Julian Assange wrote:
> Once you are within a few UDP, the underlaying grainyness of the
> representation is going to get you, so that smoothe, monotonic line
> segment you have below, will look like an appalling zigzag at
> best. This is my point. Near the limits of precession, the error
> introduced by rounding is trivial compared to the error introduced by
> the precission itself.
No I disagree. If you plot sin(a+x) against x for very small values of
x it should at worst look something like a computer's attempt to pixellate
a straight line, EG for example
XX
X
XX
X
X
XX
X
XX
(blah blah)
the point being that this is a straight line with slope a bit less than
1/3.
For example the code to spot when to stop with something like Newton iteration
will frequently depend on this, as will many many other iterative approximation
algorithms. There is good public domain code for transcendental functions
which behaves properly, and if your system sin function does not, then you
should complain fiercely.
