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Pipelined Vector Processing and Scientific Computation John G. Zabolitzky

Pipelined Vector Processing and Scientific Computation John G. Zabolitzky. Applications of High-Performance Computing. Weather prediction, climatic simulation fluid dynamics simulation (aerodynamics for aerospace, automobile, combustion, ....) basic science cosmology

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Pipelined Vector Processing and Scientific Computation John G. Zabolitzky

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  1. Pipelined Vector Processing and Scientific ComputationJohn G. Zabolitzky Eine Zeitreise in die Welt der Computer.

  2. Applications of High-Performance Computing • Weather prediction, climatic simulation • fluid dynamics simulation (aerodynamics for aerospace, automobile, combustion, ....) • basic science • cosmology • quantum mechanical many-body problems • chemistry • solid-state • quantum fluids • high-energy physics • cryptography • weapons research • energy research • nuclear reactor simulation • fusion research • many many more Eine Zeitreise in die Welt der Computer.

  3. Terminal State of Scalar Computing: CDC 7600, 1968 • Maximum RISC performance of 1 operation/cycle achieved • No further improvement possible without change of paradigm • 36 MHz => 36 MIPS => 5 MFLOPS real Eine Zeitreise in die Welt der Computer.

  4. Pipelined Scalar Execution Eine Zeitreise in die Welt der Computer.

  5. Eine Zeitreise in die Welt der Computer.

  6. Scalar Code Example • DO i=1,100 a(i)=b(i)*c(i) • load b, inc addesss • load c, inc address • multiply • store a, inc address • decrement count, loop? • 5 instructions = cycles (optimum) for one multiply • pipelined multiply: could start one multiply each and every cycle => only 20% efficient use • expensive multiplier sits idle most of the time Eine Zeitreise in die Welt der Computer.

  7. Architectural Alternatives • * Pipelined Scalar (RISC) as outlined before • * Pipelined Vector (this presentation further down) • * SIMD (Single Instruction Multiple Data) parallel arithmetic (e.g., ILLIAC IV) • too expensive, inefficient: larger number of lightly used multipliers • * Superscalar = multiple issue in one cycle • all modern single-chip CPUs (Intel to TI); keep all functions busy • * VLIW (Very Long Instruction Word) = Variant of Superscalar • * MIMD (Multiple Instruction Multiple Data) true parallel streams, e.g. Cray T3E, IBM Blue Gene, IBM Cell: may be superimposed on top of ANY CPU architecture Eine Zeitreise in die Welt der Computer.

  8. Vector Computation • Scientific codes have high percentage in looping over simple data structures • DO i=1,100 a(i) = b*c(i) + d(i) • simple logical structure ==> • set up such that one multiply/cycle • one instruction for entire loop • MFLOP rate = cycle rate or multiple thereof • specialized for scientific/engineering tasks Eine Zeitreise in die Welt der Computer.

  9. Vector Pipeline c(i)=a(i)*b(i) Inventor: Henry Ford Eine Zeitreise in die Welt der Computer.

  10. Need to Vectorize; some automatic, high quality requires hand-optimization • Naive scalar code for matrix multiply • s=0.0 • do j=1,n • s=s+a(i,j)*b(j,k) • Recursive on s => adder pipeline blocked • vector code for matrix multiply • do i=1,n • c(i,k) = c(i,k) + a(i,j)*b(j,k) • Independent vector elements, but 1.5x bandwidth • Frequently good idea: exchange inner/outer loop Eine Zeitreise in die Welt der Computer.

  11. First Vector Computers • Control Data Corporation (CDC) STAR-100 [STring ARray 100 MFLOPS] • memory-to-memory architecture • therefore long startup times (~n00 cycles) • very slow scalar unit (~2 MFLOPS) • overall disappointing performance • contracted 1967, announced 1972, delivered 1974 • total of 4 machines, 2 Lawrence Livermore Lab • Thornton (CDC) and Fernbach (LLL) loose their jobs Eine Zeitreise in die Welt der Computer.

  12. CDC STAR-100 Photograph courtesy of Charles Babbage Institute, University of Minnesota, Minneapolis Eine Zeitreise in die Welt der Computer.

  13. Texas Instruments ASC • Advanced Scientific Computer, early 1970s • architecturally similar to CDC STAR-100 • 7 units sold • TI dropped out of mainframe computer manufacturing after this machine Eine Zeitreise in die Welt der Computer.

  14. Vector Performance I • MFLOP rate (MFLOPS) as function of vector length n • scalar: ~constant (only some loop overhead, then n * loop time) • vector: (n = length of vector) • # cycles = startup + n / nflop_per_cycle • rate/clock = #ops / #cycles ~ n / (startup + n) • half rate at vectorlength n ~ startup • full rate needs n >> startup => “Long Vector Machine” Eine Zeitreise in die Welt der Computer.

  15. Performance vs. Startup, Length Eine Zeitreise in die Welt der Computer.

  16. Vector Performance II • Vector/Scalar Subsections • ALL codes have some scalar (non-vectorizable) sections • total time = (scalar fraction)/(scalar rate) + (vector fraction)/(vector rate) • example: 10% / 1 MFLOPS + 90% / 100 MFLOPS = • 100 / (0.1 * 100 + 0.9 * 1) = 9.2 MFLOPS !!! Eine Zeitreise in die Welt der Computer.

