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// Copyright (c) 2018 Google LLC.
// Licensed 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
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASI,
// See the License for the specific language governing permissions and
// limitations under the License.
#include <algorithm>
#include <memory>
#include <string>
#include <vector>
#include "source/opt/tree_iterator.h"
namespace spvtools {
namespace opt {
class Loop;
class ScalarEvolutionAnalysis;
class SEConstantNode;
class SERecurrentNode;
class SEAddNode;
class SEMultiplyNode;
class SENegative;
class SEValueUnknown;
class SECantCompute;
// Abstract class representing a node in the scalar evolution DAG. Each node
// contains a vector of pointers to its children and each subclass of SENode
// implements GetType and an As method to allow casting. SENodes can be hashed
// using the SENodeHash functor. The vector of children is sorted when a node is
// added. This is important as it allows the hash of X+Y to be the same as Y+X.
class SENode {
enum SENodeType {
using ChildContainerType = std::vector<SENode*>;
explicit SENode(ScalarEvolutionAnalysis* parent_analysis)
: parent_analysis_(parent_analysis), unique_id_(++NumberOfNodes) {}
virtual SENodeType GetType() const = 0;
virtual ~SENode() {}
virtual inline void AddChild(SENode* child) {
// If this is a constant node, assert.
if (AsSEConstantNode()) {
assert(false && "Trying to add a child node to a constant!");
// Find the first point in the vector where |child| is greater than the node
// currently in the vector.
auto find_first_less_than = [child](const SENode* node) {
return child->unique_id_ <= node->unique_id_;
auto position = std::find_if_not(children_.begin(), children_.end(),
// Children are sorted so the hashing and equality operator will be the same
// for a node with the same children. X+Y should be the same as Y+X.
children_.insert(position, child);
// Get the type as an std::string. This is used to represent the node in the
// dot output and is used to hash the type as well.
std::string AsString() const;
// Dump the SENode and its immediate children, if |recurse| is true then it
// will recurse through all children to print the DAG starting from this node
// as a root.
void DumpDot(std::ostream& out, bool recurse = false) const;
// Checks if two nodes are the same by hashing them.
bool operator==(const SENode& other) const;
// Checks if two nodes are not the same by comparing the hashes.
bool operator!=(const SENode& other) const;
// Return the child node at |index|.
inline SENode* GetChild(size_t index) { return children_[index]; }
inline const SENode* GetChild(size_t index) const { return children_[index]; }
// Iterator to iterate over the child nodes.
using iterator = ChildContainerType::iterator;
using const_iterator = ChildContainerType::const_iterator;
// Iterate over immediate child nodes.
iterator begin() { return children_.begin(); }
iterator end() { return children_.end(); }
// Constant overloads for iterating over immediate child nodes.
const_iterator begin() const { return children_.cbegin(); }
const_iterator end() const { return children_.cend(); }
const_iterator cbegin() { return children_.cbegin(); }
const_iterator cend() { return children_.cend(); }
// Collect all the recurrent nodes in this SENode
std::vector<SERecurrentNode*> CollectRecurrentNodes() {
std::vector<SERecurrentNode*> recurrent_nodes{};
if (auto recurrent_node = AsSERecurrentNode()) {
for (auto child : GetChildren()) {
auto child_recurrent_nodes = child->CollectRecurrentNodes();
return recurrent_nodes;
// Collect all the value unknown nodes in this SENode
std::vector<SEValueUnknown*> CollectValueUnknownNodes() {
std::vector<SEValueUnknown*> value_unknown_nodes{};
if (auto value_unknown_node = AsSEValueUnknown()) {
for (auto child : GetChildren()) {
auto child_value_unknown_nodes = child->CollectValueUnknownNodes();
return value_unknown_nodes;
// Iterator to iterate over the entire DAG. Even though we are using the tree
// iterator it should still be safe to iterate over. However, nodes with
// multiple parents will be visited multiple times, unlike in a tree.
using dag_iterator = TreeDFIterator<SENode>;
using const_dag_iterator = TreeDFIterator<const SENode>;
// Iterate over all child nodes in the graph.
dag_iterator graph_begin() { return dag_iterator(this); }
dag_iterator graph_end() { return dag_iterator(); }
const_dag_iterator graph_begin() const { return graph_cbegin(); }
const_dag_iterator graph_end() const { return graph_cend(); }
const_dag_iterator graph_cbegin() const { return const_dag_iterator(this); }
const_dag_iterator graph_cend() const { return const_dag_iterator(); }
// Return the vector of immediate children.
const ChildContainerType& GetChildren() const { return children_; }
ChildContainerType& GetChildren() { return children_; }
// Return true if this node is a cant compute node.
bool IsCantCompute() const { return GetType() == CanNotCompute; }
// Implements a casting method for each type.
