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.
is Real Time programming still a Real Issue? (Score:3, Interesting)
However, with the the maturity of operating systems, many of them now include device drivers, APIs, objects and other goodies that insulate the average programmer from the hassle of issues like latency. So my question is, other than good academic study, would it pay for the rest of us to spend the $$ on such a book?
Though I admit, having to write my share of real-time apps back in the day has me curious enough to put the book on my wishlist.
Re:is Real Time programming still a Real Issue? (Score:4, Interesting)
Hey, I understand completely what you're saying. I for one am glad I don't have to deal with such as latency and pre-emption. In fact, here is a link to a nifty article entitled "Real Time Issues in Linux [helsinki.fi]" that essentially sums up what you asked with a resounding yes.
Re:is Real Time programming still a Real Issue? (Score:3, Interesting)
Re:Wow, I'm old, I haven't seen Runge-Kutta in yea (Score:3, Interesting)
Funny this topic should come up. I just did a 'Store Locator' for the company I work for (I'm the IT Manager, belive it or not). All I have is your basic HS diploma, and in creating the search, I realized I don't know a damn thing about sine and cosine. I don't know how they're used, or how they're applied. I have a feeling that they're somehow related to geometry (which makes sense, seeing I have to get a distance between two points on a curve - the earth), but I'm not sure.
Sure, it's probably taken me longer to write this post, than it took to find the php code I used as a basis for the search, but how much math is REALLY needed overall?
I slept through school, I did really bad, all because I felt it was worthless. I did feel that my business class, business law, and basic Algebra has been useful. But overall, it wasn't worth my time. Hell I had a physics teacher who'd pick on me because I was flunking (it's amazing what good test grades + 0 homework does to you), but I just found physics interesting - jeez, it was only HS. I was testing the waters, not padding my GPA. I believe that's what's HS is FOR.
And if you KNOW what you want to do (I knew I wanted to fix/program computers when I played on my Apple ][ in 6th grade), what the hell is college for?
The ease of the internet sure hasn't helped my perception.
Am I the only one?
Re:Wow, I'm old, I haven't seen Runge-Kutta in yea (Score:4, Interesting)
Now I've always been big on math but I was kind of surprised at how few people were willing to take a single class to earn a full-fledged minor.
Forth Algorithms (Score:4, Interesting)
Unfortunately, it's tricky to find Forth books these days.
That's a shame, because along with Smalltalk, Lisp and APL, I think Forth is one of the "mind expanding" languages all programmers should at least experience, instead of just deciding C/Java/C++/VB is the one true language.
Math in CS programs (Score:2, Interesting)
I don't know of other programs, but I know at the University of Waterloo (where I am a computer science student), we must take quite a lot of math courses, ranging from linear algebra, calc, classical algebra, combinatorics & optimization and statistics. The math content for the CS program is very high, and in the end you get a BMath degree.
Maybe this is different at other schools (well, actually I know it is at most, most don't do nearly as much math), but I would hope not. I think to be a solid programmer a solid math background is a requirement.
oh, and btw, for anyone nitpicking, UW now offers a BCS program, as well as the typical BMath Honours CS. The BCS seems to offer a bit more flexibility, so BCS students may not choose to take 'as much' math.
Neglected subject, good review, integer!=assembly (Score:5, Interesting)
A year (or so) ago I attended a lecture given by Guy Steele (of Lisp/Java/ Crunchly fame) on his proposal to alter how IEEE floating point numbers are mapped to real numbers. It quickly flew over my head, but gave a great insight into the whole field. Steele then had a fair old "discussion" with the one person in the audience whose head hadn't been overflown (sic), as there was plainly still much controversy left in this area. On trying to do some "why didn't I get this stuff at college" reading, I found there wasn't a great deal of literature.
The reviewer's concern that coprocessor-less systems should be covered is valid, but I'm not sure going as far as assembly is necessary. For example, I once had the privilige of reading through Hitachi's libm implementation for their H8 series microprocessor/microcontroller (one would be generous to call H8 a 16-bit system, and ungenerous to call it an 8-bit system). With one small exception (I think the cos table lookup) the whole thing was in (quite readable) C, and (at least for basic libm stuff) performance was perfectly acceptable. For didactic purposes, a C (or sane C++) implementation would be the thing one would want to find in a book - I get very annoyed at embedded books where the examples are written in asm for the author's favourite (obscure) microcontroller.
