Fix sign of zero part from ctan / ctanh when argument infinite (bug 17118).

C99/C11 Annex G specifies the sign of the zero part of the result of
ctan (x +/- i * Inf) and ctanh (+/-Inf + i * y).  This patch fixes glibc
to follow that specification, along the lines I described in my review
of Andreas's previous patch for this issue
<https://sourceware.org/ml/libc-alpha/2014-08/msg00142.html>.

Tested for x86_64.

2015-09-17  Joseph Myers  <joseph@codesourcery.com>
	    Andreas Schwab  <schwab@suse.de>

	[BZ #17118]
	* math/s_ctan.c (__ctan): Determine sign of zero real part of
	result when imaginary part of argument is infinite using sine and
	cosine.
	* math/s_ctanf.c (__ctanf): Likewise.
	* math/s_ctanl.c (__ctanl): Likewise.
	* math/s_ctanh.c (__ctanh): Determine sign of zero imaginary part
	of result when real part of argument is infinite using sine and
	cosine.
	* math/s_ctanhf.c (__ctanhf): Likewise.
	* math/s_ctanhl.c (__ctanhl): Likewise.
	* math/libm-test.inc (ctan_test_data): Add more tests of ctan.
	(ctanh_test_data): Add more tests of ctanh.

7 files changed, 176 insertions, 6 deletions

diff --git a/math/libm-test.inc b/math/libm-test.inc
index 5594b9d638..42d608595b 100644
--- a/math/libm-test.inc
+++ b/math/libm-test.inc
@@ -6551,13 +6551,73 @@ static const struct test_c_c_data ctan_test_data[] =
   {
     TEST_c_c (ctan, 0, plus_infty, 0.0, 1.0),
     TEST_c_c (ctan, 1, plus_infty, 0.0, 1.0),
+    TEST_c_c (ctan, 2, plus_infty, minus_zero, 1.0),
+    TEST_c_c (ctan, 3, plus_infty, minus_zero, 1.0),
+    TEST_c_c (ctan, 4, plus_infty, 0.0, 1.0),
+    TEST_c_c (ctan, min_value, plus_infty, 0.0, 1.0),
+    TEST_c_c (ctan, min_subnorm_value, plus_infty, 0.0, 1.0),
+    TEST_c_c (ctan, 0x1p127, plus_infty, 0.0, 1.0),
+    TEST_c_c (ctan, 0x1.11p127, plus_infty, minus_zero, 1.0),
+#ifndef TEST_FLOAT
+    TEST_c_c (ctan, 0x1p1023, plus_infty, minus_zero, 1.0),
+    TEST_c_c (ctan, 0x1.5p1023, plus_infty, 0.0, 1.0),
+#endif
+#if defined TEST_LDOUBLE && LDBL_MAX_EXP >= 16384
+    TEST_c_c (ctan, 0x1p16383L, plus_infty, 0.0, 1.0),
+    TEST_c_c (ctan, 0x1.2p16383L, plus_infty, minus_zero, 1.0),
+#endif
     TEST_c_c (ctan, minus_zero, plus_infty, minus_zero, 1.0),
     TEST_c_c (ctan, -1, plus_infty, minus_zero, 1.0),
+    TEST_c_c (ctan, -2, plus_infty, 0.0, 1.0),
+    TEST_c_c (ctan, -3, plus_infty, 0.0, 1.0),
+    TEST_c_c (ctan, -4, plus_infty, minus_zero, 1.0),
+    TEST_c_c (ctan, -min_value, plus_infty, minus_zero, 1.0),
+    TEST_c_c (ctan, -min_subnorm_value, plus_infty, minus_zero, 1.0),
+    TEST_c_c (ctan, -0x1p127, plus_infty, minus_zero, 1.0),
+    TEST_c_c (ctan, -0x1.11p127, plus_infty, 0.0, 1.0),
+#ifndef TEST_FLOAT
+    TEST_c_c (ctan, -0x1p1023, plus_infty, 0.0, 1.0),
+    TEST_c_c (ctan, -0x1.5p1023, plus_infty, minus_zero, 1.0),
+#endif
+#if defined TEST_LDOUBLE && LDBL_MAX_EXP >= 16384
+    TEST_c_c (ctan, -0x1p16383L, plus_infty, minus_zero, 1.0),
+    TEST_c_c (ctan, -0x1.2p16383L, plus_infty, 0.0, 1.0),
+#endif
 
