Fix ctan, ctanh overflow (bug 11521).

11 files changed, 403 insertions, 97 deletions

diff --git a/ChangeLog b/ChangeLog
index 109b6a100a..3686491a2d 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,19 @@
+2012-04-09  Joseph Myers  <joseph@codesourcery.com>
+
+	[BZ #11521]
+	* math/s_ctan.c: Include <float.h>.
+	(__ctan): Avoid internal overflow or cancellation in calculating
+	denominator.
+	* math/s_ctanf.c: Likewise.
+	* math/s_ctanl.c: Likewise.
+	* math/s_ctanh.c: Likewise.
+	* math/s_ctanhf.c: Likewise.
+	* math/s_ctanhl.c: Likewise.
+	* math/libm-test.inc (ctan_test): Add more tests.
+	(ctanh_test): Likewise.
+	* sysdeps/i386/fpu/libm-test-ulps: Update.
+	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
+
 2012-04-09  Andreas Jaeger  <aj@suse.de>
 
 	[BZ #6894]
diff --git a/NEWS b/NEWS
index 2636c22864..bb303f8b93 100644
--- a/NEWS
+++ b/NEWS
@@ -14,13 +14,13 @@ Version 2.16
   4596, 4822, 5077, 5461, 5805, 5993, 6471, 6486, 6578, 6649, 6730, 6770,
   6884, 6890, 6894, 6895, 6907, 6911, 9739, 9902, 10110, 10135, 10140,
   10153, 10210, 10254, 10346, 10545, 10716, 11174, 11322, 11365, 11451,
-  11494, 12047, 12340, 13058, 13525, 13526, 13527, 13528, 13529, 13530,
-  13531, 13532, 13533, 13547, 13551, 13552, 13553, 13555, 13559, 13566,
-  13583, 13592, 13618, 13637, 13656, 13658, 13673, 13691, 13695, 13704,
-  13705, 13706, 13726, 13738, 13760, 13761, 13786, 13792, 13806, 13824,
-  13840, 13841, 13844, 13846, 13851, 13852, 13854, 13871, 13873, 13879,
-  13883, 13892, 13895, 13908, 13910, 13911, 13912, 13913, 13915, 13916,
-  13917, 13918, 13919, 13920, 13921, 13926, 13928, 13938, 13963
+  11494, 11521, 12047, 12340, 13058, 13525, 13526, 13527, 13528, 13529,
+  13530, 13531, 13532, 13533, 13547, 13551, 13552, 13553, 13555, 13559,
+  13566, 13583, 13592, 13618, 13637, 13656, 13658, 13673, 13691, 13695,
+  13704, 13705, 13706, 13726, 13738, 13760, 13761, 13786, 13792, 13806,
+  13824, 13840, 13841, 13844, 13846, 13851, 13852, 13854, 13871, 13873,
+  13879, 13883, 13892, 13895, 13908, 13910, 13911, 13912, 13913, 13915,
+  13916, 13917, 13918, 13919, 13920, 13921, 13926, 13928, 13938, 13963
 
 * ISO C11 support:
 
diff --git a/math/libm-test.inc b/math/libm-test.inc
index 0533483749..a551b9f3f4 100644
--- a/math/libm-test.inc
+++ b/math/libm-test.inc
@@ -2840,6 +2840,36 @@ ctan_test (void)
   TEST_c_c (ctan, 0.75L, 1.25L, 0.160807785916206426725166058173438663L, 0.975363285031235646193581759755216379L);
   TEST_c_c (ctan, -2, -3, 0.376402564150424829275122113032269084e-2L, -1.00323862735360980144635859782192726L);
 
+  TEST_c_c (ctan, 1, 45, 1.490158918874345552942703234806348520895e-39L, 1.000000000000000000000000000000000000001L);
+  TEST_c_c (ctan, 1, 47, 2.729321264492904590777293425576722354636e-41L, 1.0);
+
+#ifndef TEST_FLOAT
+  TEST_c_c (ctan, 1, 355, 8.140551093483276762350406321792653551513e-309L, 1.0);
+  TEST_c_c (ctan, 1, 365, 1.677892637497921890115075995898773550884e-317L, 1.0);
+#endif
+
+#if defined TEST_LDOUBLE && LDBL_MAX_EXP >= 16384
+  TEST_c_c (ctan, 1, 5680, 4.725214596136812019616700920476949798307e-4934L, 1.0);
+  TEST_c_c (ctan, 1, 5690, 9.739393181626937151720816611272607059057e-4943L, 1.0);
+#endif
+
+  TEST_c_c (ctan, 0x3.243f6cp-1, 0, -2.287733242885645987394874673945769518150e7L, 0.0);
+
+  TEST_c_c (ctan, 0x1p127, 1, 0.2446359391192790896381501310437708987204L, 0.9101334047676183761532873794426475906201L);
+
+#ifndef TEST_FLOAT
+  TEST_c_c (ctan, 0x1p1023, 1, -0.2254627924997545057926782581695274244229L, 0.8786063118883068695462540226219865087189L);
+#endif
+
+#if defined TEST_LDOUBLE && LDBL_MAX_EXP >= 16384
+  TEST_c_c (ctan, 0x1p16383L, 1, 0.1608598776370396607204448234354670036772L, 0.8133818522051542536316746743877629761488L);
+#endif
+
+  TEST_c_c (ctan, 50000, 50000, plus_zero, 1.0);
+  TEST_c_c (ctan, 50000, -50000, plus_zero, -1.0);
+  TEST_c_c (ctan, -50000, 50000, minus_zero, 1.0);
+  TEST_c_c (ctan, -50000, -50000, minus_zero, -1.0);
+
   END (ctan, complex);
 }
 
