Fix atanf spurious underflows (bug 18196).

The sysdeps/ieee754/flt-32 version of atanf produces spurious
underflow exceptions for some large arguments, because of computations
that compute x^-4.  This patch fixes this by adjusting the threshold
for large arguments (for which +/- pi/2 can just be returned, the
correct result being roughly +/- pi/2 - 1/x) from 2^34 to 2^25.

Tested for x86_64 and x86.

	[BZ #18196]
	* sysdeps/ieee754/flt-32/s_atanf.c (__atanf): Use 2^25 not 2^34 as
	threshold for large arguments.
	* math/auto-libm-test-in: Add another test of atan.
	* math/auto-libm-test-out: Regenerated.

5 files changed, 35 insertions, 3 deletions

diff --git a/ChangeLog b/ChangeLog
index f6bf877b16..1179142c92 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,5 +1,11 @@
 2015-05-14  Joseph Myers  <joseph@codesourcery.com>
 
+	[BZ #18196]
+	* sysdeps/ieee754/flt-32/s_atanf.c (__atanf): Use 2^25 not 2^34 as
+	threshold for large arguments.
+	* math/auto-libm-test-in: Add another test of atan.
+	* math/auto-libm-test-out: Regenerated.
+
 	[BZ #16339]
 	* sysdeps/i386/fpu/s_log1p.S (dbl_min): New object.
 	(__log1p): Force underflow exception for results with small
diff --git a/NEWS b/NEWS
index a9b0138b3e..c46ee35103 100644
--- a/NEWS
+++ b/NEWS
@@ -16,8 +16,8 @@ Version 2.22
   17964, 17965, 17967, 17969, 17978, 17987, 17991, 17996, 17998, 17999,
   18007, 18019, 18020, 18029, 18030, 18032, 18036, 18038, 18039, 18042,
   18043, 18046, 18047, 18068, 18080, 18093, 18100, 18104, 18110, 18111,
-  18125, 18128, 18138, 18185, 18197, 18206, 18210, 18211, 18247, 18287,
-  18319, 18333, 18346, 18397, 18409.
+  18125, 18128, 18138, 18185, 18196, 18197, 18206, 18210, 18211, 18247,
+  18287, 18319, 18333, 18346, 18397, 18409.
 
 * Cache information can be queried via sysconf() function on s390 e.g. with
   _SC_LEVEL1_ICACHE_SIZE as argument.
diff --git a/math/auto-libm-test-in b/math/auto-libm-test-in
index 7e5c7bb254..1deb99ad0d 100644
--- a/math/auto-libm-test-in
+++ b/math/auto-libm-test-in
@@ -239,6 +239,7 @@ atan 0x1p-5
 atan 2.5
 atan 10
 atan 1e6
+atan 0x1p31
 atan 0x1p-100
 atan 0x1p-600
 atan 0x1p-10000
diff --git a/math/auto-libm-test-out b/math/auto-libm-test-out
index 7c8a3fb8ff..9f6bbbbf6f 100644
--- a/math/auto-libm-test-out
+++ b/math/auto-libm-test-out
@@ -7796,6 +7796,31 @@ atan 1e6
 = atan tonearest ldbl-128ibm 0xf.424p+16L : 0x1.921fa47d4b30ce822275563fcb8p+0L : inexact-ok
 = atan towardzero ldbl-128ibm 0xf.424p+16L : 0x1.921fa47d4b30ce822275563fcb8p+0L : inexact-ok
 = atan upward ldbl-128ibm 0xf.424p+16L : 0x1.921fa47d4b30ce822275563fccp+0L : inexact-ok
+atan 0x1p31
+= atan downward flt-32 0x8p+28f : 0x1.921fb4p+0f : inexact-ok
+= atan tonearest flt-32 0x8p+28f : 0x1.921fb6p+0f : inexact-ok
+= atan towardzero flt-32 0x8p+28f : 0x1.921fb4p+0f : inexact-ok
+= atan upward flt-32 0x8p+28f : 0x1.921fb6p+0f : inexact-ok
+= atan downward dbl-64 0x8p+28 : 0x1.921fb54242d18p+0 : inexact-ok
+= atan tonearest dbl-64 0x8p+28 : 0x1.921fb54242d18p+0 : inexact-ok
+= atan towardzero dbl-64 0x8p+28 : 0x1.921fb54242d18p+0 : inexact-ok
+= atan upward dbl-64 0x8p+28 : 0x1.921fb54242d19p+0 : inexact-ok
+= atan downward ldbl-96-intel 0x8p+28L : 0x1.921fb54242d18468p+0L : inexact-ok
+= atan tonearest ldbl-96-intel 0x8p+28L : 0x1.921fb54242d1846ap+0L : inexact-ok
+= atan towardzero ldbl-96-intel 0x8p+28L : 0x1.921fb54242d18468p+0L : inexact-ok
+= atan upward ldbl-96-intel 0x8p+28L : 0x1.921fb54242d1846ap+0L : inexact-ok
+= atan downward ldbl-96-m68k 0x8p+28L : 0x1.921fb54242d18468p+0L : inexact-ok
+= atan tonearest ldbl-96-m68k 0x8p+28L : 0x1.921fb54242d1846ap+0L : inexact-ok
+= atan towardzero ldbl-96-m68k 0x8p+28L : 0x1.921fb54242d18468p+0L : inexact-ok
+= atan upward ldbl-96-m68k 0x8p+28L : 0x1.921fb54242d1846ap+0L : inexact-ok
+= atan downward ldbl-128 0x8p+28L : 0x1.921fb54242d18469898cc519ac62p+0L : inexact-ok
+= atan tonearest ldbl-128 0x8p+28L : 0x1.921fb54242d18469898cc519ac63p+0L : inexact-ok
+= atan towardzero ldbl-128 0x8p+28L : 0x1.921fb54242d18469898cc519ac62p+0L : inexact-ok
+= atan upward ldbl-128 0x8p+28L : 0x1.921fb54242d18469898cc519ac63p+0L : inexact-ok
+= atan downward ldbl-128ibm 0x8p+28L : 0x1.921fb54242d18469898cc519acp+0L : inexact-ok
+= atan tonearest ldbl-128ibm 0x8p+28L : 0x1.921fb54242d18469898cc519ac8p+0L : inexact-ok
+= atan towardzero ldbl-128ibm 0x8p+28L : 0x1.921fb54242d18469898cc519acp+0L : inexact-ok
+= atan upward ldbl-128ibm 0x8p+28L : 0x1.921fb54242d18469898cc519ac8p+0L : inexact-ok
 atan 0x1p-100
 = atan downward flt-32 0x1p-100f : 0xf.fffffp-104f : inexact-ok
 = atan tonearest flt-32 0x1p-100f : 0x1p-100f : inexact-ok
diff --git a/sysdeps/ieee754/flt-32/s_atanf.c b/sysdeps/ieee754/flt-32/s_atanf.c
index 159391894f..be2addbdff 100644
--- a/sysdeps/ieee754/flt-32/s_atanf.c
+++ b/sysdeps/ieee754/flt-32/s_atanf.c
@@ -60,7 +60,7 @@ float __atanf(float x)
 
 	GET_FLOAT_WORD(hx,x);
 	ix = hx&0x7fffffff;
-	if(ix>=0x50800000) {	/* if |x| >= 2^34 */
+	if(ix>=0x4c000000) {	/* if |x| >= 2^25 */
 	    if(ix>0x7f800000)
 		return x+x;		/* NaN */
 	    if(hx>0) return  atanhi[3]+atanlo[3];