Examples and First Homework in APM 505 Fall 2012
Contents
Class exercise on oating point arithmetic
Single precision
Exercises
Make sure the data are cleared, clear the screen and close gures
clc
c
IEEE 754 FLOATING POINT
REPRESENTATION
Alark Joshi
Slides courtesy of Computer Organization and Design, 4th edition
FLOATING POINT
Representation for non-integral numbers
Like scientific notation
2.34
Understanding the IEEE 754 oating point number
system
S. K. Ghoshal
Supercomputer Education and Research Centre
Indian Institute of Science,
Bangalore 560 012 India.
March 27, 1997
Chapter 1
IEEE 754
26
CHAPTER 1. SCIENTIFIC COMPUTING
amples. The IEEE oating-point standard can be found in [131]. A useful tutorial on
oating-point arithmetic and the IEEE standard is [97]. Although it is no substitut
Exponential Notation
The following are equivalent
representations of 1,234
FLOATING POINT
NUMBERS
123,400.0
12,340.0
x 10-1
1,234.0
x 100
123.4
Englander Ch. 5
x 10-2
x 101
12.34
1.234
x 102
x 103
Th
Floating point
Floating point
In computing, floating point describes a system for representing real numbers which supports a wide range of
values. Numbers are in general represented approximately to a
Floating-point arithmetic
Floating-point computations are vital to many applications. However, its
pretty hard to implement a floating-point system.
Today well look at the IEEE 754 floating-point arit
Appunti sulla rappresentazione dellinformazione
Roberto Beraldi
DISPENSA PER IL CORSO DI
FONDAMENTI DI INFORMATICA
CORSI DI LAUREA IN INGEGNERIA
CHIMICA, DEI MATERIALI,NUCLEARE (vecchi ordinamenti)
An
Floating-Point Numbers
Floating-point number system characterized by
four integers:
p
[L, U ]
base or radix
precision
exponent range
Number x represented as
dp1
d
d
x = d0 + 1 + 2 + + p1 E ,
2
where
0
18
CHAPTER
BUNDLES
2.
Example 2.1 (The tangent bundle). If M is a smooth n-dimensional
manifold, its tangent bundle
TM=
Tx M
x M
Chapter 2
Bundles
Contents
2.1 Vector bundles
.
17
2.2 Smoothness
.
26
164
APPENDIX
ALGEBRA
A.
MULTILINEAR
A.1 Vector spaces and linear maps
We assume the reader is somewhat familiar with linear algebra, so at least
most of this section should be reviewits main purpose i
96
4.1
Direct sums, tensor products and bun-dles
of linear maps
Suppose E : E ! M and F : F ! M are two vector bundles of rank m and `
respectively, and assume they are either both real (F = R) or bot
70
CHAPTER 3. CONNECTIONS
bundle interesting. We prefer to think of sections as \vector valued"
maps on M , which can be added and multiplied by scalars, and we'd
like to think of the directional deri
196
APPENDIX B. LIE GROUPS AND LIE ALGEBRAS
this notion is already familiar to the reader. From a geometric
perspective, it becomes more interesting if we assume that G is also a
topological space or
116
CHAPTER 5. CURVATURE ON BUNDLES
Chapter 5
v
0
p0
Curvature on Bundles
Contents
2
Figure 5.1: Parallel transport along a closed path on S .
Flat sections and connections . . . . . . . . . . 115
Int
c 2008 by Chris Wendl
Paper or electronic copies for noncommercial use may be made freely
without explicit permission from the author. All other rights reserved.
Lecture Notes on Bundles and Connectio