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A Parallel Search Algorithm for CLNS Addition Optimization

A Parallel Search Algorithm for CLNS Addition Optimization. P. Vouzis and M. Arnold, Dept. of Computer Science & Engineering, Lehigh University, Bethlehem, USA. The Logarithmic Number System (LNS). x is a two’s complement representation with k integer bits l fractional bits.

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A Parallel Search Algorithm for CLNS Addition Optimization

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  1. A Parallel Search Algorithm for CLNS Addition Optimization P. Vouzis and M. Arnold, Dept. of Computer Science & Engineering, Lehigh University, Bethlehem, USA ISCAS 2006

  2. The Logarithmic Number System (LNS) • x is a two’s complement representation with • k integer bits • l fractional bits

  3. Arithmetic Operations in LNS

  4. Arithmetic Operations in LNS

  5. Arithmetic Operations in LNS

  6. Arithmetic Operations in LNS

  7. ] X [ m I Re [ X ] Complex Logarithmic Number System (CLNS)

  8. Complex Logarithmic Number System (CLNS)

  9. Complex Logarithmic Number System (CLNS)

  10. Complex Logarithmic Number System (CLNS)

  11. CLNS Addition

  12. CLNS Addition

  13. CLNS Addition

  14. Co-Transformation

  15. Co-Transformation

  16. Co-Transformation

  17. The Contour Lines of the Real Part

  18. The Contour Lines of the Real Part

  19. The Contour Lines of the Real Part

  20. The Contour Lines of the Real Part

  21. The Contour Lines of the Real Part

  22. The Contour Lines of the Real Part

  23. The Contour Lines of the Real Part

  24. The Contour Lines of the Real Part

  25. The Contour Lines of the Real Part

  26. The Contour Lines of the Real Part

  27. The Contour Lines of the Imaginary Part

  28. The Contour Lines of the Imaginary Part

  29. Memory Savings

  30. Conclusions • Co-transformation applied on CLNS addition • Study of the properties of CLNS addition • Analytical formulas for the memory requirements for CLNS addition • 3D LUT replaced by smaller 2D LUTs and circuitry • Substantial memory savings compared to a pure tabulation of the 3D functions

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