     TEST_c_c (ctan, 0, minus_infty, 0.0, -1.0),
     TEST_c_c (ctan, 1, minus_infty, 0.0, -1.0),
+    TEST_c_c (ctan, 2, minus_infty, minus_zero, -1.0),
+    TEST_c_c (ctan, 3, minus_infty, minus_zero, -1.0),
+    TEST_c_c (ctan, 4, minus_infty, 0.0, -1.0),
+    TEST_c_c (ctan, min_value, minus_infty, 0.0, -1.0),
+    TEST_c_c (ctan, min_subnorm_value, minus_infty, 0.0, -1.0),
+    TEST_c_c (ctan, 0x1p127, minus_infty, 0.0, -1.0),
+    TEST_c_c (ctan, 0x1.11p127, minus_infty, minus_zero, -1.0),
+#ifndef TEST_FLOAT
+    TEST_c_c (ctan, 0x1p1023, minus_infty, minus_zero, -1.0),
+    TEST_c_c (ctan, 0x1.5p1023, minus_infty, 0.0, -1.0),
+#endif
+#if defined TEST_LDOUBLE && LDBL_MAX_EXP >= 16384
+    TEST_c_c (ctan, 0x1p16383L, minus_infty, 0.0, -1.0),
+    TEST_c_c (ctan, 0x1.2p16383L, minus_infty, minus_zero, -1.0),
+#endif
     TEST_c_c (ctan, minus_zero, minus_infty, minus_zero, -1.0),
     TEST_c_c (ctan, -1, minus_infty, minus_zero, -1.0),
+    TEST_c_c (ctan, -2, minus_infty, 0.0, -1.0),
+    TEST_c_c (ctan, -3, minus_infty, 0.0, -1.0),
+    TEST_c_c (ctan, -4, minus_infty, minus_zero, -1.0),
+    TEST_c_c (ctan, -min_value, minus_infty, minus_zero, -1.0),
+    TEST_c_c (ctan, -min_subnorm_value, minus_infty, minus_zero, -1.0),
+    TEST_c_c (ctan, -0x1p127, minus_infty, minus_zero, -1.0),
+    TEST_c_c (ctan, -0x1.11p127, minus_infty, 0.0, -1.0),
+#ifndef TEST_FLOAT
+    TEST_c_c (ctan, -0x1p1023, minus_infty, 0.0, -1.0),
+    TEST_c_c (ctan, -0x1.5p1023, minus_infty, minus_zero, -1.0),
+#endif
+#if defined TEST_LDOUBLE && LDBL_MAX_EXP >= 16384
+    TEST_c_c (ctan, -0x1p16383L, minus_infty, minus_zero, -1.0),
+    TEST_c_c (ctan, -0x1.2p16383L, minus_infty, 0.0, -1.0),
+#endif
 
     TEST_c_c (ctan, plus_infty, 0, qnan_value, qnan_value, INVALID_EXCEPTION),
     TEST_c_c (ctan, plus_infty, 2, qnan_value, qnan_value, INVALID_EXCEPTION),
@@ -6569,7 +6629,11 @@ static const struct test_c_c_data ctan_test_data[] =
     TEST_c_c (ctan, minus_infty, -2, qnan_value, qnan_value, INVALID_EXCEPTION),
 
     TEST_c_c (ctan, qnan_value, plus_infty, 0.0, 1.0, IGNORE_ZERO_INF_SIGN),
+    TEST_c_c (ctan, plus_infty, plus_infty, 0.0, 1.0, IGNORE_ZERO_INF_SIGN),
+    TEST_c_c (ctan, minus_infty, plus_infty, 0.0, 1.0, IGNORE_ZERO_INF_SIGN),
     TEST_c_c (ctan, qnan_value, minus_infty, 0.0, -1.0, IGNORE_ZERO_INF_SIGN),
+    TEST_c_c (ctan, plus_infty, minus_infty, 0.0, -1.0, IGNORE_ZERO_INF_SIGN),
+    TEST_c_c (ctan, minus_infty, minus_infty, 0.0, -1.0, IGNORE_ZERO_INF_SIGN),
 
