lib/int_sqrt: optimize small argument
commit 3f3295709edea6268ff1609855f498035286af73 upstream.
The current int_sqrt() computation is sub-optimal for the case of small
@x. Which is the interesting case when we're going to do cumulative
distribution functions on idle times, which we assume to be a random
variable, where the target residency of the deepest idle state gives an
upper bound on the variable (5e6ns on recent Intel chips).
In the case of small @x, the compute loop:
while (m != 0) {
b = y + m;
y >>= 1;
if (x >= b) {
x -= b;
y += m;
}
m >>= 2;
}
can be reduced to:
while (m > x)
m >>= 2;
Because y==0, b==m and until x>=m y will remain 0.
And while this is computationally equivalent, it runs much faster
because there's less code, in particular less branches.
cycles: branches: branch-misses:
OLD:
hot: 45.109444 +- 0.044117 44.333392 +- 0.002254 0.018723 +- 0.000593
cold: 187.737379 +- 0.156678 44.333407 +- 0.002254 6.272844 +- 0.004305
PRE:
hot: 67.937492 +- 0.064124 66.999535 +- 0.000488 0.066720 +- 0.001113
cold: 232.004379 +- 0.332811 66.999527 +- 0.000488 6.914634 +- 0.006568
POST:
hot: 43.633557 +- 0.034373 45.333132 +- 0.002277 0.023529 +- 0.000681
cold: 207.438411 +- 0.125840 45.333132 +- 0.002277 6.976486 +- 0.004219
Averages computed over all values <128k using a LFSR to generate order.
Cold numbers have a LFSR based branch trace buffer 'confuser' ran between
each int_sqrt() invocation.
Link: http://lkml.kernel.org/r/20171020164644.876503355@infradead.org
Fixes: 30493cc9dddb ("lib/int_sqrt.c: optimize square root algorithm")
Signed-off-by: Peter Zijlstra (Intel) <peterz@infradead.org>
Suggested-by: Anshul Garg <aksgarg1989@gmail.com>
Acked-by: Linus Torvalds <torvalds@linux-foundation.org>
Cc: Davidlohr Bueso <dave@stgolabs.net>
Cc: Thomas Gleixner <tglx@linutronix.de>
Cc: Ingo Molnar <mingo@kernel.org>
Cc: Will Deacon <will.deacon@arm.com>
Cc: Joe Perches <joe@perches.com>
Cc: David Miller <davem@davemloft.net>
Cc: Matthew Wilcox <mawilcox@microsoft.com>
Cc: Kees Cook <keescook@chromium.org>
Cc: Michael Davidson <md@google.com>
Signed-off-by: Andrew Morton <akpm@linux-foundation.org>
Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>
Signed-off-by: Arnd Bergmann <arnd@arndb.de>
Signed-off-by: Greg Kroah-Hartman <gregkh@linuxfoundation.org>
1 file changed