Fix ctan, ctanh of subnormals in round-upwards mode (bug 14328).

11 files changed, 937 insertions, 19 deletions

diff --git a/ChangeLog b/ChangeLog
index dd5b5df..e23a9ac 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,25 @@
+2012-07-04  Joseph Myers  <joseph@codesourcery.com>
+
+	[BZ #14328]
+	* math/s_ctan.c (__ctan): Do not call sinh and cosh for subnormals
+	or multiply small sinh result by itself.
+	* math/s_ctanf.c (__ctanf): Likewise.
+	* math/s_ctanh.c (__ctanh): Likewise.
+	* math/s_ctanhf.c (__ctanhf): Likewise.
+	* math/s_ctanhl.c (__ctanhl): Likewise.
+	* math/s_ctanl.c (__ctanl): Likewise.
+	* math/libm-test.inc (ctan_test_tonearest): New function.
+	(ctan_test_towardzero): Likewise.
+	(ctan_test_downward): Likewise.
+	(ctan_test_upward): Likewise.
+	(ctanh_test_tonearest): Likewise.
+	(ctanh_test_towardzero): Likewise.
+	(ctanh_test_downward): Likewise.
+	(ctanh_test_upward): Likewise.
+	(main): Call these new functions.
+	* sysdeps/i386/fpu/libm-test-ulps: Update.
+	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
+
 2012-07-03  Mike Frysinger  <vapier@gentoo.org>
 
 	* .gitignore: Delete /ports entry.
diff --git a/NEWS b/NEWS
index a24c3fb..e49e4ea 100644
--- a/NEWS
+++ b/NEWS
@@ -9,7 +9,7 @@ Version 2.17
 
 * The following bugs are resolved with this release:
 
-  14283
+  14283, 14328
 
 
 Version 2.16
diff --git a/math/libm-test.inc b/math/libm-test.inc
index 3e33348..514ad06 100644
--- a/math/libm-test.inc
+++ b/math/libm-test.inc
@@ -3319,6 +3319,138 @@ ctan_test (void)
 
 
 static void
+ctan_test_tonearest (void)
+{
+  int save_round_mode;
+  errno = 0;
+  FUNC(ctan) (BUILD_COMPLEX (0.7L, 1.2L));
+  if (errno == ENOSYS)
+    /* Function not implemented.  */
+    return;
+
+  START (ctan_tonearest);
+
+  save_round_mode = fegetround ();
+
+  if (!fesetround (FE_TONEAREST))
+    {
+      TEST_c_c (ctan, 0x1.921fb6p+0, 0x1p-149, -2.287733242885645987394874673945769518150e7L, 7.334008549954377778731880988481078535821e-31L);
+
+#ifndef TEST_FLOAT
+      TEST_c_c (ctan, 0x1.921fb54442d18p+0, 0x1p-1074, 1.633123935319536975596773704152891653086e16L, 1.317719414943508315995636961402669067843e-291L);
+#endif
+
+#if defined TEST_LDOUBLE && LDBL_MIN_EXP <= -16381
+      TEST_c_c (ctan, 0x1.921fb54442d1846ap+0L, 0x1p-16445L, -3.986797629811710706723242948653362815645e19L, 5.793882568875674066286163141055208625180e-4912L);
+#endif
+    }
+
+  fesetround (save_round_mode);
+
+  END (ctan_tonearest, complex);
+}
+
+
+static void
+ctan_test_towardzero (void)
+{
+  int save_round_mode;
+  errno = 0;
+  FUNC(ctan) (BUILD_COMPLEX (0.7L, 1.2L));
+  if (errno == ENOSYS)
+    /* Function not implemented.  */
+    return;
+
+  START (ctan_towardzero);
+
+  save_round_mode = fegetround ();
+
+  if (!fesetround (FE_TOWARDZERO))
+    {
+      TEST_c_c (ctan, 0x1.921fb6p+0, 0x1p-149, -2.287733242885645987394874673945769518150e7L, 7.334008549954377778731880988481078535821e-31L);
+
+#ifndef TEST_FLOAT
+      TEST_c_c (ctan, 0x1.921fb54442d18p+0, 0x1p-1074, 1.633123935319536975596773704152891653086e16L, 1.317719414943508315995636961402669067843e-291L);
+#endif
+
+#if defined TEST_LDOUBLE && LDBL_MIN_EXP <= -16381
+      TEST_c_c (ctan, 0x1.921fb54442d1846ap+0L, 0x1p-16445L, -3.986797629811710706723242948653362815645e19L, 5.793882568875674066286163141055208625180e-4912L);
+#endif
+    }
+
+  fesetround (save_round_mode);
+
+  END (ctan_towardzero, complex);
+}
+
+
+static void
+ctan_test_downward (void)
+{
+  int save_round_mode;
+  errno = 0;
+  FUNC(ctan) (BUILD_COMPLEX (0.7L, 1.2L));
+  if (errno == ENOSYS)
+    /* Function not implemented.  */
+    return;
+
+  START (ctan_downward);
+
+  save_round_mode = fegetround ();
+
+  if (!fesetround (FE_DOWNWARD))
+    {
+      TEST_c_c (ctan, 0x1.921fb6p+0, 0x1p-149, -2.287733242885645987394874673945769518150e7L, 7.334008549954377778731880988481078535821e-31L);
+
+#ifndef TEST_FLOAT
+      TEST_c_c (ctan, 0x1.921fb54442d18p+0, 0x1p-1074, 1.633123935319536975596773704152891653086e16L, 1.317719414943508315995636961402669067843e-291L);
+#endif
+
+#if defined TEST_LDOUBLE && LDBL_MIN_EXP <= -16381
+      TEST_c_c (ctan, 0x1.921fb54442d1846ap+0L, 0x1p-16445L, -3.986797629811710706723242948653362815645e19L, 5.793882568875674066286163141055208625180e-4912L);
+#endif
+    }
+
+  fesetround (save_round_mode);
+
+  END (ctan_downward, complex);
+}
+
+
+static void
+ctan_test_upward (void)
+{
+  int save_round_mode;
+  errno = 0;
+  FUNC(ctan) (BUILD_COMPLEX (0.7L, 1.2L));
+  if (errno == ENOSYS)
+    /* Function not implemented.  */
+    return;
+
+  START (ctan_upward);
+
+  save_round_mode = fegetround ();
+
+  if (!fesetround (FE_UPWARD))
+    {
+      TEST_c_c (ctan, 0x1.921fb6p+0, 0x1p-149, -2.287733242885645987394874673945769518150e7L, 7.334008549954377778731880988481078535821e-31L);
+
+#ifndef TEST_FLOAT
+      TEST_c_c (ctan, 0x1.921fb54442d18p+0, 0x1p-1074, 1.633123935319536975596773704152891653086e16L, 1.317719414943508315995636961402669067843e-291L);
+#endif
+
+#if defined TEST_LDOUBLE && LDBL_MIN_EXP <= -16381
+      TEST_c_c (ctan, 0x1.921fb54442d1846ap+0L, 0x1p-16445L, -3.986797629811710706723242948653362815645e19L, 5.793882568875674066286163141055208625180e-4912L);
+#endif
+    }
+
+  fesetround (save_round_mode);
+
+  END (ctan_upward, complex);
+}
+
+
+static void
 ctanh_test (void)
 {
   errno = 0;
@@ -3408,6 +3540,138 @@ ctanh_test (void)
 
