Math Toolkit for Real-Time Programming 153
| Math Toolkit for Real-Time Programming | |
| author | Jack W. Crenshaw |
| pages | 466 |
| publisher | CMP Books |
| rating | 8 |
| reviewer | oxgoad |
| ISBN | 1929629095 |
| summary | A casual discussion of algorithms ranging from abs to numerical calculus. |
Who & What
Jack W. Crenshaw, Ph.D. (Physics) wrote his first computer program in 1956 for an IBM 650. He has been working with real-time software for embedded systems ever since -- contributing several years to NASA during the Mercury, Gemini, and Apollo programs. In addition to other activities, he is currently a contributing editor for Embedded Systems Programming magazine and author of the Programmer's Toolbox column.
In Math Toolkit for Real-Time Programming, his effort is focused on describing the pitfalls of vendor-provided math libraries and providing robust replacements. In section one he gives a thorough overview of constants and the various manners in which to declare them, naming conventions, and error handling. As the work progresses, in section two, he builds a library of proven algorithms ranging from square roots to trigonometrical functions to logarithms. Did you suffer through calculus in college with a barely passing grade? Section three will teach you more about numerical calculus in a half-hour than you may have learned in three semesters.
Kudos
Math Toolkit is written in an easy to understand anecdotal manner. You might be tempted to think that the author was animatedly relating the history of computing square roots while having lunch with you. This method works very well and keeps what could be a rather heavy subject from becoming too much of a burden. Most chapters have historical tidbits liberally sprinkled throughout.
Even if college algebra left you with post-traumatic stress disorder, you will not have any trouble with section two. Indeed, you may find yourself intently following the author on the trail of the perfect arctangent algorithm -- much as a sleuth on the trail of a villain.
The depth of knowledge shown, and its presentation, is exceptional. The author's years of experience are evident in his self-confident writing style. You will rarely see a clearer overview of numerical calculus.Quibbles
The cover of the book states: "Do big math on small machines." This, combined with the Real-Time Programming phrase in the title, might lead one to believe that the book's primary audience is intended to be the embedded microcontroller crowd. Sadly, not so. There is very little here for the die-hard assembler programmer other than some very handy integer square root and sine routines - and these examples are in C++. Based on the cover, I would have liked to see a greater emphasis on processors lacking a floating point unit. Also, some code examples in pseudo-assembler would have been welcome, as the author chose C++ as the language of choice for all examples.
Crimes
As is so often the case nowadays, there are various typographical errors scattered throughout. This seems to be an epidemic in current technical books. Fortunately, it didn't affect the readability of Math Toolkit.
Conclusions
I believe Math Toolkit for Real-Time Programming would be a great, perhaps mandatory, addition to the bookshelf of anyone that is involved in writing code that has a heavy math component. Other than the somewhat misleading cover, I cannot find anything truly negative to say about this work. Congratulations are in order to Mr. Crenshaw on a job well done.
The book also includes a CD-ROM of all example source code. In reality, to get the best benefit from the book, you should mostly ignore the CD-ROM and work through the examples. To quote the author: "Never trust a person who merely hands you an equation."
Table of Contents
- Getting The Constants Right
- A Few Easy Pieces
- Dealing with Errors
- Fundamental Functions
- Getting the Sines Right
- Arctangents: An Angle-Space Odyssey
- Logging in the Answers
- Numerical Calculus
- Calculus by the Numbers
- Putting Numerical Calculus to Work
- The Runge-Kutta Method
- Dynamic Simulation
- Appendix A: A C++ Tools Library
Disclosure
I received a review copy of this book from the publisher. Thus, my loyalties and opinions may be completely skewed. Caveat Lector.
You can purchase Math Toolkit for Real-Time Programming from bn.com. Slashdot welcomes readers' book reviews -- to see your own review here, read the book review guidelines, then visit the submission page.
Wow, I'm old, I haven't seen Runge-Kutta in years (Score:5, Insightful)
I wonder how much better could we be if coders knew basic math, if they know how those little bitty chips actually computed the sine of something instead of assuming it works. We would probably have rock solid operating systems without all the glitzy GUI stuf..
flimsy review (Score:5, Insightful)
Re:is Real Time programming still a Real Issue? (Score:5, Insightful)
The above generally doesn't apply to anyone doing serious embedded work with small and midrange microcontrollers. Often an operating system is thin to non-existent on these platforms. Some of the lower-range parts may have a 2-byte hardware stack, 28 bytes of RAM and maybe 512 bytes of program memory. Obviously, you won't be doing much sophisticated numerical work on these smallest of microcontrollers, but for more midrange parts, I've found this book to be a godsend.
