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Instruction Scheduling combining scheduling with allocation Copyright 2011, Keith D. Cooper & Linda Torczon, all rights reserved. Students enrolled in Comp 512 at Rice University have explicit permission to make copies of these materials for their personal use. Faculty from other educational institutions may use these materials for nonprofit educational purposes, provided this copyright notice is preserved. Comp 512 Spring 2011 COMP 512, Rice University1

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2 Combining Scheduling & Allocation Sometimes, combining two optimizations can produce solutions that cannot be obtained by solving them independently Requires bilateral interactions between optimizations Click and Cooper, Combining Analyses, Combining Optimizations, TOPLAS 17(2), March 1995. Combining two optimizations can be a challenge ( SCCP ) Scheduling & allocation are a classic example Scheduling changes variable lifetimes Renaming in the allocator changes dependences Spilling changes the underlying code false dependences

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COMP 512, Rice University3 Many authors have tried to combine allocation & scheduling Underallocate to leave room for the scheduler Can result in underutilization of registers Preallocate to use all registers Can create false dependences Solving the problems together can produce solutions that cannot be obtained by solving them independently See Click and Cooper, Combining Analyses, Combining Optimizations, TOPLAS 17(2), March 1995. In general, these papers try to combine global allocators with local or regional schedulers an algorithmic mismatch Combining Scheduling & Allocation Before we go there, a long digression about how much improvement we might expect …

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COMP 512, Rice University4 Quick Review of Local Scheduling Given a sequence of machine operations, reorder the operations so that Data dependences are respected Execution time is minimized Demand for registers is kept below k Vocabulary: An operation is an indivisible command An instruction is a set of operations that issue in the same cycle A dependence graph is constructed to represent necessary delays (Nodes are operations; edges show the flow of values; edge weights represent operation latencies)

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COMP 512, Rice University5 Scheduling Example Many operations have non-zero latencies Modern machines can issue several operations per cycle Execution time is order-dependent ( and has been since the 60s ) Assumed latencies (conservative) Operation Cycles load3 store3 loadI1 add1 mult2 fadd1 fmult2 shift 1 branch 0 to 8 Loads & stores may or may not block > Non-blocking fill those issue slots Branch costs vary with path taken Branches typically have delay slots > Fill slots with unrelated operations > Percolates branch upward Scheduler should hide the latencies List scheduling is dominant algorithm

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COMP 512, Rice University6 Example w w * 2 * x * y * z Simple scheduleSchedule loads early 2 registers, 20 cycles3 registers, 13 cycles Reordering operations for speed is called instruction scheduling

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COMP 512, Rice University7 Instruction Scheduling (The Abstract View) To capture properties of the code, build a dependence graph G Nodes n G are operations with type(n) and delay(n) An edge e = (n 1,n 2 ) G if & only if n 2 uses the result of n 1 The Code a b c d e f g h i The Dependence Graph

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COMP 512, Rice University8 Instruction Scheduling (Definitions) A correct schedule S maps each n N into a non-negative integer representing its cycle number, and 1. S(n) 0, for all n N, obviously 2. If (n 1,n 2 ) E, S(n 1 ) + delay(n 1 ) S(n 2 ) 3. For each type of operation ( functional unit ), t, there are no more operations of type t in any cycle than the target machine can issue The length of a schedule S, denoted L(S), is L(S) = max n N (S(n) + delay(n)) The goal is to find the shortest possible correct schedule. S is time-optimal if L(S) L(S 1 ), for all other schedules S 1 A schedule might also be optimal in terms of registers or power, or ….

