Description
Small Model of Type : GAMS
Main file : fngamma2.gms includes : fnset_x.inc [html] fntest_x.inc [html]
$title 'Test correctness of gamma intrinsic' (FNGAMMA2,SEQ=184)

$include fnset_x.inc

reps0 = 1e-12;
reps1 = 1e-12;
* mathnew seems pretty sloppy on 2nd derivs for gamma
reps2 = 1e-8;
relToInput = 0;
set T / t1*t5,
        t11*t19
        t21*t24,
        t30*t39
        t41
 /;

* ecDOMAIN=1
* ecSINGULAR=2
* ecOVERFLOW=3

$offDigit
table data(T,V)
        x       f_                      fx_                     fxx_            rc_     ec_
t1      0     1e299                     -1e299                  1e299           1       2
t2     167   9.00369170577843e+297 4.60538543750298e+298        1e299           3       3
t3     167.2 2.50470014291271e+298      1e299                   1e299           2       3
t4     168    1e299                     1e299                   1e299           1       3
t5     200    1e299                     1e299                   1e299           1       3

* the results for t11 and following were obtained via AD techniques using C++,
* operator overloading, and the GNU GMP/MPFR library with 128-bit precision,
* using the same algorithm for f_ as is used in mathnew, and the same
* constants (which are expressed with varying precision)
* The results agree with Matlab and Mathematica, at least to the
* precision that we can expect to get from mathnew.
*       x       f_                      fx_                     fxx_            rc_     ec_
t11   1.1    0.95135076986687694   -0.40313958879496883    1.5344026430087969
t12   1.2    0.91816874239976062   -0.26538739835740634    1.2403736810281688
t13   1.3    0.89747069630627720   -0.15184386483996461    1.0436498185554464
t14   1.4    0.88726381750307530   -.054464285364277855    0.9131050681684681
t15   1.5    0.88622692545275803    .032338397448885034    0.8296269073766023
t16   1.6    0.89351534928769028    0.11262533379171629    0.7812182092671105
t17   1.7    0.90863873285329047    0.18949467676429813    0.7602807857968788
t18   1.8    0.93138377098024272    0.26543639583830106    0.7620528501995596
t19   1.9    0.96176583190738744    0.34256575607418686    0.7836845153955821

*       x       f_                      fx_                     fxx_            rc_     ec_
t21     1       1                  -0.57721566490153280    1.9781119906559450
t22     2       1                   0.42278433509846720    0.8236806608528795
t23     3       2                   1.84556867019693441    2.4929299919026934
t24     4       6                   7.53670601059080322   11.1699273161019490

*       x       f_                      fx_                     fxx_            rc_     ec_
t30    13   479001600             1.2099556529671019e9    3.09464168186868391e9
t31    13.1 6.16897056913806032e8 1.56319183480344967e9   4.00999842248353189e9
t32    13.2 7.95120469074831396e8 2.02108495363419775e9   5.19989073043754923e9
t33    13.3 1.02564002516962921e9 2.61507356531350175e9   6.74773847056521706e9
t34    13.4 1.32402477401656776e9 3.38616348223977668e9   8.76262298431965663e9
t35    13.5 1.71054206831957322e9 4.38787507497616271e9   1.1387273471779630e10
t36    13.6 2.21159357330380622e9 5.69010910083087566e9   1.4808566532857686e10
t37    13.7 2.86159549906601985e9 7.38422048505039388e9   1.9271338079886285e10
t38    13.8 3.70544205227829227e9 9.58968163820238767e9   2.5096563559100057e10
t39    13.9 4.80173506817199650e9 1.2462838690899158e10   3.2705302406668464e10

*       x       f_                      fx_                     fxx_            rc_     ec_
t41    100  9.33262154439437e+155 4.29315696145646e+156   1.97585963221017e+157
;
$onDigit

loop {T,
  data(T,  'f')  = gamma.value(   data(T,'x'));
  data(T, 'fx')  = gamma.grad(1:  data(T,'x'));
  data(T,'fxx')  = gamma.hess(1:1:data(T,'x'));
  data(T, 'rc')  = mathlastrc;
  data(T, 'ec')  = mathlastec;
};

display data;

abort$(execerror lt 8)  'Should get execution errors';
execerror = 0;

$include fntest_x.inc