I had at first thought that this might be a discussion of the US style
definition of round in the standard prelude that always bites me...
... Then that it might be the bug in floor within the standard issue
of GMP.
Instead its a discussion of FP problems.
(1) My friend Jean-Michel Muller at Lyon has published a number of
papers on the extension of IEEE 754 to cover transcendentals to
within 1ULP. He has heuristic data to indicate that you need
`about' twice the mantissa size for the internal registers
to make the gaurantee possible.
(2) If anyone is interested (then to 40dp):
tan(10^100)
0.4012319619908143541857543436532949583239
sin(10^100)
-0.3723761236612766882620866955531642957197
(3) The above from a small library of Exact Arithmetic functions that
my PhD studen and I have been working on. Rather gratifyingly
Norbert Muller (Trier) and I agree on our results to a 1000 decimal
places.
Just let me know if you need more digits...
---
David Lester
