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Optimized log using carefully generated lookup table with 1/c and log(c)
values for small intervalls around 1. The log(c) is very near a double
precision value, it has about 62 bits precision. The algorithm is
log(2^k x) = k log(2) + log(c) + log(x/c), where the last term is
approximated by a polynomial of x/c - 1. Near 1 a single polynomial of
x - 1 is used.
There is separate code path when fma instruction is not available for
computing x/c - 1 precisely, in which case the table size is doubled.
The code uses __builtin_fma under __FP_FAST_FMA to ensure it is inlined
as an instruction.
With the default configuration settings the worst case error is 0.519 ULP
(and 0.520 without fma), the rodata size is 2192 bytes (4240 without fma).
The non-nearest rounding error is less than 1 ULP.
Improvements on Cortex-A72 compared to current glibc master:
log thruput: 3.28x in [0.01 11.1]
log latency: 2.23x in [0.01 11.1]
log thruput: 1.56x in [0.999 1.001]
log latency: 1.57x in [0.999 1.001]
Tested on
aarch64-linux-gnu (defined __FP_FAST_FMA)
arm-linux-gnueabihf (!defined __FP_FAST_FMA)
x86_64-linux-gnu (!defined __FP_FAST_FMA)
powerpc64le-linux-gnu (defined __FP_FAST_FMA)
targets.
* NEWS: Mention log improvement.
* math/Makefile (type-double-routines): Add e_log_data.
* sysdeps/i386/fpu/e_log_data.c: New file.
* sysdeps/ia64/fpu/e_log_data.c: New file.
* sysdeps/ieee754/dbl-64/e_log.c: Rewrite.
* sysdeps/ieee754/dbl-64/e_log_data.c: New file.
* sysdeps/ieee754/dbl-64/math_config.h (__log_data): Add.
* sysdeps/ieee754/dbl-64/ulog.h: Remove.
* sysdeps/ieee754/dbl-64/ulog.tbl: Remove.
* sysdeps/m68k/m680x0/fpu/e_log_data.c: New file.
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* All files with FSF copyright notices: Update copyright dates
using scripts/update-copyrights.
* locale/programs/charmap-kw.h: Regenerated.
* locale/programs/locfile-kw.h: Likewise.
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* crypt/crypt.c: Changed copying permission notice to Lesser GPL
from Library GPL.
* crypt/crypt_util.c: Likewise.
* crypt/ufc.c: Likewise.
* elf/dl-conflict.c: Likewise.
* elf/dl-iteratephdr.c: Likewise.
* iconv/iconvconfig.h: Likewise.
* linuxthreads/Examples/ex10.c: Likewise.
* linuxthreads/Examples/ex11.c: Likewise.
* linuxthreads/Examples/ex13.c: Likewise.
* linuxthreads/Examples/ex8.c: Likewise.
* linuxthreads/Examples/ex9.c: Likewise.
* linuxthreads/barrier.c: Likewise.
* linuxthreads/events.c: Likewise.
* linuxthreads/lockfile.c: Likewise.
* linuxthreads/no-tsd.c: Likewise.
* linuxthreads/pt-machine.c: Likewise.
* linuxthreads/ptclock_gettime.c: Likewise.
* linuxthreads/ptclock_settime.c: Likewise.
* linuxthreads/rwlock.c: Likewise.
* linuxthreads/sysdeps/alpha/pspinlock.c: Likewise.
* linuxthreads/sysdeps/alpha/pt-machine.h: Likewise.
* linuxthreads/sysdeps/arm/pspinlock.c: Likewise.
* linuxthreads/sysdeps/arm/pt-machine.h: Likewise.
* linuxthreads/sysdeps/cris/pspinlock.c: Likewise.
* linuxthreads/sysdeps/cris/pt-machine.h: Likewise.
* linuxthreads/sysdeps/hppa/pspinlock.c: Likewise.
* linuxthreads/sysdeps/hppa/pt-machine.h: Likewise.
* linuxthreads/sysdeps/i386/i686/pt-machine.h: Likewise.
* linuxthreads/sysdeps/i386/pspinlock.c: Likewise.
* linuxthreads/sysdeps/i386/pt-machine.h: Likewise.
* linuxthreads/sysdeps/i386/useldt.h: Likewise.
* linuxthreads/sysdeps/ia64/pspinlock.c: Likewise.
* linuxthreads/sysdeps/ia64/pt-machine.h: Likewise.
* linuxthreads/sysdeps/m68k/pspinlock.c: Likewise.
