Survey of Error Analysis, p. 1227

[David Hough]

> Apropos some of this conversation, perhaps some of you can enlighten me
> concerning the current validity of an old article -- W. Kahan, A
> Survey of Error Analysis, in Information Processing 71, North-Holland
> Publishing Company(1972) on page 1214.  If it is not completely
> obsolete or wrong then the section starting at the bottom of page 1227
> might be of interest.  

The anecdote in question is an account of the travails of an engineering
student whose aeronautics application  
runs into difficulty in x**y due to log(1+x) being computed
incorrectly.  Part of the problem is a poor log routine that fails to
understand the importance of accurate results for log arguments near 1;
another part is due to poor (Cray-style) subtraction that for representable
x and y, fails to produce an x-y that is close to the correct value,
and so is the same as a poor log routine.  You can find a better pow
function in 4.3 BSD, based on expm1 and log1p; there is stuff better
than that in Sun's Fortran 1.3 and C 1.0, but that may not be 
forthcoming publicly any time soon.

The IFIP paper anecdote is not particularly relevant to base conversion,
but people still write dumb log and pow functions and still build
Cray-style floating-point subtraction hardware without guard digits.