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| 1 | +# This file is a part of Julia. License is MIT: https://julialang.org/license |
| 2 | + |
| 3 | +using Core.Compiler: DomTree, CFG, BasicBlock, StmtRange, dominates |
| 4 | + |
| 5 | +struct SCCStackItem |
| 6 | + v::Int32 |
| 7 | + # which child of `v` to scan |
| 8 | + child::Int32 |
| 9 | + # the location of `parent` in the stack |
| 10 | + parent::Int32 |
| 11 | + # the index in the (pre-order traversal of the) DFS tree |
| 12 | + preorder::Int32 |
| 13 | + # the minimum node (by pre-order index) reachable from any node in the DFS sub-tree rooted at `v` |
| 14 | + minpreorder::Int32 |
| 15 | + # whether this node is reachable from BasicBlock #1 |
| 16 | + live::Bool |
| 17 | +end |
| 18 | + |
| 19 | +function SCCStackItem(item::SCCStackItem; child=item.child, |
| 20 | + minpreorder=item.minpreorder, live=item.live) |
| 21 | + return SCCStackItem( |
| 22 | + item.v, # v |
| 23 | + child, # child |
| 24 | + item.parent, # parent |
| 25 | + item.preorder, # preorder |
| 26 | + minpreorder, # minpreorder |
| 27 | + live, # live |
| 28 | + ) |
| 29 | +end |
| 30 | + |
| 31 | +struct CFGReachability |
| 32 | + irreducible::BitVector # BBNumber -> Bool |
| 33 | + scc::Vector{Int} # BBNumber -> SCCNumber |
| 34 | + domtree::DomTree |
| 35 | + |
| 36 | + _worklist::Vector{Int} # for node removal |
| 37 | + _stack::Vector{SCCStackItem} # for Tarjan's SCC algorithm |
| 38 | +end |
| 39 | + |
| 40 | +function CFGReachability(cfg::CFG, domtree::DomTree) |
| 41 | + n_blocks = length(cfg.blocks) |
| 42 | + reachability = CFGReachability( |
| 43 | + BitVector(undef, n_blocks), # irreducible |
| 44 | + zeros(Int, n_blocks), # scc |
| 45 | + domtree, # domtree |
| 46 | + Int[], # _worklist |
| 47 | + SCCStackItem[], # _stack |
| 48 | + ) |
| 49 | + tarjan!(reachability, cfg) |
| 50 | + return reachability |
| 51 | +end |
| 52 | + |
| 53 | +bb_unreachable(reach::CFGReachability, bb::Int) = reach.scc[bb] == 0 |
| 54 | + |
| 55 | +bb_in_irreducible_loop(reach::CFGReachability, bb::Int) = reach.irreducible[bb] |
| 56 | + |
| 57 | +# Returns `true` if a node is 'rooted' as reachable, i.e. it is has an incoming |
| 58 | +# edge from a resolved SCC other than its own (or it is BasicBlock #1). |
| 59 | +# |
| 60 | +# `tarjan!` takes the transitive closure of this relation in order to detect |
| 61 | +# which BasicBlocks are unreachable. |
| 62 | +function _bb_externally_reachable(reach::CFGReachability, cfg::CFG, bb::Int) |
| 63 | + (; scc) = reach |
| 64 | + bb == 1 && return true |
| 65 | + for pred in cfg.blocks[bb].preds |
| 66 | + scc[pred] <= 0 && continue |
| 67 | + dominates(reach.domtree, bb, pred) && continue |
| 68 | + @assert scc[pred] != scc[bb] |
| 69 | + return true |
| 70 | + end |
| 71 | + return false |
| 72 | +end |
| 73 | + |
| 74 | +""" |
| 75 | + tarjan!(reach::CFGReachability, cfg::CFG, root::Int=1) |
| 76 | +
|
| 77 | +Tarjan's strongly-connected components algorithm. Traverses the CFG starting at `root`, ignoring |
| 78 | +nodes with resolved SCC's and updating outputs for all un-resolved nodes. |
| 79 | +
|
| 80 | +Returns true if any node was discovered to be unreachable, false otherwise. |
| 81 | +
|
| 82 | +Outputs: |
| 83 | + - `reach.scc`: strongly-connected components, ignoring backedges to (natural) loops |
| 84 | + - `reach.irreducible`: true iff a BasicBlock is part of a (non-trivial) SCC / irreducible loop |
| 85 | + - `reach._worklist`: if performing an incremental update (`root != 1`), any traversed nodes that |
| 86 | + are unreachable from BasicBlock #1 are enqueued to this worklist |
| 87 | +""" |
| 88 | +function tarjan!(reach::CFGReachability, cfg::CFG; root::Int=1) |
| 89 | + (; scc, irreducible, domtree) = reach |
| 90 | + scc[root] != 0 && return scc |
| 91 | + live = _bb_externally_reachable(reach, cfg, root) |
| 92 | + |
| 93 | + # the original algorithm has a separate stack and worklist (unrelated to `reach._worklist`) |
| 94 | + # here we use a single combined stack for improved memory/cache efficiency |
