Re: [PATCH] irq/timings: Fix model validity

[Daniel Lezcano <daniel.lezcano@linaro.org>]

On 07/11/2018 14:05, Peter Zijlstra wrote:
> On Wed, Nov 07, 2018 at 11:52:31AM +0100, Daniel Lezcano wrote:
>>> @@ -146,11 +152,38 @@ static void irqs_update(struct irqt_stat *irqs, u64 ts)
>>>  	 */
>>>  	diff = interval - irqs->avg;
>>>  
>>> +	/*
>>> +	 * Online average algorithm:
>>> +	 *
>>> +	 *  new_average = average + ((value - average) / count)
>>> +	 *
>>> +	 * The variance computation depends on the new average
>>> +	 * to be computed here first.
>>> +	 *
>>> +	 */
>>> +	irqs->avg = irqs->avg + (diff >> IRQ_TIMINGS_SHIFT);
>>> +
>>> +	/*
>>> +	 * Online variance algorithm:
>>> +	 *
>>> +	 *  new_variance = variance + (value - average) x (value - new_average)
>>> +	 *
>>> +	 * Warning: irqs->avg is updated with the line above, hence
>>> +	 * 'interval - irqs->avg' is no longer equal to 'diff'
>>> +	 */
>>> +	irqs->variance = irqs->variance + (diff * (interval - irqs->avg));
>>> +
>>>  	/*
>>>  	 * Increment the number of samples.
>>>  	 */
>>>  	irqs->nr_samples++;
> 
> FWIW, I'm confused on this. The normal (Welford's) online algorithm
> does:
> 
> 	count++;
> 	delta = value - mean;
> 	mean += delta / count;
> 	M2 += delta * (value - mean);
> 
> But the above uses:
> 
> 	mean += delta / 32;
> 
> Which, for count >> 32, over-estimates the mean adjustment. But worse,
> it significantly under-estimates the mean during training.
> 
> How is the computed variance still correct with this? I can not find any
> comments that clarifies this. I'm thinking that since the mean will
> slowly wander towards it's actual location (assuming an actual standard
> distribution input) the resulting variance will be far too large, since
> the (value - mean) term will be much larger than 'expected'.

You are right, initially it was divided by min(count, 32) but for
optimization reason, we decided to change that by a power of two
constant assuming the number of samples will reach quickly 32 and the
compiler will replace that by a shift.

https://lkml.org/lkml/2017/3/23/696

>>> @@ -158,16 +191,12 @@ static void irqs_update(struct irqt_stat *irqs, u64 ts)
>>>  	 * more than 32 and dividing by 32 instead of 31 is enough
>>>  	 * precise.
>>>  	 */
>>> +	variance = irqs->variance >> IRQ_TIMINGS_SHIFT;
> 
> Worse; variance is actually (as the comment states):
> 
> 	s^2 = M2 / (count -1)
> 
> But instead you compute:
> 
> 	s^2 = M2 / 32;
> 
> Which is again much larger than the actual result; assuming count >> 32.
> 
> So you compute a variance that is inflated in two different ways.
> 
> 
> I'm not seeing how this thing works reliably.

I have to revisit this part of code soon, I will double check that.


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