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Modified Accelerated GCD Algorithm Implementation

Modified Accelerated GCD Algorithm Implementation

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Modified Accelerated GCD Algorithm Implementation

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  1. Modified Accelerated GCD Algorithm Implementation KHIC 202 April 16th, 2007 2:00 PM

  2. Team GCD • DJ Selgo • Team Leader • Lead Tester • Jason Prodonovich • Architect • Configuration Management Specialist • Professor Ken Weber • Faculty Advisor

  3. Project Implementation of the Modified Accelerated GCD Algorithm http://raider.muc.edu/~prodonjs/sceblog/

  4. Presentation Outline • Definitions / Overview • Initial Goals • Development Environment / Tools • Results • Issues Encountered • Demonstration • Q&A

  5. Definitions • GNU • GMP • Multiple Precision Integers • Team GCD • GCD • Euclidean, Binary, K-ary, B-mod, Extended

  6. Project Overview • Sidi Mohammed Sedjelmaci and the Modified Jebelean-Weber Algorithm • What does it do? • How does it work? • Why should we care?

  7. Initial Goals • Modify existing mpn/gcd.c to implement M-JWA algorithm • Develop and execute thorough testing suite to show correctness • Time the new module against the original across multiple architectures

  8. Development Environment / Tools • GNU Linux (Kubuntu distribution) • C (gcc) • Bash shell • Make • Libtool • GNU Debugger (gdb) • Electric Fence (lefence) • GNU Profiler (gprof) • OpenSSH

  9. Results (x86 Pentium M)

  10. Results (x86 Pentium M)

  11. Results (PowerPC G5 64-bit)

  12. Results (PowerPC G5 64-bit)

  13. Results (x86 Core 2 Duo 64-bit)

  14. Results (x86 Core 2 Duo 64-bit)

  15. What Gives? • Profiling (gprof) data taken from runs of 200,000 1024-bit integers

  16. What Gives? • Profiling (gprof) data taken from runs of 200,000 1024-bit integers

  17. Issues Encountered • Initial learning curve • Memory overflow issues (segmentation faults) • Inexperience with development tools

  18. Wrapping Up • Produced a successful, bugfree* implementation of Sedjelmaci’s algorithm • Gained tremendous experience in an unfamiliar environment with unfamiliar tools • Laid foundation for future work into a more efficient Extended GCD algorithm based on an Accelerated algorithm