CSE 8351 Computer Arithmetic Fall 2005 Instructor: Peter-Michael Seidel

CSE 8351 Computer ArithmeticSeidel - Fall Administrative Issues Class times: TTh 5:00-6:20 Office hours: (SIC301) W 2-3, Th 2-3 Course Webpage: 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 –Project40% –Paper Summaries/Presentations 40% –Examination 20% 8000 level - Research focus in class –Quality Research is based on a combination of Knowledge (facts) / Skills (methodology) / Motivation (effort)

CSE 8351 Computer ArithmeticSeidel - Fall I. Introduction (1 class) II. Historical Perspectives(1 class) III. Simple Algorithms for Arithmetic Unit Design in Hardware (3 classes) Addition/Multiplication/ SRT Division/Square Root / Reciprocal Approximation IV. (Long) Arithmetic Algorithms in Software(4 classes) Addition / Multiplication (Karatsuba/FFT) / Division (Karatsuba) / Powering V. Redundant Radix Representations and Partial Compressions (3 classes) General Framework, Classification and Hardware / On-line Arithmetic VI. Highly Parallel Add/Multiply/Divide/Square Root Algorithms (5 classes) Parallel Adders/ Parallel Multiplication / Booth, High Radix Digit Speculation/ Conversion Methods // Low-Power Multiplication VII. (IEEE) Floating-Point Arithmetic & Rounding(5 classes) Standard / Representatives / Rounding Multiplication, Division / Addition / Dual Path / Pipelined-Packet FP expansions in Software Transcendental functions VIII. Vector and Matrix Arithmetic, Arithmetic for Encryption (3 classes) Matrix Multiplication (LUP decomposition) / RSA and modular Arithmetic Tentative Content

CSE 8351 Computer ArithmeticSeidel - Fall 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

CSE 8351 Computer ArithmeticSeidel - Fall 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 Selected Project Topics