 
 static void
+ctanh_test_tonearest (void)
+{
+  int save_round_mode;
+  errno = 0;
+  FUNC(ctanh) (BUILD_COMPLEX (0.7L, 1.2L));
+  if (errno == ENOSYS)
+    /* Function not implemented.  */
+    return;
+
+  START (ctanh_tonearest);
+
+  save_round_mode = fegetround ();
+
+  if (!fesetround (FE_TONEAREST))
+    {
+      TEST_c_c (ctanh, 0x1p-149, 0x1.921fb6p+0, 7.334008549954377778731880988481078535821e-31L, -2.287733242885645987394874673945769518150e7L);
+
+#ifndef TEST_FLOAT
+      TEST_c_c (ctanh, 0x1p-1074, 0x1.921fb54442d18p+0, 1.317719414943508315995636961402669067843e-291L, 1.633123935319536975596773704152891653086e16L);
+#endif
+
+#if defined TEST_LDOUBLE && LDBL_MIN_EXP <= -16381
+      TEST_c_c (ctanh, 0x1p-16445L, 0x1.921fb54442d1846ap+0L, 5.793882568875674066286163141055208625180e-4912L, -3.986797629811710706723242948653362815645e19L);
+#endif
+    }
+
+  fesetround (save_round_mode);
+
+  END (ctanh_tonearest, complex);
+}
+
+
+static void
+ctanh_test_towardzero (void)
+{
+  int save_round_mode;
+  errno = 0;
+  FUNC(ctanh) (BUILD_COMPLEX (0.7L, 1.2L));
+  if (errno == ENOSYS)
+    /* Function not implemented.  */
+    return;
+
+  START (ctanh_towardzero);
+
+  save_round_mode = fegetround ();
+
+  if (!fesetround (FE_TOWARDZERO))
+    {
+      TEST_c_c (ctanh, 0x1p-149, 0x1.921fb6p+0, 7.334008549954377778731880988481078535821e-31L, -2.287733242885645987394874673945769518150e7L);
+
+#ifndef TEST_FLOAT
+      TEST_c_c (ctanh, 0x1p-1074, 0x1.921fb54442d18p+0, 1.317719414943508315995636961402669067843e-291L, 1.633123935319536975596773704152891653086e16L);
+#endif
+
+#if defined TEST_LDOUBLE && LDBL_MIN_EXP <= -16381
+      TEST_c_c (ctanh, 0x1p-16445L, 0x1.921fb54442d1846ap+0L, 5.793882568875674066286163141055208625180e-4912L, -3.986797629811710706723242948653362815645e19L);
+#endif
+    }
+
+  fesetround (save_round_mode);
+
+  END (ctanh_towardzero, complex);
+}
+
+
+static void
+ctanh_test_downward (void)
+{
+  int save_round_mode;
+  errno = 0;
+  FUNC(ctanh) (BUILD_COMPLEX (0.7L, 1.2L));
+  if (errno == ENOSYS)
+    /* Function not implemented.  */
+    return;
+
+  START (ctanh_downward);
+
+  save_round_mode = fegetround ();
+
+  if (!fesetround (FE_DOWNWARD))
+    {
+      TEST_c_c (ctanh, 0x1p-149, 0x1.921fb6p+0, 7.334008549954377778731880988481078535821e-31L, -2.287733242885645987394874673945769518150e7L);
+
+#ifndef TEST_FLOAT
+      TEST_c_c (ctanh, 0x1p-1074, 0x1.921fb54442d18p+0, 1.317719414943508315995636961402669067843e-291L, 1.633123935319536975596773704152891653086e16L);
+#endif
+
+#if defined TEST_LDOUBLE && LDBL_MIN_EXP <= -16381
+      TEST_c_c (ctanh, 0x1p-16445L, 0x1.921fb54442d1846ap+0L, 5.793882568875674066286163141055208625180e-4912L, -3.986797629811710706723242948653362815645e19L);
+#endif
+    }
+
+  fesetround (save_round_mode);
+
+  END (ctanh_downward, complex);
+}
+
+
+static void
+ctanh_test_upward (void)
+{
+  int save_round_mode;
+  errno = 0;
+  FUNC(ctanh) (BUILD_COMPLEX (0.7L, 1.2L));
+  if (errno == ENOSYS)
+    /* Function not implemented.  */
+    return;
+
+  START (ctanh_upward);
+
+  save_round_mode = fegetround ();
+
+  if (!fesetround (FE_UPWARD))
+    {
+      TEST_c_c (ctanh, 0x1p-149, 0x1.921fb6p+0, 7.334008549954377778731880988481078535821e-31L, -2.287733242885645987394874673945769518150e7L);
+
+#ifndef TEST_FLOAT
+      TEST_c_c (ctanh, 0x1p-1074, 0x1.921fb54442d18p+0, 1.317719414943508315995636961402669067843e-291L, 1.633123935319536975596773704152891653086e16L);
+#endif
+
+#if defined TEST_LDOUBLE && LDBL_MIN_EXP <= -16381
+      TEST_c_c (ctanh, 0x1p-16445L, 0x1.921fb54442d1846ap+0L, 5.793882568875674066286163141055208625180e-4912L, -3.986797629811710706723242948653362815645e19L);
+#endif
+    }
+
+  fesetround (save_round_mode);
+
+  END (ctanh_upward, complex);
+}
+
+
+static void
 erf_test (void)
 {
   errno = 0;
@@ -8909,7 +9173,15 @@ main (int argc, char **argv)
   csinh_test ();
   csqrt_test ();
   ctan_test ();
+  ctan_test_tonearest ();
+  ctan_test_towardzero ();
+  ctan_test_downward ();
+  ctan_test_upward ();
   ctanh_test ();
+  ctanh_test_tonearest ();
+  ctanh_test_towardzero ();
+  ctanh_test_downward ();
+  ctanh_test_upward ();
 
