CS267 L13 Floating Point.1 Demmel Sp 1999 CS 267 Applications of Parallel Computers Lecture 13: Floating Point Arithmetic James Demmel

Slides:

Advertisements

Similar presentations

Spring 2013 Advising Starts this week! CS2710 Computer Organization1.

Advertisements

Computer Engineering FloatingPoint page 1 Floating Point Number system corresponding to the decimal notation 1,837 * 10 significand exponent A great number.

Tanenbaum, Structured Computer Organization, Fifth Edition, (c) 2006 Pearson Education, Inc. All rights reserved Floating-point Numbers.

Avoiding Measurement Errors from Manipulating Data in Software

ITEC 352 Lecture 7 Binary(2). Review Homework due on Friday Questions Binary Addition Subtraction Encoding.

Introduction to Scientific Computing ICE / ICE 508 Prof. Hyuckjae Lee KAIST- ICC

1 CSE1301 Computer Programming Lecture 30: Real Number Representation.

CS 61C L15 Floating Point I (1) Krause, Spring 2005 © UCB This day in history… TA Danny Krause inst.eecs.berkeley.edu/~cs61c-td inst.eecs.berkeley.edu/~cs61c.

CS267 L13 Floating Point.1 Demmel Sp 1999 CS 267 Applications of Parallel Computers Lecture 13: Floating Point Arithmetic James Demmel

CS 61C L15 Floating Point I (1) Garcia, Fall 2004 © UCB Lecturer PSOE Dan Garcia inst.eecs.berkeley.edu/~cs61c CS61C : Machine.

02/28/2005CS267 Lecture 11 CS 267: Applications of Parallel Computers Floating Point Arithmetic James Demmel

Outline Chapter 1 Hardware, Software, Programming, Web surfing, … Chapter Goals –Describe the layers of a computer system –Describe the concept.

CS 61C L10 Floating Point (1) A Carle, Summer 2005 © UCB inst.eecs.berkeley.edu/~cs61c/su05 CS61C : Machine Structures Lecture #10: Floating Point

02/16/2006CS267 Lecture 10 CS 267: Applications of Parallel Computers Floating Point Arithmetic James Demmel

Computer Science 210 Computer Organization Floating Point Representation.

1.6 Signed Binary Numbers.

Simple Data Type Representation and conversion of numbers

CS105 INTRODUCTION TO COMPUTER CONCEPTS BINARY VALUES & NUMBER SYSTEMS Instructor: Cuong (Charlie) Pham.

ECE 8053 Introduction to Computer Arithmetic (Website: Course & Text Content: Part 1: Number Representation.

1 COMS 161 Introduction to Computing Title: Numeric Processing Date: October 22, 2004 Lecture Number: 24.

CISE301_Topic11 CISE-301: Numerical Methods Topic 1: Introduction to Numerical Methods and Taylor Series Lectures 1-4:

Introduction to Numerical Analysis I

Computer Architecture

Introduction. 2COMPSCI Computer Science Fundamentals.

Computer Architecture and Operating Systems CS 3230 :Assembly Section Lecture 10 Department of Computer Science and Software Engineering University of.

Floating Point. Agenda  History  Basic Terms  General representation of floating point  Constructing a simple floating point representation  Floating.

Computer Science Engineering B.E.(4 th sem) c omputer system organization Topic-Floating and decimal arithmetic S ubmitted to– Prof. Shweta Agrawal Submitted.

Floating Point Numbers Expressions Scanner Input Algorithms to Programs Shirley Moore CS 1401 Spring 2013 February 12, 2013.

ECE 8053 Introduction to Computer Arithmetic (Website: Course & Text Content: Part 1: Number Representation.

Floating Point Arithmetic

COMP201 Computer Systems Floating Point Numbers. Floating Point Numbers  Representations considered so far have a limited range dependent on the number.

Lecture 41 Arithmetic Clauses The ROUNDED clause –Place ROUNDED after the variable that holds the result ADD A TO B ROUNDED. ADD A TO B GIVING C ROUNDED.

Lecture notes Reading: Section 3.4, 3.5, 3.6 Multiplication

Computer Organization and Design Information Encoding II Montek Singh Wed, Aug 29, 2012 Lecture 3.

