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Guys & Gals,

I'm trying to locate a book, but no amount of Google-Fu and other searching brings back a result that fits my recollection. Here is what I *think* I remember about it (it's my age), so if it jogs your memory as to a possible title, please give me a pointer and I'll be ever so grateful.

I think I saw it mentioned in the MoHPC forums somewhere, probably within the last year.
I think it was in a discussion about the WP 34S; or if not then probably about the internal routines employed by electronic calculators.
It was a book with the collected wisdom of assembly language and/or binary arithmetic tricks.
It had these sort of recipes: "To multiply two 8-bit numbers that are both even: shift one left 3 times and then AND with the XOR of the other." (that's a made up example, I hope it doesn't really work that way!).
I remember it being quite a hefty tome, and getting complicated and esoteric quite quickly.

Many thanks.

Chris Randle
Perhaps what Paul Dale wrote in this thread?

Quote:I've posted this list before but here are some good texts on numeric mathematics:

- The Algebraic Eigenvalue Problem by J. H. Wilkinson -- very in-depth and a great introduction to error analysis from when it was being invented.
- Elementary Functions by Jean-Michel Muller -- a good reference on how to implement functions in many different ways. This one covers many/all of the standard algorithms -- CORDIC, series expansions, partial fractions, polynomial approximations.
- Accuracy and Stability of Numerical Algorithms by Nicholas J. Higgam -- another great book on error anlysis.
- Matrix Computations by Gene H. Golub and Charles F. Van Loan -- pretty much what it says but one of the canonical texts in numerical analysis.
- Handbook of Mathematical Functions by Abramowitz & Stegun -- A&S is the bible for mathematical and physical functions.
- NIST Handbook of Mathematical Functions -- an updated version of A&S although the overlap is deliberately kept low.
- An Atlas of Functions by Oldham, Myland & Spanier -- lots of functions and their properties. Not really essential if you have A&S but easier reading.
- Numerical Recipes by Press, Teukolsky, Vetterling and Flannery -- doesn't get good comments from numerical analysis circles but it is easy to read and contains code that can be used with sufficient care and attention to detail.

Be prepared to pay anything from $500 - $1k for these in hard copy.

And before you start these read and digest all of William Kahan's writings.

To which I might add Vol 2 of Knuth's "The Art of Computer Programming" ("Seminumerical Algorithms")

The (short) thread also lists some online publications / notes that you might find interesting.
Hi Chris,

perhaps you had "How Computers do Math" by Clive Maxfield and Alvin Brown in mind. It's a wonderful book and I had a lot of fun reading it.

Best regards

There are always sites like these. Not so much about getting numerically accurate results but about doing things in a weird and wonderful way.

- Pauli
Thank you everyone who has replied.

I've been through all the lists and threads mentioned. There are some corkers there, but none is the one I am trying to remember/find. "The Definitive Guide to How Computers Do Math" was surprisingly good; a definite cut above the usual books on the subject - I've ordered a copy of that for my kids (but mostly for me!). It's very much in the vein of Maxfield's other "Beebop Boogie to the Boolean Algebra" and Petzold's "Code". Thanks Karl.

But the closest so far is Paul Dale's suggesting of Bit Twiddling. That's exactly the sort of thing it contained. It was a fully-fledged book though, and I'm sure it was a paid-for item, because I decided not to buy it at the time. I remember it being more of a reference work than a teaching endeavour, something along the lines of the NIST Handbook of Mathematical Functions, but focusing more on binary arithmetic. Also, I seem to remember the author's foreword mentioning that he'd compiled the algorithms over the course of his programming career, and was surprised that nobody had ever committed that sort of thing to print, so he did. If that helps jog any memories.

Thanks again for the trouble taken so far. It's certainly revealed some great books & resources I hadn't seen before.


Sorry to be a late comer. Might I suggest ...
Hacker's Delight by Henry S. Warren Jr.
...In Hacker's Delight, veteran programmer Hank Warren shares the collected wisdom -- namely tips and tricks -- from his considerable experience in the world of application development. The resulting work is an irresistible collection that will help even the most seasoned programmers better their craft ... A collection useful programming advice the author has collected over the years; small algorithms that make the programmer's task easier...
Hacker's Delight
for under $20.00 at Amazon
From the Back Cover
"This is the first book that promises to tell the deep, dark secrets of computer arithmetic, and it delivers in spades. It contains every trick I knew plus many, many more. A godsend for library developers, compiler writers, and lovers of elegant hacks, it deserves a spot on your shelf right next to Knuth."
Bingo. That's the one. Thank you, it was driving me mad trying to find it.

It has been mentioned (if Google can be believed) three times before on hpmuseum.org: in 2007, 08 and 09. The earliest thread also has a few more
interesting books listed, should anyone else be interested.


Well, SlideRule, you already have my thanks, and I shall presume to add my employer's as I can now return to those tasks that they pay me to do.
(10-22-2015 12:09 PM)SlideRule Wrote: [ -> ]Might I suggest ...
Hacker's Delight by Henry S. Warren Jr.
Yes, this book is a gem. Those who appreciate clever little solutions on bit and byte level will for sure find inspiration reading it.


(10-22-2015 12:09 PM)SlideRule Wrote: [ -> ]Might I suggest ...
Hacker's Delight by Henry S. Warren Jr.
I'll third that recommendation. An excellent book! I lost my copy in an office fire last year, although that gives me a good excuse to buy the second edition.
The book has reached my desk, too. Not cheap but worth it.

BTW, if you are looking for an easy read on your pillow, forget it! :-D
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