   /* Bessel functions:  */
   j0_test ();
diff --git a/math/s_ctan.c b/math/s_ctan.c
index 78117b3..89c0fef 100644
--- a/math/s_ctan.c
+++ b/math/s_ctan.c
@@ -83,10 +83,22 @@ __ctan (__complex__ double x)
 	}
       else
 	{
-	  double sinhix = __ieee754_sinh (__imag__ x);
-	  double coshix = __ieee754_cosh (__imag__ x);
+	  double sinhix, coshix;
+	  if (fabs (__imag__ x) > DBL_MIN)
+	    {
+	      sinhix = __ieee754_sinh (__imag__ x);
+	      coshix = __ieee754_cosh (__imag__ x);
+	    }
+	  else
+	    {
+	      sinhix = __imag__ x;
+	      coshix = 1.0;
+	    }
 
-	  den = cosrx * cosrx + sinhix * sinhix;
+	  if (fabs (sinhix) > fabs (cosrx) * DBL_EPSILON)
+	    den = cosrx * cosrx + sinhix * sinhix;
+	  else
+	    den = cosrx * cosrx;
 	  __real__ res = sinrx * cosrx / den;
 	  __imag__ res = sinhix * coshix / den;
 	}
diff --git a/math/s_ctanf.c b/math/s_ctanf.c
index 4cba559..2559f83 100644
--- a/math/s_ctanf.c
+++ b/math/s_ctanf.c
@@ -83,10 +83,22 @@ __ctanf (__complex__ float x)
 	}
       else
 	{
-	  float sinhix = __ieee754_sinhf (__imag__ x);
-	  float coshix = __ieee754_coshf (__imag__ x);
+	  float sinhix, coshix;
+	  if (fabsf (__imag__ x) > FLT_MIN)
+	    {
+	      sinhix = __ieee754_sinhf (__imag__ x);
+	      coshix = __ieee754_coshf (__imag__ x);
+	    }
+	  else
+	    {
+	      sinhix = __imag__ x;
+	      coshix = 1.0f;
+	    }
 
