExpr, CondExpr) \ if ((SrcExpr).Match(ret) && (CondExpr)) { \ return RecursiveRewrite((ResExpr).Eval()); \ } // NOTE for developers: // // We mainly focus on index expression simplification. // Besides the RewriteSimplifier, some cases can be better // handled by CanonicalSimplifier. // // try to prove x equals val RewriteSimplifier::Impl::CompareResult RewriteSimplifier::Impl:: TryCompare(const PrimExpr& x, int64_t val) { PrimExpr diff = this->VisitExpr(x); if (const auto* ptr = diff.as<IntImmNode>()) { if (ptr->value == val) { return kEQ; } else if (ptr->value > val) { return kGT; } else if (ptr->value < val) { return kLT; } } ConstIntBound dbound = analyzer_->const_int_bound(diff); if (dbound->min_value > val) { return kGT; } if (dbound->max_value < val) { return kLT; } if (dbound->min_value >= val) { return kGE; } if (dbound->max_value <= val) { return kLE; } if (val == 0) { ModularSet dmod = analyzer_->modular_set(diff); if (dmod->base != 0) { return kNE; } } return kUnknown; } void RewriteSimplifier::Impl:: Update(const Var& var, const PrimExpr& info, bool can_override) { if (!can_override) { auto it = var_map_.find(var); if (it != var_map_.end()) { CHECK(ExprDeepEqual()(it->second, info)) << "Trying to update var \'" << var << "\'" << " with a different value: " << "original=" << it->second << ", new=" << info; } } var_map_[var] = info; } PrimExpr RewriteSimplifier::Impl:: VisitExpr_(const AddNode* op) { PrimExpr ret = IRMutatorWithAnalyzer::VisitExpr_(op); op = ret.as<AddNode>(); PrimExpr const_res = TryConstFold<AddNode>(op->a, op->b); if (const_res.defined()) return const_res; // Pattern var to match any expression PVar<PrimExpr> x, y, z, b1, b2, s1, s2; // Pattern var match IntImm PVar<IntImm> c1, c2, c3; // Pattern var for lanes in broadcast and ramp PVar<int> lanes; // Vector rules if (op->dtype.lanes() != 1) { TVM_TRY_REWRITE(ramp(b1, s1, lanes) + ramp(b2, s2, lanes), ramp(b1 + b2, s1 + s2, lanes)); TVM_TRY_REWRITE(ramp(b1, s1, lanes) + broadcast(x, lanes), ramp(b1 + x, s1, lanes)); TVM_TRY_REWRITE(broadcast(x, lanes) + ramp(b1, s1, lanes), ramp(x + b1, s1, lanes)); TVM_TRY_REWRITE(broadcast(x, lanes) + broadcast(y, lanes), broadcast(x + y, lanes)); } if (IsIndexType(op->dtype)) { // Index rules // cancelation rules TVM_TRY_REWRITE((x - y) + y, x); TVM_TRY_REWRITE(x + (y - x), y); TVM_TRY_REWRITE((x - y) + (y - z), x - z); TVM_TRY_REWRITE((x - y) + (z - x), z - y); TVM_TRY_REWRITE(min(x, y - z) + z, min(x + z, y)); TVM_TRY_REWRITE(min(x - z, y) + z, min(x, y + z)); TVM_TRY_REWRITE(max(x, y - z) + z, max(x + z, y)); TVM_TRY_REWRITE(max(x - z, y) + z, max(x, y + z)); TVM_TRY_REWRITE_IF(min(x, y + z * c1) + z * c2, min(x + z * c2, y), c1.Eval()->value == -c2.Eval()->value); TVM_TRY_REWRITE_IF(max(x, y + z * c1) + z * c2, max(x + z * c2, y), c1.Eval()->value == -c2.Eval()->value); TVM_TRY_REWRITE_IF(min(y + z * c1, x) + z * c2, min(x + z * c2, y), c1.Eval()->value == -c2.Eval()->value); TVM_TRY_REWRITE_IF(max(y + z * c1, x) + z * c2, max(x + z * c2, y), c1.Eval()->value == -c2.Eval()->value); TVM_TRY_REWRITE(max(x, y) + min(x, y), x + y); TVM_TRY_REWRITE(min(x, y) + max(x, y), x + y); TVM_TRY_REWRITE(max(x, y) + min(y, x), x + y); TVM_TRY_REWRITE(min(x, y) + max(y, x), x + y); TVM_TRY_REWRITE_IF(min(x, y + c1) + c2, min(x + c2, y), c1.Eval()->value == -c2.Eval()->value); TVM_TRY_REWRITE_IF(min(x + c1, y) + c2, min(x, y + c2), c1.Eval()->value == -c2.Eval()->value); TVM_TRY_REWRITE_IF(max(x, y + c1) + c2, max(x + c2, y), c1.Eval()->value == -c2.Eval()->value); TVM_TRY_REWRITE_IF(max(x + c1, y) + c2, max(x, y + c2), c1.Eval()->value == -c2.Eval()->value); // constant folding // NOTE: canonicalization might better at this. TVM_TRY_REWRITE((x + c1) + c2, x + (c1 + c2)); // mul co-efficient folding TVM_TRY_REWRITE(x + x, x * 2); TVM_TRY_REWRITE(x * y + x, x * (y + 1)); TVM_TRY_REWRITE(y * x + x, x * (y + 1)); TVM_TRY_REWRITE(x + y * x, x * (1 + y)); TVM_TRY_REWRITE(x + x * y, x * (1 + y)); TVM_TRY_REWRITE(x * y + x * z, x * (y + z)); TVM_TRY_REWRITE(y * x + x * z, x * (y + z)); TVM_TRY_REWRITE(x * y + z * x, x * (y + z)); TVM_TRY_REWRITE(y * x + z * x, x * (y + z)); // DivMod rules // truc div TVM_TRY_REWRITE(truncdiv(x, c1) * c1 + truncmod(x, c1), x); // floor div TVM_TRY_REWRITE(floordiv(x, c1) * c1 + floormod(x, c1), x); // canonicalization rule // will try rewrite again after canonicalization. TVM_TRY_RECURSIVE_REWRITE(x + (c1 - y), (x - y) + c1); TVM_TRY_RECURSIVE_REWRITE(x + c1 + y, (x + y) + c1); TVM_TRY_RECURSIVE_REWRITE(x + (c1 + y), (x + 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); // DivMod rules // truc div TVM_TRY_RECURSIVE_REWRITE(truncmod(y, c1) + x * c1, x * c1 + truncmod(y, c1)); // floor div TVM_TRY_RECURSIVE_REWRITE(floormod(y, c1) + x * c1, x * c1 + floormod(y, c1)); } // condition rules. TVM_TRY_REWRITE(select(x, b1, b2) + select(x, s1, s2), select(x, b1 + s1, b2 + s2)); // default value return ret; } std::function<void()> RewriteSimplifier::Impl::EnterConstraint(const PrimExpr& constraint) { size_t old_literal_size = literal_constraints_.size(); literal_constraints_.push_back(constraint); size_t new_literal_size = literal_constraints_.size(); auto frecover = [old_literal_size, new_literal_size, this]() { CHECK_EQ(literal_constraints_.size(), new_literal_size); literal_constraints_.resize(old_literal_size); }; return frecover; } PrimExpr RewriteSimplifier::Impl:: VisitExpr_(const SubNode* op) { PrimExpr ret = IRMutatorWithAnalyzer::VisitExpr_(op); op = ret.as<SubNode>(); PrimExpr const_res = TryConstFold<SubNode>(op->a, op->b); if (const_res.defined()) return const_res; // Pattern var to match any expression PVar<PrimExpr> x, y, z, b1, b2, s1, s2; // Pattern var match IntImm PVar<IntImm> c1, c2, c3; // Pattern var for lanes in broadcast and ramp PVar<int> lanes; // Vector rules if (op->dtype.lanes() != 1) { TVM_TRY_REWRITE(ramp(b1, s1, lanes) - ramp(b2, s2, lanes), ramp(b1 - b2, s1 - s2, lanes)); TVM_TRY_REWRITE(ramp(b1, s1, lanes) - broadcast(x, lanes), ramp(b1 - x, s1, lanes)); TVM_TRY_REWRITE(broadcast(x, lanes) - ramp(b1, s1, lanes), ramp(x - b1, 0 - s1, lanes)); TVM_TRY_REWRITE(broadcast(x, lanes) - broadcast(y, lanes), broadcast(x - y, lanes)); } if (IsIndexType(op->dtype)) { // Index rules // cancelation rules TVM_TRY_REWRITE((x + y) - y, x); TVM_TRY_REWRITE((x + y) - x, y); TVM_TRY_REWRITE(x - (y + x), 0 - y); TVM_TRY_REWRITE(x - (x + y), 0 - y); TVM_TRY_REWRITE(min(x, y) - x, min(0, y - x)); TVM_TRY_REWRITE(min(x, y) - y, min(x - y, 0)); TVM_TRY_REWRITE(max(x, y) - x, max(0, y - x)); TVM_TRY_REWRITE(max(x, y) - y, max(x - y, 0)); TVM_TRY_REWRITE(x - max(x, y), min(0, x - y)); TVM_TRY_REWRITE(y - max(x, y), min(y - x, 0)); TVM_TRY_REWRITE(x - min(x, y), max(0, x - y)); TVM_TRY_REWRITE(y - min(x, y), max(y - x, 0)); // mul co-efficient folding TVM_TRY_REWRITE(x - x, ZeroWithTypeLike(x)); TVM_TRY_REWRITE(x * y - x, x * (y - 1)); TVM_TRY_REWRITE(y * x - x, x * (y - 1)); TVM_TRY_REWRITE(x - y * x, x * (1 - y)); TVM_TRY_REWRITE(x - x * y, x * (1 - y)); TVM_TRY_REWRITE(x * y - x * z, x * (y - z)); TVM_TRY_REWRITE(y * x - x * z, x * (y - z)); TVM_TRY_REWRITE(x * y - z * x, x * (y - z)); TVM_TRY_REWRITE(y * x - z * x, x * (y - z)); // constant cancelation TVM_TRY_REWRITE((x + c1) - c2, x + (c1 - c2)); TVM_TRY_REWRITE((c1 - x) - (c2 - y), (y - x) + (c1 - c2)); // cancelization rule involving 4 operands TVM_TRY_REWRITE((x + y) - (x + z), y - z); TVM_TRY_REWRITE((x + y) - (z + x), y - z); TVM_TRY_REWRITE((y + x) - (z + x), y - z); TVM_TRY_REWRITE((y + x) - (x + z), y - z); TVM_TRY_REWRITE(min(x + y, z) - x, min(y, z - x)); TVM_TRY_REWRITE(min(y + x, z) - x, min(y, z - x)); TVM_TRY_REWRITE(min(z, x + y) - x, min(z - x, y)); TVM_TRY_REWRITE(min(z, y + x) - x, min(z - x, y)); TVM_TRY_REWRITE(max(x + y, z) - x, max(y, z - x)); TVM_TRY_REWRITE(max(y + x, z) - x, max(y, z - x)); TVM_TRY_REWRITE(max(z, x + y) - x, max(z - x, y)); TVM_TRY_REWRITE(max(z, y + x) - x, max(z - x, y)); TVM_TRY_REWRITE(x - min(x + y, z), max(0 - y, x - z)); TVM_TRY_REWRITE(x - min(y + x, z), max(0 - y, x - z)); TVM_TRY_REWRITE(x - min(z, x + y), max(x - z, 0 - y)); TVM_TRY_REWRITE(x - min(z, y + x), max(x - z, 0 - y)); TVM_TRY_REWRITE(min(x, y) - min(y, x), ZeroWithTypeLike(x)); TVM_TRY_REWRITE(max(x, y) - max(y, x), ZeroWithTypeLike(x)); TVM_TRY_REWRITE_IF(min(b1, b2) - min(s1, s2), b1 - s1, CanProveEqual(((b1 - s1) - (b2 - s2)).Eval(), 0)); TVM_TRY_REWRITE_IF(min(b1, b2) - min(s1, s2), b1 - s2, CanProveEqual(((b1 - s2) - (b2 - s1)).Eval(), 0)); TVM_TRY_REWRITE_IF(max(b1, b2) - max(s1, s2), b1 - s1, CanProveEqual(((b1 - s1) - (b2 - s2)).Eval(), 0)); TVM_TRY_REWRITE_IF(max(b1, b2) - max(s1, s2), b1 - s2, CanProveEqual(((b1 - s2) - (b2 - s1)).Eval(), 0)); // DivMod rules // trucdiv // NOTE: c*(x/c) + x % c == x is true all division mode. TVM_TRY_REWRITE_IF(x - truncdiv(x, c1) * c1, truncmod(x, c1), c1.Eval()->value != 0); TVM_TRY_REWRITE_IF(truncdiv(x, c1) * c1 - x, 0 - truncmod(x, c1), c1.Eval()->value != 0); TVM_TRY_REWRITE_IF(x - (truncdiv(x + y, c1)) * c1, truncmod(x + y, c1) - y, c1.Eval()->value != 0); TVM_TRY_REWRITE_IF((truncdiv(x + y, c1)) * c1 - x, y - truncmod(x + y, c1), c1.Eval()->value != 0); TVM_TRY_REWRITE_IF(x - truncdiv(x - y, c1) * c1, truncmod(x - y, c1) + y, c1.Eval()->value != 0); TVM_TRY_REWRITE_IF(truncdiv(x - y, c1) * c1 - x, 0 - truncmod(x - y, c1) - y, c1.Eval()->value != 0); TVM_TRY_REWRITE_IF(x * c2 - truncdiv(x, c1) * c3, truncmod(x, c1) * c2, c1.Eval()->value != 0 && c3.Eval()->value == c1.Eval()->value * c2.Eval()->value); TVM_TRY_REWRITE_IF(truncdiv(x, c1) * c3 - x * c2, 0 - truncmod(x, c1) * c2, c1.Eval()->value != 0 && c3.Eval()->value == c1.Eval()->value * c2.Eval()->value); TVM_TRY_REWRITE_IF(x * c2 - truncdiv(x + y, c1) * c3, (truncmod(x + y, c1) - y) * c2, c1.Eval()->value != 0 && c3.Eval()->value == c1.Eval()->value * c2.Eval()->value); TVM_TRY_REWRITE_IF(truncdiv(x + y, c1) * c3 - x * c2, (y - truncmod(x + y, c1)) * c2, c1.Eval()->value != 0 && c3.Eval()->value == c1.Eval()->value * c2.Eval()->value); TVM_TRY_REWRITE_IF(x * c2 - truncdiv(x - y, c1) * c3, (truncmod(x - y, c1) + y) * c2, c1.Eval()->value != 0 && c3.Eval()->value == c1.Eval()->value * c2.Eval()->value); TVM_TRY_REWRITE_IF(truncdiv(x - y, c1) * c3 - x * c2, (0 - truncmod(x - y, c1) - y) * c2, c1.Eval()->value != 0 && c3.Eval()->value == c1.Eval()->value * c2.Eval()->value); // Proof in the case of floordiv, need positive condition. // let x = a * c3 + r // (x + c1) / c3 - x / c3 => (r + c1) / c3 // NOTE: the use of floormod(c2, c3) was intentional to simplify the const. TVM_TRY_REWRITE_IF(truncdiv(x + c1, c3) - truncdiv(x + c2, c3), truncdiv(truncmod(x + floormod(c2, c3), c3) + (c1 - c2), c3), CanProveGreaterEqual(x.Eval(), -c2.Eval()->value) && c1.Eval()->value >= c2.Eval()->value && c3.Eval()->value > 0); TVM_TRY_REWRITE_IF(truncdiv(x + c1, c3) - truncdiv(x, c3), truncdiv(truncmod(x, c3) + c1, c3), CanProveGreaterEqual(x.Eval(), 0) && c1.Eval()->value >= 0 && c3.Eval()->value > 0); // floordiv TVM_TRY_REWRITE_IF(x - floordiv(x, c1) * c1, floormod(x, c1), c1.Eval()->value != 0); TVM_TRY_REWRITE_IF(floordiv(x, c1) * c1 - x, 0 - floormod(x, c1), c1.Eval()->value != 0); TVM_TRY_REWRITE_IF(x - floordiv(x + y, c1) * c1, floormod(x + y, c1) - y, c1.Eval()->value != 0); TVM_TRY_REWRITE_IF(floordiv(x + y, c1) * c1 - x, y - floormod(x + y, c1), c1.Eval()->value != 0); TVM_TRY_REWRITE_IF(x - floordiv(x - y, c1) * c1, floormod(x - y, c1) + y, c1.Eval()->value != 0); TVM_TRY_REWRITE_IF(floordiv(x - y, c1) * c1 - x, 0 - floormod(x - y, c1) - y, c1.Eval()->value != 0); TVM_TRY_REWRITE_IF(x * c2 - floordiv(x, c1) * c3, floormod(x, c1) * c2, c1.Eval()->value != 0 && c3.Eval()->value == c1.Eval()->value * c2.Eval()->value); TVM_TRY_REWRITE_IF(floordiv(x, c1) * c3 - x * c2, 0 - floormod(x, c1) * c2, c1.Eval()->value != 0 && c3.Eval()->value == c1.Eval()->value * c2.Eval()->value); TVM_TRY_REWRITE_IF(x * c2 - floordiv(x + y, c1) * c3, (floormod(x + y, c1) - y) * c2, c1.Eval()->value != 0 && c3.Eval()->value == c1.Eval()->value * c2.Eval()->value); TVM_TRY_REWRITE_IF(floordiv(x + y, c1) * c3 - x * c2, (y - floormod(x + y, c1)) * c2, c1.Eval()->value != 0 && c3.Eval()->value == c1.Eval()->value * c2.Eval()->value); TVM_TRY_REWRITE_IF(x * c2 - floordiv(x - y, c1) * c3, (floormod(x - y, c1) + y) * c2, c1.Eval()->value != 0 && c3.Eval()->value == c1.Eval()->value * c2.Eval()->value); TVM_TRY_REWRITE_IF(floordiv(x - y, c1) * c3 - x * c2, (0 - floormod(x - y, c1) - y) * c2, c1.Eval()->value != 0 && c3.Eval()->value == c1.Eval()->value * c2.Eval()->value); TVM_TRY_REWRITE_IF(floordiv(x + c1, c3) - floordiv(x + c2, c3), floordiv(floormod(x + floormod(c2, c3), c3) + (c1 - c2), c3), c3.Eval()->value > 0); TVM_TRY_REWRITE_IF(floordiv(x + c1, c3) - floordiv(x, c3), floordiv(floormod(x, c3) + c1, c3), c3.Eval()->value > 0); // canonicalization rule // will try rewrite again after canonicalization. TVM_TRY_REWRITE(x - c1, x + (0 - c1)); TVM_TRY_RECURSIVE_REWRITE((x + c1) - y, (x - y) + c1); TVM_TRY_RECURSIVE_REWRITE(x - (y - z), (x + z) - y); TVM_TRY_RECURSIVE_REWRITE(x - y * c1, x + y * (0 - c1)); } // condition rules. TVM_TRY_REWRITE(select(x, b1, b2) - select(x, s1, s2), select(x, b1 - s1, b2 - s2)); TVM_TRY_REWRITE(select(x, y, z) - z, select(x, y - z, ZeroWithTypeLike(z))); TVM_TRY_REWRITE(select(x, y, z) - y, select(x, ZeroWithTypeLike(y), z - y)); return ret; } PrimExpr RewriteSimplifier::Impl:: VisitExpr_(const MulNode* op) { PrimExpr ret = IRMutatorWithAnalyzer::VisitExpr_(op); op = ret.as<MulNode>(); PrimExpr const_res = TryConstFold<MulNode>(op->a, op->b); if (const_res.defined()) return const_res; // Pattern var to match any expression PVar<PrimExpr> x, y, z, b1, b2, s1, s2; // Pattern var match IntImm PVar<IntImm> c1, c2; // Pattern var for lanes in broadcast and ramp PVar<int> lanes; // Vector rules if (op->dtype.lanes() != 1) { TVM_TRY_REWRITE(broadcast(x, lanes) * broadcast(y, lanes), broadcast(x * y, lanes)); TVM_TRY_REWRITE(ramp(b1, s1, lanes) * broadcast(x, lanes), ramp(b1 * x, s1 * x, lanes)); TVM_TRY_REWRITE(broadcast(x, lanes) * ramp(b1, s1, lanes), ramp(b1 * x, s1 * x, lanes)); } if (IsIndexType(op->dtype)) { // constant simplification rule TVM_TRY_REWRITE((x + c1) * c2, x * c2 + c1 * c2); TVM_TRY_REWRITE((x * c1) * c2, x * (c1 * c2)); TVM_TRY_REWRITE(min(x, y) * max(x, y), x * y); TVM_TRY_REWRITE(max(x, y) * min(x, y), x * y); // canonicalization TVM_TRY_RECURSIVE_REWRITE(x * (c1 * y), (x * y) * c1); TVM_TRY_RECURSIVE_REWRITE(c1 * x, x * c1); TVM_TRY_RECURSIVE_REWRITE_IF( (x - y) * c1, (y - x) * (0 - c1), c1.Eval()->value < 0); } return ret; } PrimExpr RewriteSimplifier::Impl:: VisitExpr_(const DivNode* op) { PrimExpr ret = IRMutatorWithAnalyzer::VisitExpr_(op); op = ret.as<DivNode>(); PrimExpr const_res = TryConstFold<DivNode>(op->a, op->b); if (const_res.defined()) return const_res; // Pattern var to match any expression PVar<PrimExpr> x, y, z, b1; // Pattern var match IntImm PVar<IntImm> c1, c2, c3; // Pattern var for lanes in broadcast and ramp PVar<int> lanes; // x / 2.0 = x * 0.5 if (const FloatImmNode* ptr = op->b.as<FloatImmNode>()) { CHECK(op->dtype.is_float()); return op->a * make_const(op->b.dtype(), 1.0 / ptr->value); } // Vector rules if (op->dtype.lanes() != 1) { // NOTE: use div as the pattern also works for float. TVM_TRY_REWRITE(div(broadcast(x, lanes), broadcast(y, lanes)), broadcast(div(x, y), lanes)); // ramp / bcast if ((div(ramp(b1, c1, lanes), broadcast(c2, lanes))).Match(ret)) { int64_t c1val = c1.Eval()->value; int64_t c2val = c2.Eval()->value; if (c1val % c2val == 0) { return ramp(div(b1, c2), div(c1, c2), lanes).Eval(); } // If all possible indices in ramp are the same. if (CanProveGreaterEqual(b1.Eval(), 0)) { ModularSet bmod = analyzer_->modular_set(b1.Eval()); int64_t ramp_min = bmod->base / c2val; int64_t ramp_max = (bmod->base + (lanes.Eval() - 1) * c1val) / c2val; if (bmod->coeff % c2val == 0 && ramp_min == ramp_max) { return broadcast(div(b1, c2), lanes).Eval(); } } } } if (IsIndexType(op->dtype)) { // Be-aware of the division rules: // We adopt the default C division uses truncation instead of floordiv. // This means most rules need to check non-negativeness of the operands. // TryConstFold doesn't work for negative cases because it is also used by legacy // parts of tvm which still assume euclidean div. In this simplifier we assume that the division // is truncated, so perform const folding again. // NOTE: trunc div required if (truncdiv(c1, c2).Match(ret)) { int64_t c1val = c1.Eval()->value; int64_t c2val = c2.Eval()->value; return make_const(op->dtype, truncdiv(c1val, c2val)); } // while it is always true for trunc div // restrict to common case(positive div) TVM_TRY_REWRITE_IF(truncdiv(truncdiv(x, c1), c2), truncdiv(x, c1 * c2), c1.Eval()->value > 0 && c2.Eval()->value > 0); TVM_TRY_REWRITE_IF(truncdiv(truncdiv(x, c1) + c2, c3), truncdiv(x + c1 * c2, c1 * c3), c1.Eval()->value > 0 && c2.Eval()->value >= 0 && c3.Eval()->value > 0 && CanProveGreaterEqual(x.Eval(), 0)); if (truncdiv(x * c1, c2).Match(ret)) { int64_t c1val = c1.Eval()->value; int64_t c2val = c2.Eval()->value; if (c1val > 0 && c2val > 0) { if (c1val % c2val == 0) return (x * truncdiv(c1, c2)).Eval(); if (c2val % c1val == 0) return truncdiv(x, truncdiv(c2, c1)).Eval(); } } TVM_TRY_REWRITE(truncdiv(x, x), OneWithTypeLike(x)); TVM_TRY_REWRITE(truncdiv(x * c1, x), c1); TVM_TRY_REWRITE(truncdiv(c1 * x, x), c1); // Rules involving 2-operands. TVM_TRY_REWRITE_IF(truncdiv(x * c1 + y, c2), x * truncdiv(c1, c2) + truncdiv(y, c2), c1.Eval()->value >= 0 && c2.Eval()->value > 0 && c1.Eval()->value % c2.Eval()->value == 0 && CanProveGreaterEqual(x.Eval(), 0) && CanProveGreaterEqual(y.Eval(), 0)); TVM_TRY_REWRITE_IF(truncdiv(min(x * c1, y), c2), min(x * truncdiv(c1, c2), truncdiv(y, c2)), c1.Eval()->value >= 0 && c2.Eval()->value > 0 && c1.Eval()->value % c2.Eval()->value == 0 && CanProveGreaterEqual(x.Eval(), 0) && CanProveGreaterEqual(y.Eval(), 0)); TVM_TRY_REWRITE_IF(truncdiv(max(x * c1, y), c2), max(x * truncdiv(c1, c2), truncdiv(y, c2)), c1.Eval()->value >= 0 && c2.Eval()->value > 0 && c1.Eval()->value % c2.Eval()->value == 0 && CanProveGreaterEqual(x.Eval(), 0) && CanProveGreaterEqual(y.Eval(), 0)); TVM_TRY_REWRITE_IF(truncdiv(y + x * c1, c2), truncdiv(y, c2) + x * truncdiv(c1, c2), c1.Eval()->value >= 0 && c2.Eval()->value > 0 && c1.Eval()->value % c2.Eval()->value == 0 && CanProveGreaterEqual(x.Eval(), 0) && CanProveGreaterEqual(y.Eval(), 0)); TVM_TRY_REWRITE_IF(truncdiv(min(y, x * c1), c2), min(truncdiv(y, c2), x * truncdiv(c1, c2)), c1.Eval()->value >= 0 && c2.Eval()->value > 0 && c1.Eval()->value % c2.Eval()->value == 0 && CanProveGreaterEqual(x.Eval(), 0) && CanProveGreaterEqual(y.Eval(), 0)); TVM_TRY_REWRITE_IF(truncdiv(max(y, x * c1), c2), max(truncdiv(y, c2), x * truncdiv(c1, c2)), c1.Eval()->value >= 0 && c2.Eval()->value > 0 && c1.Eval()->value % c2.Eval()->value == 0 && CanProveGreaterEqual(x.Eval(), 0) && CanProveGreaterEqual(y.Eval(), 0)); // Rules involving 3-operands. TVM_TRY_REWRITE_IF(truncdiv(x * c1 + y + z, c2), x * truncdiv(c1, c2) + truncdiv(y + z, c2), c1.Eval()->value >= 0 && c2.Eval()->value > 0 && c1.Eval()->value % c2.Eval()->value == 0 && CanProveGreaterEqual(x.Eval(), 0) && CanProveGreaterEqual((y + z).Eval(), 0)); TVM_TRY_REWRITE_IF(truncdiv(x * c1 - y + z, c2), x * truncdiv(c1, c2) + truncdiv(z - y, c2), c1.Eval()->value >= 0 && c2.Eval()->value > 0 && c1.Eval()->value % c2.Eval()->value == 0 && CanProveGreaterEqual(x.Eval(), 0) && CanProveGreaterEqual((z - y).Eval(), 0)); TVM_TRY_REWRITE_IF(truncdiv(x * c1 + y - z, c2), x * truncdiv(c1, c2) + truncdiv(y - z, c2), c1.Eval()->value >= 0 && c2.Eval()->value > 0 && c1.Eval()->value % c2.Eval()->value == 0 && CanProveGreaterEqual(x.Eval(), 0) && CanProveGreaterEqual((y - z).Eval(), 0)); TVM_TRY_REWRITE_IF(truncdiv(y + x * c1 + z, c2), x * truncdiv(c1, c2) + truncdiv(y + z, c2), c1.Eval()->value > 0 && c2.Eval()->value > 0 && c1.Eval()->value % c2.Eval()->value == 0 && CanProveGreaterEqual(x.Eval(), 0) && CanProveGreaterEqual((y + z).Eval(), 0)); TVM_TRY_REWRITE_IF(truncdiv(x + c1, c2), truncdiv(x, c2) + truncdiv(c1, c2), c1.Eval()->value > 0 && c2.Eval()->value > 0 && c1.Eval()->value % c2.Eval()->value == 0 && CanProveGreaterEqual(x.Eval(), 0)); TVM_TRY_REWRITE_IF(truncdiv(x + y, x), truncdiv(y, x) + 1, CanProveGreaterEqual(x.Eval(), 0) && CanProveGreaterEqual(y.Eval(), 0)); TVM_TRY_REWRITE_IF(truncdiv(y + x, x), truncdiv(y, x) + 1, CanProveGreaterEqual(x.Eval(), 0) && CanProveGreaterEqual(y.Eval(), 0)); TVM_TRY_REWRITE_IF(truncdiv((x + y) + z, x), truncdiv(y + z, x) + 1, CanProveGreaterEqual(x.Eval(), 0) && CanProveGreaterEqual((y + z).Eval(), 0)); TVM_TRY_REWRITE_IF(truncdiv((y + x) + z, x), truncdiv(y + z, x) + 1, CanProveGreaterEqual(x.Eval(), 0) && CanProveGreaterEqual((y + z).Eval(), 0)); TVM_TRY_REWRITE_IF(truncdiv(y + (z + x), x), truncdiv(y + z, x) + 1, CanProveGreaterEqual(x.Eval(), 0) && CanProveGreaterEqual((y + z).Eval(), 0)); TVM_TRY_REWRITE_IF(truncdiv(y + (x + z), x), truncdiv(y + z, x) + 1, CanProveGreaterEqual(x.Eval(), 0) && CanProveGreaterEqual((y + z).Eval(), 0)); TVM_TRY_REWRITE_IF(truncdiv(x * y, y), x, CanProveGreaterEqual(x.Eval(), 0) && CanProveGreaterEqual(y.Eval(), 0)); TVM_TRY_REWRITE_IF(truncdiv(y * x, y), x, CanProveGreaterEqual(x.Eval(), 0) && CanProveGreaterEqual(y.Eval(), 0)); TVM_TRY_REWRITE_IF(truncdiv(x * z + y, z), x + truncdiv(y, z), CanProveGreaterEqual(x.Eval(), 0) && CanProveGreaterEqual(y.Eval(), 0) && CanProveGreaterEqual(z.Eval(), 0)); TVM_TRY_REWRITE_IF(truncdiv(z * x + y, z), x + truncdiv(y, z), CanProveGreaterEqual(x.Eval(), 0) && CanProveGreaterEqual(y.Eval(), 0) && CanProveGreaterEqual(z.Eval(), 0)); TVM_TRY_REWRITE_IF(truncdiv(y + x * z, z), truncdiv(y, z) + x, CanProveGreaterEqual(x.Eval(), 0) && CanProveGreaterEqual(y.Eval(), 0) && CanProveGreaterEqual(z.Eval(), 0)); TVM_TRY_REWRITE_IF(truncdiv(y + z * x, z), truncdiv(y, z) + x, CanProveGreaterEqual(x.Eval(), 0) && CanProveGreaterEqual(y.Eval(), 0) && CanProveGreaterEqual(z.Eval(), 0)); } return ret; } PrimExpr RewriteSimplifier::Impl:: VisitExpr_(const ModNode* op) { PrimExpr ret = IRMutatorWithAnalyzer::VisitExpr_(op); op = ret.as<ModNode>(); PrimExpr const_res = TryConstFold<ModNode>(op->a, op->b); if (const_res.defined()) return const_res; // Pattern var to match any expression PVar<PrimExpr> x, y, z, b1; // Pattern var match IntImm PVar<IntImm> c1, c2; // Pattern var for lanes in broadcast and ramp PVar<int> lanes; // Vector rules if (op->dtype.lanes() != 1) { TVM_TRY_REWRITE(truncmod(broadcast(x, lanes), broadcast(y, lanes)), broadcast(truncmod(x, y), lanes)); // ramp % bcast if (truncmod(ramp(b1, c1, lanes), broadcast(c2, lanes)).Match(ret)) { int64_t c1val = c1.Eval()->value; int64_t c2val = c2.Eval()->value; if (c1val % c2val == 0) { return broadcast(truncmod(b1, c2), lanes).Eval(); } // If all possible indices in ramp are the same. if (CanProveGreaterEqual(b1.Eval(), 0)) { ModularSet bmod = analyzer_->modular_set(b1.Eval()); int64_t ramp_min = bmod->base / c2val; int64_t ramp_max = (bmod->base + (lanes.Eval() - 1) * c1val) / c2val; if (bmod->coeff % c2val == 0) { if (ramp_min == ramp_max) { return ramp(truncmod(bmod->base, c2), c1, lanes).Eval(); } else { return truncmod(ramp(truncmod(bmod->base, c2), c1, lanes), broadcast(c2, lanes)).Eval(); } } } } } if (IsIndexType(op->dtype)) { // Be-aware of the division rules: // We adopt the default C division uses truncation instead of floordiv. // This means most rules need to check non-negativeness of the operands. TVM_TRY_REWRITE_IF(truncmod(x * c1, c2), ZeroWithTypeLike(x), c2.Eval()->value != 0 && c1.Eval()->value % c2.Eval()->value == 0); TVM_TRY_REWRITE_IF(truncmod(x * c1 + y, c2), truncmod(y, c2), c2.Eval()->value > 0 && c1.Eval()->value % c2.Eval()->value == 0 && CanProveGreaterEqual((x * c1).Eval(), 0) && CanProveGreaterEqual(y.Eval(), 0)); TVM_TRY_REWRITE_IF(truncmod(x + c1, c2), truncmod(x, c2), c2.Eval()->value > 0 && c1.Eval()->value >= 0 && c1.Eval()->value % c2.Eval()->value == 0 && CanProveGreaterEqual(x.Eval(), 0)); TVM_TRY_REWRITE_IF(truncmod(x + y * c1, c2), truncmod(x, c2), c2.Eval()->value > 0 && c1.Eval()->value % c2.Eval()->value == 0 && CanProveGreaterEqual(x.Eval(), 0) && CanProveGreaterEqual((y * c1).Eval(), 0)); // canonicalization: x % c == x % (-c) for truncated division // NOTE: trunc div required TVM_TRY_RECURSIVE_REWRITE_IF( truncmod(x, c1), truncmod(x, PConst<PrimExpr>(make_const(op->dtype, -c1.Eval()->value))), c1.Eval()->value < 0); // try modular analysis if (truncmod(x, c1).Match(ret)) { ModularSet mod = analyzer_->modular_set(x.Eval()); int64_t c1val = c1.Eval()->value; if (mod->coeff % c1val == 0 && c1val > 0 && CanProveGreaterEqual(x.Eval(), 0)) { return truncmod(mod->base, c1).Eval(); } } } return ret; } PrimExpr RewriteSimplifier::Impl:: VisitExpr_(const FloorDivNode* op) { PrimExpr ret = IRMutatorWithAnalyzer::VisitExpr_(op); op = ret.as<FloorDivNode>(); PrimExpr const_res = TryConstFold<FloorDivNode>(op->a, op->b); if (const_res.defined()) return const_res; // Pattern var to match any expression PVar<PrimExpr> x, y, z, b1; // Pattern var match IntImm PVar<IntImm> c1, c2, c3; // Pattern var for lanes in broadcast and ramp PVar<int> lanes; // Vector rules if (op->dtype.lanes() != 1) { TVM_TRY_REWRITE(floordiv(broadcast(x, lanes), broadcast(y, lanes)), broadcast(floordiv(x, y), lanes)); // ramp // bcast if (floordiv(ramp(b1, c1, lanes), broadcast(c2, lanes)).Match(ret)) { int64_t c1val = c1.Eval()->value; int64_t c2val = c2.Eval()->value; if (c1val % c2val == 0) { return ramp(floordiv(b1, c2), floordiv(c1, c2), lanes).Eval(); } // If all possible indices in ramp are the same. ModularSet bmod = analyzer_->modular_set(b1.Eval()); int64_t ramp_min = floordiv(bmod->base, c2val); int64_t ramp_max = floordiv(bmod->base + (lanes.Eval() - 1) * c1val, c2val); if (bmod->coeff % c2val == 0 && ramp_min == ramp_max) { return broadcast(floordiv(b1, c2), lanes).Eval(); } } } if (IsIndexType(op->dtype)) { // Be-aware of the division rules: this is floor division. TVM_TRY_REWRITE_IF(floordiv(floordiv(x, c1), c2), floordiv(x, c1 * c2), c1.Eval()->value > 0 && c2.Eval()->value > 0); TVM_TRY_REWRITE_IF(floordiv(floordiv(x, c1) + c2, c3), floordiv(x + c1 * c2, c1 * c3), c1.Eval()->value > 0 && c3.Eval()->value > 0); if (floordiv(x * c1, c2).Match(ret)) { int64_t c1val = c1.Eval()->value; int64_t c2val = c2.Eval()->value; if (c1val > 0 && c2val > 0) { if (c1val % c2val == 0) return (x * floordiv(c1, c2)).Eval(); if (c2val % c1val == 0) return floordiv(x, floordiv(c2, c1)).Eval(); } } TVM_TRY_REWRITE(floordiv(x, x), OneWithTypeLike(x)); TVM_TRY_REWRITE(floordiv(x * c1, x), c1); TVM_TRY_REWRITE(floordiv(c1 * x, x), c1); // Rules involving 2-operands. TVM_TRY_REWRITE_IF(floordiv(x * c1 + y, c2), x * floordiv(c1, c2) + floordiv(y, c2), c2.Eval()->value > 0 && c1.Eval()->value % c2.Eval()->value == 0); TVM_TRY_REWRITE_IF(floordiv(min(x * c1, y), c2), min(x * floordiv(c1, c2), floordiv(y, c2)), c2.Eval()->value > 0 && c1.Eval()->value % c2.Eval()->value == 0); TVM_TRY_REWRITE_IF(floordiv(max(x * c1, y), c2), max(x * floordiv(c1, c2), floordiv(y, c2)), c2.Eval()->value > 0 && c1.Eval()->value % c2.Eval()->value == 0); TVM_TRY_REWRITE_IF(floordiv(y + x * c1, c2), floordiv(y, c2) + x * floordiv(c1, c2), c2.Eval()->value > 0 && c1.Eval()->value % c2.Eval()->value == 0); TVM_TRY_REWRITE_IF(floordiv(min(y, x * c1), c2), min(floordiv(y, c2), x * floordiv(c1, c2)), c2.Eval()->value > 0 && c1.Eval()->value % c2.Eval()->value == 0); TVM_TRY_REWRITE_IF(floordiv(max(y, x * c1), c2), max(floordiv(y, c2), x * floordiv(c1, c2)), c2.Eval()->value > 0 && c1.Eval()->value % c2.Eval()->value == 0); // Rules involving 3-operands. TVM_TRY_REWRITE_IF(floordiv(x * c1 + y + z, c2), x * floordiv(c1, c2) + floordiv(y + z, c2), c2.Eval()->value > 0 && c1.Eval()->value % c2.Eval()->value == 0); TVM_TRY_REWRITE_IF(floordiv(x * c1 - y + z, c2), x * floordiv(c1, c2) + floordiv(z - y, c2), c2.Eval()->value > 0 && c1.Eval()->value % c2.Eval()->value == 0); TVM_TRY_REWRITE_IF(floordiv(x * c1 + y - z, c2), x * floordiv(c1, c2) + floordiv(y - z, c2), c2.Eval()->value > 0 && c1.Eval()->value % c2.Eval()->value == 0); TVM_TRY_REWRITE_IF(floordiv(y + x * c1 + z, c2), x * floordiv(c1, c2) + floordiv(y + z, c2), c2.Eval()->value > 0 && c1.Eval()->value % c2.Eval()->value == 0); TVM_TRY_REWRITE_IF(floordiv(x + c1, c2), floordiv(x, c2) + floordiv(c1, c2), c2.Eval()->value > 0 && c1.Eval()->value % c2.Eval()->value == 0); TVM_TRY_REWRITE_IF(floordiv(x + y, x), floordiv(y, x) + 1, CanProveGreaterEqual(x.Eval(), 0)); TVM_TRY_REWRITE_IF(floordiv(y + x, x), floordiv(y, x) + 1, CanProveGreaterEqual(x.Eval(), 0)); TVM_TRY_REWRITE_IF(floordiv((x + y) + z, x), floordiv(y + z, x) + 1, CanProveGreaterEqual(x.Eval(), 0)); TVM_TRY_REWRITE_IF(floordiv((y + x) + z, x), floordiv(y + z, x) + 1, CanProveGreaterEqual(x.Eval(), 0)); TVM_TRY_REWRITE_IF(floordiv(y + (z + x), x), floordiv(y + z, x) + 1, CanProveGreaterEqual(x.Eval(), 0)); TVM_TRY_REWRITE_IF(floordiv(y + (x + z), x), floordiv(y + z, x) + 1, CanProveGreaterEqual(x.Eval(), 0)); TVM_TRY_REWRITE_IF(floordiv(x * y, y), x, CanProveGreaterEqual(y.Eval(), 0)); TVM_TRY_REWRITE_IF(floordiv(y * x, y), x, CanProveGreaterEqual(y.Eval(), 0)); TVM_TRY_REWRITE_IF(floordiv(x * z + y, z), x + floordiv(y, z), CanProveGreaterEqual(z.Eval(), 0)); TVM_TRY_REWRITE_IF(floordiv(z * x + y, z), x + floordiv(y, z), CanProveGreaterEqual(z.Eval(), 0)); TVM_TRY_REWRITE_IF(floordiv(y + x * z, z), floordiv(y, z) + x, CanProveGreaterEqual(z.Eval(), 0)); TVM_TRY_REWRITE_IF(floordiv(y + z * x, z), floordiv(y, z) + x, CanProveGreaterEqual(z.Eval(), 0)); } return ret; } PrimExpr RewriteSimplifier::Impl:: VisitExpr_(const FloorModNode* op) { PrimExpr ret = IRMutatorWithAnalyzer::VisitExpr_(op); op = ret.as<FloorModNode>(); PrimExpr const_res = TryConstFold<FloorModNode>(op->a, op->b); if (const_res.defined()) return const_res; // Pattern var to match any expression PVar<PrimExpr> x, y, z, b1; // Pattern var match IntImm PVar<IntImm> c1, c2; // Pattern var for lanes in broadcast and ramp PVar<int> lanes; // Vector rules if (op->dtype.lanes() != 1) { TVM_TRY_REWRITE(floormod(broadcast(x, lanes), broadcast(y, lanes)), broadcast(floormod(x, y), lanes)); // floormod(ramp, bcast) if (floormod(ramp(b1, c1, lanes), broadcast(c2, lanes)).Match(ret)) { int64_t c1val = c1.Eval()->value; int64_t c2val = c2.Eval()->value; if (c1val % c2val == 0) { return broadcast(floormod(b1, c2), lanes).Eval(); } // If all possible indices in ramp are the same. ModularSet bmod = analyzer_->modular_set(b1.Eval()); int64_t ramp_min = floordiv(bmod->base, c2val); int64_t ramp_max = floordiv(bmod->base + (lanes.Eval() - 1) * c1val, c2val); if (bmod->coeff % c2val == 0) { if (ramp_min == ramp_max) { return ramp(floormod(bmod->base, c2), c1, lanes).Eval(); } else { return floormod(ramp(floormod(bmod->base, c2), c1, lanes), broadcast(c2, lanes)).Eval(); } } } } if (IsIndexType(op->dtype)) { // Be-aware of the division rules: we use floordiv/floormod here TVM_TRY_REWRITE_IF(floormod(x * c1, c2), ZeroWithTypeLike(x), c2.Eval()->value != 0 && c1.Eval()->value % c2.Eval()->value == 0); TVM_TRY_REWRITE_IF(floormod(x * c1 + y, c2), floormod(y, c2), c2.Eval()->value > 0 && c1.Eval()->value % c2.Eval()->value == 0); TVM_TRY_REWRITE_IF(floormod(x + c1, c2), floormod(x, c2), c2.Eval()->value > 0 && c1.Eval()->value % c2.Eval()->value == 0); TVM_TRY_REWRITE_IF(floormod(x + y * c1, c2), floormod(x, c2), c2.Eval()->value > 0 && c1.Eval()->value % c2.Eval()->value == 0); // try modular analysis if (floormod(x, c1).Match(ret)) { ModularSet mod = analyzer_->modular_set(x.Eval()); int64_t c1val = c1.Eval()->value; if (mod->coeff % c1val == 0 && c1val > 0) { return floormod(mod->base, c1).Eval(); } } } return ret; } PrimExpr RewriteSimplifier::Impl:: VisitExpr_(const MinNode* op) { PrimExpr ret = IRMutatorWithAnalyzer::VisitExpr_(op); op = ret.as<MinNode>(); PrimExpr const_res = TryConstFold<MinNode>(op->a, op->b); if (const_res.defined()) return const_res; // Pattern var to match any expression PVar<PrimExpr> x, y, z, s1, s2; // Pattern var match IntImm PVar<IntImm> c1, c2; PVar<int> lanes; // vector rule if (op->dtype.lanes() != 1) { TVM_TRY_REWRITE(min(broadcast(x, lanes), broadcast(y, lanes)), broadcast(min(x, y), lanes)); TVM_TRY_REWRITE(min(min(x, broadcast(y, lanes)), broadcast(z, lanes)), min(x, broadcast(min(y, z), lanes))); } if (IsIndexType(op->dtype)) { TVM_TRY_REWRITE(min(x, x), x); // constant int bound ConstIntBound a_bound = analyzer_->const_int_bound(op->a); ConstIntBound b_bound = analyzer_->const_int_bound(op->b); if (a_bound->max_value <= b_bound->min_value) { return op->a; } if (b_bound->max_value <= a_bound->min_value) { return op->b; } // constant comparison if (min(x + c1, x + c2).Match(ret)) { if (c1.Eval()->value < c2.Eval()->value) { return (x + c1).Eval(); } else { return (x + c2).Eval(); } } if (min(x + c1, x).Match(ret) || min(x, x + c1).Match(ret)) { if (c1.Eval()->value < 0) { return (x + c1).Eval(); } else { return x.Eval(); } } if (min(c1 - x, c2 - x).Match(ret)) { if (c1.Eval()->value < c2.Eval()->value) { return (c1 - x).Eval(); } else { return (c2 - x).Eval(); } } // DivMod rules // Divide up rounding: truc div // NOTE: trucdiv(x, y) >= floordiv(x, y) TVM_TRY_REWRITE_IF(min(truncdiv(x + c1, c2) * c2, x), x, c2.Eval()->value > 0 && c1.Eval()->value + 1 == c2.Eval()->value); TVM_TRY_REWRITE_IF(min(truncdiv(x + c1, c2) * c2, max(x, c2)), max(x, c2), c2.Eval()->value > 0 && c1.Eval()->value + 1 == c2.Eval()->value && CanProveGreaterEqual(x.Eval(), 0)); TVM_TRY_REWRITE_IF(min(x, truncdiv(x + c1, c2) * c2), x, c2.Eval()->value > 0 && c1.Eval()->value + 1 == c2.Eval()->value); TVM_TRY_REWRITE_IF(min(max(x, c2), truncdiv(x + c1, c2) * c2), max(x, c2), c2.Eval()->value > 0 && c1.Eval()->value + 1 == c2.Eval()->value && CanProveGreaterEqual(x.Eval(), 0)); // Divide up rounding: floor div TVM_TRY_REWRITE_IF(min(floordiv(x + c1, c2) * c2, x), x, c2.Eval()->value > 0 && c1.Eval()->value + 1 == c2.Eval()->value); TVM_TRY_REWRITE_IF(min(floordiv(x + c1, c2) * c2, max(x, c2)), max(x, c2), c2.Eval()->value > 0 && c1.Eval()->value + 1 == c2.Eval()->value); TVM_TRY_REWRITE_IF(min(x, floordiv(x + c1, c2) * c2), x, c2.Eval()->value > 0 && c1.Eval()->value + 1 == c2.Eval()->value); TVM_TRY_REWRITE_IF(min(max(x, c2), floordiv(x + c1, c2) * c2), max(x, c2), c2.Eval()->value > 0 && c1.Eval()->value + 1 == c2.Eval()->value); TVM_TRY_REWRITE_IF(min(x, floordiv(x, c2) * c2), floordiv(x, c2) * c2, c2.Eval()->value > 0); TVM_TRY_REWRITE_IF(min(floordiv(x, c2) * c2, x), floordiv(x, c2) * c2, c2.Eval()->value > 