Google Git
Sign in
apache / tvm / HEAD / . / src / arith / rewrite_simplify.cc
blob: e333f85a327990c1287bd9f8efbfac42075c6288 [file] [log] [blame]
/*
* 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 "rewrite_simplify.h"
#include <tvm/arith/analyzer.h>
#include <tvm/tir/builtin.h>
#include <tvm/tir/op.h>
#include <algorithm>
#include <tuple>
#include <utility>
#include "../target/datatype/registry.h"
#include "conjunctive_normal_form.h"
#include "const_fold.h"
#include "constraint_extract.h"
#include "pattern_match.h"
#include "scalable_expression.h"
namespace tvm {
namespace arith {
using namespace tir;
TVM_FFI_STATIC_INIT_BLOCK() { RewriteSimplifierStatsNode::RegisterReflection(); }
// Note: When using matches_one_of or PMatchesOneOf alongside these
// macros, be careful which patterns are used in the ResExpr. While
// the different source expressions may be in terms of different PVar,
// the ResExpr should only contain patterns that are defined in
// *every* SrcExpr given.
//
// Allowed (replacement does not use either c1 or y):
// TVM_TRY_REWRITE(matches_one_of(x + c1 - c1, x + y - y), x)
//
// Forbidden (c3 undefined if the first pattern matches):
// TVM_TRY_REWRITE(matches_one_of(floormod(x*c1,c2), floormod(x*c1 + c3, c2)),
// floormod(x*floormod(c1,c2) + floormod(c3,c2), c2))
// macro for doing simple rewrite
#define TVM_TRY_REWRITE(SrcExpr, ResExpr) \
RecordAttemptedRewrite(); \
if ((SrcExpr).Match(ret)) { \
RecordRewrite(); \
return (ResExpr).Eval(); \
}
// macro for rewrite + recursively rewrite ResExpr
#define TVM_TRY_RECURSIVE_REWRITE(SrcExpr, ResExpr) \
RecordAttemptedRewrite(); \
if ((SrcExpr).Match(ret)) { \
RecordRewrite(); \
return RecursiveRewrite((ResExpr).Eval()); \
}
// macro rewrite only if CondExor is true after match.
#define TVM_TRY_REWRITE_IF(SrcExpr, ResExpr, CondExpr) \
RecordAttemptedRewrite(); \
if ((SrcExpr).Match(ret, [&]() { return (CondExpr); })) { \
RecordRewrite(); \
return (ResExpr).Eval(); \
}
// macro rewrite + recursive_rewrite only if CondExor is true after match.
#define TVM_TRY_RECURSIVE_REWRITE_IF(SrcExpr, ResExpr, CondExpr) \
RecordAttemptedRewrite(); \
if ((SrcExpr).Match(ret, [&]() { return (CondExpr); })) { \
RecordRewrite(); \
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.
//
/* Utility for rewriting only boolean portions of an expression
*
* Performs a subset of simplifications done by RewriteSimplifier,
* sufficient to negate a simplified expression. Intended for
* application on an expression that has previously been simplified.
*
* \param expr The boolean expression to be normalized
*
* \returns The normalized boolean expression
*/
PrimExpr NormalizeBooleanOperators(PrimExpr expr) {
PVar<PrimExpr> x, y;
while (true) {
if ((!!x).Match(expr)) {
expr = x.Eval();
} else if ((!(x || y)).Match(expr)) {
return NormalizeBooleanOperators(!x.Eval()) && NormalizeBooleanOperators(!y.Eval());
} else if ((!(x && y)).Match(expr)) {
return NormalizeBooleanOperators(!x.Eval()) || NormalizeBooleanOperators(!y.Eval());
} else if ((x >= y).Match(expr) || (!(x < y)).Match(expr) || (!(y > x)).Match(expr)) {
return y.Eval() <= x.Eval();
} else if ((x > y).Match(expr) || (!(x <= y)).Match(expr) || (!(y >= x)).Match(expr)) {
return y.Eval() < x.Eval();
} else if ((!(x == y)).Match(expr)) {
return x.Eval() != y.Eval();
} else if ((!(x != y)).Match(expr)) {
return x.Eval() == y.Eval();
} else {
return expr;
}
}
}
std::tuple<PrimExpr, int64_t> ExtractConstantOffset(const PrimExpr& expr) {
PVar<PrimExpr> x;
PVar<IntImm> c1;
// Any (c1+x) terms are normalized into (x+c1), so we don't need to
// check for it.
if ((x + c1).Match(expr)) {
return {x.Eval(), c1.Eval()->value};
} else if ((x - c1).Match(expr)) {
return {x.Eval(), -c1.Eval()->value};
} else if ((c1 - x).Match(expr)) {
return {x.Eval(), c1.Eval()->value};
} else {
return {expr, 0};
}
}
CompareResult RewriteSimplifier::Impl::TryCompare(const PrimExpr& x, const PrimExpr& y) {
CompareResult output = CompareResult::kUnknown;
auto is_finished = [&output]() {
return output == CompareResult::kEQ || output == CompareResult::kLT ||
output == CompareResult::kGT;
};
output = CompareResult(output & TryCompareUsingConstIntBounds(x, y));
if (is_finished()) return output;
output = CompareResult(output & TryCompareUsingKnownInequalities(x, y));
if (is_finished()) return output;
output = CompareResult(output & TryComparisonOfProductAndSum(x, y));
return output;
}
CompareResult RewriteSimplifier::Impl::TryCompareUsingConstIntBounds(const PrimExpr& x,
const PrimExpr y) {
return TryCompare(x - y, 0);
}
CompareResult RewriteSimplifier::Impl::TryCompareUsingKnownInequalities(const PrimExpr& x,
const PrimExpr& y) {
bool propagate_inequalities = enabled_extensions_ & kTransitivelyProveInequalities;
return analyzer_->transitive_comparisons.TryCompare(x, y, propagate_inequalities);
}
CompareResult RewriteSimplifier::Impl::TryComparisonOfProductAndSum(const PrimExpr& x,
const PrimExpr& y) {
bool check_comparison_of_product_and_sum = enabled_extensions_ & kComparisonOfProductAndSum;
if (!check_comparison_of_product_and_sum) {
return CompareResult::kUnknown;
}
auto opt_special_case =
[&]() -> std::optional<std::tuple<PrimExpr, PrimExpr, PrimExpr, PrimExpr>> {
// Match expressions of the form `(A+B)*C - (A*B)*D`. Depending on
// previous simplifications, the exact form of the expression may vary.
PVar<PrimExpr> A, B, C, D;
// diff is `(A+B)*C - (A*B)*D`.
PrimExpr diff = this->VisitExpr(x - y);
if (PMatchesOneOf{
(A + B) * C + (A * B) * D,
(A + B) * C + (B * A) * D,
(A * B) * D + (A + B) * C,
(B * A) * D + (A + B) * C,
}
.Match(diff)) {
return std::tuple{A.Eval(), B.Eval(), C.Eval(), -D.Eval()};
} else if (PMatchesOneOf{
(A + B) * C + (A * B),
(A + B) * C + (B * A),
(A * B) + (A + B) * C,
(B * A) + (A + B) * C,
}
.Match(diff)) {
return std::tuple{A.Eval(), B.Eval(), C.Eval(), Integer(-1)};
} else {
return std::nullopt;
}
}();
if (!opt_special_case.has_value()) {
return CompareResult::kUnknown;
}
auto [A, B, C, D] = *opt_special_case;
auto A_bound = analyzer_->const_int_bound(A);
auto B_bound = analyzer_->const_int_bound(B);
auto C_bound = analyzer_->const_int_bound(C);
auto D_bound = analyzer_->const_int_bound(D);
auto negate = [](ConstIntBound bound) {
return ConstIntBound(-bound->max_value, -bound->min_value);
};
auto is_negative = [](const ConstIntBound& bound) { return bound->max_value < 0; };
auto is_positive = [](const ConstIntBound& bound) { return bound->min_value > 0; };
// If D is negative, then we'll be providing an upper bound for
// `(A*B)*D`, rather than a lower bound. To avoid code duplication,
// flip all the signs here, find a lower bound, then flip the sign
// to produce the upper bound of the original expression.