-	  den = cosrx * cosrx + sinhix * sinhix;
+	  if (fabsf (sinhix) > fabsf (cosrx) * FLT_EPSILON)
+	    den = cosrx * cosrx + sinhix * sinhix;
+	  else
+	    den = cosrx * cosrx;
 	  __real__ res = sinrx * cosrx / den;
 	  __imag__ res = sinhix * coshix / den;
 	}
diff --git a/math/s_ctanh.c b/math/s_ctanh.c
index 201871e..d288b7d 100644
--- a/math/s_ctanh.c
+++ b/math/s_ctanh.c
@@ -83,10 +83,22 @@ __ctanh (__complex__ double x)
 	}
       else
 	{
-	  double sinhrx = __ieee754_sinh (__real__ x);
-	  double coshrx = __ieee754_cosh (__real__ x);
+	  double sinhrx, coshrx;
+	  if (fabs (__real__ x) > DBL_MIN)
+	    {
+	      sinhrx = __ieee754_sinh (__real__ x);
+	      coshrx = __ieee754_cosh (__real__ x);
+	    }
+	  else
+	    {
+	      sinhrx = __real__ x;
+	      coshrx = 1.0;
+	    }
 
-	  den = sinhrx * sinhrx + cosix * cosix;
+	  if (fabs (sinhrx) > fabs (cosix) * DBL_EPSILON)
+	    den = sinhrx * sinhrx + cosix * cosix;
+	  else
+	    den = 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 e505155..ca36a83 100644
--- a/math/s_ctanhf.c
+++ b/math/s_ctanhf.c
@@ -83,10 +83,22 @@ __ctanhf (__complex__ float x)
 	}
       else
 	{
-	  float sinhrx = __ieee754_sinhf (__real__ x);
-	  float coshrx = __ieee754_coshf (__real__ x);
+	  float sinhrx, coshrx;
+	  if (fabsf (__real__ x) > FLT_MIN)
+	    {
+	      sinhrx = __ieee754_sinhf (__real__ x);
+	      coshrx = __ieee754_coshf (__real__ x);
+	    }
+	  else
+	    {
+	      sinhrx = __real__ x;
+	      coshrx = 1.0f;
+	    }
 
-	  den = sinhrx * sinhrx + cosix * cosix;
+	  if (fabsf (sinhrx) > fabsf (cosix) * FLT_EPSILON)
+	    den = sinhrx * sinhrx + cosix * cosix;
+	  else
+	    den = 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 e5d6779..dbf1612 100644
--- a/math/s_ctanhl.c
+++ b/math/s_ctanhl.c
@@ -83,10 +83,22 @@ __ctanhl (__complex__ long double x)
 	}
       else
 	{
-	  long double sinhrx = __ieee754_sinhl (__real__ x);
-	  long double coshrx = __ieee754_coshl (__real__ x);
+	  long double sinhrx, coshrx;
+	  if (fabsl (__real__ x) > LDBL_MIN)
+	    {
+	      sinhrx = __ieee754_sinhl (__real__ x);
+	      coshrx = __ieee754_coshl (__real__ x);
+	    }
+	  else
+	    {
+	      sinhrx = __real__ x;
+	      coshrx = 1.0L;
+	    }
 
-	  den = sinhrx * sinhrx + cosix * cosix;
+	  if (fabsl (sinhrx) > fabsl (cosix) * LDBL_EPSILON)
+	    den = sinhrx * sinhrx + cosix * cosix;
+	  else
+	    den = 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 12d700c..4fe2611 100644
--- a/math/s_ctanl.c
+++ b/math/s_ctanl.c
@@ -83,10 +83,22 @@ __ctanl (__complex__ long double x)
 	}
       else
 	{
-	  long double sinhix = __ieee754_sinhl (__imag__ x);
-	  long double coshix = __ieee754_coshl (__imag__ x);
+	  long double sinhix, coshix;
+	  if (fabsl (__imag__ x) > LDBL_MIN)
+	    {
+	      sinhix = __ieee754_sinhl (__imag__ x);
+	      coshix = __ieee754_coshl (__imag__ x);
+	    }
+	  else
+	    {
+	      sinhix = __imag__ x;
+	      coshix = 1.0L;
+	    }
 
-	  den = cosrx * cosrx + sinhix * sinhix;
+	  if (fabsl (sinhix) > fabsl (cosrx) * LDBL_EPSILON)
+	    den = cosrx * cosrx + sinhix * sinhix;
+	  else
+	    den = cosrx * cosrx;
 	  __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 4661aea..6f41f02 100644
--- a/sysdeps/i386/fpu/libm-test-ulps
+++ b/sysdeps/i386/fpu/libm-test-ulps
@@ -1437,6 +1437,93 @@ idouble: 1
 ildouble: 2
 ldouble: 2
 