     TEST_c_c (ctan, 0, qnan_value, 0.0, qnan_value),
     TEST_c_c (ctan, minus_zero, qnan_value, minus_zero, qnan_value),
@@ -6598,12 +6662,72 @@ static const struct test_c_c_data ctanh_test_data[] =
   {
     TEST_c_c (ctanh, plus_infty, 0, 1.0, 0.0),
     TEST_c_c (ctanh, plus_infty, 1, 1.0, 0.0),
+    TEST_c_c (ctanh, plus_infty, 2, 1.0, minus_zero),
+    TEST_c_c (ctanh, plus_infty, 3, 1.0, minus_zero),
+    TEST_c_c (ctanh, plus_infty, 4, 1.0, 0.0),
+    TEST_c_c (ctanh, plus_infty, min_value, 1.0, 0.0),
+    TEST_c_c (ctanh, plus_infty, min_subnorm_value, 1.0, 0.0),
+    TEST_c_c (ctanh, plus_infty, 0x1p127, 1.0, 0.0),
+    TEST_c_c (ctanh, plus_infty, 0x1.11p127, 1.0, minus_zero),
+#ifndef TEST_FLOAT
+    TEST_c_c (ctanh, plus_infty, 0x1p1023, 1.0, minus_zero),
+    TEST_c_c (ctanh, plus_infty, 0x1.5p1023, 1.0, 0.0),
+#endif
+#if defined TEST_LDOUBLE && LDBL_MAX_EXP >= 16384
+    TEST_c_c (ctanh, plus_infty, 0x1p16383L, 1.0, 0.0),
+    TEST_c_c (ctanh, plus_infty, 0x1.2p16383L, 1.0, minus_zero),
+#endif
     TEST_c_c (ctanh, plus_infty, minus_zero, 1.0, minus_zero),
     TEST_c_c (ctanh, plus_infty, -1, 1.0, minus_zero),
+    TEST_c_c (ctanh, plus_infty, -2, 1.0, 0.0),
+    TEST_c_c (ctanh, plus_infty, -3, 1.0, 0.0),
+    TEST_c_c (ctanh, plus_infty, -4, 1.0, minus_zero),
+    TEST_c_c (ctanh, plus_infty, -min_value, 1.0, minus_zero),
+    TEST_c_c (ctanh, plus_infty, -min_subnorm_value, 1.0, minus_zero),
+    TEST_c_c (ctanh, plus_infty, -0x1p127, 1.0, minus_zero),
+    TEST_c_c (ctanh, plus_infty, -0x1.11p127, 1.0, 0.0),
+#ifndef TEST_FLOAT
+    TEST_c_c (ctanh, plus_infty, -0x1p1023, 1.0, 0.0),
+    TEST_c_c (ctanh, plus_infty, -0x1.5p1023, 1.0, minus_zero),
+#endif
+#if defined TEST_LDOUBLE && LDBL_MAX_EXP >= 16384
+    TEST_c_c (ctanh, plus_infty, -0x1p16383L, 1.0, minus_zero),
+    TEST_c_c (ctanh, plus_infty, -0x1.2p16383L, 1.0, 0.0),
+#endif
     TEST_c_c (ctanh, minus_infty, 0, -1.0, 0.0),
     TEST_c_c (ctanh, minus_infty, 1, -1.0, 0.0),
+    TEST_c_c (ctanh, minus_infty, 2, -1.0, minus_zero),
+    TEST_c_c (ctanh, minus_infty, 3, -1.0, minus_zero),
+    TEST_c_c (ctanh, minus_infty, 4, -1.0, 0.0),
+    TEST_c_c (ctanh, minus_infty, min_value, -1.0, 0.0),
+    TEST_c_c (ctanh, minus_infty, min_subnorm_value, -1.0, 0.0),
+    TEST_c_c (ctanh, minus_infty, 0x1p127, -1.0, 0.0),
+    TEST_c_c (ctanh, minus_infty, 0x1.11p127, -1.0, minus_zero),
+#ifndef TEST_FLOAT
+    TEST_c_c (ctanh, minus_infty, 0x1p1023, -1.0, minus_zero),
+    TEST_c_c (ctanh, minus_infty, 0x1.5p1023, -1.0, 0.0),
+#endif
+#if defined TEST_LDOUBLE && LDBL_MAX_EXP >= 16384
+    TEST_c_c (ctanh, minus_infty, 0x1p16383L, -1.0, 0.0),
+    TEST_c_c (ctanh, minus_infty, 0x1.2p16383L, -1.0, minus_zero),
+#endif
     TEST_c_c (ctanh, minus_infty, minus_zero, -1.0, minus_zero),
     TEST_c_c (ctanh, minus_infty, -1, -1.0, minus_zero),
+    TEST_c_c (ctanh, minus_infty, -2, -1.0, 0.0),
+    TEST_c_c (ctanh, minus_infty, -3, -1.0, 0.0),
+    TEST_c_c (ctanh, minus_infty, -4, -1.0, minus_zero),
+    TEST_c_c (ctanh, minus_infty, -min_value, -1.0, minus_zero),
+    TEST_c_c (ctanh, minus_infty, -min_subnorm_value, -1.0, minus_zero),
+    TEST_c_c (ctanh, minus_infty, -0x1p127, -1.0, minus_zero),
+    TEST_c_c (ctanh, minus_infty, -0x1.11p127, -1.0, 0.0),
+#ifndef TEST_FLOAT
+    TEST_c_c (ctanh, minus_infty, -0x1p1023, -1.0, 0.0),
+    TEST_c_c (ctanh, minus_infty, -0x1.5p1023, -1.0, minus_zero),
+#endif
+#if defined TEST_LDOUBLE && LDBL_MAX_EXP >= 16384
+    TEST_c_c (ctanh, minus_infty, -0x1p16383L, -1.0, minus_zero),
+    TEST_c_c (ctanh, minus_infty, -0x1.2p16383L, -1.0, 0.0),
+#endif
 