//
// Before: (A+B)*C < (A*B)*D
// After: (A*B)*(-D) < (A + B)*(-C)
bool is_upper_bound = is_negative(D_bound);
if (is_upper_bound) {
C_bound = negate(C_bound);
D_bound = negate(D_bound);
}
// Before: (A+B)*C < (A*B)*D
// After: ((-A) + (-B))*(-C) < ((-A)*(-B))*D
if (is_negative(C_bound)) {
A_bound = negate(A_bound);
B_bound = negate(B_bound);
C_bound = negate(C_bound);
}
bool all_terms_positive = (is_positive(A_bound) && is_positive(B_bound) && is_positive(C_bound) &&
is_positive(D_bound));
if (!all_terms_positive) {
return CompareResult::kUnknown;
}
// (A + B) * C < (A * B) * D
// (A + B) * C / (A*B*C*D) < (A * B) * D / (A*B*C*D)
// 1/(A*D) + 1/(B*D) < 1/C
// (A*B*C*D) * ( (A+B)/(A*B*D) - 1/C )
// (A*B*C*D) * ( (1/A + 1/B)/D - 1/C )
// (A*B*C*D) * (1/(A*D) + 1/(B*D) - 1/C)
//
// The constant (A*B*C*D) is positive, and its minimum value is the
// product of the minimum values of A, B, C, and D. If the reciprocal
// term (1/(A*D) + 1/(B*D) - 1/C) is positive, then this constant can
// be used to provide a lower bound on the expression.
bool reciprocal_term_is_positive = [&]() {
if (D_bound->max_value == ConstIntBound::kPosInf) {
// If D can grow without bound, the `1/(A*D)` and `1/(B*D)`
// terms will approach zero, at which point the `-1/C` term
// will determine the sign the sign.
return false;
}
if (std::min(A_bound->max_value, B_bound->max_value) * D_bound->max_value <=
C_bound->min_value) {
// 1/(A*D) + 1/(B*D) - 1/C is positive if 1/C < 1/(A*D) + 1/(B*D).
// Since each term is positive, this condition can hold if either
// A*D <= C or B*D <= C.
return true;
}
if (A_bound->max_value != ConstIntBound::kPosInf &&
B_bound->max_value != ConstIntBound::kPosInf) {
// Even if neither term is sufficient on its own, if both A and B
// have known upper bounds, the inequality 1/C < 1/(A*D) + 1/(B*D)
// may still be provable.
//
// The maximum value of the LHS is found when C is minimized. The
// minimum value of the RHS is found when A, B, and D are
// maximized. If the condition holds in this case, then it holds
// in all cases.
//
// 1/C_min < 1/(A_max * D_max) + 1/(B_max*D_max)
// A_max*B_max*D_max < C_min*B_max + C_min*A_max
// A_max*B_max*D_max < C_min*(A_max + B_max)
//
if (A_bound->max_value * B_bound->max_value * D_bound->max_value <
C_bound->min_value * (A_bound->max_value + B_bound->max_value)) {
return true;
}
}
return false;
}();
if (!reciprocal_term_is_positive) {
return CompareResult::kUnknown;
}
if (is_upper_bound) {
// If we flipped the sign of the original expression, flip the sign of
// the resulting set of possible values.
return CompareResult::kLT;
} else {
return CompareResult::kGT;
}
}
// try to prove x equals val
CompareResult RewriteSimplifier::Impl::TryCompare(const PrimExpr& x, int64_t val) {
// NOTE on implementation: this function can be called many times and can be a bottleneck,
// As a result, we keep comparison here lightweight.
// We only do constant int bound analysis here.
//
// For stronger comparison proof that is out of the recursive simplifcation
// consider look at analyzer::CanProveStrong
PrimExpr diff = this->VisitExpr(x);
if (const auto* ptr = diff.as<IntImmNode>()) {
if (ptr->value == val) {
return CompareResult::kEQ;
} else if (ptr->value > val) {
return CompareResult::kGT;
} else if (ptr->value < val) {
return CompareResult::kLT;
}
}
ConstIntBound dbound = analyzer_->const_int_bound(diff);
if (dbound->min_value == val && dbound->max_value == val) {
return CompareResult::kEQ;
}
if (dbound->min_value > val) {
return CompareResult::kGT;
}
if (dbound->max_value < val) {
return CompareResult::kLT;
}
if (dbound->min_value >= val) {
return CompareResult::kGE;
}
if (dbound->max_value <= val) {
return CompareResult::kLE;
}
// modular analysis
if (val == 0) {
ModularSet dmod = analyzer_->modular_set(diff);
if (dmod->base != 0) {
return CompareResult::kNE;
}
}
return CompareResult::kUnknown;
}
PrimExpr RewriteSimplifier::Impl::VisitExpr(const PrimExpr& e) {
stats_.nodes_visited++;
return IRMutatorWithAnalyzer::VisitExpr(e);
}
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()) {
ICHECK(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>();
if (auto const_res = TryConstFold<Add>(op->a, op->b)) return const_res.value();
// 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 match FloatImm
PVar<FloatImm> c4;
// Pattern var for lanes in broadcast and ramp
PVar<PrimExpr> lanes;
// Vector rules
if (op->dtype.is_scalable_or_fixed_length_vector()) {
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));
TVM_TRY_REWRITE_IF(x + broadcast(c4, lanes), x, c4.Eval()->value == 0.0f);
}
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((PMatchesOneOf{
max(x, y) + min(x, y),
min(x, y) + max(x, y),
max(x, y) + min(y, x),
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(matches_one_of(x * y + x, y * x + x, x + y * x, x + x * y), (y + 1) * x);
TVM_TRY_REWRITE(matches_one_of(x * y + x * z, y * x + x * z, x * y + z * x, y * x + z * x),
(y + z) * x);
// DivMod rules
// truc div
TVM_TRY_REWRITE(truncdiv(x, c1) * c1 + truncmod(x, c1), x);
// floor div
TVM_TRY_REWRITE(
matches_one_of(floordiv(x, y) * y + floormod(x, y), y * floordiv(x, y) + floormod(x, y),
floormod(x, y) + floordiv(x, y) * y, floormod(x, y) + y * floordiv(x, y)),
x);
TVM_TRY_REWRITE_IF(floordiv(floormod(x, c2) + c1, c2) + floordiv(x, c2), floordiv(x + c1, c2),
c2.Eval()->value > 0);
TVM_TRY_RECURSIVE_REWRITE(floordiv(x, 2) + floormod(x, 2), floordiv(x + 1, 2));
// Simplify (x + 1) % 2 + x % 2 => 1
// NOTE: we should avoid simplifying (x + 1) %2 => 1 - x % 2 though
// mainly because introducing extra negative signs to expression can harm itertaor
// analysis which usually relies on positive itertator co-efficients.
TVM_TRY_REWRITE_IF(floormod(x + c1, 2) + floormod(x, 2), OneWithTypeLike(x),
floormod(c1.Eval()->value, 2) == 1);
TVM_TRY_REWRITE_IF(floormod(x, 2) + floormod(x + c1, 2), OneWithTypeLike(x),
floormod(c1.Eval()->value, 2) == 1);
// canonicalization rule
// will try rewrite again after canonicalization.
TVM_TRY_RECURSIVE_REWRITE(matches_one_of(x + (c1 - y), (c1 - y) + x), (x - y) + c1);
TVM_TRY_RECURSIVE_REWRITE(matches_one_of((x + c1) + y, x + (c1 + y), x + (y + c1)),
(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();
// we will compare the already simplified result with the constraint,
// so simplify the constraint as well
PrimExpr new_constraint = operator()(constraint);
for (const PrimExpr& subconstraint : ExtractConstraints(new_constraint, false)) {
if (SideEffect(subconstraint) <= CallEffectKind::kPure) {
literal_constraints_.push_back(subconstraint);
PrimExpr negation;
if (subconstraint.dtype().is_bool()) {
// We could apply NormalizeBooleanOperators during
// TryMatchLiteralConstraint, but that would require
// performing a rewrite of each expression being checked.
