Multiprocessor Memory Allocation - University of Delaware

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  • 1.Introduction to Optimization John Cavazos University of Delaware
  • 2.Lecture Overview Motivation Loop Transformations
  • 3.Why study compiler optimizations? Moore’s Law Chip density doubles every 18 months Reflected in CPU performance doubling every 18 months Proebsting’s Law Compilers double CPU performance every 18 years 4% improvement per year because of optimizations!
  • 4.Why study compiler optimizations? Corollary 1 year of code optimization research = 1 month of hardware improvements No need for compiler research… Just wait a few months!
  • 5.Free Lunch is over Moore’s Law Chip density doubles every 18 months PAST : Reflected CPU performance doubling every 18 months CURRENT: Density doubling reflected in more cores on chip! Corollary Cores will become simpler Just wait a few months… Your code might get slower! Many optimizations now being done by hand! (autotuning)
  • 6.Optimizations: The Big Picture What are our goals? Simple Goal: Make execution time as small as possible Which leads to: Achieve execution of many (all, in the best case) instructions in parallel Find independent instructions
  • 7.Dependences We will concentrate on data dependences Simple example of data dependence: S1 PI = 3.14 S2 R = 5.0 S3 AREA = PI * R ** 2 Statement S3 cannot be moved before either S1 or S2 without compromising correct results S1 S2 S3
  • 8.Dependences Formally: Data dependence from S1 to S2 (S2 depends on S1) if: 1. Both statements access same memory location and one of them stores onto it, and 2. There is a feasible execution path from S1 to S2
  • 9.Load Store Classification Dependences classified in terms of load-store order: 1. True dependence (RAW hazard) 2. Antidependence (WAR hazard) 3. Output dependence (WAW hazard)
  • 10.Dependence in Loops Let us look at two different loops: DO I = 1, N S1 A(I+1) = A(I)+ B(I) ENDDO DO I = 1, N S1 A(I+2) = A(I)+B(I) ENDDO In both cases, statement S1 depends on itself
  • 11.Transformations We call a transformation safe if the transformed program has the same "meaning" as the original program But, what is the "meaning" of a program? For our purposes: Two programs are equivalent if, on the same inputs: They produce the same outputs in the same order
  • 12.Loop Transformations Compilers have always focused on loops Higher execution counts Repeated, related operations Much of real work takes place in loops *
  • 13.Several effects to attack Overhead Decrease control-structure cost per iteration Locality Spatial locality  use of co-resident data Temporal locality  reuse of same data Parallelism Execute independent iterations of loop in parallel *
  • 14.Eliminating Overhead Loop unrolling (the oldest trick in the book) To reduce overhead, replicate the loop body Sources of Improvement Less overhead per useful operation Longer basic blocks for local optimization do i = 1 to 100 by 1 a(i) = a(i) + b(i) end do i = 1 to 100 by 4 a(i) = a(i) + b(i) a(i+1) = a(i+1) + b(i+1) a(i+2) = a(i+2) + b(i+2) a(i+3) = a(i+3) + b(i+3) end becomes (unroll by 4)
  • 15.Loop Fusion Two loops over same iteration space  one loop Safe if does not change the values used or defined by any statement in either loop (i.e., does not violate dependences) do i = 1 to n c(i) = a(i) + b(i) end do j = 1 to n d(j) = a(j) * e(j) end becomes (fuse) do i = 1 to n c(i) = a(i) + b(i) d(i) = a(i) * e(i) end * For big arrays, a(i) may not be in the cache a(i) will be found in the cache
  • 16.Loop Fusion Advantages Enhance temporal locality Reduce control overhead Longer blocks for local optimization & scheduling Can convert inter-loop reuse to intra-loop reuse *
  • 17.Loop Fusion of Parallel Loops Parallel loop fusion legal if dependences loop independent Source and target of flow dependence map to same loop iteration Each iteration can execute in parallel *
  • 18.Loop distribution (fission) Single loop with independent statements  multiple loops Starts by constructing statement level dependence graph Safe to perform distribution if: No cycles in the dependence graph Statements forming cycle in dependence graph put in same loop
  • 19.Loop distribution (fission) Has the following dependence graph (1) for I = 1 to N do (2) A[I] = A[i] + B[i-1] (3) B[I] = C[I-1]*X+C (4) C[I] = 1/B[I] (5) D[I] = sqrt(C[I]) (6) endfor
  • 20.Loop distribution (fission) becomes (fission) (1) for I = 1 to N do (2) A[I] = A[i] + B[i-1] (3) B[I] = C[I-1]*X+C (4) C[I] = 1/B[I] (5) D[I] = sqrt(C[I]) (6) endfor (1) for I = 1 to N do A[I] = A[i] + B[i-1] (3) endfor (4) for B[I] = C[I-1]*X+C C[I] = 1/B[I] endfor for D[I] = sqrt(C[I]) endfor
  • 21.21 Loop Fission Advantages Enables other transformations E.g., Vectorization Resulting loops have smaller cache footprints More reuse hits in the cache *
  • 22.Loop Tiling (blocking) Want to exploit temporal locality in loop nest.
  • 23.Loop Tiling (blocking)
  • 24.Loop Tiling (blocking)
  • 25.Loop Tiling (blocking)
  • 26.Loop Tiling (blocking)
  • 27.27 Loop Tiling Effects Reduces volume of data between reuses Works on one “tile” at a time (tile size is B by B) Choice of tile size is crucial
  • 28.Scalar Replacement Allocators never keep c(i) in a register We can trick the allocator by rewriting the references The plan Locate patterns of consistent reuse Make loads and stores use temporary scalar variable Replace references with temporary’s name
  • 29.29 Scalar Replacement do i = 1 to n do j = 1 to n a(i) = a(i) + b(j) end end do i = 1 to n t = a(i) do j = 1 to n t = t + b(j) end a(i) = t end becomes (scalar replacement) Almost any register allocator can get t into a register
  • 30.30 Scalar Replacement Effects Decreases number of loads and stores Keeps reused values in names that can be allocated to registers In essence, this exposes the reuse of a(i) to subsequent passes