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#pragma once
#include <torch/csrc/jit/tensorexpr/bounds_overlap.h>
#include <torch/csrc/jit/tensorexpr/eval.h>
#include <torch/csrc/jit/tensorexpr/hash_provider.h>
#include <torch/csrc/jit/tensorexpr/ir.h>
#include <torch/csrc/jit/tensorexpr/ir_mutator.h>
#include <torch/csrc/jit/tensorexpr/ir_visitor.h>
#include <torch/csrc/jit/tensorexpr/types.h>
#include <utility>
/* IR Simplification
*
* Simplifies expressions in two stages:
* 1. Recursively traverse the map combining similar operations into Terms
* (interacted via Multiplication) and Polynomials (interacted via Addition). We
* reorder the components of each Term or Polynomial into a consistent order to
* allow combination or cancelling of like terms.
* 2. Once the format of the tree is minimal, expand each Term into a sequence
* of Muls, and each Polynomial into a sequence of Ads.
*/
namespace torch::jit::tensorexpr {
// A bunch of helpers for determine the Dtype of the output of a multi argument
// Term or Polynomial.
template <class ExprType>
Dtype promoteTypesVec(const ExprPtr& s, const std::vector<ExprType>& v) {
Dtype t = s->dtype();
bool first = true;
for (const auto& e : v) {
if (first) {
t = Dtype(t.scalar_type(), e->dtype().lanes());
first = false;
}
t = promoteTypes(t, e->dtype());
}
return t;
}
template <class ExprType>
Dtype promoteTypesVec(const std::vector<ExprType>& v) {
if (v.empty()) {
throw malformed_input("empty list of types");
}
Dtype t = v[0]->dtype();
for (const auto& e : v) {
t = promoteTypes(t, e->dtype());
}
return t;
}
template <class ExprType>
Dtype promoteTypesMap(
const ExprPtr& s,
std::unordered_map<SimplifierHashType, ExprType>& m) {
Dtype t = s->dtype();
bool first = true;
for (auto& e : m) {
if (first) {
t = Dtype(t.scalar_type(), e.second->dtype().lanes());
first = false;
}
t = promoteTypes(t, e.second->dtype());
}
return t;
}
template <class ExprType>
Dtype promoteTypesVar(ExprType e) {
return e->dtype();
}
template <class ExprType, class... Args>
Dtype promoteTypesVar(ExprType e, Args... es) {
Dtype lhs = e->dtype();
Dtype rhs = promoteTypesVar(es...);
if (e->isConstant()) {
lhs = Dtype(lhs.scalar_type(), rhs.lanes());
}
return promoteTypes(lhs, rhs);
}
// Uses the evaluator to fold an Expression with constant terms.
// E.g. evaluateOp(Add(3, 4)) => 7.
// Expr v must not have any unbound Vars.
inline ExprPtr evaluateOp(const ExprPtr& v) {
ExprHandle handle(v);
ExprEval<SimpleIREvaluator> eval(handle);
switch (v->dtype().scalar_type()) {
#define TYPE_CASE(Type, Name) \
case ScalarType::Name: { \
Type val = eval.value<Type>(); \
return getImmediateByType(v->dtype().scalar_type(), val); \
}
AT_FORALL_SCALAR_TYPES_AND3(Bool, Half, BFloat16, TYPE_CASE)
#undef TYPE_CASE
default:
LOG(FATAL) << "Unsupported datatype: " << v->dtype();
return nullptr;
}
return nullptr;
}
// A Term represents a grouping of Exprs through multiplication.
// E.g. product(scalar, *variables).
class Term : public ExprNode<Term> {
public:
template <class... Args>
Term(HashProvider& hasher, ExprPtr s, Args... ts)
: ExprNodeBase(promoteTypesVar(s, ts...)), scalar_(s), hasher_(hasher) {
CHECK(s->isConstant());
addComponent(ts...);
sort();
}
Term(HashProvider& hasher, ExprPtr s, std::vector<ExprPtr> v)
: ExprNodeBase(promoteTypesVec(s, v)),
variables_(std::move(v)),
scalar_(std::move(s)),
hasher_(hasher) {
sort();
}
// Convenience constructor from a map of hash -> var, used when merging Terms.