* linuxthreads/sysdeps/m68k/pt-machine.h: Likewise.
* linuxthreads/sysdeps/mips/pspinlock.c: Likewise.
* linuxthreads/sysdeps/mips/pt-machine.h: Likewise.
* linuxthreads/sysdeps/powerpc/pspinlock.c: Likewise.
* linuxthreads/sysdeps/powerpc/pt-machine.h: Likewise.
* linuxthreads/sysdeps/pthread/bits/initspin.h: Likewise.
* linuxthreads/sysdeps/pthread/bits/libc-lock.h: Likewise.
* linuxthreads/sysdeps/pthread/bits/libc-tsd.h: Likewise.
* linuxthreads/sysdeps/pthread/getcpuclockid.c: Likewise.
* linuxthreads/sysdeps/pthread/posix-timer.h: Likewise.
* linuxthreads/sysdeps/pthread/timer_create.c: Likewise.
* linuxthreads/sysdeps/pthread/timer_delete.c: Likewise.
* linuxthreads/sysdeps/pthread/timer_getoverr.c: Likewise.
* linuxthreads/sysdeps/pthread/timer_gettime.c: Likewise.
* linuxthreads/sysdeps/pthread/timer_routines.c: Likewise.
* linuxthreads/sysdeps/pthread/timer_settime.c: Likewise.
* linuxthreads/sysdeps/pthread/tst-timer.c: Likewise.
* linuxthreads/sysdeps/s390/pspinlock.c: Likewise.
* linuxthreads/sysdeps/s390/s390-32/pt-machine.h: Likewise.
* linuxthreads/sysdeps/s390/s390-64/pt-machine.h: Likewise.
* linuxthreads/sysdeps/sh/pspinlock.c: Likewise.
* linuxthreads/sysdeps/sh/pt-machine.h: Likewise.
* linuxthreads/sysdeps/sparc/sparc32/pspinlock.c: Likewise.
* linuxthreads/sysdeps/sparc/sparc32/pt-machine.h: Likewise.
* linuxthreads/sysdeps/sparc/sparc32/sparcv9/pspinlock.c: Likewise.
* linuxthreads/sysdeps/sparc/sparc64/pspinlock.c: Likewise.
* linuxthreads/sysdeps/sparc/sparc64/pt-machine.h: Likewise.
* linuxthreads/sysdeps/unix/sysv/linux/bits/local_lim.h: Likewise.
* linuxthreads/sysdeps/unix/sysv/linux/bits/posix_opt.h: Likewise.
* linuxthreads/sysdeps/unix/sysv/linux/bits/sigthread.h: Likewise.
* linuxthreads/sysdeps/unix/sysv/linux/hppa/bits/initspin.h: Likewise.
* linuxthreads/sysdeps/unix/sysv/linux/i386/bits/posix_opt.h: Likewise.
* linuxthreads/tststack.c: Likewise.
* linuxthreads/unload.c: Likewise.
* linuxthreads/weaks.c: Likewise.
* linuxthreads/wrapsyscall.c: Likewise.
* malloc/arena.c: Likewise.
* malloc/hooks.c: Likewise.
* malloc/malloc.c: Likewise.
* posix/glob/Makefile.ami: Likewise.
* posix/glob/Makefile.in: Likewise.
* stdlib/gmp-impl.h: Likewise.
* stdlib/gmp.h: Likewise.
* sysdeps/generic/dl-iteratephdr-static.c: Likewise.
* sysdeps/generic/strnlen.c: Likewise.
* sysdeps/mach/hurd/powerpc/bits/sigcontext.h: Likewise.
* sysdeps/mach/hurd/recvmsg.c: Likewise.
* sysdeps/mach/hurd/sendmsg.c: Likewise.
* sysdeps/mach/hurd/spawni.c: Likewise.
* sysdeps/mach/powerpc/machine-sp.h: Likewise.
* sysdeps/mach/powerpc/sysdep.h: Likewise.
* sysdeps/mach/powerpc/thread_state.h: Likewise.
* sysdeps/unix/bsd/bsd4.4/bits/socket.h: Likewise.
* sysdeps/unix/sysv/linux/ia64/dl-iteratephdr-static.c: Likewise.
* sysdeps/x86_64/gmp-mparam.h: Likewise.
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* manual/contrib.texi: Removed licenses, added acknowledgements
for contributions by Intel, IBM, Craig Metz.
* LICENSES: New file, contains the text of all non-FSF licenses in the
distribution that require putting the notice in the accompanying
documentation.
* README.template, README: Mention LICENSES.