0); TVM_TRY_REWRITE(min(max(x, y), min(x, y)), min(x, y)); TVM_TRY_REWRITE(min(max(x, y), min(y, x)), min(x, y)); TVM_TRY_REWRITE(min(min(x, y), max(x, y)), min(x, y)); TVM_TRY_REWRITE(min(min(x, y), max(y, x)), min(x, y)); TVM_TRY_REWRITE(min(max(x, y), x), x); TVM_TRY_REWRITE(min(max(x, y), y), y); TVM_TRY_REWRITE(min(min(x, y), x), min(x, y)); TVM_TRY_REWRITE(min(min(x, y), y), min(x, y)); TVM_TRY_REWRITE(min(x, max(x, y)), x); TVM_TRY_REWRITE(min(y, max(x, y)), y); TVM_TRY_REWRITE(min(x, min(x, y)), min(x, y)); TVM_TRY_REWRITE(min(y, min(x, y)), min(x, y)); TVM_TRY_REWRITE(min(min(min(x, y), z), y), min(min(x, y), z)); TVM_TRY_REWRITE(min(min(min(min(x, y), z), s1), y), min(min(min(x, y), z), s1)); TVM_TRY_REWRITE(min(min(min(min(min(x, y), z), s1), s2), y), min(min(min(min(x, y), z), s1), s2)); TVM_TRY_REWRITE(min(max(x, y), max(x, z)), max(min(y, z), x)); TVM_TRY_REWRITE(min(max(x, y), max(z, x)), max(min(y, z), x)); TVM_TRY_REWRITE(min(max(y, x), max(x, z)), max(min(y, z), x)); TVM_TRY_REWRITE(min(max(y, x), max(z, x)), max(min(y, z), x)); TVM_TRY_REWRITE(min(min(x, y), min(x, z)), min(min(y, z), x)); TVM_TRY_REWRITE(min(min(x, y), min(z, x)), min(min(y, z), x)); TVM_TRY_REWRITE(min(min(y, x), min(x, z)), min(min(y, z), x)); TVM_TRY_REWRITE(min(min(y, x), min(z, x)), min(min(y, z), x)); TVM_TRY_REWRITE(min(y + x, z + x), min(y, z) + x); TVM_TRY_REWRITE(min(y + x, x + z), min(y, z) + x); TVM_TRY_REWRITE(min(x + y, x + z), min(y, z) + x); TVM_TRY_REWRITE(min(x + y, z + x), min(y, z) + x); // sub distribution TVM_TRY_REWRITE(min(y - x, z - x), min(y, z) - x); TVM_TRY_REWRITE(min(x - y, x - z), x - max(y, z)); // constant folding rule. TVM_TRY_REWRITE(min(min(x, c1), c2), min(x, min(c1, c2))); // scaling rule if (min(truncdiv(x, c1), truncdiv(y, c1)).Match(ret)) { if (c1.Eval()->value > 0) { return truncdiv(min(x, y), c1).Eval(); } else { return truncdiv(max(x, y), c1).Eval(); } } if (min(floordiv(x, c1), floordiv(y, c1)).Match(ret)) { if (c1.Eval()->value > 0) { return floordiv(min(x, y), c1).Eval(); } else { return floordiv(max(x, y), c1).Eval(); } } if (min(x * c1, y * c1).Match(ret)) { if (c1.Eval()->value > 0) { return (min(x, y) * c1).Eval(); } else { return (max(x, y) * c1).Eval(); } } if (min(x * c1, c2).Match(ret)) { int64_t c1val = c1.Eval()->value; int64_t c2val = c2.Eval()->value; if (c2val % c1val == 0) { if (c2val / c1val >= 0) { return (min(x, c2val / c1val) * c1val).Eval(); } else { return (max(x, c2val / c1val) * c1val).Eval(); } } } // canonicalization TVM_TRY_RECURSIVE_REWRITE(min(min(x, c1), y), min(min(x, y), c1)); TVM_TRY_RECURSIVE_REWRITE_IF( min(c1 - x, c2), c1 - max(x, c1 - c2), c2.Eval()->value != 0); } // condition rules. TVM_TRY_REWRITE(min(select(x, y, z), select(x, s1, s2)), select(x, min(y, s1), min(z, s2))); return ret; } PrimExpr RewriteSimplifier::Impl:: VisitExpr_(const MaxNode* op) { PrimExpr ret = IRMutatorWithAnalyzer::VisitExpr_(op); op = ret.as<MaxNode>(); PrimExpr const_res = TryConstFold<MaxNode>(op->a, op->b); if (const_res.defined()) return const_res; // Pattern var to match any expression PVar<PrimExpr> x, y, z, s1, s2; // Pattern var match IntImm PVar<IntImm> c1, c2; PVar<int> lanes; // vector rule if (op->dtype.lanes() != 1) { TVM_TRY_REWRITE(max(broadcast(x, lanes), broadcast(y, lanes)), broadcast(max(x, y), lanes)); TVM_TRY_REWRITE(max(max(x, broadcast(y, lanes)), broadcast(z, lanes)), max(x, broadcast(max(y, z), lanes))); } if (IsIndexType(op->dtype)) { TVM_TRY_REWRITE(max(x, x), x); // constant int bound ConstIntBound a_bound = analyzer_->const_int_bound(op->a); ConstIntBound b_bound = analyzer_->const_int_bound(op->b); if (a_bound->min_value >= b_bound->max_value) { return op->a; } if (b_bound->min_value >= a_bound->max_value) { return op->b; } // constant comparison if (max(x + c1, x + c2).Match(ret)) { if (c1.Eval()->value > c2.Eval()->value) { return (x + c1).Eval(); } else { return (x + c2).Eval(); } } if (max(x + c1, x).Match(ret) || max(x, x + c1).Match(ret)) { if (c1.Eval()->value > 0) { return (x + c1).Eval(); } else { return x.Eval(); } } if (max(c1 - x, c2 - x).Match(ret)) { if (c1.Eval()->value > c2.Eval()->value) { return (c1 - x).Eval(); } else { return (c2 - x).Eval(); } } // DivMod rules // Divide up rounding: truc div // NOTE: trucdiv(x, y) >= floordiv(x, y) TVM_TRY_REWRITE_IF(max(truncdiv(x + c1, c2) * c2, x), truncdiv(x + c1, c2) * c2, c2.Eval()->value > 0 && c1.Eval()->value + 1 == c2.Eval()->value); TVM_TRY_REWRITE_IF(max(x, truncdiv(x + c1, c2) * c2), truncdiv(x + c1, c2) * c2, c2.Eval()->value > 0 && c1.Eval()->value + 1 == c2.Eval()->value); // Divide up rounding: floor div TVM_TRY_REWRITE_IF(max(floordiv(x + c1, c2) * c2, x), floordiv(x + c1, c2) * c2, c2.Eval()->value > 0 && c1.Eval()->value + 1 == c2.Eval()->value); TVM_TRY_REWRITE_IF(max(x, floordiv(x + c1, c2) * c2), floordiv(x + c1, c2) * c2, c2.Eval()->value > 0 && c1.Eval()->value + 1 == c2.Eval()->value); TVM_TRY_REWRITE_IF(max(floordiv(x, c2) * c2, x), x, c2.Eval()->value > 0); TVM_TRY_REWRITE_IF(max(x, floordiv(x, c2) * c2), x, c2.Eval()->value > 0); TVM_TRY_REWRITE(max(min(x, y), max(x, y)), max(x, y)); TVM_TRY_REWRITE(max(min(x, y), max(y, x)), max(x, y)); TVM_TRY_REWRITE(max(max(x, y), min(x, y)), max(x, y)); TVM_TRY_REWRITE(max(max(x, y), min(y, x)), max(x, y)); TVM_TRY_REWRITE(max(min(x, y), x), x); TVM_TRY_REWRITE(max(min(x, y), y), y); TVM_TRY_REWRITE(max(max(x, y), x), max(x, y)); TVM_TRY_REWRITE(max(max(x, y), y), max(x, y)); TVM_TRY_REWRITE(max(x, min(x, y)), x); TVM_TRY_REWRITE(max(y, min(x, y)), y); TVM_TRY_REWRITE(max(x, max(x, y)), max(x, y)); TVM_TRY_REWRITE(max(y, max(x, y)), max(x, y)); TVM_TRY_REWRITE(max(max(max(x, y), z), y), max(max(x, y), z)); TVM_TRY_REWRITE(max(max(max(max(x, y), z), s1), y), max(max(max(x, y), z), s1)); TVM_TRY_REWRITE(max(max(max(max(max(x, y), z), s1), s2), y), max(max(max(max(x, y), z), s1), s2)); // max/max cancelation TVM_TRY_REWRITE(max(max(x, y), max(x, z)), max(max(y, z), x)); TVM_TRY_REWRITE(max(max(x, y), max(z, x)), max(max(y, z), x)); TVM_TRY_REWRITE(max(max(y, x), max(x, z)), max(max(y, z), x)); TVM_TRY_REWRITE(max(max(y, x), max(z, x)), max(max(y, z), x)); // max/min distribution TVM_TRY_REWRITE(max(min(x, y), min(x, z)), min(max(y, z), x)); TVM_TRY_REWRITE(max(min(x, y), min(z, x)), min(max(y, z), x)); TVM_TRY_REWRITE(max(min(y, x), min(x, z)), min(max(y, z), x)); TVM_TRY_REWRITE(max(min(y, x), min(z, x)), min(max(y, z), x)); // add distribution TVM_TRY_REWRITE(max(y + x, z + x), max(y, z) + x); TVM_TRY_REWRITE(max(y + x, x + z), max(y, z) + x); TVM_TRY_REWRITE(max(x + y, x + z), max(y, z) + x); TVM_TRY_REWRITE(max(x + y, z + x), max(y, z) + x); // sub distribution TVM_TRY_REWRITE(max(y - x, z - x), max(y, z) - x); TVM_TRY_REWRITE(max(x - y, x - z), x - min(y, z)); // constant folding rule. TVM_TRY_REWRITE(max(max(x, c1), c2), max(x, max(c1, c2))); // scaling rule if (max(truncdiv(x, c1), truncdiv(y, c1)).Match(ret)) { if (c1.Eval()->value > 0) { return truncdiv(max(x, y), c1).Eval(); } else { return truncdiv(min(x, y), c1).Eval(); } } if (max(floordiv(x, c1), floordiv(y, c1)).Match(ret)) { if (c1.Eval()->value > 0) { return floordiv(max(x, y), c1).Eval(); } else { return floordiv(min(x, y), c1).Eval(); } } if (max(x * c1, y * c1).Match(ret)) { if (c1.Eval()->value > 0) { return (max(x, y) * c1).Eval(); } else { return (min(x, y) * c1).Eval(); } } if (max(x * c1, c2).Match(ret)) { int64_t c1val = c1.Eval()->value; int64_t c2val = c2.Eval()->value; if (c2val % c1val == 0) { if (c2val / c1val >= 0) { return (max(x, c2val / c1val) * c1val).Eval(); } else { return (min(x, c2val / c1val) * c1val).Eval(); } } } // canonicalization TVM_TRY_RECURSIVE_REWRITE(max(max(x, c1), y), max(max(x, y), c1)); TVM_TRY_RECURSIVE_REWRITE_IF( max(c1 - x, c2), c1 - min(x, c1 - c2), c2.Eval()->value != 0); } // condition rules. TVM_TRY_REWRITE(max(select(x, y, z), select(x, s1, s2)), select(x, max(y, s1), max(z, s2))); return ret; } PrimExpr RewriteSimplifier::Impl:: VisitExpr_(const EQNode* op) { PrimExpr ret = IRMutatorWithAnalyzer::VisitExpr_(op); op = ret.as<EQNode>(); PrimExpr const_res = TryConstFold<EQNode>(op->a, op->b); if (const_res.defined()) return const_res; // Pattern var to match any expression PVar<PrimExpr> x, y; // Pattern var match IntImm PVar<IntImm> c1; PVar<int> lanes; // vector rule if (op->dtype.lanes() != 1) { TVM_TRY_REWRITE(broadcast(x, lanes) == broadcast(y, lanes), broadcast(x == y, lanes)); } if (IsIndexType(op->a.dtype())) { CompareResult result = TryCompare(op->a - op->b, 0); if (result == kEQ) { return make_const(op->dtype, true); } else if (result == kNE || result == kGT || result == kLT) { return make_const(op->dtype, false); } TVM_TRY_REWRITE(x - c1 == 0, x == c1); TVM_TRY_REWRITE(c1 - x == 0, x == c1); TVM_TRY_REWRITE(x + c1 == 0, x == 0 - c1); TVM_TRY_REWRITE(x * y == 0, x == 0 || y == 0); } return ret; } PrimExpr RewriteSimplifier::Impl:: VisitExpr_(const NENode* op) { return this->VisitExpr(NotNode::make(op->a == op->b)); } PrimExpr RewriteSimplifier::Impl:: VisitExpr_(const LENode* op) { return this->VisitExpr(NotNode::make(op->b < op->a)); } PrimExpr RewriteSimplifier::Impl:: VisitExpr_(const GTNode* op) { return this->VisitExpr(op->b < op->a); } PrimExpr RewriteSimplifier::Impl:: VisitExpr_(const GENode* op) { return this->VisitExpr(NotNode::make(op->a < op->b)); } PrimExpr RewriteSimplifier::Impl:: VisitExpr_(const LTNode* op) { PrimExpr ret = IRMutatorWithAnalyzer::VisitExpr_(op); op = ret.as<LTNode>(); PrimExpr const_res = TryConstFold<LTNode>(op->a, op->b); if (const_res.defined()) return const_res; // Pattern var to match any expression PVar<PrimExpr> x, y, z, s1, s2; // Pattern var match IntImm PVar<IntImm> c1, c2; PVar<int> lanes; // vector rule if (op->dtype.lanes() != 1) { TVM_TRY_REWRITE(broadcast(x, lanes) < broadcast(y, lanes), broadcast(x < y, lanes)); TVM_TRY_REWRITE(ramp(x, s1, lanes) < ramp(y, s1, lanes), broadcast(x < y, lanes)); } if (IsIndexType(op->a.dtype())) { CompareResult result = TryCompare(op->a - op->b, 0); if (result == kLT) { return make_const(op->dtype, true); } if (result == kEQ || result == kGT || result == kGE) { return make_const(op->dtype, false); } TVM_TRY_REWRITE(x + y < x + z, y < z); TVM_TRY_REWRITE(x + y < z + x, y < z); TVM_TRY_REWRITE(y + x < x + z, y < z); TVM_TRY_REWRITE(y + x < z + x, y < z); TVM_TRY_REWRITE(y - x < z - x, y < z); TVM_TRY_REWRITE(x - y < x - z, z < y); TVM_TRY_REWRITE(x < x + z, 0 < z); TVM_TRY_REWRITE(x < z + x, 0 < z); TVM_TRY_REWRITE(x < x - z, z < 0); TVM_TRY_REWRITE(c1 < x + c2, c1 - c2 < x); TVM_TRY_REWRITE(c1 < c2 - x, x < c2 - c1); TVM_TRY_REWRITE_IF(x * c1 < y * c1, x < y, c1.Eval()->value > 0); TVM_TRY_REWRITE_IF(x * c1 < y * c1, y < x, c1.Eval()->value < 0); // constant cancelation: only need to make use of one mod // truc div TVM_TRY_REWRITE_IF(x * c2 < c1, x < truncdiv(c1 - 1, c2) + 1, c1.Eval()->value > 0 && c2.Eval()->value > 0); // NOTE: trunc div required TVM_TRY_REWRITE_IF(x * c2 < c1, x < truncdiv(c1, c2), c1.Eval()->value <= 0 && c2.Eval()->value > 0); // NOTE: trunc div required (euclidean is ok too, floored is not) TVM_TRY_REWRITE_IF(x * c2 < c1, truncdiv(c1 - 1, c2) - 1 < x, c1.Eval()->value > 0 && c2.Eval()->value < 0); // NOTE: trunc div required (floored is ok too, euclidean is not) TVM_TRY_REWRITE_IF(x * c2 < c1, truncdiv(c1, c2) < x, c1.Eval()->value <= 0 && c2.Eval()->value < 0); // NOTE: trunc div required TVM_TRY_REWRITE_IF(c1 < x * c2, truncdiv(c1 + 1, c2) - 1 < x, c1.Eval()->value < 0 && c2.Eval()->value > 0); TVM_TRY_REWRITE_IF(c1 < x * c2, truncdiv(c1, c2) < x, c1.Eval()->value >= 0 && c2.Eval()->value > 0); // NOTE: trunc div required (floored is ok too, euclidean is not) TVM_TRY_REWRITE_IF(c1 < x * c2, x < truncdiv(c1 + 1, c2) + 1, c1.Eval()->value < 0 && c2.Eval()->value < 0); // NOTE: trunc div required (euclidean is ok too, floored is not) TVM_TRY_REWRITE_IF(c1 < x * c2, x < truncdiv(c1, c2), c1.Eval()->value >= 0 && c2.Eval()->value < 0); // DivMod rules // trucdiv TVM_TRY_REWRITE_IF(truncdiv(x, c1) < c2, x < c1 * c2, c1.Eval()->value > 0 && c2.Eval()->value > 0); // NOTE: trunc div required TVM_TRY_REWRITE_IF(truncdiv(x, c1) < c2, x < c1 * (c2 - 1) + 1, c1.Eval()->value > 0 && c2.Eval()->value <= 0); TVM_TRY_REWRITE_IF(c1 < truncdiv(x, c2), (c1 + 1) * c2 - 1 < x, c1.Eval()->value >= 0 && c2.Eval()->value > 0); // NOTE: trunc div required TVM_TRY_REWRITE_IF(c1 < truncdiv(x, c2), c1 * c2 < x, c1.Eval()->value < 0 && c2.Eval()->value > 0); // invariance for any div mod: x - (x / c1) * c1 == x % c1 TVM_TRY_REWRITE_IF(truncdiv(x, c1) * c1 < x, 0 < truncmod(x, c1), c1.Eval()->value > 0); TVM_TRY_REWRITE_IF(truncdiv(x, c1) * c1 < x + y, 0 < truncmod(x, c1) + y, c1.Eval()->value > 0); TVM_TRY_REWRITE_IF(truncdiv(x, c1) * c1 < x - y, y < truncmod(x, c1), c1.Eval()->value > 0); TVM_TRY_REWRITE_IF(truncdiv(x + c2, c1) * c1 < x, c2 < truncmod(x + c2, c1), c1.Eval()->value > 0); TVM_TRY_REWRITE_IF(truncdiv(x + c2, c1) * c1 < x + y, c2 < truncmod(x + c2, c1) + y, c1.Eval()->value > 0); TVM_TRY_REWRITE_IF(truncdiv(x + c2, c1) * c1 < x - y, y < truncmod(x + c2, c1) + (0 - c2), c1.Eval()->value > 0); // floordiv TVM_TRY_REWRITE_IF(floordiv(x, c1) < c2, x < c1 * c2, c1.Eval()->value > 0); TVM_TRY_REWRITE_IF(c1 < floordiv(x, c2), (c1 + 1) * c2 - 1 < x, c2.Eval()->value > 0); TVM_TRY_REWRITE_IF(floordiv(x, c1) * c1 < x, 0 < floormod(x, c1), c1.Eval()->value > 0); TVM_TRY_REWRITE_IF(floordiv(x, c1) * c1 < x + y, 0 < floormod(x, c1) + y, c1.Eval()->value > 0); TVM_TRY_REWRITE_IF(floordiv(x, c1) * c1 < x - y, y < floormod(x, c1), c1.Eval()->value > 0); TVM_TRY_REWRITE_IF(floordiv(x + c2, c1) * c1 < x, c2 < floormod(x + c2, c1), c1.Eval()->value > 0); TVM_TRY_REWRITE_IF(floordiv(x + c2, c1) * c1 < x + y, c2 < floormod(x + c2, c1) + y, c1.Eval()->value > 0); TVM_TRY_REWRITE_IF(floordiv(x + c2, c1) * c1 < x - y, y < floormod(x + c2, c1) + (0 - c2), c1.Eval()->value > 0); // canonicalization rule TVM_TRY_RECURSIVE_REWRITE(min(x, y) < z, x < z || y < z); TVM_TRY_RECURSIVE_REWRITE(max(x, y) < z, x < z && y < z); TVM_TRY_RECURSIVE_REWRITE(z < min(x, y), z < x && z < y); TVM_TRY_RECURSIVE_REWRITE(z < max(x, y), z < x || z < y); TVM_TRY_RECURSIVE_REWRITE(x < c1 - y, x + y < c1); TVM_TRY_RECURSIVE_REWRITE(x < c1 + y, x - y < c1); TVM_TRY_RECURSIVE_REWRITE(c1 - y < x, c1 < x + y); TVM_TRY_RECURSIVE_REWRITE(c1 + y < x, c1 < x - y); TVM_TRY_RECURSIVE_REWRITE(x + c1 < c2, x < c2 - c1); TVM_TRY_RECURSIVE_REWRITE(x - c1 < c2, x < c2 + c1); TVM_TRY_REWRITE(x - c1 < 0, x < c1); } return ret; } PrimExpr RewriteSimplifier::Impl:: VisitExpr_(const NotNode* op) { PrimExpr ret = IRMutatorWithAnalyzer::VisitExpr_(op); op = ret.as<NotNode>(); PrimExpr const_res = TryConstFold<NotNode>(op->a); if (const_res.defined()) return const_res; // Pattern var to match any expression PVar<PrimExpr> x, y; PVar<int> lanes; if (op->dtype.lanes() != 1) { TVM_TRY_REWRITE(!broadcast(x, lanes), broadcast(!x, lanes)); } TVM_TRY_REWRITE(!