Re: [PATCH] Optimize int_sqrt for small values for faster idle

[Eric Dumazet]

On Thu, 2016-01-28 at 13:42 -0800, Andi Kleen wrote:
> From: Andi Kleen <ak@xxxxxxxxxxxxxxx>
> 
> The menu cpuidle governor does at least two int_sqrt() each time
> we go into idle in get_typical_interval to compute stddev
> 
> int_sqrts take 100-120 cycles each. Short idle latency is important
> for many workloads.
> 
> I instrumented the function on my workstation and most values are
> 16bit only and most others 32bit (50% percentile is 122094,
> 75% is 3699533).
> 
> sqrt is implemented by starting with an initial estimation,
> and then iterating. int_sqrt currently only uses a fixed
> estimating which is good for 64bits worth of input.
> 
> This patch adds some checks at the beginning to start with
> a better estimate for values fitting in 8, 16bit and 32bit.
> This makes int_sqrt between 60+% faster for values in 16bit,
> and still somewhat faster (between 10 and 30%) for larger values
> upto 32bit. Full 64bit is slightly slower.
> 
> This optimizes the short idle calls and does not hurt the
> long sleep (which probably do not care) much.
> 
> An alternative would be a full table drive approach, or
> trying some inverted sqrt optimization, but this simple change
> already seems to have a good payoff.
> 
> Signed-off-by: Andi Kleen <ak@xxxxxxxxxxxxxxx>
> ---
>  lib/int_sqrt.c | 10 +++++++++-
>  1 file changed, 9 insertions(+), 1 deletion(-)
> 
> diff --git a/lib/int_sqrt.c b/lib/int_sqrt.c
> index 1ef4cc3..2479ccf 100644
> --- a/lib/int_sqrt.c
> +++ b/lib/int_sqrt.c
> @@ -21,7 +21,15 @@ unsigned long int_sqrt(unsigned long x)
>  	if (x <= 1)
>  		return x;

The above test (x <= 1) should also be moved

>  
> -	m = 1UL << (BITS_PER_LONG - 2);
> +	if (x <= 0xffff) {
> +		if (m <= 0xff)

m or x ?  if (x <= 0xff) looks more correct.

> +			m = 1UL << (8 - 2);
> +		else
> +			m = 1UL << (16 - 2);
> +	} else if (x <= 0xffffffff)
> +		m = 1UL << (32 - 2);
> +	else
> +		m = 1UL << (BITS_PER_LONG - 2);
>  	while (m != 0) {
>  		b = y + m;
>  		y >>= 1;