// This way, we only apply a rewrite for each constraint being
// applied.
negation = NormalizeBooleanOperators(Not(subconstraint));
} else {
negation = subconstraint == make_zero(subconstraint.dtype());
}
literal_constraints_.push_back(Not(negation));
}
}
stats_.constraints_entered++;
size_t new_literal_size = literal_constraints_.size();
auto frecover = [old_literal_size, new_literal_size, this]() {
ICHECK_EQ(literal_constraints_.size(), new_literal_size);
literal_constraints_.resize(old_literal_size);
};
return frecover;
}
void RewriteSimplifier::Impl::SetEnabledExtensions(Extension flags) { enabled_extensions_ = flags; }
RewriteSimplifier::Extension RewriteSimplifier::Impl::GetEnabledExtensions() const {
return enabled_extensions_;
}
PrimExpr RewriteSimplifier::Impl::VisitExpr_(const SubNode* op) {
PrimExpr ret = IRMutatorWithAnalyzer::VisitExpr_(op);
op = ret.as<SubNode>();
if (auto const_res = TryConstFold<Sub>(op->a, op->b)) return const_res.value();
// 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<PrimExpr> lanes;
// Vector rules
if (op->dtype.is_scalable_or_fixed_length_vector()) {
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(matches_one_of((x + y) - y, (y + x) - y), x);
TVM_TRY_REWRITE(matches_one_of(x - (y + x), x - (x + y)), 0 - y);
TVM_TRY_REWRITE(matches_one_of(min(x, y) - y, x - max(y, x)), min(x - y, 0));
TVM_TRY_REWRITE(matches_one_of(x - max(x, y), min(y, x) - y), min(0, x - y));
TVM_TRY_REWRITE(matches_one_of(max(x, y) - y, x - min(y, x)), max(x - y, 0));
TVM_TRY_REWRITE(matches_one_of(x - min(x, y), max(y, x) - y), max(0, x - y));
// mul co-efficient folding: pefer co-effiicent to stay at rhs
TVM_TRY_REWRITE(x - x, ZeroWithTypeLike(x));
TVM_TRY_REWRITE(matches_one_of(x * y - x, y * x - x), (y - 1) * x);
TVM_TRY_REWRITE(matches_one_of(x - y * x, x - x * y), (1 - y) * x);
TVM_TRY_REWRITE(matches_one_of(x * y - x * z, y * x - x * z, x * y - z * x, y * x - z * x),
(y - z) * x);
// 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(
matches_one_of((x + y) - (x + z), (x + y) - (z + x), (y + x) - (z + x), (y + x) - (x + z)),
y - z);
TVM_TRY_REWRITE(matches_one_of(min(x + y, z) - x, min(y + x, z) - x), min(y, z - x));
TVM_TRY_REWRITE(matches_one_of(min(z, x + y) - x, min(z, y + x) - x), min(z - x, y));
TVM_TRY_REWRITE(matches_one_of(max(x + y, z) - x, max(y + x, z) - x), max(y, z - x));
TVM_TRY_REWRITE(matches_one_of(max(z, x + y) - x, max(z, y + x) - x), max(z - x, y));
TVM_TRY_REWRITE(matches_one_of(x - min(x + y, z), x - min(y + x, z)), max(0 - y, x - z));
TVM_TRY_REWRITE(matches_one_of(x - min(z, x + y), x - min(z, y + x)), max(x - z, 0 - y));
TVM_TRY_REWRITE(matches_one_of(x - max(x + y, z), x - max(y + x, z)), min(0 - y, x - z));
TVM_TRY_REWRITE(matches_one_of(x - max(z, x + y), x - max(z, y + x)), min(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(matches_one_of(min(b1, b2) - min(s1, s2), min(b1, b2) - min(s2, s1)),
b1 - s1, CanProveEqual(((b1 - s1) - (b2 - s2)).Eval(), 0));
TVM_TRY_REWRITE_IF(matches_one_of(max(b1, b2) - max(s1, s2), max(b1, b2) - max(s2, s1)),
b1 - s1, CanProveEqual(((b1 - s1) - (b2 - s2)).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_RECURSIVE_REWRITE(
floordiv(x + c1, 2) - floordiv(x + c2, 2),
floormod(x, 2) * (floormod(c1, 2) - floormod(c2, 2)) + (floordiv(c1, 2) - floordiv(c2, 2)));
TVM_TRY_RECURSIVE_REWRITE(floordiv(x, 2) - floordiv(x + c2, 2),
floormod(x, 2) * (0 - floormod(c2, 2)) - floordiv(c2, 2));
TVM_TRY_RECURSIVE_REWRITE(floordiv(x + c1, 2) - floordiv(x, 2),
floormod(x, 2) * floormod(c1, 2) + floordiv(c1, 2));
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_RECURSIVE_REWRITE(floordiv(x + 1, 2) - floormod(x, 2), floordiv(x, 2));
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 + c1), (x - y) + (0 - c1));
TVM_TRY_RECURSIVE_REWRITE(x - (y - z), (x + z) - y);
TVM_TRY_RECURSIVE_REWRITE(x - y * c1, x + y * (0 - c1));
} else {
// Cancellation rules. Deliberately off of the integer path, to
// avoid introducing checks on the side effects for the fast path.
//
// These simplifications do not preserve NaN/Inf that may occur in
// the inputs. For IEEE floats, `NaN - NaN` is `NaN`, and does
// not cancel out. However, since models should not encounter NaN
// in the first place, this allows better simplification for the
// supported path.
TVM_TRY_REWRITE_IF(x - x, ZeroWithTypeLike(x),
SideEffect(x.Eval()) <= CallEffectKind::kReadState);
TVM_TRY_REWRITE_IF((x + y) - y, x, SideEffect(y.Eval()) <= CallEffectKind::kReadState);
TVM_TRY_REWRITE_IF((x + y) - x, y, SideEffect(x.Eval()) <= CallEffectKind::kReadState);
TVM_TRY_REWRITE_IF(x - (y + x), 0 - y, SideEffect(x.Eval()) <= CallEffectKind::kReadState);
TVM_TRY_REWRITE_IF(x - (x + y), 0 - y, SideEffect(x.Eval()) <= CallEffectKind::kReadState);
}
// 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>();
if (auto const_res = TryConstFold<Mul>(op->a, op->b)) return const_res.value();
// 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 match FloatImm
PVar<FloatImm> c3;
// Pattern var for lanes in broadcast and ramp
PVar<PrimExpr> lanes;
// Vector rules
if (op->dtype.is_scalable_or_fixed_length_vector()) {
TVM_TRY_REWRITE(broadcast(x, lanes) * broadcast(y, lanes), broadcast(x * y, lanes));
TVM_TRY_REWRITE(matches_one_of(ramp(b1, s1, lanes) * broadcast(x, lanes),
broadcast(x, lanes) * ramp(b1, s1, lanes)),
ramp(b1 * x, s1 * x, lanes));
TVM_TRY_REWRITE_IF(broadcast(c3, lanes) * x, broadcast(c3, lanes), c3.Eval()->value == 0.0f);
}
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(matches_one_of(min(x, y) * max(x, y), max(x, y) * min(x, y)), x * y);
// Two representations of const*ceildiv(x, c1)
TVM_TRY_REWRITE_IF(floordiv(x - floormod(x, c2), c1) * c1, x - floormod(x, c2),
c1.Eval()->value == -c2.Eval()->value);
// 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>();
if (auto const_res = TryConstFold<Div>(op->a, op->b)) return const_res.value();
// 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<PrimExpr> lanes;
// x / 2.0 = x * 0.5
if (const FloatImmNode* ptr = op->b.as<FloatImmNode>()) {
ICHECK(op->dtype.is_float() || op->dtype.is_bfloat16() ||
datatype::Registry::Global()->GetTypeRegistered(op->dtype.code()));
return op->a * make_const(op->b.dtype(), 1.0 / ptr->value);
}
// Vector rules
if (op->dtype.is_scalable_or_fixed_length_vector()) {
// 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;
ICHECK(c2val != 0) << "division by zero";
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) && !arith::ExtractVscaleFactor(lanes.Eval())) {
ModularSet bmod = analyzer_->modular_set(b1.Eval());
int64_t ramp_min = bmod->base / c2val;
auto lanes_int = lanes.Eval().as<IntImmNode>()->value;
int64_t ramp_max = (bmod->base + (lanes_int - 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(matches_one_of(truncdiv(x * c1, x), 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(matches_one_of(truncdiv(x + y, x), truncdiv(y + x, x)), truncdiv(y, x) + 1,
CanProveGreaterEqual(x.Eval(), 0) && CanProveGreaterEqual(y.Eval(), 0));
TVM_TRY_REWRITE_IF(
matches_one_of(truncdiv((x + y) + z, x), truncdiv((y + x) + z, x), truncdiv(y + (z + x), x),
truncdiv(y + (x + z), x)),
truncdiv(y + z, x) + 1,
CanProveGreaterEqual(x.Eval(), 0) && CanProveGreaterEqual((y + z).Eval(), 0));
TVM_TRY_REWRITE_IF(matches_one_of(truncdiv(x * y, y), truncdiv(y * x, y)), x,
CanProveGreaterEqual(x.Eval(), 0) && CanProveGreaterEqual(y.Eval(), 0));
TVM_TRY_REWRITE_IF(matches_one_of(truncdiv(x * z + y, z), 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(matches_one_of(truncdiv(y + x * z, z), 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>();
if (auto const_res = TryConstFold<Mod>(op->a, op->b)) return const_res.value();
// 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<PrimExpr> lanes;
// Vector rules
if (op->dtype.is_scalable_or_fixed_length_vector()) {
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;
ICHECK(c2val != 0) << "division by zero";
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());
if (!arith::ExtractVscaleFactor(lanes.Eval())) {
auto lanes_int = lanes.Eval().as<IntImmNode>()->value;
int64_t ramp_min = bmod->base / c2val;
int64_t ramp_max = (bmod->base + (lanes_int - 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();
}
}
} else { /* Special case for scalable vectors */
ModularSet bmod = analyzer_->modular_set(b1.Eval());
if (bmod->coeff % c2val == 0) {
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>();
if (auto const_res = TryConstFold<FloorDiv>(op->a, op->b)) return const_res.value();
// 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<PrimExpr> lanes;
// Vector rules
if (op->dtype.is_scalable_or_fixed_length_vector()) {
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;
ICHECK(c2val != 0) << "division by zero";
if (c1val % c2val == 0) {
return ramp(floordiv(b1, c2), floordiv(c1, c2), lanes).Eval();
}
// If all possible indices in ramp are the same.
