Hi,
I've noticed that the complex tan and cot functions return NaN if the
argument z=x+i*y has a large negative imaginary part y, such as
y=-1e7. However, the functions should either return -i or i in that
case.
I noticed that the corresponding hyperbolic functions do not have this
problem, so I propose to fix this bug by using
tan(z)=-i*tanh(i*z)
and using the same algorithm for the calculation of the complex tan
and tanh functions, see attached patch.
I would also like to add unit tests for that (and also for the complex
tan and cot functions for arguments with large positive imaginary
part, and also for the complex tanh and coth functions for large real
parts). I tried to understand how the Lisp file complex/test.el works
and modified it (see the patch). However, it seems that emacs refuses
to evaluate the functions for the arguments I've added, it leaves
lines like
{FN (tan), ARG(-3.45266983001243932001e-04,8.3886080e+06),
RES(tan(-3.452669830012439320e-4, 8.388608e6), 60)},
which are then removed by the 'clean' function in test.el and never
get written to results.h.
Therefore, I've temporarily added the expected results as hardcoded
values to results.h. I would appreciate any comments on how to improve
this from people who know Lisp better then me.
Best regards,
Frank
=== modified file 'complex/math.c'
--- complex/math.c 2010-05-07 11:53:23 +0000
+++ complex/math.c 2012-02-23 09:40:14 +0000
@@ -489,14 +489,10 @@
}
else
{
- double u = exp (-I);
- double C = 2 * u / (1 - pow (u, 2.0));
- double D = 1 + pow (cos (R), 2.0) * pow (C, 2.0);
-
- double S = pow (C, 2.0);
- double T = 1.0 / tanh (I);
-
- GSL_SET_COMPLEX (&z, 0.5 * sin (2 * R) * S / D, T / D);
+ double D = pow (cos (R), 2.0) + pow (sinh (I), 2.0);
+ double F = 1 + pow (cos (R) / sinh (I), 2.0);
+
+ GSL_SET_COMPLEX (&z, 0.5 * sin (2 * R) / D, 1.0 / (tanh (I) * F));
}
return z;
=== modified file 'complex/test.c'
--- complex/test.c 2010-05-06 20:07:31 +0000
+++ complex/test.c 2012-02-23 09:46:58 +0000
@@ -93,6 +93,199 @@
struct fz listz[] =
{
#include "results.h"
+ /* The following data can in principle be generated by making the following
+ * additions to test.el:
+ *
+ * (setq zcirc_large_imag (append (combine circ inf)))
+ * (setq zicirc_large_real (append (combine inf circ)))
+ *
+ * then later on, in the function test2 (), add
+ *
+ * (loop1 "tan" zcirc_large_imag)
+ * (loop1 "cot" zcirc_large_imag)
+ * (loop1 "tanh" zicirc_large_real)
+ * (loop1 "coth" zicirc_large_real)
+ *
+ * The problem is that emacs refuses to evaluate the tan, cot, tanh,
+ * and coth functions for these values, such that the clean () function
+ * removes them from the output.