     TEST_c_c (ctanh, 0, plus_infty, qnan_value, qnan_value, INVALID_EXCEPTION),
     TEST_c_c (ctanh, 2, plus_infty, qnan_value, qnan_value, INVALID_EXCEPTION),
@@ -6615,7 +6739,11 @@ static const struct test_c_c_data ctanh_test_data[] =
     TEST_c_c (ctanh, -2, minus_infty, qnan_value, qnan_value, INVALID_EXCEPTION),
 
     TEST_c_c (ctanh, plus_infty, qnan_value, 1.0, 0.0, IGNORE_ZERO_INF_SIGN),
+    TEST_c_c (ctanh, plus_infty, plus_infty, 1.0, 0.0, IGNORE_ZERO_INF_SIGN),
+    TEST_c_c (ctanh, plus_infty, minus_infty, 1.0, 0.0, IGNORE_ZERO_INF_SIGN),
     TEST_c_c (ctanh, minus_infty, qnan_value, -1.0, 0.0, IGNORE_ZERO_INF_SIGN),
+    TEST_c_c (ctanh, minus_infty, plus_infty, -1.0, 0.0, IGNORE_ZERO_INF_SIGN),
+    TEST_c_c (ctanh, minus_infty, minus_infty, -1.0, 0.0, IGNORE_ZERO_INF_SIGN),
 
