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

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

On Mon, Dec 1, 2025 at 11:03 AM Raymond Toy via Maxima-bugs <
max...@li...> wrote:

> Here's one way for doing cabs(x+%i*y), where x is a number. Divide by the
> arg by sqrt(x) to get cabs(sqrt(x)+%i*y/sqrt(x)) = sqrt(y^2/x+x). The
> final answer will be sqrt(x)*sqrt(y^2/x+x). Something similiar if y is a
> number.
>
I don't know how to do this if both x and y are more complicated
> expressions composed of numbers + variables.
>
Can you give some examples? Are you thinking of, say, cabs((x+1e200)+%i)?
That only overflows if you expand the result.... And I agree that basic
*cabs* shouldn't worry about cases like this.

> One alternative is to convert the floats to bfloats if we get an overflow.
> We don't normally do that anywhere else, so this would be very odd.
>
I agree that this would be odd, but maybe we should consider it. After all,
we *do* currently convert floats to rats in some cases. For example,
*keepfloat* doesn't prevent *solve* from rationalizing, so that
*solve(x^2+1e200*x-1)
*doesn't overflow -- it returns rationals. I don't love that behavior, but
generalizing the classic Forsythe paper
<http://i.stanford.edu/pub/cstr/reports/cs/tr/66/40/CS-TR-66-40.pdf> for
the general case of *solve* seems hard....

> I don't think a nounform would be a bad answer, if we printed a warning
> that there would be a potential overflow when computing the result. I
> personally think if a user is doing numerical stuff, it's his responsiblity
> to deal with numerical issues that might arise. We'll be careful to limit
> overflows, but we can't solve all the potential numerical issues that might
> arise.
>
For the purely numeric case, we should do as well as existing purely
numeric libraries, which are pretty good at *cabs, *etc.


> ------------------------------
>
> *[bugs:#4638] <https://sourceforge.net/p/maxima/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 02:21 PM UTC
> *Owner:* nobody
>
> cabs and carg on complex floats overflow and underflow even when the
> result is perfectly representable:
>
> 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
>
> Tested in Maxima 5.48.1 SBCL 2.5.7 MacOS Intel
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