+ */
+ {FN (tan), ARG(-3.45266983001243932001e-04,8.3886080e+06), RES(0.0, 1.0)},
+ {FN (tan), ARG(-3.45266983001243932001e-04,-8.3886080e+06), RES(0.0, -1.0)},
+ {FN (tan), ARG(3.45266983001243932001e-04,8.3886080e+06), RES(0.0, 1.0)},
+ {FN (tan), ARG(3.45266983001243932001e-04,-8.3886080e+06), RES(0.0, -1.0)},
+ {FN (tan), ARG(1.57045105981189525579e+00,8.3886080e+06), RES(0.0, 1.0)},
+ {FN (tan), ARG(1.57045105981189525579e+00,-8.3886080e+06), RES(0.0, -1.0)},
+ {FN (tan), ARG(-1.57045105981189525579e+00,8.3886080e+06), RES(0.0, 1.0)},
+ {FN (tan), ARG(-1.57045105981189525579e+00,-8.3886080e+06), RES(0.0, -1.0)},
+ {FN (tan), ARG(1.57114159377789786021e+00,8.3886080e+06), RES(0.0, 1.0)},
+ {FN (tan), ARG(1.57114159377789786021e+00,-8.3886080e+06), RES(0.0, -1.0)},
+ {FN (tan), ARG(-1.57114159377789786021e+00,8.3886080e+06), RES(0.0, 1.0)},
+ {FN (tan), ARG(-1.57114159377789786021e+00,-8.3886080e+06), RES(0.0, -1.0)},
+ {FN (tan), ARG(3.14124738660679181379e+00,8.3886080e+06), RES(0.0, 1.0)},
+ {FN (tan), ARG(3.14124738660679181379e+00,-8.3886080e+06), RES(0.0, -1.0)},
+ {FN (tan), ARG(-3.14124738660679181379e+00,8.3886080e+06), RES(0.0, 1.0)},
+ {FN (tan), ARG(-3.14124738660679181379e+00,-8.3886080e+06), RES(0.0, -1.0)},
+ {FN (tan), ARG(3.14193792057279441821e+00,8.3886080e+06), RES(0.0, 1.0)},
+ {FN (tan), ARG(3.14193792057279441821e+00,-8.3886080e+06), RES(0.0, -1.0)},
+ {FN (tan), ARG(-3.14193792057279441821e+00,8.3886080e+06), RES(0.0, 1.0)},
+ {FN (tan), ARG(-3.14193792057279441821e+00,-8.3886080e+06), RES(0.0, -1.0)},
+ {FN (tan), ARG(4.71204371340168837179e+00,8.3886080e+06), RES(0.0, 1.0)},
+ {FN (tan), ARG(4.71204371340168837179e+00,-8.3886080e+06), RES(0.0, -1.0)},
+ {FN (tan), ARG(-4.71204371340168837179e+00,8.3886080e+06), RES(0.0, 1.0)},
+ {FN (tan), ARG(-4.71204371340168837179e+00,-8.3886080e+06), RES(0.0, -1.0)},
+ {FN (tan), ARG(4.71273424736769097620e+00,8.3886080e+06), RES(0.0, 1.0)},
+ {FN (tan), ARG(4.71273424736769097620e+00,-8.3886080e+06), RES(0.0, -1.0)},
+ {FN (tan), ARG(-4.71273424736769097620e+00,8.3886080e+06), RES(0.0, 1.0)},
+ {FN (tan), ARG(-4.71273424736769097620e+00,-8.3886080e+06), RES(0.0, -1.0)},
+ {FN (tan), ARG(6.28284004019658492979e+00,8.3886080e+06), RES(0.0, 1.0)},
+ {FN (tan), ARG(6.28284004019658492979e+00,-8.3886080e+06), RES(0.0, -1.0)},
+ {FN (tan), ARG(-6.28284004019658492979e+00,8.3886080e+06), RES(0.0, 1.0)},
+ {FN (tan), ARG(-6.28284004019658492979e+00,-8.3886080e+06), RES(0.0, -1.0)},
