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

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

I tried using SBCL native complexes (following Barton's idea) and I don't get overflow, but the answer is off by a hundred ULPs, which is the sort of thing to expect with "naive" complex float division.
~~~
(defun $cldiv (a b)
  (let* ((recta (risplit a))
	 (ac (complex (car recta) (cdr recta))) ; will err out if not numeric
	 (rectb (risplit b))
	 (bc (complex (car rectb) (cdr rectb)))
	 (q (/ ac bc)))
    (add (realpart q) (mul '$%i (imagpart q)))))

bfdiv(a,b):=block([fpprec:32],float(rectform(bfloat(a)/bfloat(b))));
bfcabs(a):=block([fpprex:100],float(cabs(bfloat(a))));

clq: cldiv(1.13e-100*%i+5.43e-10,5.7e-312*%i+1.2e-311);
   => 3.691993880674702e301 - 1.7536970933199895e301 %i

bfq: bfdiv(1.13e-100*%i+5.43e-10,5.7e-312*%i+1.2e-311);
   =>3.6919938806746145e301 - 1.7536970933199478e301 %i
   
bfdiv(clq,bfq)
   => 1.0000000000000238 - 1.0515920681324065e-17 %i

qr: bfcabs(%) => 1.0000000000000238
(qr-1)/unit_in_last_place(qr) => 107
~~~




---

**[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:** Wed Dec 03, 2025 07:23 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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