ills
illsM Computing, Volume 5, number 4, October 1995, pages 14-15
During my first year in college, I asked my computer science professor what are the qualities to look for in a "good" computer program. To my surprise, his answer was that a good program:
I was flabbergasted. A "reasonable approximation" instead of a "correct answer"? Could that really be true?
Since then, I have learned that some questions have a precise answer (like "42"), and that other answers can be approximated arbitrarily precisely, depending on the time we want to spend finding that result. Indeed my professor was all too proud when he could announce that he had used the university's supercomputer to calculate "a couple of" digits of π, and that he was the first to actually implement the latest discovered optimization, and could actually calculate a million decimals "over the weekend".
Since then, I have attended many meetings of mathematicians and physicists, where they discussed the pros and cons of mathematical methods and algorithms, and I think that the annual meeting of the users of supercomputers worldwide is still filled with papers that tell us that "last year, this subroutine still took 5 hours, but I thought a bit longer and deeper, and now it works in 20 minutes".
That may sound pejorative, but I don't mean it that way. What I do mean, is that no matter how much effort went into an optimization, there is always a way of doing it even better.
"To be written in a reasonable amount of time". Is that really it? Don't we want to keep trying until we have the perfect version?
Of course we don't. We don't want any wrong results either, but there are many cases where we will have to live with "as close as we can get in the time we have".
Many is the time I have spent a couple of hours to figure out how to fine-tune the lay-out of a report, so that I could fit just that much more on one page, that the total report would be 20 pages shorter, and I would have a better synopsis of the information presented. For a report that has to be prepared every month, it makes sense to put in that kind of effort. For a quick survey that is going to be run once and once only, such fine-tuning is generally a waste of time.
And... with today's tools and ODBC connectivity: should I really still spend much time on the formatting of tables in reports, or should I aim at producing an SQL mapping (or failing such a tool on the system at hand, a simple tab or comma separated list), that can be fed directly into a popular spreadsheet program?
"... and uses a reasonable amount of resources..." Well, what is reasonable?
Some may feel that any effort spent on calculating any more digits of esoteric numbers like π or e is a waste of time to begin with, for others finding algorithms that make it possible to fill a multi-terabyte database with more digits and then prove that there still is no repeating pattern is their life's fulfillment.
As far as the number π is concerned, most people seem to remember the first 10 or so digits well after their college years, and just type the first five or six digits if ever they need the number in a practical application. Mathematical purists often insist on writing 4 times the arctangent of 1, and I have seen colleagues who "included" a header file at the start of their programs that defined a constant to the level of their favorite precision.
I have yet to see software that actually calculated a value for π when it was needed in a computation. Everyone seems to have found their favorite way of obtaining this value in a manner that imposes a minimum strain on the computer that has to do the work eventually.
Now... isn't figuring out 4.0*arctan(1.0) more work than evaluating the constant 3.14159265358979? Sure it is, but software isn't just written and executed, it is also maintained and audited and validated. If I were to do a code review, I'd recognize the formula immediately as correct (and the number of typos that can be made in that formula is pretty limited), whereas seeing that the constant number doesn't contain any typos actually takes me about 5 to 10 times as long as it took me to type it in the first place. Somehow, the human eye wants to be really really sure that something is correct when one is reviewing code.
The message: well, sometimes the time that the computer needs is not the only thing that counts. Just keep in mind:
WRITE !,LINE
uses a whole lot less computer resources than
DO box^%window(LINE)
(assuming that the latter utility pops up a window), but most people seem to have a really strong preference for the more expensive variant.
During my college years, I got to do a lot of work on machines that were called super-computers in their time. The one I had access to in the early seventies was a wonder of speed that performed a floating point division in 5 nanoseconds.
Today I'm working on a Pentium that dwarfs this supercomputer of way-back-when. So... why do I keep finding myself dissatisfied with the performance of my Pentium, while we used to share a "lesser" machine between over a 100 people at a time, and were raving about its "speed"?
The answer, of course, lies in all the other demands that we put on the machines of today. On the machines of the '60s and '70s, there were no windows, text was not immediately adjusted while we typed it, if shown at all, letters were not proportionally spaced (in fact, we only had a couple of terminals that knew about the existence of lower case letters), and I could go on: today, we have much more powerful machines, and we're using all that power for... well, mostly not the activities that are programmed inside our own software. At some PCs, my typing is carefully overseen by a curious paperclip in the lower right corner, at some other PCs, my typing happens simultaneously in a formatted window, and in a window that shows the internal codes for my text-processor (indeed, I do use both major word processors).
Now, isn't that little animated paperclip an absolute waste of CPU cycles? So far I tend to think so, but already twice over the past month, it has been able to answer a question I had to put to it...
I still hate it, but don't be surprised if I change my mind about it soon!
In short, today we have considerably more computer resources available than we had 20 years ago. Certain usage that used to be luxury or used to be severely frowned upon has now become common place and fashionable, and the use of computer resources for
has become a "reasonable" use of our resources.
Ed de Moel is past chairman of the MDC
and works with Jacquard Systems Research.
His experience includes developing software for research in medicine
and physics.
Over the past ten years, Ed's has mostly focused on the production
of tools for data management and analysis, and tools for the support
of day-to-day operation of medical systems.
Ed can be
reached by e-mail.