Pratt on Pentium in public at Stanford

[David Hough]

> 		EE380 Computer Systems Colloquium
> 
> 		      Winter Quarter 1994-1995
> 
> 			  Lecture #1
> 
> Date:		Wednesday, Jan 11,1994  
> 
> Time:		4:15-5:30 pm
> 
> Location:	Skilling Auditorium
> 
> Speaker:	Vaughan Pratt
> 		Computer Systems Laboratory
> 		Stanford University
> 
> Title:		 Aspects of the Pentium Division Flaw
> 
> 
> 			Abstract
> 
> 
> 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 dividend-divisor 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,
> translating to 27,000 years of real time at 1000 divisions a day.
> 
> 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 1.0, then
> random *calculations* started from that constant produce a division
> error once every few minutes.  An even higher rate is obtained when
> dividing small (<1000) integers "bruised" by subtracting one millionth,
> where every 2,500 divisions encounter a relative error of size one in
> ten million while a relative error of size one in a hundred thousand
> occurs every 70,000 divisions.
> 
> 			Biography.
> 
> Professor Pratt obtained his Ph.D. from Stanford under Don
> Knuth and served on the MIT faculty from 1972 to 1982 before joining
> Stanford.  He helped found Sun Microsystems in 1982, whose logo he
> designed.  He has worked in artificial intelligence and computer
> graphics, and his current research spans theory of computation and
> computer systems.
> 
> ************************************************************************
> * EE380 is the Computer Systems Laboratory Colloquium.  The Colloquium *
> * meets most Wednesdays throughout the academic year.                  *
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