Re:is Real Time programming still a Real Issue? (Score:4, Interesting)
I work with a group of eight other people updating 40 year old Assembler on an IBM Series 1. Something tells me that if this was included in our training programs, those that are
SUF
FER
ING
through the digit-crunching wouldn't have such a hard time. Most people consider this back-in-the-day, but there's an aaaawwwful lot out there that still reeks of old german engineering, and chunk-button ATMs.
Under covered subject; average review... (Score:4, Interesting)
To be honest, a lot of embedded coding is done with C or C++ these days. I've been following Crenshaw's articles in Embedded Developer magazine for years now. He explains a lot of what they try to teach in college Calc, etc. in simple, practical terms, and reduces it to usable algorithms.
I'd probably buy the book and add it to my shelf.
College Math (Score:3, Interesting)
Link & More (Score:1, Interesting)
Re:Math in CS programs (Score:2, Interesting)
I think this may provide some insight into whether or not it's a GoodThing for CS students to have more math in their degrees. Microsoft hires more programmers from Waterloo than anywhere else. And just look at the QUALITY of their code.
On a somewhat tangential note, I'm in Communications Engineering at Carleton, and we badly need a stochastics course in our program, so Digital Comm doesn't keep flying over our heads. Sometimes more math is good.
No, computers don't need math (Score:3, Interesting)
Scientific or engineering programming, they need the math because they are math programming. The rest, forget it, maybe you add some numbers for a shopping cart, multiply for sales tax, but programming has little use for math.
I learned long ago that when an 8 bitter needs trig functions, you use a look up table generated externally.
Yes, it's an interesting book... (Score:3, Interesting)
As for the title, I agree it's a bit misleading. The book has pretty little to do about real-time (in fact nothing, as far as I could see). What it really should be called is "Computer arithmetic and a little of numerical methods for dummies". This book will help you understand how to write your own libm, and give you some ideas for more advanced tasks, but that's about it.
For me, who didn't know much of this stuff, it was very interesting. It will probably not save you that course in numerical algorithms (which I for one haven't taken), but even then, it will probably contain some interesting tidbits you didn't know.
On the other hand, if you have years of experience in writing computer math routines, it will probably quickly become dull, but that's true about anything you already know.
Re:is Real Time programming still a Real Issue? (Score:3, Interesting)
Decimal libraries (Score:3, Interesting)
The only library I know that supports it is the BC-library sometimes used with PHP. (Well, I guess you could say that COBOL has such also.) It actually uses strings to hold the results so that there is no machine-based limitation on precision size. Plus, that improves its cross-language use since almost everything supports dynamic strings these days.
(Not the fasted approach I suppose, but most biz apps are not math intensive anyhow. Most code is devoted to comparing strings, codes, and ID's and moving things around from place to place. IBM used to include decimal-friendly operations in its CPU's. Those days seem gone for some reason, yet biz apps are still a huge domain.)
Amazon link, too (Score:2, Interesting)
For those who don't support Slashdot's Amazon embargo, here's their link to the book [amazon.com]. Not only are they selling the book for $35, they have 25 sample pages, including the entire index and the first half of the first chapter. (And no, I'm not in Amazon's affiliates program and don't make a dime if you buy the book using the link that I provided, as a quick glance at the URL will prove.)
Re:Wow, I'm old, I haven't seen Runge-Kutta in yea (Score:3, Interesting)
integer square root (Score:2, Interesting)
If you still need a decent integer square root algo, check out this page. [azillionmonkeys.com] I used the mborg_isqrt2 variant on that page as a starting point for writing my highly optimized Intellivision version [spatula-city.org] for SDK-1600. [spatula-city.org] My optimized version takes about 600 - 700 cycles for a 16-bit square root, on a machine where most operations take 6 to 8 cycles. (The version I was replacing took 4000 - 10000 cycles.)
This book looks like it might be interesting to me. Here at work, we had our own math expert, but he's retired (or semi-retired). We've contracted with him to do math libraries, and that works for now. But what about 10 years from now? There's a lot of subtlety in some of these algorithms (it's not always just as easy as whipping through a Taylor series expansion), so it's probably time someone in our group started learning. :-)
--Joe