+ {FN (tan), ARG(6.28353057416258753420e+00,8.3886080e+06), RES(0.0, 1.0)},
+ {FN (tan), ARG(6.28353057416258753420e+00,-8.3886080e+06), RES(0.0, -1.0)},
+ {FN (tan), ARG(-6.28353057416258753420e+00,8.3886080e+06), RES(0.0, 1.0)},
+ {FN (tan), ARG(-6.28353057416258753420e+00,-8.3886080e+06), RES(0.0, -1.0)},
+ {FN (tan), ARG(9.42443269378637893396e+00,8.3886080e+06), RES(0.0, 1.0)},
+ {FN (tan), ARG(9.42443269378637893396e+00,-8.3886080e+06), RES(0.0, -1.0)},
+ {FN (tan), ARG(-9.42443269378637893396e+00,8.3886080e+06), RES(0.0, 1.0)},
+ {FN (tan), ARG(-9.42443269378637893396e+00,-8.3886080e+06), RES(0.0, -1.0)},
+ {FN (tan), ARG(9.42512322775237976202e+00,8.3886080e+06), RES(0.0, 1.0)},
+ {FN (tan), ARG(9.42512322775237976202e+00,-8.3886080e+06), RES(0.0, -1.0)},
+ {FN (tan), ARG(-9.42512322775237976202e+00,8.3886080e+06), RES(0.0, 1.0)},
+ {FN (tan), ARG(-9.42512322775237976202e+00,-8.3886080e+06), RES(0.0, -1.0)},
+ {FN (cot), ARG(-3.45266983001243932001e-04,8.3886080e+06), RES(0.0, -1.0)},
+ {FN (cot), ARG(-3.45266983001243932001e-04,-8.3886080e+06), RES(0.0, 1.0)},
+ {FN (cot), ARG(3.45266983001243932001e-04,8.3886080e+06), RES(0.0, -1.0)},
+ {FN (cot), ARG(3.45266983001243932001e-04,-8.3886080e+06), RES(0.0, 1.0)},
+ {FN (cot), ARG(1.57045105981189525579e+00,8.3886080e+06), RES(0.0, -1.0)},
+ {FN (cot), ARG(1.57045105981189525579e+00,-8.3886080e+06), RES(0.0, 1.0)},
+ {FN (cot), ARG(-1.57045105981189525579e+00,8.3886080e+06), RES(0.0, -1.0)},
+ {FN (cot), ARG(-1.57045105981189525579e+00,-8.3886080e+06), RES(0.0, 1.0)},
+ {FN (cot), ARG(1.57114159377789786021e+00,8.3886080e+06), RES(0.0, -1.0)},
+ {FN (cot), ARG(1.57114159377789786021e+00,-8.3886080e+06), RES(0.0, 1.0)},
+ {FN (cot), ARG(-1.57114159377789786021e+00,8.3886080e+06), RES(0.0, -1.0)},
+ {FN (cot), ARG(-1.57114159377789786021e+00,-8.3886080e+06), RES(0.0, 1.0)},
+ {FN (cot), ARG(3.14124738660679181379e+00,8.3886080e+06), RES(0.0, -1.0)},
+ {FN (cot), ARG(3.14124738660679181379e+00,-8.3886080e+06), RES(0.0, 1.0)},
+ {FN (cot), ARG(-3.14124738660679181379e+00,8.3886080e+06), RES(0.0, -1.0)},
+ {FN (cot), ARG(-3.14124738660679181379e+00,-8.3886080e+06), RES(0.0, 1.0)},
+ {FN (cot), ARG(3.14193792057279441821e+00,8.3886080e+06), RES(0.0, -1.0)},
+ {FN (cot), ARG(3.14193792057279441821e+00,-8.3886080e+06), RES(0.0, 1.0)},
+ {FN (cot), ARG(-3.14193792057279441821e+00,8.3886080e+06), RES(0.0, -1.0)},
