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const_int_bound.cc
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const_int_bound.cc
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/*
* 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 tvm/arith/const_int_bound.cc
*/
#include <tvm/runtime/registry.h>
#include <tvm/arith/analyzer.h>
#include <tvm/tir/expr_functor.h>
#include <algorithm>
#include "int_operator.h"
#include "pattern_match.h"
namespace tvm {
namespace arith {
using namespace tir;
TVM_REGISTER_NODE_TYPE(ConstIntBoundNode);
ConstIntBound::ConstIntBound(
int64_t min_value, int64_t max_value) {
auto node = make_object<ConstIntBoundNode>();
node->min_value = min_value;
node->max_value = max_value;
data_ = std::move(node);
}
ConstIntBound MakeConstIntBound(int64_t min_value, int64_t max_value) {
return ConstIntBound(min_value, max_value);
}
TVM_REGISTER_GLOBAL("arith.ConstIntBound")
.set_body_typed(MakeConstIntBound);
inline void PrintBoundValue(std::ostream& os, int64_t val) {
if (val == ConstIntBound::kPosInf) {
os << "pos_inf";
} else if (val == ConstIntBound::kNegInf) {
os << "neg_inf";
} else {
os << val;
}
}
TVM_STATIC_IR_FUNCTOR(ReprPrinter, vtable)
.set_dispatch<ConstIntBoundNode>([](const ObjectRef& node, ReprPrinter* p) {
auto* op = static_cast<const ConstIntBoundNode*>(node.get());
p->stream << "ConstIntBound[";
PrintBoundValue(p->stream, op->min_value);
p->stream << ',';
PrintBoundValue(p->stream, op->max_value);
p->stream << ']';
});
// internal entry for const int bound
struct ConstIntBoundAnalyzer::Entry {
int64_t min_value;
int64_t max_value;
bool is_const(int64_t value) const {
return min_value == max_value && min_value == value;
}
bool operator==(const Entry& other) const {
return min_value == other.min_value && max_value == other.max_value;
}
};
class ConstIntBoundAnalyzer::Impl :
public ExprFunctor<ConstIntBoundAnalyzer::Entry(const PrimExpr&)> {
public:
/*! \brief additional bound info about expr \in bound */
struct BoundInfo {
/*! \brief The expr */
PrimExpr expr;
/*! \brief The additional bound */
Entry bound;
BoundInfo() {}
BoundInfo(PrimExpr expr, Entry bound)
: expr(expr), bound(bound) {
}
};
void Bind(const Var& var, const Range& range, bool override) {
Entry a = VisitExpr(range->min);
Entry b = VisitExpr(range->extent);
Entry ret;
ret.min_value = a.min_value;
ret.max_value = InfAwareAdd(a.max_value, InfAwareAdd(b.max_value, -1));
Update(var, ret, override);
}
void Update(const Var& var,
const Entry& info,
bool override) {
if (!override) {
auto it = var_map_.find(var);
if (it != var_map_.end()) {
CHECK(it->second == info)
<< "Trying to update var \'" << var << "\'"
<< " with a different const bound: "
<< "original=" << ConstIntBound(it->second.min_value, it->second.max_value)
<< ", new=" << ConstIntBound(info.min_value, info.max_value);
}
}
var_map_[var] = info;
}
void Update(const Var& var,
const ConstIntBound& info,
bool override) {
Update(var, MakeBound(info->min_value, info->max_value), override);
}
// Override visitor behaviors
Entry VisitExprDefault_(const Object* op) final {
return Everything(
static_cast<const PrimExprNode*>(op)->dtype);
}
Entry VisitExpr(const PrimExpr& expr) final {
Entry res = ExprFunctor::VisitExpr(expr);
tir::ExprDeepEqual equal;
// a linear search over additional info
// assume we won't have a lot of conditions
for (const BoundInfo& info : additional_info_) {
if (equal(expr, info.expr)) {
res = Intersect(res, info.bound);
}
}
if (bound_) {
const PrimExprNode* op = expr.as<PrimExprNode>();
auto val = bound_->find(op);
if (val != bound_->end()) {
auto everything = Everything(op->dtype);
CHECK(
(val->second->min_value == res.min_value && val->second->max_value == res.max_value) ||
(val->second->min_value == everything.min_value &&
val->second->max_value == everything.max_value))
<< "Detected bound for " << expr << "conflicts with memorization";
