=== 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)