* sysdeps/mach/hurd/net/if_ppp.h: Replaced CMU license with a
new one modelled on the modern BSD license, per recent letter
of permission from CMU.
* sysdeps/unix/sysv/linux/net/if_ppp.h: Likewise.
* sysdeps/ieee754/dbl-64/MathLib.h: Changed the copyright holder
from IBM to FSF, per the recent Software Letter. Changed the
distribution terms from GPL to LGPL.
* sysdeps/ieee754/dbl-64/asincos.tbl: Added FSF copyright and
copying permission notice (Lesser GPL), per recent IBM Software Letter.
* sysdeps/ieee754/dbl-64/powtwo.tbl: Likewise.
* sysdeps/ieee754/dbl-64/root.tbl: Likewise.
* sysdeps/ieee754/dbl-64/sincos.tbl: Likewise.
* sysdeps/ieee754/dbl-64/uatan.tbl: Likewise.
* sysdeps/ieee754/dbl-64/uexp.tbl: Likewise.
* sysdeps/ieee754/dbl-64/ulog.tbl: Likewise.
* sysdeps/ieee754/dbl-64/upow.tbl: Likewise.
* sysdeps/ieee754/dbl-64/utan.tbl: Likewise.
* sysdeps/ieee754/dbl-64/atnat.h: Changed the copyright holder
from IBM to FSF, per the recent Software Letter. Corrected the
text of the copying permission notice to say Lesser GPL instead
of GPL in warranty disclaimer paragraph.
* sysdeps/ieee754/dbl-64/atnat2.h: Likewise.
* sysdeps/ieee754/dbl-64/branred.h: Likewise.
* sysdeps/ieee754/dbl-64/dla.h: Likewise.
* sysdeps/ieee754/dbl-64/doasin.h: Likewise.
* sysdeps/ieee754/dbl-64/dosincos.h: Likewise.
* sysdeps/ieee754/dbl-64/mpa.h: Likewise.
* sysdeps/ieee754/dbl-64/mpa2.h: Likewise.
* sysdeps/ieee754/dbl-64/mpatan.h: Likewise.
* sysdeps/ieee754/dbl-64/mpexp.h: Likewise.
* sysdeps/ieee754/dbl-64/mplog.h: Likewise.
* sysdeps/ieee754/dbl-64/mpsqrt.h: Likewise.
* sysdeps/ieee754/dbl-64/mydefs.h: Likewise.
* sysdeps/ieee754/dbl-64/sincos32.h: Likewise.
* sysdeps/ieee754/dbl-64/uasncs.h: Likewise.
* sysdeps/ieee754/dbl-64/uexp.h: Likewise.
* sysdeps/ieee754/dbl-64/ulog.h: Likewise.
* sysdeps/ieee754/dbl-64/upow.h: Likewise.
* sysdeps/ieee754/dbl-64/urem.h: Likewise.
* sysdeps/ieee754/dbl-64/uroot.h: Likewise.
* sysdeps/ieee754/dbl-64/usncs.h: Likewise.
* sysdeps/ieee754/dbl-64/utan.h: Likewise.
* sysdeps/ieee754/dbl-64/branred.c: Corrected the text of the copying
permission notice to say Lesser GPL instead of GPL in warranty
disclaimer paragraph.
* sysdeps/ieee754/dbl-64/doasin.c: Likewise.
* sysdeps/ieee754/dbl-64/dosincos.c: Likewise.
* sysdeps/ieee754/dbl-64/e_asin.c: Likewise.
* sysdeps/ieee754/dbl-64/e_atan2.c: Likewise.
* sysdeps/ieee754/dbl-64/e_exp.c: Likewise.
* sysdeps/ieee754/dbl-64/e_log.c: Likewise.
* sysdeps/ieee754/dbl-64/e_pow.c: Likewise.
* sysdeps/ieee754/dbl-64/e_remainder.c: Likewise.
* sysdeps/ieee754/dbl-64/e_sqrt.c: Likewise.
* sysdeps/ieee754/dbl-64/halfulp.c: Likewise.
* sysdeps/ieee754/dbl-64/mpa.c: Likewise.
* sysdeps/ieee754/dbl-64/mpatan.c: Likewise.
* sysdeps/ieee754/dbl-64/mpatan2.c: Likewise.
* sysdeps/ieee754/dbl-64/mpexp.c: Likewise.
* sysdeps/ieee754/dbl-64/mplog.c: Likewise.
* sysdeps/ieee754/dbl-64/mpsqrt.c: Likewise.
