On Fri, Mar 22, 2019 at 04:44:15PM +0100, Arnd Bergmann wrote:
> From: Peter Zijlstra <peterz@xxxxxxxxxxxxx>
>
> 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@xxxxxxxxxxxxx
> Fixes: 30493cc9dddb ("lib/int_sqrt.c: optimize square root algorithm")
> Signed-off-by: Peter Zijlstra (Intel) <peterz@xxxxxxxxxxxxx>
> Suggested-by: Anshul Garg <aksgarg1989@xxxxxxxxx>
> Acked-by: Linus Torvalds <torvalds@xxxxxxxxxxxxxxxxxxxx>
> Cc: Davidlohr Bueso <dave@xxxxxxxxxxxx>
> Cc: Thomas Gleixner <tglx@xxxxxxxxxxxxx>
> Cc: Ingo Molnar <mingo@xxxxxxxxxx>
> Cc: Will Deacon <will.deacon@xxxxxxx>
> Cc: Joe Perches <joe@xxxxxxxxxxx>
> Cc: David Miller <davem@xxxxxxxxxxxxx>
> Cc: Matthew Wilcox <mawilcox@xxxxxxxxxxxxx>
> Cc: Kees Cook <keescook@xxxxxxxxxxxx>
> Cc: Michael Davidson <md@xxxxxxxxxx>
> Signed-off-by: Andrew Morton <akpm@xxxxxxxxxxxxxxxxxxxx>
> Signed-off-by: Linus Torvalds <torvalds@xxxxxxxxxxxxxxxxxxxx>
> (cherry picked from commit 3f3295709edea6268ff1609855f498035286af73)
> Signed-off-by: Arnd Bergmann <arnd@xxxxxxxx>
> ---
> lib/int_sqrt.c | 3 +++
> 1 file changed, 3 insertions(+)
Also added to 4.14.y and 4.9.y