The book is not aimed at PC users.
Re:Wow, I'm old, I haven't seen Runge-Kutta in yea (Score:3, Insightful)
But to get a job writing computer graphics software, or audio processing, or designing any sort of embedded hardware, knowledge of advanced math is required. The people who want to do this kind of work pursue higher educations, and if they enjoy what they're doing then that's great, too.
Re:Wow, I'm old, I haven't seen Runge-Kutta in yea (Score:1, Insightful)
A) Create superb programs
B) Fix them
and
C) Put some thought into the design so that others can use-, understand and change it easily.
not
Just hack something up and yell 'FINISHED!' when it seems to run "Good enough".
Re:An indispensible treasure (Score:1, Insightful)
Re:is Real Time programming still a Real Issue? (Score:4, Insightful)
Re:is Real Time programming still a Real Issue? (Score:2, Insightful)
It means predictable (bounded) latency! It's a
secondary issue if that latency is low or high.
My Linux is reasonably fast, but it's still far from real time: each time I touch my xawtv window, the whole machine freezes for a second...
Re:Wow, I'm old, I haven't seen Runge-Kutta in yea (Score:5, Insightful)
College (esp for computer engineering and CS) fundamentally teaches you:
1. How to solve problems
2. A toolset (ie math, algorithms) to go about solving those problems
True, you may not ever use calculus, but as a computer scientist you will use matrix theory because it is the best way to solve some problems.
This is not only for scientific/research either. If you try to write anything performance related, you'll have to use higher math. Computer science ain't easy.
Let me stress again that college teaches you about your subject matter and how to solve problems for it. You can come up with this stuff by yourself, in my experience only a tiny percent working without a college degree will ever accrue enough to offset what they missed in college.
Re:No, computers don't need math (Score:3, Insightful)
Re:Numerical Recipes (Score:3, Insightful)
Re:No, computers don't need math (Score:3, Insightful)
Re:Wow, I'm old, I haven't seen Runge-Kutta in yea (Score:3, Insightful)
I changed majors from CS to Mathematics halfway through because I realized that programming is easy; you can always learn a new language or a new technique by picking up the appropriate O'Reilly book on the subject. But writing good programs -- programs that are robust, that scale well, that do as much as possible as quickly as possible -- is really applied math. And math is hard.
You simply have no idea how much you don't know, and with the attitude you have, you probably never will.
Math ~= Calculus (Score:5, Insightful)
But by "math" the reference is almost always to calculus.
But math is not just calculus.
Math includes (and this is a MINIMAL list :
- algebra Every program using symbols to represent things that might vary is using algebra. Algebra isnt just manipulating big expressions to find values of x and y - it is really about using names to refer to values. (For example x=y+1 is fundamentally an algebraic expression.
And there's more - check out Glassner's "Digital Image Synthesis", or Knuth's "Art of Computer Programming", - find places where mathematics is not mentioned. Let alone such things as wavelets, the Mandelbrot set, grammars, text (or UI) layout, automata (and on, and on, and on...). I can show you a very hard mathematical problem (which I'm still working on) based on an algorithm you all know, but that is often coded incorrectly.boolean logic Using logical expressions and understanding what they do is just the predicate calculus. Using logic languages (prolog primarily) is, well, logic.
Linear Algebra Try to program more than minimal graphics without linear algebra.
The structure of numbers computing square roots and the like. This kind of computing also typically involves calculus and its relatives
Calculus many parts of computational mathematics, including things like square roots, sin/cos and the like. Also, finding tangents and normals to surfaces which is a big part of reflection models in graphics. The logic involved is also used in the analysis of algorithms.
logical reasoning Every time someone writes a loop or a recursive function, they are essentially using mathematical induction (albeit informally). Propagation of pre/post conditions (not just in procedure calls, but on the statement to statement level is also logical reasoning (and informal proofs).
Fourier analysis Fourier analysis is essential in image manipulation (including compression), graphics in general, Most algorithms involving sound processing also rely on fourier analysis
Graph Theory Where doesn't graph theory show up? Dependency graphs, path algorithms of all sorts. Trees are graphs. Garbage collection involves graph theory. Programs are (on several levels) graphs. The internet as a network is a graph. Websites are graphs (and it can be interesting and revealing to look at them as such).
Number Theory Cryptography!
If you're not doing any of these things, you may be programming, but you're probably not programming well.
Juris Hartmanis said (half jokingly) in his Turing Award lecture that "Computer Science is the engineering of mathematics" I think its about as good a definition as any I have ever heard.