# NUMA mechanics for sPAPR (pseries machines)

NUMA in sPAPR works different than the System Locality Distance Information Table (SLIT) in ACPI. The logic is explained in the LOPAPR 1.1 chapter 15, “Non Uniform Memory Access (NUMA) Option”. This document aims to complement this specification, providing details of the elements that impacts how QEMU views NUMA in pseries.

## Associativity and ibm,associativity property

Associativity is defined as a group of platform resources that has similar mean performance (or in our context here, distance) relative to everyone else outside of the group.

The format of the ibm,associativity property varies with the value of bit 0 of byte 5 of the ibm,architecture-vec-5 property. The format with bit 0 equal to zero is deprecated. The current format, with the bit 0 with the value of one, makes ibm,associativity property represent the physical hierarchy of the platform, as one or more lists that starts with the highest level grouping up to the smallest. Considering the following topology:

    Mem M1 ---- Proc P1    |
    -----------------      | Socket S1  ---|
          chip C1          |               |
                                           | HW module 1 (MOD1)
    Mem M2 ---- Proc P2    |               |
    -----------------      | Socket S2  ---|
          chip C2          |

The ibm,associativity property for the processors would be:

- P1: {MOD1, S1, C1, P1}

- P2: {MOD1, S2, C2, P2}

Each allocable resource has an ibm,associativity property. The LOPAPR specification allows multiple lists to be present in this property, considering that the same resource can have multiple connections to the platform.

## Relative Performance Distance and ibm,associativity-reference-points

The ibm,associativity-reference-points property is an array that is used to define the relevant performance/distance related boundaries, defining the NUMA levels for the platform.

The definition of its elements also varies with the value of bit 0 of byte 5 of the ibm,architecture-vec-5 property. The format with bit 0 equal to zero is also deprecated. With the current format, each integer of the ibm,associativity-reference-points represents an 1 based ordinal index (i.e. the first element is 1) of the ibm,associativity array. The first boundary is the most significant to application performance, followed by less significant boundaries. Allocated resources that belongs to the same performance boundaries are expected to have relative NUMA distance that matches the relevancy of the boundary itself. Resources that belongs to the same first boundary will have the shortest distance from each other. Subsequent boundaries represents greater distances and degraded performance.

Using the previous example, the following setting reference points defines three NUMA levels:

- ibm,associativity-reference-points = {0x3, 0x2, 0x1}

The first NUMA level (0x3) is interpreted as the third element of each ibm,associativity array, the second level is the second element and the third level is the first element. Let’s also consider that elements belonging to the first NUMA level have distance equal to 10 from each other, and each NUMA level doubles the distance from the previous. This means that the second would be 20 and the third level 40. For the P1 and P2 processors, we would have the following NUMA levels:

    * ibm,associativity-reference-points = {0x3, 0x2, 0x1}

    * P1: associativity{MOD1, S1, C1, P1}

    First NUMA level (0x3) => associativity[2] = C1
    Second NUMA level (0x2) => associativity[1] = S1
    Third NUMA level (0x1) => associativity[0] = MOD1

    * P2: associativity{MOD1, S2, C2, P2}

    First NUMA level (0x3) => associativity[2] = C2
    Second NUMA level (0x2) => associativity[1] = S2
    Third NUMA level (0x1) => associativity[0] = MOD1

    P1 and P2 have the same third NUMA level, MOD1: Distance between them = 40

Changing the ibm,associativity-reference-points array changes the performance distance attributes for the same associativity arrays, as the following example illustrates:

    * ibm,associativity-reference-points = {0x2}

    * P1: associativity{MOD1, S1, C1, P1}

    First NUMA level (0x2) => associativity[1] = S1

    * P2: associativity{MOD1, S2, C2, P2}

    First NUMA level (0x2) => associativity[1] = S2

    P1 and P2 does not have a common performance boundary. Since this is a one level
    NUMA configuration, distance between them is one boundary above the first
    level, 20.