}
(*bound_)[op] = ConstIntBound(res.min_value, res.max_value);
}
return res;
}
Entry VisitExpr_(const RampNode* op) final {
// op = {base + i * stride | 0 <= i < lanes}
// Entry(op) = Union(Entry(base + i * stride) | 0 <= i < lanes)
// Note that `base + i * stride` is linear w.r.t. `i`
// Entry(op) = Union(Entry(base + i * stride) | i = 0, i = lanes-1)
Entry a = VisitExpr(op->base);
Entry b = VisitExpr(op->base + (op->lanes - 1) * op->stride);
return Union(a, b);
}
Entry VisitExpr_(const CastNode* op) final {
Entry a = VisitExpr(op->value);
Entry b = Everything(op->dtype);
return Intersect(a, b);
}
Entry VisitExpr_(const IntImmNode* op) final {
return MakeBound(op->value, op->value);
}
Entry VisitExpr_(const AddNode* op) final {
Entry a = VisitExpr(op->a);
Entry b = VisitExpr(op->b);
Entry ret;
ret.min_value = InfAwareAdd(a.min_value, b.min_value);
ret.max_value = InfAwareAdd(a.max_value, b.max_value);
return ret;
}
Entry VisitExpr_(const SubNode* op) final {
Entry a = VisitExpr(op->a);
Entry b = VisitExpr(op->b);
Entry ret;
ret.min_value = InfAwareAdd(a.min_value, -b.max_value);
ret.max_value = InfAwareAdd(a.max_value, -b.min_value);
return ret;
}
Entry VisitExpr_(const MulNode* op) final {
Entry a = VisitExpr(op->a);
Entry b = VisitExpr(op->b);
return BinaryOpBoundry(a, b, InfAwareMul);
}
Entry VisitExpr_(const DivNode* op) final {
Entry a = VisitExpr(op->a);
Entry b = VisitExpr(op->b);
CHECK(!b.is_const(0)) << "divide by zero";
// assume no division by 0
if (b.min_value == 0) b.min_value = 1;
if (b.max_value == 0) b.max_value = -1;
return BinaryOpBoundry(a, b, InfAwareDiv);
}
Entry VisitExpr_(const ModNode* op) final {
Entry a = VisitExpr(op->a);
Entry b = VisitExpr(op->b);
if (b.min_value > 0) {
int64_t b_max_cap = InfAwareAdd(b.max_value, -1);
if (a.min_value >= 0) {
// 0 <= [a_min, a_max] < b_min
if (a.max_value < b.min_value) return a;
// other case, we can get close to 0
return MakeBound(0,
std::min(a.max_value, b_max_cap));
} else {
return MakeBound(std::max(a.min_value, -b_max_cap),
std::min(std::max(a.max_value, (int64_t)0), b_max_cap));
}
} else {
CHECK(!b.is_const(0)) << "mod by zero";
// mod by negative value is rare,
// and we just use the simpliest rule.
return Everything(op->dtype);
}
}
Entry VisitExpr_(const FloorDivNode* op) final {
Entry a = VisitExpr(op->a);
Entry b = VisitExpr(op->b);
CHECK(!b.is_const(0)) << "floordiv by zero";
// assume no division by 0
if (b.min_value == 0) b.min_value = 1;
if (b.max_value == 0) b.max_value = -1;
return BinaryOpBoundry(a, b, InfAwareFloorDiv);
}
Entry VisitExpr_(const FloorModNode* op) final {
Entry a = VisitExpr(op->a);
Entry b = VisitExpr(op->b);
if (b.min_value > 0) {
int64_t b_max_cap = InfAwareAdd(b.max_value, -1);
if (a.min_value >= 0) {
// 0 <= [a_min, a_max] < b_min
if (a.max_value < b.min_value) return a;
// other case, we can get close to 0
return MakeBound(0, std::min(a.max_value, b_max_cap));
} else {
return MakeBound(0, b_max_cap);
}
} else {
CHECK(!b.is_const(0)) << "floormod by zero";
// mod by negative value is rare,
// and we just use the simpliest rule.
return Everything(op->dtype);
}
}
Entry VisitExpr_(const MinNode* op) final {
Entry a = VisitExpr(op->a);
Entry b = VisitExpr(op->b);
Entry ret;
ret.min_value = std::min(a.min_value, b.min_value);
ret.max_value = std::min(a.max_value, b.max_value);
return ret;
}
Entry VisitExpr_(const MaxNode* op) final {
Entry a = VisitExpr(op->a);
Entry b = VisitExpr(op->b);
Entry ret;
ret.min_value = std::max(a.min_value, b.min_value);
ret.max_value = std::max(a.max_value, b.max_value);
return ret;
}
Entry VisitExpr_(const SelectNode* op) final {
Entry a = VisitExpr(op->true_value);
Entry b = VisitExpr(op->false_value);
return Union(a, b);
}
Entry VisitExpr_(const CallNode* op) final {
// only special handle >> and & which can be
// used for index calculation.