* sysdeps/ieee754/dbl-64/mptan.c: Likewise.
* sysdeps/ieee754/dbl-64/s_atan.c: Likewise.
* sysdeps/ieee754/dbl-64/s_sin.c: Likewise.
* sysdeps/ieee754/dbl-64/s_tan.c: Likewise.
* sysdeps/ieee754/dbl-64/sincos32.c: Likewise.
* sysdeps/ieee754/dbl-64/slowexp.c: Likewise.
* sysdeps/ieee754/dbl-64/slowpow.c: Likewise.
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2001-03-11 Ulrich Drepper <drepper@redhat.com>
Last-bit accurate math library implementation by IBM Haifa.
Contributed by Abraham Ziv <ziv@il.ibm.com>, Moshe Olshansky
<olshansk@il.ibm.com>, Ealan Henis <ealan@il.ibm.com>, and
Anna Reitman <reitman@il.ibm.com>.
* math/Makefile (dbl-only-routines): New variable.
(libm-routines): Add $(dbl-only-routines).
* sysdeps/ieee754/dbl-64/e_acos.c: Empty, definition is in e_asin.c.
* sysdeps/ieee754/dbl-64/e_asin.c: Replaced with accurate asin
implementation.
* sysdeps/ieee754/dbl-64/e_atan2.c: Replaced with accurate atan2
implementation.
* sysdeps/ieee754/dbl-64/e_exp.c: Replaced with accurate exp
implementation.
* sysdeps/ieee754/dbl-64/e_lgamma_r.c: Don't use __kernel_sin and
__kernel_cos.
* sysdeps/ieee754/dbl-64/e_log.c: Replaced with accurate log
implementation.
* sysdeps/ieee754/dbl-64/e_remainder.c: Replaced with accurate
remainder implementation.
* sysdeps/ieee754/dbl-64/e_pow.c: Replaced with accurate pow
implementation.
* sysdeps/ieee754/dbl-64/e_sqrt.c: Replaced with accurate sqrt
implementation.
* sysdeps/ieee754/dbl-64/k_cos.c: Empty, definition is in s_sin.c.
* sysdeps/ieee754/dbl-64/k_sin.c: Empty, definition is in s_sin.c.
* sysdeps/ieee754/dbl-64/s_atan.c: Replaced with accurate atan
implementation.
* sysdeps/ieee754/dbl-64/s_cos.c: Empty, definition is in s_sin.c.
* sysdeps/ieee754/dbl-64/s_sin.c: Replaced with accurate sin/cos
implementation.
* sysdeps/ieee754/dbl-64/s_sincos.c: Rewritten to not use __kernel_sin
and __kernel_cos.
* sysdeps/ieee754/dbl-64/s_tan.c: Replaced with accurate tan
implementation.
* sysdeps/ieee754/dbl-64/Dist: Add new non-code files.
* sysdeps/ieee754/dbl-64/MathLib.h: New file.
* sysdeps/ieee754/dbl-64/asincos.tbl: New file.
* sysdeps/ieee754/dbl-64/atnat.h: New file.
* sysdeps/ieee754/dbl-64/atnat2.h: New file.
* sysdeps/ieee754/dbl-64/branred.c: New file.
* sysdeps/ieee754/dbl-64/branred.h: New file.
* sysdeps/ieee754/dbl-64/dla.h: New file.
* sysdeps/ieee754/dbl-64/doasin.c: New file.
* sysdeps/ieee754/dbl-64/doasin.h: New file.
* sysdeps/ieee754/dbl-64/dosincos.c: New file.
* sysdeps/ieee754/dbl-64/dosincos.h: New file.
* sysdeps/ieee754/dbl-64/endian.h: New file.
* sysdeps/ieee754/dbl-64/halfulp.c: New file.
* sysdeps/ieee754/dbl-64/mpa.c: New file.
* sysdeps/ieee754/dbl-64/mpa.h: New file.
* sysdeps/ieee754/dbl-64/mpa2.h: New file.
* sysdeps/ieee754/dbl-64/mpatan.c: New file.
* sysdeps/ieee754/dbl-64/mpatan.h: New file.
* sysdeps/ieee754/dbl-64/mpatan2.c: New file.
* sysdeps/ieee754/dbl-64/mpexp.c: New file.
* sysdeps/ieee754/dbl-64/mpexp.h: New file.
* sysdeps/ieee754/dbl-64/mplog.c: New file.
* sysdeps/ieee754/dbl-64/mplog.h: New file.
