Re: [PATCH] ftrace: fix stddev calculation in function profiler (again)

[Matthias Schiffer <mschiffer@universe-factory.net>]

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On 03/24/2018 05:26 PM, Matthias Schiffer wrote:
> It is well-known that it is not possible to accurately calculate variances
> just by accumulating squared samples; in fact, such an approach can even
> result in negative numbers. An earlier attempt to fix the calculation
> referred to Welford's method, but did not implement it correctly, leading
> to meeaningless output like the following:
> 
>   nf_conntrack_proto_fini     50    373.523 us    7.470 us    3234315951 us
> 
> Welford's method uses one do_div() in the tracing path; this cannot be
> avoided. The average time is added to struct ftrace_profile, so only a
> single division is required. I also considered the following alternatives:
> 
> 1) Only keeping the avg field and removing the aggregated time would
> greatly lead to severe rounding errors in calculating the total time based
> on counter and avg.
> 
> 2) Calculating both the old and the new average in profile_graph_return()
> instead of storing it in struct ftrace_profile would require a second
> division.
> 
> 3) I managed to transform Welford's equations in a way that uses the total
> time instead of the average and requires only a single division.
> Unfortunately, the divisor is counter^3 in this case, easily overflowing
> even 64bit integers.
> 
> Ruling out the above alternatives, I chose the present approach to fix the
> issue.
> 
> Fixes: e330b3bcd831 ("tracing: Show sample std dev in function profiling")
> Fixes: 52d85d763086 ("ftrace: Fix stddev calculation in function profiler")
> Signed-off-by: Matthias Schiffer <mschiffer@universe-factory.net>


Hmm, in further testing, I'm seeing profile_graph_return() being called
without rec->counter getting incremented a lot, completely throwing off the
stddev calculation (and also slightly displacing the average). Is this
expected?

Should we possibly move the counter increment to profile_graph_return() in
the CONFIG_FUNCTION_GRAPH_TRACER case, or introduce a second counter for
returns?

Matthias



> ---
>  kernel/trace/ftrace.c | 33 +++++++++++++++++++--------------
>  1 file changed, 19 insertions(+), 14 deletions(-)
> 
> diff --git a/kernel/trace/ftrace.c b/kernel/trace/ftrace.c
> index eac9ce2c57a2..16dce67b855a 100644
> --- a/kernel/trace/ftrace.c
> +++ b/kernel/trace/ftrace.c
> @@ -460,7 +460,8 @@ struct ftrace_profile {
>  	unsigned long			counter;
>  #ifdef CONFIG_FUNCTION_GRAPH_TRACER
>  	unsigned long long		time;
> -	unsigned long long		time_squared;
> +	unsigned long long		avg;
> +	unsigned long long		stddev;
>  #endif
>  };
>  
> @@ -580,7 +581,6 @@ static int function_stat_show(struct seq_file *m, void *v)
>  	int ret = 0;
>  #ifdef CONFIG_FUNCTION_GRAPH_TRACER
>  	static struct trace_seq s;
> -	unsigned long long avg;
>  	unsigned long long stddev;
>  #endif
>  	mutex_lock(&ftrace_profile_lock);
> @@ -592,9 +592,7 @@ static int function_stat_show(struct seq_file *m, void *v)
>  	}
>  
>  #ifdef CONFIG_FUNCTION_GRAPH_TRACER
> -	avg = rec->time;
> -	do_div(avg, rec->counter);
> -	if (tracing_thresh && (avg < tracing_thresh))
> +	if (tracing_thresh && (rec->avg < tracing_thresh))
>  		goto out;
>  #endif
>  
> @@ -608,24 +606,19 @@ static int function_stat_show(struct seq_file *m, void *v)
>  	if (rec->counter <= 1)
>  		stddev = 0;
>  	else {
> -		/*
> -		 * Apply Welford's method:
> -		 * s^2 = 1 / (n * (n-1)) * (n * \Sum (x_i)^2 - (\Sum x_i)^2)
> -		 */
> -		stddev = rec->counter * rec->time_squared -
> -			 rec->time * rec->time;
> +		stddev = rec->stddev;
>  
>  		/*
>  		 * Divide only 1000 for ns^2 -> us^2 conversion.
>  		 * trace_print_graph_duration will divide 1000 again.
>  		 */
> -		do_div(stddev, rec->counter * (rec->counter - 1) * 1000);
> +		do_div(stddev, 1000 * (rec->counter - 1));
>  	}
>  
>  	trace_seq_init(&s);
>  	trace_print_graph_duration(rec->time, &s);
>  	trace_seq_puts(&s, "    ");
> -	trace_print_graph_duration(avg, &s);
> +	trace_print_graph_duration(rec->avg, &s);
>  	trace_seq_puts(&s, "    ");
>  	trace_print_graph_duration(stddev, &s);
>  	trace_print_seq(m, &s);
> @@ -905,8 +898,20 @@ static void profile_graph_return(struct ftrace_graph_ret *trace)
>  
>  	rec = ftrace_find_profiled_func(stat, trace->func);
>  	if (rec) {
> +		unsigned long long avg, delta1, delta2;
> +
>  		rec->time += calltime;
> -		rec->time_squared += calltime * calltime;
> +
> +		/* Apply Welford's method */
> +		delta1 = calltime - rec->avg;
> +
> +		avg = rec->time;
> +		do_div(avg, rec->counter);
> +		rec->avg = avg;
> +
> +		delta2 = calltime - rec->avg;
> +
> +		rec->stddev += delta1 * delta2;
>  	}
>  
>   out:
> 



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