Fix powf inaccuracy (bug 18956).

The flt-32 version of powf can be inaccurate because of bugs in the
extra-precision calculation of (x-1)/(x+1) or (x-1.5)/(x+1.5) as part
of calculating log(x) with extra precision: a constant used (as part
of adding 1 or 1.5 through integer arithmetic) is incorrect, and then
the code fails to mask a computed high part before using it in
arithmetic that relies on s_h*t_h being exactly representable.  This
patch fixes these bugs.

Tested for x86_64 and x86.  x86_64 ulps for powf removed and
regenerated to reflect reduced ulps from the increased accuracy for
existing tests.

	[BZ #18956]
	* sysdeps/ieee754/flt-32/e_powf.c (__ieee754_powf): Add 0x00400000
	not 0x0040000 for high bit of mantissa.  Mask with 0xfffff000 when
	extracting high part.
	* math/auto-libm-test-in: Add another test of pow.
	* math/auto-libm-test-out: Regenerated.
	* sysdeps/x86_64/fpu/libm-test-ulps: Update.

1 files changed, 25 insertions, 0 deletions

diff --git a/math/auto-libm-test-out b/math/auto-libm-test-out
index 4126a7cd07..bcfa832b7d 100644
--- a/math/auto-libm-test-out
+++ b/math/auto-libm-test-out
@@ -226489,6 +226489,31 @@ pow 0x9.8b82ap-4 -0x1.99907ap+12
 = pow tonearest ldbl-128ibm 0x9.8b82ap-4L -0x1.99907ap+12L : plus_infty : inexact-ok overflow errno-erange
 = pow towardzero ldbl-128ibm 0x9.8b82ap-4L -0x1.99907ap+12L : 0xf.ffffffffffffbffffffffffffcp+1020L : inexact-ok overflow errno-erange-ok
 = pow upward ldbl-128ibm 0x9.8b82ap-4L -0x1.99907ap+12L : plus_infty : inexact-ok overflow errno-erange
+pow 0xd.73035p-4 -0x1.47bb8p+8
+= pow downward flt-32 0xd.73035p-4f -0x1.47bb8p+8f : 0x4.52398p+80f : inexact-ok
+= pow tonearest flt-32 0xd.73035p-4f -0x1.47bb8p+8f : 0x4.523988p+80f : inexact-ok
+= pow towardzero flt-32 0xd.73035p-4f -0x1.47bb8p+8f : 0x4.52398p+80f : inexact-ok
+= pow upward flt-32 0xd.73035p-4f -0x1.47bb8p+8f : 0x4.523988p+80f : inexact-ok
+= pow downward dbl-64 0xd.73035p-4 -0x1.47bb8p+8 : 0x4.523987c590d3p+80 : inexact-ok
+= pow tonearest dbl-64 0xd.73035p-4 -0x1.47bb8p+8 : 0x4.523987c590d3p+80 : inexact-ok
+= pow towardzero dbl-64 0xd.73035p-4 -0x1.47bb8p+8 : 0x4.523987c590d3p+80 : inexact-ok
+= pow upward dbl-64 0xd.73035p-4 -0x1.47bb8p+8 : 0x4.523987c590d34p+80 : inexact-ok
+= pow downward ldbl-96-intel 0xd.73035p-4L -0x1.47bb8p+8L : 0x4.523987c590d3192p+80L : inexact-ok
+= pow tonearest ldbl-96-intel 0xd.73035p-4L -0x1.47bb8p+8L : 0x4.523987c590d31928p+80L : inexact-ok
+= pow towardzero ldbl-96-intel 0xd.73035p-4L -0x1.47bb8p+8L : 0x4.523987c590d3192p+80L : inexact-ok
+= pow upward ldbl-96-intel 0xd.73035p-4L -0x1.47bb8p+8L : 0x4.523987c590d31928p+80L : inexact-ok
+= pow downward ldbl-96-m68k 0xd.73035p-4L -0x1.47bb8p+8L : 0x4.523987c590d3192p+80L : inexact-ok
+= pow tonearest ldbl-96-m68k 0xd.73035p-4L -0x1.47bb8p+8L : 0x4.523987c590d31928p+80L : inexact-ok
+= pow towardzero ldbl-96-m68k 0xd.73035p-4L -0x1.47bb8p+8L : 0x4.523987c590d3192p+80L : inexact-ok
+= pow upward ldbl-96-m68k 0xd.73035p-4L -0x1.47bb8p+8L : 0x4.523987c590d31928p+80L : inexact-ok
+= pow downward ldbl-128 0xd.73035p-4L -0x1.47bb8p+8L : 0x4.523987c590d3192757b32fb92c7p+80L : inexact-ok
+= pow tonearest ldbl-128 0xd.73035p-4L -0x1.47bb8p+8L : 0x4.523987c590d3192757b32fb92c74p+80L : inexact-ok
+= pow towardzero ldbl-128 0xd.73035p-4L -0x1.47bb8p+8L : 0x4.523987c590d3192757b32fb92c7p+80L : inexact-ok
+= pow upward ldbl-128 0xd.73035p-4L -0x1.47bb8p+8L : 0x4.523987c590d3192757b32fb92c74p+80L : inexact-ok
+= pow downward ldbl-128ibm 0xd.73035p-4L -0x1.47bb8p+8L : 0x4.523987c590d3192757b32fb92cp+80L : inexact-ok
+= pow tonearest ldbl-128ibm 0xd.73035p-4L -0x1.47bb8p+8L : 0x4.523987c590d3192757b32fb92cp+80L : inexact-ok
+= pow towardzero ldbl-128ibm 0xd.73035p-4L -0x1.47bb8p+8L : 0x4.523987c590d3192757b32fb92cp+80L : inexact-ok
+= pow upward ldbl-128ibm 0xd.73035p-4L -0x1.47bb8p+8L : 0x4.523987c590d3192757b32fb92ep+80L : inexact-ok
 sin 0
 = sin downward flt-32 0x0p+0f : 0x0p+0f : inexact-ok
 = sin tonearest flt-32 0x0p+0f : 0x0p+0f : inexact-ok