if (!arith::ExtractVscaleFactor(lanes.Eval())) {
ModularSet bmod = analyzer_->modular_set(b1.Eval());
int64_t ramp_min = floordiv(bmod->base, c2val);
auto lanes_int = lanes.Eval().as<IntImmNode>()->value;
int64_t ramp_max = floordiv(bmod->base + (lanes_int - 1) * c1val, c2val);
if (ramp_min == ramp_max) {
// If b1 can divide c2
if (bmod->coeff % c2val == 0) {
return broadcast(floordiv(b1, c2), lanes).Eval();
}
// If all indices can be guaranteed to settle inside a coeff range
if (c2val % bmod->coeff == 0 && bmod->base + (lanes_int - 1) * c1val < bmod->coeff) {
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 + y, c2).Match(ret) || floordiv(x * c1, c2).Match(ret) ||
floordiv(y + x * c1, c2).Match(ret)) {
int64_t c1val = c1.Eval()->value;
int64_t c2val = c2.Eval()->value;
PrimExpr yval = y.EvalOr(Integer(0));
if (c2val == 0) return ret;
// try eliminate residue part
PrimExpr residue =
floordiv(x.Eval() * floormod(c1.Eval(), c2val) + floormod(yval, c2val), c2val);
PrimExpr y_div = CanProveEqual(floordiv(yval, c2val), 0) ? 0 : floordiv(yval, c2val);
auto bound = analyzer_->const_int_bound(residue);
if (bound.defined() && bound->max_value == bound->min_value) {
return x.Eval() * floordiv(c1val, c2.Eval()) + (y_div + Integer(bound->max_value));
}
// try simplify divisor
if (c1val > 0 && c2val > 0 && c2val % c1val == 0 &&
CanProveLess(floormod(yval, c2val), c1val)) {
// assume c2 == a * c1, x == a * x' + b, y = d * c2 + e then
// (x * c1 + y) // c2
// ==> ((a * x' + b) * c1 + d * a * c1 + e) // (a * c1)
// ==> x' + d + (b * c1 + e) // c2
// ==> x' + d since 0 <= b * c1 <= (a-1) * c1, 0 <= e < c1
// ==> x // (c2 // c1) + (y // c2)
return floordiv(x.Eval(), floordiv(c2val, c1val)) + y_div;
}
}
TVM_TRY_REWRITE(floordiv(x, x), OneWithTypeLike(x));
TVM_TRY_REWRITE(matches_one_of(floordiv(x * c1, x), floordiv(c1 * x, x)), c1);
TVM_TRY_REWRITE(floordiv(floormod(x, 2) + 1, 2), floormod(x, 2));
// Rules involving 2-operands.
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(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), floordiv(x, floordiv(c2, c1)),
c1.Eval()->value > 0 && c2.Eval()->value > 0 &&
c2.Eval()->value % c1.Eval()->value == 0 &&
CanProveEqual(floordiv(y.Eval() + z.Eval(), c1.Eval()), 0));
TVM_TRY_REWRITE_IF(matches_one_of(floordiv(x * c1 - y + z, c2), floordiv(x * c1 + z - y, 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(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 * c1, x * c2), floordiv(c1, c2), c2.Eval()->value > 0);
TVM_TRY_REWRITE_IF(matches_one_of(floordiv(x + y, x), floordiv(y + x, x)), floordiv(y, x) + 1,
CanProveGreaterEqual(x.Eval(), 0));
TVM_TRY_REWRITE_IF(matches_one_of(floordiv((x + y) + z, x), floordiv((y + x) + z, x),
floordiv(y + (z + x), x), floordiv(y + (x + z), x)),
floordiv(y + z, x) + 1, CanProveGreaterEqual(x.Eval(), 0));
TVM_TRY_REWRITE_IF(matches_one_of(floordiv(x * y, y), floordiv(y * x, y)), x,
CanProveGreaterEqual(y.Eval(), 0));
TVM_TRY_REWRITE_IF(matches_one_of(floordiv(x * z + y, z), floordiv(z * x + y, z)),
x + floordiv(y, z), CanProveGreaterEqual(z.Eval(), 0));
TVM_TRY_REWRITE_IF(matches_one_of(floordiv(y + x * z, z), floordiv(y + z * x, z)),
floordiv(y, z) + x, CanProveGreaterEqual(z.Eval(), 0));
TVM_TRY_REWRITE_IF(floordiv(x * z * c1 + y, z * c1), x + floordiv(y, z * c1),
CanProveGreaterEqual(z.Eval() * c1.Eval(), 0));
TVM_TRY_REWRITE_IF(floordiv(x - floormod(x, c1), c1), floordiv(x, c1), c1.Eval()->value != 0);
// Scalable divisor
TVM_TRY_REWRITE_IF(floordiv(x, y), ZeroWithTypeLike(x),
ContainsVscaleCall(y.Eval()) && CanProveGreaterEqual(x.Eval(), 0) &&
CanProveGreaterEqual(y.Eval(), 0) && CanProve(x.Eval() < y.Eval()));
}
return ret;
}
PrimExpr RewriteSimplifier::Impl::VisitExpr_(const FloorModNode* op) {
PrimExpr ret = IRMutatorWithAnalyzer::VisitExpr_(op);
op = ret.as<FloorModNode>();
if (auto const_res = TryConstFold<FloorMod>(op->a, op->b)) return const_res.value();
// 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<PrimExpr> lanes;
// Vector rules
if (op->dtype.is_scalable_or_fixed_length_vector()) {
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;
ICHECK(c2val != 0) << "division by zero";
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());
if (!arith::ExtractVscaleFactor(lanes.Eval())) {
int64_t ramp_min = floordiv(bmod->base, c2val);
auto lanes_int = lanes.Eval().as<IntImmNode>()->value;
int64_t ramp_max = floordiv(bmod->base + (lanes_int - 1) * c1val, c2val);
if (ramp_min == ramp_max) {
// If b1 can divide c2
if (bmod->coeff % c2val == 0) {
return ramp(floormod(bmod->base, c2), c1, lanes).Eval();
}
// If all indices can be guaranteed to settle inside a coeff range
if (c2val % bmod->coeff == 0 && bmod->base + (lanes_int - 1) * c1val < bmod->coeff) {
return ramp(floormod(b1, c2), c1, lanes).Eval();
}
}
// If b1 can divide c2
if (bmod->coeff % c2val == 0) {
return floormod(ramp(floormod(bmod->base, c2), c1, lanes), broadcast(c2, lanes)).Eval();
}
} else { /* scalable vectors */
if (bmod->coeff % c2val == 0) {
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), floormod(x * floormod(c1, c2), c2),
c2.Eval()->value != 0);
TVM_TRY_REWRITE_IF(floormod(x * c1 + y, c2), floormod(x, floordiv(c2, c1)) * c1 + y,
c1.Eval()->value > 0 && c2.Eval()->value > 0 &&
c2.Eval()->value % c1.Eval()->value == 0 &&
CanProveEqual(floordiv(y.Eval(), c1.Eval()), 0));
TVM_TRY_REWRITE_IF(floormod(x * c1 + y, c2), floormod(x * floormod(c1, c2) + y, c2),
c2.Eval()->value > 0);
// (x + 5) % 2 -> (x + 1) %2, (x + 3) % 3 => x
TVM_TRY_REWRITE_IF(
floormod(x + c1, c2), floormod(x + floormod(c1, c2), c2),
c2.Eval()->value > 0 && (c1.Eval()->value >= c2.Eval()->value || c1.Eval()->value < 0));
TVM_TRY_REWRITE_IF(floormod(x + y * c1, c2), floormod(x + y * floormod(c1, c2), c2),
c2.Eval()->value > 0);
TVM_TRY_REWRITE_IF(floormod(x * c1, x * c2), x * floormod(c1, c2), c2.Eval()->value != 0);
TVM_TRY_REWRITE(matches_one_of(floormod(x * y, y), floormod(y * x, y)), ZeroWithTypeLike(y));
// x = ay + b, then (ay + b + (ny - ay - b) % y) % y -> (b + (-b) % y) % y -> 0
TVM_TRY_REWRITE_IF(
matches_one_of(floormod(x + floormod(z, y), y), floormod(floormod(z, y) + x, y)),
ZeroWithTypeLike(x), CanProveEqual(floormod(x.Eval() + z.Eval(), y.Eval()), 0));
// x = ay + b, then (ay + b - (ay + b) % +-y) % y -> (b - b % +-y) % y -> 0
TVM_TRY_REWRITE_IF(
matches_one_of(floormod(x - floormod(x, z), y), floormod(floormod(x, z) - x, y)),
ZeroWithTypeLike(x),
CanProveEqual(y.Eval() - z.Eval(), 0) || CanProveEqual(y.Eval() + z.Eval(), 0));
TVM_TRY_REWRITE_IF(floormod(x * z * c1 + y, z * c1), floormod(y, z * c1),
CanProveGreaterEqual(z.Eval() * c1.Eval(), 0));
// Scalable divisor
