[Octave-bug-tracker] [bug #53543] regression: new gammainc inaccurate for small real inputs

[Colin Macdonald]

URL:
  <http://savannah.gnu.org/bugs/?53543>

                 Summary: regression: new gammainc inaccurate for small real
inputs
                 Project: GNU Octave
            Submitted by: cbm
            Submitted on: Sun 01 Apr 2018 06:38:38 PM UTC
                Category: Octave Function
                Severity: 3 - Normal
                Priority: 5 - Normal
              Item Group: Inaccurate Result
                  Status: None
             Assigned to: None
         Originator Name: 
        Originator Email: 
             Open/Closed: Open
         Discussion Lock: Any
                 Release: dev
        Operating System: Any

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Details:

Downstream symbolic pkg: https://github.com/cbm755/octsympy/issues/877

@mtmiller noted:

>> format long
>> x = 1/1000;
>> a = gammainc (x, 1);
>> b = quad (@(t) exp(-t), 0, x);
>> c = double (gammainc (sym(1) / 1000, 1));
>> a, b, c
a =    9.995001666249781e-04
b =    9.995001666250085e-04
c =    9.995001666250085e-04

(in particular, note the results are worse than just using quadrature).

Previously these sorts of things passed with "assert (..., -eps)".

@mtmiller thought "this might be a case of `exp (x) - 1` vs `expm1 (x)`"





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