[SystemSafety] Critical systems Linux

[Olwen Morgan]

On 22/11/2018 15:33, Peter Bernard Ladkin wrote:
> <snip>

> ... accurate microprocessor arithmetic is a complex thing in itself for which Kahan won the Turing Award and Jerry Coonen got his PhD.

Indeed. Floating-point arithmetic errors weren't hard to find in the 
days before microprocessors acquired hardware floating-point units. NAG 
published some terrific howlers that their tests had come across. Then, 
of course, there was the famous Pentium long division bug (PENTIUM = 
_P_roduces _E_rroneous _N_umbers _T_hrough _I_ncorrect _U_nderstanding 
of _M_athematics).

AFAI recall, Kahan relied quite heavily on work by Cody and Waite to 
find errors in implementations of the elementary functions:

Cody, W. J. Jr. and Waite, W, "Software Manual for the Elementary 
Functions", Prentice Hall, 1980

It's a cracker of a book and gives what, AFAI am aware, is the original 
FORTRAN implementation of the machar function to be found translated 
into C in Kahan's paranoia. Brian Wichmann and his colleagues also used 
it for tests of numerical accuracy in the 1981 Pascal Compiler 
Validation Suite.


Ah ... happy days ... :-)


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