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Tue Mar 12 16:09:26 2002 UTC (17 years, 3 months ago) by jhr
File size: 6581 byte(s)
Tue Mar 12 16:09:26 2002 UTC (17 years, 3 months ago) by jhr
File size: 6581 byte(s)
Added functor to compute block and edge frequencies from edge probabilities.
(* compute-freqs-fn.sml * * COPYRIGHT (c) 2002 Bell Labs, Lucent Technologies. * * Compute block and edge weights (frequencies) from edge probabilities. * This algorithm uses symbolic simplification of the frequency equations. * It handles unstructured loops. *) functor ComputeFreqsFn ( structure CFG : CONTROL_FLOW_GRAPH ) : COMPUTE_EXECUTION_FREQUENCIES = struct structure CFG = CFG structure Prob = Probability structure F = Format (* flags *) val dumpFreqs = MLRiscControl.mkFlag ( "dump-frequencies", "when true, block and edge frequencies are output") val dumpCFG = MLRiscControl.mkFlag ( "dump-cfg-after-frequencies", "when true, the CFG is output after frequency computation") fun pr s = TextIO.output(!MLRiscControl.debug_stream, s) fun prf (fmt, items) = pr(F.format fmt items) (* Complete edge probabilities; we use the edge weights to store this * information. *) structure CompleteProbs = CompleteProbsFn ( structure CFG = CFG fun recordProb (CFG.EDGE{w, ...}, p) = (w := p)) fun getProb (CFG.EDGE{w, ...}) = !w (* fudge factor for infinite loops. *) val epsilon = 1.0e~6 (***** Representation of equations *****) type var = Graph.node_id datatype def = Unknown | Sum of sum withtype term = (real * var) and sum = {terms : term list, c : real} val zero = {c = 0.0, terms = []} val one = {c = 1.0, terms = []} (* multiply a term by a scalar *) fun scale (coeff : real) (a, x) = (coeff*a, x) fun compute (cfg as Graph.GRAPH methods) = let val {in_edges, out_edges, node_info, capacity, ...} = methods val defs = Array.array(capacity(), Unknown) fun getVar id = Array.sub(defs, id) fun setVar (id, s) = Array.update(defs, id, s) (* if a node has been visited, then it has a definition *) fun visited id = ( case Array.sub(defs, id) of Unknown => false | _ => true) (** computations on sums **) (* if a variable is defined, compute the normal form of its definition * and return it. If the variable is unknown or its definition is * already in normal form, then return NONE. *) fun normalizeVar v = (case getVar v of Unknown => Unknown | Sum s => (case normalizeSum s of NONE => Sum s | SOME s' => let val sum = Sum s' in setVar(v, sum); sum end (* end case *)) (* end case *)) (* normalize a sum of scaled variables; if the sum is already normalized, * then return NONE. *) and normalizeSum ({terms, c} : sum) = let fun extract ((t as (b, y))::r, ts, todo : (real * sum) list) = ( case normalizeVar y of Unknown => extract(r, t::ts, todo) | Sum s => extract(r, ts, (b, s)::todo) (* end case *)) | extract ([], _, []) = NONE | extract ([], ts, todo) = SOME(addDefs ({terms=List.rev ts, c=c}, todo)) and addDefs (acc, []) = acc | addDefs (acc, (coeff, sum)::r) = addDefs (addScaled(acc, coeff, sum), r) in extract (terms, [], []) end (* compute r1 + coeff*r2, where r1 and r2 are normalized; the result * is normalized. *) and addScaled (r1 : sum, coeff : real, r2 : sum) = let fun combine ([], ts) = List.map (scale coeff) ts | combine (ts, []) = ts | combine (ts1 as (t1::r1), ts2 as (t2::r2)) = if (#2 t1 < #2 t2) then t1 :: combine(r1, ts2) else if (#2 t1 = #2 t2) then (#1 t1 + (coeff * #1 t2), #2 t1) :: combine (r1, r2) else (scale coeff t2) :: combine(ts1, r2) in { c = #c r1 + coeff * #c r2, terms = combine(#terms r1, #terms r2) } end (* add the term (a*x) to a normalized term; we assume that x is Undefined. *) fun addScaledVar ({c, terms}, a : real, x) = let fun insert [] = [(a, x)] | insert ((t as (b, y))::r) = if (y < x) then t :: insert r else if (y = x) then (a+b, x) :: r else (a, x) :: t :: r in {c = c, terms = insert terms} end (* given a list of incoming edges, create the rhs sum. *) fun makeRHS preds = let fun f ((src, _, e), acc) = let val prob = getProb e in case normalizeVar src of Unknown => addScaledVar (acc, prob, src) | Sum sum => addScaled (acc, prob, sum) (* end case *) end in List.foldl f zero preds end (* Simplify the equation "x = rhs" by checking for x in rhs. We assume that * x is undefined and that the rhs is normaized. We return the simplified * rhs. *) fun simplify (x, rhs as {terms, c}) = let fun removeX ([], _) = rhs | removeX ((t as (a, y))::r, ts) = if (x < y) then rhs else if (x = y) then let val s = 1.0 / Real.max(1.0 - a, epsilon) val terms = List.revAppend(ts, r) in {c = s*c, terms = List.map (scale s) terms} end else removeX(r, t::ts) in removeX (terms, []) end (* INVARIANT: the variables corresponding to marked nodes are not Unknown * in the rhs of any equation. *) fun dfs id = if (visited id) then () else let val rhs = makeRHS (in_edges id) val rhs = simplify (id, rhs) in setVar (id, Sum rhs); followEdges (out_edges id) end and followEdges [] = () | followEdges ((_, dst, _)::r) = (dfs dst; followEdges r) val [root] = #entries methods () in (* initialize edge probabilities *) CompleteProbs.completeProbs cfg; (* initialize the root *) setVar (root, Sum one); (* traverse the successors of the root *) followEdges (out_edges root); (* record block and edge frequencies in CFG *) #forall_nodes methods (fn (id, CFG.BLOCK{freq, ...}) => ( case normalizeVar id of Unknown => freq := 0.0 | Sum{c, terms=[]} => freq := c | _ => raise Fail (concat[ "block ", Int.toString id, " unresolved" ]) (* end case *))); #forall_edges methods (fn (src, _, CFG.EDGE{w, ...}) => let val CFG.BLOCK{freq, ...} = node_info src in w := !w * !freq end); if !dumpFreqs then let fun bfreq (id, CFG.BLOCK{kind, freq, ...}) = prf("\tbfreq(%s %d) = %f\n", [ F.STR(CFG.kindName kind), F.INT id, F.REAL(!freq) ]) fun freq (src, dst, info as CFG.EDGE{w, ...}) = prf("\tfreq(%d->%d:%s) = %f\n", [ F.INT src, F.INT dst, F.STR(CFG.show_edge info), F.REAL(!w) ]) in pr "[ computed frequencies ]\n"; #forall_nodes methods bfreq; #forall_edges methods freq end else (); if !dumpCFG then CFG.dump ( !MLRiscControl.debug_stream, "after frequency computation", cfg) else () end end
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