These changes will be active for all platforms that don't provide
their own exp() routines. They will also be active for ieee754
versions of ccos, ccosh, cosh, csin, csinh, sinh, exp10, gamma, and
erf.
Typical performance gains is typically around 5x when measured on
Sparc s7 for common values between exp(1) and exp(40).
Using the glibc perf tests on sparc,
sparc (nsec) x86 (nsec)
old new old new
max 17629 395 5173 144
min 399 54 15 13
mean 5317 200 1349 23
The extreme max times for the old (ieee754) exp are due to the
multiprecision computation in the old algorithm when the true value is
very near 0.5 ulp away from an value representable in double
precision. The new algorithm does not take special measures for those
cases. The current glibc exp perf tests overrepresent those values.
Informal testing suggests approximately one in 200 cases might
invoke the high cost computation. The performance advantage of the new
algorithm for other values is still large but not as large as indicated
by the chart above.
Glibc correctness tests for exp() and expf() were run. Within the
test suite 3 input values were found to cause 1 bit differences (ulp)
when "FE_TONEAREST" rounding mode is set. No differences in exp() were
seen for the tested values for the other rounding modes.
Typical example:
exp(-0x1.760cd2p+0) (-1.46113312244415283203125)
new code: 2.31973271630014299393707e-01 0x1.db14cd799387ap-3
old code: 2.31973271630014271638132e-01 0x1.db14cd7993879p-3
exp = 2.31973271630014285508337 (high precision)
Old delta: off by 0.49 ulp
New delta: off by 0.51 ulp
In addition, because ieee754_exp() is used by other routines, cexp()
showed test results with very small imaginary input values where the
imaginary portion of the result was off by 3 ulp when in upward
rounding mode, but not in the other rounding modes. For x86, tgamma
showed a few values where the ulp increased to 6 (max ulp for tgamma
is 5). Sparc tgamma did not show these failures. I presume the tgamma
differences are due to compiler optimization differences within the
gamma function.The gamma function is known to be difficult to compute
accurately.
* sysdeps/ieee754/dbl-64/e_exp.c: Include <math-svid-compat.h> and
<errno.h>. Include "eexp.tbl".
(half): New constant.
(one): Likewise.
(__ieee754_exp): Rewrite.
(__slowexp): Remove prototype.
* sysdeps/ieee754/dbl-64/eexp.tbl: New file.
* sysdeps/ieee754/dbl-64/slowexp.c: Remove file.
* sysdeps/i386/fpu/slowexp.c: Likewise.
* sysdeps/ia64/fpu/slowexp.c: Likewise.
* sysdeps/m68k/m680x0/fpu/slowexp.c: Likewise.
* sysdeps/x86_64/fpu/multiarch/slowexp-avx.c: Likewise.
* sysdeps/x86_64/fpu/multiarch/slowexp-fma.c: Likewise.
* sysdeps/x86_64/fpu/multiarch/slowexp-fma4.c: Likewise.
* sysdeps/generic/math_private.h (__slowexp): Remove prototype.
* sysdeps/ieee754/dbl-64/e_pow.c: Remove mention of slowexp.c in
comment.
* sysdeps/powerpc/power4/fpu/Makefile [$(subdir) = math]
(CPPFLAGS-slowexp.c): Remove variable.
* sysdeps/x86_64/fpu/multiarch/Makefile (libm-sysdep_routines):
Remove slowexp-fma, slowexp-fma4 and slowexp-avx.
(CFLAGS-slowexp-fma.c): Remove variable.
(CFLAGS-slowexp-fma4.c): Likewise.
(CFLAGS-slowexp-avx.c): Likewise.
* sysdeps/x86_64/fpu/multiarch/e_exp-avx.c (__slowexp): Do not
define as macro.
* sysdeps/x86_64/fpu/multiarch/e_exp-fma.c (__slowexp): Likewise.
* sysdeps/x86_64/fpu/multiarch/e_exp-fma4.c (__slowexp): Likewise.
* math/Makefile (type-double-routines): Remove slowexp.
* manual/probes.texi (slowexp_p6): Remove.
(slowexp_p32): Likewise.
Clean up calls to malloc_printerr and trim its argument list.
This also removes a few bits of work done before calling
malloc_printerr (such as unlocking operations).
The tunable/environment variable still enables the lightweight
additional malloc checking, but mallopt (M_CHECK_ACTION)
no longer has any effect.
Create a new node for tunables documentation and add notes for the
malloc tunables.
* manual/tunables.texi: New chapter.
* manual/Makefile (chapters): Add it.
* manual/probes.texi (@node): Point to the Tunables chapter.
Use the term "triggered" instead of "hit" when talking about probe
points.
ChangeLog:
2014-02-11 Will Newton <will.newton@linaro.org>
* manual/probes.texi (Mathematical Function Probes): Use
"triggered" instead of "hit".
Add some documentation of the setjmp, longjmp and longjmp_target
Systemtap probe points.
ChangeLog:
2014-02-11 Will Newton <will.newton@linaro.org>
* manual/probes.texi (Internal Probes): Add documentation
of setjmp, longjmp and longjmp_target probes.
Add systemtap probes to various slow paths in libm so that application
developers may use systemtap to find out if their applications are
hitting these slow paths. We have added probes for pow, exp, log,
tan, atan and atan2.
for ChangeLog
* malloc/arena.c (new_heap): New memory_heap_new probe.
(grow_heap): New memory_heap_more probe.
(shrink_heap): New memory_heap_less probe.
(heap_trim): New memory_heap_free probe.
* malloc/malloc.c (sysmalloc): New memory_sbrk_more probe.
(systrim): New memory_sbrk_less probe.
* manual/probes.texi: Document them.