@@ -2899,6 +2929,36 @@ ctanh_test (void)
   TEST_c_c (ctanh, 0.75L, 1.25L, 1.37260757053378320258048606571226857L, 0.385795952609750664177596760720790220L);
   TEST_c_c (ctanh, -2, -3, -0.965385879022133124278480269394560686L, 0.988437503832249372031403430350121098e-2L);
 
+  TEST_c_c (ctanh, 45, 1, 1.000000000000000000000000000000000000001L, 1.490158918874345552942703234806348520895e-39L);
+  TEST_c_c (ctanh, 47, 1, 1.0, 2.729321264492904590777293425576722354636e-41L);
+
+#ifndef TEST_FLOAT
+  TEST_c_c (ctanh, 355, 1, 1.0, 8.140551093483276762350406321792653551513e-309L);
+  TEST_c_c (ctanh, 365, 1, 1.0, 1.677892637497921890115075995898773550884e-317L);
+#endif
+
+#if defined TEST_LDOUBLE && LDBL_MAX_EXP >= 16384
+  TEST_c_c (ctanh, 5680, 1, 1.0, 4.725214596136812019616700920476949798307e-4934L);
+  TEST_c_c (ctanh, 5690, 1, 1.0, 9.739393181626937151720816611272607059057e-4943L);
+#endif
+
+  TEST_c_c (ctanh, 0, 0x3.243f6cp-1, 0.0, -2.287733242885645987394874673945769518150e7L);
+
+  TEST_c_c (ctanh, 1, 0x1p127, 0.9101334047676183761532873794426475906201L, 0.2446359391192790896381501310437708987204L);
+
+#ifndef TEST_FLOAT
+  TEST_c_c (ctanh, 1, 0x1p1023, 0.8786063118883068695462540226219865087189L, -0.2254627924997545057926782581695274244229L);
+#endif
+
+#if defined TEST_LDOUBLE && LDBL_MAX_EXP >= 16384
+  TEST_c_c (ctanh, 1, 0x1p16383L, 0.8133818522051542536316746743877629761488L, 0.1608598776370396607204448234354670036772L);
+#endif
+
+  TEST_c_c (ctanh, 50000, 50000, 1.0, plus_zero);
+  TEST_c_c (ctanh, 50000, -50000, 1.0, minus_zero);
+  TEST_c_c (ctanh, -50000, 50000, -1.0, plus_zero);
+  TEST_c_c (ctanh, -50000, -50000, -1.0, minus_zero);
+
   END (ctanh, complex);
 }
 
diff --git a/math/s_ctan.c b/math/s_ctan.c
index c838fadebb..78117b3103 100644
--- a/math/s_ctan.c
+++ b/math/s_ctan.c
@@ -1,5 +1,5 @@
 /* Complex tangent function for double.
-   Copyright (C) 1997, 2005, 2011 Free Software Foundation, Inc.
+   Copyright (C) 1997-2012 Free Software Foundation, Inc.
    This file is part of the GNU C Library.
    Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
 
@@ -20,9 +20,8 @@
 #include <complex.h>
 #include <fenv.h>
 #include <math.h>
-
 #include <math_private.h>
-
+#include <float.h>
 
 __complex__ double
 __ctan (__complex__ double x)
@@ -51,24 +50,45 @@ __ctan (__complex__ double x)
     }
   else
     {
-      double sin2rx, cos2rx;
+      double sinrx, cosrx;
       double den;
+      const int t = (int) ((DBL_MAX_EXP - 1) * M_LN2 / 2);
 
