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E-raamat: Math Toolkit for Real-Time Programming

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  • Formaat: 466 pages
  • Ilmumisaeg: 09-Jan-2000
  • Kirjastus: CMP Books
  • Keel: eng
  • ISBN-13: 9781482296747
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Math Toolkit for Real-Time ProgrammingSuurem pilt
  • Formaat: 466 pages
  • Ilmumisaeg: 09-Jan-2000
  • Kirjastus: CMP Books
  • Keel: eng
  • ISBN-13: 9781482296747
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A book/CD-ROM package for those who write software for real-time, embedded systems. Explains how to program all the mathematical processes needed in digital signal processing, real-time computing, and embedded computing systems. Coverage includes fundamental functions, basics of calculus, implementing and using the Runge-Kutta method, and dynamic simulations. Explains how and why methods work, and also discusses alternative approaches. The CD-ROM contains code samples. The author is a design engineer, and a contributing editor for a programing magazine. Annotation c. Book News, Inc., Portland, OR (booknews.com)
Preface xi
Who This Book Is For xi
Computers are for Computing xi
About This Book xiv
About Programming Style xv
On Readability xviii
About the Programs xviii
About the Author xix
Section I Foundations 1(40)
Getting the Constants Right
3(14)
Related Constants
6(1)
Time Marches On
7(2)
Does Anyone Do It Right?
9(3)
A C++ Solution
12(2)
Header File or Executable?
14(2)
Gilding the Lily
16(1)
A Few Easy Pieces
17(8)
About Function Calls
17(3)
What's in a Name?
20(2)
What's Your Sign?
22(1)
The Modulo Function
23(2)
Dealing with Errors
25(16)
Appropriate Responses
27(1)
Belt and Suspenders
28(3)
C++ Features and Frailties
28(3)
Is It Safe?
31(2)
Taking Exception
33(2)
The Functions that Time Forgot
35(2)
Doing it in Four Quadrants
37(4)
Section II Fundamental Functions 41(194)
Square Root
43(46)
The Convergence Criterion
48(1)
The Initial Guess
49(8)
Improving the Guess
57(1)
The Best Guess
58(4)
Putting it Together
62(1)
Integer Square Roots
63(5)
The Initial Guess
65(1)
Approximating the Coefficients
66(2)
Tweaking the Floating-Point Algorithm
68(1)
Good-Bye to Newton
68(4)
Successive Approximation
69(1)
Eliminating the Multiplication
70(2)
The Friden Algorithm
72(6)
Getting Shifty
74(4)
The High School Algorithm
78(5)
Doing It in Binary
83(3)
Implementing It
84(1)
Better Yet
85(1)
Why Any Other Method?
86(1)
Conclusions
87(2)
Getting the Sines Right
89(38)
The Functions Defined
89(2)
The Series Definitions
91(3)
Why Radians?
93(1)
Cutting Things Short
94(10)
Term Limits
95(2)
Little Jack's Horner
97(7)
Home on the Range
104(8)
A Better Approach
106(1)
Tightening Up
107(5)
The Integer Versions
112(7)
BAM!
113(6)
Chebyshev It!
119(1)
What About Table Lookups?
120(7)
Arctangents: An Angle-Space Odyssey
127(54)
Going Off on an Arctangent
128(14)
Necessity is the Mother of Invention
134(2)
Rigor Mortis
136(3)
How Well Does It Work?
139(1)
Is There a Rule?
140(2)
From Continued Fraction to Rational Fraction
142(19)
Back Home on the Reduced Range
144(3)
The Incredible Shrinking Range
147(2)
Choosing the Range
149(1)
Equal Inputs
150(1)
Folding Paper
151(1)
Balanced Range
152(2)
An Alternative Approach
154(4)
More on Equal Inputs
158(3)
Problems at the Origin
161(5)
Getting Crude
163(3)
Don't Chebyshev It---Minimax It!
166(10)
Smaller and Smaller
173(3)
Combinations and Permutations
176(1)
A Look Backward
177(4)
Logging In the Answers
181(54)
Last of the Big-Time Functions
181(1)
The Dark Ages
182(1)
A Minireview of Logarithms
182(10)
Take a Number
186(3)
Where's the Point?
189(1)
Other Bases and the Exponential Function
190(2)
Can You Log It?
192(12)
Back to Continued Fractions
195(1)
Rational Polynomials
196(1)
What's Your Range?
197(2)
Familiar Ground
199(3)
Minimax
202(2)
Putting It Together
204(4)
On to the Exponential
208(7)
Range Limits Again
210(5)
Minimaxed Version
215(1)
The Bitlog Function
215(17)
The Assignment
215(1)
The Approach
216(1)
The Function
217(2)
The Light Dawns
219(7)
The Code
226(1)
Why Does It Work?
