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Original patch from: gentoo/src/patchsets/glibc/2.9/0090_all_glibc-math-tests.patch
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-= BEGIN original header =-
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yann@1365
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From: "Joseph S. Myers" <joseph at codesourcery dot com>
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yann@1365
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To: libc-alpha at sourceware dot org
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yann@1365
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Date: Tue, 15 Jul 2008 14:43:04 +0000 (UTC)
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yann@1365
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Subject: expm1 ulps
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If you test glibc on i686 with GCC 4.3, you get a test-ildoubl failure:
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yann@1365
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Failure: Test: expm1 (1) == M_El - 1.0
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Result:
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is: 1.71828182845904523532e+00 0xd.bf0a8b14576953500000p-3
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should be: 1.71828182845904523543e+00 0xd.bf0a8b14576953600000p-3
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difference: 1.08420217248550443401e-19 0x8.00000000000000000000p-66
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ulp : 1.0000
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max.ulp : 0.0000
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Maximal error of `expm1'
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is : 1 ulp
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accepted: 0 ulp
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What happens is that the inline expansion of expm1l uses __builtin_expm1l,
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and GCC 4.3 optimizes calls to __builtin_expm1l with constant argument to
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a correctly rounded result using MPFR. The result returned is thus the
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value of e-1 rounded once to long double precision. However, the test
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expects M_El - 1.0, and the result of rounding e to long double precision,
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then subtracting 1, differs in the last place from the result of rounding
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e-1 to long double precision (the latter has smaller exponent, and the
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last bit is 1).
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There are two obvious approaches possible to fixing this. The first patch
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yann@1365
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below changes the expectation to a decimal expansion for e-1 (taken from
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that of M_El) rather than doing arithmetic in the expected value. This in
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turn requires ulps to be set for the out-of-line version of expm1. It
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might also need ulps to be set for the inline version for older compilers
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if they should continue to pass the test, and possibly for other targets.
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The second patch below takes the alternative approach of keeping the
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existing expectation (which has the wrong bit in the last place) and
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setting ulps for the inline expansion of expm1, which avoids the risk of
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breaking the test for other targets.
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2008-07-15 Joseph Myers <joseph@codesourcery.com>
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* sysdeps/i386/fpu/libm-test-ulps: Add inline long double ulps for
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expm1.
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-= END original header =-
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diff -durN glibc-2_9.orig/sysdeps/i386/fpu/libm-test-ulps glibc-2_9/sysdeps/i386/fpu/libm-test-ulps
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--- glibc-2_9.orig/sysdeps/i386/fpu/libm-test-ulps 2006-01-15 18:59:37.000000000 +0100
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+++ glibc-2_9/sysdeps/i386/fpu/libm-test-ulps 2009-02-02 22:00:47.000000000 +0100
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@@ -453,6 +453,10 @@
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ildouble: 8
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ldouble: 8
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+# expm1
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+Test "expm1 (1) == M_El - 1.0":
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+ildouble: 1
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+
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# gamma
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Test "gamma (-0.5) == log(2*sqrt(pi))":
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double: 1
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@@ -1134,6 +1138,9 @@
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ildouble: 8
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ldouble: 8
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+Function: "expm1":
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+ildouble: 1
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+
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Function: "gamma":
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double: 1
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idouble: 1
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