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Refactor dominator computation

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* module/language/cps/cse.scm:
* module/language/cps/dfg.scm (compute-idoms, compute-dom-edges): Move
  these procedures from cse.scm to dfg.scm.
  Remove loop-detection code; that can come back later but it is
  bitrotten for now.
This commit is contained in:
Andy Wingo 2014-06-15 22:02:29 +02:00
parent 803a1ee7c7
commit 38c7bd0e77
2 changed files with 30 additions and 255 deletions
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60
module/language/cps/cse.scm
View file

@ -248,68 +248,8 @@ be that both true and false proofs are available."
(values min-label label-count min-var var-count))))) (values min-label label-count min-var var-count)))))
fun kfun 0 self 0)))) fun kfun 0 self 0))))
(define (compute-idoms dfg min-label label-count)
(define (label->idx label) (- label min-label))
(define (idx->label idx) (+ idx min-label))
(let ((idoms (make-vector label-count #f)))
(define (common-idom d0 d1)
;; We exploit the fact that a reverse post-order is a topological
;; sort, and so the idom of a node is always numerically less than
;; the node itself.
(cond
((= d0 d1) d0)
((< d0 d1) (common-idom d0 (vector-ref idoms (label->idx d1))))
(else (common-idom (vector-ref idoms (label->idx d0)) d1))))
(define (compute-idom preds)
(define (has-idom? pred)
(vector-ref idoms (label->idx pred)))
(match preds
(() min-label)
((pred . preds)
(if (has-idom? pred)
(let lp ((idom pred) (preds preds))
(match preds
(() idom)
((pred . preds)
(lp (if (has-idom? pred)
(common-idom idom pred)
idom)
preds))))
(compute-idom preds)))))
;; This is the iterative O(n^2) fixpoint algorithm, originally from
;; Allen and Cocke ("Graph-theoretic constructs for program flow
;; analysis", 1972). See the discussion in Cooper, Harvey, and
;; Kennedy's "A Simple, Fast Dominance Algorithm", 2001.
(let iterate ((n 0) (changed? #f))
(cond
((< n label-count)
(let ((idom (vector-ref idoms n))
(idom* (compute-idom (lookup-predecessors (idx->label n) dfg))))
(cond
((eqv? idom idom*)
(iterate (1+ n) changed?))
(else
(vector-set! idoms n idom*)
(iterate (1+ n) #t)))))
(changed?
(iterate 0 #f))
(else idoms)))))
;; Compute a vector containing, for each node, a list of the nodes that ;; Compute a vector containing, for each node, a list of the nodes that
;; it immediately dominates. These are the "D" edges in the DJ tree. ;; it immediately dominates. These are the "D" edges in the DJ tree.
(define (compute-dom-edges idoms min-label)
(define (label->idx label) (- label min-label))
(define (idx->label idx) (+ idx min-label))
(define (vector-push! vec idx val)
(let ((v vec) (i idx))
(vector-set! v i (cons val (vector-ref v i)))))
(let ((doms (make-vector (vector-length idoms) '())))
(let lp ((n 0))
(when (< n (vector-length idoms))
(let ((idom (vector-ref idoms n)))
(vector-push! doms (label->idx idom) (idx->label n)))
(lp (1+ n))))
doms))
(define (compute-equivalent-subexpressions fun dfg) (define (compute-equivalent-subexpressions fun dfg)
(define (compute min-label label-count min-var var-count avail effects) (define (compute min-label label-count min-var var-count avail effects)

225
module/language/cps/dfg.scm
View file

@ -67,6 +67,9 @@
control-point? control-point?
lookup-bound-syms lookup-bound-syms
compute-idoms
compute-dom-edges
;; Data flow analysis. ;; Data flow analysis.
compute-live-variables compute-live-variables
dfa-k-idx dfa-k-sym dfa-k-count dfa-k-in dfa-k-out dfa-k-idx dfa-k-sym dfa-k-count dfa-k-in dfa-k-out
@ -337,56 +340,36 @@ body continuation in the prompt."