-      __sincos (2.0 * __real__ x, &sin2rx, &cos2rx);
+      /* tan(x+iy) = (sin(2x) + i*sinh(2y))/(cos(2x) + cosh(2y))
+	 = (sin(x)*cos(x) + i*sinh(y)*cosh(y)/(cos(x)^2 + sinh(y)^2). */
 
-      den = cos2rx + __ieee754_cosh (2.0 * __imag__ x);
+      __sincos (__real__ x, &sinrx, &cosrx);
 
-      if (den == 0.0)
+      if (fabs (__imag__ x) > t)
 	{
-	  __complex__ double ez = __cexp (1.0i * x);
-	  __complex__ double emz = __cexp (-1.0i * x);
+	  /* Avoid intermediate overflow when the real part of the
+	     result may be subnormal.  Ignoring negligible terms, the
+	     imaginary part is +/- 1, the real part is
+	     sin(x)*cos(x)/sinh(y)^2 = 4*sin(x)*cos(x)/exp(2y).  */
+	  double exp_2t = __ieee754_exp (2 * t);
 
-	  res = (ez - emz) / (ez + emz) * -1.0i;
+	  __imag__ res = __copysign (1.0, __imag__ x);
+	  __real__ res = 4 * sinrx * cosrx;
+	  __imag__ x = fabs (__imag__ x);
+	  __imag__ x -= t;
+	  __real__ res /= exp_2t;
+	  if (__imag__ x > t)
+	    {
+	      /* Underflow (original imaginary part of x has absolute
+		 value > 2t).  */
+	      __real__ res /= exp_2t;
+	    }
+	  else
+	    __real__ res /= __ieee754_exp (2 * __imag__ x);
 	}
       else
 	{
-	  __real__ res = sin2rx / den;
-	  __imag__ res = __ieee754_sinh (2.0 * __imag__ x) / den;
+	  double sinhix = __ieee754_sinh (__imag__ x);
+	  double coshix = __ieee754_cosh (__imag__ x);
+
+	  den = cosrx * cosrx + sinhix * sinhix;
+	  __real__ res = sinrx * cosrx / den;
+	  __imag__ res = sinhix * coshix / den;
 	}
     }
 
diff --git a/math/s_ctanf.c b/math/s_ctanf.c
index 5f7f28ad07..4cba559a44 100644
--- a/math/s_ctanf.c
+++ b/math/s_ctanf.c
@@ -1,5 +1,5 @@
 /* Complex tangent function for float.
-   Copyright (C) 1997, 2005, 2011 Free Software Foundation, Inc.
+   Copyright (C) 1997-2012 Free Software Foundation, Inc.
    This file is part of the GNU C Library.
    Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
 
@@ -21,7 +21,7 @@
 #include <fenv.h>
 #include <math.h>
 #include <math_private.h>
-
+#include <float.h>
 
 __complex__ float
 __ctanf (__complex__ float x)
@@ -50,25 +50,45 @@ __ctanf (__complex__ float x)
     }
   else
     {
-      float sin2rx, cos2rx;
+      float sinrx, cosrx;
       float den;
+      const int t = (int) ((FLT_MAX_EXP - 1) * M_LN2 / 2);
 
-      __sincosf (2.0 * __real__ x, &sin2rx, &cos2rx);
-
-      den = cos2rx + __ieee754_coshf (2.0 * __imag__ x);
+      /* tan(x+iy) = (sin(2x) + i*sinh(2y))/(cos(2x) + cosh(2y))
+	 = (sin(x)*cos(x) + i*sinh(y)*cosh(y)/(cos(x)^2 + sinh(y)^2). */
 
+      __sincosf (__real__ x, &sinrx, &cosrx);
 
-      if (den == 0.0)
+      if (fabsf (__imag__ x) > t)
 	{
-	  __complex__ float ez = __cexpf (1.0i * x);
-	  __complex__ float emz = __cexpf (-1.0i * x);
+	  /* Avoid intermediate overflow when the real part of the
+	     result may be subnormal.  Ignoring negligible terms, the
+	     imaginary part is +/- 1, the real part is
+	     sin(x)*cos(x)/sinh(y)^2 = 4*sin(x)*cos(x)/exp(2y).  */
+	  float exp_2t = __ieee754_expf (2 * t);
 
