Thanks for the response.  I'm still a little confused by the 21 thing.  By my 
calculations 21*47,619,047 yields 999,999,987.

The 8192 block size looks like a nice bit map for 65536; 65536/8 is 8192, so 
the first area fits nice into a bitmap of 8K.  Also when the theoretical limit 
of 255tb (268,434,453 cyl) and divid it by 8192, the result is 7FFF + a little, 
or a nice half word.  The current limit of 262,668 cyl on a bit map bases would 
fit nicely into 3+, 8192 blocks plus the original bit map for the first 65520 
tracks or four total; (262,668-65520)/(8*8192) = 3.008+.  All of this with the 
assumption that allocation is in 21 bit chunks.

OK, my brain hurts.

The CA sizes makes a lot of sense to me.  315 (21*15) does yield some nice 
number for CAs; (1,3,5,7,9,15).  IMHO, a CA larger than 15 tracks doesn't make 
a lot of sense and that really opens up the use of the 000 of the CCW 
(CCCC000H) for EVA cylinder values.

Hmmm.  In a world of powers of two, this is a interesting venture.

Chip Grantham
Sr. Software Engineer
Syncsort Incorporated
P: 201-882-8337  |  C: TBD  |   F: 201-573-5176
E: [email protected]
www.syncsort.com

INTEGRATING BIG DATA… SMARTER

-----Original Message-----
From: IBM Mainframe Discussion List [mailto:[email protected]] On Behalf 
Of John Chase
Sent: Monday, September 16, 2013 7:58 AM
To: [email protected]
Subject: Re: Makes you go hmmmm, EVA MSU of 21 Cyls

On Thu, 12 Sep 2013 09:13:39 -0500, Chip Grantham wrote:

>I've finally taken the time to try to understand the numbers behind the way 
>EAVs were implemented.  I found a great discussion in the redbook "z/OS v1.12 
>Implimentation"  SG24-7853-00 manual, chapter 20.  Any time spend you happen 
>to spend here is worth it. (not unlike all redbooks).   Thanks to those that 
>wrote it.
>
>I did happen into a segment that makes me go hmmm.  20.4.3 Multicylinder unit 
>section says the 21-cylinder value for the MCU is derived from being the 
>smallest unit that can map out the largest possible EAV and stay within the 
>index architecture (with a block size of 8192), as follows:
>* It is also a value that divides evenly into the 1 GB storage segments
>of an IBM DS8000,
>* These 1 GB segments are the allocation unit in the IBM DS8000 and are 
>equivalent to 1,113 cylinders.
>
>I'm sure the "index architecture" references the index vtoc architecture, 
>which has always been a curious archeture to me.  Has this design ever been 
>made open?  Just curious as to why it made 21 the magic number?
>
>I also ran into a math issue when I divided 21 into 1GB (or 1,073,741,824/21 = 
>51,130,563.0476...).  I suspect that's because the 1GB storage segment is a 
>number used in the DS8000 degisn, and its really close to the 1GB value. 
>Wondering if that's true or some other reason.

IIRC, when discussing disk storage, "the industry" uses the decimal meanings of 
KB, MB, GB, etc.  Thus, a 1GB disk allocation would be 1,000,000,000 bytes, 
which divided by 21 yields 47,619,047.

    -jc-

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