(!x), x); TVM_TRY_REWRITE(!(x <= y), y < x); TVM_TRY_REWRITE(!(x >= y), x < y); TVM_TRY_REWRITE(!(x < y), y <= x); TVM_TRY_REWRITE(!(x > y), x <= y); TVM_TRY_REWRITE(!(x == y), x != y); TVM_TRY_REWRITE(!(x != y), x == y); TVM_TRY_RECURSIVE_REWRITE(!(x || y), (!x) && (!y)); TVM_TRY_RECURSIVE_REWRITE(!(x && y), (!x) || (!y)); return ret; } PrimExpr RewriteSimplifier::Impl:: VisitExpr_(const AndNode* op) { PrimExpr ret = IRMutatorWithAnalyzer::VisitExpr_(op); op = ret.as<AndNode>(); PrimExpr const_res = TryConstFold<AndNode>(op->a, op->b); if (const_res.defined()) return const_res; // Pattern var to match any expression PVar<PrimExpr> x, y; // Pattern var match IntImm PVar<IntImm> c1, c2; PVar<int> lanes; if (op->dtype.lanes() != 1) { TVM_TRY_REWRITE(broadcast(x, lanes) && broadcast(y, lanes), broadcast(x && y, lanes)); } auto cfalse = PConst<PrimExpr>(make_const(op->dtype, false)); TVM_TRY_REWRITE(x == y && x != y, cfalse); TVM_TRY_REWRITE(x != y && x == y, cfalse); TVM_TRY_REWRITE(x && !x, cfalse); TVM_TRY_REWRITE(x <= y && y < x, cfalse); TVM_TRY_REWRITE(y < x && x <= y, cfalse); TVM_TRY_REWRITE_IF(x < c1 && c2 < x, cfalse, c2.Eval()->value + 1 >= c1.Eval()->value); TVM_TRY_REWRITE_IF(c2 < x && x < c1, cfalse, c2.Eval()->value + 1 >= c1.Eval()->value); TVM_TRY_REWRITE_IF(x < c1 && c2 <= x, cfalse, c2.Eval()->value >= c1.Eval()->value); TVM_TRY_REWRITE_IF(c2 <= x && x < c1, cfalse, c2.Eval()->value >= c1.Eval()->value); TVM_TRY_REWRITE_IF(x <= c1 && c2 < x, cfalse, c2.Eval()->value >= c1.Eval()->value); TVM_TRY_REWRITE_IF(c2 < x && x <= c1, cfalse, c2.Eval()->value >= c1.Eval()->value); TVM_TRY_REWRITE_IF(x <= c1 && c2 <= x, cfalse, c2.Eval()->value > c1.Eval()->value); TVM_TRY_REWRITE_IF(c2 <= x && x <= c1, cfalse, c2.Eval()->value > c1.Eval()->value); TVM_TRY_REWRITE(x == c1 && x != c2, x == c1 && c1 != c2); TVM_TRY_REWRITE(x != c2 && x == c1, x == c1 && c1 != c2); return ret; } PrimExpr RewriteSimplifier::Impl:: VisitExpr_(const OrNode* op) { PrimExpr ret = IRMutatorWithAnalyzer::VisitExpr_(op); op = ret.as<OrNode>(); PrimExpr const_res = TryConstFold<OrNode>(op->a, op->b); if (const_res.defined()) return const_res; // Pattern var to match any expression PVar<PrimExpr> x, y; // Pattern var match IntImm PVar<IntImm> c1, c2; PVar<int> lanes; if (op->dtype.lanes() != 1) { TVM_TRY_REWRITE(broadcast(x, lanes) || broadcast(y, lanes), broadcast(x || y, lanes)); } auto ctrue = PConst<PrimExpr>(make_const(op->dtype, true)); TVM_TRY_REWRITE(x == y || x != y, ctrue); TVM_TRY_REWRITE(x != y || x == y, ctrue); TVM_TRY_REWRITE(x || !x, ctrue); TVM_TRY_REWRITE(x <= y || y < x, ctrue); TVM_TRY_REWRITE(y < x || x <= y, ctrue); TVM_TRY_REWRITE_IF(x < c1 || c2 < x, ctrue, c2.Eval()->value < c1.Eval()->value); TVM_TRY_REWRITE_IF(c2 < x || x < c1, ctrue, c2.Eval()->value < c1.Eval()->value); TVM_TRY_REWRITE_IF(x <= c1 || c2 < x, ctrue, c2.Eval()->value <= c1.Eval()->value); TVM_TRY_REWRITE_IF(c2 < x || x <= c1, ctrue, c2.Eval()->value <= c1.Eval()->value); TVM_TRY_REWRITE_IF(x < c1 || c2 <= x, ctrue, c2.Eval()->value <= c1.Eval()->value); TVM_TRY_REWRITE_IF(c2 <= x || x < c1, ctrue, c2.Eval()->value <= c1.Eval()->value); TVM_TRY_REWRITE_IF(x <= c1 || c2 <= x, ctrue, c2.Eval()->value <= c1.Eval()->value + 1); TVM_TRY_REWRITE_IF(c2 <= x || x <= c1, ctrue, c2.Eval()->value <= c1.Eval()->value + 1); TVM_TRY_REWRITE(x != c1 || x == c2, x != c1 || c1 == c2); TVM_TRY_REWRITE(x == c2 || x != c1, x != c1 || c1 == c2); return ret; } PrimExpr RewriteSimplifier::Impl:: VisitExpr_(const SelectNode* op) { PrimExpr ret = IRMutatorWithAnalyzer::VisitExpr_(op); op = ret.as<SelectNode>(); if (op == nullptr) return ret; // Pattern var to match any expression PVar<PrimExpr> x, y; TVM_TRY_REWRITE(select(x, y, y), y); return ret; } PrimExpr RewriteSimplifier::Impl:: VisitExpr_(const CallNode* op) { // add condition context to if_then_else PrimExpr ret = IRMutatorWithAnalyzer::VisitExpr_(op); op = ret.as<CallNode>(); if (op == nullptr) return ret; if (op->is_intrinsic(CallNode::likely) && is_const(op->args[0])) { return op->args[0]; } else if (op->is_intrinsic(CallNode::shift_right)) { if (op->args[0].as<IntImmNode>() && op->args[1].as<IntImmNode>()) { // the operator overload will eagerly constant fold. return op->args[0] >> op->args[1]; } } else if (op->is_intrinsic(CallNode::bitwise_and)) { if (op->args[0].as<IntImmNode>() && op->args[1].as<IntImmNode>()) { // the operator overload will eagerly constant fold. return op->args[0] & op->args[1]; } } ExprDeepEqual expr_equal; if (op->is_intrinsic(CallNode::likely)) { for (const auto& constraint : literal_constraints_) { // Cases such as for (i, 0, bound) {if (likely(iter_var < bound)) { .. } } if (expr_equal(constraint, op->args[0])) { return make_const(op->dtype, true); } } } return ret; } PrimExpr RewriteSimplifier::Impl:: VisitExpr_(const VarNode* op) { Var var = GetRef<Var>(op); auto it = var_map_.find(var); if (it != var_map_.end()) { return it->second; } return GetRef<PrimExpr>(op); } PrimExpr RewriteSimplifier::Impl:: VisitExpr_(const CastNode* op) { PrimExpr ret = IRMutatorWithAnalyzer::VisitExpr_(op); op = ret.as<CastNode>(); return cast(op->dtype, op->value); } PrimExpr RewriteSimplifier::Impl:: VisitExpr_(const LetNode* op) { PrimExpr value = this->VisitExpr(op->value); if (!tir::HasSideEffect(value)) { // it is fine to discard the let binding // because the value will always be inlined in the simplifier. analyzer_->Bind(op->var, value); return this->VisitExpr(op->body); } PrimExpr body = this->VisitExpr(op->body); if (value.same_as(op->value) && body.same_as(op->body)) { return GetRef<PrimExpr>(op); } else { return LetNode::make(op->var, value, body); } } PrimExpr RewriteSimplifier::operator()(const PrimExpr& expr) { // Run simplification in post order PrimExpr res = expr; int max_iter = 2; for (int i = 0; i < max_iter; ++i) { PrimExpr new_expr = impl_->operator()(res); if (new_expr.same_as(res)) return res; res = new_expr; } return res; } void RewriteSimplifier::Update(const Var& var, const PrimExpr& info, bool override) { impl_->Update(var, info, override); } std::function<void()> RewriteSimplifier::EnterConstraint(const PrimExpr& constraint) { return impl_->EnterConstraint(constraint); } RewriteSimplifier::RewriteSimplifier(Analyzer* parent) : impl_(new Impl(parent)) { } RewriteSimplifier::~RewriteSimplifier() { delete impl_; } } // namespace arith } // namespace tvm