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Missing asymptotic behavior of the airy Ai function
From: |
Jackson Vanover |
Subject: |
Missing asymptotic behavior of the airy Ai function |
Date: |
Wed, 4 Mar 2020 10:01:10 -0800 |
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;
}
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