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Performance of mathematical software

Performance of mathematical software. Agner Fog Technical University of Denmark www.agner.org. Agenda. Intel and AMD microarchitecture Performance bottlenecks Parallelization C++ vector classes, example Instruction set dispatching Performance measuring Hands-on examples.

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Performance of mathematical software

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  1. Performance of mathematical software Agner Fog Technical University of Denmark www.agner.org

  2. Agenda • Intel and AMD microarchitecture • Performance bottlenecks • Parallelization • C++ vector classes, example • Instruction set dispatching • Performance measuring • Hands-on examples

  3. AMD Microarchitecture • 2 threads per CPU unit • 4 instructions per clock • Out-of-order execution

  4. Intel Micro-architecture

  5. Typical bottlenecks • Installation of program • Program start, load framework and libraries • System database • Network • File input / output • Graphics • RAM access, cache utilization • Algorithm • Dependency chains • CPU pipeline • CPU execution units Speed

  6. Efficient cache use • Store data in contiguous blocks • Avoid advanced data containers such as resizable data structures, linked lists, etc. • Store local data inside the function they are used in

  7. Branch prediction

  8. Out-Of-Order Execution x = a / b; y = c * d; z = x + y;

  9. Dependency chains x = a + b + c + d; x = (a + b) + (c + d);

  10. Loop-carrieddependency chain for (i = 0; i < n; i++) { sum += x[i]; } for (i = 0; i < n; i += 2) { sum1 += x[i]; sum2 += x[i+1]; } sum = sum1 + sum2;

  11. Levels of parallelization • Multiple threads running in different CPU units • Out-of-order execution • SIMD instructions

  12. SIMD programming methods • Assembly language • Intrinsic functions • Vector classes • Automatic vectorization by compiler

  13. Obstacles to automatic vectorization • Pointer aliasing • Array alignment • Array size • Algebraic reduction • Branches • Table lookup

  14. Vector math libraries Short vectors Long vectors Intel VML Intel IPP Yeppp • Intel SVML • AMD libm • Agner’s VCL

  15. Example Exponential function in vector classes

  16. Instruction set dispatching Future extensions

  17. Performance measurement • Profiler • Insert measuring instruments into code • Performance monitor counters

  18. When timing results are unstable • Stop other running programs • Warm up CPU with heavy work • Disable power saving features in BIOS setup • Disable hyperthreading • Use “core clock cycles” counter (Intel only)

  19. Example Measuring latency and throughput of machine instruction

  20. Hands-on example Compare performance of different mathematical function libraries http://cern.agner.org

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