Anatomy of the Pentium Bug

The Pentium computer chip’s division algorithm relies on a table from which five entries were inadvertently omitted, with the result that 1738 single precision dividenddivisor pairs yield relative errors whose most significant bit is uniformly distributed from the 14th to the 23rd (least significant) bit. This corresponds to a rate of one error every 40 billion random single precision divisions. The same general pattern appears at double precision, with an error rate of one in every 9 billion divisions or 75 minutes of division time. These rates assume randomly distributed data. The distribution of the faulty pairs themselves however is far from random, with the effect that if the data is so nonrandom as to be just the constant 1, then random calculations started from that constant produce a division error once every few minutes, and these errors will sometimes propagate many more steps. A much higher rate yet is obtained when dividing small (< 100) integers “bruised” by ...

• Type: Conference
• Year: 1995
• Where: TAPSOFT
• Authors: Vaughan R. Pratt
• Keywords: Relative Errors, Single Precision, Single Precision Divisions, Software Engineering, TAPSOFT 1995