(values k-map succs))))) (values k-map succs)))))
;; Dominator analysis. (define (compute-idoms dfg min-label label-count)
(define-record-type $dominator-analysis (define preds (dfg-preds dfg))
(make-dominator-analysis min-label idoms dom-levels loop-header irreducible)
dominator-analysis?
;; Label corresponding to first entry in idoms, dom-levels, etc
(min-label dominator-analysis-min-label)
;; Vector of k-idx -> k-idx
(idoms dominator-analysis-idoms)
;; Vector of k-idx -> dom-level
(dom-levels dominator-analysis-dom-levels)
;; Vector of k-idx -> k-idx or -1
(loop-header dominator-analysis-loop-header)
;; Vector of k-idx -> true or false value
(irreducible dominator-analysis-irreducible))
(define (compute-dom-levels idoms)
(let ((dom-levels (make-vector (vector-length idoms) #f)))
(define (compute-dom-level n)
(or (vector-ref dom-levels n)
(let ((dom-level (1+ (compute-dom-level (vector-ref idoms n)))))
(vector-set! dom-levels n dom-level)
dom-level)))
(vector-set! dom-levels 0 0)
(let lp ((n 0))
(when (< n (vector-length idoms))
(compute-dom-level n)
(lp (1+ n))))
dom-levels))
(define (compute-idoms preds min-label label-count)
(define (label->idx label) (- label min-label)) (define (label->idx label) (- label min-label))
(define (idx->label idx) (+ idx min-label)) (define (idx->label idx) (+ idx min-label))
(let ((idoms (make-vector label-count 0))) (define (idx->dfg-idx idx) (- (idx->label idx) (dfg-min-label dfg)))
(let ((idoms (make-vector label-count #f)))
(define (common-idom d0 d1) (define (common-idom d0 d1)
;; We exploit the fact that a reverse post-order is a topological ;; We exploit the fact that a reverse post-order is a topological
;; sort, and so the idom of a node is always numerically less than ;; sort, and so the idom of a node is always numerically less than
;; the node itself. ;; the node itself.
(cond (cond
((= d0 d1) d0) ((= d0 d1) d0)
((< d0 d1) (common-idom d0 (vector-ref idoms d1))) ((< d0 d1) (common-idom d0 (vector-ref idoms (label->idx d1))))
(else (common-idom (vector-ref idoms d0) d1)))) (else (common-idom (vector-ref idoms (label->idx d0)) d1))))
(define (compute-idom preds) (define (compute-idom preds)
(define (has-idom? pred)
(vector-ref idoms (label->idx pred)))
(match preds (match preds
(() 0) (() min-label)
((pred . preds) ((pred . preds)
(let lp ((idom (label->idx pred)) (preds preds)) (if (has-idom? pred)
(match preds (let lp ((idom pred) (preds preds))
(() idom) (match preds
((pred . preds) (() idom)
(lp (common-idom idom (label->idx pred)) preds))))))) ((pred . preds)
(lp (if (has-idom? pred)
(common-idom idom pred)
idom)
preds))))
(compute-idom preds)))))
;; This is the iterative O(n^2) fixpoint algorithm, originally from ;; This is the iterative O(n^2) fixpoint algorithm, originally from
;; Allen and Cocke ("Graph-theoretic constructs for program flow ;; Allen and Cocke ("Graph-theoretic constructs for program flow
;; analysis", 1972). See the discussion in Cooper, Harvey, and ;; analysis", 1972). See the discussion in Cooper, Harvey, and
@ -395,7 +378,7 @@ body continuation in the prompt."