// clang-format off
#define DeclareCastMethod(target) \
virtual target* As##target() { return nullptr; } \
virtual const target* As##target() const { return nullptr; }
#undef DeclareCastMethod
// Get the analysis which has this node in its cache.
inline ScalarEvolutionAnalysis* GetParentAnalysis() const {
return parent_analysis_;
ChildContainerType children_;
ScalarEvolutionAnalysis* parent_analysis_;
// The unique id of this node, assigned on creation by incrementing the static
// node count.
uint32_t unique_id_;
// The number of nodes created.
static uint32_t NumberOfNodes;
// clang-format on
// Function object to handle the hashing of SENodes. Hashing algorithm hashes
// the type (as a string), the literal value of any constants, and the child
// pointers which are assumed to be unique.
struct SENodeHash {
size_t operator()(const std::unique_ptr<SENode>& node) const;
size_t operator()(const SENode* node) const;
// A node representing a constant integer.
class SEConstantNode : public SENode {
SEConstantNode(ScalarEvolutionAnalysis* parent_analysis, int64_t value)
: SENode(parent_analysis), literal_value_(value) {}
SENodeType GetType() const final { return Constant; }
int64_t FoldToSingleValue() const { return literal_value_; }
SEConstantNode* AsSEConstantNode() override { return this; }
const SEConstantNode* AsSEConstantNode() const override { return this; }
inline void AddChild(SENode*) final {
assert(false && "Attempting to add a child to a constant node!");
int64_t literal_value_;
// A node representing a recurrent expression in the code. A recurrent
// expression is an expression whose value can be expressed as a linear
// expression of the loop iterations. Such as an induction variable. The actual
// value of a recurrent expression is coefficent_ * iteration + offset_, hence
// an induction variable i=0, i++ becomes a recurrent expression with an offset
// of zero and a coefficient of one.
class SERecurrentNode : public SENode {
SERecurrentNode(ScalarEvolutionAnalysis* parent_analysis, const Loop* loop)
: SENode(parent_analysis), loop_(loop) {}
SENodeType GetType() const final { return RecurrentAddExpr; }
inline void AddCoefficient(SENode* child) {
coefficient_ = child;
inline void AddOffset(SENode* child) {
offset_ = child;
inline const SENode* GetCoefficient() const { return coefficient_; }
inline SENode* GetCoefficient() { return coefficient_; }
inline const SENode* GetOffset() const { return offset_; }
inline SENode* GetOffset() { return offset_; }
// Return the loop which this recurrent expression is recurring within.
const Loop* GetLoop() const { return loop_; }
SERecurrentNode* AsSERecurrentNode() override { return this; }
const SERecurrentNode* AsSERecurrentNode() const override { return this; }
SENode* coefficient_;
SENode* offset_;
const Loop* loop_;
// A node representing an addition operation between child nodes.
class SEAddNode : public SENode {
explicit SEAddNode(ScalarEvolutionAnalysis* parent_analysis)
: SENode(parent_analysis) {}
SENodeType GetType() const final { return Add; }
SEAddNode* AsSEAddNode() override { return this; }
const SEAddNode* AsSEAddNode() const override { return this; }
// A node representing a multiply operation between child nodes.
class SEMultiplyNode : public SENode {
explicit SEMultiplyNode(ScalarEvolutionAnalysis* parent_analysis)
: SENode(parent_analysis) {}
SENodeType GetType() const final { return Multiply; }
SEMultiplyNode* AsSEMultiplyNode() override { return this; }
const SEMultiplyNode* AsSEMultiplyNode() const override { return this; }
// A node representing a unary negative operation.
class SENegative : public SENode {
explicit SENegative(ScalarEvolutionAnalysis* parent_analysis)
: SENode(parent_analysis) {}
SENodeType GetType() const final { return Negative; }
SENegative* AsSENegative() override { return this; }
const SENegative* AsSENegative() const override { return this; }
// A node representing a value which we do not know the value of, such as a load
// instruction.
class SEValueUnknown : public SENode {
// SEValueUnknowns must come from an instruction |unique_id| is the unique id
// of that instruction. This is so we cancompare value unknowns and have a
// unique value unknown for each instruction.
SEValueUnknown(ScalarEvolutionAnalysis* parent_analysis, uint32_t result_id)
: SENode(parent_analysis), result_id_(result_id) {}
SENodeType GetType() const final { return ValueUnknown; }
SEValueUnknown* AsSEValueUnknown() override { return this; }
const SEValueUnknown* AsSEValueUnknown() const override { return this; }
inline uint32_t ResultId() const { return result_id_; }
uint32_t result_id_;
// A node which we cannot reason about at all.
class SECantCompute : public SENode {
explicit SECantCompute(ScalarEvolutionAnalysis* parent_analysis)
: SENode(parent_analysis) {}
SENodeType GetType() const final { return CanNotCompute; }
SECantCompute* AsSECantCompute() override { return this; }
const SECantCompute* AsSECantCompute() const override { return this; }
} // namespace opt
} // namespace spvtools