• Peter Zijlstra's avatar
    lib/int_sqrt: optimize initial value compute · f8ae107e
    Peter Zijlstra authored
    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.orgSigned-off-by: default avatarPeter Zijlstra (Intel) <peterz@infradead.org>
    Suggested-by: default avatarJoe Perches <joe@perches.com>
    Acked-by: default avatarWill Deacon <will.deacon@arm.com>
    Acked-by: default avatarLinus 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: default avatarAndrew Morton <akpm@linux-foundation.org>
    Signed-off-by: default avatarLinus Torvalds <torvalds@linux-foundation.org>
    f8ae107e
int_sqrt.c 712 Bytes