(cond (cond
((< n label-count) ((< n label-count)
(let ((idom (vector-ref idoms n)) (let ((idom (vector-ref idoms n))
(idom* (compute-idom (vector-ref preds (idx->label n))))) (idom* (compute-idom (vector-ref preds (idx->dfg-idx n)))))
(cond (cond
((eqv? idom idom*) ((eqv? idom idom*)
(iterate (1+ n) changed?)) (iterate (1+ n) changed?))
@ -408,168 +391,20 @@ body continuation in the prompt."
;; Compute a vector containing, for each node, a list of the nodes that ;; Compute a vector containing, for each node, a list of the nodes that
;; it immediately dominates. These are the "D" edges in the DJ tree. ;; it immediately dominates. These are the "D" edges in the DJ tree.
(define (compute-dom-edges idoms) (define (compute-dom-edges idoms min-label)
(define (label->idx label) (- label min-label))
(define (idx->label idx) (+ idx min-label))
(let ((doms (make-vector (vector-length idoms) '()))) (let ((doms (make-vector (vector-length idoms) '())))
(let lp ((n 0)) (let lp ((n 0))
(when (< n (vector-length idoms)) (when (< n (vector-length idoms))
(let ((idom (vector-ref idoms n))) (let ((idom (vector-ref idoms n)))
(vector-push! doms idom n)) (vector-push! doms (label->idx idom) (idx->label n)))
(lp (1+ n)))) (lp (1+ n))))
doms)) doms))
;; Compute a vector containing, for each node, a list of the successors ;; There used to be some loop detection code here, but it bitrotted.
;; of that node that are not dominated by that node. These are the "J" ;; We'll need it again eventually but for now it can be found in the git
;; edges in the DJ tree. ;; history.
(define (compute-join-edges preds min-label idoms)
(define (dominates? n1 n2)
(or (= n1 n2)
(and (< n1 n2)
(dominates? n1 (vector-ref idoms n2)))))
(let ((joins (make-vector (vector-length idoms) '())))
(let lp ((n 0))
(when (< n (vector-length idoms))
(for-each (lambda (pred)
(let ((pred (- pred min-label)))
(unless (dominates? pred n)
(vector-push! joins pred n))))
(vector-ref preds (+ n min-label)))
(lp (1+ n))))
joins))
;; Compute a vector containing, for each node, a list of the back edges
;; to that node. If a node is not the entry of a reducible loop, that
;; list is empty.
(define (compute-reducible-back-edges joins idoms)
(define (dominates? n1 n2)
(or (= n1 n2)
(and (< n1 n2)
(dominates? n1 (vector-ref idoms n2)))))
(let ((back-edges (make-vector (vector-length idoms) '())))
(let lp ((n 0))
(when (< n (vector-length joins))
(for-each (lambda (succ)
(when (dominates? succ n)
(vector-push! back-edges succ n)))
(vector-ref joins n))
(lp (1+ n))))
back-edges))
;; Compute the levels in the dominator tree at which there are
;; irreducible loops, as an integer. If a bit N is set in the integer,
;; that indicates that at level N in the dominator tree, there is at
;; least one irreducible loop.
(define (compute-irreducible-dom-levels doms joins idoms dom-levels)
(define (dominates? n1 n2)
(or (= n1 n2)
(and (< n1 n2)
(dominates? n1 (vector-ref idoms n2)))))
(let ((pre-order (make-vector (vector-length doms) #f))
(last-pre-order (make-vector (vector-length doms) #f))
(res 0)
(count 0))
;; Is MAYBE-PARENT an ancestor of N on the depth-first spanning tree
;; computed from the DJ graph? See Havlak 1997, "Nesting of
;; Reducible and Irreducible Loops".
(define (ancestor? a b)
(let ((w (vector-ref pre-order a))
(v (vector-ref pre-order b)))
(and (<= w v)
(<= v (vector-ref last-pre-order w)))))
;; Compute depth-first spanning tree of DJ graph.
(define (recurse n)
(unless (vector-ref pre-order n)
(visit n)))
(define (visit n)
;; Pre-order visitation index.