| 95 | + stack = reach._stack |
| 96 | + push!(stack, SCCStackItem( |
| 97 | + root, # v |
| 98 | + 1, # child |
| 99 | + 0, # parent |
| 100 | + 1, # preorder |
| 101 | + 1, # minpreorder |
| 102 | + live, # live |
| 103 | + )) |
| 104 | + scc[root] = -1 |
| 105 | + cursor = length(stack) |
| 106 | + |
| 107 | + # worklist length before any new unreachable nodes are added |
| 108 | + worklist_len = length(reach._worklist) |
| 109 | + |
| 110 | + # last (pre-order) DFS label assigned to a node |
| 111 | + preorder_id = 1 |
| 112 | + while true |
| 113 | + (; v, child, minpreorder, live) = item = stack[cursor] |
| 114 | + |
| 115 | + bb = cfg.blocks[v] |
| 116 | + if child <= length(bb.succs) # queue next child |
| 117 | + stack[cursor] = item = SCCStackItem(item; child=child+1) |
| 118 | + succ = bb.succs[child] |
| 119 | + |
| 120 | + # ignore any back-edges in a (natural) loop (see `kill_edge!`) |
| 121 | + if dominates(domtree, succ, convert(Int, v)) |
| 122 | + # This check ensures that reducible CFG's will contain no SCC's. The vast majority |
| 123 | + # of functions have reducible CFG's, so this optimization is very important. |
| 124 | + continue |
| 125 | + end |
| 126 | + |
| 127 | + if scc[succ] < 0 |
| 128 | + # next child is already in DFS tree |
| 129 | + child_preorder = stack[-scc[succ]].preorder |
| 130 | + |
| 131 | + # only need to update `minpreorder` for `v` |
| 132 | + stack[cursor] = item = SCCStackItem(item; |
| 133 | + minpreorder=min(minpreorder, child_preorder)) |
| 134 | + elseif scc[succ] == 0 |
| 135 | + # next child is a new element in DFS tree |
| 136 | + preorder_id += 1 |
| 137 | + live = live || _bb_externally_reachable(reach, cfg, succ) |
| 138 | + push!(stack, SCCStackItem( |
| 139 | + succ, # v |
| 140 | + 1, # child |
| 141 | + cursor, # parent (index in stack) |
| 142 | + preorder_id, # preorder |
| 143 | + preorder_id, # minpreorder |
| 144 | + live, # live |
| 145 | + )) |
| 146 | + scc[succ] = -length(stack) |
| 147 | + cursor = length(stack) |
| 148 | + else end # next child is a resolved SCC (do nothing) |
| 149 | + else # v's children are processed, finalize v |
| 150 | + if item.minpreorder == item.preorder |
| 151 | + has_one_element = stack[end].v == v |
| 152 | + while true |
| 153 | + item = pop!(stack) |
| 154 | + if live |
| 155 | + scc[item.v] = v |
| 156 | + scan_subgraph!(reach, cfg, convert(Int, item.v), |
| 157 | + #= filter =# (pred,x)->(!dominates(domtree, x, pred) && scc[x] > typemax(Int)÷2), |
| 158 | + #= action =# (x)->(scc[x] -= typemax(Int)÷2;), |
| 159 | + ) |
| 160 | + else # this offset marks a node as 'maybe-dead' |
| 161 | + scc[item.v] = v + typemax(Int)÷2 |
| 162 | + push!(reach._worklist, item.v) |
| 163 | + end |
| 164 | + irreducible[item.v] = !has_one_element |
| 165 | + (item.v == v) && break |
| 166 | + end |
| 167 | + item.parent == 0 && break # all done |
| 168 | + elseif live |
| 169 | + stack[item.parent] = SCCStackItem(stack[item.parent]; live=true) |
| 170 | + end |
| 171 | + |
| 172 | + # update `minpreorder` for parent |
| 173 | + parent = stack[item.parent] |
| 174 | + minpreorder = min(parent.minpreorder, item.minpreorder) |
| 175 | + stack[item.parent] = SCCStackItem(parent; minpreorder) |
| 176 | + |
| 177 | + cursor = item.parent |
| 178 | + end |
| 179 | + end |
| 180 | + |
| 181 | + worklist = reach._worklist |
| 182 | + |
| 183 | + # filter the worklist, leaving any nodes not proven to be reachable from BB #1 |
| 184 | + n_filtered = 0 |
| 185 | + for i = (worklist_len + 1):length(worklist) |
| 186 | + @assert worklist[i] != 1 |
| 187 | + @assert scc[worklist[i]] > 0 |
| 188 | + if scc[worklist[i]] > typemax(Int)÷2 |
| 189 | + # node is unreachable, enqueue it |
| 190 | + scc[worklist[i]] = 0 |
| 191 | + worklist[i - n_filtered] = worklist[i] |
| 192 | + else |
| 193 | + n_filtered += 1 |
| 194 | + end |
| 195 | + end |
| 196 | + resize!(worklist, length(worklist) - n_filtered) |
| 197 | + |
| 198 | + return length(worklist) > worklist_len # if true, a (newly) unreachable node was enqueued |
| 199 | +end |