TVM_TRY_REWRITE_IF(floormod(x, y), x,
ContainsVscaleCall(y.Eval()) && CanProveGreaterEqual(x.Eval(), 0) &&
CanProveGreaterEqual(y.Eval(), 0) && CanProve(x.Eval() < y.Eval()));
if (floormod(x, c1).Match(ret)) {
int64_t c1val = c1.Eval()->value;
if (c1val > 0) {
// try modular analysis
ModularSet mod = analyzer_->modular_set(x.Eval());
if (mod->coeff % c1val == 0) {
return floormod(mod->base, c1).Eval();
}
// floormod(x,c1) is a no-op when x is already in the
// appropriate range.
ConstIntBound bound = analyzer_->const_int_bound(x.Eval());
if (bound->min_value >= 0 && bound->max_value < c1val) {
return x.Eval();
}
}
}
}
return ret;
}
PrimExpr RewriteSimplifier::Impl::VisitExpr_(const MinNode* op) {
PrimExpr ret = IRMutatorWithAnalyzer::VisitExpr_(op);
op = ret.as<MinNode>();
if (auto const_res = TryConstFold<Min>(op->a, op->b)) return const_res.value();
// Pattern var to match any expression
PVar<PrimExpr> x, y, z, s1, s2;
// Pattern var match IntImm
PVar<IntImm> c1, c2;
PVar<PrimExpr> lanes;
// vector rule
if (op->dtype.is_scalable_or_fixed_length_vector()) {
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
// NOTE: trucdiv(x, y) >= floordiv(x, y)
TVM_TRY_REWRITE_IF(
matches_one_of(min(truncdiv(x + c1, c2) * c2, x), min(x, truncdiv(x + c1, c2) * c2),
min(floordiv(x + c1, c2) * c2, x), min(x, floordiv(x + c1, c2) * c2)),
x, c2.Eval()->value > 0 && c1.Eval()->value + 1 == c2.Eval()->value);
TVM_TRY_REWRITE_IF(matches_one_of(min(truncdiv(x + c1, c2) * c2, max(x, c2)),
min(max(x, c2), truncdiv(x + c1, c2) * c2),
min(floordiv(x + c1, c2) * c2, max(x, c2)),
min(max(x, c2), floordiv(x + c1, c2) * c2)),
max(x, c2),
c2.Eval()->value > 0 && c1.Eval()->value + 1 == c2.Eval()->value &&
CanProveGreaterEqual(x.Eval(), 1));
TVM_TRY_REWRITE_IF(matches_one_of(min(x, floordiv(x, c2) * c2), min(floordiv(x, c2) * c2, x)),
floordiv(x, c2) * c2, c2.Eval()->value > 0);
TVM_TRY_REWRITE((PMatchesOneOf{
min(max(x, y), min(x, y)),
min(max(x, y), min(y, x)),
min(min(x, y), max(x, y)),
min(min(x, y), max(y, x)),
min(min(x, y), x),
min(min(x, y), y),
min(x, min(x, y)),
min(y, min(x, y)),
}),
min(x, y));
TVM_TRY_REWRITE((PMatchesOneOf{
min(max(x, y), x),
min(max(y, x), x),
min(x, max(x, y)),
min(x, max(y, x)),
}),
x);
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((PMatchesOneOf{
min(max(x, y), max(x, z)),
min(max(x, y), max(z, x)),
min(max(y, x), max(x, z)),
min(max(y, x), max(z, x)),
}),
max(min(y, z), x));
TVM_TRY_REWRITE((PMatchesOneOf{
min(min(x, y), min(x, z)),
min(min(x, y), min(z, x)),
min(min(y, x), min(x, z)),
min(min(y, x), min(z, x)),
}),
min(min(y, z), x));
TVM_TRY_REWRITE((PMatchesOneOf{
min(y + x, z + x),
min(y + x, x + z),
min(x + y, x + z),
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 (c1val == 0) {
return c2val < 0 ? c2.Eval() : c1.Eval();
}
if (c2val % c1val == 0) {
if (c1val > 0) {
return (min(x, c2val / c1val) * c1val).Eval();
} else {
return (max(x, c2val / c1val) * c1val).Eval();
}
}
}
// vscale expression comparison
if (ContainsVscaleCall(op->a) || ContainsVscaleCall(op->b)) {
if (analyzer_->CanProve(op->a <= op->b)) {
return op->a;
}
if (analyzer_->CanProve(op->b <= op->a)) {
return op->b;
}
}
// 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>();
if (auto const_res = TryConstFold<Max>(op->a, op->b)) return const_res.value();
// Pattern var to match any expression
PVar<PrimExpr> x, y, z, s1, s2;
// Pattern var match IntImm
PVar<IntImm> c1, c2;
PVar<PrimExpr> lanes;
// vector rule
if (op->dtype.is_scalable_or_fixed_length_vector()) {
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((PMatchesOneOf{
max(truncdiv(x + c1, c2) * c2, x),
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((PMatchesOneOf{
max(floordiv(x + c1, c2) * c2, x),
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((PMatchesOneOf{
max(floordiv(x, c2) * c2, x),
max(x, floordiv(x, c2) * c2),
}),
x, c2.Eval()->value > 0);
TVM_TRY_REWRITE((PMatchesOneOf{
max(min(x, y), x),
max(min(y, x), x),
max(x, min(x, y)),
max(x, min(y, x)),
}),
x);
TVM_TRY_REWRITE((PMatchesOneOf{
max(min(x, y), max(x, y)),
max(min(x, y), max(y, x)),
max(max(x, y), min(x, y)),
max(max(x, y), min(y, x)),
max(max(x, y), x),
max(max(x, y), y),
max(x, max(x, y)),
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((PMatchesOneOf{
max(max(x, y), max(x, z)),
max(max(x, y), max(z, x)),
max(max(y, x), max(x, z)),
max(max(y, x), max(z, x)),
}),
max(max(y, z), x));
// max/min distribution
TVM_TRY_REWRITE((PMatchesOneOf{
max(min(x, y), min(x, z)),
max(min(x, y), min(z, x)),
max(min(y, x), min(x, z)),
max(min(y, x), min(z, x)),
}),
min(max(y, z), x));
// add distribution
TVM_TRY_REWRITE((PMatchesOneOf{
max(y + x, z + x),
max(y + x, x + z),
max(x + y, x + z),
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 (c1val == 0) {
return c2val > 0 ? c2.Eval() : c1.Eval();
}
if (c2val % c1val == 0) {
if (c1val > 0) {
return (max(x, c2val / c1val) * c1val).Eval();
} else {
return (min(x, c2val / c1val) * c1val).Eval();
}
}
}
// vscale expression comparison
if (ContainsVscaleCall(op->a) || ContainsVscaleCall(op->b)) {
if (analyzer_->CanProve(op->a >= op->b)) {
return op->a;
}
if (analyzer_->CanProve(op->b >= op->a)) {
return op->b;
}
}
// 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;
}
ffi::Optional<PrimExpr> RewriteSimplifier::Impl::TryMatchLiteralConstraint(
const PrimExpr& expr) const {
PrimExpr negation = Not(expr);
ExprDeepEqual expr_equal;
for (const auto& constraint : literal_constraints_) {
if (expr_equal(constraint, expr)) {
return make_const(expr->dtype, true);
}
if (expr_equal(constraint, negation)) {
return make_const(expr->dtype, false);
}
}
return std::nullopt;
}
PrimExpr RewriteSimplifier::Impl::VisitExpr_(const EQNode* op) {
EQ ret = Downcast<EQ>(IRMutatorWithAnalyzer::VisitExpr_(op));
op = ret.get();
if (auto const_res = TryConstFold<EQ>(op->a, op->b)) {
return const_res.value();
}
if (auto match = TryMatchLiteralConstraint(ret)) {
return match.value();
}
return ApplyRewriteRules(ret);
}
PrimExpr RewriteSimplifier::Impl::ApplyRewriteRules(EQ ret) {
// Pattern var to match any expression
PVar<PrimExpr> x, y;
// Pattern var match IntImm
PVar<IntImm> c1, c2;
PVar<PrimExpr> lanes;
PConst<PrimExpr> ctrue(make_const(ret->dtype, true));
// vector rule
if (ret->dtype.is_scalable_or_fixed_length_vector()) {
TVM_TRY_REWRITE(broadcast(x, lanes) == broadcast(y, lanes), broadcast(x == y, lanes));
}
if (IsIndexType(ret->a.dtype())) {
CompareResult result = TryCompare(ret->a, ret->b);
if (result == CompareResult::kEQ) {
return make_const(ret->dtype, true);
} else if (result == CompareResult::kNE || result == CompareResult::kGT ||
result == CompareResult::kLT) {
