This patch fixes bug 16356, bad results from x86 / x86_64 expl /
exp10l in directed rounding modes, the most serious of the bugs shown
up by my patch expanding libm test coverage. When I fixed bug 16293,
I thought it was only necessary to set round-to-nearest when using
frndint in expm1 functions, because in other cases the cancellation
error from having the resulting fractional part close to 1 or -1 would
not be significant. However, in expl and exp10l, the way the final
fractional part gets computed (something more complicated than a
simple subtraction, because more precision is needed than you'd get
that way) can result in a value outside the range [-1, 1] when the
argument to frndint was very close to an integer and was rounded the
"wrong" way because of the rounding mode - and the f2xm1 instruction
has undefined results if its argument is outside [-1, 1], so resulting
in the large errors seen. So this patch removes the USE_AS_EXPM1L
conditionals on the round-to-nearest settings, so all of expl, expm1l
and exp10l now get round-to-nearest used for frndint (meaning the
final fractional part can at most be slightly above 0.5 in
magnitude). Associated tests of exp and exp10 are added and testing
of exp10 in directed rounding modes enabled.
Tested x86_64 and x86 and ulps updated accordingly.
* sysdeps/i386/fpu/e_expl.S (IEEE754_EXPL): Also set
round-to-nearest for [!USE_AS_EXPM1L].
* sysdeps/x86_64/fpu/e_expl.S (IEEE754_EXPL): Likewise.
* math/auto-libm-test-in: Do not expect cosh tests to fail. Add
more tests of exp and exp10. Expect some exp10 tests to miss
exceptions or fail in directed rounding modes.
* math/auto-libm-test-out: Regenerated.
* math/libm-test.inc (exp10_tonearest_test_data): New array.
(exp10_test_tonearest): New function.
(exp10_towardzero_test_data): New array.
(exp10_test_towardzero): New function.
(exp10_downward_test_data): New array.
(exp10_test_downward): New function.
(exp10_upward_test_data): New array.
(exp10_test_upward): New function.
(main): Call the new functions.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
Various libm functions have inadequate test coverage in libm-test.inc
/ auto-libm-test-in - failing to cover all the usual special cases
(infinities, NaNs, zero, large and small finite values, subnormals) as
well as a reasonable range of ordinary inputs and, where appropriate,
inputs close to the thresholds for underflow and overflow.
This patch improves test coverage for real functions [a-c]* (with the
expectation of adding more coverage for other functions later).
Tested x86_64 and x86 and ulps updated accordingly (and eight glibc
bugs and one C11 DR filed for issues found in the process).
* math/auto-libm-test-in: Add more tests of acos, acosh, asin,
asinh, atan, atan2, atanh, cbrt, cos and cosh.
* math/auto-libm-test-out: Regenerated.
* math/libm-test.inc (acosh_test_data): Add more tests.
(atanh_test_data): Likewise.
(ceil_test_data): Likewise.
(copysign_test_data): Likewise.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
This patch moves tests of cpow to auto-libm-test-in, adding the
required support to gen-auto-libm-tests.
Tested x86_64 and x86 and ulps updated accordingly.
* math/auto-libm-test-in: Add tests of cpow.
* math/auto-libm-test-out: Regenerated.
* math/libm-test.inc (cpow_test_data): Use AUTO_TESTS_cc_c.
* * math/gen-auto-libm-tests.c (func_calc_method): Add value
mpc_cc_c.
(func_calc_desc): Add mpc_cc_c union field.
(test_functions): Add cpow.
(special_fill_2pi): New function.
(special_real_inputs): Add 2pi.
(calc_generic_results): Handle mpc_cc_c.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
This patch moves tests of ccos, ccosh, cexp, clog, csqrt, ctan and
ctanh to auto-libm-test-in, adding the required support to
gen-auto-libm-tests. Other TEST_c_c functions aren't moved for now
(although the relevant table entries are put in gen-auto-libm-tests
for it to know how to handle them): clog10 because of a known MPC bug
causing it to hang for at least some pure imaginary inputs (fixed in
SVN, but I'd rather not rely on unreleased versions of MPFR or MPC
even if relying on very recent releases); the inverse trig and
hyperbolic functions because of known slowness in special cases; and
csin / csinh because of observed slowness that I need to investigate
and report to the MPC maintainers. Slowness can be bypassed by moving
to incremental generation (only for new / changed tests) rather than
regenerating the whole of auto-libm-test-out every time, but that
needs implementing. (This patch takes the time for running
gen-auto-libm-tests from about one second to seven, on my system,
which I think is reasonable. The slow functions would make it take
several minutes at least, which seems unreasonable.)
