A related bug report from JE Campagne (campagne@lal.in2p3.fr):

Dear developpers

I am running GSL 1.16 with such architecture

Linux opera3.lal.in2p3.fr 2.6.32-220.13.1.el6.x86_64 #1 SMP Tue Apr 17
15:16:22 CDT 2012 x86_64 x86_64 x86_64 GNU/Linux

and  gcc compilor version gcc (GCC) 4.4.5 20110214

I have a problem both with
gsl_sf_bessel_jl_e(int l, double x, gsl_sf_result* r)
or
gsl_sf_bessel_jl (int l, double x)

routine that fails to compute with l>~256 and produce such message

#include <gsl/gsl_sf_bessel.h>
#include <gsl/gsl_errno.h>
#include <stdlib.h>

int main(int argc, char* argv[]){

   If xval=10 it crashes for l=244
   but if xval=1 it crashes for l=149

   double xval = 1.0;
   int lmin=100;
   int lmax=200;

   gsl_sf_result result;

   for( int l=lmin;l<=lmax;l++){
     int status = gsl_sf_bessel_jl_e(l,xval,&result);
     printf("order[%d]: %s",l,gsl_strerror(status));
     if ( status == 0 ) printf("\t result: %le",result.val);
     printf("\n");
   }
}

and the execution output
order[100]: success      result: 7.444728e-190
order[101]: success      result: 3.667442e-192
order[102]: success      result: 1.789038e-194
order[103]: success      result: 8.642896e-197
order[104]: success      result: 4.135451e-199
order[105]: success      result: 1.959973e-201
order[106]: success      result: 9.201951e-204
order[107]: success      result: 4.280069e-206
order[108]: success      result: 1.972424e-208
order[109]: success      result: 9.006687e-211
order[110]: success      result: 4.075506e-213
order[111]: success      result: 1.827618e-215
order[112]: success      result: 8.122905e-218
order[113]: success      result: 3.578441e-220
order[114]: success      result: 1.562668e-222
order[115]: success      result: 6.764920e-225
order[116]: success      result: 2.903452e-227
order[117]: success      result: 1.235534e-229
order[118]: success      result: 5.213315e-232
order[119]: success      result: 2.181341e-234
order[120]: success      result: 9.051363e-237
order[121]: success      result: 3.724903e-239
order[122]: success      result: 1.520394e-241
order[123]: success      result: 6.155540e-244
order[124]: success      result: 2.472144e-246
order[125]: success      result: 9.849335e-249
order[126]: success      result: 3.893078e-251
order[127]: success      result: 1.526721e-253
order[128]: success      result: 5.940636e-256
order[129]: success      result: 2.293716e-258
order[130]: success      result: 8.788311e-261
order[131]: success      result: 3.341611e-263
order[132]: success      result: 1.261003e-265
order[133]: success      result: 4.722924e-268
order[134]: success      result: 1.755758e-270
order[135]: success      result: 6.478899e-273
order[136]: success      result: 2.373255e-275
order[137]: success      result: 8.630131e-278
order[138]: success      result: 3.115611e-280
order[139]: success      result: 1.116721e-282
order[140]: success      result: 3.974145e-285
order[141]: success      result: 1.404309e-287
order[142]: success      result: 4.927460e-290
order[143]: success      result: 1.716906e-292
order[144]: success      result: 5.940921e-295
order[145]: success      result: 2.041577e-297
order[146]: success      result: 6.967922e-300
order[147]: success      result: 2.362034e-302
order[148]: success      result: 7.953067e-305
gsl: gamma.c:1467: ERROR: underflow
Default GSL error handler invoked.
Abort (core dumped)