In a hypothetical platform where all resources inside the same hardware module is considered to be on the same performance boundary:

    * ibm,associativity-reference-points = {0x1}

    * P1: associativity{MOD1, S1, C1, P1}

    First NUMA level (0x1) => associativity[0] = MOD0

    * P2: associativity{MOD1, S2, C2, P2}

    First NUMA level (0x1) => associativity[0] = MOD0

    P1 and P2 belongs to the same first order boundary. The distance between then
    is 10.

# How the pseries Linux guest calculates NUMA distances

Another key difference between ACPI SLIT and the LOPAPR regarding NUMA is how the distances are expressed. The SLIT table provides the NUMA distance value between the relevant resources. LOPAPR does not provide a standard way to calculate it. We have the ibm,associativity for each resource, which provides a common-performance hierarchy, and the ibm,associativity-reference-points array that tells which level of associativity is considered to be relevant or not.

The result is that each OS is free to implement and to interpret the distance as it sees fit. For the pseries Linux guest, each level of NUMA duplicates the distance of the previous level, and the maximum amount of levels is limited to MAX_DISTANCE_REF_POINTS = 4 (from arch/powerpc/mm/numa.c in the kernel tree). This results in the following distances:

- both resources in the first NUMA level: 10

- resources one NUMA level apart: 20

- resources two NUMA levels apart: 40

- resources three NUMA levels apart: 80

- resources four NUMA levels apart: 160

# pseries NUMA mechanics

Starting in QEMU 5.2, the pseries machine considers user input when setting NUMA topology of the guest. The overall design is:

- ibm,associativity-reference-points is set to {0x4, 0x3, 0x2, 0x1}, allowing for 4 distinct NUMA distance values based on the NUMA levels

- ibm,max-associativity-domains supports multiple associativity domains in all NUMA levels, granting user flexibility

- ibm,associativity for all resources varies with user input

These changes are only effective for pseries-5.2 and newer machines that are created with more than one NUMA node (disconsidering NUMA nodes created by the machine itself, e.g. NVLink 2 GPUs). The now legacy support has been around for such a long time, with users seeing NUMA distances 10 and 40 (and 80 if using NVLink2 GPUs), and there is no need to disrupt the existing experience of those guests.

To bring the user experience x86 users have when tuning up NUMA, we had to operate under the current pseries Linux kernel logic described in How the pseries Linux guest calculates NUMA distances. The result is that we needed to translate NUMA distance user input to pseries Linux kernel input.

## Translating user distance to kernel distance

User input for NUMA distance can vary from 10 to 254. We need to translate that to the values that the Linux kernel operates on (10, 20, 40, 80, 160). This is how it is being done:

- user distance 11 to 30 will be interpreted as 20

- user distance 31 to 60 will be interpreted as 40

- user distance 61 to 120 will be interpreted as 80

- user distance 121 and beyond will be interpreted as 160

- user distance 10 stays 10

The reasoning behind this approximation is to avoid any round up to the local distance (10), keeping it exclusive to the 4th NUMA level (which is still exclusive to the node_id). All other ranges were chosen under the developer discretion of what would be (somewhat) sensible considering the user input. Any other strategy can be used here, but in the end the reality is that we’ll have to accept that a large array of values will be translated to the same NUMA topology in the guest, e.g. this user input:

        0   1   2
    0  10  31 120
    1  31  10  30
    2 120  30  10

And this other user input:

        0   1   2
    0  10  60  61
    1  60  10  11
    2  61  11  10

Will both be translated to the same values internally:

        0   1   2
    0  10  40  80
    1  40  10  20
    2  80  20  10

Users are encouraged to use only the kernel values in the NUMA definition to avoid being taken by surprise with that the guest is actually seeing in the topology. There are enough potential surprises that are inherent to the associativity domain assignment process, discussed below.

