discard """
cmd: "nim c --gc:orc -d:useMalloc -d:nimStressOrc $file"
valgrind: "leaks"
output: "done"
"""
import tables
import sets
import net
type
BasicBlock = object
inEdges: seq[ref BasicBlock]
outEdges: seq[ref BasicBlock]
name: int
proc newBasicBlock(name: int): ref BasicBlock =
new(result)
result.inEdges = newSeq[ref BasicBlock]()
result.outEdges = newSeq[ref BasicBlock]()
result.name = name
proc hash(x: ref BasicBlock): int {.inline.} =
result = x.name
type
BasicBlockEdge = object
fr: ref BasicBlock
to: ref BasicBlock
Cfg = object
basicBlockMap: Table[int, ref BasicBlock]
edgeList: seq[BasicBlockEdge]
startNode: ref BasicBlock
proc newCfg(): Cfg =
result.basicBlockMap = initTable[int, ref BasicBlock]()
result.edgeList = newSeq[BasicBlockEdge]()
proc createNode(self: var Cfg, name: int): ref BasicBlock =
#var node: ref BasicBlock
result = self.basicBlockMap.getOrDefault(name)
if result == nil:
result = newBasicBlock(name)
self.basicBlockMap.add name, result
if self.startNode == nil:
self.startNode = result
proc addEdge(self: var Cfg, edge: BasicBlockEdge) =
self.edgeList.add(edge)
proc getNumNodes(self: Cfg): int =
self.basicBlockMap.len
proc newBasicBlockEdge(cfg: var Cfg, fromName: int, toName: int) =
var newEdge = BasicBlockEdge()
newEdge.fr = cfg.createNode(fromName)
newEdge.to = cfg.createNode(toName)
newEdge.fr.outEdges.add(newEdge.to)
newEdge.to.inEdges.add(newEdge.fr)
cfg.addEdge(newEdge)
type
SimpleLoop = object
basicBlocks: seq[ref BasicBlock] # TODO: set here
children: seq[ref SimpleLoop] # TODO: set here
parent: ref SimpleLoop
header: ref BasicBlock
isRoot: bool
isReducible: bool
counter: int
nestingLevel: int
depthLevel: int
proc newSimpleLoop(): ref SimpleLoop =
new(result)
result.basicBlocks = newSeq[ref BasicBlock]()
result.children = newSeq[ref SimpleLoop]()
result.parent = nil
result.header = nil
result.isRoot = false
result.isReducible = true
result.counter = 0
result.nestingLevel = 0
result.depthLevel = 0
proc addNode(self: ref SimpleLoop, bb: ref BasicBlock) =
self.basicBlocks.add bb
proc addChildLoop(self: ref SimpleLoop, loop: ref SimpleLoop) =
self.children.add loop
proc setParent(self: ref SimpleLoop, parent: ref SimpleLoop) =
self.parent = parent
self.parent.addChildLoop(self)
proc setHeader(self: ref SimpleLoop, bb: ref BasicBlock) =
self.basicBlocks.add(bb)
self.header = bb
proc setNestingLevel(self: ref SimpleLoop, level: int) =
self.nestingLevel = level
if level == 0: self.isRoot = true
var loop_counter: int = 0
type
Lsg = object
loops: seq[ref SimpleLoop]
root: ref SimpleLoop
proc createNewLoop(self: var Lsg): ref SimpleLoop =
var s = newSimpleLoop()
loop_counter += 1
s.counter = loop_counter
s
proc addLoop(self: var Lsg, l: ref SimpleLoop) =
self.loops.add l
proc newLsg(): Lsg =
result.loops = newSeq[ref SimpleLoop]()
result.root = result.createNewLoop()
result.root.setNestingLevel(0)
result.addLoop(result.root)
proc getNumLoops(self: Lsg): int =
self.loops.len
type
UnionFindNode = object
parent: ref UnionFindNode
bb: ref BasicBlock
l: ref SimpleLoop
dfsNumber: int
proc newUnionFindNode(): ref UnionFindNode =
new(result)
result.parent = nil
result.bb = nil
result.l = nil
result.dfsNumber = 0
proc initNode(self: ref UnionFindNode, bb: ref BasicBlock, dfsNumber: int) =
self.parent = self
self.bb = bb
self.dfsNumber = dfsNumber
proc findSet(self: ref UnionFindNode): ref UnionFindNode =
var nodeList = newSeq[ref UnionFindNode]()
var node = self
while node != node.parent:
