1. CS 612: Software Design for High-performance Architectures

2. Administration Instructor: Keshav Pingali –457 Rhodes Hall –pingali@cs.cornell.edu TA: Milind Kulkarni –490 Rhodes Hall –milind@cs.cornell.edu

3. Course content Understand high-end programming paradigms, compilers and runtime systems –Applications requirements –Shared-memory programming –Optimistic and pessimistic parallelization –Transactional memory –Memory hierarchy optimization –Self-optimizing systems Focus on software problem for multicore processors

4. Problem Silicon designers can choose a variety of methods to increase processor performance Commercial end-customers are demanding –More capable systems with more capable processors –That new systems stay within their existing power/thermal infrastructure Processor frequency and power consumption seem to be scaling in lockstep How can the industry-standard PC and Server industries stay on our historic performance curve without burning a hole in our motherboards?

5. What is a processor? A single chip package that fits in a socket ≥1 core (not much point in <1 core…) –Cores can have functional units, cache, etc. associated with them, just as today –Cores can be fast or slow, just as today Shared resources –More cache –Other integration: memory controllers, high-speed serial links, etc. One system interface no matter how many cores –Number of signal pins doesn’t scale with number of cores

6. ILP Problem Functional units –Superscalar is known territory –Diminishing returns for adding more functional blocks –Alternatives like VLIW have been considered and rejected by the market –Single-threaded architectural performance is pegged Data paths –Increasing bandwidth between functional units in a core makes a difference Such as comprehensive 64-bit design, but then where to?

7. ILP Problem (contd.) Pipeline –Deeper pipeline buys frequency at expense of increased cache miss penalty and lower instructions per clock –Shallow pipeline gives better instructions per clock at the expense of frequency scaling –Max frequency per core requires deeper pipelines –Industry converging on middle ground…9 to 11 stages Successful RISC CPUs are in the same range Cache –Cache size buys performance at expense of die size –Deep pipeline cache miss penalties are reduced by larger caches

8. Power problem Moore’s Law isn’t dead, more transistors for everyone! –But…it doesn’t really mention scaling transistor power Chemistry and physics at nano-scale –Stretching materials science –Transistor leakage current is increasing As manufacturing economies and frequency increase, power consumption is increasing disproportionately There are no process or architectural quick-fixes

9. Static Current vs. Frequency Frequency Static Current Embedded Parts Very High Leakage and Power Fast, High Power Fast, Low Power 1.01.5 15 0 Non-linear as processors approach max frequency

10. Power vs. Frequency In AMD’s process, for 200MHz frequency steps, two steps back on frequency cuts power consumption by ~40% from maximum frequency Substantially lower power with lower frequency Result is dual-core running at n-2 in same thermal envelope as single-core running at top speed

11. AMD Multi-Core Processor Dual-core AMD Opteron™ processor is 199mm 2 in 90nm Single-core AMD Opteron processor is 193mm 2 in 130nm

12. Multi-Core Processor Architecture

13. Multi-Core Software More aggregate performance for: –Multi-threaded apps –Transactions: many instances of same app –Multi-tasking Problem –Most apps are not multithreaded –Writing multithreaded code increases software costs dramatically (factor of 3 for some game engines)

14. First problem: Parallelization “We are the cusp of a transition to multicore, multithreaded architectures, and we still have not demonstrated the ease of programming the move will require… I have talked with a few people at Microsoft Research who say this is also at or near the top of their list [of critical CS research problems].” Justin Rattner, Senior Fellow, Intel

15. Second problem: memory hierarchy “…The CPU chip industry has now reached the point that instructions can be executed more quickly than the chips can be fed with code and data. Future chip design is memory design. Future software design is also memory design..… Controlling memory access patterns will drive hardware and software designs for the foreseeable future.” Richard Sites, DEC

16. Memory Hierarchy of SGI Octane R10 K processor: –4-way superscalar, 2 fpo/cycle, 195MHz Peak performance: 390 Mflops Experience: sustained performance is less than 10% of peak –Processor often stalls waiting for memory system to load data size access time (cycles) 21070 64 32KB (I) 32KB (D) 1MB 128MB Regs L1 cache L2 cache Memory

17. Memory-wall solutions Latency avoidance: –multi-level memory hierarchies (caches) Latency tolerance: –Pre-fetching –multi-threading Techniques are not mutually exclusive: –Most microprocessors have caches and pre-fetching –Modest multi-threading is coming into vogue –Our focus: memory hierarchies

18. Hiding latency in numerical codes Most numerical kernels: O(n 3 ) work, O(n 2 ) data –all factorization codes Cholesky factorization: A = LL T (A is spd) LU factorization: A = LU LU factorization with pivoting: A = LU QR factorization: A = QR (Q is orthogonal) –BLAS-3: matrix multiplication  use latency avoidance techniques Matrix-vector product: O(n 2 ) work, O(n 2 ) data –use latency tolerance techniques such as pre-fetching –particularly important for iterative solution of large sparse systems

19. Software problem Caches are useful only if programs have locality of reference –temporal locality: program references to given memory address are clustered together in time –spatial locality: program references clustered in address space are clustered in time Problem: –Programs obtained by expressing most algorithms in the straight-forward way do not have much locality of reference –Worrying about locality when coding algorithms complicates the software process enormously.

