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): ...
The idea to run benchmarks for a constant number of iterations is
problematic. While the benchmarks may run for 10 seconds on x86_64,
they could run for about 30 seconds on powerpc and worse, over 3
minutes on arm. Besides that, adding a new benchmark is cumbersome
since one needs to find out the number of iterations needed for a
sufficient runtime.
A better idea would be to run each benchmark for a specific amount of
time. This patch does just that. The run time defaults to 10 seconds
and it is configurable at command line:
make BENCH_DURATION=5 bench
Appending benchmark program output on every run could result in a case
where the benchmark run was cancelled, resulting in a partially
written file. This file gets used again on the next run, resulting in
results being appended to old results.
It could have been possible to remove the file before every benchmark
run, but it is easier to just write the output to bench.out-tmp only
once.
Benchmark programs are generated using parameters from the Makefile,
so it is necessary to rebuild them whenever the parameters in the
Makefile are updated. Hence, added a dependency for the generated C
source on the Makefile so that it gets regenerated when the Makefile
is updated.
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.
The branch prediction hints is actually hurts performance in this case.
The assembly implementation make two assumptions: 1. 'fabs (x) < 2^52'
is unlikely and 2. 'x > 0.0' is unlike (if 1. is true). Since it a
general floating point function, expected input is not bounded and then
it is better to let the hardware handle the branches.
