[PATCH 3.16 094/136] lib/int_sqrt: optimize small argument

[Ben Hutchings]

3.16.54-rc1 review patch.  If anyone has any objections, please let me know.

------------------

From: Peter Zijlstra <peterz@xxxxxxxxxxxxx>

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@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>
Signed-off-by: Ben Hutchings <ben@xxxxxxxxxxxxxxx>
---
 lib/int_sqrt.c | 3 +++
 1 file changed, 3 insertions(+)

--- a/lib/int_sqrt.c
+++ b/lib/int_sqrt.c
@@ -22,6 +22,9 @@ unsigned long int_sqrt(unsigned long x)
 		return x;
 
 	m = 1UL << (BITS_PER_LONG - 2);
+	while (m > x)
+		m >>= 2;
+
 	while (m != 0) {
 		b = y + m;
 		y >>= 1;