lib/int_sqrt: optimize initial value compute

The initial value (@m) compute is:

	m = 1UL << (BITS_PER_LONG - 2);
	while (m > x)
		m >>= 2;

Which is a linear search for the highest even bit smaller or equal to @x
We can implement this using a binary search using __fls() (or better when
its hardware implemented).

	m = 1UL << (__fls(x) & ~1UL);

Especially for small values of @x; which are the more common arguments
when doing a CDF on idle times; the linear search is near to worst case,
while the binary search of __fls() is a constant 6 (or 5 on 32bit)
branches.

      cycles:                 branches:              branch-misses:

PRE:

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

SOFTWARE FLS:

hot:   29.576176 +- 0.028850  26.666730 +- 0.004511  0.019463 +- 0.000663
cold: 165.947136 +- 0.188406  26.666746 +- 0.004511  6.133897 +- 0.004386

HARDWARE FLS:

hot:   24.720922 +- 0.025161  20.666784 +- 0.004509  0.020836 +- 0.000677
cold: 132.777197 +- 0.127471  20.666776 +- 0.004509  5.080285 +- 0.003874

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/[email protected]
Signed-off-by: Peter Zijlstra (Intel) <[email protected]>
Suggested-by: Joe Perches <[email protected]>
Acked-by: Will Deacon <[email protected]>
Acked-by: Linus Torvalds <[email protected]>
Cc: Anshul Garg <[email protected]>
Cc: Davidlohr Bueso <[email protected]>
Cc: David Miller <[email protected]>
Cc: Ingo Molnar <[email protected]>
Cc: Kees Cook <[email protected]>
Cc: Matthew Wilcox <[email protected]>
Cc: Michael Davidson <[email protected]>
Cc: Thomas Gleixner <[email protected]>
Signed-off-by: Andrew Morton <[email protected]>
Signed-off-by: Linus Torvalds <[email protected]>

diff --git a/lib/int_sqrt.c b/lib/int_sqrt.c
index 036c96781ea85058eecbbb613460710e15107073..67bb300b5b46735995658d0b5e355aee79b16183 100644 (file)
--- a/lib/int_sqrt.c
+++ b/lib/int_sqrt.c
@@ -8,6 +8,7 @@
 
 #include <linux/kernel.h>
 #include <linux/export.h>
+#include <linux/bitops.h>
 
 /**
  * int_sqrt - rough approximation to sqrt
@@ -22,10 +23,7 @@ unsigned long int_sqrt(unsigned long x)
        if (x <= 1)
                return x;
 
-       m = 1UL << (BITS_PER_LONG - 2);
-       while (m > x)
-               m >>= 2;
-
+       m = 1UL << (__fls(x) & ~1UL);
        while (m != 0) {
                b = y + m;
                y >>= 1;