Tested x86_64 and x86 and ulps updated accordingly.
* math/auto-libm-test-in: Add tests of ccos, ccosh, cexp, clog,
csqrt, ctan and ctanh.
* math/auto-libm-test-out: Regenerated.
* math/libm-test.inc (TEST_COND_x86_64): New macro.
(TEST_COND_x86): Likewise.
(ccos_test_data): Use AUTO_TESTS_c_c.
(ccosh_test_data): Likewise.
(cexp_test_data): Likewise.
(clog_test_data): Likewise.
(csqrt_test_data): Likewise.
(ctan_test_data): Likewise.
(ctan_tonearest_test_data): Likewise.
(ctan_towardzero_test_data): Likewise.
(ctan_downward_test_data): Likewise.
(ctan_upward_test_data): Likewise.
(ctanh_test_data): Likewise.
(ctanh_tonearest_test_data): Likewise.
(ctanh_towardzero_test_data): Likewise.
(ctanh_downward_test_data): Likewise.
(ctanh_upward_test_data): Likewise.
* math/gen-auto-libm-tests.c (func_calc_method): Add value
mpc_c_c.
(func_calc_desc): Add mpc_c_c union field.
(FUNC_mpc_c_c): New macro.
(test_functions): Add cacos, cacosh, casin, casinh, catan, catanh,
ccos, ccosh, cexp, clog, clog10, csin, csinh, csqrt, ctan and
ctanh.
(special_fill_min_subnorm_p120): New function.
(special_real_inputs): Add min_subnorm_p120.
(calc_generic_results): Handle mpc_c_c.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
This patch moves tests of cabs and carg to auto-libm-test-in, adding
the required support to gen-auto-libm-tests.
Tested x86_64 and x86; no ulps updates needed.
* math/auto-libm-test-in: Add tests of cabs and carg.
* math/auto-libm-test-out: Regenerated.
* math/libm-test.inc (cabs_test_data): Use AUTO_TESTS_c_f.
(carg_test_data): Likewise.
* math/gen-auto-libm-tests.c (func_calc_method): Add value
mpc_c_f.
(func_calc_desc): Add mpc_c_f union field.
(test_functions): Add cabs and carg.
(calc_generic_results): Handle mpc_c_f.
This patch moves tests of sincos to auto-libm-test-in, adding the
required support to gen-auto-libm-tests.
Tested x86_64 and x86 and ulps updated accordingly.
(auto-libm-test-out diffs omitted below.)
* math/auto-libm-test-in: Add tests of sincos.
* math/auto-libm-test-out: Regenerated.
* math/libm-test.inc (sincos_test_data): Use AUTO_TESTS_fFF_11.
* math/gen-auto-libm-tests.c (func_calc_method): Add value
mpfr_f_11.
(func_calc_desc): Add mpfr_f_11 union field.
(test_functions): Add sincos.
(calc_generic_results): Handle mpfr_f_11.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
Bug 16293 is inaccuracy of x86/x86_64 versions of expm1, near 0 in
directed rounding modes, that arises from frndint rounding the
exponent to 1 or -1 instead of 0, resulting in large cancellation
error. This inaccuracy in turn affects other functions such as sinh
that use expm1. This patch fixes the problem by setting
round-to-nearest mode temporarily around the affected calls to
frndint. I don't think this is needed for other uses of frndint, such
as in exp itself, as only for expm1 is the cancellation error
significant.
Tested x86_64 and x86 and ulps updated accordingly.
* sysdeps/i386/fpu/e_expl.S (IEEE754_EXPL) [USE_AS_EXPM1L]: Set
round-to-nearest mode when using frndint.
* sysdeps/i386/fpu/s_expm1.S (__expm1): Likewise.
* sysdeps/i386/fpu/s_expm1f.S (__expm1f): Likewise.
* sysdeps/x86_64/fpu/e_expl.S (IEEE754_EXPL) [USE_AS_EXPM1L]:
Likewise.
* math/auto-libm-test-in: Add more tests of expm1. Do not expect
sinh test to fail.
* math/auto-libm-test-out: Regenerated.
* math/libm-test.inc (TEST_COND_x86_64): Remove macro.
(TEST_COND_x86): Likewise.
(expm1_tonearest_test_data): New array.
(expm1_test_tonearest): New function.
(expm1_towardzero_test_data): New array.
(expm1_test_towardzero): New function.
(expm1_downward_test_data): New array.
(expm1_test_downward): New function.
(expm1_upward_test_data): New array.
(expm1_test_upward): New function.
