[Maxima-bugs] [maxima:bugs] Re: #4645 rectform/polarform complex division overflow

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

I'm not aware of any Lisp that does anything fancy with complex division other than taking care not to overflow or underflow unnessarily.  My limited understanding is for the worst cases, you need to use extra precision., as your bfloat result shows.

A Google search returns this [paper on HW complex division that is correctly rounded](http://arith.cs.ucla.edu/publications/CmplexDiv-ASAP03.pdf).  I very briefly skimmed it. It's pretty complicated and I can't say I understand it.


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**[bugs:#4645] rectform/polarform complex division overflow**

**Status:** open
**Group:** None
**Labels:** rectform 
**Created:** Wed Dec 03, 2025 07:23 PM UTC by Stavros Macrakis
**Last Updated:** Thu Dec 04, 2025 06:19 PM UTC
**Owner:** nobody


~~~
fpprintprec:5$

q: (1.13e-100*%i+5.43e-10)/(5.7e-312*%i+1.2e-311)
rectform(q) => OVERFLOW
float(rectform(bfloat(q))) => 3.692e+301-1.7537e+301*%i

polarform(q) => OVERFLOW
polarform(bfloat(q)) => 4.0873b301*%e^-(4.4345b-1*%i)
~~~



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