var parent = node.parent
if parent != parent.parent: nodeList.add node
node = parent
for iter in nodeList: iter.parent = node.parent
node
proc union(self: ref UnionFindNode, unionFindNode: ref UnionFindNode) =
self.parent = unionFindNode
const
BB_NONHEADER = 1 # a regular BB
BB_REDUCIBLE = 2 # reducible loop
BB_SELF = 3 # single BB loop
BB_IRREDUCIBLE = 4 # irreducible loop
BB_DEAD = 5 # a dead BB
# # Marker for uninitialized nodes.
UNVISITED = -1
# # Safeguard against pathologic algorithm behavior.
MAXNONBACKPREDS = (32 * 1024)
type
HavlakLoopFinder = object
cfg: Cfg
lsg: Lsg
proc newHavlakLoopFinder(cfg: sink Cfg, lsg: sink Lsg): HavlakLoopFinder =
result.cfg = cfg
result.lsg = lsg
proc isAncestor(w: int, v: int, last: seq[int]): bool =
w <= v and v <= last[w]
proc dfs(currentNode: ref BasicBlock, nodes: var seq[ref UnionFindNode], number: var Table[ref BasicBlock, int], last: var seq[int], current: int): int =
nodes[current].initNode(currentNode, current)
number[currentNode] = current
var lastid = current
for target in currentNode.outEdges:
if number[target] == UNVISITED:
lastid = dfs(target, nodes, number, last, lastid + 1)
last[number[currentNode]] = lastid
return lastid
proc findLoops(self: var HavlakLoopFinder): int =
var startNode = self.cfg.startNode
if startNode == nil: return 0
var size = self.cfg.getNumNodes
var nonBackPreds = newSeq[HashSet[int]]()
var backPreds = newSeq[seq[int]]()
var number = initTable[ref BasicBlock, int]()
var header = newSeq[int](size)
var types = newSeq[int](size)
var last = newSeq[int](size)
var nodes = newSeq[ref UnionFindNode]()
for i in 1..size:
nonBackPreds.add initHashSet[int](1)
backPreds.add newSeq[int]()
nodes.add newUnionFindNode()
# Step a:
# - initialize all nodes as unvisited.
# - depth-first traversal and numbering.
# - unreached BB's are marked as dead.
#
for v in self.cfg.basicBlockMap.values: number[v] = UNVISITED
discard dfs(startNode, nodes, number, last, 0)
# Step b:
# - iterate over all nodes.
#
# A backedge comes from a descendant in the DFS tree, and non-backedges
# from non-descendants (following Tarjan).
#
# - check incoming edges 'v' and add them to either
# - the list of backedges (backPreds) or
# - the list of non-backedges (nonBackPreds)
#
for w in 0 ..< size:
header[w] = 0
types[w] = BB_NONHEADER
var nodeW = nodes[w].bb
if nodeW != nil:
for nodeV in nodeW.inEdges:
var v = number[nodeV]
if v != UNVISITED:
if isAncestor(w, v, last):
backPreds[w].add v
else:
nonBackPreds[w].incl v
else:
types[w] = BB_DEAD
# Start node is root of all other loops.
header[0] = 0
# Step c:
#
# The outer loop, unchanged from Tarjan. It does nothing except
# for those nodes which are the destinations of backedges.
# For a header node w, we chase backward from the sources of the
# backedges adding nodes to the set P, representing the body of
# the loop headed by w.
#
# By running through the nodes in reverse of the DFST preorder,
# we ensure that inner loop headers will be processed before the
# headers for surrounding loops.
for w in countdown(size - 1, 0):
# this is 'P' in Havlak's paper
var nodePool = newSeq[ref UnionFindNode]()
var nodeW = nodes[w].bb
if nodeW != nil: # dead BB
# Step d:
for v in backPreds[w]:
if v != w:
nodePool.add nodes[v].findSet
else:
types[w] = BB_SELF
# Copy nodePool to workList.
#
var workList = newSeq[ref UnionFindNode]()
for x in nodePool: workList.add x
if nodePool.len != 0: types[w] = BB_REDUCIBLE
# work the list...
#
while workList.len > 0:
var x = workList[0]
workList.del(0)
# Step e:
#
# Step e represents the main difference from Tarjan's method.
# Chasing upwards from the sources of a node w's backedges. If
# there is a node y' that is not a descendant of w, w is marked
# the header of an irreducible loop, there is another entry
# into this loop that avoids w.
#
# The algorithm has degenerated. Break and
# return in this case.
#
var nonBackSize = nonBackPreds[x.dfsNumber].len
if nonBackSize > MAXNONBACKPREDS: return 0
for iter in nonBackPreds[x.dfsNumber]:
var y = nodes[iter]
var ydash = y.findSet
if not isAncestor(w, ydash.dfsNumber, last):
types[w] = BB_IRREDUCIBLE
nonBackPreds[w].incl ydash.dfsNumber
else:
if ydash.dfsNumber != w and not nodePool.contains(ydash):
workList.add ydash
nodePool.add ydash
# Collapse/Unionize nodes in a SCC to a single node
# For every SCC found, create a loop descriptor and link it in.
#
if (nodePool.len > 0) or (types[w] == BB_SELF):
var l = self.lsg.createNewLoop
l.setHeader(nodeW)
l.isReducible = types[w] != BB_IRREDUCIBLE
# At this point, one can set attributes to the loop, such as:
#
# the bottom node:
# iter = backPreds(w).begin();
# loop bottom is: nodes(iter).node;
#
# the number of backedges:
# backPreds(w).size()
#
# whether this loop is reducible:
# types(w) != BB_IRREDUCIBLE
#
nodes[w].l = l
for node in nodePool:
# Add nodes to loop descriptor.
header[node.dfsNumber] = w
node.union(nodes[w])
# Nested loops are not added, but linked together.
var node_l = node.l
if node_l != nil:
node_l.setParent(l)
else:
l.addNode(node.bb)
self.lsg.addLoop(l)
result = self.lsg.getNumLoops
type
LoopTesterApp = object
cfg: Cfg
lsg: Lsg
proc newLoopTesterApp(): LoopTesterApp =
result.cfg = newCfg()
result.lsg = newLsg()
proc buildDiamond(self: var LoopTesterApp, start: int): int =
var bb0 = start
newBasicBlockEdge(self.cfg, bb0, bb0 + 1)
newBasicBlockEdge(self.cfg, bb0, bb0 + 2)
newBasicBlockEdge(self.cfg, bb0 + 1, bb0 + 3)
newBasicBlockEdge(self.cfg, bb0 + 2, bb0 + 3)
result = bb0 + 3
proc buildConnect(self: var LoopTesterApp, start1: int, end1: int) =
newBasicBlockEdge(self.cfg, start1, end1)
proc buildStraight(self: var LoopTesterApp, start: int, n: int): int =
for i in 0..n-1:
self.buildConnect(start + i, start + i + 1)
result = start + n
proc buildBaseLoop(self: var LoopTesterApp, from1: int): int =
var header = self.buildStraight(from1, 1)
var diamond1 = self.buildDiamond(header)
var d11 = self.buildStraight(diamond1, 1)
var diamond2 = self.buildDiamond(d11)
var footer = self.buildStraight(diamond2, 1)
self.buildConnect(diamond2, d11)
self.buildConnect(diamond1, header)
self.buildConnect(footer, from1)
result = self.buildStraight(footer, 1)
proc run(self: var LoopTesterApp) =
discard self.cfg.createNode(0)
discard self.buildBaseLoop(0)
discard self.cfg.createNode(1)
self.buildConnect(0, 2)
for i in 1..8:
# yes, it's 8 and it's correct.
var h = newHavlakLoopFinder(self.cfg, newLsg())
discard h.findLoops()
echo "done"
var l = newLoopTesterApp()
l.run()