+ {FN (cot), ARG(-3.14193792057279441821e+00,-8.3886080e+06), RES(0.0, 1.0)},
+ {FN (cot), ARG(4.71204371340168837179e+00,8.3886080e+06), RES(0.0, -1.0)},
+ {FN (cot), ARG(4.71204371340168837179e+00,-8.3886080e+06), RES(0.0, 1.0)},
+ {FN (cot), ARG(-4.71204371340168837179e+00,8.3886080e+06), RES(0.0, -1.0)},
+ {FN (cot), ARG(-4.71204371340168837179e+00,-8.3886080e+06), RES(0.0, 1.0)},
+ {FN (cot), ARG(4.71273424736769097620e+00,8.3886080e+06), RES(0.0, -1.0)},
+ {FN (cot), ARG(4.71273424736769097620e+00,-8.3886080e+06), RES(0.0, 1.0)},
+ {FN (cot), ARG(-4.71273424736769097620e+00,8.3886080e+06), RES(0.0, -1.0)},
+ {FN (cot), ARG(-4.71273424736769097620e+00,-8.3886080e+06), RES(0.0, 1.0)},
+ {FN (cot), ARG(6.28284004019658492979e+00,8.3886080e+06), RES(0.0, -1.0)},
+ {FN (cot), ARG(6.28284004019658492979e+00,-8.3886080e+06), RES(0.0, 1.0)},
+ {FN (cot), ARG(-6.28284004019658492979e+00,8.3886080e+06), RES(0.0, -1.0)},
+ {FN (cot), ARG(-6.28284004019658492979e+00,-8.3886080e+06), RES(0.0, 1.0)},
+ {FN (cot), ARG(6.28353057416258753420e+00,8.3886080e+06), RES(0.0, -1.0)},
+ {FN (cot), ARG(6.28353057416258753420e+00,-8.3886080e+06), RES(0.0, 1.0)},
+ {FN (cot), ARG(-6.28353057416258753420e+00,8.3886080e+06), RES(0.0, -1.0)},
+ {FN (cot), ARG(-6.28353057416258753420e+00,-8.3886080e+06), RES(0.0, 1.0)},
+ {FN (cot), ARG(9.42443269378637893396e+00,8.3886080e+06), RES(0.0, -1.0)},
+ {FN (cot), ARG(9.42443269378637893396e+00,-8.3886080e+06), RES(0.0, 1.0)},
+ {FN (cot), ARG(-9.42443269378637893396e+00,8.3886080e+06), RES(0.0, -1.0)},
+ {FN (cot), ARG(-9.42443269378637893396e+00,-8.3886080e+06), RES(0.0, 1.0)},
+ {FN (cot), ARG(9.42512322775237976202e+00,8.3886080e+06), RES(0.0, -1.0)},
+ {FN (cot), ARG(9.42512322775237976202e+00,-8.3886080e+06), RES(0.0, 1.0)},
+ {FN (cot), ARG(-9.42512322775237976202e+00,8.3886080e+06), RES(0.0, -1.0)},
+ {FN (cot), ARG(-9.42512322775237976202e+00,-8.3886080e+06), RES(0.0, 1.0)},
+ {FN (tanh), ARG(8.3886080e+06,-3.45266983001243932001e-04), RES(1.0, 0.0)},
+ {FN (tanh), ARG(8.3886080e+06,3.45266983001243932001e-04), RES(1.0, 0.0)},
+ {FN (tanh), ARG(-8.3886080e+06,-3.45266983001243932001e-04), RES(-1.0, 0.0)},
+ {FN (tanh), ARG(-8.3886080e+06,3.45266983001243932001e-04), RES(-1.0, 0.0)},
+ {FN (tanh), ARG(8.3886080e+06,1.57045105981189525579e+00), RES(1.0, 0.0)},
+ {FN (tanh), ARG(8.3886080e+06,-1.57045105981189525579e+00), RES(1.0, 0.0)},
+ {FN (tanh), ARG(-8.3886080e+06,1.57045105981189525579e+00), RES(-1.0, 0.0)},