return make_const(ret->dtype, false);
}
TVM_TRY_REWRITE(c1 == x, x == c1);
TVM_TRY_REWRITE(x - c1 == c2, x == c2 + c1);
TVM_TRY_REWRITE(c1 - x == c2, x == c1 - c2);
TVM_TRY_REWRITE(x + c1 == c2, x == c2 - c1);
TVM_TRY_RECURSIVE_REWRITE(x * y == 0, x == 0 || y == 0);
TVM_TRY_REWRITE(x == x, ctrue);
} else {
// Mimic the cancellation rules for SubNode. For Index datatypes,
// we skip the check for side effects.
//
// These simplifications do not preserve NaN/Inf that may occur in
// the inputs. For IEEE floats, `NaN - NaN` is `NaN`, and does
// not cancel out. However, since models should not encounter NaN
// in the first place, this allows better simplification for the
// supported path.
TVM_TRY_REWRITE_IF(x == x, ctrue, SideEffect(x.Eval()) <= CallEffectKind::kReadState);
}
return ret;
}
PrimExpr RewriteSimplifier::Impl::VisitExpr_(const NENode* op) {
PrimExpr ret = IRMutatorWithAnalyzer::VisitExpr_(op);
op = ret.as<NENode>();
if (auto const_res = TryConstFold<NE>(op->a, op->b)) return const_res.value();
if (auto match = TryMatchLiteralConstraint(ret)) return match.value();
if (IsIndexType(op->a.dtype())) {
CompareResult result = TryCompare(op->a, op->b);
if (result == CompareResult::kNE || result == CompareResult::kGT ||
result == CompareResult::kLT) {
return make_const(op->dtype, true);
} else if (result == CompareResult::kEQ) {
return make_const(op->dtype, false);
} else if (result == CompareResult::kGE) {
// Known: a >= b
//
// a != b
// (a < b) or (b < a)
// False or (b < a)
// b < a
return ApplyRewriteRules(LT(op->b, op->a));
} else if (result == CompareResult::kLE) {
// Known: a <= b
//
// a != b
// (a < b) or (b < a)
// (a < b) or False
// a < b
return ApplyRewriteRules(LT(op->a, op->b));
}
}
return ApplyRewriteRules(Not(ApplyRewriteRules(EQ(op->a, op->b))));
}
PrimExpr RewriteSimplifier::Impl::VisitExpr_(const LENode* op) {
PrimExpr ret = IRMutatorWithAnalyzer::VisitExpr_(op);
op = ret.as<LENode>();
ICHECK(op);
if (auto const_res = TryConstFold<LE>(op->a, op->b)) return const_res.value();
if (auto match = TryMatchLiteralConstraint(ret)) return match.value();
// Check for applicable rewrites before attempting to prove/disprove
// the inequality. This preserves earlier behavior, where (A<=B*x)
// simplifies to (ceildiv(A,B)<=x) when (A%B!=0). Performing the
// TryCompare first would simplify to the equivalent
// (floordiv(A,B)<x) in these cases instead.
ret = ApplyRewriteRules(Not(ApplyRewriteRules(LT(op->b, op->a))));
if (auto op = ret.as<LENode>(); op && IsIndexType(op->a.dtype())) {
CompareResult result = TryCompare(op->a, op->b);
if (result == CompareResult::kLE || result == CompareResult::kLT ||
result == CompareResult::kEQ) {
return make_const(op->dtype, true);
} else if (result == CompareResult::kGT) {
return make_const(op->dtype, false);
} else if (result == CompareResult::kNE) {
// Known: a != b
//
// a <= b
// (a < b) or (a == b)
// (a < b) or False
// a < b
return ApplyRewriteRules(LT(op->a, op->b));
} else if (result == CompareResult::kGE) {
// Known: a >= b
//
// a <= b
// (a < b) or (a == b)
// False or (a == b)
// a == b
return ApplyRewriteRules(EQ(op->a, op->b));
}
}
return ret;
}
PrimExpr RewriteSimplifier::Impl::VisitExpr_(const GTNode* op) {
return this->VisitExpr(op->b < op->a);
}
PrimExpr RewriteSimplifier::Impl::VisitExpr_(const GENode* op) {
return this->VisitExpr(op->b <= op->a);
}
PrimExpr RewriteSimplifier::Impl::VisitExpr_(const LTNode* op) {
LT node = Downcast<LT>(IRMutatorWithAnalyzer::VisitExpr_(op));
op = node.get();
if (auto const_res = TryConstFold<LT>(op->a, op->b)) return const_res.value();
if (auto match = TryMatchLiteralConstraint(node)) return match.value();
return ApplyRewriteRules(node);
}
PrimExpr RewriteSimplifier::Impl::ApplyRewriteRules(LT ret) {
// Pattern var to match any expression
PVar<PrimExpr> x, y, z, s1, s2;
// Pattern var match IntImm
PVar<IntImm> c1, c2;
PVar<PrimExpr> lanes;
// vector rule
if (ret->dtype.is_scalable_or_fixed_length_vector()) {
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(ret->a.dtype())) {
CompareResult result = TryCompare(ret->a, ret->b);
if (result == CompareResult::kLT) {
return make_const(ret->dtype, true);
}
if (result == CompareResult::kEQ || result == CompareResult::kGT ||
result == CompareResult::kGE) {
return make_const(ret->dtype, false);
}
// clang-format off
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_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);
// clang-format on
TVM_TRY_RECURSIVE_REWRITE(matches_one_of(c1 < x + c2, c1 - x < c2), c1 - c2 < x);
TVM_TRY_RECURSIVE_REWRITE(matches_one_of(c1 < c2 - x, x + c1 < c2), x < c2 - c1);
TVM_TRY_RECURSIVE_REWRITE(c1 < x - c2, c1 + c2 < x);
TVM_TRY_RECURSIVE_REWRITE(x - c2 < c1, x < c1 + c2);
TVM_TRY_RECURSIVE_REWRITE(x < c1 - y, x + y < c1);
TVM_TRY_RECURSIVE_REWRITE(c1 - y < x, c1 < x + y);
TVM_TRY_RECURSIVE_REWRITE(x < c1 + y, x - y < c1);
TVM_TRY_RECURSIVE_REWRITE(c1 + y < x, c1 < x - y);
auto merge_constants = [&]() -> ffi::Optional<PrimExpr> {
auto [lhs, lhs_offset] = ExtractConstantOffset(ret->a);
auto [rhs, rhs_offset] = ExtractConstantOffset(ret->b);
if (lhs_offset == 0 && rhs_offset == 0) {
return std::nullopt;
}
int64_t diff = rhs_offset - lhs_offset;
if (diff == 0) {
return lhs < rhs;
} else if (diff == 1) {
return lhs <= rhs;
} else if (diff < 0 && rhs_offset != 0) {
return lhs + make_const(lhs.dtype(), -diff) < rhs;
} else if (diff > 0 && lhs_offset != 0) {
return lhs < rhs + make_const(rhs.dtype(), diff);
}
return std::nullopt;
}();
if (merge_constants) {
return RecursiveRewrite(merge_constants.value());
}
auto common_factor = [&]() -> int64_t {
auto modular_a = analyzer_->modular_set(ret->a);
auto modular_b = analyzer_->modular_set(ret->b);
auto gcd_lhs = ZeroAwareGCD(modular_a->base, modular_a->coeff);
auto gcd_rhs = ZeroAwareGCD(modular_b->base, modular_b->coeff);
return ZeroAwareGCD(gcd_lhs, gcd_rhs);
}();
if (common_factor > 1) {
return RecursiveRewrite(floordiv(ret->a, common_factor) < floordiv(ret->b, common_factor));
}
}
return ret;
}
PrimExpr RewriteSimplifier::Impl::VisitExpr_(const NotNode* op) {
Not ret = Downcast<Not>(IRMutatorWithAnalyzer::VisitExpr_(op));
if (auto const_res = TryConstFold<Not>(ret->a)) return const_res.value();
if (auto match = TryMatchLiteralConstraint(ret)) return match.value();
return ApplyRewriteRules(ret);
}
PrimExpr RewriteSimplifier::Impl::ApplyRewriteRules(Not ret) {
// Pattern var to match any expression
PVar<PrimExpr> x, y;
PVar<PrimExpr> lanes;
if (ret->dtype.is_scalable_or_fixed_length_vector()) {
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 = [&]() -> PrimExpr {
// If this extension isn't enabled, just delegate out.
