From e02920bc029019443326eecaa7b267b78ff2892e Mon Sep 17 00:00:00 2001 From: Joseph Myers Date: Mon, 29 Jun 2015 23:29:35 +0000 Subject: Improve tgamma accuracy (bug 18613). In non-default rounding modes, tgamma can be slightly less accurate than permitted by glibc's accuracy goals. Part of the problem is error accumulation, addressed in this patch by setting round-to-nearest for internal computations. However, there was also a bug in the code dealing with computing pow (x + n, x + n) where x + n is not exactly representable, providing another source of error even in round-to-nearest mode; it was necessary to address both bugs to get errors for all testcases within glibc's accuracy goals. Given this second fix, accuracy in round-to-nearest mode is also improved (hence regeneration of ulps for tgamma should be from scratch - truncate libm-test-ulps or at least remove existing tgamma entries - so that the expected ulps can be reduced). Some additional complications also arose. Certain tgamma tests should strictly, according to IEEE semantics, overflow or not depending on the rounding mode; this is beyond the scope of glibc's accuracy goals for any function without exactly-determined results, but gen-auto-libm-tests doesn't handle being lax there as it does for underflow. (libm-test.inc also doesn't handle being lax about whether the result in cases very close to the overflow threshold is infinity or a finite value close to overflow, but that doesn't cause problems in this case though I've seen it cause problems with random test generation for some functions.) Thus, spurious-overflow markings, with a comment, are added to auto-libm-test-in (no bug in Bugzilla because the issue is with the testsuite, not a user-visible bug in glibc). And on x86, after the patch I saw ERANGE issues as previously reported by Carlos (see my commentary in ), which needed addressing by ensuring excess range and precision were eliminated at various points if FLT_EVAL_METHOD != 0. I also noticed and fixed a cosmetic issue where 1.0f was used in long double functions and should have been 1.0L. This completes the move of all functions to testing in all rounding modes with ALL_RM_TEST, so gen-libm-have-vector-test.sh is updated to remove the workaround for some functions not using ALL_RM_TEST. Tested for x86_64, x86, mips64 and powerpc. [BZ #18613] * sysdeps/ieee754/dbl-64/e_gamma_r.c (gamma_positive): Take log of X_ADJ not X when adjusting exponent. (__ieee754_gamma_r): Do intermediate computations in round-to-nearest then adjust overflowing and underflowing results as needed. * sysdeps/ieee754/flt-32/e_gammaf_r.c (gammaf_positive): Take log of X_ADJ not X when adjusting exponent. (__ieee754_gammaf_r): Do intermediate computations in round-to-nearest then adjust overflowing and underflowing results as needed. * sysdeps/ieee754/ldbl-128/e_gammal_r.c (gammal_positive): Take log of X_ADJ not X when adjusting exponent. (__ieee754_gammal_r): Do intermediate computations in round-to-nearest then adjust overflowing and underflowing results as needed. Use 1.0L not 1.0f as numerator of division. * sysdeps/ieee754/ldbl-128ibm/e_gammal_r.c (gammal_positive): Take log of X_ADJ not X when adjusting exponent. (__ieee754_gammal_r): Do intermediate computations in round-to-nearest then adjust overflowing and underflowing results as needed. Use 1.0L not 1.0f as numerator of division. * sysdeps/ieee754/ldbl-96/e_gammal_r.c (gammal_positive): Take log of X_ADJ not X when adjusting exponent. (__ieee754_gammal_r): Do intermediate computations in round-to-nearest then adjust overflowing and underflowing results as needed. Use 1.0L not 1.0f as numerator of division. * math/libm-test.inc (tgamma_test_data): Remove one test. Moved to auto-libm-test-in. (tgamma_test): Use ALL_RM_TEST. * math/auto-libm-test-in: Add one test of tgamma. Mark some other tests of tgamma with spurious-overflow. * math/auto-libm-test-out: Regenerated. * math/gen-libm-have-vector-test.sh: Do not check for START. * sysdeps/i386/fpu/libm-test-ulps: Update. * sysdeps/x86_64/fpu/libm-test-ulps: Likewise. --- math/auto-libm-test-in | 10 +++++++--- 1 file changed, 7 insertions(+), 3 deletions(-) (limited to 'math/auto-libm-test-in') diff --git a/math/auto-libm-test-in b/math/auto-libm-test-in index f4313a2..f783c5b 100644 --- a/math/auto-libm-test-in +++ b/math/auto-libm-test-in @@ -2682,19 +2682,22 @@ tgamma 0x1p-113 tgamma -0x1p-113 tgamma 0x1p-127 tgamma -0x1p-127 -tgamma 0x1p-128 +# IEEE semantics mean overflow very close to the threshold depends on +# the rounding mode; gen-auto-libm-tests does not reflect that glibc +# does not try to achieve this. +tgamma 0x1p-128 spurious-overflow:flt-32 tgamma -0x1p-128 tgamma 0x1p-149 tgamma -0x1p-149 tgamma 0x1p-1023 tgamma -0x1p-1023 -tgamma 0x1p-1024 +tgamma 0x1p-1024 spurious-overflow:dbl-64 spurious-overflow:ldbl-128ibm tgamma -0x1p-1024 tgamma 0x1p-1074 tgamma -0x1p-1074 tgamma 0x1p-16383 tgamma -0x1p-16383 -tgamma 0x1p-16384 +tgamma 0x1p-16384 spurious-overflow:ldbl-96-intel spurious-overflow:ldbl-96-m68k spurious-overflow:ldbl-128 tgamma -0x1p-16384 tgamma 0x1p-16445 tgamma -0x1p-16445 @@ -3075,6 +3078,7 @@ tgamma 0x6.db8c603359a971081bc4a2e9dfdp+8 tgamma 0x6.db8c603359a971081bc4a2e9dfd4p+8 tgamma 1e3 tgamma -100000.5 +tgamma max tgamma -0x3.06644cp+0 tgamma -0x6.fe4636e0c5064p+0 -- cgit v1.1