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

[Stavros M. <mac...@us...>]

In addition to the 0.0/-0.0 case that you mention

    (hypotenouse-binary64 1e-170 0.0) => 0.0  -- should be 1e-170

it isn't right for denormalized numbers:

    (hypotenouse-binary64 1e-323 1e-323) => 3.1467296279827185e-308
    (* 1e-323 (sqrt 2.0)) => 1.4821969375237396e-323

PS By the way, although I appreciate the spelling *hypotenouse* as being more faithful to the Greek (ὑποτείνουσα), that's not the usual English spelling.


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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:** Tue Dec 02, 2025 03:16 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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