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COMP 512, Rice University9 Whats so difficult? Critical Points All operands must be available when an operation issues Multiple operations can be ready (& often are …) Moving an operation can lengthen register lifetimes or it can shorten register lifetimes Operands can have multiple predecessors (not SSA ) Together, these issues make scheduling hard ( NP-C omplete) Local scheduling is the simple case Restricted to straight-line code Consistent and predictable latencies

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COMP 512, Rice University10 Instruction Scheduling The big picture 1. Build a dependence graph, D 2. Compute a priority function over the nodes in D 3. Use list scheduling to construct a schedule, 1 cycle at a time a. Use a queue of operations that are ready b. At each cycle I. Choose a ready operation and schedule it II. Update the ready queue Local list scheduling The dominant algorithm for twenty years A greedy, heuristic, local technique

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COMP 512, Rice University11 Local List Scheduling Cycle 1 Ready leaves of D Active Ø while (Ready Active Ø) if (Ready Ø) then remove an op from Ready S( op ) Cycle Active Active op Cycle Cycle + 1 for each op Active if (S( op ) + delay( op ) Cycle) then remove op from Active for each successor s of op in D if (s is ready) then Ready Ready s Removal in priority order op has completed execution If successors operands are ready, put it on Ready Can improve efficiency by using a set of Queues (1 more than maximum delay on target machine) see 412 notes

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COMP 512, Rice University12 Scheduling Example 1. Build the dependence graph The Code a b c d e f g h i The Dependence Graph

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COMP 512, Rice University13 Scheduling Example 1. Build the dependence graph 2. Determine priorities: longest latency-weighted path The Code a b c d e f g h i The Dependence Graph 3 5 8 7 9 10 12 10 13

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COMP 512, Rice University14 Scheduling Example 1. Build the dependence graph 2. Determine priorities: longest latency-weighted path 3. Perform list scheduling loadAIr0,@w r1 1) a: addr1,r1 r14) b: loadAIr0,@x r2 2) c: multr1,r2 r15) d: loadAIr0,@y r3 3) e: multr1,r3 r17) f:loadAIr0,@z r26) g: multr1,r2 r1 9) h: 11) i:storeAIr1 r0,@w The Code a b c d e f g h i The Dependence Graph 3 5 8 7 9 10 12 10 13 New register name used

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COMP 512, Rice University15 Local Scheduling As long as we stay within a single block List scheduling does well Problem is hard, so tie-breaking matters More descendants in dependence graph Prefer operation with a last use over one with none Breadth first makes progress on all paths Tends toward more ILP & fewer interlocks Depth first tries to complete uses of a value Tends to use fewer registers Classic work on this is Gibbons & Muchnick (PLDI 86)

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COMP 512, Rice University16 Local Scheduling Forward and backward can produce different results cbr cmpstore 1 store 2 store 3 store 4 store 5 add 1 add 2 add 3 add 4 addI loadI 1 lshiftloadI 2 loadI 3 loadI 4 Block from SPEC benchmark go Operation loadloadIaddaddIstorecmp Latency 112141 1 255555 77776 88888 Latency to the cbr Subscript to identify

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COMP 512, Rice University17 Local Scheduling Int Mem 1 loadI 1 lshift 2 loadI 2 loadI 3 3 loadI 4 add 1 4 add 2 add 3 5 add 4 addIstore 1 6 cmpstore 2 7 store 3 8 store 4 9 store 5 10 11 12 13 cbr ForwardScheduleForwardSchedule Int Mem 1 loadI 4 2 addIlshift 3 add 4 loadI 3 4 add 3 loadI 2 store 5 5 add 2 loadI 1 store 4 6 add 1 store 3 7 store 2 8 store 1 9 10 11 cmp 12 cbr 13 BackwardScheduleBackwardSchedule Using latency to root as the priority

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COMP 512, Rice University18 Local Scheduling Priority function strongly affects properties of result Longest latency-weighted path biases result toward finishing the long paths as soon as possible execution speed is paramount may use more registers than the minimum Depth-first approach can reduce demand for registers minimize lifetimes of values Sethi-Ullman numbering, extended to DAGs

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COMP 512, Rice University19 Iterative Repair Scheduling The Problem List scheduling has dominated field for 20 years Anecdotal evidence both good & bad, little solid evidence No intuitive paradigm for how it works It works well, but will it work well in the future ? Is there room for improvement? ( e.g., with allocation? ) Our Idea Try more powerful algorithms from other domains Look for better schedules Look for understanding of the solution space This led us to iterative repair scheduling