if (!(enabled_extensions_ & kApplyConstraintsToBooleanBranches)) {
return IRMutatorWithAnalyzer::VisitExpr_(op);
}
PrimExpr a = op->a;
PrimExpr b = op->b;
// Alternate which branch is used as the constraint, and which is
// being simplified. Because some sub-analyzers expect their
// constraints to already be simplified, each branch may require
// more than one update. The loop condition allows each branch to
// be visited up to twice, but only performs the second visit if
// necessary.
size_t iterations_since_update = 0;
for (size_t i = 0; i < 4; i++) {
PrimExpr& to_update = (i % 2 == 0) ? a : b;
const PrimExpr& constraint = (i % 2 == 0) ? b : a;
With<ConstraintContext> context(analyzer_, constraint);
PrimExpr updated = VisitExpr(to_update);
if (!to_update.same_as(updated)) {
to_update = updated;
iterations_since_update = 0;
} else {
iterations_since_update++;
if (iterations_since_update >= 2) {
break;
}
}
}
// Only construct a new object if a change has been made.
// Otherwise, follow ExprMutator's convention of returning the
// original object.
if (a.same_as(op->a) && b.same_as(op->b)) {
return ffi::GetRef<PrimExpr>(op);
} else {
return And(a, b);
}
}();
op = ret.as<AndNode>();
if (auto const_res = TryConstFold<And>(op->a, op->b)) return const_res.value();
if (auto match = TryMatchLiteralConstraint(ret)) return match.value();
if ((enabled_extensions_ & RewriteSimplifier::kConvertBooleanToAndOfOrs) &&
!recursively_visiting_boolean_) {
return SimplifyAsAndOfOrs(ret, analyzer_);
}
// Pattern var to match any expression
PVar<PrimExpr> x, y, z;
// Pattern var match IntImm
PVar<IntImm> c1, c2, c3;
PVar<PrimExpr> lanes;
if (op->dtype.is_scalable_or_fixed_length_vector()) {
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((PMatchesOneOf{
x < c1 && c2 <= x,
c2 <= x && x < c1,
x <= c1 && c2 < x,
c2 < x && x <= c1,
}),
cfalse, c2.Eval()->value >= c1.Eval()->value);
TVM_TRY_REWRITE_IF((PMatchesOneOf{
x <= c1 && c2 <= x,
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(matches_one_of(x == c1 && x != c2, x != c2 && x == c1), x == c1 && c1 != c2);
TVM_TRY_RECURSIVE_REWRITE(matches_one_of(floordiv(x, c2) == c1 && floormod(x, c2) == c3,
floormod(x, c2) == c3 && floordiv(x, c2) == c1),
x == c1 * c2 + c3);
TVM_TRY_RECURSIVE_REWRITE_IF((PMatchesOneOf{
0 <= x - y * c1 && x - y * c1 < c1,
x - y * c1 < c1 && 0 <= x - y * c1,
}),
y == floordiv(x, c1), c1.Eval()->value > 0);
TVM_TRY_RECURSIVE_REWRITE((PMatchesOneOf{
c1 < x - y * c1 && x - y * c1 <= 0,
x - y * c1 < c1 && 0 <= x - y * c1,
}),
y == floordiv(x, c1));
TVM_TRY_RECURSIVE_REWRITE_IF((PMatchesOneOf{
0 <= x + y * c2 && x + y * c2 < c1,
x + y * c2 < c1 && 0 <= x + y * c2,
}),
y == floordiv(x, c1), c2.Eval()->value == -c1.Eval()->value);
TVM_TRY_RECURSIVE_REWRITE_IF(x < c1 && floormod(x, c2) < c3,
x < c1 - c2 + c3 && floormod(x, c2) < c3,
c1.Eval()->value % c2.Eval()->value == 0);
TVM_TRY_RECURSIVE_REWRITE_IF(
x < c1 && floormod(x, c2) < c3, x < c1 - floormod(c1, c2) + c3 && floormod(x, c2) < c3,
(c1.Eval()->value % c2.Eval()->value + c2.Eval()->value) % c2.Eval()->value >
c3.Eval()->value);
TVM_TRY_RECURSIVE_REWRITE_IF(x <= c1 && floormod(x, c2) < c3,
x < c1 + 1 - c2 + c3 && floormod(x, c2) < c3,
(c1.Eval()->value + 1) % c2.Eval()->value == 0);
TVM_TRY_RECURSIVE_REWRITE_IF(
x <= c1 && floormod(x, c2) < c3, x < c1 + 1 - floormod(c1, c2) + c3 && floormod(x, c2) < c3,
(((c1.Eval()->value + 1) % c2.Eval()->value) + c2.Eval()->value) % c2.Eval()->value >
c3.Eval()->value);
TVM_TRY_RECURSIVE_REWRITE(matches_one_of(floordiv(x, c2) == c1 && floormod(x, c2) < c3,
floormod(x, c2) < c3 && floordiv(x, c2) == c1),
c1 * c2 <= x && x < c1 * c2 + c3);
TVM_TRY_RECURSIVE_REWRITE(matches_one_of(floordiv(x, c2) == c1 && floormod(x, c2) <= c3,
floormod(x, c2) <= c3 && floordiv(x, c2) == c1),
c1 * c2 <= x && x <= c1 * c2 + c3);
TVM_TRY_RECURSIVE_REWRITE(matches_one_of(floordiv(x, c2) == c1 && c3 <= floormod(x, c2),
c3 <= floormod(x, c2) && floordiv(x, c2) == c1),
c1 * c2 + c3 <= x && x < (c1 + 1) * c2);
TVM_TRY_RECURSIVE_REWRITE(matches_one_of(floordiv(x, c2) == c1 && c3 < floormod(x, c2),
c3 < floormod(x, c2) && floordiv(x, c2) == c1),
c1 * c2 + c3 < x && x < (c1 + 1) * c2);
TVM_TRY_RECURSIVE_REWRITE(x && (y && z), (x && y) && z);
return ret;
}
PrimExpr RewriteSimplifier::Impl::VisitExpr_(const OrNode* op) {
PrimExpr orig = ffi::GetRef<PrimExpr>(op);
PrimExpr ret = [&]() -> PrimExpr {
// If this extension isn't enabled, just delegate out.
if (!(enabled_extensions_ & kApplyConstraintsToBooleanBranches)) {
return IRMutatorWithAnalyzer::VisitExpr_(op);
}
PrimExpr a = op->a;
PrimExpr b = op->b;
// Alternate which branch is used as the constraint, and which
// is being simplified. Because some sub-analyzers expect their
// constraints to already be simplified, each branch may require
// more than update. The loop condition allows each branch to be
// visited up to twice, but only if performs the second visit if
// necessary.
size_t iterations_since_update = 0;
for (size_t i = 0; i < 4; i++) {
PrimExpr& to_update = (i % 2 == 0) ? a : b;
const PrimExpr& constraint = (i % 2 == 0) ? b : a;
With<ConstraintContext> context(analyzer_, NormalizeBooleanOperators(Not(constraint)));
PrimExpr updated = VisitExpr(to_update);
if (!to_update.same_as(updated)) {
to_update = updated;
iterations_since_update = 0;
} else {
iterations_since_update++;
if (iterations_since_update >= 2) {
break;
}
}
}
// Only construct a new object if a change has been made.