+# ctan_downward
+Test "Real part of: ctan_downward (0x1.921fb54442d1846ap+0 + 0x1p-16445 i) == -3.986797629811710706723242948653362815645e19 + 5.793882568875674066286163141055208625180e-4912 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: ctan_downward (0x1.921fb54442d18p+0 + 0x1p-1074 i) == 1.633123935319536975596773704152891653086e16 + 1.317719414943508315995636961402669067843e-291 i":
+double: 1
+idouble: 1
+ildouble: 2
+ldouble: 2
+Test "Imaginary part of: ctan_downward (0x1.921fb54442d18p+0 + 0x1p-1074 i) == 1.633123935319536975596773704152891653086e16 + 1.317719414943508315995636961402669067843e-291 i":
+ildouble: 3
+ldouble: 3
+Test "Real part of: ctan_downward (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 3
+ldouble: 3
+Test "Imaginary part of: ctan_downward (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i":
+float: 3
+ifloat: 3
+ildouble: 4
+ldouble: 4
+
+# ctan_tonearest
+Test "Imaginary part of: ctan_tonearest (0x1.921fb54442d1846ap+0 + 0x1p-16445 i) == -3.986797629811710706723242948653362815645e19 + 5.793882568875674066286163141055208625180e-4912 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: ctan_tonearest (0x1.921fb54442d18p+0 + 0x1p-1074 i) == 1.633123935319536975596773704152891653086e16 + 1.317719414943508315995636961402669067843e-291 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: ctan_tonearest (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i":
+float: 1
+ifloat: 1
+Test "Imaginary part of: ctan_tonearest (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+
+# ctan_towardzero
+Test "Real part of: ctan_towardzero (0x1.921fb54442d18p+0 + 0x1p-1074 i) == 1.633123935319536975596773704152891653086e16 + 1.317719414943508315995636961402669067843e-291 i":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: ctan_towardzero (0x1.921fb54442d18p+0 + 0x1p-1074 i) == 1.633123935319536975596773704152891653086e16 + 1.317719414943508315995636961402669067843e-291 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: ctan_towardzero (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: ctan_towardzero (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i":
+float: 3
+ifloat: 3
+ildouble: 4
+ldouble: 4
+
+# ctan_upward
+Test "Real part of: ctan_upward (0x1.921fb54442d1846ap+0 + 0x1p-16445 i) == -3.986797629811710706723242948653362815645e19 + 5.793882568875674066286163141055208625180e-4912 i":
+ildouble: 2
+ldouble: 2
+Test "Imaginary part of: ctan_upward (0x1.921fb54442d1846ap+0 + 0x1p-16445 i) == -3.986797629811710706723242948653362815645e19 + 5.793882568875674066286163141055208625180e-4912 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: ctan_upward (0x1.921fb54442d18p+0 + 0x1p-1074 i) == 1.633123935319536975596773704152891653086e16 + 1.317719414943508315995636961402669067843e-291 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: ctan_upward (0x1.921fb54442d18p+0 + 0x1p-1074 i) == 1.633123935319536975596773704152891653086e16 + 1.317719414943508315995636961402669067843e-291 i":
+double: 1
+idouble: 1
+ildouble: 4
+ldouble: 4
+Test "Real part of: ctan_upward (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i":
+float: 1
+ifloat: 1
+ildouble: 2
+ldouble: 2
+Test "Imaginary part of: ctan_upward (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+
 # ctanh
 Test "Real part of: ctanh (-2 - 3 i) == -0.965385879022133124278480269394560686 + 0.988437503832249372031403430350121098e-2 i":
 float: 1
@@ -1488,6 +1575,93 @@ idouble: 1
 ildouble: 2
 ldouble: 2
 
