Signed infinity and signed zero Re: [Maxima] proposal to change acos

Basically, if you have a system that has signed
infinities (as IEEE 754) you end up with signed zeros.

For a probably too-long discussion of this, see extrat.pdf
in www.cs.berkeley.edu/~fateman/papers/   also refs.

Projective and affine mode rational numbers are also
possible. This would give us in affine mode,
one (unsigned + or -   infinity) which is 1/0.

Why introduce this?  because a +b/c  should be
computed as   a    if  c=1/0.   This allows one
to continue to compute, even after a division by 0.

If you have +inf and -inf you should also have +0 and -0,
and 0/0= undef. (projective mode)

This could/should be added to the Lisp, and then allowed
to show through for Maxima.

RJF


Raymond Toy wrote:

>>>>>>"Barton" == Barton Willis  writes:
> 
> 
> [snip]
> 
>     Barton> (5)  Since we last talked about such things, GCL has fixed some bugs in 
>     Barton> its acosh function; see
>     Barton> (there may be other important messages, but I can't find them right now)
> 
>     Barton> http://www.math.utexas.edu/pipermail/maxima/2002/002955.html
>     Barton> http://www.math.utexas.edu/pipermail/maxima/2002/002949.html
> 
>     Barton> Maybe 5.9.3 would be a good time to:
> 
>     Barton> (a)  make the Maxima acosh function the same as the CL acosh function.
> 
> Yes.
> 
>     Barton> (b) move numerical evaluation for exponetial-like
>     Barton>     functions to CL.  Then Maxima would not have to use
>     Barton>     rectform to evaluate things like sin(1.0 + 5.0 * %i).
> 
> I've done some of this for the elliptic functions.  One question:
> What should maxima do with sin(1 + 5.0*%i)?  Leave it?  Apply "numeric
> contagion" and pretend it was sin(1.0+5.0*%i) and evaluate
> numerically, even without the numer or float flags?
> 
>     Barton> (c) check for other branch cut inconsistencies.
> 
> I think this is important and we should do that soon.
> 
> Let me also add that we should try to evaluate the special functions
> as accurately as possible, even for bigfloats.  sinh is one example
> where we do not do a very good job for small x.  In the thread
> mentioned above, we also do not evaluate acosh(4100) very well either.
> (We should fix the problem that eps is too small in trigi.lisp.)
> 
> Also, in the thread mentioned above, we talked about letting Lisp
> evaluate the functions.  One thing that needs to be considered is what
> to do about signed zeroes.  Should maxima support that?  My current
> (highly uninformed) feeling is not to support signed zeroes.  If so,
> we will need to exercise a little care when calling Lisp functions for
> evaluation because cmucl and sbcl support signed zeroes.
> 
> Ray
> 
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