-	  res = (ez - emz) / (ez + emz) * -1.0i;
+	  __imag__ res = __copysignf (1.0, __imag__ x);
+	  __real__ res = 4 * sinrx * cosrx;
+	  __imag__ x = fabsf (__imag__ x);
+	  __imag__ x -= t;
+	  __real__ res /= exp_2t;
+	  if (__imag__ x > t)
+	    {
+	      /* Underflow (original imaginary part of x has absolute
+		 value > 2t).  */
+	      __real__ res /= exp_2t;
+	    }
+	  else
+	    __real__ res /= __ieee754_expf (2 * __imag__ x);
 	}
       else
 	{
-	  __real__ res = sin2rx / den;
-	  __imag__ res = __ieee754_sinhf (2.0 * __imag__ x) / den;
+	  float sinhix = __ieee754_sinhf (__imag__ x);
+	  float coshix = __ieee754_coshf (__imag__ x);
+
+	  den = cosrx * cosrx + sinhix * sinhix;
+	  __real__ res = sinrx * cosrx / den;
+	  __imag__ res = sinhix * coshix / den;
 	}
     }
 
diff --git a/math/s_ctanh.c b/math/s_ctanh.c
index 9cecb8bdb7..201871e7ec 100644
--- a/math/s_ctanh.c
+++ b/math/s_ctanh.c
@@ -1,5 +1,5 @@
 /* Complex hyperbole tangent for double.
-   Copyright (C) 1997, 2005, 2011 Free Software Foundation, Inc.
+   Copyright (C) 1997-2012 Free Software Foundation, Inc.
    This file is part of the GNU C Library.
    Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
 
@@ -21,7 +21,7 @@
 #include <fenv.h>
 #include <math.h>
 #include <math_private.h>
-
+#include <float.h>
 
 __complex__ double
 __ctanh (__complex__ double x)
@@ -50,24 +50,45 @@ __ctanh (__complex__ double x)
     }
   else
     {
-      double sin2ix, cos2ix;
+      double sinix, cosix;
       double den;
+      const int t = (int) ((DBL_MAX_EXP - 1) * M_LN2 / 2);
 
-      __sincos (2.0 * __imag__ x, &sin2ix, &cos2ix);
+      /* tanh(x+iy) = (sinh(2x) + i*sin(2y))/(cosh(2x) + cos(2y))
+	 = (sinh(x)*cosh(x) + i*sin(y)*cos(y))/(sinh(x)^2 + cos(y)^2).  */
 
-      den = (__ieee754_cosh (2.0 * __real__ x) + cos2ix);
+      __sincos (__imag__ x, &sinix, &cosix);
 
-      if (den == 0.0)
+      if (fabs (__real__ x) > t)
 	{
-	  __complex__ double ez = __cexp (x);
-	  __complex__ double emz = __cexp (-x);
+	  /* Avoid intermediate overflow when the imaginary part of
+	     the result may be subnormal.  Ignoring negligible terms,
+	     the real part is +/- 1, the imaginary part is
+	     sin(y)*cos(y)/sinh(x)^2 = 4*sin(y)*cos(y)/exp(2x).  */
+	  double exp_2t = __ieee754_exp (2 * t);
 
-	  res = (ez - emz) / (ez + emz);
+	  __real__ res = __copysign (1.0, __real__ x);
+	  __imag__ res = 4 * sinix * cosix;
+	  __real__ x = fabs (__real__ x);
+	  __real__ x -= t;
+	  __imag__ res /= exp_2t;
+	  if (__real__ x > t)
+	    {
+	      /* Underflow (original real part of x has absolute value
+		 > 2t).  */
+	      __imag__ res /= exp_2t;
+	    }
+	  else
+	    __imag__ res /= __ieee754_exp (2 * __real__ x);
 	}
       else
 	{
-	  __real__ res = __ieee754_sinh (2.0 * __real__ x) / den;
-	  __imag__ res = sin2ix / den;
+	  double sinhrx = __ieee754_sinh (__real__ x);
+	  double coshrx = __ieee754_cosh (__real__ x);
+
+	  den = sinhrx * sinhrx + cosix * cosix;
+	  __real__ res = sinhrx * coshrx / den;
+	  __imag__ res = sinix * cosix / den;
 	}
     }
 
diff --git a/math/s_ctanhf.c b/math/s_ctanhf.c
index fce5aaf290..e505155774 100644
--- a/math/s_ctanhf.c
+++ b/math/s_ctanhf.c
@@ -1,5 +1,5 @@
 /* Complex hyperbole tangent for float.
-   Copyright (C) 1997, 2005, 2011 Free Software Foundation, Inc.
+   Copyright (C) 1997-2012 Free Software Foundation, Inc.
    This file is part of the GNU C Library.
    Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
 
@@ -21,7 +21,7 @@
 #include <fenv.h>
 #include <math.h>
 #include <math_private.h>
-
+#include <float.h>
 
 __complex__ float
 __ctanhf (__complex__ float x)
@@ -50,24 +50,45 @@ __ctanhf (__complex__ float x)
     }
   else
     {
-      float sin2ix, cos2ix;
+      float sinix, cosix;
       float den;
+      const int t = (int) ((FLT_MAX_EXP - 1) * M_LN2 / 2);
 