* sysdeps/ieee754/dbl-64/mpsqrt.c: New file.
* sysdeps/ieee754/dbl-64/mpsqrt.h: New file.
* sysdeps/ieee754/dbl-64/mptan.c: New file.
* sysdeps/ieee754/dbl-64/mydefs.h: New file.
* sysdeps/ieee754/dbl-64/powtwo.tbl: New file.
* sysdeps/ieee754/dbl-64/root.tbl: New file.
* sysdeps/ieee754/dbl-64/sincos.tbl: New file.
* sysdeps/ieee754/dbl-64/sincos32.c: New file.
* sysdeps/ieee754/dbl-64/sincos32.h: New file.
* sysdeps/ieee754/dbl-64/slowexp.c: New file.
* sysdeps/ieee754/dbl-64/slowpow.c: New file.
* sysdeps/ieee754/dbl-64/uasncs.h: New file.
* sysdeps/ieee754/dbl-64/uatan.tbl: New file.
* sysdeps/ieee754/dbl-64/uexp.h: New file.
* sysdeps/ieee754/dbl-64/uexp.tbl: New file.
* sysdeps/ieee754/dbl-64/ulog.h: New file.
* sysdeps/ieee754/dbl-64/ulog.tbl: New file.
* sysdeps/ieee754/dbl-64/upow.h: New file.
* sysdeps/ieee754/dbl-64/upow.tbl: New file.
* sysdeps/ieee754/dbl-64/urem.h: New file.
* sysdeps/ieee754/dbl-64/uroot.h: New file.
* sysdeps/ieee754/dbl-64/usncs.h: New file.
* sysdeps/ieee754/dbl-64/utan.h: New file.
* sysdeps/ieee754/dbl-64/utan.tbl: New file.
* sysdeps/i386/fpu/branred.c: New file.
* sysdeps/i386/fpu/doasin.c: New file.
* sysdeps/i386/fpu/dosincos.c: New file.
* sysdeps/i386/fpu/halfulp.c: New file.
* sysdeps/i386/fpu/mpa.c: New file.
* sysdeps/i386/fpu/mpatan.c: New file.
* sysdeps/i386/fpu/mpatan2.c: New file.
* sysdeps/i386/fpu/mpexp.c: New file.
* sysdeps/i386/fpu/mplog.c: New file.
* sysdeps/i386/fpu/mpsqrt.c: New file.
* sysdeps/i386/fpu/mptan.c: New file.
* sysdeps/i386/fpu/sincos32.c: New file.
* sysdeps/i386/fpu/slowexp.c: New file.
* sysdeps/i386/fpu/slowpow.c: New file.
* sysdeps/ia64/fpu/branred.c: New file.
* sysdeps/ia64/fpu/doasin.c: New file.
* sysdeps/ia64/fpu/dosincos.c: New file.
* sysdeps/ia64/fpu/halfulp.c: New file.
* sysdeps/ia64/fpu/mpa.c: New file.
* sysdeps/ia64/fpu/mpatan.c: New file.
* sysdeps/ia64/fpu/mpatan2.c: New file.
* sysdeps/ia64/fpu/mpexp.c: New file.
* sysdeps/ia64/fpu/mplog.c: New file.
* sysdeps/ia64/fpu/mpsqrt.c: New file.
* sysdeps/ia64/fpu/mptan.c: New file.
* sysdeps/ia64/fpu/sincos32.c: New file.
* sysdeps/ia64/fpu/slowexp.c: New file.
* sysdeps/ia64/fpu/slowpow.c: New file.
* sysdeps/m68k/fpu/branred.c: New file.
* sysdeps/m68k/fpu/doasin.c: New file.
* sysdeps/m68k/fpu/dosincos.c: New file.
* sysdeps/m68k/fpu/halfulp.c: New file.
* sysdeps/m68k/fpu/mpa.c: New file.
* sysdeps/m68k/fpu/mpatan.c: New file.
* sysdeps/m68k/fpu/mpatan2.c: New file.
* sysdeps/m68k/fpu/mpexp.c: New file.
* sysdeps/m68k/fpu/mplog.c: New file.
* sysdeps/m68k/fpu/mpsqrt.c: New file.
* sysdeps/m68k/fpu/mptan.c: New file.
* sysdeps/m68k/fpu/sincos32.c: New file.
* sysdeps/m68k/fpu/slowexp.c: New file.
* sysdeps/m68k/fpu/slowpow.c: New file.
* iconvdata/gconv-modules: Add a number of alias, mostly for IBM
codepages.
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