5 ms·
"The error was estimated to occur once in every 9 billion divisions. (I doubt any large program has ever been written that is as bug-free as the buggy Pentium c
by gvb 16y ago
"The error was estimated to occur once in every 9 billion divisions. (I doubt any large program has ever been written that is as bug-free as the buggy Pentium chips.)"
That is assuming uniform distribution of divisions. That assumption is obviously false since we can cause the FDIV bug[1] to occur every time we calculate 4195835 / 3145727.
(The parenthetical editorializing is hyperbole as well. "Large" is poorly defined. If one calculates the number of bugs exercised per instruction executed, the probability of a bug occurring is going to be extremely small. In addition, there are "large" programs with very few bugs[2], none of which have occurred in real life[3]. Yet.)
[1] http://en.wikipedia.org/wiki/Pentium_FDIV_bug http://en.wikipedia.org/wiki/Pentium_FDIV_bug
[2] http://en.wikipedia.org/wiki/Space_Shuttle#Flight_systems http://en.wikipedia.org/wiki/Space_Shuttle#Flight_systems
[3] http://www.cs.berkeley.edu/~bonachea/294-8/hw1.html http://www.cs.berkeley.edu/~bonachea/294-8/hw1.html
- wglb 16y agoThat is assuming uniform distribution of divisions Absolutely correct. In fact, there were very simple cases, such as numbers like 5 / 15 that were very close to the failure. Vendors of equipment made statements about low probability of error as well that were not substantiated. In fact, my thinking was that the probability was not estimable. What is likely is that many programs run with errors (some reproducible on various hardware) that are simply not noticed.