linux/lib/int_sqrt.c
Peter Zijlstra 083aa6a5d3 lib/int_sqrt: optimize initial value compute
commit f8ae107eef upstream.

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/20171020164644.936577234@infradead.org
Signed-off-by: Peter Zijlstra (Intel) <peterz@infradead.org>
Suggested-by: Joe Perches <joe@perches.com>
Acked-by: Will Deacon <will.deacon@arm.com>
Acked-by: Linus Torvalds <torvalds@linux-foundation.org>
Cc: Anshul Garg <aksgarg1989@gmail.com>
Cc: Davidlohr Bueso <dave@stgolabs.net>
Cc: David Miller <davem@davemloft.net>
Cc: Ingo Molnar <mingo@kernel.org>
Cc: Kees Cook <keescook@chromium.org>
Cc: Matthew Wilcox <mawilcox@microsoft.com>
Cc: Michael Davidson <md@google.com>
Cc: Thomas Gleixner <tglx@linutronix.de>
Signed-off-by: Andrew Morton <akpm@linux-foundation.org>
Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>
Cc: Joe Perches <joe@perches.com>
Signed-off-by: Greg Kroah-Hartman <gregkh@linuxfoundation.org>
2019-04-05 22:31:24 +02:00

41 lines
712 B
C

// SPDX-License-Identifier: GPL-2.0
/*
* Copyright (C) 2013 Davidlohr Bueso <davidlohr.bueso@hp.com>
*
* Based on the shift-and-subtract algorithm for computing integer
* square root from Guy L. Steele.
*/
#include <linux/kernel.h>
#include <linux/export.h>
#include <linux/bitops.h>
/**
* int_sqrt - rough approximation to sqrt
* @x: integer of which to calculate the sqrt
*
* A very rough approximation to the sqrt() function.
*/
unsigned long int_sqrt(unsigned long x)
{
unsigned long b, m, y = 0;
if (x <= 1)
return x;
m = 1UL << (__fls(x) & ~1UL);
while (m != 0) {
b = y + m;
y >>= 1;
if (x >= b) {
x -= b;
y += m;
}
m >>= 2;
}
return y;
}
EXPORT_SYMBOL(int_sqrt);