(main): Run the new test functions.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
This patch moves tests of jn and yn to auto-libm-test-in, adding the
required support for gen-auto-libm-tests (and adding a missing
assertion there and fixing logic that was broken for functions with
integer arguments).
Tested x86_64 and x86 and ulps updated accordingly.
* math/auto-libm-test-in: Add tests of jn and yn.
* math/auto-libm-test-out: Regenerated.
* math/libm-test.inc (jn_test_data): Use AUTO_TESTS_if_f.
(yn_test_data): Likewise.
* math/gen-auto-libm-tests.c (func_calc_method): Add value
mpfr_if_f.
(func_calc_desc): Add mpfr_if_f union field.
(FUNC_mpfr_if_f): New macro.
(test_functions): Add jn and yn.
(calc_generic_results): Assert type of second input for
mpfr_ff_f. Handle mpfr_if_f.
(output_for_one_input_case): Disable all checking for arguments
fitting floating-point types in case of an integer argument.
* sysdeps/i386/fpu/libm-test-ulps: Update.
* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
http://sourceware.org/ml/libc-alpha/2013-08/msg00084.html
Another batch of ieee854 macros and union replacement. These four
files also have bugs fixed with this patch. The fact that the two
doubles in an IBM long double may have different signs means that
negation and absolute value operations can't just twiddle one sign bit
as you can with ieee864 style extended double. fmodl, remainderl,
erfl and erfcl all had errors of this type. erfl also returned +1 for
large magnitude negative input where it should return -1. The hypotl
error is innocuous since the value adjusted twice is only used as a
flag. The e_hypotl.c tests for large "a" and small "b" are mutually
exclusive because we've already exited when x/y > 2**120. That allows
some further small simplifications.
[BZ #15734], [BZ #15735]
* sysdeps/ieee754/ldbl-128ibm/e_fmodl.c (__ieee754_fmodl): Rewrite
all uses of ieee875 long double macros and unions. Simplify test
for 0.0L. Correct |x|<|y| and |x|=|y| test. Use
ldbl_extract_mantissa value for ix,iy exponents. Properly
normalize after ldbl_extract_mantissa, and don't add hidden bit
already handled. Don't treat low word of ieee854 mantissa like
low word of IBM long double and mask off bit when testing for
zero.
* sysdeps/ieee754/ldbl-128ibm/e_hypotl.c (__ieee754_hypotl): Rewrite
all uses of ieee875 long double macros and unions. Simplify tests
for 0.0L and inf. Correct double adjustment of k. Delete dead code
adjusting ha,hb. Simplify code setting kld. Delete two600 and
two1022, instead use their values. Recognise that tests for large
"a" and small "b" are mutually exclusive. Rename vars. Comment.
* sysdeps/ieee754/ldbl-128ibm/e_remainderl.c (__ieee754_remainderl):
Rewrite all uses of ieee875 long double macros and unions. Simplify
test for 0.0L and nan. Correct negation.
* sysdeps/ieee754/ldbl-128ibm/s_erfl.c (__erfl): Rewrite all uses of
ieee875 long double macros and unions. Correct output for large
magnitude x. Correct absolute value calculation.
(__erfcl): Likewise.
* math/libm-test.inc: Add tests for errors discovered in IBM long
double versions of fmodl, remainderl, erfl and erfcl.
In 128-bit IBM long double the precision of the type
decreases as you approach subnormal numbers, equaling
that of a double for subnormal numbers. Therefore
adjust the computation in ulp to use 2^(MIN_EXP - MANT_DIG)
which is correct for FP_SUBNORMAL for all types.
The current value used for ulp near zero is wrong,
and this commit fixes it such that ulp(0) is the smallest
subnormal value nearest to zero, which makes the most
sense for testing values near zero. Note that this is not
what Java does; they use the nearest normal value, which
is less accurate than what we want for glibc. Note that
there is no correct implementation of ulp since there
is no strict mathmatical definition that is accepted by
all groups using IEEE 754.
Previously with the large ulp values near zero there
were tests that previously passed, but were in fact
billions of ulp away from the precise answer. With this
commit we now need to disable one of the cpow tests which
is revealed to be inaccurate (bug 14473).
---
2013-05-24 Carlos O'Donell <carlos@redhat.com>
* math/libm-test.inc (MAX_EXP): Define.
(ULPDIFF): Define.
(ulp): New function.
(check_float_internal): Use ULPDIFF.
(cpow_test): Disable failing test.
(check_ulp): Test ulp() implemetnation.
(main): Call check_ulp before starting tests.
Allan McRae
Joseph Myers
Alan Modra
Siddhesh Poyarekar
Andreas Schwab
David S. Miller
Carlos O'Donell