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Chinese Arithmetic on Many-core Processors

This project explores the implementation of Chinese arithmetic on many-core processors, focusing on highly precise integer calculations. The algorithm utilizes locally defined modulo keys that are relatively prime, allowing for fast operations including addition, subtraction, and multiplication, while ensuring virtually unlimited integer size without loss of accuracy. The framework does not support division or negative numbers. Performance is enhanced through distributed computing, leveraging random operations on generated integers to maximize efficiency. Relevant literature includes works by Dewdney and Knuth.

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Chinese Arithmetic on Many-core Processors

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  1. Chinese Arithmetic on Many-core Processors Jonathan Mee’s CDA6938 Semester Project

  2. Motivation • Highly Precise Calculations • Excellent Many-core Speedup • Integers Not Real Numbers • Virtually Unlimited Integer Size without Loss of Accuracy

  3. Chinese Arithmetic • Static Set of Modulo Keys • Keys Must Be Relatively Prime • Local Set of Corresponding Mods • Additions, Subtractions, and Multiplications Performed on Local Sets • Divisions Not Supported • Negative Numbers Not Supported by My Algorithm

  4. Example

  5. Algorithm Sections Generate Distribute Mod Mod Mod Arithmetic Arithmetic Arithmetic Collect Collect Collect Verify

  6. Generate • Numbers Generated Randomly • Addition, Subtraction, Multiplication, and Division Operations Ordered Randomly • Clearly Done on CPU

  7. Distribute

  8. Mod

  9. Arithmetic

  10. Collect

  11. Verify

  12. Results

  13. Works Cited Dewdney, A. K. The (New) Turing Omnibus. New York: Owl Books, 1993. Knuth, Donald E. The Art of Computer Programming. Ed. Michael A. Harrison. 2nd ed. 2 vols. Reading: Addison-Wesley Publishing Company, 1969.

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