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bug #50459: Non termination of the incomplete gamma function due to floating-point rounding errors

Submitted by:  Fonenantsoa Maurica <fmaurica>
Submitted on:  Sat 04 Mar 2017 06:56:45 PM UTC  
 
Category:  None Severity:  3 - Normal
Operating System:  Status:  None
Assigned to:  None Open/Closed:  Open
Release:  2.3

Sat 04 Mar 2017 06:56:45 PM UTC, original submission:

Bug of non termination of the incomplete gamma function due to floating-point rounding errors in GSL 2.3

The function
int gsl_sf_gamma_inc_e(const double a, const double x, gsl_sf_result* result) from gsl/gsl_sf_gamma.h
does not terminate for any value of a and x such that a < -2^52 && 0 < x <= 0.25

For example, the call to gsl_sf_gamma_inc_e in the following program:
#include <stdio.h>
#include <gsl/gsl_sf_gamma.h>
int main (void)
{
double a = -1E25, x = 0.1;
gsl_sf_result* result;
printf ("%i\n", gsl_sf_gamma_inc_e(a, x, result));
return 0;
}

does not terminate as explained below:
int gsl_sf_gamma_inc_e(const double a, const double x, gsl_sf_result* result)
{
...
else
{
...
double alpha = da; // alpha = 0
...
do
{
...
alpha -= 1.0; // when alpha reaches -2^-52 (~4.5E15)
// then alpha - 1 is rounded to alpha itself
// thus alpha will not be updated anymore
} while(alpha > a); // a = -1E25
...
}
}

To guarantee termination for any possible input, the case a < -2^52 && 0 < x <= 0.25 should be prevented.

Fonenantsoa Maurica <fmaurica>

 

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    Follows 1 latest change.

    Date Changed by Updated Field Previous Value => Replaced by
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