| 200 | + |
| 201 | +""" |
| 202 | +Scan the subtree rooted at `root`, excluding `root` itself |
| 203 | +
|
| 204 | +Note: This function will not detect cycles for you. The `filter` provided must |
| 205 | + protect against infinite cycle traversal. |
| 206 | +""" |
| 207 | +function scan_subgraph!(reach::CFGReachability, cfg::CFG, root::Int, filter, action) |
| 208 | + worklist = reach._worklist |
| 209 | + start_len = length(worklist) |
| 210 | + |
| 211 | + push!(worklist, root) |
| 212 | + while length(worklist) > start_len |
| 213 | + v = pop!(worklist) |
| 214 | + for succ in cfg.blocks[v].succs |
| 215 | + !filter(v, succ) && continue |
| 216 | + action(succ) |
| 217 | + push!(worklist, succ) |
| 218 | + end |
| 219 | + end |
| 220 | +end |
| 221 | + |
| 222 | +function enqueue_if_unreachable!(reach::CFGReachability, cfg::CFG, bb::Int) |
| 223 | + (; domtree, scc) = reach |
| 224 | + @assert scc[bb] != 0 |
| 225 | + |
| 226 | + bb == 1 && return false |
| 227 | + if bb_in_irreducible_loop(reach, bb) |
| 228 | + # irreducible CFG |
| 229 | + # this requires a full scan of the irreducible loop |
| 230 | + |
| 231 | + scc′ = scc[bb] |
| 232 | + scc[bb] = 0 |
| 233 | + scan_subgraph!(reach, cfg, bb, # set this SCC to 0 |
| 234 | + #= filter =# (pred,x)->(!dominates(domtree, x, pred) && scc[x] == scc′), |
| 235 | + #= action =# (x)->(scc[x] = 0;), |
| 236 | + ) |
| 237 | + |
| 238 | + # re-compute the SCC's for this portion of the CFG, adding any freshly |
| 239 | + # unreachable nodes to `reach._worklist` |
| 240 | + return tarjan!(reach, cfg; root=bb) |
| 241 | + else |
| 242 | + # target is a reducible CFG node |
| 243 | + # this node lives iff it still has an incoming forward edge |
| 244 | + for pred in cfg.blocks[bb].preds |
| 245 | + !dominates(domtree, bb, pred) && return false # forward-edge |
| 246 | + end |
| 247 | + scc[bb] = 0 |
| 248 | + push!(reach._worklist, bb) |
| 249 | + return true |
| 250 | + end |
| 251 | +end |
| 252 | + |
| 253 | +""" |
| 254 | +Remove from `cfg` and `reach` the edge (from → to), as well as any blocks/edges |
| 255 | +this causes to become unreachable. |
| 256 | +
|
| 257 | +Calls: |
| 258 | + - `block_callback` for every unreachable block. |
| 259 | + - `edge_callback` for every unreachable edge into a reachable block (may also |
| 260 | + be called for blocks which are later discovered to be unreachable). |
| 261 | +""" |
| 262 | +function kill_edge!(reach::CFGReachability, cfg::CFG, from::Int, to::Int, |
| 263 | + edge_callback=nothing, block_callback=nothing) |
| 264 | + (reach.scc[from] == 0) && return # source is already unreachable |
| 265 | + @assert reach.scc[to] != 0 |
| 266 | + |
| 267 | + # delete (from → to) edge |
| 268 | + preds, succs = cfg.blocks[to].preds, cfg.blocks[from].succs |
| 269 | + deleteat!(preds, findfirst(x::Int->x==from, preds)::Int) |
| 270 | + deleteat!(succs, findfirst(x::Int->x==to, succs)::Int) |
| 271 | + |
| 272 | + # check for unreachable target |
| 273 | + enqueued = enqueue_if_unreachable!(reach, cfg, to) |
| 274 | + if !enqueued && edge_callback !== nothing |
| 275 | + edge_callback(from, to) |
| 276 | + end |
| 277 | + while !isempty(reach._worklist) |
| 278 | + node = convert(Int, pop!(reach._worklist)) |
| 279 | + |
| 280 | + # already marked unreachable, just need to notify |
| 281 | + @assert reach.scc[node] == 0 && node != 1 |
| 282 | + if block_callback !== nothing |
| 283 | + block_callback(node) |
| 284 | + end |
| 285 | + |
| 286 | + for succ in cfg.blocks[node].succs |
| 287 | + # delete (node → succ) edge |
| 288 | + preds = cfg.blocks[succ].preds |
| 289 | + deleteat!(preds, findfirst(x::Int->x==node, preds)::Int) |
| 290 | + |
| 291 | + # check for newly unreachable target |
| 292 | + reach.scc[succ] == 0 && continue |
| 293 | + enqueued = enqueue_if_unreachable!(reach, cfg, succ) |
| 294 | + if !enqueued && edge_callback !== nothing |
| 295 | + edge_callback(node, succ) |
| 296 | + end |
| 297 | + end |
| 298 | + end |
| 299 | +end |
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