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Math Toolkit for Real-Time Programming
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.
KudosMath 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. QuibblesThe 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.
CrimesAs 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.
ConclusionsI 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
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.
Someone marked this question redundant? Guess that shows you jerks are everywhere.
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" that essentially sums up what you asked with a resounding yes.
healyourchurchwebsite.com - WWJB?
When I went for my Comp Sci bachelor's I was amazed at how many math-phobics there were in my Comp Sci classes. As part of earning the degree you had to take 4 specified math classes (Calc 1 & 2, Linear Systems, Probability). You only had to take one more math class to get a minor in mathematics, Calculus 3.
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.
The Forth literature contains many examples of high-performance hardware-integer-math-only routines. A core feature of most Forth algos is rescaling to a power of two space at the start of the algo and from it at the end. This allows bit shift operators to do their stuff. It can take non-trivial fiddling to rescale algorithms - hence, it's nice to just look them up.
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.
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.
## W.Finlay McWalter ## http://www.mcwalter.org ##
Yes. Banks, old satallite programs, messaging systems...etc.
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.
{...reality is wrong, Dreams are for real...}
Embedded != Assembly coding.
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.
I am not merely a "consumer" or a "taxpayer". I am a Citizen of the State of Texas