This just in from the "Risks in Computing" (RISKS-24.51) Usenet group:
Date: Sun, 10 Dec 2006 15:27:13 -0500 From: Martin Ewing <[EMAIL PROTECTED]> Subject: Trig error checking (Re: McIlroy, RISKS-24.49) Doug McIlroy's report of the effect of missing punched cards on trig accuracy (RISKS-29.49) brought to mind another troubling trig episode. In the early 1990's, we were heavy into scientific calculations on the Digital VAX-11/780 -- ephemerides which required every last drop of precision. Sometimes the answers weren't checking out. Eventually we found that our VAX floating point unit (a very large circuit board) was malfunctioning. It gave slightly wrong results, but quietly - there were no system error reports. The diagnostic was that sin**2 + cos**2 was intermittently not quite equal to 1 for various arguments. [NOTE: This is a positive example of circular reasoning! PGN] Field service got us new boards, but how could we have confidence this bug was not recurring? In the end we ran a background routine that checked sin**2 + cos**2 forever. (Today, we would make it a screensaver program.) There is a RISKS issue -- how do you know your CPU is giving good results? There aren't any check bits for trig functions. (Alluded to in RISKS-16.68.) -- Devon McCormick ^me^ at acm. org is my preferred e-mail ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
