[Octave-bug-tracker] [bug #48316] besselj gives NaN for moderately large inputs (1e10)

[Colin Macdonald]

URL:
  <http://savannah.gnu.org/bugs/?48316>

                 Summary: besselj gives NaN for moderately large inputs (1e10)
                 Project: GNU Octave
            Submitted by: cbm
            Submitted on: Sun 26 Jun 2016 05:55:18 AM GMT
                Category: Octave Function
                Severity: 3 - Normal
                Priority: 5 - Normal
              Item Group: Incorrect Result
                  Status: None
             Assigned to: None
         Originator Name: 
        Originator Email: 
             Open/Closed: Open
         Discussion Lock: Any
                 Release: dev
        Operating System: Other

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Details:

Octave gives "besselj(1, 1e10)" as "NaN + NaNI".

Octave:

>> O = besselj(1, 10.^[5:12]')
O =
   0.00184675756288257 +                    0i
  -0.000725968356813763 +                    0i
  0.000236899240312058 +                    0i
  7.30639118155185e-05 +                    0i
  -5.21042264155388e-06 +                    0i
                 NaN +               NaNi
                 NaN +               NaNi
                 NaN +               NaNi


Symbolic pkg, converted to double:

>> S = double(besselj(1, sym(10).^[5:12]'))
S =
   0.00184675756288257
  -0.000725968356813763
  0.000236899240312058
  7.30639118155185e-05
  -5.21042264155388e-06
  -7.67650817568416e-06
  9.95266266795786e-07
  -7.91380268385044e-07


The relative accuracy is fine before blow-up:

>> abs(O-S)./abs(S)
ans =
  1.17416838493212e-16
  1.49345651543824e-16
  1.14415961302507e-16
                     0
  1.62565113336314e-16
                                NaN
                                NaN
                                NaN


(Ironically, I found this when I went looking for a function with good
relative error behaviour even though it decays to zero!  viz., #48307)





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