Fix tanf spurious underflows (bug 18221).

The flt-32 implementation of tanf produces spurious underflow
exceptions for some small arguments, through computing values on the
order of x^5.  This patch fixes this by adjusting the threshold for
returning x (or, as applicable, +/- 1/x) to 2**-13 (the next term in
the power series being x^3/3).

Tested for x86_64 and x86.

	[BZ #18221]
	* sysdeps/ieee754/flt-32/k_tanf.c (__kernel_tanf): Use 2**-13 not
	2**-28 as threshold for returning x or +/- 1/x.
	* math/auto-libm-test-in: Add more tests of tan.
	* math/auto-libm-test-out: Regenerated.

5 files changed, 60 insertions, 2 deletions

diff --git a/ChangeLog b/ChangeLog
index 2b29214422..92b4e2dac0 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,5 +1,11 @@
 2015-05-15  Joseph Myers  <joseph@codesourcery.com>
 
+	[BZ #18221]
+	* sysdeps/ieee754/flt-32/k_tanf.c (__kernel_tanf): Use 2**-13 not
+	2**-28 as threshold for returning x or +/- 1/x.
+	* math/auto-libm-test-in: Add more tests of tan.
+	* math/auto-libm-test-out: Regenerated.
+
 	[BZ #18220]
 	* sysdeps/ieee754/flt-32/e_lgammaf_r.c (__ieee754_lgammaf_r): Use
 	2**26 not 2**58 as threshold for returning x * (log (x) - 1).
diff --git a/NEWS b/NEWS
index b85ba6017d..44803fad66 100644
--- a/NEWS
+++ b/NEWS
@@ -17,7 +17,7 @@ Version 2.22
   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, 18196, 18197, 18206, 18210, 18211,
-  18217, 18220, 18247, 18287, 18319, 18333, 18346, 18397, 18409.
+  18217, 18220, 18221, 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 2a88403aa7..e483569dad 100644
--- a/math/auto-libm-test-in
+++ b/math/auto-libm-test-in
@@ -2418,6 +2418,8 @@ tan pi/4
 tan 0.75
 tan 0x1p65
 tan -0x1p65
+tan 0x1p-27
+tan -0x1p-27
 tan 0xc.9p-4
 tan 0xc.908p-4
 tan 0xc.90cp-4
diff --git a/math/auto-libm-test-out b/math/auto-libm-test-out
index 0aa7b75c3b..d7bfbb3b7c 100644
--- a/math/auto-libm-test-out
+++ b/math/auto-libm-test-out
@@ -186618,6 +186618,56 @@ tan -0x1p65
 = tan tonearest ldbl-128ibm -0x2p+64L : 0xc.17b0bfdb2b8061e7b11d500874p-8L : inexact-ok
 = tan towardzero ldbl-128ibm -0x2p+64L : 0xc.17b0bfdb2b8061e7b11d50087p-8L : inexact-ok
 = tan upward ldbl-128ibm -0x2p+64L : 0xc.17b0bfdb2b8061e7b11d500874p-8L : inexact-ok
+tan 0x1p-27
+= tan downward flt-32 0x2p-28f : 0x2p-28f : inexact-ok
+= tan tonearest flt-32 0x2p-28f : 0x2p-28f : inexact-ok
+= tan towardzero flt-32 0x2p-28f : 0x2p-28f : inexact-ok
+= tan upward flt-32 0x2p-28f : 0x2.000004p-28f : inexact-ok
+= tan downward dbl-64 0x2p-28 : 0x2p-28 : inexact-ok
+= tan tonearest dbl-64 0x2p-28 : 0x2p-28 : inexact-ok
+= tan towardzero dbl-64 0x2p-28 : 0x2p-28 : inexact-ok
+= tan upward dbl-64 0x2p-28 : 0x2.0000000000002p-28 : inexact-ok
+= tan downward ldbl-96-intel 0x2p-28L : 0x2.00000000000002a8p-28L : inexact-ok
+= tan tonearest ldbl-96-intel 0x2p-28L : 0x2.00000000000002acp-28L : inexact-ok
+= tan towardzero ldbl-96-intel 0x2p-28L : 0x2.00000000000002a8p-28L : inexact-ok
+= tan upward ldbl-96-intel 0x2p-28L : 0x2.00000000000002acp-28L : inexact-ok
+= tan downward ldbl-96-m68k 0x2p-28L : 0x2.00000000000002a8p-28L : inexact-ok
+= tan tonearest ldbl-96-m68k 0x2p-28L : 0x2.00000000000002acp-28L : inexact-ok
+= tan towardzero ldbl-96-m68k 0x2p-28L : 0x2.00000000000002a8p-28L : inexact-ok