+# ctanh_downward
+Test "Real part of: ctanh_downward (0x1p-1074 + 0x1.921fb54442d18p+0 i) == 1.317719414943508315995636961402669067843e-291 + 1.633123935319536975596773704152891653086e16 i":
+ildouble: 3
+ldouble: 3
+Test "Imaginary part of: ctanh_downward (0x1p-1074 + 0x1.921fb54442d18p+0 i) == 1.317719414943508315995636961402669067843e-291 + 1.633123935319536975596773704152891653086e16 i":
+double: 1
+idouble: 1
+ildouble: 2
+ldouble: 2
+Test "Real part of: ctanh_downward (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i":
+float: 3
+ifloat: 3
+ildouble: 4
+ldouble: 4
+Test "Imaginary part of: ctanh_downward (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 3
+ldouble: 3
+Test "Imaginary part of: ctanh_downward (0x1p-16445 + 0x1.921fb54442d1846ap+0 i) == 5.793882568875674066286163141055208625180e-4912 - 3.986797629811710706723242948653362815645e19 i":
+ildouble: 1
+ldouble: 1
+
+# ctanh_tonearest
+Test "Real part of: ctanh_tonearest (0x1p-1074 + 0x1.921fb54442d18p+0 i) == 1.317719414943508315995636961402669067843e-291 + 1.633123935319536975596773704152891653086e16 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: ctanh_tonearest (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: ctanh_tonearest (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i":
+float: 1
+ifloat: 1
+Test "Real part of: ctanh_tonearest (0x1p-16445 + 0x1.921fb54442d1846ap+0 i) == 5.793882568875674066286163141055208625180e-4912 - 3.986797629811710706723242948653362815645e19 i":
+ildouble: 1
+ldouble: 1
+
+# ctanh_towardzero
+Test "Real part of: ctanh_towardzero (0x1p-1074 + 0x1.921fb54442d18p+0 i) == 1.317719414943508315995636961402669067843e-291 + 1.633123935319536975596773704152891653086e16 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: ctanh_towardzero (0x1p-1074 + 0x1.921fb54442d18p+0 i) == 1.317719414943508315995636961402669067843e-291 + 1.633123935319536975596773704152891653086e16 i":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "Real part of: ctanh_towardzero (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i":
+float: 3
+ifloat: 3
+ildouble: 4
+ldouble: 4
+Test "Imaginary part of: ctanh_towardzero (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i":
+ildouble: 1
+ldouble: 1
+
+# ctanh_upward
+Test "Real part of: ctanh_upward (0x1p-1074 + 0x1.921fb54442d18p+0 i) == 1.317719414943508315995636961402669067843e-291 + 1.633123935319536975596773704152891653086e16 i":
+double: 1
+idouble: 1
+ildouble: 4
+ldouble: 4
+Test "Imaginary part of: ctanh_upward (0x1p-1074 + 0x1.921fb54442d18p+0 i) == 1.317719414943508315995636961402669067843e-291 + 1.633123935319536975596773704152891653086e16 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: ctanh_upward (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: ctanh_upward (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i":
+float: 1
+ifloat: 1
+ildouble: 2
+ldouble: 2
+Test "Real part of: ctanh_upward (0x1p-16445 + 0x1.921fb54442d1846ap+0 i) == 5.793882568875674066286163141055208625180e-4912 - 3.986797629811710706723242948653362815645e19 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: ctanh_upward (0x1p-16445 + 0x1.921fb54442d1846ap+0 i) == 5.793882568875674066286163141055208625180e-4912 - 3.986797629811710706723242948653362815645e19 i":
+ildouble: 2
+ldouble: 2
+
 # erf
 Test "erf (1.25) == 0.922900128256458230136523481197281140":
 double: 1
@@ -2878,6 +3052,56 @@ ifloat: 1
 ildouble: 1
 ldouble: 1
 
+Function: Real part of "ctan_downward":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 3
+ldouble: 3
+
+Function: Imaginary part of "ctan_downward":
+float: 3
+ifloat: 3
+ildouble: 4
+ldouble: 4
+
+Function: Real part of "ctan_tonearest":
+float: 1
+ifloat: 1
+
+Function: Imaginary part of "ctan_tonearest":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+
+Function: Real part of "ctan_towardzero":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+
+Function: Imaginary part of "ctan_towardzero":
+float: 3
+ifloat: 3
+ildouble: 4
+ldouble: 4
+
+Function: Real part of "ctan_upward":
+float: 1
+ifloat: 1
+ildouble: 2
+ldouble: 2
+
+Function: Imaginary part of "ctan_upward":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 4
+ldouble: 4
+
 Function: Real part of "ctanh":
 double: 1
 float: 1
@@ -2894,6 +3118,56 @@ ifloat: 1
 ildouble: 2
 ldouble: 2
 
+Function: Real part of "ctanh_downward":
+float: 3
+ifloat: 3
+ildouble: 4
+ldouble: 4
+
+Function: Imaginary part of "ctanh_downward":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 3
+ldouble: 3
+
+Function: Real part of "ctanh_tonearest":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+
+Function: Imaginary part of "ctanh_tonearest":
+float: 1
+ifloat: 1
+
+Function: Real part of "ctanh_towardzero":
+float: 3
+ifloat: 3
+ildouble: 4
+ldouble: 4
+
+Function: Imaginary part of "ctanh_towardzero":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+
+Function: Real part of "ctanh_upward":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
+ildouble: 4
+ldouble: 4
+
+Function: Imaginary part of "ctanh_upward":
+float: 1
+ifloat: 1
+ildouble: 2
+ldouble: 2
+
 Function: "erf":
 double: 1
 idouble: 1
diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps
index 3374b5f..765c7a0 100644
--- a/sysdeps/x86_64/fpu/libm-test-ulps
+++ b/sysdeps/x86_64/fpu/libm-test-ulps
@@ -1304,6 +1304,93 @@ Test "Real part of: ctan (1 + 47 i) == 2.729321264492904590777293425576722354636
 ildouble: 2
 ldouble: 2
 