-      __sincosf (2.0 * __imag__ x, &sin2ix, &cos2ix);
+      /* tanh(x+iy) = (sinh(2x) + i*sin(2y))/(cosh(2x) + cos(2y))
+	 = (sinh(x)*cosh(x) + i*sin(y)*cos(y))/(sinh(x)^2 + cos(y)^2).  */
 
-      den = (__ieee754_coshf (2.0 * __real__ x) + cos2ix);
+      __sincosf (__imag__ x, &sinix, &cosix);
 
-      if (den == 0.0f)
+      if (fabsf (__real__ x) > t)
 	{
-	  __complex__ float ez = __cexpf (x);
-	  __complex__ float emz = __cexpf (-x);
+	  /* Avoid intermediate overflow when the imaginary part of
+	     the result may be subnormal.  Ignoring negligible terms,
+	     the real part is +/- 1, the imaginary part is
+	     sin(y)*cos(y)/sinh(x)^2 = 4*sin(y)*cos(y)/exp(2x).  */
+	  float exp_2t = __ieee754_expf (2 * t);
 
-	  res = (ez - emz) / (ez + emz);
+	  __real__ res = __copysignf (1.0, __real__ x);
+	  __imag__ res = 4 * sinix * cosix;
+	  __real__ x = fabsf (__real__ x);
+	  __real__ x -= t;
+	  __imag__ res /= exp_2t;
+	  if (__real__ x > t)
+	    {
+	      /* Underflow (original real part of x has absolute value
+		 > 2t).  */
+	      __imag__ res /= exp_2t;
+	    }
+	  else
+	    __imag__ res /= __ieee754_expf (2 * __real__ x);
 	}
       else
 	{
-	  __real__ res = __ieee754_sinhf (2.0 * __real__ x) / den;
-	  __imag__ res = sin2ix / den;
+	  float sinhrx = __ieee754_sinhf (__real__ x);
+	  float coshrx = __ieee754_coshf (__real__ x);
+
+	  den = sinhrx * sinhrx + cosix * cosix;
+	  __real__ res = sinhrx * coshrx / den;
+	  __imag__ res = sinix * cosix / den;
 	}
     }
 
diff --git a/math/s_ctanhl.c b/math/s_ctanhl.c
index d22e13a975..e5d677903f 100644
--- a/math/s_ctanhl.c
+++ b/math/s_ctanhl.c
@@ -1,5 +1,5 @@
 /* Complex hyperbole tangent for long double.
-   Copyright (C) 1997, 2005, 2011 Free Software Foundation, Inc.
+   Copyright (C) 1997-2012 Free Software Foundation, Inc.
    This file is part of the GNU C Library.
    Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
 
@@ -21,7 +21,7 @@
 #include <fenv.h>
 #include <math.h>
 #include <math_private.h>
-
+#include <float.h>
 
 __complex__ long double
 __ctanhl (__complex__ long double x)
@@ -50,24 +50,45 @@ __ctanhl (__complex__ long double x)
     }
   else
     {
-      long double sin2ix, cos2ix;
+      long double sinix, cosix;
       long double den;
+      const int t = (int) ((LDBL_MAX_EXP - 1) * M_LN2l / 2);
 
-      __sincosl (2.0 * __imag__ x, &sin2ix, &cos2ix);
+      /* tanh(x+iy) = (sinh(2x) + i*sin(2y))/(cosh(2x) + cos(2y))
+	 = (sinh(x)*cosh(x) + i*sin(y)*cos(y))/(sinh(x)^2 + cos(y)^2).  */
 
-      den = (__ieee754_coshl (2.0 * __real__ x) + cos2ix);
+      __sincosl (__imag__ x, &sinix, &cosix);
 
-      if (den == 0.0L)
+      if (fabsl (__real__ x) > t)
 	{
-	  __complex__ long double ez = __cexpl (x);
-	  __complex__ long double emz = __cexpl (-x);
+	  /* Avoid intermediate overflow when the imaginary part of
+	     the result may be subnormal.  Ignoring negligible terms,
+	     the real part is +/- 1, the imaginary part is
+	     sin(y)*cos(y)/sinh(x)^2 = 4*sin(y)*cos(y)/exp(2x).  */
+	  long double exp_2t = __ieee754_expl (2 * t);
 
