linux-kernel - Re: [PATCH v4 6/8] tracing/histogram: Optimize division by a power of 2

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Date:   Tue, 26 Oct 2021 22:21:23 -0400
From:   Steven Rostedt <rostedt@...dmis.org>
To:     Kalesh Singh <kaleshsingh@...gle.com>
Cc:     surenb@...gle.com, hridya@...gle.com, namhyung@...nel.org,
        kernel-team@...roid.com, Jonathan Corbet <corbet@....net>,
        Ingo Molnar <mingo@...hat.com>, Shuah Khan <shuah@...nel.org>,
        Masami Hiramatsu <mhiramat@...nel.org>,
        Tom Zanussi <zanussi@...nel.org>, linux-doc@...r.kernel.org,
        linux-kernel@...r.kernel.org, linux-kselftest@...r.kernel.org
Subject: Re: [PATCH v4 6/8] tracing/histogram: Optimize division by a power
 of 2

On Tue, 26 Oct 2021 18:31:21 -0700
Kalesh Singh <kaleshsingh@...gle.com> wrote:

> And IIUC max_div is an arbitrary value we decide on that's <= 2^shift?
> Is there a rule of thumb for choosing this?

The way I came up with the max was to figure out at what point is it no
longer guaranteed to be accurate. That is, what number can make the
mult/shift no longer match the division.

If we have some number div that is not a power of two. At some point:

	(X * mult) >> shift != X / div

Now I simply picked

  max = 1 << shift / (mult * div - (1 << shift))

Because that will always be within the precision of the actual number.

But I believe we can make max bigger, but because that deals with
truncation, it's not simple math.

That is, the above X / div is truncated and not the real number.

I'm sure there's an algorithm somewhere that can give as the real max.

-- Steve