How to align on the right - partition alignment algorithm

 In MSDOS 6.22 there are alignment restrictions for partitions. This means a partition of size capacity = /start - end/ = end - start, partition boundaries (start, end) must coincide with certain boundaries; in this case cylinder boundaries.

The following alignment algorithm is taken from the libvirt virtualization API.

In short, the algorithm will make sure allocated continuous space is aligned on the right, that is on the end. If the available free space for alignment already starts at a given boundary value, it will be fully aligned [1].

We'll have:

1. Input: c := capacity, l := alignment interval, s := start
2. Output: e := end

All of these values are in ZZ (actually NN). For e: c <= e - s; e + 1 = n*l (for some natural n), that is, the required capacity fits into the allocated space and the end is aligned while it must end one unit before the next interval starts.

Let r := l - (c mod l). We understand r as the extra space required to reach the interval boundary, e.g. if l is 512 (think of sector size) and I need to allocate capacity 618, then 1*l won't cover c, instead I'd have to used 2*l = 1024 >= 618. But then I have 1024 - 618 = 406 = 512 - (618 mod 512) of extra space I need to allocate that wasn't really required.

The algorithm handles three cases:

1. s = m*l, for some m (the start is aligned at a boundary)
2. s != m*l; s mod l <= r (the start offset fits into the extra space reserved for alignment)
3. s != m*l; s mod l > r (the start offset doesn't fit) 

For 1. the correct e is quite easy, we already know how much extra space to align and subtract 1 to have the partition end just before the next boundary in order to have the next partition start exactly at boundary.

(1)    e = s + c + r - 1

This is the base for the other two cases.

For 2. (1) would surpass the boundary:

boundary=s       ...         s+c          boundary=s+c+r

         |                ...           |                        |

boundary          s         ...       s+c   boundary       s+c+r

         |               |                      |                |              |

But we know that s mod l <= r, therefore s+c+r - s mod l >= s + c proving that the alignment on the right would fit the required capacity. Thus:

(2)    e = s + c + r - s mod l - 1

And e is still on boundary: e = s + c + r - s mod l - 1 =  (c + r) + (s - s mod l) - 1 = n_1*l + n_2*l - 1.

Now for 3. from the above,   e - s = s + c + r - s mod l - s = c + r - s mod l < c. If we originally had defined r to be 2*l - (c mod l), then e - s > c. But we didn't do that because for 1. and 2. that would be a waste of space. However, here for 3. we don't have another choice, so we add another l:

(3)    e = s + c + r + l - s mod l - 1

In the referenced algorithm, you'll see that s mod l is always subtracted. Let's keep in mind that s is at a boundary iff s mod l = 0. So we can actually summarize

                 

(4)    e = s + c + r + d - s mod l - 1, where d := 0 if s mod l < r, else d := l.

QED.

[1]  I wonder if the need for a first partition not starting exactly at the second cylinder to save space or some other MSDOS restrictions are the reason for not aligning the partition start, too.

Set up Crypto Card passthrough with KVM on IBM Z (vfio-ap)

Crypto Cards on IBM Z systems provide secure key encryption.

This security feature can be passed through to KVM guests.

The passthrough is available through the vfio_ap kernel module (paired with the homonymous driver). It uses another passthrough interface, namely, the VFIO mediated device framework (represented by kernel module vfio_mdev).

More details can be found kernel doc. Here, the focus is on setting up a single passthrough using libvirt.

What we need

1. A System Z host with a crypto card, KVM guest
2. lszcrypt command (from s390tools, often comes preinstalled with distro, package name can be s390utils, too)

What we do

1. Identify the device
2. Mark device queues as not usable by host
3. Create mediated device
4. Assign crypto device to mediated device
5. Attach mediated device to guest
6. Verify setup

Identify the device

# lszcrypt -V

CARD.DOMAIN TYPE  MODE        STATUS  REQUESTS  PENDING HWTYPE QDEPTH FUNCTIONS  DRIVER     

--------------------------------------------------------------------------------------------

01          CEX5C CCA-Coproc  online         1        0     11     08 S--D--N--  cex4card   

01.0011     CEX5C CCA-Coproc  online         1        0     11     08 S--D--N--  cex4queue  

We need two pieces of information:

• HWTYPE: passthrough is only supported if this number is >= 10
• CARD.DOMAIN: 0x01 (adapter id), 0x0011 (domain id)

Mark device queues as not usable by host

• Mark adapter not usable by host:
• echo -0x01 > /sys/bus/ap/apmask
• Mark device queues not usable by host:
• echo -0x0011 > /sys/bus/ap/aqmask

lszcrypt now should only list the card, not the queue.