227(4)
What Did He Know and When Did He Know It?
231(1)
The Integer Exponential
232(2)
Wrap-Up
234(1)
Postscript
234(1)
References
234(1)
Section III Numerical Calculus 235(210)
I Don't Do Calculus
237(26)
Clearing the Fog
239(1)
Galileo Did It
239(8)
Seeing the Calculus of It
242(1)
Generalizing the Results
243(2)
A Leap of Faith
245(2)
Down the Slope
247(2)
Symbolism
249(6)
Big-Time Operators
253(1)
Some Rules
253(2)
Getting Integrated
255(8)
More Rules
258(2)
Some Gotchas
260(3)
Calculus by the Numbers
263(28)
First Approximations
266(5)
Improving the Approximation
269(2)
A Point of Order
271(8)
Higher and Higher
273(3)
Differentiation
276(3)
More Points of Order
279(1)
Tabular Points
279(2)
Inter and Extra
280(1)
The Taylor Series
281(1)
Deltas and Dels
282(4)
Big-Time Operators
284(2)
The z-Transform
286(5)
The Secret Formula
287(4)
Putting Numerical Calculus to Work
291(42)
What's It All About?
291(2)
Differentiation
293(4)
The Example
294(3)
Backward Differences
297(1)
Seeking Balance
298(4)
Getting Some z's
302(3)
Numerical Integration
305(12)
Quadrature
305(8)
Trajectories
313(1)
Defining the Goal
314(3)
Predictors and Correctors
317(2)
Error Control
319(2)
Problems in Paradise
321(2)
Interpolation
323(2)
Paradise Regained
325(3)
A Parting Gift
328(3)
References
331(2)
The Runge-Kutta Method
333(22)
Golf and Cannon Balls
333(1)
Multistep Methods
334(1)
Single-Step Methods
335(1)
What's the Catch?
336(1)
Basis of the Method
337(2)
First Order
339(1)
Second Order
340(3)
A Graphical Interpretation
343(3)
Implementing the Algorithm
346(1)
A Higher Power
346(2)
Fourth Order
348(1)
Error Control
349(1)
Comparing Orders
350(1)
Merson's Method
351(3)
Higher and Higher
354(1)
Dynamic Simulation
355(90)
The Concept
355(3)
Reducing Theory to Practice
358(10)
The Basics
359(3)
How'd I Do?
362(1)
What's Wrong with this Picture?
363(1)
Home Improvements
364(1)
A Step Function
365(1)
Cleaning Up
366(2)
Generalizing
368(3)
The Birth of QUAD1
369(1)
The Simulation Compiler
370(1)
Real-Time Sims
371(1)
Control Systems
372(1)
Back to Work
372(7)
Printing the Rates
374(2)
Higher Orders
376(3)
Affairs of State
379(5)
Some Examples
381(3)
Vector Integration
384(1)
The Test Case
384(1)
The Software
385(15)
What's Wrong?
390(1)
Crunching Bytes
391(1)
A Few Frills
392(2)
Printing Prettier
394(1)
Print Frequency
395(2)
Summarizing
397(3)
A Matter of Dimensions
400(4)
Back to State Vectors
404(2)
On the Importance of Being Objective
406(9)
Step Size Control
415(12)
One Good Step
418(9)
What About Discontinuities?
427(4)
Multiple Boundaries
430(1)
Integrating in Real Time
431(4)
Why R-K Won't Work
431(1)
The First-Order Case
432(2)
Is First-Order Good Enough?
434(1)
Higher Orders
434(1)
The Adams Family
435(8)
Doing It
436(2)
The Coefficients
438(2)
Doing it by Differences
440(2)
No Forward References?
442(1)
Wrapping Up
443(2)
Appendix A A C++ Tools Library 445(12)
Index 457(17)
What's on the CD-ROM? 474


Jack Crenshaw holds a Ph.D. in physics from Auburn University (specialties in math, electronics, and advanced dynamics). He wrote his first computer program in 1956 and his first microcomputer software a real-time, floating-point, Kalman filter-driven controller in 1976. He has been working with real-time software for embedded systems ever since, and thinks he might be beginning to get the hang of it. He is currently a senior principal design engineer for Alliant TechSystems, Inc., a contributing editor for Embedded Systems Programming magazine, and author of the popular 'Programmer's Toolbox' column. In his spare time, he likes to dabble in compiler theory, guidance and control theory, and help rehabilitate orphaned and injured wildlife.
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