+ {FN (tanh), ARG(-8.3886080e+06,-1.57045105981189525579e+00), RES(-1.0, 0.0)},
+ {FN (tanh), ARG(8.3886080e+06,1.57114159377789786021e+00), RES(1.0, 0.0)},
+ {FN (tanh), ARG(8.3886080e+06,-1.57114159377789786021e+00), RES(1.0, 0.0)},
+ {FN (tanh), ARG(-8.3886080e+06,1.57114159377789786021e+00), RES(-1.0, 0.0)},
+ {FN (tanh), ARG(-8.3886080e+06,-1.57114159377789786021e+00), RES(-1.0, 0.0)},
+ {FN (tanh), ARG(8.3886080e+06,3.14124738660679181379e+00), RES(1.0, 0.0)},
+ {FN (tanh), ARG(8.3886080e+06,-3.14124738660679181379e+00), RES(1.0, 0.0)},
+ {FN (tanh), ARG(-8.3886080e+06,3.14124738660679181379e+00), RES(-1.0, 0.0)},
+ {FN (tanh), ARG(-8.3886080e+06,-3.14124738660679181379e+00), RES(-1.0, 0.0)},
+ {FN (tanh), ARG(8.3886080e+06,3.14193792057279441821e+00), RES(1.0, 0.0)},
+ {FN (tanh), ARG(8.3886080e+06,-3.14193792057279441821e+00), RES(1.0, 0.0)},
+ {FN (tanh), ARG(-8.3886080e+06,3.14193792057279441821e+00), RES(-1.0, 0.0)},
+ {FN (tanh), ARG(-8.3886080e+06,-3.14193792057279441821e+00), RES(-1.0, 0.0)},
+ {FN (tanh), ARG(8.3886080e+06,4.71204371340168837179e+00), RES(1.0, 0.0)},
+ {FN (tanh), ARG(8.3886080e+06,-4.71204371340168837179e+00), RES(1.0, 0.0)},
+ {FN (tanh), ARG(-8.3886080e+06,4.71204371340168837179e+00), RES(-1.0, 0.0)},
+ {FN (tanh), ARG(-8.3886080e+06,-4.71204371340168837179e+00), RES(-1.0, 0.0)},
+ {FN (tanh), ARG(8.3886080e+06,4.71273424736769097620e+00), RES(1.0, 0.0)},
+ {FN (tanh), ARG(8.3886080e+06,-4.71273424736769097620e+00), RES(1.0, 0.0)},
+ {FN (tanh), ARG(-8.3886080e+06,4.71273424736769097620e+00), RES(-1.0, 0.0)},
+ {FN (tanh), ARG(-8.3886080e+06,-4.71273424736769097620e+00), RES(-1.0, 0.0)},
+ {FN (tanh), ARG(8.3886080e+06,6.28284004019658492979e+00), RES(1.0, 0.0)},
+ {FN (tanh), ARG(8.3886080e+06,-6.28284004019658492979e+00), RES(1.0, 0.0)},
+ {FN (tanh), ARG(-8.3886080e+06,6.28284004019658492979e+00), RES(-1.0, 0.0)},
+ {FN (tanh), ARG(-8.3886080e+06,-6.28284004019658492979e+00), RES(-1.0, 0.0)},
+ {FN (tanh), ARG(8.3886080e+06,6.28353057416258753420e+00), RES(1.0, 0.0)},
+ {FN (tanh), ARG(8.3886080e+06,-6.28353057416258753420e+00), RES(1.0, 0.0)},
+ {FN (tanh), ARG(-8.3886080e+06,6.28353057416258753420e+00), RES(-1.0, 0.0)},
+ {FN (tanh), ARG(-8.3886080e+06,-6.28353057416258753420e+00), RES(-1.0, 0.0)},
+ {FN (tanh), ARG(8.3886080e+06,9.42443269378637893396e+00), RES(1.0, 0.0)},
+ {FN (tanh), ARG(8.3886080e+06,-9.42443269378637893396e+00), RES(1.0, 0.0)},
