| 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 |