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.

6 files changed, 49 insertions, 11 deletions

diff --git a/ChangeLog b/ChangeLog
index 951b3f5a4f..e70cd2fbdc 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,13 @@
+2015-09-26  Joseph Myers  <joseph@codesourcery.com>
+
+	[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.
+
 2015-09-25  Joseph Myers  <joseph@codesourcery.com>
 
 	[BZ #18825]
diff --git a/NEWS b/NEWS
index 168e641120..aa9ca4bc9d 100644
--- a/NEWS
+++ b/NEWS
@@ -15,8 +15,8 @@ Version 2.23
   18084, 18086, 18240, 18265, 18370, 18421, 18480, 18525, 18595, 18610,
   18618, 18647, 18661, 18674, 18675, 18681, 18757, 18778, 18781, 18787,
   18789, 18790, 18795, 18796, 18803, 18820, 18823, 18824, 18825, 18857,
-  18863, 18870, 18872, 18873, 18875, 18887, 18921, 18951, 18952, 18961,
-  18966, 18967, 18970, 18977, 18980, 18981, 19003.
+  18863, 18870, 18872, 18873, 18875, 18887, 18921, 18951, 18952, 18956,
+  18961, 18966, 18967, 18970, 18977, 18980, 18981, 19003.
 
 * The obsolete header <regexp.h> has been removed.  Programs that require
   this header must be updated to use <regex.h> instead.
diff --git a/math/auto-libm-test-in b/math/auto-libm-test-in
index 4b93857efb..e86be23fc8 100644
--- a/math/auto-libm-test-in
+++ b/math/auto-libm-test-in
@@ -3219,6 +3219,7 @@ pow 0x1.ce78f2p+0 -0x2.7f1f78p+4
 pow 0xf.fffffp+124 -0x5.b5b648p+0
 pow 0x1.430d4cp+0 0x5.0e462p+4
 pow 0x9.8b82ap-4 -0x1.99907ap+12
+pow 0xd.73035p-4 -0x1.47bb8p+8
 
 sin 0
 sin -0
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
diff --git a/sysdeps/ieee754/flt-32/e_powf.c b/sysdeps/ieee754/flt-32/e_powf.c
index 18042960c2..c72fe37d3b 100644
--- a/sysdeps/ieee754/flt-32/e_powf.c
+++ b/sysdeps/ieee754/flt-32/e_powf.c
@@ -166,7 +166,9 @@ __ieee754_powf(float x, float y)
 	    GET_FLOAT_WORD(is,s_h);
 	    SET_FLOAT_WORD(s_h,is&0xfffff000);
 	/* t_h=ax+bp[k] High */
-	    SET_FLOAT_WORD(t_h,((ix>>1)|0x20000000)+0x0040000+(k<<21));
+	    SET_FLOAT_WORD (t_h,
+			    ((((ix>>1)|0x20000000)+0x00400000+(k<<21))
+			     & 0xfffff000));
 	    t_l = ax - (t_h-bp[k]);
 	    s_l = v*((u-s_h*t_h)-s_h*t_l);
 	/* compute log(ax) */
diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps
index 127a8e1b4d..12c3dd1e01 100644
--- a/sysdeps/x86_64/fpu/libm-test-ulps
+++ b/sysdeps/x86_64/fpu/libm-test-ulps
@@ -1966,8 +1966,8 @@ Function: "log_vlen8_avx2":
 float: 2
 
 Function: "pow":
-float: 3
-ifloat: 3
+float: 1
+ifloat: 1
 ildouble: 1
 ldouble: 1
 
@@ -2003,25 +2003,25 @@ ldouble: 2
 
 Function: "pow_downward":
 double: 1
-float: 4
+float: 1
 idouble: 1
-ifloat: 4
+ifloat: 1
 ildouble: 4
 ldouble: 4
 
 Function: "pow_towardzero":
 double: 1
-float: 8
+float: 1
 idouble: 1
-ifloat: 8
+ifloat: 1
 ildouble: 1
 ldouble: 1
 
 Function: "pow_upward":
 double: 1
-float: 8
+float: 1
 idouble: 1
-ifloat: 8
+ifloat: 1
 ildouble: 2
 ldouble: 2