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.

2 files changed, 52 insertions, 0 deletions

diff --git a/math/auto-libm-test-in b/math/auto-libm-test-in
index 2a88403..e483569 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 0aa7b75..d7bfbb3 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