(vector-set! pre-order n count)
(set! count (1+ count))
(for-each recurse (vector-ref doms n))
(for-each recurse (vector-ref joins n))
;; Pre-order visitation index of last descendant.
(vector-set! last-pre-order (vector-ref pre-order n) (1- count)))
(visit 0)
(let lp ((n 0))
(when (< n (vector-length joins))
(for-each (lambda (succ)
;; If this join edge is not a loop back edge but it
;; does go to an ancestor on the DFST of the DJ
;; graph, then we have an irreducible loop.
(when (and (not (dominates? succ n))
(ancestor? succ n))
(set! res (logior (ash 1 (vector-ref dom-levels succ))))))
(vector-ref joins n))
(lp (1+ n))))
res))
(define (compute-nodes-by-level dom-levels)
(let* ((max-level (let lp ((n 0) (max-level 0))
(if (< n (vector-length dom-levels))
(lp (1+ n) (max (vector-ref dom-levels n) max-level))
max-level)))
(nodes-by-level (make-vector (1+ max-level) '())))
(let lp ((n (1- (vector-length dom-levels))))
(when (>= n 0)
(vector-push! nodes-by-level (vector-ref dom-levels n) n)
(lp (1- n))))
nodes-by-level))
;; Collect all predecessors to the back-nodes that are strictly
;; dominated by the loop header, and mark them as belonging to the loop.
;; If they already have a loop header, that means they are either in a
;; nested loop, or they have already been visited already.
(define (mark-loop-body header back-nodes preds min-label idoms loop-headers)
(define (strictly-dominates? n1 n2)
(and (< n1 n2)
(let ((idom (vector-ref idoms n2)))
(or (= n1 idom)
(strictly-dominates? n1 idom)))))
(define (visit node)
(when (strictly-dominates? header node)
(cond
((vector-ref loop-headers node) => visit)
(else
(vector-set! loop-headers node header)
(for-each (lambda (pred) (visit (- pred min-label)))
(vector-ref preds (+ node min-label)))))))
(for-each visit back-nodes))
(define (mark-irreducible-loops level idoms dom-levels loop-headers)
;; FIXME: Identify strongly-connected components that are >= LEVEL in
;; the dominator tree, and somehow mark them as irreducible.
(warn 'irreducible-loops-at-level level))
;; "Identifying Loops Using DJ Graphs" by Sreedhar, Gao, and Lee, ACAPS
;; Technical Memo 98, 1995.
(define (identify-loops preds min-label idoms dom-levels)
(let* ((doms (compute-dom-edges idoms))
(joins (compute-join-edges preds min-label idoms))
(back-edges (compute-reducible-back-edges joins idoms))
(irreducible-levels
(compute-irreducible-dom-levels doms joins idoms dom-levels))
(loop-headers (make-vector (vector-length idoms) #f))
(nodes-by-level (compute-nodes-by-level dom-levels)))
(let lp ((level (1- (vector-length nodes-by-level))))
(when (>= level 0)
(for-each (lambda (n)
(let ((edges (vector-ref back-edges n)))
(unless (null? edges)
(mark-loop-body n edges preds min-label
idoms loop-headers))))
(vector-ref nodes-by-level level))
(when (logbit? level irreducible-levels)
(mark-irreducible-loops level idoms dom-levels loop-headers))
(lp (1- level))))
loop-headers))
(define (analyze-dominators dfg min-label label-count)
(let* ((idoms (compute-idoms (dfg-preds dfg) min-label label-count))
(dom-levels (compute-dom-levels idoms))
(loop-headers (identify-loops (dfg-preds dfg) min-label idoms dom-levels)))
(make-dominator-analysis min-label idoms dom-levels loop-headers #f)))
;; Compute the maximum fixed point of the data-flow constraint problem. ;; Compute the maximum fixed point of the data-flow constraint problem.
;; ;;