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Remove the slow paths from pow. Like several other double precision math
functions, pow is exactly rounded. This is not required from math functions
and causes major overheads as it requires multiple fallbacks using higher
precision arithmetic if a result is close to 0.5ULP. Ridiculous slowdowns
of up to 100000x have been reported when the highest precision path triggers.
All GLIBC math tests pass on AArch64 and x64 (with ULP of pow set to 1).
The worst case error is ~0.506ULP. A simple test over a few hundred million
values shows pow is 10% faster on average. This fixes BZ #13932.
[BZ #13932]
* sysdeps/ieee754/dbl-64/uexp.h (err_1): Remove.
* benchtests/pow-inputs: Update comment for slow path cases.
* manual/probes.texi (slowpow_p10): Delete removed probe.
(slowpow_p10): Likewise.
* math/Makefile: Remove halfulp.c and slowpow.c.
* sysdeps/aarch64/libm-test-ulps: Set ULP of pow to 1.
* sysdeps/generic/math_private.h (__exp1): Remove error argument.
(__halfulp): Remove.
(__slowpow): Remove.
* sysdeps/i386/fpu/halfulp.c: Delete file.
* sysdeps/i386/fpu/slowpow.c: Likewise.
* sysdeps/ia64/fpu/halfulp.c: Likewise.
* sysdeps/ia64/fpu/slowpow.c: Likewise.
* sysdeps/ieee754/dbl-64/e_exp.c (__exp1): Remove error argument,
improve comments and add error analysis.
* sysdeps/ieee754/dbl-64/e_pow.c (__ieee754_pow): Add error analysis.
(power1): Remove function:
(log1): Remove error argument, add error analysis.
(my_log2): Remove function.
* sysdeps/ieee754/dbl-64/halfulp.c: Delete file.
* sysdeps/ieee754/dbl-64/slowpow.c: Likewise.
* sysdeps/m68k/m680x0/fpu/halfulp.c: Likewise.
* sysdeps/m68k/m680x0/fpu/slowpow.c: Likewise.
* sysdeps/powerpc/power4/fpu/Makefile: Remove CPPFLAGS-slowpow.c.
* sysdeps/x86_64/fpu/libm-test-ulps: Set ULP of pow to 1.
* sysdeps/x86_64/fpu/multiarch/Makefile: Remove slowpow-fma.c,
slowpow-fma4.c, halfulp-fma.c, halfulp-fma4.c.
* sysdeps/x86_64/fpu/multiarch/e_pow-fma.c (__slowpow): Remove define.
* sysdeps/x86_64/fpu/multiarch/e_pow-fma4.c (__slowpow): Likewise.
* sysdeps/x86_64/fpu/multiarch/halfulp-fma.c: Delete file.
* sysdeps/x86_64/fpu/multiarch/halfulp-fma4.c: Likewise.
* sysdeps/x86_64/fpu/multiarch/slowpow-fma.c: Likewise.
* sysdeps/x86_64/fpu/multiarch/slowpow-fma4.c: Likewise.
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These inputs cover all normal processing paths for pow including all
its slow paths.
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This patch adds some more directives to the benchmark inputs file,
moving functionality from the Makefile and making the code generation
script a bit cleaner. The function argument and return types that
were earlier added as variables in the makefile and passed to the
script via command line arguments are now the 'args' and 'ret'
directive respectively. 'args' should be a colon separated list of
argument types (skipped if the function doesn't accept any arguments)
and 'ret' should be the return type.
Additionally, an 'includes' directive may have a comma separated list
of headers to include in the source. For example, the pow input file
now looks like this:
42.0, 42.0
1.0000000000000020, 1.5
I did this to unclutter the benchtests Makefile a bit and eventually
eliminate dependency of the tests on the Makefile and have tests
depend on their respective include files only.
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Some math functions have distinct performance characteristics in
specific domains of inputs, where some inputs return via a fast path
while other inputs require multiple precision calculations, that too
at different precision levels. The way to implement different domains
was to have a separate source file and benchmark definition, resulting
in separate programs.
This clutters up the benchmark, so this change allows these domains to
be consolidated into the same input file. To do this, the input file
format is now enhanced to allow comments with a preceding # and
directives with two # at the begining of a line. A directive that
looks like:
tells the benchmark generation script that what follows is a different
domain of inputs. The value of the 'name' directive (in this case,
foo) is used in the output. The two input domains are then executed
sequentially and their results collated separately. with the above
directive, there would be two lines in the result that look like:
func(): ....
func(foo): ...
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Separate benchmarks for the fast and slow implementations of pow and
exp since measuring both together doesn't make sense. Adjust the
iterations for pow and exp accordingly so that they run long enough
for the measurements to be meaningful.
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See benchtests/Makefile to know how to use it.
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