// Copyright (c) 2015-2016 The Khronos Group Inc.
//
// 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
//
// 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.
#ifndef SOURCE_CFA_H_
#define SOURCE_CFA_H_
#include <algorithm>
#include <cassert>
#include <cstdint>
#include <functional>
#include <map>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
namespace spvtools {
// Control Flow Analysis of control flow graphs of basic block nodes |BB|.
template <class BB>
class CFA {
using bb_ptr = BB*;
using cbb_ptr = const BB*;
using bb_iter = typename std::vector<BB*>::const_iterator;
using get_blocks_func = std::function<const std::vector<BB*>*(const BB*)>;
struct block_info {
cbb_ptr block; ///< pointer to the block
bb_iter iter; ///< Iterator to the current child node being processed
};
/// Returns true if a block with @p id is found in the @p work_list vector
///
/// @param[in] work_list Set of blocks visited in the the depth first
/// traversal
/// of the CFG
/// @param[in] id The ID of the block being checked
///
/// @return true if the edge work_list.back().block->id() => id is a back-edge
static bool FindInWorkList(const std::vector<block_info>& work_list,
uint32_t id);
public:
/// @brief Depth first traversal starting from the \p entry BasicBlock
///
/// This function performs a depth first traversal from the \p entry
/// BasicBlock and calls the pre/postorder functions when it needs to process
/// the node in pre order, post order. It also calls the backedge function
/// when a back edge is encountered.
///
/// @param[in] entry The root BasicBlock of a CFG
/// @param[in] successor_func A function which will return a pointer to the
/// successor nodes
/// @param[in] preorder A function that will be called for every block in a
/// CFG following preorder traversal semantics
/// @param[in] postorder A function that will be called for every block in a
/// CFG following postorder traversal semantics
/// @param[in] backedge A function that will be called when a backedge is
/// encountered during a traversal
/// NOTE: The @p successor_func and predecessor_func each return a pointer to
/// a
/// collection such that iterators to that collection remain valid for the
/// lifetime of the algorithm.
static void DepthFirstTraversal(
const BB* entry, get_blocks_func successor_func,
std::function<void(cbb_ptr)> preorder,
std::function<void(cbb_ptr)> postorder,
std::function<void(cbb_ptr, cbb_ptr)> backedge);
/// @brief Calculates dominator edges for a set of blocks
///
/// Computes dominators using the algorithm of Cooper, Harvey, and Kennedy
/// "A Simple, Fast Dominance Algorithm", 2001.
///
/// The algorithm assumes there is a unique root node (a node without
/// predecessors), and it is therefore at the end of the postorder vector.
///
/// This function calculates the dominator edges for a set of blocks in the
/// CFG.
/// Uses the dominator algorithm by Cooper et al.
///
/// @param[in] postorder A vector of blocks in post order traversal
/// order
/// in a CFG
/// @param[in] predecessor_func Function used to get the predecessor nodes of
/// a
/// block
///
/// @return the dominator tree of the graph, as a vector of pairs of nodes.
/// The first node in the pair is a node in the graph. The second node in the
/// pair is its immediate dominator in the sense of Cooper et.al., where a
/// block
/// without predecessors (such as the root node) is its own immediate
/// dominator.
static std::vector<std::pair<BB*, BB*>> CalculateDominators(
const std::vector<cbb_ptr>& postorder, get_blocks_func predecessor_func);
// Computes a minimal set of root nodes required to traverse, in the forward
// direction, the CFG represented by the given vector of blocks, and successor
// and predecessor functions. When considering adding two nodes, each having
// predecessors, favour using the one that appears earlier on the input blocks
// list.