Term(
HashProvider& hasher,
const ExprPtr& s,
std::unordered_map<SimplifierHashType, ExprPtr> varmap)
: ExprNodeBase(promoteTypesMap(s, varmap)), scalar_(s), hasher_(hasher) {
for (auto& p : varmap) {
addComponent(p.second);
}
sort();
}
ExprPtr scalar() const {
return scalar_;
}
const std::vector<ExprPtr>& variables() const {
return variables_;
}
HashProvider& hasher() const {
return hasher_;
}
// Produce a hash of just the variable components of this term, to determine
// if it can be combined with another term.
SimplifierHashType hashVars() const;
private:
std::vector<ExprPtr> variables_;
ExprPtr scalar_;
HashProvider& hasher_;
void addComponent() {}
void addComponent(ExprPtr e) {
variables_.push_back(std::move(e));
}
template <class... Es>
void addComponent(ExprPtr e, Es&&... es) {
addComponent(std::move(e));
addComponent(std::forward<Es>(es)...);
}
// Sort by hash to normalize order of components.
void sort();
};
// Polynomial represents a grouping of Exprs by addition.
// E.g. sum(*variables, scalar).
// This would better be called Expression, but, naming conflict...
class Polynomial : public ExprNode<Polynomial> {
public:
template <class... Args>
Polynomial(HashProvider& hasher, ExprPtr s, Args... ts)
: ExprNodeBase(promoteTypesVar(s, ts...)), scalar_(s), hasher_(hasher) {
CHECK(s->isConstant());
addTerm(ts...);
sort();
}
Polynomial(HashProvider& hasher, const ExprPtr& s, std::vector<TermPtr> v)
: ExprNodeBase(promoteTypesVec(s, v)),
variables_(std::move(v)),
scalar_(s),
hasher_(hasher) {
sort();
}
// Helper constructor for list of terms with no scalar component.
Polynomial(HashProvider& hasher, std::vector<TermPtr> terms)
: ExprNodeBase(promoteTypesVec(terms)),
variables_(std::move(terms)),
scalar_(getImmediateByType(dtype(), 0)),
hasher_(hasher) {
sort();
}
// Convenience constructor for map of hash -> var, used when merging
// Polynomials.
Polynomial(
HashProvider& hasher,
const ExprPtr& s,
std::unordered_map<SimplifierHashType, TermPtr> varmap)
: ExprNodeBase(promoteTypesMap(s, varmap)), scalar_(s), hasher_(hasher) {
for (auto& p : varmap) {
addTerm(p.second);
}
sort();
}
ExprPtr scalar() const {
return scalar_;
}
const std::vector<TermPtr>& variables() const {
return variables_;
}
HashProvider& hasher() const {
return hasher_;
}
SimplifierHashType hashVars() const;
private:
std::vector<TermPtr> variables_;
ExprPtr scalar_;
HashProvider& hasher_;
void addTerm(TermPtr t) {
variables_.push_back(std::move(t));
}
template <class... Ts>
void addTerm(TermPtr t, Ts&&... ts) {
addTerm(std::move(t));
addTerm(std::forward<Ts>(ts)...);
}
// Sort by hash to normalize order of terms.
void sort();
};
class RoundOff : public BinaryOpNode<RoundOff> {
public:
RoundOff(ExprPtr lhs, ExprPtr rhs)
: BinaryOpNode(std::move(lhs), std::move(rhs), IRNodeType::kOther) {}
};
class MaxTerm : public ExprNode<MaxTerm> {
public:
template <class... Args>
MaxTerm(HashProvider& hasher, ExprPtr s, bool p, Args... ts)
: ExprNodeBase(s ? promoteTypesVar(s, ts...) : promoteTypesVar(ts...)),
scalar_(s),
hasher_(hasher),
propagate_nans_(p) {
addComponent(ts...);
uniquefy();
}
MaxTerm(
HashProvider& hasher,
const ExprPtr& s,
bool p,
std::vector<ExprPtr> v)
: ExprNodeBase(s ? promoteTypesVec(s, v) : promoteTypesVec(v)),
variables_(std::move(v)),
scalar_(s),
hasher_(hasher),
propagate_nans_(p) {
uniquefy();
}
bool propagate_nans() const {
return propagate_nans_;
}
ExprPtr scalar() const {
return scalar_;
}
const std::vector<ExprPtr>& variables() const {
return variables_;
}
HashProvider& hasher() const {
return hasher_;
}
private:
std::vector<ExprPtr> variables_;
ExprPtr scalar_;
HashProvider& hasher_;
bool propagate_nans_;
void addComponent() {}
void addComponent(ExprPtr e) {
variables_.push_back(std::move(e));
}
template <class... Es>
void addComponent(ExprPtr e, Es&&... es) {
addComponent(std::move(e));
addComponent(std::forward<Es>(es)...);
}
// Uniquefy the terms using their hash.