// Otherwise, follow ExprMutator's convention of returning the
// original object.
if (a.same_as(op->a) && b.same_as(op->b)) {
return ffi::GetRef<PrimExpr>(op);
} else {
return Or(a, b);
}
}();
op = ret.as<OrNode>();
if (auto const_res = TryConstFold<Or>(op->a, op->b)) return const_res.value();
if (auto match = TryMatchLiteralConstraint(ret)) return match.value();
if ((enabled_extensions_ & RewriteSimplifier::kConvertBooleanToAndOfOrs) &&
!recursively_visiting_boolean_) {
return SimplifyAsAndOfOrs(ret, analyzer_);
}
// Pattern var to match any expression
PVar<PrimExpr> x, y, z;
// Pattern var match IntImm
PVar<IntImm> c1, c2;
PVar<PrimExpr> lanes;
if (op->dtype.is_scalable_or_fixed_length_vector()) {
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(x < y || y < x, x != y);
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 != c1 || x == c2, x != c1 || c1 == c2);
TVM_TRY_REWRITE(x == c2 || x != c1, x != c1 || c1 == c2);
TVM_TRY_RECURSIVE_REWRITE(x < y || x == y, x <= y);
TVM_TRY_RECURSIVE_REWRITE(x < y || y == x, x <= y);
TVM_TRY_RECURSIVE_REWRITE(x == y || x < y, x <= y);
TVM_TRY_RECURSIVE_REWRITE(y == x || x < y, x <= y);
TVM_TRY_RECURSIVE_REWRITE(x || (y || z), (x || y) || z);
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->op.same_as(tir::builtin::likely()) && is_const_int(op->args[0])) {
return op->args[0];
} else if (op->op.same_as(tir::builtin::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->op.same_as(tir::builtin::shift_left())) {
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->op.same_as(Op::Get("tir.ceil"))) {
PrimExpr ceil_arg = op->args[0];
if (auto arg_int = op->args[0].as<IntImmNode>()) {
return cast(op->dtype, IntImm(arg_int->dtype, arg_int->value));
} else if (auto arg_float = ceil_arg.as<FloatImmNode>()) {
return cast(op->dtype, FloatImm(arg_float->dtype, std::ceil(arg_float->value)));
} else if (auto arg_call = ceil_arg.as<CallNode>()) {
// ceil(log2(cast(n,"float64"))) is used as the implementation of
// topi.math.ceil_log2, and appears in iteration bounds.
if (arg_call->op.same_as(Op::Get("tir.log2"))) {
PrimExpr log_arg = arg_call->args[0];
if (auto as_float = log_arg.as<FloatImmNode>()) {
// ceil(log2(n)) can be simplified, and should produce the
// same integer result regardless of the target's rounding
// conventions.
return FloatImm(op->dtype, std::ceil(std::log2(as_float->value)));
}
}
}
} else if (op->op.same_as(Op::Get("tir.clz"))) {
if (const auto* arg_int = op->args[0].as<IntImmNode>()) {
int bits = arg_int->dtype.bits();
if (arg_int->value == 0) return make_const(op->dtype, bits);
for (int i = bits - 1; i >= 0; --i) {
if ((int64_t(1) << i) & arg_int->value) {
return IntImm(op->dtype, bits - i - 1);
}
}
LOG(FATAL) << "Should not reach here";
}
}
if (op->op.same_as(tir::builtin::likely())) {
// Cases such as for (i, 0, bound) {if (likely(iter_var < bound)) { .. } }
if (auto match = TryMatchLiteralConstraint(op->args[0])) {
return match.value();
}
}
if (op->op.same_as(tir::builtin::if_then_else())) {
// Simplify nested if_then_else
// if (cond) { if (inner_cond) { inner_then_expr } else { inner_else_expr } } else { else_expr }
// => if (cond && inner_cond) { inner_then_expr } else { else_expr }
const PrimExpr& cond = op->args[0];
const PrimExpr& then_expr = op->args[1];
const PrimExpr& else_expr = op->args[2];
const CallNode* inner_call = then_expr.as<CallNode>();
if (inner_call != nullptr && inner_call->op.same_as(tir::builtin::if_then_else())) {
const PrimExpr& inner_cond = inner_call->args[0];
const PrimExpr& inner_then_expr = inner_call->args[1];
const PrimExpr& inner_else_expr = inner_call->args[2];
// Only check constant cases to avoid recursion
if (is_const_number(inner_else_expr) && is_const_number(else_expr) &&
analyzer_->CanProve(inner_else_expr == else_expr)) {
return if_then_else(cond && inner_cond, inner_then_expr, else_expr);
}
}
}
return ret;
}
PrimExpr RewriteSimplifier::Impl::VisitExpr_(const VarNode* op) {
Var var = ffi::GetRef<Var>(op);
if (op->dtype == DataType::Bool()) {
if (auto match = TryMatchLiteralConstraint(var)) {
return match.value();
}
}
auto it = var_map_.find(var);
if (it != var_map_.end()) {
return it->second;
}
return ffi::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);
}
bool RewriteSimplifier::Impl::CanInlineLet(const LetNode* op) {
// Only inline trivial bindings to avoid deep expression explosion
// when we need let to construct complicated expressions.
if (is_const_number(op->value)) return true;
if (op->value.as<VarNode>()) return true;
return false;
}
PrimExpr RewriteSimplifier::Impl::VisitExpr_(const LetNode* op) {
PrimExpr value = this->VisitExpr(op->value);
if (CanInlineLet(op)) {
// 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 ffi::GetRef<PrimExpr>(op);
} else {
return Let(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 allow_override) {
impl_->Update(var, info, allow_override);
}
std::function<void()> RewriteSimplifier::EnterConstraint(const PrimExpr& constraint) {
return impl_->EnterConstraint(constraint);
}
void RewriteSimplifier::SetEnabledExtensions(Extension flags) {
impl_->SetEnabledExtensions(flags);
}
RewriteSimplifier::Extension RewriteSimplifier::GetEnabledExtensions() const {
return impl_->GetEnabledExtensions();
}
ObjectRef RewriteSimplifier::GetStatsCounters() const { return impl_->GetStatsCounters(); }
void RewriteSimplifier::ResetStatsCounters() { impl_->ResetStatsCounters(); }
void RewriteSimplifier::SetMaximumRewriteSteps(int64_t maximum) {
impl_->SetMaximumRewriteSteps(maximum);
}
RewriteSimplifier::RewriteSimplifier(Analyzer* parent) : impl_(new Impl(parent)) {}
RewriteSimplifier::~RewriteSimplifier() { delete impl_; }
TVM_STATIC_IR_FUNCTOR(ReprPrinter, vtable)
.set_dispatch<RewriteSimplifierStatsNode>([](const ObjectRef& node, ReprPrinter* p) {
auto* ptr = node.as<RewriteSimplifierStatsNode>();
p->stream << "RewriteSimplifierStats(nodes_visited = " << ptr->nodes_visited
<< ", constraints_entered = " << ptr->constraints_entered
<< ", rewrites_attempted = " << ptr->rewrites_attempted
<< ", rewrites_performed = " << ptr->rewrites_performed
<< ", max_recursive_depth = " << ptr->max_recursive_depth
<< ", num_recursive_rewrites = " << ptr->num_recursive_rewrites << ")";
});
} // namespace arith
} // namespace tvm