static std::vector<BB*> TraversalRoots(const std::vector<BB*>& blocks,
get_blocks_func succ_func,
get_blocks_func pred_func);
static void ComputeAugmentedCFG(
std::vector<BB*>& ordered_blocks, BB* pseudo_entry_block,
BB* pseudo_exit_block,
std::unordered_map<const BB*, std::vector<BB*>>* augmented_successors_map,
std::unordered_map<const BB*, std::vector<BB*>>*
augmented_predecessors_map,
get_blocks_func succ_func, get_blocks_func pred_func);
};
template <class BB>
bool CFA<BB>::FindInWorkList(const std::vector<block_info>& work_list,
uint32_t id) {
for (const auto b : work_list) {
if (b.block->id() == id) return true;
}
return false;
}
template <class BB>
void CFA<BB>::DepthFirstTraversal(
const BB* entry, get_blocks_func successor_func,
std::function<void(cbb_ptr)> preorder,
std::function<void(cbb_ptr)> postorder,
std::function<void(cbb_ptr, cbb_ptr)> backedge) {
std::unordered_set<uint32_t> processed;
/// NOTE: work_list is the sequence of nodes from the root node to the node
/// being processed in the traversal
std::vector<block_info> work_list;
work_list.reserve(10);
work_list.push_back({entry, std::begin(*successor_func(entry))});
preorder(entry);
processed.insert(entry->id());
while (!work_list.empty()) {
block_info& top = work_list.back();
if (top.iter == end(*successor_func(top.block))) {
postorder(top.block);
work_list.pop_back();
} else {
BB* child = *top.iter;
top.iter++;
if (FindInWorkList(work_list, child->id())) {
backedge(top.block, child);
}
if (processed.count(child->id()) == 0) {
preorder(child);
work_list.emplace_back(
block_info{child, std::begin(*successor_func(child))});
processed.insert(child->id());
}
}
}
}
template <class BB>
std::vector<std::pair<BB*, BB*>> CFA<BB>::CalculateDominators(
const std::vector<cbb_ptr>& postorder, get_blocks_func predecessor_func) {
struct block_detail {
size_t dominator; ///< The index of blocks's dominator in post order array
size_t postorder_index; ///< The index of the block in the post order array
};
const size_t undefined_dom = postorder.size();
std::unordered_map<cbb_ptr, block_detail> idoms;
for (size_t i = 0; i < postorder.size(); i++) {
idoms[postorder[i]] = {undefined_dom, i};
}
idoms[postorder.back()].dominator = idoms[postorder.back()].postorder_index;
bool changed = true;
while (changed) {
changed = false;
for (auto b = postorder.rbegin() + 1; b != postorder.rend(); ++b) {
const std::vector<BB*>& predecessors = *predecessor_func(*b);
// Find the first processed/reachable predecessor that is reachable
// in the forward traversal.
auto res = std::find_if(std::begin(predecessors), std::end(predecessors),
[&idoms, undefined_dom](BB* pred) {
return idoms.count(pred) &&
idoms[pred].dominator != undefined_dom;
});
if (res == end(predecessors)) continue;
const BB* idom = *res;
size_t idom_idx = idoms[idom].postorder_index;
// all other predecessors
for (const auto* p : predecessors) {
if (idom == p) continue;
// Only consider nodes reachable in the forward traversal.
// Otherwise the intersection doesn't make sense and will never
// terminate.
if (!idoms.count(p)) continue;
if (idoms[p].dominator != undefined_dom) {
size_t finger1 = idoms[p].postorder_index;
size_t finger2 = idom_idx;
while (finger1 != finger2) {
while (finger1 < finger2) {
finger1 = idoms[postorder[finger1]].dominator;
}
while (finger2 < finger1) {
finger2 = idoms[postorder[finger2]].dominator;
}
}
idom_idx = finger1;
}
}
if (idoms[*b].dominator != idom_idx) {
idoms[*b].dominator = idom_idx;
changed = true;
}
}
}
std::vector<std::pair<bb_ptr, bb_ptr>> out;
for (auto idom : idoms) {
// NOTE: performing a const cast for convenient usage with
// UpdateImmediateDominators
out.push_back({const_cast<BB*>(std::get<0>(idom)),
const_cast<BB*>(postorder[std::get<1>(idom).dominator])});
}
// Sort by postorder index to generate a deterministic ordering of edges.
