Fix ldbl-96, ldbl-128ibm atanhl inaccuracy (bug 18046, bug 18047).

The threshold in ldbl-96 atanhl for when to return the argument,
0x1p-28, is a bit too big, and that in ldbl-128ibm atanhl is much too
big (the relevant condition being x^3/3 being < 0.5ulp of x),
resulting in errors a bit above the limits of those considered
acceptable in glibc in the ldbl-96 case, and in large errors in the
ldbl-128ibm case.  This patch changes those implementations to use
more appropriate thresholds and adds tests around the thresholds for
various formats.

Tested for x86_64, x86 and powerpc.  x86_64 and x86 ulps updated
accordingly.

	[BZ #18046]
	[BZ #18047]
	* sysdeps/ieee754/ldbl-128ibm/e_atanhl.c (__ieee754_atanhl): Use
	0x1p-56L as threshold for just returning the argument.
	* sysdeps/ieee754/ldbl-96/e_atanhl.c (__ieee754_atanhl): Use
	0x1p-32L as threshold for just returning the argument.
	* math/auto-libm-test-in: Add more tests of atanh.
	* math/auto-libm-test-out: Regenerated.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulp: Likewise.

ChangeLog

@@ -1,3 +1,16 @@
+2015-02-27  Joseph Myers  <joseph@codesourcery.com>
+
+	[BZ #18046]
+	[BZ #18047]
+	* sysdeps/ieee754/ldbl-128ibm/e_atanhl.c (__ieee754_atanhl): Use
+	0x1p-56L as threshold for just returning the argument.
+	* sysdeps/ieee754/ldbl-96/e_atanhl.c (__ieee754_atanhl): Use
+	0x1p-32L as threshold for just returning the argument.
+	* math/auto-libm-test-in: Add more tests of atanh.
+	* math/auto-libm-test-out: Regenerated.
+	* sysdeps/i386/fpu/libm-test-ulps: Update.
+	* sysdeps/x86_64/fpu/libm-test-ulp: Likewise.
+
 2015-02-27  Wilco Dijkstra  wdijkstr@arm.com
 
 	* string/bcopy.c (bcopy): Call memmove for performance.

NEWS

@@ -12,7 +12,8 @@ Version 2.22
   4719, 14841, 13064, 14094, 15319, 15467, 15790, 15969, 16351, 16560,
   16783, 17269, 17523, 17569, 17588, 17792, 17836, 17912, 17916, 17932,
   17944, 17949, 17964, 17965, 17967, 17969, 17978, 17987, 17991, 17996,
-  17998, 17999, 18019, 18020, 18029, 18030, 18032, 18038, 18039.
+  17998, 17999, 18019, 18020, 18029, 18030, 18032, 18038, 18039, 18046,
+  18047.
 
 * Character encoding and ctype tables were updated to Unicode 7.0.0, using
   new generator scripts contributed by Pravin Satpute and Mike FABIAN (Red

math/auto-libm-test-in

@@ -300,7 +300,38 @@ atanh 0.25
 atanh 0x1p-5
 atanh 0x1p-10
 atanh 0x1.2345p-20
+atanh 0x1p-8
+atanh 0x1p-9
+atanh 0x1p-10
+atanh 0x1p-11
+atanh 0x1p-12
+atanh 0x1p-13
+atanh 0x1p-24
+atanh 0x1p-25
+atanh 0x1p-26
+atanh 0x1p-27
+atanh 0x1p-28
+atanh 0x1p-29
+atanh 0x1p-30
+atanh 0x1p-31
+atanh 0x1p-32
+atanh 0x1p-33
+atanh 0x1p-48
+atanh 0x1p-49
+atanh 0x1p-50
+atanh 0x1p-51
+atanh 0x1p-52
+atanh 0x1p-53
+atanh 0x1p-54
+atanh 0x1p-55
+atanh 0x1p-56
+atanh 0x1p-57
+atanh 0x1p-58
+atanh 0x1p-59
+atanh 0x1p-100
 # Bug 16352: underflow exception may be missing.
+atanh 0x1p-500 missing-underflow
+atanh 0x1p-5000 missing-underflow
 atanh min missing-underflow
 atanh -min missing-underflow
 atanh min_subnorm missing-underflow

sysdeps/i386/fpu/libm-test-ulps

@@ -150,6 +150,8 @@ ildouble: 2
 ldouble: 1
 
 Function: "atanh_towardzero":
+double: 1
+float: 1
 idouble: 1
 ifloat: 1
 ildouble: 4

sysdeps/ieee754/ldbl-128ibm/e_atanhl.c

@@ -54,7 +54,7 @@ __ieee754_atanhl(long double x)
 	    if (t == one)
 		return x/zero;
 	}
-	if(ix<0x3e20000000000000LL&&(huge+x)>zero) return x;	/* x<2**-29 */
+	if(ix<0x3c70000000000000LL&&(huge+x)>zero) return x;	/* x<2**-56 */
 	x = fabsl (x);
 	if(ix<0x3fe0000000000000LL) {		/* x < 0.5 */
 	    t = x+x;

sysdeps/ieee754/ldbl-96/e_atanhl.c

@@ -52,9 +52,9 @@ __ieee754_atanhl(long double x)
 	    return (x-x)/(x-x);
 	if(ix==0x3fff)
 	    return x/zero;
-	if(ix<0x3fe3) {
+	if(ix<0x3fdf) {
 	    math_force_eval(huge+x);
-	    return x;	/* x<2**-28 */
+	    return x;	/* x<2**-32 */
 	}
 	SET_LDOUBLE_EXP(x,ix);
 	if(ix<0x3ffe) {		/* x < 0.5 */

sysdeps/x86_64/fpu/libm-test-ulps

@@ -170,7 +170,9 @@ ildouble: 1
 ldouble: 1
 
 Function: "atanh":
+double: 1
 float: 1
+idouble: 1
 ifloat: 1
 ildouble: 1
 ldouble: 1
@@ -184,7 +186,9 @@ ildouble: 2
 ldouble: 2
 
 Function: "atanh_towardzero":
+double: 1
 float: 1
+idouble: 1
 ifloat: 1
 ildouble: 2
 ldouble: 2