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11/21/2002© 2002 Hal Perkins & UW CSEO-1 CSE 582 – Compilers Instruction Scheduling Hal Perkins Autumn 2002
11/21/2002© 2002 Hal Perkins & UW CSEO-2 Agenda Instruction scheduling issues – latencies List scheduling Credits: Adapted from slides by Keith Cooper, Rice University
11/21/2002© 2002 Hal Perkins & UW CSEO-3 Issues Many operations have non-zero latencies Modern machines can issue several operations per cycle Loads & Stores may or may not block may be slots after load/store for other work Branch costs vary Branches on modern processors typically have delay slots GOAL: Scheduler should reorder instructions to hide latencies and take advantage of delay slots
11/21/2002© 2002 Hal Perkins & UW CSEO-4 Some Idealized Latencies OperationCycles LOAD3 STORE3 ADD1 MULT2 SHIFT1 BRANCH0 TO 8
11/21/2002© 2002 Hal Perkins & UW CSEO-5 Example: w = w*2*x*y*z; Simple schedule 1 LOAD r1 <- w 4 ADD r1 <- r1,r1 5 LOADr2 <- x 8 MULTr1 <- r1,r2 9 LOAD r2 <- y 12 MULTr1 <- r1,r2 13 LOADr2 <- z 16 MULTr1 <- r1,r2 18 STORE w <- r1 21 r1 free 2 registers, 20 cycles Loads early 1LOADr1 <- w 2LOADr2 <- x 3LOADr3 <- y 4ADDr1 <- r1,r1 5MULTr1 <- r1,r2 6LOADr2 <- z 7MULTr1 <- r1,r3 9MULTr1 <- r1,r2 11 STOREw <- r1 14 r1 is free 3 registers, 13 cycles
11/21/2002© 2002 Hal Perkins & UW CSEO-6 Instruction Scheduling Problem Given a code fragment for some machine and latencies for each operation, reorder to minimize execution time Constraints Produce correct code Minimize wasted cycles Avoid spilling registers Do this efficiently
11/21/2002© 2002 Hal Perkins & UW CSEO-7 Precedence Graph Nodes n are operations Attributes of each node type – kind of operation delay – latency If node n2 uses the result of node n1, there is an edge e = (n1,n2) in the graph
11/21/2002© 2002 Hal Perkins & UW CSEO-8 Example Graph Code a LOAD r1 <- w b ADD r1 <- r1,r1 c LOADr2 <- x d MULTr1 <- r1,r2 e LOAD r2 <- y f MULTr1 <- r1,r2 g LOADr2 <- z h MULTr1 <- r1,r2 i STORE w <- r1
11/21/2002© 2002 Hal Perkins & UW CSEO-9 Schedules (1) A correct schedule S maps each node n into a non-negative integer representing its cycle number, and S (n ) >= 0 for all nodes n (obvious) If (n1,n2) is an edge, then S(n1)+delay(n1) <= S(n2) For each type t there are no more operations of type t in any cycle than the target machine can issue
11/21/2002© 2002 Hal Perkins & UW CSEO-10 Schedules (2) The length of a schedule S, denoted L(S) is L(S) = max n ( S(n )+delay(n ) ) The goal is to find the shortest possible correct schedule Other possible goals: minimize use of registers, power, space, …
11/21/2002© 2002 Hal Perkins & UW CSEO-11 Constraints Main points All operands must be available Multiple operations can be ready at any given point Moving operations can lengthen register lifetimes Moving uses near definitions can shorten register lifetimes Operations can have multiple predecessors Collectively this makes scheduling NP-complete Local scheduling is the simpler case Straight-line code Consistent, predictable latencies
11/21/2002© 2002 Hal Perkins & UW CSEO-12 Algorithm Overview Build a precedence graph P Compute a priority function over the nodes in P (typical: longest latency-weighted path) Use list scheduling to construct a schedule, one cycle at a time Use queue of operations that are ready At each cycle Chose a ready operation and schedule it Update ready queue Rename registers to avoid false dependencies and conflicts
11/21/2002© 2002 Hal Perkins & UW CSEO-13 List Scheduling Algorithm Cycle = 1; Ready = leaves of P; Active = empty; while (Ready and/or Active are not empty) if (Ready is not empty) remove an op from Ready; S(op) = Cycle; Active = Active + op; Cycle++; for each op in Active if (S(op) + delay(op) <= Cycle) remove op from Active; for each successor s of op in P if (s is ready – i.e., all operands available) add s to Ready
11/21/2002© 2002 Hal Perkins & UW CSEO-14 Example Code a LOAD r1 <- w b ADD r1 <- r1,r1 c LOADr2 <- x d MULTr1 <- r1,r2 e LOAD r2 <- y f MULTr1 <- r1,r2 g LOADr2 <- z h MULTr1 <- r1,r2 i STORE w <- r1
11/21/2002© 2002 Hal Perkins & UW CSEO-15 Variations Backward list scheduling Work from the root to the leaves Schedules instructions from end to beginning of the block In practice, try both and pick the result that minimizes costs Little extra expense since the precedence graph and other information can be reused Global scheduling and loop scheduling Extend basic idea in more aggressive compilers
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