Date:   Mon, 14 Mar 2022 08:52:30 -0700
From:   Randy Dunlap <rdunlap@...radead.org>
To:     Jui-Tse Huang <juitse.huang@...il.com>,
        Jonathan Corbet <corbet@....net>,
        Peter Zijlstra <peterz@...radead.org>,
        Valentin Schneider <valentin.schneider@....com>,
        Mauro Carvalho Chehab <mchehab+huawei@...nel.org>,
        Huaixin Chang <changhuaixin@...ux.alibaba.com>,
        Beata Michalska <beata.michalska@....com>,
        Chun-Hung Tseng <henrybear327@...il.com>,
        linux-doc@...r.kernel.org, linux-kernel@...r.kernel.org
Cc:     Ching-Chun Huang <jserv@...s.ncku.edu.tw>,
        Yiwei Lin <s921975628@...il.com>
Subject: Re: [PATCH v2] docs/scheduler: Introduce the doc of load average



On 3/14/22 01:47, Jui-Tse Huang wrote:
> The load average is one of a common as well as easy observed statistic
> provied by Linux, but still not well documented, which makes the numbers
> that users observes from the output of top, htop or other system
> monitoring application are only numbers. This patch gives a discussion
> on how Linux calculates the load average as well as what metrics are
> concerned while calculating the load average.
> 
> The discussion flow is divided into several parts:
> 1. The expression used to get the load average.
> 2. Why Linux choose such average method from the other.
> 2. The meaning of each term in the expression.
> 3. The metrics, that is, the type of tasks that will be covered in the
>    calculation.
> 4. A brief explanation over the fixed-point nubmer since the weights
>    defined in the Linux kernel are based on it.
> 
> Signed-off-by: Jui-Tse Huang <juitse.huang@...il.com>
> Signed-off-by: Yiwei Lin <s921975628@...il.com>
> Co-Developed-by: Yiwei Lin <s921975628@...il.com>
> 
> ---
> v1 -> v2:
>     fix typo: '$cat /proc/laodavg' -> '$cat /proc/loadavg'
> 
>  Documentation/scheduler/index.rst        |  1 +
>  Documentation/scheduler/load-average.rst | 77 ++++++++++++++++++++++++
>  2 files changed, 78 insertions(+)
>  create mode 100644 Documentation/scheduler/load-average.rst
> 
> diff --git a/Documentation/scheduler/index.rst b/Documentation/scheduler/index.rst
> index 88900aabdbf7..bdc779b4190f 100644
> --- a/Documentation/scheduler/index.rst
> +++ b/Documentation/scheduler/index.rst
> @@ -17,6 +17,7 @@ Linux Scheduler
>      sched-nice-design
>      sched-rt-group
>      sched-stats
> +    load-average
>  
>      text_files
>  
> diff --git a/Documentation/scheduler/load-average.rst b/Documentation/scheduler/load-average.rst
> new file mode 100644
> index 000000000000..589320ee1cd7
> --- /dev/null
> +++ b/Documentation/scheduler/load-average.rst
> @@ -0,0 +1,77 @@
> +============
> +Load Average
> +============
> +
> +Load average is a basic statistic provided by almost all operating systems that
> +aims to report the usage of system hardware resources. In Linux kernel, the
> +load average is calculated via the following expression::
> +
> +                / 0                                      , if t = 0
> +    load_{t} = |
> +                \ laod_{t - 1} * exp + active * (1 - exp), otherwise

                     load_

> +
> +The expression represents the exponential moving average of the historical
> +loading of the system. There are several reasons that Linux kernel chooses
> +exponential moving average from other similar average equations such as simple
> +moving average or cumulative moving average:
> +
> +#. The exponential moving average consumes fixed memory space, while the simple
> +   moving average has O(n) space complexity where n is the number of timeslice

                                                                        timeslices

> +   within a given interval.
> +#. The exponential moving average not only applies a higher weight to the most
> +   recent record but also declines the weight exponentially, which makes the
> +   resulting load average reflect the situation of the current system. Neither
> +   the simple moving average nor cumulative moving average has this feature.
> +
> +In the expression, the load_{t} in the expression indicates the calculated load

Don't need the second             "in the expression" above.

> +average at the given time t.
> +The active is the most recent recorded system load. In Linux, the system load
> +means the number of tasks in the state of TASK_RUNNING or TASK_UNINTERRUPTIBLE
> +of the entire system. Tasks with TASK_UNINTERRUPTIBLE state are usually waiting
> +for disk I/O or holding an uninterruptible lock, which is considered as a part
> +of system resource, thus, Linux kernel covers them while calculating the load
> +average.
> +The exp means the weight applied to the previous report of load average, while
> +(1 - exp) is the weight applied to the most recently recorded system load.
> +There are three different weights defined in the Linux kernel, in
> +include/linux/sched/loadavg.h, to perform statistics in various timescales::
> +
> +    // include/linux/sched/loadavg.h
> +    ...
> +    #define EXP_1    1884    /* 1/exp(5sec/1min) as fixed-point */
> +    #define EXP_5    2014    /* 1/exp(5sec/5min) */
> +    #define EXP_15   2037    /* 1/exp(5sec/15min) */
> +    ...
> +
> +According to the expression shown on the top of this page, the weight (exp)
> +controls how much of the last load load_{t - 1} will take place in the
> +calculation of current load, while (1 - exp) is the weight applied to the most
> +recent record of system load active.
> +
> +Due to the security issue, the weights are defined as fixed-point numbers based
> +on the unsigned integer rather than floating-pointing numbers. The introduction
> +of the fixed-point number keeps the FPU away from the calculation process. Since
> +the precession of the fixed-point used in the Linux kernel is 11 bits, a
> +fixed-point can be converted to a floating-point by dividing it by 2048, as the
> +expression shown below::

              shows below::
or
  as in the expressions shown below::

> +
> +    EXP_1  = 1884 / 2048 = 0.919922
> +    EXP_5  = 2014 / 2048 = 0.983398
> +    EXP_15 = 2037 / 2048 = 0.994629
> +
> +Which indicates the weights applied to active are::
> +
> +    (1 - EXP_1)  = (1 - 0.919922) = 0.080078
> +    (1 - EXP_5)  = (1 - 0.983398) = 0.016602
> +    (1 - EXP_15) = (1 - 0.994629) = 0.005371
> +
> +The load average will be updated every 5 seconds. Each time the scheduler_tick()
> +be called, the function calc_global_load_tick() will also be invoked, which
> +makes the active of each CPU core be calculated and be merged globally, finally,

                                                                 globally. Finally,

> +the load average will be updated with that global active.
> +
> +As a user, the load average can be observed via top, htop, or other system
> +monitor application, or more directly, by the following command::
> +
> +    $ cat /proc/loadavg
> +

thanks.
-- 
~Randy

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