if (op->is_intrinsic(CallNode::shift_right)) {
return VisitRightShift(op);
} else if (op->is_intrinsic(CallNode::bitwise_and)) {
return VisitBitwiseAnd(op);
} else {
return Everything(op->dtype);
}
}
Entry VisitExpr_(const VarNode* op) final {
Var v = GetRef<Var>(op);
auto it = var_map_.find(v);
if (it != var_map_.end()) {
return it->second;
} else {
return Everything(op->dtype);
}
}
Entry VisitExpr_(const SizeVarNode* op) final {
SizeVar v = GetRef<SizeVar>(op);
auto it = var_map_.find(v);
if (it != var_map_.end()) {
return it->second;
} else {
return MakeBound(0, kPosInf);
}
}
Entry VisitRightShift(const CallNode* op) {
Entry a = VisitExpr(op->args[0]);
Entry b = VisitExpr(op->args[1]);
return BinaryOpBoundry(a, b, InfAwareRightShift);
}
Entry VisitBitwiseAnd(const CallNode* op) {
Entry a = VisitExpr(op->args[0]);
Entry b = VisitExpr(op->args[1]);
// handle positive index case.
if (a.min_value >= 0 && b.min_value >= 0) {
return MakeBound(0, std::min(a.max_value, b.max_value));
} else {
if (b.min_value >= 0) {
return MakeBound(0, b.max_value);
}
if (a.min_value >= 0) {
return MakeBound(0, a.max_value);
}
return Everything(op->dtype);
}
}
std::function<void()> EnterConstraint(const PrimExpr& constraint) {
std::vector<BoundInfo> info = DetectBoundInfo(constraint);
if (info.size() == 0) return nullptr;
size_t old_size = additional_info_.size();
additional_info_.insert(additional_info_.end(), info.begin(), info.end());
size_t new_size = old_size + info.size();
auto frecover = [old_size, new_size, this]() {
CHECK_EQ(additional_info_.size(), new_size);
additional_info_.resize(old_size);
};
return frecover;
}
private:
friend class ConstIntBoundAnalyzer;
// internal variable map
std::unordered_map<Var, Entry, ObjectHash, ObjectEqual> var_map_;
// additional bound info
std::vector<BoundInfo> additional_info_;
// look up table for memorization
std::unordered_map<const PrimExprNode*, ConstIntBound>* bound_{nullptr};
// constants: the limit value means umlimited
// NOTE: kNegInf/kPosInf are used to represent infinity.
static const constexpr int64_t kNegInf = ConstIntBound::kNegInf;
static const constexpr int64_t kPosInf = ConstIntBound::kPosInf;
static_assert(-kNegInf == kPosInf, "invariant of inf");
// internal helper functions
/*!
* \brief Get boundary of binary op who are monotonic wrt to one argument.
* \param param a The entry of the left operand.
* \param param a The entry of the right operand.
* \param op The operator.
* \tparam F the operator function type.
* \return The result.
*/
template<typename F>
static Entry BinaryOpBoundry(Entry a, Entry b, const F& op) {
Entry ret;
// The boundary point must be shihft of the original boundary.
int64_t v1 = op(a.min_value, b.min_value);
int64_t v2 = op(a.max_value, b.max_value);
int64_t v3 = op(a.min_value, b.max_value);
int64_t v4 = op(a.max_value, b.min_value);
ret.min_value = std::min(std::min(std::min(v1, v2), v3), v4);
ret.max_value = std::max(std::max(std::max(v1, v2), v3), v4);
return ret;
}
/*!
* \brief Compute x + y, aware of inf.
* \param x The left operand.
* \param y The right operand.
* \return the result.
*/
static int64_t InfAwareAdd(int64_t x, int64_t y) {
if (x == kPosInf) {
CHECK(y != kNegInf);
return kPosInf;
}
if (x == kNegInf) {
CHECK(y != kPosInf);
return kNegInf;
}
if (y == kPosInf || y == kNegInf) return y;
if (WillOverflow<AddNode>(x, y, kNegInf, kPosInf)) {
if (x > 0) return kPosInf;
return kNegInf;
}
return x + y;
}
/*!
* \brief Compute x * y, aware of inf.
* \param x The left operand.
* \param y The right operand.
* \return the result.
*/
static int64_t InfAwareMul(int64_t x, int64_t y) {
if (!WillOverflow<MulNode>(x, y, kNegInf, kPosInf)) return x * y;
if ((x > 0 && y > 0) || (x < 0 && y < 0)) return kPosInf;
return kNegInf;
}
/*!
* \brief Compute x / y, aware of inf.
* \param x The left operand.
* \param y The right operand.
* \return the result.
*/
static int64_t InfAwareDiv(int64_t x, int64_t y) {
CHECK_NE(y, 0);
if (x == kPosInf || x == kNegInf) {
if (y > 0) return x;
return -x;
}
return x / y;
}
/*!
* \brief Compute floodiv(x, y), aware of inf.
