[Maxima-discuss] bfloat accuracy, %pi

[Richard F. <fa...@be...>]

consider
    v:  18190586279576483
which has the interesting property that it is
only 17 digits long but it is very nearly a multiple
of pi/2
in particular,
5790243448268414.5b0*%pi

is
18190586279576483.000000000000000025...b16

consequently

cos(v),numer   comes out -0.84
cos(v),bfloat comes out 2.55...b-17

so the answers
differ by 16 orders of magnitude.

This is not actually so surprising to me because we are using machine floats
for the first, and software floats for the second.

However, cos(v),bfloat should be more accurate  (good for fpprec decimal 
digits)
but is not so.  Increasing fpprec changes many of the digits that should 
be right.
So the computation of how many digits of pi are needed to normalize
the answer is apparently inadequate.
Thoughts?


RJF