+# ctan_downward
+Test "Real part of: ctan_downward (0x1.921fb54442d1846ap+0 + 0x1p-16445 i) == -3.986797629811710706723242948653362815645e19 + 5.793882568875674066286163141055208625180e-4912 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: ctan_downward (0x1.921fb54442d18p+0 + 0x1p-1074 i) == 1.633123935319536975596773704152891653086e16 + 1.317719414943508315995636961402669067843e-291 i":
+ildouble: 2
+ldouble: 2
+Test "Imaginary part of: ctan_downward (0x1.921fb54442d18p+0 + 0x1p-1074 i) == 1.633123935319536975596773704152891653086e16 + 1.317719414943508315995636961402669067843e-291 i":
+ildouble: 3
+ldouble: 3
+Test "Real part of: ctan_downward (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i":
+double: 2
+float: 1
+idouble: 2
+ifloat: 1
+ildouble: 3
+ldouble: 3
+Test "Imaginary part of: ctan_downward (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i":
+float: 1
+ifloat: 1
+ildouble: 4
+ldouble: 4
+
+# ctan_tonearest
+Test "Imaginary part of: ctan_tonearest (0x1.921fb54442d1846ap+0 + 0x1p-16445 i) == -3.986797629811710706723242948653362815645e19 + 5.793882568875674066286163141055208625180e-4912 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: ctan_tonearest (0x1.921fb54442d18p+0 + 0x1p-1074 i) == 1.633123935319536975596773704152891653086e16 + 1.317719414943508315995636961402669067843e-291 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: ctan_tonearest (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i":
+float: 1
+ifloat: 1
+Test "Imaginary part of: ctan_tonearest (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+
+# ctan_towardzero
+Test "Real part of: ctan_towardzero (0x1.921fb54442d18p+0 + 0x1p-1074 i) == 1.633123935319536975596773704152891653086e16 + 1.317719414943508315995636961402669067843e-291 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: ctan_towardzero (0x1.921fb54442d18p+0 + 0x1p-1074 i) == 1.633123935319536975596773704152891653086e16 + 1.317719414943508315995636961402669067843e-291 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: ctan_towardzero (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: ctan_towardzero (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i":
+float: 1
+ifloat: 1
+ildouble: 4
+ldouble: 4
+
+# ctan_upward
+Test "Real part of: ctan_upward (0x1.921fb54442d1846ap+0 + 0x1p-16445 i) == -3.986797629811710706723242948653362815645e19 + 5.793882568875674066286163141055208625180e-4912 i":
+ildouble: 2
+ldouble: 2
+Test "Imaginary part of: ctan_upward (0x1.921fb54442d1846ap+0 + 0x1p-16445 i) == -3.986797629811710706723242948653362815645e19 + 5.793882568875674066286163141055208625180e-4912 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: ctan_upward (0x1.921fb54442d18p+0 + 0x1p-1074 i) == 1.633123935319536975596773704152891653086e16 + 1.317719414943508315995636961402669067843e-291 i":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: ctan_upward (0x1.921fb54442d18p+0 + 0x1p-1074 i) == 1.633123935319536975596773704152891653086e16 + 1.317719414943508315995636961402669067843e-291 i":
+ildouble: 4
+ldouble: 4
+Test "Real part of: ctan_upward (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i":
+double: 2
+float: 1
+idouble: 2
+ifloat: 1
+ildouble: 2
+ldouble: 2
+Test "Imaginary part of: ctan_upward (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i":
+double: 1
+float: 2
+idouble: 1
+ifloat: 2
+ildouble: 1
+ldouble: 1
+
 # ctanh
 Test "Real part of: ctanh (-2 - 3 i) == -0.965385879022133124278480269394560686 + 0.988437503832249372031403430350121098e-2 i":
 double: 1
@@ -1359,6 +1446,93 @@ Test "Imaginary part of: ctanh (47 + 1 i) == 1.0 + 2.729321264492904590777293425
 ildouble: 2
 ldouble: 2
 