  17. Vector Version of Amdahl’s Law Eine Zeitreise in die Welt der Computer.

  18. Vector Computer Design Guide • Must have SHORT vector startup => can work with short vectors • Must have FASTEST POSSIBLE scalar unit => can afford scalar sections • irregular data structures ==> need gather, scatter, merge operations (and a few more) • x(i) = a(index(i)) * b(i) • y(index(i)) = c(i) + d(i) • where (a(i) > b(i)) c(i) = d(i) Eine Zeitreise in die Welt der Computer.

  19. Cray Research, Inc. • Founded by Seymour Cray (father of CDC 6600/7600) in 1972 (STAR-100 known) • first Cray-1 delivered in 1976 to Los Alamos Scientific Laboratory (LASL) • 8 vector registers of 64 elements each • Vector load/store instructions • fastest scalar computer of its time • 160 MFLOPS peak rate ( 2 ops/cycle @ 80 MHz), few cycles startup Eine Zeitreise in die Welt der Computer.

  20. Seymour Cray Cray-1 1976 Single Processor 80 MFLOPS 1 Mword = 8 Mbyte Photograph courtesy of Charles Babbage Institute, University of Minnesota, Minneapolis Eine Zeitreise in die Welt der Computer.

  21. Large working set: - 8 vector registers, 64 words - 8 scalar registers - 8 address registers - large instruction buffer Performance Features: - vector processing: one operation affects 64 vector elements, streamed through functional unit - small vector startup time - chaining between vector ops - large, fast semiconductor memory Eine Zeitreise in die Welt der Computer.

  22. Cray Research, Inc. cnt’d • 1982 Cray-XMP (Steve Chen improvements, up to 4 processors, shared memory) • 1985 Cray-2, 256 Mword memory, 4 processors, immersion cooled • 1988 Cray-YMP (last Chen machine) • 1991 Cray C90 (up to 16 vector CPUs, shared memory) • 1993 Cray T3D (massively parallel Alpha) • one and only Cray-3 delivered to NCAR (Cray Comp Corp) • 1994 Cray J90 (up to 32 vector CPUs, shared memory), air cooled • 1995 Cray T3E (most successful MPP machine), Cray T90 (parallel vector, immersion cooled) • Cray-4 abandoned (Cray Computer Corporation ch. 11) • 1996 acquired by Silicon Graphics • 1998 Cray SV1 (parallel vector, air cooled) • 1999 acquired by Teradata => Cray, Inc. • 2002 Cray X1, parallel vector, immersion spray cooled • 2004 Cray X1e, enhanced version of X1 • Cray XT3, AMD based 3D Torus massively parallel machine Eine Zeitreise in die Welt der Computer.

  23. CDC Cyber 200 Family • - 1980, enhanced version of STAR-100 • - reduced startup time, ~ 50 cycles • - fast scalar unit • - rich instruction repertoire • - still memory-to-memory, 400 MFLOPS peak • - Cyber 203, Cyber 205, ETA-10 [10 GFLOPS] • - vector FORTRAN language extensions provided • - terminated in 1989 since unprofitable • - around 40 Cyber 200, 34 ETA-10 sold Eine Zeitreise in die Welt der Computer.

  24. Minnesota Supercomputer Center Minneapolis, 1986 Cray-2, CDC Cyber 205 Eine Zeitreise in die Welt der Computer.

  25. NEC Japan • - 1983 SX-1 single processor vector 650 MFLOPS • - 1985 SX-2 single processor vector 1300 MFLOPS • - 1990 SX-3 four processors at ~ 5 GFLOPS each, 4 Gbyte = 0.5 Gword memory • - 1995 SX-4 32 processors at ~ 2 GFLOPS each (CMOS; all previous ECL) • - 1998 SX-5 upto 512 processors 8 GFLOPS each • - 2002 SX-6 upto 1024 processors 8 GFLOPS each • - 2004 SX-7 upto 2048 processors 8.8 GFLOPS each • - 2004 SX-8 upto 4096 processors 16 GFLOPS each Eine Zeitreise in die Welt der Computer.

  26. IBM - Sony - Toshiba CELL processor - 8 vector CPUs + GPU on single chip - 256 kbyte = 32 kword local storage (very small !!) - 12 word/cycle internal interconnect = 386 Gbyte/sec - 24 Gbyte/sec = 3 Gword/sec main memory - 76 Gbyte/sec = 9.5 Gword/sec communication - @ 4 GHz clock 256 GFLOPS (32 bit) peak - 26 GFLOPS (64 bit) peak - max 4.5 Gbyte addressable, 512 Mbyte implemented - system interconnect ? - used within Sony Playstation 3 - Mercury, IBM blades available; 512 Mbyte only - highly imbalanced for scientific computation Eine Zeitreise in die Welt der Computer.

  27. IBM - Sony - Toshiba CELL processor - 90 nm SOI, 8 layers Cu interconnect - 234 M Transistors - 221 mm² die size - significant potential in future revisions - but: 80W @ 1.1V 4.0 GHz is too much - 180W @ 1.4V 5.6 GHz is much too much - work needed in power reduction - larger internal memory - 64 bit arithmetic improved Eine Zeitreise in die Welt der Computer.

  28. IBM - Sony - Toshiba CELL processor From: S. Williams et. al., Lawrence Berkeley Laboratory - single Cell chip performance - compared with Cray X1E single vector processor and several commodity microprocessors (AMD, Intel) - already current version shows impressive speedup, at cost of significant programming complexity (explicit storage moves as opposed to caching) - slightly enhanced Cell (Cell+) simulation provides very significant additional speedup (more efficient DP) - current version insufficient for major impact - future versions may change that, great potential Eine Zeitreise in die Welt der Computer.

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