std::sort(
out.begin(), out.end(),
[&idoms](const std::pair<bb_ptr, bb_ptr>& lhs,
const std::pair<bb_ptr, bb_ptr>& rhs) {
assert(lhs.first);
assert(lhs.second);
assert(rhs.first);
assert(rhs.second);
auto lhs_indices = std::make_pair(idoms[lhs.first].postorder_index,
idoms[lhs.second].postorder_index);
auto rhs_indices = std::make_pair(idoms[rhs.first].postorder_index,
idoms[rhs.second].postorder_index);
return lhs_indices < rhs_indices;
});
return out;
}
template <class BB>
std::vector<BB*> CFA<BB>::TraversalRoots(const std::vector<BB*>& blocks,
get_blocks_func succ_func,
get_blocks_func pred_func) {
// The set of nodes which have been visited from any of the roots so far.
std::unordered_set<const BB*> visited;
auto mark_visited = [&visited](const BB* b) { visited.insert(b); };
auto ignore_block = [](const BB*) {};
auto ignore_blocks = [](const BB*, const BB*) {};
auto traverse_from_root = [&mark_visited, &succ_func, &ignore_block,
&ignore_blocks](const BB* entry) {
DepthFirstTraversal(entry, succ_func, mark_visited, ignore_block,
ignore_blocks);
};
std::vector<BB*> result;
// First collect nodes without predecessors.
for (auto block : blocks) {
if (pred_func(block)->empty()) {
assert(visited.count(block) == 0 && "Malformed graph!");
result.push_back(block);
traverse_from_root(block);
}
}
// Now collect other stranded nodes. These must be in unreachable cycles.
for (auto block : blocks) {
if (visited.count(block) == 0) {
result.push_back(block);
traverse_from_root(block);
}
}
return result;
}
template <class BB>
void CFA<BB>::ComputeAugmentedCFG(
std::vector<BB*>& ordered_blocks, BB* pseudo_entry_block,
BB* pseudo_exit_block,
std::unordered_map<const BB*, std::vector<BB*>>* augmented_successors_map,
std::unordered_map<const BB*, std::vector<BB*>>* augmented_predecessors_map,
get_blocks_func succ_func, get_blocks_func pred_func) {
// Compute the successors of the pseudo-entry block, and
// the predecessors of the pseudo exit block.
auto sources = TraversalRoots(ordered_blocks, succ_func, pred_func);
// For the predecessor traversals, reverse the order of blocks. This
// will affect the post-dominance calculation as follows:
// - Suppose you have blocks A and B, with A appearing before B in
// the list of blocks.
// - Also, A branches only to B, and B branches only to A.
// - We want to compute A as dominating B, and B as post-dominating B.
// By using reversed blocks for predecessor traversal roots discovery,
// we'll add an edge from B to the pseudo-exit node, rather than from A.
// All this is needed to correctly process the dominance/post-dominance
// constraint when A is a loop header that points to itself as its
// own continue target, and B is the latch block for the loop.
std::vector<BB*> reversed_blocks(ordered_blocks.rbegin(),
ordered_blocks.rend());
auto sinks = TraversalRoots(reversed_blocks, pred_func, succ_func);
// Wire up the pseudo entry block.
(*augmented_successors_map)[pseudo_entry_block] = sources;
for (auto block : sources) {
auto& augmented_preds = (*augmented_predecessors_map)[block];
const auto preds = pred_func(block);
augmented_preds.reserve(1 + preds->size());
augmented_preds.push_back(pseudo_entry_block);
augmented_preds.insert(augmented_preds.end(), preds->begin(), preds->end());
}
// Wire up the pseudo exit block.
(*augmented_predecessors_map)[pseudo_exit_block] = sinks;
for (auto block : sinks) {
auto& augmented_succ = (*augmented_successors_map)[block];
const auto succ = succ_func(block);
augmented_succ.reserve(1 + succ->size());
augmented_succ.push_back(pseudo_exit_block);
augmented_succ.insert(augmented_succ.end(), succ->begin(), succ->end());
}
}
} // namespace spvtools
#endif // SOURCE_CFA_H_