[Maxima-bugs] [maxima:bugs] Re: #4638 cabs/carg/polarform overflow and underflow

[Raymond T. <rt...@us...>]

Your example of `cabs(x+1e200+%i)` is nice and is only a problem if the result is expanded.  I don't have an example off the top of my head that would be a problem.

I'm somewhat opposed to converting to bfloats because we don't do that anywhere else, but I believe people have proposed this before.

I agree that for numeric values we should do a good job.  Matching existing libraries is pretty hard.  Take a look at [fdlibm hypot](https://www.netlib.org/fdlibm/e_hypot.c).  It's fairly complicated and not even correctly rounded.  The ones that do correctly rounded results like [core-math hypot64](https://gitlab.inria.fr/core-math/core-math/-/blob/master/src/binary64/hypot/hypot.c) are even more complicated.

FWIW, several years ago I translated lots of [fdlibm C  routines to Javascript ](https://github.com/rtoy/fdlibm-js) (to get Chrome to fix it's broken trig functions!)  We couldn't really do this in a portable way in Lisp.  We have to figure out for each lisp how to get the actual bits of a float64 out.


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**[bugs:#4638] cabs/carg/polarform overflow and underflow**

**Status:** open
**Group:** None
**Labels:** cabs carg 
**Created:** Sat Nov 29, 2025 07:18 AM UTC by Stavros Macrakis
**Last Updated:** Mon Dec 01, 2025 05:18 PM UTC
**Owner:** nobody


``cabs`` and ``carg`` on complex floats overflow and underflow even when the result is perfectly representable:
<pre>
cabs(1e-170 + %i*1e-170) => 0.0
but float(cabs(bfloat(1e-170 + %i*1e-170))) => 1.414213562373095e-170
cabs(1e170 + %i*1e+170) => overflow
but float(cabs(bfloat(1e170 + %i*1e170))) => 1.4142135623730952e170
carg(1e170 + %i*1e+170)) => overflow
but float(carg(bfloat(1e170 + %i*1e+170))) => 0.7853981633974483
carg(1e-310 + %i*1e-310) => overflow
but carg(1b-310 + %i*1b-310) => 7.853981633974483b-1
polarform(1e170 + %i*1e+170) => overflow
</pre>

Tested in Maxima 5.48.1 SBCL 2.5.7 MacOS Intel


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