void uniquefy();
};
class MinTerm : public ExprNode<MinTerm> {
public:
template <class... Args>
MinTerm(HashProvider& hasher, ExprPtr s, bool p, Args... ts)
: ExprNodeBase(s ? promoteTypesVar(s, ts...) : promoteTypesVar(ts...)),
scalar_(s),
hasher_(hasher),
propagate_nans_(p) {
addComponent(ts...);
uniquefy();
}
MinTerm(
HashProvider& hasher,
const ExprPtr& s,
bool p,
std::vector<ExprPtr> v)
: ExprNodeBase(s ? promoteTypesVec(s, v) : promoteTypesVec(v)),
variables_(std::move(v)),
scalar_(s),
hasher_(hasher),
propagate_nans_(p) {
uniquefy();
}
bool propagate_nans() const {
return propagate_nans_;
}
ExprPtr scalar() const {
return scalar_;
}
const std::vector<ExprPtr>& variables() const {
return variables_;
}
HashProvider& hasher() const {
return hasher_;
}
private:
std::vector<ExprPtr> variables_;
ExprPtr scalar_;
HashProvider& hasher_;
bool propagate_nans_;
void addComponent() {}
void addComponent(ExprPtr e) {
variables_.push_back(std::move(e));
}
template <class... Es>
void addComponent(ExprPtr e, Es&&... es) {
addComponent(std::move(e));
addComponent(std::forward<Es>(es)...);
}
// Uniquefy the terms using their hash.
void uniquefy();
};
// Context-sensitive IR simplification
using VarBoundInfo = std::unordered_map<VarPtr, analysis::Bound>;
class TORCH_API SimplifierUnderContext : public IRMutator {
public:
~SimplifierUnderContext() override = default;
// Add boundary info for index variables in for-loops
StmtPtr mutate(const ForPtr& v) override;
ExprPtr mutate(const DivPtr& v) override;
ExprPtr mutate(const ModPtr& v) override;
ExprPtr mutate(const CompareSelectPtr& v) override;
ExprPtr mutate(const IfThenElsePtr& v) override;
protected:
bool getLoopBoundInfo(const ExprPtr& expr, analysis::Bound* loop_bound_info);
protected:
// NOLINTNEXTLINE(cppcoreguidelines-non-private-member-variables-in-classes)
HashProvider hasher_;
VarBoundInfo var_bound_info_;
};
// Stmt simplification should occur in both modes.
class TORCH_API PolynomialBase : public IRMutator {
public:
~PolynomialBase() override = default;
StmtPtr mutate(const BlockPtr& v) override;
StmtPtr mutate(const CondPtr& v) override;
StmtPtr mutate(const ForPtr& v) override;
// Trivially factorize terms by GCD of scalar components.
TermPtr factorizePolynomial(const PolynomialPtr& poly);
HashProvider& hasher() {
return hasher_;
}
protected:
// NOLINTNEXTLINE(cppcoreguidelines-non-private-member-variables-in-classes)
HashProvider hasher_;
};
// Simplify the IR by combining arithmetic expressions over common terms.
class TORCH_API PolynomialTransformer : public PolynomialBase {
public:
using PolynomialBase::mutate;
// Inserts term into the provided map, in the case of a hash collision
// combines the term with the existing and updates the map.
void addOrUpdateTerm(
std::unordered_map<SimplifierHashType, TermPtr>& varmap,
const TermPtr& term);
// Add Polynomial expressions, combining Terms representing the same
// variables.
ExprPtr addPolynomials(const PolynomialPtr& lhs, const PolynomialPtr& rhs);
// Insert a new Term into the provided polynomial. If the new term has
// common variables to an existing term it is combined.