-	  res = (ez - emz) / (ez + emz);
+	  __real__ res = __copysignl (1.0, __real__ x);
+	  __imag__ res = 4 * sinix * cosix;
+	  __real__ x = fabsl (__real__ x);
+	  __real__ x -= t;
+	  __imag__ res /= exp_2t;
+	  if (__real__ x > t)
+	    {
+	      /* Underflow (original real part of x has absolute value
+		 > 2t).  */
+	      __imag__ res /= exp_2t;
+	    }
+	  else
+	    __imag__ res /= __ieee754_expl (2 * __real__ x);
 	}
       else
 	{
-	  __real__ res = __ieee754_sinhl (2.0 * __real__ x) / den;
-	  __imag__ res = sin2ix / den;
+	  long double sinhrx = __ieee754_sinhl (__real__ x);
+	  long double coshrx = __ieee754_coshl (__real__ x);
+
+	  den = sinhrx * sinhrx + cosix * cosix;
+	  __real__ res = sinhrx * coshrx / den;
+	  __imag__ res = sinix * cosix / den;
 	}
     }
 
diff --git a/math/s_ctanl.c b/math/s_ctanl.c
index 112dd723d8..12d700cad9 100644
--- a/math/s_ctanl.c
+++ b/math/s_ctanl.c
@@ -1,5 +1,5 @@
 /* Complex tangent function for long double.
-   Copyright (C) 1997, 2005, 2011 Free Software Foundation, Inc.
+   Copyright (C) 1997-2012 Free Software Foundation, Inc.
    This file is part of the GNU C Library.
    Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
 
@@ -20,9 +20,8 @@
 #include <complex.h>
 #include <fenv.h>
 #include <math.h>
-
 #include <math_private.h>
-
+#include <float.h>
 
 __complex__ long double
 __ctanl (__complex__ long double x)
@@ -51,25 +50,45 @@ __ctanl (__complex__ long double x)
     }
   else
     {
-      long double sin2rx, cos2rx;
+      long double sinrx, cosrx;
       long double den;
+      const int t = (int) ((LDBL_MAX_EXP - 1) * M_LN2l / 2);
 
-      __sincosl (2.0 * __real__ x, &sin2rx, &cos2rx);
-
-      den = cos2rx + __ieee754_coshl (2.0 * __imag__ x);
+      /* tan(x+iy) = (sin(2x) + i*sinh(2y))/(cos(2x) + cosh(2y))
+	 = (sin(x)*cos(x) + i*sinh(y)*cosh(y)/(cos(x)^2 + sinh(y)^2). */
 
+      __sincosl (__real__ x, &sinrx, &cosrx);
 
-      if (den == 0.0)
+      if (fabsl (__imag__ x) > t)
 	{
-	  __complex__ long double ez = __cexpl (1.0i * x);
-	  __complex__ long double emz = __cexpl (-1.0i * x);
+	  /* Avoid intermediate overflow when the real part of the
+	     result may be subnormal.  Ignoring negligible terms, the
+	     imaginary part is +/- 1, the real part is
+	     sin(x)*cos(x)/sinh(y)^2 = 4*sin(x)*cos(x)/exp(2y).  */
+	  long double exp_2t = __ieee754_expl (2 * t);
 
-	  res = (ez - emz) / (ez + emz) * -1.0i;
+	  __imag__ res = __copysignl (1.0, __imag__ x);
+	  __real__ res = 4 * sinrx * cosrx;
+	  __imag__ x = fabsl (__imag__ x);
+	  __imag__ x -= t;
+	  __real__ res /= exp_2t;
+	  if (__imag__ x > t)
+	    {
+	      /* Underflow (original imaginary part of x has absolute
+		 value > 2t).  */
+	      __real__ res /= exp_2t;
+	    }
+	  else
+	    __real__ res /= __ieee754_expl (2 * __imag__ x);
 	}
       else
 	{
-	  __real__ res = sin2rx / den;
-	  __imag__ res = __ieee754_sinhl (2.0 * __imag__ x) / den;
+	  long double sinhix = __ieee754_sinhl (__imag__ x);
+	  long double coshix = __ieee754_coshl (__imag__ x);
+
+	  den = cosrx * cosrx + sinhix * sinhix;
+	  __real__ res = sinrx * cosrx / den;
+	  __imag__ res = sinhix * coshix / den;
 	}
     }
 
