Original patch from: gentoo/src/patchsets/glibc/2.9/0090_all_glibc-math-tests.patch

-= BEGIN original header =-

From: "Joseph S. Myers" <joseph at codesourcery dot com>

To: libc-alpha at sourceware dot org

Date: Tue, 15 Jul 2008 14:43:04 +0000 (UTC)

Subject: expm1 ulps

If you test glibc on i686 with GCC 4.3, you get a test-ildoubl failure:

Failure: Test: expm1 (1) == M_El - 1.0

Result:

 is:          1.71828182845904523532e+00   0xd.bf0a8b14576953500000p-3

 should be:   1.71828182845904523543e+00   0xd.bf0a8b14576953600000p-3

 difference:  1.08420217248550443401e-19   0x8.00000000000000000000p-66

 ulp       :  1.0000

 max.ulp   :  0.0000

Maximal error of `expm1'

 is      : 1 ulp

 accepted: 0 ulp

What happens is that the inline expansion of expm1l uses __builtin_expm1l,

and GCC 4.3 optimizes calls to __builtin_expm1l with constant argument to

a correctly rounded result using MPFR.  The result returned is thus the

value of e-1 rounded once to long double precision.  However, the test

expects M_El - 1.0, and the result of rounding e to long double precision,

then subtracting 1, differs in the last place from the result of rounding

e-1 to long double precision (the latter has smaller exponent, and the

last bit is 1).

There are two obvious approaches possible to fixing this.  The first patch

below changes the expectation to a decimal expansion for e-1 (taken from

that of M_El) rather than doing arithmetic in the expected value.  This in

turn requires ulps to be set for the out-of-line version of expm1.  It

might also need ulps to be set for the inline version for older compilers

if they should continue to pass the test, and possibly for other targets.

The second patch below takes the alternative approach of keeping the

existing expectation (which has the wrong bit in the last place) and

setting ulps for the inline expansion of expm1, which avoids the risk of

breaking the test for other targets.

2008-07-15  Joseph Myers  <joseph@codesourcery.com>

        * sysdeps/i386/fpu/libm-test-ulps: Add inline long double ulps for

        expm1.

-= END original header =-

diff -durN glibc-2_9.orig/sysdeps/i386/fpu/libm-test-ulps glibc-2_9/sysdeps/i386/fpu/libm-test-ulps

--- glibc-2_9.orig/sysdeps/i386/fpu/libm-test-ulps	2006-01-15 18:59:37.000000000 +0100

+++ glibc-2_9/sysdeps/i386/fpu/libm-test-ulps	2009-02-02 22:00:47.000000000 +0100

@@ -453,6 +453,10 @@

 ildouble: 8

 ldouble: 8

+# expm1

+Test "expm1 (1) == M_El - 1.0":

+ildouble: 1

+

 # gamma

 Test "gamma (-0.5) == log(2*sqrt(pi))":

 double: 1

@@ -1134,6 +1138,9 @@

 ildouble: 8

 ldouble: 8

+Function: "expm1":

+ildouble: 1

+

 Function: "gamma":

 double: 1

 idouble: 1