CSCI-365 Computer Organization Lecture Note: Some slides and/or pictures in the following are adapted from: Computer Organization and Design, Patterson.

CS 61C L3.2.1 Floating Point 1 (1) K. Meinz, Summer 2004 © UCB CS61C : Machine Structures Lecture Floating Point Kurt Meinz inst.eecs.berkeley.edu/~cs61c.

Computer Engineering FloatingPoint page 1 Floating Point Number system corresponding to the decimal notation 1,837 * 10 significand exponent A great number.

CEC 220 Digital Circuit Design Binary Codes

Data Types 2 Arithmetic funtions ans laws.

2016 N5 Prelim Revision. HTML Absolute/Relative addressing in HTML.

Negative binary numbers 1 Computer Architectures M.

o History of Floating Point o Defining Floating Point Arithmetic o Floating Point Representation o Floating Point Format o Floating Point Precisions o.

COSC2410: LAB 2 BINARY ARITHMETIC SIGNED NUMBERS FLOATING POINT REPRESENTATION BOOLEAN ALGEBRA 1.

Introduction to Numerical Analysis I

Dr. Clincy Professor of CS

Introduction To Computer Science

Computer Architecture & Operations I

Number Systems and Binary Arithmetic

Floating Point Number system corresponding to the decimal notation

CS 232: Computer Architecture II

Lecture 17 Floating point

IEEE floating point format

Morgan Kaufmann Publishers

April 2006 Saeid Nooshabadi

A Level Computing Component 2

Chapter 6 Floating Point

Data Structures Mohammed Thajeel To the second year students

ECE/CS 552: Floating Point

Common Subexpression Elimination

BCD = Binary Coded Decimal

Systems Architecture I

Floating Point Representation

CS 61C: Great Ideas in Computer Architecture Floating Point Arithmetic

CS 101 – Sept. 4 Number representation Integer Unsigned √ Signed √

How Computers Work Part 1 6 February 2008.

Systems Architecture I

CS 105 “Tour of the Black Holes of Computing!”

COMS 161 Introduction to Computing

COMS 161 Introduction to Computing

Classwork: Explicit & Recursive Definitions of

Presentation transcript:

CS267 L13 Floating Point.1 Demmel Sp 1999 CS 267 Applications of Parallel Computers Lecture 13: Floating Point Arithmetic James Demmel

CS267 L13 Floating Point.2 Demmel Sp 1999 Outline °History °IEEE Floating point formats °Error analysis °Ex: Polynomial evaluation °Extra precision °Cray arithmetic - a pathological example °Exception Handling °Using Exception Handling to go faster °Heterogeneous computing

CS267 L13 Floating Point.3 Demmel Sp 1999 History °In the beginning was darkness… °ACM Turing Award 1989 to W. Kahan for design of the IEEE Floating Point Standard

CS267 L13 Floating Point.4 Demmel Sp 1999 IEEE Floating Point Formats °Scientific notation in decimal or binary °List of formats, sizes ranges °Definitions (macheps) °What is an exception?

CS267 L13 Floating Point.5 Demmel Sp 1999 Error Analysis °Basic error formula °Example: adding n numbers °Def of Numerical stability Ex: log(1-x)/x? (too complicated)

CS267 L13 Floating Point.6 Demmel Sp 1999 Example: polynomial evaluation °Picture from ma221 text, error bounds

CS267 L13 Floating Point.7 Demmel Sp 1999 Simulating extra precision °Priest/Shewchuk

CS267 L13 Floating Point.8 Demmel Sp 1999 Cray Arithmetic °History °Impact: D&C code? °Impact: x/sqrt(x^2+y^2)

CS267 L13 Floating Point.9 Demmel Sp 1999 Exception Handling °List 5 cases, responses

CS267 L13 Floating Point.10 Demmel Sp 1999 Using Exception Handling to Design Faster Algorithms °Sturm Sequence loops °comparison of triangular solve

CS267 L13 Floating Point.11 Demmel Sp 1999 Hazards of Heterogeneous Computing °Subnormals °Multiply-accumulate °Cray/IEEE °Compiler differences °Repeatability/debugging/nonassociativity