yann@1201: Original patch from: gentoo/src/patchsets/glibc/2.9/0090_all_glibc-math-tests.patch
yann@1201: 
yann@1201: -= BEGIN original header =-
yann@1201: From: "Joseph S. Myers" <joseph at codesourcery dot com>
yann@1201: To: libc-alpha at sourceware dot org
yann@1201: Date: Tue, 15 Jul 2008 14:43:04 +0000 (UTC)
yann@1201: Subject: expm1 ulps
yann@1201: 
yann@1201: If you test glibc on i686 with GCC 4.3, you get a test-ildoubl failure:
yann@1201: 
yann@1201: Failure: Test: expm1 (1) == M_El - 1.0
yann@1201: Result:
yann@1201:  is:          1.71828182845904523532e+00   0xd.bf0a8b14576953500000p-3
yann@1201:  should be:   1.71828182845904523543e+00   0xd.bf0a8b14576953600000p-3
yann@1201:  difference:  1.08420217248550443401e-19   0x8.00000000000000000000p-66
yann@1201:  ulp       :  1.0000
yann@1201:  max.ulp   :  0.0000
yann@1201: Maximal error of `expm1'
yann@1201:  is      : 1 ulp
yann@1201:  accepted: 0 ulp
yann@1201: 
yann@1201: What happens is that the inline expansion of expm1l uses __builtin_expm1l,
yann@1201: and GCC 4.3 optimizes calls to __builtin_expm1l with constant argument to
yann@1201: a correctly rounded result using MPFR.  The result returned is thus the
yann@1201: value of e-1 rounded once to long double precision.  However, the test
yann@1201: expects M_El - 1.0, and the result of rounding e to long double precision,
yann@1201: then subtracting 1, differs in the last place from the result of rounding
yann@1201: e-1 to long double precision (the latter has smaller exponent, and the
yann@1201: last bit is 1).
yann@1201: 
yann@1201: There are two obvious approaches possible to fixing this.  The first patch
yann@1201: below changes the expectation to a decimal expansion for e-1 (taken from
yann@1201: that of M_El) rather than doing arithmetic in the expected value.  This in
yann@1201: turn requires ulps to be set for the out-of-line version of expm1.  It
yann@1201: might also need ulps to be set for the inline version for older compilers
yann@1201: if they should continue to pass the test, and possibly for other targets.
yann@1201: The second patch below takes the alternative approach of keeping the
yann@1201: existing expectation (which has the wrong bit in the last place) and
yann@1201: setting ulps for the inline expansion of expm1, which avoids the risk of
yann@1201: breaking the test for other targets.
yann@1201: 
yann@1201: 2008-07-15  Joseph Myers  <joseph@codesourcery.com>
yann@1201: 
yann@1201:         * sysdeps/i386/fpu/libm-test-ulps: Add inline long double ulps for
yann@1201:         expm1.
yann@1201: 
yann@1201: -= END original header =-
yann@1201: 
yann@1201: diff -durN glibc-2_9.orig/sysdeps/i386/fpu/libm-test-ulps glibc-2_9/sysdeps/i386/fpu/libm-test-ulps
yann@1201: --- glibc-2_9.orig/sysdeps/i386/fpu/libm-test-ulps	2006-01-15 18:59:37.000000000 +0100
yann@1201: +++ glibc-2_9/sysdeps/i386/fpu/libm-test-ulps	2009-02-02 22:00:47.000000000 +0100
yann@1201: @@ -453,6 +453,10 @@
yann@1201:  ildouble: 8
yann@1201:  ldouble: 8
yann@1201:  
yann@1201: +# expm1
yann@1201: +Test "expm1 (1) == M_El - 1.0":
yann@1201: +ildouble: 1
yann@1201: +
yann@1201:  # gamma
yann@1201:  Test "gamma (-0.5) == log(2*sqrt(pi))":
yann@1201:  double: 1
yann@1201: @@ -1134,6 +1138,9 @@
yann@1201:  ildouble: 8
yann@1201:  ldouble: 8
yann@1201:  
yann@1201: +Function: "expm1":
yann@1201: +ildouble: 1
yann@1201: +
yann@1201:  Function: "gamma":
yann@1201:  double: 1
yann@1201:  idouble: 1