
Twin prime conjecture and the Pentium division bug  - wglb
http://www.johndcook.com/blog/2011/02/07/twin-prime-conjecture-pentium-bug/
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gvb
"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>

[2] <http://en.wikipedia.org/wiki/Space_Shuttle#Flight_systems>

[3] <http://www.cs.berkeley.edu/~bonachea/294-8/hw1.html>

~~~
wglb
_That 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.

