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

[Barton W. <wil...@us...>]

I have an experimental way to fix the `cabs` overflow case for complex binary64 numbers, but mixed binary64 & symbolic cases can still fail: Example

OK:
~~~
(%i10) cabs(5.0e154 + %i);
float-float case (debug message)
(%o10)                              5.0e154
~~~
Still overflows
~~~
(%i11) cabs(5.0e154 + %i*x);
Maxima encountered a Lisp error:
 arithmetic error FLOATING-POINT-OVERFLOW signalled
~~~
Returning a `cabs` nounform isn't an option for `cabs(5.0e154 + %i*x)`, I think, so I'm stuck. 


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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:** Sat Nov 29, 2025 07:18 AM 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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