+# ctanh_downward
+Test "Real part of: ctanh_downward (0x1p-1074 + 0x1.921fb54442d18p+0 i) == 1.317719414943508315995636961402669067843e-291 + 1.633123935319536975596773704152891653086e16 i":
+ildouble: 3
+ldouble: 3
+Test "Imaginary part of: ctanh_downward (0x1p-1074 + 0x1.921fb54442d18p+0 i) == 1.317719414943508315995636961402669067843e-291 + 1.633123935319536975596773704152891653086e16 i":
+ildouble: 2
+ldouble: 2
+Test "Real part of: ctanh_downward (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i":
+float: 1
+ifloat: 1
+ildouble: 4
+ldouble: 4
+Test "Imaginary part of: ctanh_downward (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i":
+double: 2
+float: 1
+idouble: 2
+ifloat: 1
+ildouble: 3
+ldouble: 3
+Test "Imaginary part of: ctanh_downward (0x1p-16445 + 0x1.921fb54442d1846ap+0 i) == 5.793882568875674066286163141055208625180e-4912 - 3.986797629811710706723242948653362815645e19 i":
+ildouble: 1
+ldouble: 1
+
+# ctanh_tonearest
+Test "Real part of: ctanh_tonearest (0x1p-1074 + 0x1.921fb54442d18p+0 i) == 1.317719414943508315995636961402669067843e-291 + 1.633123935319536975596773704152891653086e16 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: ctanh_tonearest (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: ctanh_tonearest (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i":
+float: 1
+ifloat: 1
+Test "Real part of: ctanh_tonearest (0x1p-16445 + 0x1.921fb54442d1846ap+0 i) == 5.793882568875674066286163141055208625180e-4912 - 3.986797629811710706723242948653362815645e19 i":
+ildouble: 1
+ldouble: 1
+
+# ctanh_towardzero
+Test "Real part of: ctanh_towardzero (0x1p-1074 + 0x1.921fb54442d18p+0 i) == 1.317719414943508315995636961402669067843e-291 + 1.633123935319536975596773704152891653086e16 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: ctanh_towardzero (0x1p-1074 + 0x1.921fb54442d18p+0 i) == 1.317719414943508315995636961402669067843e-291 + 1.633123935319536975596773704152891653086e16 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: ctanh_towardzero (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i":
+float: 1
+ifloat: 1
+ildouble: 4
+ldouble: 4
+Test "Imaginary part of: ctanh_towardzero (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+
+# ctanh_upward
+Test "Real part of: ctanh_upward (0x1p-1074 + 0x1.921fb54442d18p+0 i) == 1.317719414943508315995636961402669067843e-291 + 1.633123935319536975596773704152891653086e16 i":
+ildouble: 4
+ldouble: 4
+Test "Imaginary part of: ctanh_upward (0x1p-1074 + 0x1.921fb54442d18p+0 i) == 1.317719414943508315995636961402669067843e-291 + 1.633123935319536975596773704152891653086e16 i":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "Real part of: ctanh_upward (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i":
+double: 1
+float: 2
+idouble: 1
+ifloat: 2
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: ctanh_upward (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i":
+double: 2
+float: 1
+idouble: 2
+ifloat: 1
+ildouble: 2
+ldouble: 2
+Test "Real part of: ctanh_upward (0x1p-16445 + 0x1.921fb54442d1846ap+0 i) == 5.793882568875674066286163141055208625180e-4912 - 3.986797629811710706723242948653362815645e19 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: ctanh_upward (0x1p-16445 + 0x1.921fb54442d1846ap+0 i) == 5.793882568875674066286163141055208625180e-4912 - 3.986797629811710706723242948653362815645e19 i":
+ildouble: 2
+ldouble: 2
+
 # erf
 Test "erf (1.25) == 0.922900128256458230136523481197281140":
 double: 1
@@ -2669,6 +2843,58 @@ ifloat: 1
 ildouble: 1
 ldouble: 1
 
+Function: Real part of "ctan_downward":
+double: 2
+float: 1
+idouble: 2
+ifloat: 1
+ildouble: 3
+ldouble: 3
+
+Function: Imaginary part of "ctan_downward":
+float: 1
+ifloat: 1
+ildouble: 4
+ldouble: 4
+
+Function: Real part of "ctan_tonearest":
+float: 1
+ifloat: 1
+
+Function: Imaginary part of "ctan_tonearest":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+
+Function: Real part of "ctan_towardzero":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+
+Function: Imaginary part of "ctan_towardzero":
+float: 1
+ifloat: 1
+ildouble: 4
+ldouble: 4
+
+Function: Real part of "ctan_upward":
+double: 2
+float: 1
+idouble: 2
+ifloat: 1
+ildouble: 2
+ldouble: 2
+
+Function: Imaginary part of "ctan_upward":
+double: 1
+float: 2
+idouble: 1
+ifloat: 2
+ildouble: 4
+ldouble: 4
+
 Function: Real part of "ctanh":
 double: 1
 float: 1
@@ -2685,6 +2911,58 @@ ifloat: 2
 ildouble: 2
 ldouble: 2
 
+Function: Real part of "ctanh_downward":
+float: 1
+ifloat: 1
+ildouble: 4
+ldouble: 4
+
+Function: Imaginary part of "ctanh_downward":
+double: 2
+float: 1
+idouble: 2
+ifloat: 1
+ildouble: 3
+ldouble: 3
+
+Function: Real part of "ctanh_tonearest":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+
+Function: Imaginary part of "ctanh_tonearest":
+float: 1
+ifloat: 1
+
+Function: Real part of "ctanh_towardzero":
+float: 1
+ifloat: 1
+ildouble: 4
+ldouble: 4
+
+Function: Imaginary part of "ctanh_towardzero":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+
+Function: Real part of "ctanh_upward":
+double: 1
+float: 2
+idouble: 1
+ifloat: 2
+ildouble: 4
+ldouble: 4
+
+Function: Imaginary part of "ctanh_upward":
+double: 2
+float: 1
+idouble: 2
+ifloat: 1
+ildouble: 2
+ldouble: 2
+
 Function: "erf":
 double: 1
 idouble: 1