[bug #58067] Missing asymptotic behavior of the airy Ai function

[Jackson Vanover]

URL:
  <https://savannah.gnu.org/bugs/?58067>

                 Summary: Missing asymptotic behavior of the airy Ai function
                 Project: GNU Scientific Library
            Submitted by: jacksonvanover
            Submitted on: Sat 28 Mar 2020 05:28:49 PM UTC
                Category: Accuracy problem
                Severity: 3 - Normal
        Operating System: Ubuntu 18.04
                  Status: None
             Assigned to: None
             Open/Closed: Open
                 Release: 2.6
         Discussion Lock: Any

    _______________________________________________________

Details:

Using version 2.6 of GSL from ftp://ftp.gnu.org/gnu/gsl/gsl-2.6.tar.gz

OS is Ubuntu 18.04.2 LTS

Hardware is a Dell workstation with a 3.60 GHz Intel i7-4790 and 32 GB
of RAM

Compiler is gcc 7.4.0 with the -w option

As the airy Ai function approaches positive infinity, its output goes to
zero. The mathematical libraries mpmath, scipy, and jmat all represent
this behavior, returning zero for large arguments (somewhere just
past 100). On the other hand, GSL invokes the error handler with an
underflow error, even though the proper behavior (theoretically) seems
straightforward to represent

#include <gsl/gsl_sf.h>
#include <stdio.h>
#include <gsl/gsl_math.h>
#include <float.h>

int main (void){
        double out;
        out = gsl_sf_airy_Ai(113, GSL_PREC_DOUBLE);

        printf("%.*f\n", DBL_DIG-1, out);
        printf("%.21e\n", out);
        return 0;
}




    _______________________________________________________

Reply to this item at:

  <https://savannah.gnu.org/bugs/?58067>

_______________________________________________
  Message sent via Savannah
  https://savannah.gnu.org/