Date: Tue, 7 Jul 2015 10:09:13 +0200
From: Peter Zijlstra <peterz@infradead.org>
To: Frederic Weisbecker <fweisbec@gmail.com>
Cc: Fredrik =?iso-8859-1?Q?Markstr=F6m?= 
	<fredrik.markstrom@gmail.com>,
        mingo@redhat.com, linux-kernel@vger.kernel.org,
        Rik van Riel <riel@redhat.com>, Jason Low <jason.low2@hp.com>
Subject: Re: [PATCH 1/1] cputime: Make the reported utime+stime correspond to
 the actual runtime.
Message-ID: <20150707080913.GT18673@twins.programming.kicks-ass.net>
References: <20150629145837.GE3644@twins.programming.kicks-ass.net>
 <CAKdL+dRPEenCzi14SWypOv6Vv+x2X0bHQXXc-G6gqUT+VhOtUw@mail.gmail.com>
 <20150630093054.GK19282@twins.programming.kicks-ass.net>
 <CAKdL+dR68T7LMZ_ndwihvMo_SaUB1G++JaZ28RXiqaHs9gpP0g@mail.gmail.com>
 <20150630121812.GG3644@twins.programming.kicks-ass.net>
 <CAKdL+dTTgfKrskE5d6OxktxJ4SHeMvmRPka4oAQ97LJmDefn6A@mail.gmail.com>
 <20150702121126.GP3644@twins.programming.kicks-ass.net>
 <20150702130701.GP18673@twins.programming.kicks-ass.net>
 <20150707005135.GH4981@lerouge>
 <20150707075954.GN3644@twins.programming.kicks-ass.net>
MIME-Version: 1.0
Content-Type: text/plain; charset=us-ascii
Content-Disposition: inline
In-Reply-To: <20150707075954.GN3644@twins.programming.kicks-ass.net>
User-Agent: Mutt/1.5.21 (2012-12-30)
Sender: linux-kernel-owner@vger.kernel.org
Content-Length: 1645
Lines: 50

On Tue, Jul 07, 2015 at 09:59:54AM +0200, Peter Zijlstra wrote:
> > > +	/*
> > > +	 * Make sure stime doesn't go backwards; this preserves monotonicity
> > > +	 * for utime because rtime is monotonic.
> > > +	 *
> > > +	 *  utime_i+1 = rtime_i+1 - stime_i
> > > +	 *            = rtime_i+1 - (rtime_i - stime_i)
> > > +	 *            = (rtime_i+1 - rtime_i) + stime_i
> > > +	 *            >= stime_i
> > > +	 */

Argh, just noticed I messed that up, it should read:

+       /*
+        * Make sure stime doesn't go backwards; this preserves monotonicity
+        * for utime because rtime is monotonic.
+        *
+        *  utime_i+1 = rtime_i+1 - stime_i
+        *            = rtime_i+1 - (rtime_i - utime_i)
+        *            = (rtime_i+1 - rtime_i) + utime_i
+        *            >= utime_i
+        */

I got some [us] confusion. Typing is hard.

So we compute: utime = rtime - stime, which we'll denote as:

	utime_i+1 = rtime_i+1 - stime_i

since: stime_i + utime_i = rtime_i, we can write: stime_i = rtime_i -
utime_i and substitute in the above:

		 = rtime_i+1 - (rtime_i - utime_i)

Rearrange terms:

		= (rtime_i+1 - rtime_i) + utime_i

And since we have: rtime_i+1 >= rtime_i, which we can write like:
rtime_i+1 - rtime_i >= 0, substitution gives:

		>= utime_i

And we've proven that the new utime must be equal or greater than the
previous utime, because rtime is monotonic.
--
To unsubscribe from this list: send the line "unsubscribe linux-kernel" in
the body of a message to majordomo@vger.kernel.org
More majordomo info at  http://vger.kernel.org/majordomo-info.html
Please read the FAQ at  http://www.tux.org/lkml/