     TEST_c_c (ctanh, qnan_value, 0, qnan_value, 0.0),
     TEST_c_c (ctanh, qnan_value, minus_zero, qnan_value, minus_zero),
diff --git a/math/s_ctan.c b/math/s_ctan.c
index bcf5cfcec0..7ed6abd814 100644
--- a/math/s_ctan.c
+++ b/math/s_ctan.c
@@ -32,7 +32,14 @@ __ctan (__complex__ double x)
     {
       if (__isinf_ns (__imag__ x))
 	{
-	  __real__ res = __copysign (0.0, __real__ x);
+	  if (isfinite (__real__ x) && fabs (__real__ x) > 1.0)
+	    {
+	      double sinrx, cosrx;
+	      __sincos (__real__ x, &sinrx, &cosrx);
+	      __real__ res = __copysign (0.0, sinrx * cosrx);
+	    }
+	  else
+	    __real__ res = __copysign (0.0, __real__ x);
 	  __imag__ res = __copysign (1.0, __imag__ x);
 	}
       else if (__real__ x == 0.0)
diff --git a/math/s_ctanf.c b/math/s_ctanf.c
index 683ab6e544..d87f775f23 100644
--- a/math/s_ctanf.c
+++ b/math/s_ctanf.c
@@ -32,7 +32,14 @@ __ctanf (__complex__ float x)
     {
       if (__isinf_nsf (__imag__ x))
 	{
-	  __real__ res = __copysignf (0.0, __real__ x);
+	  if (isfinite (__real__ x) && fabsf (__real__ x) > 1.0f)
+	    {
+	      float sinrx, cosrx;
+	      __sincosf (__real__ x, &sinrx, &cosrx);
+	      __real__ res = __copysignf (0.0f, sinrx * cosrx);
+	    }
+	  else
+	    __real__ res = __copysignf (0.0, __real__ x);
 	  __imag__ res = __copysignf (1.0, __imag__ x);
 	}
       else if (__real__ x == 0.0)
diff --git a/math/s_ctanh.c b/math/s_ctanh.c
index 76a0501a73..a41cd1a0a6 100644
--- a/math/s_ctanh.c
+++ b/math/s_ctanh.c
@@ -33,7 +33,14 @@ __ctanh (__complex__ double x)
       if (__isinf_ns (__real__ x))
 	{
 	  __real__ res = __copysign (1.0, __real__ x);
-	  __imag__ res = __copysign (0.0, __imag__ x);
+	  if (isfinite (__imag__ x) && fabs (__imag__ x) > 1.0)
+	    {
+	      double sinix, cosix;
+	      __sincos (__imag__ x, &sinix, &cosix);
+	      __imag__ res = __copysign (0.0, sinix * cosix);
+	    }
+	  else
+	    __imag__ res = __copysign (0.0, __imag__ x);
 	}
       else if (__imag__ x == 0.0)
 	{
diff --git a/math/s_ctanhf.c b/math/s_ctanhf.c
index 9d15c3ef0c..3ce8ac1ac4 100644
--- a/math/s_ctanhf.c
+++ b/math/s_ctanhf.c
@@ -33,7 +33,14 @@ __ctanhf (__complex__ float x)
       if (__isinf_nsf (__real__ x))
 	{
 	  __real__ res = __copysignf (1.0, __real__ x);
-	  __imag__ res = __copysignf (0.0, __imag__ x);
+	  if (isfinite (__imag__ x) && fabsf (__imag__ x) > 1.0f)
+	    {
+	      float sinix, cosix;
+	      __sincosf (__imag__ x, &sinix, &cosix);
+	      __imag__ res = __copysignf (0.0f, sinix * cosix);
+	    }
+	  else
+	    __imag__ res = __copysignf (0.0, __imag__ x);
 	}
       else if (__imag__ x == 0.0)
 	{
diff --git a/math/s_ctanhl.c b/math/s_ctanhl.c
index 9c15bb3a4a..2fc54a85d0 100644
--- a/math/s_ctanhl.c
+++ b/math/s_ctanhl.c
@@ -40,7 +40,14 @@ __ctanhl (__complex__ long double x)
       if (__isinf_nsl (__real__ x))
 	{
 	  __real__ res = __copysignl (1.0, __real__ x);
-	  __imag__ res = __copysignl (0.0, __imag__ x);
+	  if (isfinite (__imag__ x) && fabsl (__imag__ x) > 1.0L)
+	    {
+	      long double sinix, cosix;
+	      __sincosl (__imag__ x, &sinix, &cosix);
+	      __imag__ res = __copysignl (0.0L, sinix * cosix);
+	    }
+	  else
+	    __imag__ res = __copysignl (0.0, __imag__ x);
 	}
       else if (__imag__ x == 0.0)
 	{
diff --git a/math/s_ctanl.c b/math/s_ctanl.c
index 48ab81b64b..9090c1ad96 100644
--- a/math/s_ctanl.c
+++ b/math/s_ctanl.c
@@ -39,7 +39,14 @@ __ctanl (__complex__ long double x)
     {
       if (__isinf_nsl (__imag__ x))
 	{
-	  __real__ res = __copysignl (0.0, __real__ x);
+	  if (isfinite (__real__ x) &&  fabsl (__real__ x) > 1.0L)
+	    {
+	      long double sinrx, cosrx;
+	      __sincosl (__real__ x, &sinrx, &cosrx);
+	      __real__ res = __copysignl (0.0L, sinrx * cosrx);
+	    }
+	  else
+	    __real__ res = __copysignl (0.0, __real__ x);
 	  __imag__ res = __copysignl (1.0, __imag__ x);
 	}
       else if (__real__ x == 0.0)