$title 'Test correctness of arctan2 intrinsic eXceptions' (FNATAN2X,SEQ=276)

$onText

arctan2(y,x) = arctan(y/x), but adjusted for the correct quadrant
so we return the angle the vector (x,y) makes with (1,0).

ENUM            VAL
----            ---
rcOK            0
rcFUNC          1
rcGRAD          2
rcHESS          3
rcSYSTEM        4

ecOK            0
ecDOMAIN        1
ecSINGULAR      2
ecOVERFLOW      3

$offText

$include fnset_xy.inc

reps = 2e-13;
relToInput = 0;
set T / t1 * t23, t31 * t34 /;

$set OFLO  1.e299

table data(T,V)
        y       x       f_              fy_     fx_     fyy_    fyx_    fxx_    rc_     ec_
t1      0       0                                                                1       2
t2     -2       0  -1.5707963267949      0       0.5     0      0.25     0
t3      0       4    0                  0.25     0       0     -0.0625   0
t4    1e-160    0   1.5707963267949      0     -1e160    0     %OFLO%    0       3       2
t5    1e40      1   1.5707963267949    1e-80   -1e-40  -2e-120 1e-80   2e-120
t6    1e-200 1e-220 1.5707963267949    1e180   -1e200  -%OFLO% %OFLO%  %OFLO%    3       2
t7    1e-160 1e-200 1.5707963267949    1e120   -1e160  -2e280  %OFLO%  2e280     3       2
t8    1e-180 1e-192 1.5707963267939    1e168   -1e180  -%OFLO% %OFLO%  %OFLO%    3       2
t9    1e-148 1e-140 1e-8               1e140   -1e132  -2e272  -1e280  2e272
t10   1e-149 1e-140 1e-9               1e140   -1e131  -2e271  -1e280  2e271
t11   1e-152 1e-140 1e-12              1e140   -1e128  -2e268  -1e280  2e268
t12   1e-170 1e-160 1e-10              1e160   -1e150  -%OFLO% -%OFLO% %OFLO%    3       2
t13   1e-165 1e-155 1e-10              1e155   -1e145  -%OFLO% -%OFLO% %OFLO%    3       2
t14   1e-160 1e-150 1e-10              1e150   -1e140  -2e290  -%OFLO% 2e290     3       2
t15   1e-155 1e-145 1e-10              1e145   -1e135  -2e280  -1e290  2e280

t16   1e-149 1e-149  .7853981633974    5e148   -5e148  -5e297     0    5e297
t17   1e-150 1e-150  .7853981633974    5e149   -5e149  -%OFLO%    0    %OFLO%    3       2
t18   1e-155 1e-155  .7853981633974    5e154   -5e154  -%OFLO%    0    %OFLO%    3       2
t19   1e-160 1e-160  .7853981633974    5e159   -5e159  -%OFLO%    0    %OFLO%    3       2

t20   1e-200 1e+200  0                 1e-200    0       0        0      0
t21   1e+200 1e-200 1.5707963267949      0     -1e-200   0        0      0
t22     2       0   1.5707963267949      0      -0.5     0       0.25    0
t23     0       -4  3.1415926535898    -0.25     0       0     -.0625    0

*       y       x       f_              fy_     fx_     fyy_    fyx_    fxx_
t31     1       1   .7853981633974483   0.5    -0.5     -0.5      0      0.5
t32    -1       1  -.7853981633974483   0.5     0.5      0.5      0     -0.5
t33     1      -1   2.356194490192345  -0.5    -0.5      0.5      0     -0.5
t34    -1      -1  -2.356194490192345  -0.5     0.5     -0.5      0      0.5
;

data(T,'fxy_') = data(T,'fyx_');

loop {T,
  data(T,  'f')  = arctan2.value(   data(T,'y'),data(T,'x'));
  data(T, 'fy')  = arctan2.grad(1:  data(T,'y'),data(T,'x'));
  data(T, 'fx')  = arctan2.grad(2:  data(T,'y'),data(T,'x'));
  data(T,'fyy')  = arctan2.hess(1:1:data(T,'y'),data(T,'x'));
  data(T,'fyx')  = arctan2.hess(1:2:data(T,'y'),data(T,'x'));
  data(T,'fxy')  = arctan2.hess(2:1:data(T,'y'),data(T,'x'));
  data(T,'fxx')  = arctan2.hess(2:2:data(T,'y'),data(T,'x'));
  data(T, 'rc')  = mathlastrc;
  data(T, 'ec')  = mathlastec;
};

abort$(execerror lt 10)
 'Should get execution errors getting func/grad/hess of arctan2(y,x)';
execerror = 0;

$include fntest_xy.inc