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COMP 512, Rice University20 Iterative Repair Scheduling The Algorithm Start from some approximation to a schedule ( bad or broken ) Find & prioritize all cycles that need repair ( tried 6 schemes ) Either resource or data constraints Perform the needed repairs, in priority order Break ties randomly Reschedule dependent operations, in random order Evaluation function on repair can reject the repair ( try another ) Iterate until repair list is empty Repeat this process many times to explore the solution space Keep the best result ! Randomization & restart is a fundamental theme of our recent work Iterative repair works well on many kinds of scheduling problems. Scheduling cargo for the space shuttle Typical problems in the literature involve 10s or 100s of repairs We used it with millions of repairs

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COMP 512, Rice University21 Iterative Repair Scheduling How does iterative repair do versus list scheduling? Found many schedules that used fewer registers Found very few faster schedules Were disappointed with the results Began a study of the properties of scheduling problems Iterative repair, itself, doesnt justify the additional costs Can we identify schedulers where it will win? Can we learn about the properties of scheduling problems ? And about the behavior of list scheduling... Hopeful sign for this lecture

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COMP 512, Rice University22 Methodology Looked at blocks & extended blocks in benchmarks Used randomized version of backward & forward list scheduling If non-optimal, used IR to find its best schedule ( simple tests ) Checked these results against an IP formulation using CPLEX The Results List scheduling does quite well on a conventional uniprocessor Over 92% of blocks scheduled optimally for speed Over 73% of extended blocks scheduled optimally for speed Instruction Scheduling Study

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COMP 512, Rice University23 Scheilkes RBF Algorithm for Local Scheduling Relying on randomization & restart, we can smooth the behavior of classic list scheduling algorithms Schielkes RBF algorithm Run 5 passes of forward list scheduling and 5 passes of backward list scheduling Break each tie randomly Keep the best schedule Shortest time to completion Other metrics are possible ( shortest time + fewest registers ) In practice, this approach does very well Reuses the dependence graph Randomized Backward & Forward My algorithm of choice for list scheduling …

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COMP 512, Rice University24 Methodology Looked at blocks & extended blocks in benchmarks Applied the RBF algorithm & tested result for optimality If non-optimal, used IR to find its best schedule Checked these results against an IP formulation using CPLEX The Results List scheduling does quite well on a conventional uniprocessor Over 92% of blocks scheduled optimally for speed Over 73% of extended blocks scheduled optimally for speed Instruction Scheduling Study

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COMP 512, Rice University25 Methodology Repeated same experiment with randomly-generated blocks Generated over 85,000 random blocks of 10, 20, & 50 ops The Results List scheduling finds optimal schedules over 80% of the time Plotted % non-optimal against available ILP Peak is around 2.8 for 1 functional unit and 4.7 for 2 units Worst-case schedule length over critical path length IR scheduler usually found optimal schedules for these harder problems use it when list scheduling fails Instruction Scheduling Study 3 compute months on a pair of UltraSparc workstations

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COMP 512, Rice University26 Non-optimal list schedules (%) versus available parallelism 1 functional unit, randomly generated blocks of 10, 20, 50 ops At the peak, compiler should apply other techniques Measure parallelism in list scheduler Invoke stronger techniques when high-probability of payoff How Well Does List Scheduling Do? Most codes fall here, unless the compiler transforms them for ILP. If the compiler transforms the code, it should avoid this area! From Phil Schielkes thesis

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COMP 512, Rice University27 Instruction Scheduling Study The Lessons In general, list scheduling does well Use randomized version, both directions, a few trials To find hard problems, measure average length of ready queue If it falls in the hard region Check resulting schedule for interlocks or holes If non-optimal, run the IR scheduler If transforming for parallelism, avoid hitting the hard range CPLEX had a hard time with the easy blocks Too many optimal solutions to check out

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COMP 512, Rice University28 Combining Allocation & Scheduling The Problem Well-understood that the problems are intricately related Previous work under-allocates or under-schedules Except Goodman & Hsu Our Approach Formulate an iterative repair framework Moves for scheduling, as before Moves to decrease register pressure or to spill Allows fair competition in a combined attack Grows out of search for novel techniques from other areas