* \param x The left operand.
* \param y The right operand.
* \return the result.
*/
static int64_t InfAwareFloorDiv(int64_t x, int64_t y) {
CHECK_NE(y, 0);
if (x == kPosInf || x == kNegInf) {
if (y > 0) return x;
return -x;
}
return floordiv(x, y);
}
/*!
* \brief Compute x / y, aware of inf.
* \param x The left operand.
* \param y The right operand.
* \return the result.
*/
static int64_t InfAwareRightShift(int64_t x, int64_t y) {
if (x == kPosInf || x == kNegInf) return x;
return x >> y;
}
/*!
* \brief Make a new bound entry.
*/
static Entry MakeBound(int64_t min_value, int64_t max_value) {
Entry e;
e.min_value = min_value;
e.max_value = max_value;
return e;
}
/*!
* \brief Create union of two sets.
* \param a The left operand.
* \param b the right operand.
*/
static Entry Union(Entry a, Entry b) {
Entry ret;
ret.min_value = std::min(a.min_value, b.min_value);
ret.max_value = std::max(a.max_value, b.max_value);
return ret;
}
/*!
* \brief Create intersect of two sets.
* \param a The left operand.
* \param b the right operand.
*/
static Entry Intersect(Entry a, Entry b) {
Entry ret;
ret.min_value = std::max(a.min_value, b.min_value);
ret.max_value = std::min(a.max_value, b.max_value);
return ret;
}
/*!
* \brief return everything dtype can represent.
* \param dtype The data type.
* \return Bound that represent everything dtype can represent.
*/
static Entry Everything(DataType dtype) {
if (!dtype.is_int() && !dtype.is_uint()) {
return MakeBound(kNegInf, kPosInf);
}
Entry ret;
int64_t vbits = dtype.bits() - static_cast<int>(dtype.is_int());
if (dtype.is_uint()) {
ret.min_value = 0;
} else {
if (vbits >= 63) {
ret.min_value = kNegInf;
} else {
ret.min_value = -(static_cast<int64_t>(1) << vbits);
}
}
if (vbits >= 63) {
ret.max_value = kPosInf;
} else {
ret.max_value = (static_cast<int64_t>(1) << vbits) - 1;
}
return ret;
}
/*!
* \brief Detect additional constant bound from cond, if any
* \param cond The constraint condition.
* \return List of detected bounds.
*/
static std::vector<BoundInfo> DetectBoundInfo(const PrimExpr& cond) {
PVar<PrimExpr> x, y;
PVar<IntImm> c;
// NOTE: canonical form always use <= or <
if ((c <= x).Match(cond)) {
return {BoundInfo(x.Eval(), MakeBound(c.Eval()->value, kPosInf))};
}
if ((c < x).Match(cond)) {
return {BoundInfo(x.Eval(), MakeBound(c.Eval()->value + 1, kPosInf))};
}
if ((x <= c).Match(cond)) {
return {BoundInfo(x.Eval(), MakeBound(kNegInf, c.Eval()->value))};
}
if ((x < c).Match(cond)) {
return {BoundInfo(x.Eval(), MakeBound(kNegInf, c.Eval()->value - 1))};
}
if ((x && y).Match(cond)) {
auto ret1 = DetectBoundInfo(x.Eval());
auto ret2 = DetectBoundInfo(y.Eval());
ret1.insert(ret1.end(), ret2.begin(), ret2.end());
return ret1;
}
return {};
}
};
ConstIntBound ConstIntBoundAnalyzer::operator()(const PrimExpr& expr) {
Entry ret = impl_->VisitExpr(expr);
return ConstIntBound(ret.min_value, ret.max_value);
}
ConstIntBound ConstIntBoundAnalyzer::operator()(const PrimExpr& expr,
std::unordered_map<const PrimExprNode*, ConstIntBound>* bound) {
impl_->bound_ = bound;
Entry ret = impl_->VisitExpr(expr);
impl_->bound_ = nullptr;
return ConstIntBound(ret.min_value, ret.max_value);
}
void ConstIntBoundAnalyzer::Update(const Var& var,
const ConstIntBound& info,
bool override) {
impl_->Update(var, info, override);
}
void ConstIntBoundAnalyzer::Bind(const Var& var, const Range& range, bool override) {
impl_->Bind(var, range, override);
}
std::function<void()> ConstIntBoundAnalyzer::EnterConstraint(const PrimExpr& constraint) {
return impl_->EnterConstraint(constraint);
}
ConstIntBoundAnalyzer::ConstIntBoundAnalyzer(Analyzer* parent)
: impl_(new Impl()) {
}
ConstIntBoundAnalyzer::~ConstIntBoundAnalyzer() {
delete impl_;
}
} // namespace arith
} // namespace tvm