[PATCH -v2 1/3] lib/int_sqrt: Optimize small argument

[Peter Zijlstra <peterz@infradead.org>]

[-- Attachment #0: peterz-int_sqrt-opt-1.patch --]
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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.

Fixes: 30493cc9dddb ("lib/int_sqrt.c: optimize square root algorithm")
Suggested-by: Anshul Garg <aksgarg1989@gmail.com>
Signed-off-by: Peter Zijlstra (Intel) <peterz@infradead.org>
---
 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;