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COMP 512, Rice University29 Combining Allocation & Scheduling The Details Run IR scheduler & keep the schedule with lowest pressure Start with ALAP schedule rather than ASAP schedule Reject repair that increases maximum pressure Cycle with pressure > k triggers pressure repair Identify ops that reduce pressure & move one Lower threshold for k seems to help Ran it against the classic method Schedule, allocate, schedule ( using Briggs allocator )

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COMP 512, Rice University30 Combining Allocation & Scheduling The Results Many opportunities to lower pressure 12% of basic blocks 33% of extended blocks This can produce faster code Best case was 41.3% Average case, 16 regs, was 5.4% Average case, 32 regs, was 3.5% ( whole applications ) This approach finds faster codes that spill fewer values It is competing against a very good global allocator Rematerialization catches many of the same effects Knowing that new solutions exist does not ensure that they are better solutions! This work confirms years of suspicion, while providing an effective, albeit nontraditional, technique The opportunity is present, but the IR scheduler is still quite slow …

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COMP 512, Rice University31 Sethi-Ullman Numbering Two pass algorithm Number each subtree in the expression 1 if n is a leaf label(n) = max(label(left child),label(right child) if labels are unequal label(left child) + 1 if labels are equal Labels correspond to registers need to evaluate that subtree Use numbers to guide evaluation At each node, generate more demanding subtree first 1. generate code for larger label 2. store result in a temporary registers 3. generate code for smaller label 4. generate code for node This approach minimizes register use for a given tree

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COMP 512, Rice University32 Sethi Ullman Numbering Of course, code shape matters Deep trees use fewer registers than broad trees a + b + c + d + + + cdab 1 1 2 2 2 1 1 1 1 1 1 2 2 3 Evaluates in 2 registers Less ILP Evaluates in 3 registers More ILP

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COMP 512, Rice University33 Balancing Speed and Register Pressure Goodman & Hsu proposed a novel scheme Context: debate about prepass versus postpass scheduling Problem: tradeoff between allocation & scheduling Solution: Schedule for speed until fewer than Threshold registers Schedule for registers until more than Threshold registers Details: for speed means one of the latency-weighted priorities for registers means an incremental adaptation of SU scheme James R. Goodman and Wei-Chung Hsu, Code Scheduling and Register Allocation in Large Basic Blocks, Proceedings of the 2 nd International Conference on Supercomputing, St. Malo, France, 1988, pages 442-452.

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COMP 512, Rice University34 Local Scheduling & Register Allocation List scheduling is a local, incremental algorithm Decisions made on an operation-by-operation basis Use local (basic-block level) metrics Need a local, incremental register-allocation algorithm Bests algorithm, called bottom-up local in EaC To free a register, evict the value with furthest next use Uses local (basic-block level) metrics Combining these two algorithms leads to a fair, local algorithm for the combined problem, called IRIS Idea is due to Dae-Hwan Kim & Hyuk-Jae Lee Can use a non-local eviction heuristic ( new twist on Bests alg. ) D-H. Kim and H-J. Lee, Integrated Instruction Scheduling and Fine-Grain Register Allocation for Embedded Processors, in Embedded Computer Systems: Architectures, Modeling, and Simulation, LNCS 4017, pages 269-278.

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COMP 512, Rice University35 Original Code for Local List Scheduling Cycle 1 Ready leaves of D Active Ø while (Ready Active Ø) if (Ready Ø) then remove an op from Ready S( op ) Cycle Active Active op Cycle Cycle + 1 update the Ready queue Paraphrasing from earlier slide…

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COMP 512, Rice University36 The Combined Algorithm Sketch of the algorithm Cycle 1 Ready leaves of D Active Ø while (Ready Active Ø) if (Ready Ø) then remove an op from Ready make operands available in registers allocate a register for target S( op ) Cycle Active Active op Cycle Cycle + 1 update the Ready queue Reload Live on Exit values, if necessary Keep a list of free registers On last use, put register back on free list To free register, store value used farthest in the future

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