CSE 8351 Computer Arithmetic Fall 2005 Instructor: PeterMichael Seidel

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CSE 8351Computer ArithmeticFall
2005Instructor Peter-Michael Seidel

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Administrative Issues

• Class times TTh 500-620
• Office hours (SIC301) W 2-3, Th 2-3
• Course Webpage http//engr.smu.edu/seidel/co
  urses/cse8351/
• Class material
• Handouts, slides and references will be provided
  on course webpage
• no required textbook
• References will be provided on WWW Computer
  Arithmetic Page (to be setup)
• Grade distribution
• Project 40
• Paper Summaries/Presentations 40
• Examination 20
• 8000 level - Research focus in class
• Quality Research is based on a combination of

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Tentative Content

• Introduction (1 class)
• Historical Perspectives (1 class)
• Simple Algorithms for Arithmetic Unit Design in
  Hardware (3 classes)
• Addition/Multiplication/ SRT Division/Square Root
  / Reciprocal Approximation
• (Long) Arithmetic Algorithms in Software (4
  classes)
• Addition / Multiplication (Karatsuba/FFT) /
  Division (Karatsuba) / Powering
• Redundant Radix Representations and Partial
  Compressions (3 classes)
• General Framework, Classification and Hardware /
  On-line Arithmetic
• Highly Parallel Add/Multiply/Divide/Square Root
  Algorithms (5 classes)
• Parallel Adders/ Parallel Multiplication / Booth,
  High Radix
• Digit Speculation/ Conversion Methods //
  Low-Power Multiplication
• (IEEE) Floating-Point Arithmetic Rounding (5
  classes)
• Standard / Representatives / Rounding
• Multiplication, Division / Addition / Dual Path /
  Pipelined-Packet
• FP expansions in Software
• Transcendental functions
• Vector and Matrix Arithmetic, Arithmetic for
  Encryption (3 classes)
• Matrix Multiplication (LUP decomposition) / RSA
  and modular Arithmetic

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Importance of Number Representations

• A German merchant of the fifteenth century asked
  an eminent
• professor where he should send his son for a good
  business
• education. The professor responded that German
  universities
• would be sufficient to teach the boy addition and
  subtraction but
• he would have to go to Italy to learn
  multiplication and division.
• Before you smile indulgently, try multiplying or
  even just adding
• the Roman numerals CCLXIV, MDCCCIX, DCL, and
  MLXXXI
• without first translating them.
• John Allen
  Paulos, Beyond Numeracy

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Selected Project Topics

• Implementation Radix-k Serial FP-Adder
  
• Formal Verification of optimized Arithmetic HW
  (PVS)
• Scalable multiplicative FP-Dividers
• Effective Arithmetic on FPGAs
• Optimal Compressor Implementations
• Multiple-Path Fused Multiply-Add
• Arithmetic Optimization by combining CMOS
  Threshold logic
• Low-cost low-precision transcendentals for
  computer graphic
• Hardware acceleration for Encryption Algorithms
• Long Arithmetic based on Floating-Point
  Expansions
• Others