Georgi Guninski on Wed, 01 Feb 2023 15:27:24 +0100

 Re: Numerical instability of j_1(x)=sin(Pi*x)^2+sin(Pi*(gamma(x)+1)/x)^2

• To: Georgi Guninski <gguninski@gmail.com>, pari-dev@pari.math.u-bordeaux.fr
• Subject: Re: Numerical instability of j_1(x)=sin(Pi*x)^2+sin(Pi*(gamma(x)+1)/x)^2
• From: Georgi Guninski <gguninski@gmail.com>
• Date: Wed, 1 Feb 2023 16:25:57 +0200
• Delivery-date: Wed, 01 Feb 2023 15:27:25 +0100
• References: <CAGUWgD8FFCsz8aT-Gm-DXBTNOHFDusuBXL7G4q4jbv1yyudKcQ@mail.gmail.com> <Y9otN2gImjqOttia@math.u-bordeaux.fr>

```On Wed, Feb 1, 2023 at 11:13 AM Karim Belabas
<Karim.Belabas@math.u-bordeaux.fr> wrote:

> The result is about -exp(10^40) / (2*I), but the 'exponent' of 10^40 is
> so large that the resulting floating point number can't be represented in PARI.
> (Exponents are coded by C longs, so the hardcoded limit for exponents is 2^63;
> i.e. floats about 2^(2^63) ...)
>

Many thanks for all replies.
Doesn't the large exponent bound imply the complex numbers are bounded? :)
IIRC this is called "finitarism", but can't find it with a search.

```