20. Example: matrix multiplication Great algorithmic data reuse: each array element is touched O(N) times! All six loop permutations are computationally equivalent (even modulo round-off error). However, execution times of the six versions can be very different if machine has a cache. DO I = 1, N //assume arrays stored in row-major order DO J = 1, N DO K = 1, N C(I,J) = C(I,J) + A(I,K)*B(K,J)

21. IJK version (large cache) DO I = 1, N DO J = 1, N DO K = 1, N C(I,J) = C(I,J) + A(I,K)*B(K,J) Large cache scenario: –Matrices are small enough to fit into cache –Only cold misses, no capacity misses –Miss ratio: Data size = 3 N 2 Each miss brings in b floating-point numbers Miss ratio = 3 N 2 /b*4N 3 = 0.75/bN = 0.019 (b = 4,N=10) C B A K K

22. IJK version (small cache) DO I = 1, N DO J = 1, N DO K = 1, N C(I,J) = C(I,J) + A(I,K)*B(K,J) Small cache scenario: –Matrices are large compared to cache/row-major storage –Cold and capacity misses –Miss ratio: C: N 2 /b misses (good temporal locality) A: N 3 /b misses (good spatial locality) B: N 3 misses (poor temporal and spatial locality) Miss ratio  0.25 (b+1)/b = 0.3125 (for b = 4) C B A K K

23. MMM Experiments Simulated L1 Cache Miss Ratio for Intel Pentium III –MMM with N = 1…1300 –16KB 32B/Block 4-way 8-byte elements

24. Quantifying performance differences DO I = 1, N //assume arrays stored in row-major order DO J = 1, N DO K = 1, N C(I,J) = C(I,J) + A(I,K)*B(K,J) Octane –L2 cache hit: 10 cycles, cache miss 70 cycles Time to execute IKJ version: 2N 3 + 70*0.13*4N 3 + 10*0.87*4N 3 = 73.2 N 3 Time to execute JKI version: 2N 3 + 70*0.5*4N 3 + 10*0.5*4N 3 = 162 N 3 Speed-up = 2.2 Key transformation: loop permutation

25. Even better….. Break MMM into a bunch of smaller MMMs so that large cache model is true for each small MMM  large cache model is valid for entire computation  miss ratio will be 0.75/bt for entire computation where t is

26. Loop tiling Break big MMM into sequence of smaller MMMs where each smaller MMM multiplies sub-matrices of size txt. Parameter t (tile size) must be chosen carefully –as large as possible –working set of small matrix multiplication must fit in cache A B C It Kt Jt I K J DO It = 1,N, t DO Jt = 1,N,t DO Kt = 1,N,t DO I = It,It+t-1 DO J = Jt,Jt+t-1 DO K = Kt,Kt+t-1 C(I,J) = C(I,J)+A(I,K)*B(K,J) t t t t

27. Speed-up from tiling Miss ratio for block computation = miss ratio for large cache model = 0.75/bt = 0.001 (b = 4, t = 200) for Octane Time to execute tiled version = 2N 3 + 70*0.001*4N 3 + 10*0.999*4N 3 = 42.3N 3 Speed-up over JKI version = 4

28. Observations Locality optimized code is more complex than high-level algorithm. Loop orders and tile size must be chosen carefully –cache size is key parameter –associativity matters Actual code is even more complex: must optimize for processor resources –registers: register tiling –pipeline: loop unrolling –Optimized MMM code can be ~1000 lines of C code

29. One solution to both problems: restructuring compilers (1985-) Programmer writes high-level architecture independent code Restructuring compiler: optimizes program for –Number of cores –Number of register –Cache organization –Instruction set: mul-add? vector extensions? …

30. Two key issues P1 P2 P3 …… P 1.Program restructuring: given program P, determine set of equivalent programs P1, P2, P3,… 2.Program selection: determine which program performs best on target architecture 1 2

31. Automatic parallelization Pessimistic parallelization: –Compiler determines partial order on program operations by determining dependences –At run-time, execute operations in parallel, respecting dependences –Works reasonably well for array programs but not for irregular data structures like trees and graphs Optimistic parallelization: –Execute operations speculatively in parallel, assuming that dependences do not exist –Check at runtime if dependences are violated –If so, roll-back execution to “safe” point and re-execute sequentially –Works only if optimism is warranted –Lots of interest in “transactional memory” which is one model of optimistic parallelization

32. Automatic locality enhancement Some methodology exists for array programs but little is known for irregular programs Many compilers can perform tiling and permutation automatically (gcc) Choosing parameter values: tile sizes etc. –Compiler can use architectural models –Self-optimizing systems: system determines best values using some kind of heuristic search (ATLAS,FFTW)

33. Course outline Applications requirements –Scientific and engineering applications –Commercial work-loads Shared-memory programming –Memory consistency models –OpenMP Optimistic and pessimistic parallelization –Dependence analysis techniques for array and irregular programs –Transactional memory models and implementations Automatic locality enhancement Self-optimizing systems

34. Course work Small number of programming assignments Paper presentations and class participation –We will have papers online by next Monday –Sign up for presentation by next Thursday Substantial course project independent reading implementation work presentation