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

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

**proposal**  Attempt to detect a floating point overflow, and when it is detected, return an `abs` nounform. Examples (done with experimental code)

~~~
(%i40) cabs(2/3 +%i*x);
(%o40) sqrt(x^2+4/9)

(%i41) cabs(2.3 +%i*x);
(%o41) sqrt(x^2+5.289999999999999)

(%i42) cabs(2.3e100 +%i*x);
(%o42) sqrt(x^2+5.2899999999999995e200)
~~~

Examples of floating point overflow
~~~
(%i43) cabs(2.3e170 +%i*x);
floating point overflow detected 
(%o43) abs(%i*x+2.3e170)

(%i44) cabs(2.3 +%i*x*1.8e200);
floating point overflow detected 
(%o44) abs(1.8e200*%i*x+2.3)
~~~

I'm not sure that this will work with all Lisp varieties. 



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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 08:39 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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