ExprPtr insertTerm(const PolynomialPtr& poly, const TermPtr& term);
// Merge and simplify addition.
ExprPtr mutate(const AddPtr& v) override;
// Subtract one term from another, cancelling if necessary.
ExprPtr subTerms(const TermPtr& lhs, TermPtr rhs, bool negated);
// Subtract the RHS Polynomial from the LHS Polynomial, cancelling out where
// possible.
ExprPtr subPolynomials(const PolynomialPtr& lhs, const PolynomialPtr& rhs);
// Merge and simplify subtraction.
ExprPtr mutate(const SubPtr& v) override;
// Multiply two terms together, usually creating a new term with the variable
// lists concatenated.
TermPtr mulTerms(const TermPtr& lhs, const TermPtr& rhs);
// Multiply a Polynomial by a Term.
ExprPtr polyByTerm(const PolynomialPtr& poly, const TermPtr& term);
// Match a rounding pattern and create a RoundOff if found.
ExprPtr isRoundOff(const ExprPtr& lhs, const ExprPtr& rhs);
// Inserts a new component into a term, simplifying if possible.
ExprPtr insertIntoTerm(const TermPtr& term, const ExprPtr& expr);
// Merge and simplify multiplication.
ExprPtr mutate(const MulPtr& v) override;
ExprPtr mutate(const DivPtr& v) override;
ExprPtr mutate(const ModPtr& v) override;
ExprPtr mutate(const AndPtr& v) override;
ExprPtr mutate(const XorPtr& v) override;
ExprPtr mutate(const LshiftPtr& v) override;
ExprPtr mutate(const RshiftPtr& v) override;
ExprPtr mutate(const MaxPtr& v) override;
ExprPtr mutate(const MinPtr& v) override;
ExprPtr mutate(const CompareSelectPtr& v) override;
ExprPtr mutate(const IntrinsicsPtr& v) override;
ExprPtr mutate(const CastPtr& v) override;
ExprPtr mutate(const IfThenElsePtr& v) override;
static ExprPtr simplify(ExprPtr e);
static ExprHandle simplify(const ExprHandle& e);
static StmtPtr simplify(StmtPtr e);
};
// Expands Terms and Polynomial expressions into primitive operations.
// Does some simple factorization and reordering.
class TORCH_API TermExpander : public PolynomialBase {
PolynomialTransformer* simplifier_;
std::set<VarPtr> eliminated_allocations_;
public:
using PolynomialBase::mutate;
TermExpander(PolynomialTransformer* simplifier) : simplifier_(simplifier) {}
bool check_safe() {
return eliminated_allocations_.empty();
}
// Expand Terms out to a series of Muls.
ExprPtr mutate(const TermPtr& v) override;
// Expand Polynomials out to a series of Adds.
ExprPtr mutate(const PolynomialPtr& v) override;
// Expand MaxTerms to a series of Max ops.
ExprPtr mutate(const MaxTermPtr& v) override;
// Expand MinTerms to a series of Min ops.
ExprPtr mutate(const MinTermPtr& v) override;
// Expand RoundOff to it's component: Mul(Div(lhs, rhs), rhs).
ExprPtr mutate(const RoundOffPtr& v) override;
// Eliminate zero length allocations.
StmtPtr mutate(const AllocatePtr& v) override;
StmtPtr mutate(const FreePtr& v) override;
// Override to enable condition fusing.
BlockPtr fuseConditions(BlockPtr v);
StmtPtr fuseSyncThreads(BlockPtr block);
StmtPtr mutate(const BlockPtr& v) override;
};
class TORCH_API IRSimplifier {
public:
static StmtPtr simplify(StmtPtr s);
static ExprPtr simplify(ExprPtr e);
static ExprHandle simplify(const ExprHandle& e) {
return ExprHandle(simplify(e.node()));
}
};
// Flattens the buf and performs the simplifier on the flattened dims.
ExprPtr buf_flat_size(const BufPtr& v);
// Returns true if expressions A and B can be simplified to an equal expression.
TORCH_API bool exprEquals(const ExprPtr& A, const ExprPtr& B);
} // namespace torch::jit::tensorexpr
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