Bug#763917: mdadm: rounding errors in human_size()

[NeilBrown]

On Fri, 05 Dec 2014 13:28:00 +0300 Michael Tokarev <mjt at tls.msk.ru> wrote:

> Neil, will you take the patch in this bugreport for the next version?
> 
> http://bugs.debian.org/763917.
> 
> Thanks,
> 
> /mjt
> 
> On Fri, 3 Oct 2014 20:24:54 +0200 Jan Echternach <jan at goneko.de> wrote:
> > Package: mdadm
> > Version: 3.3.2-1
> > Severity: minor
> > Tags: patch
> > 
> > 
> > While setting up a new system, I noticed an incorrect value in the output
> > of mdadm --examine:
> > 
> >  Avail Dev Size : 2095080 (1023.16 MiB 1072.68 MB)
> > 
> > The 1023.16 MiB were quite irritating because the underlying partition has
> > a size of exactly 1023 MiB.
> > 
> > The number of sectors seems plausible: 2095080 sectors * 512 bytes/sector
> > are 1022.988 MiB or 1072.681 MB. I looked into the code and found an
> > inaccuracy in human_size() and human_size_brief(). The formula used for
> > the MiB value is essentially
> > 
> >   long cMiB = (bytes / ( (1LL<<20) / 200LL ) +1) /2;
> > 
> > but (1LL<<20) / 200LL is not an integer. It's rounded down and cMiB becomes
> > too large. The quick fix would have been multiplying by 200 before dividing
> > by 1<<20, but that might cause integer overflows in the GiB case.

Given that we are doing 64bit arithmetic, we would  need about 56bits of
bytes for there to be a rounding problem.  That's 64 petabytes.

I decide to just do the simple transformation.  If we get arrays close to
petabytes I would want to make other changes, like reporting the number of
terabytes for larger arrays.

Thanks,
NeilBrown

> > 
> > The following patch uses a more complicated formula that computes the
> > fractional portion separately from the integer portion. It also changes some
> > longs to long longs to eliminate a different cause of integer overflows.
> > 
> > 
> > --- mdadm-3.3.2/util.c	2014-10-03 19:06:51.000000000 +0200
> > +++ mdadm-3.3.2/util.c	2014-10-03 19:08:06.000000000 +0200
> > @@ -671,15 +671,17 @@
> >  	if (bytes < 5000*1024)
> >  		buf[0] = 0;
> >  	else if (bytes < 2*1024LL*1024LL*1024LL) {
> > -		long cMiB = (bytes / ( (1LL<<20) / 200LL ) +1) /2;
> > +		long cMiB = bytes / (1LL<<20) * 100
> > +			    + ((bytes % (1LL<<20)) * 200 / (1LL<<20) +1) /2;
> >  		long cMB  = (bytes / ( 1000000LL / 200LL ) +1) /2;
> >  		snprintf(buf, sizeof(buf), " (%ld.%02ld MiB %ld.%02ld MB)",
> >  			cMiB/100 , cMiB % 100,
> >  			cMB/100, cMB % 100);
> >  	} else {
> > -		long cGiB = (bytes / ( (1LL<<30) / 200LL ) +1) /2;
> > -		long cGB  = (bytes / (1000000000LL/200LL ) +1) /2;
> > -		snprintf(buf, sizeof(buf), " (%ld.%02ld GiB %ld.%02ld GB)",
> > +		long long cGiB = bytes / (1LL<<30) * 100
> > +				 + ((bytes % (1LL<<30)) * 200 / (1LL<<30) +1) /2;
> > +		long long cGB  = (bytes / (1000000000LL/200LL ) +1) /2;
> > +		snprintf(buf, sizeof(buf), " (%lld.%02lld GiB %lld.%02lld GB)",
> >  			cGiB/100 , cGiB % 100,
> >  			cGB/100, cGB % 100);
> >  	}
> > @@ -706,12 +708,14 @@
> >  		buf[0] = 0;
> >  	else if (prefix == IEC) {
> >  		if (bytes < 2*1024LL*1024LL*1024LL) {
> > -			long cMiB = (bytes / ( (1LL<<20) / 200LL ) +1) /2;
> > +			long cMiB = bytes / (1LL<<20) * 100
> 
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