+ {FN (tanh), ARG(-8.3886080e+06,9.42443269378637893396e+00), RES(-1.0, 0.0)},
+ {FN (tanh), ARG(-8.3886080e+06,-9.42443269378637893396e+00), RES(-1.0, 0.0)},
+ {FN (tanh), ARG(8.3886080e+06,9.42512322775237976202e+00), RES(1.0, 0.0)},
+ {FN (tanh), ARG(8.3886080e+06,-9.42512322775237976202e+00), RES(1.0, 0.0)},
+ {FN (tanh), ARG(-8.3886080e+06,9.42512322775237976202e+00), RES(-1.0, 0.0)},
+ {FN (tanh), ARG(-8.3886080e+06,-9.42512322775237976202e+00), RES(-1.0, 0.0)},
+ {FN (coth), ARG(8.3886080e+06,-3.45266983001243932001e-04), RES(1.0, 0.0)},
+ {FN (coth), ARG(8.3886080e+06,3.45266983001243932001e-04), RES(1.0, 0.0)},
+ {FN (coth), ARG(-8.3886080e+06,-3.45266983001243932001e-04), RES(-1.0, 0.0)},
+ {FN (coth), ARG(-8.3886080e+06,3.45266983001243932001e-04), RES(-1.0, 0.0)},
+ {FN (coth), ARG(8.3886080e+06,1.57045105981189525579e+00), RES(1.0, 0.0)},
+ {FN (coth), ARG(8.3886080e+06,-1.57045105981189525579e+00), RES(1.0, 0.0)},
+ {FN (coth), ARG(-8.3886080e+06,1.57045105981189525579e+00), RES(-1.0, 0.0)},
+ {FN (coth), ARG(-8.3886080e+06,-1.57045105981189525579e+00), RES(-1.0, 0.0)},
+ {FN (coth), ARG(8.3886080e+06,1.57114159377789786021e+00), RES(1.0, 0.0)},
+ {FN (coth), ARG(8.3886080e+06,-1.57114159377789786021e+00), RES(1.0, 0.0)},
+ {FN (coth), ARG(-8.3886080e+06,1.57114159377789786021e+00), RES(-1.0, 0.0)},
+ {FN (coth), ARG(-8.3886080e+06,-1.57114159377789786021e+00), RES(-1.0, 0.0)},
+ {FN (coth), ARG(8.3886080e+06,3.14124738660679181379e+00), RES(1.0, 0.0)},
+ {FN (coth), ARG(8.3886080e+06,-3.14124738660679181379e+00), RES(1.0, 0.0)},
+ {FN (coth), ARG(-8.3886080e+06,3.14124738660679181379e+00), RES(-1.0, 0.0)},
+ {FN (coth), ARG(-8.3886080e+06,-3.14124738660679181379e+00), RES(-1.0, 0.0)},
+ {FN (coth), ARG(8.3886080e+06,3.14193792057279441821e+00), RES(1.0, 0.0)},
+ {FN (coth), ARG(8.3886080e+06,-3.14193792057279441821e+00), RES(1.0, 0.0)},
+ {FN (coth), ARG(-8.3886080e+06,3.14193792057279441821e+00), RES(-1.0, 0.0)},
+ {FN (coth), ARG(-8.3886080e+06,-3.14193792057279441821e+00), RES(-1.0, 0.0)},
+ {FN (coth), ARG(8.3886080e+06,4.71204371340168837179e+00), RES(1.0, 0.0)},
+ {FN (coth), ARG(8.3886080e+06,-4.71204371340168837179e+00), RES(1.0, 0.0)},
+ {FN (coth), ARG(-8.3886080e+06,4.71204371340168837179e+00), RES(-1.0, 0.0)},
+ {FN (coth), ARG(-8.3886080e+06,-4.71204371340168837179e+00), RES(-1.0, 0.0)},
+ {FN (coth), ARG(8.3886080e+06,4.71273424736769097620e+00), RES(1.0, 0.0)},
+ {FN (coth), ARG(8.3886080e+06,-4.71273424736769097620e+00), RES(1.0, 0.0)},