diff --git a/sysdeps/i386/fpu/libm-test-ulps b/sysdeps/i386/fpu/libm-test-ulps
index 1c791405ab..c3a3ce0da2 100644
--- a/sysdeps/i386/fpu/libm-test-ulps
+++ b/sysdeps/i386/fpu/libm-test-ulps
@@ -1009,9 +1009,33 @@ idouble: 1
 ifloat: 1
 ildouble: 3
 ldouble: 3
+Test "Real part of: ctan (0x1p1023 + 1 i) == -0.2254627924997545057926782581695274244229 + 0.8786063118883068695462540226219865087189 i":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: ctan (0x1p1023 + 1 i) == -0.2254627924997545057926782581695274244229 + 0.8786063118883068695462540226219865087189 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: ctan (0x1p127 + 1 i) == 0.2446359391192790896381501310437708987204 + 0.9101334047676183761532873794426475906201 i":
+float: 1
+ifloat: 1
+Test "Real part of: ctan (0x3.243f6cp-1 + 0 i) == -2.287733242885645987394874673945769518150e7 + 0.0 i":
+float: 1
+ifloat: 1
+Test "Real part of: ctan (1 + 45 i) == 1.490158918874345552942703234806348520895e-39 + 1.000000000000000000000000000000000000001 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: ctan (1 + 47 i) == 2.729321264492904590777293425576722354636e-41 + 1.0 i":
+double: 1
+idouble: 1
+ildouble: 2
+ldouble: 2
 
 # ctanh
 Test "Real part of: ctanh (-2 - 3 i) == -0.965385879022133124278480269394560686 + 0.988437503832249372031403430350121098e-2 i":
+float: 1
+ifloat: 1
 ildouble: 3
 ldouble: 3
 Test "Imaginary part of: ctanh (-2 - 3 i) == -0.965385879022133124278480269394560686 + 0.988437503832249372031403430350121098e-2 i":
@@ -1019,9 +1043,14 @@ float: 1
 ifloat: 1
 ildouble: 1
 ldouble: 1
+Test "Imaginary part of: ctanh (0 + 0x3.243f6cp-1 i) == 0.0 - 2.287733242885645987394874673945769518150e7 i":
+float: 1
+ifloat: 1
 Test "Imaginary part of: ctanh (0 + pi/4 i) == 0.0 + 1.0 i":
 float: 1
 ifloat: 1
+ildouble: 1
+ldouble: 1
 Test "Real part of: ctanh (0.75 + 1.25 i) == 1.37260757053378320258048606571226857 + 0.385795952609750664177596760720790220 i":
 double: 1
 float: 1
@@ -1034,6 +1063,25 @@ idouble: 1
 ifloat: 1
 ildouble: 1
 ldouble: 1
+Test "Real part of: ctanh (1 + 0x1p1023 i) == 0.8786063118883068695462540226219865087189 - 0.2254627924997545057926782581695274244229 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: ctanh (1 + 0x1p1023 i) == 0.8786063118883068695462540226219865087189 - 0.2254627924997545057926782581695274244229 i":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: ctanh (1 + 0x1p127 i) == 0.9101334047676183761532873794426475906201 + 0.2446359391192790896381501310437708987204 i":
+float: 1
+ifloat: 1
+Test "Imaginary part of: ctanh (45 + 1 i) == 1.000000000000000000000000000000000000001 + 1.490158918874345552942703234806348520895e-39 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: ctanh (47 + 1 i) == 1.0 + 2.729321264492904590777293425576722354636e-41 i":
+double: 1
+idouble: 1
+ildouble: 2
+ldouble: 2
 
 # erf
 Test "erf (1.25) == 0.922900128256458230136523481197281140":
@@ -2342,33 +2390,35 @@ ldouble: 1
 
 Function: Real part of "ctan":
 double: 1
+float: 1
 idouble: 1
-ildouble: 1
-ldouble: 1
+ifloat: 1
+ildouble: 2
+ldouble: 2
 
 Function: Imaginary part of "ctan":
 double: 1
 float: 1
 idouble: 1
 ifloat: 1
-ildouble: 3
-ldouble: 3
+ildouble: 1
+ldouble: 1
 
 Function: Real part of "ctanh":
 double: 1
 float: 1
 idouble: 1
 ifloat: 1
-ildouble: 3
-ldouble: 3
+ildouble: 1
+ldouble: 1
 
 Function: Imaginary part of "ctanh":
 double: 1
 float: 1
 idouble: 1
 ifloat: 1
-ildouble: 1
-ldouble: 1
+ildouble: 2
+ldouble: 2
 
