E.g. known errors:
x = 0x1.000002c5e2e99p+0, y = 0x1.c9eee35374af6p+31 had an error of 639
ULP and is now correctly rounded.
x = 0x1.fffffd2e3e669p-1, y = 0x1.344c9823eb66cp+32 had an error of 428
ULP and is now correctly rounded.
C compilers may fold const values at compile time, so expressions
which try to elicit underflow/overflow by performing simple
arithemetic on suitable values will not generate the required
exceptions.
Work around this by replacing code which does these arithmetic
operations with calls to the existing __math_xflow functions that are
designed to do this correctly.
Signed-off-by: Keith Packard <keithp@keithp.com>
----
v2:
libm/math: Pass sign to __math_xflow instead of muliplying result
The IEEE spec for pow only has special case for x**0 and 1**y when x/y
are quiet NaN. For signaling NaN, the general case applies and these functions
should signal the invalid exception and return a quiet NaN.
Signed-off-by: Keith Packard <keithp@keithp.com>
I think I may have encountered a bug in the implementation of pow:
pow(-1.0, NaN) returns 1.0 when it should return NaN.
Because ix is used to check input vs 1.0 rather than hx, -1.0 is
mistaken for 1.0
The new implementation is provided under !__OBSOLETE_MATH, it uses
ISO C99 code. With default settings the worst case error in nearest
rounding mode is 0.54 ULP with inlined fma and fma contraction. It uses
a 4 KB lookup table in addition to the table in exp_data.c, on aarch64
.text+.rodata size of libm.a is increased by 2295 bytes.
Improvements on Cortex-A72:
latency: 3.3x
thruput: 4.9x
compiler warnings found this way.
* libc/stdio/freopen.c (_freopen_r): Fix bug setting _flags.
* libc/include/stdio.h (_rename): Define when building newlib.
* libc/include/sys/signal.h (_kill): Ditto.
* libc/include/sys/stat.h (_mkdir): Ditto.
* libc/include/sys/time.h (_gettimeofday): Ditto.
* libc/include/sys/times.h (_times): Ditto.
* libc/include/sys/wait.h (_wait): Ditto.
* libc/locale/lmessages.c (empty): Don't define for Cygwin.
* libc/locale/lmonetary.c (cnv): Ditto.
* libc/locale/nl_langinfo.c (nl_langinfo): Ditto for variable s.
* libc/posix/collate.c: Throughout cast to avoid compiler warning.
* libc/posix/engine.c (matcher): Initialize dp to avoid compiler
warning.
* libc/posix/glob.c: Disable on Cygwin. Explain why.
* libc/posix/regcomp.c: Fix "uninitialized" compiler warnings.
(dissect): Deliberately silence gcc compiler warning. Add comment to
explain why.
* libc/posix/wordexp.c (wordexp): Remove num_bytes variable since result
is never used.
* libc/posix/popen.c (popen): Ditto for variable last.
* libc/reent/mkdirr.c: Include sys/stat.h.
* libc/reent/renamer.c: Include stdio.h.
* libc/search/hash.c: Throughout use underscored variants of the stat
function family.
(init_hash): Add missing definition for the __USE_INTERNAL_STAT64 case.
* libc/search/hash_bigkey.c (__big_insert): Add parenthesis to avoid
compiler warning.
* libc/search/hash_page.c (overflow_page): Initalize freep to NULL to
avoid compiler warning.
* libc/stdio/asiprintf.c (_asiprintf_r): Cast unsigned char * to char *
to avoid compiler warning.
(asiprintf): Ditto.
* libc/stdio/asprintf.c (_asprintf_r): Ditto.
(asprintf): Ditto.
* libc/stdio/vasiprintf.c (_vasiprintf_r): Ditto.
* libc/stdio/vasprintf.c (_vasprintf_r): Ditto.
* libc/stdio/mktemp.c (_gettemp): Cast to unsigned char in call to
isdigit to avoid compiler warning.
* libc/stdio/vfprintf.c (_VFPRINTF_R): Initialize variables used for
grouping to avoid compiler warning. Only define and set nseps and
nrepeats if they are really used.
* libc/stdio/vfwprintf.c (_VFWPRINTF_R): Ditto. Only define state if
it is really used.
* libc/stdio/vfscanf.c (u_char): Revert to be defined as unsigned char.
(__SVFSCANF_R): Cast fmt in call to __mbtowc.
* libc/stdlib/mbtowc_r.c (JIS_state_table): Disable when building
Cygwin.
(JIS_action_table): Ditto.
* libc/stdlib/wctomb_r.c (__utf8_wctomb): Add parenthesis to avoid
compiler warning.
* libc/string/strcasestr.c: Deliberately silence gcc compiler warning.
Add comment to explain why.
* libc/time/strptime.c (strptime): Cast to unsigned char in calls to
isspace to avoid compiler warning.
* libm/math/e_atan2.c (__ieee754_atan2): Add parenthesis to avoid
compiler warning.
* libm/math/e_exp.c (__ieee754_exp): Initialize k to 0 to avoid
compiler warning. Drop setting it to 0 later.
* libm/math/ef_exp.c (__ieee754_expf): Ditto.
* libm/math/e_pow.c (__ieee754_pow): Add braces to avoid compiler
warning.
* libm/math/ef_pow.c (__ieee754_powf): Ditto.
* libm/math/er_lgamma.c (__ieee754_lgamma_r): Initialize nadj to 0 to
avoid compiler warning.
* libm/math/erf_lgamma.c (__ieee754_lgammaf_r): Ditto.
* libm/math/e_rem_pio2.c (__ieee754_rem_pio2): Ditto for variable z.
* libm/common/sf_round.c (roundf): Remove signbit variable since result
is never used.
* libm/math/e_pow.c: Fix to be consistent with glibc with regards
to treatment of NaN and +-inf arguments.
* libm/math/ef_pow.c: Ditto.
* libm/math/w_pow.c: Ditto.
* libm/math/wf_pow.c: Ditto.
* libm/math/w_acos.c: Fix domain errors to return NaN.
* libm/math/w_asin.c: Ditto.
* libm/math/wf_acos.c: Ditto.
* libm/math/wf_asin.c: Ditto.
* libm/math/w_log.c: Fix to return NaN for negative number inputs.
* libm/math/wf_log.c: Ditto.
* libm/math/wf_log10.c: Ditto.
* libm/math/w_log10.c: Ditto.
* libm/math/e_pow.c (__ieee754_pow): Fix case whereby
x is close to -1.0 and y is very large to use ax (absolute value)
instead of x.
* libm/math/ef_pow.c (__ieee754_powf): Ditto.
Andoni Arregi
Keith Packard
Keith Packard via Newlib
Nicolas Brunie
Szabolcs Nagy
Corinna Vinschen
Jeff Johnston
Thomas Fitzsimmons
Christopher Faylor