+= tan upward ldbl-96-m68k 0x2p-28L : 0x2.00000000000002acp-28L : inexact-ok
+= tan downward ldbl-128 0x2p-28L : 0x2.00000000000002aaaaaaaaaaaaaep-28L : inexact-ok
+= tan tonearest ldbl-128 0x2p-28L : 0x2.00000000000002aaaaaaaaaaaaaep-28L : inexact-ok
+= tan towardzero ldbl-128 0x2p-28L : 0x2.00000000000002aaaaaaaaaaaaaep-28L : inexact-ok
+= tan upward ldbl-128 0x2p-28L : 0x2.00000000000002aaaaaaaaaaaabp-28L : inexact-ok
+= tan downward ldbl-128ibm 0x2p-28L : 0x2.00000000000002aaaaaaaaaaaap-28L : inexact-ok
+= tan tonearest ldbl-128ibm 0x2p-28L : 0x2.00000000000002aaaaaaaaaaabp-28L : inexact-ok
+= tan towardzero ldbl-128ibm 0x2p-28L : 0x2.00000000000002aaaaaaaaaaaap-28L : inexact-ok
+= tan upward ldbl-128ibm 0x2p-28L : 0x2.00000000000002aaaaaaaaaaabp-28L : inexact-ok
+tan -0x1p-27
+= tan downward flt-32 -0x2p-28f : -0x2.000004p-28f : inexact-ok
+= tan tonearest flt-32 -0x2p-28f : -0x2p-28f : inexact-ok
+= tan towardzero flt-32 -0x2p-28f : -0x2p-28f : inexact-ok
+= tan upward flt-32 -0x2p-28f : -0x2p-28f : inexact-ok
+= tan downward dbl-64 -0x2p-28 : -0x2.0000000000002p-28 : inexact-ok
+= tan tonearest dbl-64 -0x2p-28 : -0x2p-28 : inexact-ok
+= tan towardzero dbl-64 -0x2p-28 : -0x2p-28 : inexact-ok
+= tan upward dbl-64 -0x2p-28 : -0x2p-28 : inexact-ok
+= tan downward ldbl-96-intel -0x2p-28L : -0x2.00000000000002acp-28L : inexact-ok
+= tan tonearest ldbl-96-intel -0x2p-28L : -0x2.00000000000002acp-28L : inexact-ok
+= tan towardzero ldbl-96-intel -0x2p-28L : -0x2.00000000000002a8p-28L : inexact-ok
+= tan upward ldbl-96-intel -0x2p-28L : -0x2.00000000000002a8p-28L : inexact-ok
+= tan downward ldbl-96-m68k -0x2p-28L : -0x2.00000000000002acp-28L : inexact-ok
+= tan tonearest ldbl-96-m68k -0x2p-28L : -0x2.00000000000002acp-28L : inexact-ok
+= tan towardzero ldbl-96-m68k -0x2p-28L : -0x2.00000000000002a8p-28L : inexact-ok
+= tan upward ldbl-96-m68k -0x2p-28L : -0x2.00000000000002a8p-28L : inexact-ok
+= tan downward ldbl-128 -0x2p-28L : -0x2.00000000000002aaaaaaaaaaaabp-28L : inexact-ok
+= tan tonearest ldbl-128 -0x2p-28L : -0x2.00000000000002aaaaaaaaaaaaaep-28L : inexact-ok
+= tan towardzero ldbl-128 -0x2p-28L : -0x2.00000000000002aaaaaaaaaaaaaep-28L : inexact-ok
+= tan upward ldbl-128 -0x2p-28L : -0x2.00000000000002aaaaaaaaaaaaaep-28L : inexact-ok
+= tan downward ldbl-128ibm -0x2p-28L : -0x2.00000000000002aaaaaaaaaaabp-28L : inexact-ok
+= tan tonearest ldbl-128ibm -0x2p-28L : -0x2.00000000000002aaaaaaaaaaabp-28L : inexact-ok
+= tan towardzero ldbl-128ibm -0x2p-28L : -0x2.00000000000002aaaaaaaaaaaap-28L : inexact-ok
+= tan upward ldbl-128ibm -0x2p-28L : -0x2.00000000000002aaaaaaaaaaaap-28L : inexact-ok
 tan 0xc.9p-4
 = tan downward flt-32 0xc.9p-4f : 0xf.fe04cp-4f : inexact-ok
 = tan tonearest flt-32 0xc.9p-4f : 0xf.fe04dp-4f : inexact-ok
diff --git a/sysdeps/ieee754/flt-32/k_tanf.c b/sysdeps/ieee754/flt-32/k_tanf.c
index d918826338..a67f36e283 100644
--- a/sysdeps/ieee754/flt-32/k_tanf.c
+++ b/sysdeps/ieee754/flt-32/k_tanf.c
@@ -45,7 +45,7 @@ float __kernel_tanf(float x, float y, int iy)
 	int32_t ix,hx;
 	GET_FLOAT_WORD(hx,x);
 	ix = hx&0x7fffffff;	/* high word of |x| */
-	if(ix<0x31800000)			/* x < 2**-28 */
+	if(ix<0x39000000)			/* x < 2**-13 */
 	    {if((int)x==0) {			/* generate inexact */
 		if((ix|(iy+1))==0) return one/fabsf(x);
 		else return (iy==1)? x: -one/x;