Fix cacos (+Inf + finite*i) in round-downward mode (bug 16928).

According to C99/C11 Annex G, cacos applied to a value with real part
+Inf and finite imaginary part should produce a result with real part
+0.  glibc wrongly produces a result with real part -0 in FE_DOWNWARD
mode.  This patch fixes this by checking for zero results in the
relevant case of non-finite arguments (where there should never be a
result with -0 real part), and converts the tests of cacos to
ALL_RM_TEST.

Tested x86_64 and x86 and ulps updated accordingly.

	[BZ #16928]
	* math/s_cacos.c (__cacos): Ensure zero real part of result from
	non-finite arguments is +0.
	* math/s_cacosf.c (__cacosf): Likewise.
	* math/s_cacosl.c (__cacosl): Likewise.
	* math/libm-test.inc (cacos_test): Use ALL_RM_TEST.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.

ChangeLog

@@ -1,5 +1,14 @@
 2014-05-14  Joseph Myers  <joseph@codesourcery.com>
 
+	[BZ #16928]
+	* math/s_cacos.c (__cacos): Ensure zero real part of result from
+	non-finite arguments is +0.
+	* math/s_cacosf.c (__cacosf): Likewise.
+	* math/s_cacosl.c (__cacosl): Likewise.
+	* math/libm-test.inc (cacos_test): Use ALL_RM_TEST.
+	* sysdeps/i386/fpu/libm-test-ulps: Update.
+	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
+
 	[BZ #16927]
 	* sysdeps/i386/fpu/e_acosh.S (__ieee754_acosh): Use fabs on x-1
 	value.

NEWS

@@ -17,7 +17,7 @@ Version 2.20
   16713, 16714, 16731, 16739, 16740, 16743, 16754, 16758, 16759, 16760,
   16770, 16786, 16789, 16791, 16799, 16800, 16815, 16823, 16824, 16831,
   16838, 16854, 16876, 16877, 16885, 16888, 16890, 16912, 16916, 16922,
-  16927, 16932.
+  16927, 16928, 16932.
 
 * The minimum Linux kernel version that this version of the GNU C Library
   can be used with is 2.6.32.

math/libm-test.inc

@@ -2615,9 +2615,7 @@ static const struct test_c_c_data cacos_test_data[] =
 static void
 cacos_test (void)
 {
-  START (cacos, 0);
+  ALL_RM_TEST (cacos, 0, cacos_test_data, RUN_TEST_LOOP_c_c, END_COMPLEX);
-  RUN_TEST_LOOP_c_c (cacos, cacos_test_data, );
-  END_COMPLEX;
 }
 
 static const struct test_c_c_data cacosh_test_data[] =

math/s_cacos.c

@@ -34,6 +34,8 @@ __cacos (__complex__ double x)
       y = __casin (x);
 
       __real__ res = (double) M_PI_2 - __real__ y;
+      if (__real__ res == 0.0)
+	__real__ res = 0.0;
       __imag__ res = -__imag__ y;
     }
   else

math/s_cacosf.c

@@ -34,6 +34,8 @@ __cacosf (__complex__ float x)
       y = __casinf (x);
 
       __real__ res = (float) M_PI_2 - __real__ y;
+      if (__real__ res == 0.0f)
+	__real__ res = 0.0f;
       __imag__ res = -__imag__ y;
     }
   else

math/s_cacosl.c

@@ -34,6 +34,8 @@ __cacosl (__complex__ long double x)
       y = __casinl (x);
 
       __real__ res = M_PI_2l - __real__ y;
+      if (__real__ res == 0.0L)
+	__real__ res = 0.0L;
       __imag__ res = -__imag__ y;
     }
   else

sysdeps/i386/fpu/libm-test-ulps

@@ -173,6 +173,54 @@ ifloat: 1
 ildouble: 2
 ldouble: 2
 
+Function: Real part of "cacos_downward":
+double: 2
+float: 1
+idouble: 2
+ifloat: 1
+ildouble: 2
+ldouble: 2
+
+Function: Imaginary part of "cacos_downward":
+double: 3
+float: 3
+idouble: 3
+ifloat: 3
+ildouble: 5
+ldouble: 5
+
+Function: Real part of "cacos_towardzero":
+double: 2
+float: 1
+idouble: 2
+ifloat: 1
+ildouble: 2
+ldouble: 2
+
+Function: Imaginary part of "cacos_towardzero":
+double: 3
+float: 3
+idouble: 3
+ifloat: 3
+ildouble: 5
+ldouble: 5
+
+Function: Real part of "cacos_upward":
+double: 2
+float: 2
+idouble: 2
+ifloat: 2
+ildouble: 2
+ldouble: 2
+
+Function: Imaginary part of "cacos_upward":
+double: 4
+float: 4
+idouble: 4
+ifloat: 4
+ildouble: 5
+ldouble: 5
+
 Function: Real part of "cacosh":
 double: 1
 float: 1

sysdeps/x86_64/fpu/libm-test-ulps

@@ -199,6 +199,54 @@ ifloat: 2
 ildouble: 2
 ldouble: 2
 
+Function: Real part of "cacos_downward":
+double: 1
+float: 2
+idouble: 1
+ifloat: 2
+ildouble: 2
+ldouble: 2
+
+Function: Imaginary part of "cacos_downward":
+double: 5
+float: 3
+idouble: 5
+ifloat: 3
+ildouble: 5
+ldouble: 5
+
+Function: Real part of "cacos_towardzero":
+double: 1
+float: 2
+idouble: 1
+ifloat: 2
+ildouble: 2
+ldouble: 2
+
+Function: Imaginary part of "cacos_towardzero":
+double: 5
+float: 3
+idouble: 5
+ifloat: 3
+ildouble: 5
+ldouble: 5
+
+Function: Real part of "cacos_upward":
+double: 2
+float: 2
+idouble: 2
+ifloat: 2
+ildouble: 2
+ldouble: 2
+
+Function: Imaginary part of "cacos_upward":
+double: 4
+float: 4
+idouble: 4
+ifloat: 4
+ildouble: 5
+ldouble: 5
+
 Function: Real part of "cacosh":
 double: 1
 float: 2