 Function: "erf":
 double: 1
diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps
index dce60cfb5b..46d858f298 100644
--- a/sysdeps/x86_64/fpu/libm-test-ulps
+++ b/sysdeps/x86_64/fpu/libm-test-ulps
@@ -1011,11 +1011,15 @@ ldouble: 1
 # ctan
 Test "Real part of: ctan (-2 - 3 i) == 0.376402564150424829275122113032269084e-2 - 1.00323862735360980144635859782192726 i":
 double: 1
+float: 1
 idouble: 1
+ifloat: 1
 ildouble: 1
 ldouble: 1
 Test "Imaginary part of: ctan (-2 - 3 i) == 0.376402564150424829275122113032269084e-2 - 1.00323862735360980144635859782192726 i":
+double: 1
 float: 1
+idouble: 1
 ifloat: 1
 ildouble: 2
 ldouble: 2
@@ -1029,6 +1033,26 @@ idouble: 1
 ifloat: 1
 ildouble: 3
 ldouble: 3
+Test "Real part of: ctan (0x1p1023 + 1 i) == -0.2254627924997545057926782581695274244229 + 0.8786063118883068695462540226219865087189 i":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: ctan (0x1p1023 + 1 i) == -0.2254627924997545057926782581695274244229 + 0.8786063118883068695462540226219865087189 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: ctan (0x1p127 + 1 i) == 0.2446359391192790896381501310437708987204 + 0.9101334047676183761532873794426475906201 i":
+double: 1
+idouble: 1
+Test "Real part of: ctan (0x3.243f6cp-1 + 0 i) == -2.287733242885645987394874673945769518150e7 + 0.0 i":
+float: 1
+ifloat: 1
+Test "Real part of: ctan (1 + 45 i) == 1.490158918874345552942703234806348520895e-39 + 1.000000000000000000000000000000000000001 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: ctan (1 + 47 i) == 2.729321264492904590777293425576722354636e-41 + 1.0 i":
+ildouble: 2
+ldouble: 2
 
 # ctanh
 Test "Real part of: ctanh (-2 - 3 i) == -0.965385879022133124278480269394560686 + 0.988437503832249372031403430350121098e-2 i":
@@ -1039,19 +1063,51 @@ ifloat: 2
 ildouble: 3
 ldouble: 3
 Test "Imaginary part of: ctanh (-2 - 3 i) == -0.965385879022133124278480269394560686 + 0.988437503832249372031403430350121098e-2 i":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
 ildouble: 1
 ldouble: 1
+Test "Imaginary part of: ctanh (0 + 0x3.243f6cp-1 i) == 0.0 - 2.287733242885645987394874673945769518150e7 i":
+float: 1
+ifloat: 1
 Test "Imaginary part of: ctanh (0 + pi/4 i) == 0.0 + 1.0 i":
+double: 1
 float: 1
+idouble: 1
 ifloat: 1
+ildouble: 1
+ldouble: 1
 Test "Real part of: ctanh (0.75 + 1.25 i) == 1.37260757053378320258048606571226857 + 0.385795952609750664177596760720790220 i":
 double: 1
+float: 1
 idouble: 1
+ifloat: 1
 Test "Imaginary part of: ctanh (0.75 + 1.25 i) == 1.37260757053378320258048606571226857 + 0.385795952609750664177596760720790220 i":
 double: 1
+float: 2
+idouble: 1
+ifloat: 2
+ildouble: 1
+ldouble: 1
+Test "Real part of: ctanh (1 + 0x1p1023 i) == 0.8786063118883068695462540226219865087189 - 0.2254627924997545057926782581695274244229 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: ctanh (1 + 0x1p1023 i) == 0.8786063118883068695462540226219865087189 - 0.2254627924997545057926782581695274244229 i":
+double: 1
 idouble: 1
 ildouble: 1
 ldouble: 1
+Test "Real part of: ctanh (1 + 0x1p127 i) == 0.9101334047676183761532873794426475906201 + 0.2446359391192790896381501310437708987204 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: ctanh (45 + 1 i) == 1.000000000000000000000000000000000000001 + 1.490158918874345552942703234806348520895e-39 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: ctanh (47 + 1 i) == 1.0 + 2.729321264492904590777293425576722354636e-41 i":
+ildouble: 2
+ldouble: 2
 
 # erf
 Test "erf (1.25) == 0.922900128256458230136523481197281140":
@@ -2300,34 +2356,36 @@ ldouble: 1
 
 Function: Real part of "ctan":
 double: 1
+float: 1
 idouble: 1
-ildouble: 1
-ldouble: 1
+ifloat: 1
+ildouble: 2
+ldouble: 2
 
 Function: Imaginary part of "ctan":
 double: 1
 float: 1
 idouble: 1
 ifloat: 1
-ildouble: 3
-ldouble: 3
+ildouble: 1
+ldouble: 1
 
 Function: Real part of "ctanh":
 double: 1
-float: 2
-idouble: 1
-ifloat: 2
-ildouble: 3
-ldouble: 3
-
-Function: Imaginary part of "ctanh":
-double: 1
 float: 1
 idouble: 1
 ifloat: 1
 ildouble: 1
 ldouble: 1
 
+Function: Imaginary part of "ctanh":
+double: 1
+float: 2
+idouble: 1
+ifloat: 2
+ildouble: 2
+ldouble: 2
+
 Function: "erf":
 double: 1
 idouble: 1