# lszcrypt

CARD.DOMAIN TYPE  MODE        STATUS  REQUESTS

----------------------------------------------

01          CEX5C CCA-Coproc  online         4

Create mediated device

cd /sys/devices/vfio_ap/matrix/mdev_supported_types/vfio_ap-passthrough

uuidgen > create

Assign crypto device to mediated device

Below the device dir $uuid that we just created below vfio_ap-passthrough/devices:

cd devices/$uuidgen

echo 0x01 > assign_adapter

echo 0x0011 > assign_domain

We can confirm assignment:

# lszcrypt -V

CARD.DOMAIN TYPE  MODE        STATUS  REQUESTS  PENDING HWTYPE QDEPTH FUNCTIONS  DRIVER     

--------------------------------------------------------------------------------------------

01          CEX5C CCA-Coproc  online         4        0     11     08 S--D--N--  cex4card   

01.0011     CEX5C CCA-Coproc  -              4        0     11     08 S--D--N--  vfio_ap    

Attach the mediated device to guest

Use $uuid for the mediated device and modify guest domain xml (e.g. virsh edit)

<hostdev mode='subsystem' type='mdev' model='vfio-ap'>
    <source>
      <address uuid='$uuid'/>
    </source>
</hostdev>

Verify setup

After starting the guest:

root@guest # lszcrypt -V

CARD.DOMAIN TYPE  MODE        STATUS  REQUESTS  PENDING HWTYPE QDEPTH FUNCTIONS  DRIVER     

--------------------------------------------------------------------------------------------

01          CEX5C CCA-Coproc  online         1        0     11     08 S--D--N--  cex4card   

01.0011     CEX5C CCA-Coproc  online         1        0     11     08 S--D--N--  cex4queue  

The testing effort growth

Just wondering how a proof for "Number of test cases grows exponentially" could look like...

Define a program to be a function from a set of input variables to a set of output variables,

P = Input x P|Output = I x O 
  = { (j_1,...,j_n) x (o_1,...,o_m) }
  = { (j_1,...,j_n,o_1,...,o_m) }.

Each component of Input is supposed to have at least 2 elements. (If not, the input variable will never change the image value, in other words, the program's behavior, and can therefore be eliminated. The case where an input value is determine to be defined or not, Input ≃ { 0, {0} }.)

Also, I need to restrict to the case where the dim(I) > 1 because if not each extra value to test adds exactly one test case (linear growth).

Define a feature to be a selection of a subset of input variables combined with their image, that is, it's a restriction of the program to a subset of the domain, F = P|J, J < I.

We take a test case to be the a random variable

T : Input x Ω -> Input x Output
T(i, ω) = (i, T_1(i, ω),..., T_m(i, ω)).

Each T_j is an expected output or simply expectation or post-condition.

A test passes if T_j(ω) = P(i)_j for all j, or fails otherwise, for a test execution ω.

A test case of a feature is then simply T|F = T|J x Ω where F = P|J.

For a given feature we can add new behavior minimally by

1. extending the domain of an input variable J_i by an additional value j' that defines a new behavior of the program, that is for some i, J_i' = J_i + { j' } and Input = J_1 x ... x J_i' x ... x J_n
2. extending the set of input variables by an additional dimension J_n+1

Both will result in an extended feature F'.

For 2. it is easy to see that

#T|F' = #{ (J_1,...,J_n) x J_n+1 x O } 
      = #J * #J_n+1 * # O 
      = #T|F * #J_n+1
      ≥ #T|F * 2.

As for 1., given that dim(J) > 1 each new value j' creates another full set of combinations of input variables (j_1,...,j',...,j_n), that is, the number of added test cases is

#T|F' - #T|F = #J_1,...,^J_i,...,J_n
                               ≥ 2^(n-1)

where ^J_i denotes not selecting this component.

Therefore,

#T|F' ≥ #T|F + 2^(n-1).

So, in general adding a new value to test, the lower bound for growth is 2^(n-1).  ⃞

Considering that the effort E|F of testing a feature depends on the selected test suite S|F < T|F, we might dare say that selecting S|F and the methods to evaluate T(i, ω) is a very important activity in testing.

I hope this makes sense...

ssh into libvirt guest

Libvirt sets up NAT mode per default allowing guests to communicate, for example, with the internet, with each other and with the host. A host interface vnetX will be created and normally an IP will be assigned automatically.

# virsh domifaddr vm
 Name       MAC address          Protocol     Address
-------------------------------------------------------------------------------
 vnet0      52:54:00:6f:dc:90    ipv4         192.168.122.84/24

# virsh dumpxml --inactive vm
...
    <interface type="network">
      <mac address="52:54:00:6f:dc:90">
      <source network="default"></source>
      <model type="virtio">
      <address bus="0x00" domain="0x0000" function="0x0" slot="0x03" type="pci">
    </address>
...

However, vnetX won't get the IP assigned really, that's not how it's intended. So, per default neither the ip nor any name are available to ssh. 

What you can do instead is use the NSS module libvirt-nss.

If you want to easily ssh into the guest using its libvirt name, set

# /etc/nsswitch.conf:
hosts:       files libvirt_guest dns

and make sure to have the correct sshd configuration in your guest.