+ {FN (coth), ARG(-8.3886080e+06,4.71273424736769097620e+00), RES(-1.0, 0.0)},
+ {FN (coth), ARG(-8.3886080e+06,-4.71273424736769097620e+00), RES(-1.0, 0.0)},
+ {FN (coth), ARG(8.3886080e+06,6.28284004019658492979e+00), RES(1.0, 0.0)},
+ {FN (coth), ARG(8.3886080e+06,-6.28284004019658492979e+00), RES(1.0, 0.0)},
+ {FN (coth), ARG(-8.3886080e+06,6.28284004019658492979e+00), RES(-1.0, 0.0)},
+ {FN (coth), ARG(-8.3886080e+06,-6.28284004019658492979e+00), RES(-1.0, 0.0)},
+ {FN (coth), ARG(8.3886080e+06,6.28353057416258753420e+00), RES(1.0, 0.0)},
+ {FN (coth), ARG(8.3886080e+06,-6.28353057416258753420e+00), RES(1.0, 0.0)},
+ {FN (coth), ARG(-8.3886080e+06,6.28353057416258753420e+00), RES(-1.0, 0.0)},
+ {FN (coth), ARG(-8.3886080e+06,-6.28353057416258753420e+00), RES(-1.0, 0.0)},
+ {FN (coth), ARG(8.3886080e+06,9.42443269378637893396e+00), RES(1.0, 0.0)},
+ {FN (coth), ARG(8.3886080e+06,-9.42443269378637893396e+00), RES(1.0, 0.0)},
+ {FN (coth), ARG(-8.3886080e+06,9.42443269378637893396e+00), RES(-1.0, 0.0)},
+ {FN (coth), ARG(-8.3886080e+06,-9.42443269378637893396e+00), RES(-1.0, 0.0)},
+ {FN (coth), ARG(8.3886080e+06,9.42512322775237976202e+00), RES(1.0, 0.0)},
+ {FN (coth), ARG(8.3886080e+06,-9.42512322775237976202e+00), RES(1.0, 0.0)},
+ {FN (coth), ARG(-8.3886080e+06,9.42512322775237976202e+00), RES(-1.0, 0.0)},
+ {FN (coth), ARG(-8.3886080e+06,-9.42512322775237976202e+00), RES(-1.0, 0.0)},
{"", 0, 0, 0, 0, 0}
};
=== modified file 'complex/test.el'
--- complex/test.el 2010-05-06 20:07:31 +0000
+++ complex/test.el 2012-02-23 09:44:04 +0000
@@ -244,6 +244,8 @@
(setq zcirc (append (combine circ zfinite)))
(setq zicirc (append (combine zfinite circ)))
+(setq zcirc_large_imag (append (combine circ inf)))
+(setq zicirc_large_real (append (combine inf circ)))
(defun test1 ()
(loop1 "arg" z0)
@@ -262,6 +264,7 @@
(loop1 "sin" zcirc)
(loop1 "cos" zcirc)
(loop1 "tan" zcirc)
+ (loop1 "tan" zcirc_large_imag)
(loop1 "arcsin" z0)
(loop1 "arccos" z0)
@@ -270,6 +273,7 @@
(loop1 "sinh" zicirc)
(loop1 "cosh" zicirc)
(loop1 "tanh" zicirc)
+ (loop1 "tanh" zicirc_large_real)
(loop1 "arcsinh" z0)
(loop1 "arccosh" z0)
@@ -278,6 +282,7 @@
(loop1 "csc" zcirc)
(loop1 "sec" zcirc)
(loop1 "cot" zcirc)
+ (loop1 "cot" zcirc_large_imag)
(loop1 "arccsc" z0)
(loop1 "arcsec" z0)
@@ -286,6 +291,7 @@
(loop1 "csch" zicirc)
(loop1 "sech" zicirc)
(loop1 "coth" zicirc)
+ (loop1 "coth" zicirc_large_real)
(loop1 "arccsch" z0)
(loop1 "arcsech" z0)