## How associativity domains are assigned

LOPAPR allows more than one associativity array (or ‘string’) per allocated resource. This would be used to represent that the resource has multiple connections with the board, and then the operational system, when deciding NUMA distancing, should consider the associativity information that provides the shortest distance.

The spapr implementation does not support multiple associativity arrays per resource, neither does the pseries Linux kernel. We’ll have to represent the NUMA topology using one associativity per resource, which means that choices and compromises are going to be made.

Consider the following NUMA topology entered by user input:

        0   1   2   3
    0  10  40  20  40
    1  40  10  80  40
    2  20  80  10  20
    3  40  40  20  10

All the associativity arrays are initialized with NUMA id in all associativity domains:

- node 0: 0 0 0 0

- node 1: 1 1 1 1

- node 2: 2 2 2 2

- node 3: 3 3 3 3

Honoring just the relative distances of node 0 to every other node, we find the NUMA level matches (considering the reference points {0x4, 0x3, 0x2, 0x1}) for each distance:

- distance from 0 to 1 is 40 (no match at 0x4 and 0x3, will match at 0x2)

- distance from 0 to 2 is 20 (no match at 0x4, will match at 0x3)

- distance from 0 to 3 is 40 (no match at 0x4 and 0x3, will match at 0x2)

We’ll copy the associativity domains of node 0 to all other nodes, based on the NUMA level matches. Between 0 and 1, a match in 0x2, we’ll also copy the domains 0x2 and 0x1 from 0 to 1 as well. This will give us:

- node 0: 0 0 0 0

- node 1: 0 0 1 1

Doing the same to node 2 and node 3, these are the associativity arrays after considering all matches with node 0:

- node 0: 0 0 0 0

- node 1: 0 0 1 1

- node 2: 0 0 0 2

- node 3: 0 0 3 3

The distances related to node 0 are accounted for. For node 1, and keeping in mind that we don’t need to revisit node 0 again, the distance from node 1 to 2 is 80, matching at 0x1, and distance from 1 to 3 is 40, match in 0x2. Repeating the same logic of copying all domains up to the NUMA level match:

- node 0: 0 0 0 0

- node 1: 1 0 1 1

- node 2: 1 0 0 2

- node 3: 1 0 3 3

In the last step we will analyze just nodes 2 and 3. The desired distance between 2 and 3 is 20, i.e. a match in 0x3:

- node 0: 0 0 0 0

- node 1: 1 0 1 1

- node 2: 1 0 0 2

- node 3: 1 0 0 3

The kernel will read these arrays and will calculate the following NUMA topology for the guest:

        0   1   2   3
    0  10  40  20  20
    1  40  10  40  40
    2  20  40  10  20
    3  20  40  20  10

Note that this is not what the user wanted - the desired distance between 0 and 3 is 40, we calculated it as 20. This is what the current logic and implementation constraints of the kernel and QEMU will provide inside the LOPAPR specification.

Users are welcome to use this knowledge and experiment with the input to get the NUMA topology they want, or as closer as they want. The important thing is to keep expectations up to par with what we are capable of provide at this moment: an approximation.

## Limitations of the implementation

As mentioned above, the pSeries NUMA distance logic is, in fact, a way to approximate user choice. The Linux kernel, and PAPR itself, does not provide QEMU with the ways to fully map user input to actual NUMA distance the guest will use. These limitations creates two notable limitations in our support:

- Asymmetrical topologies aren’t supported. We only support NUMA topologies where the distance from node A to B is always the same as B to A. We do not support any A-B pair where the distance back and forth is asymmetric. For example, the following topology isn’t supported and the pSeries guest will not boot with this user input:

        0   1
    0  10  40
    1  20  10

- ‘non-transitive’ topologies will be poorly translated to the guest. This is the kind of topology where the distance from a node A to B is X, B to C is X, but the distance A to C is not X. E.g.:

        0   1   2   3
    0  10  20  20  40
    1  20  10  80  40
    2  20  80  10  20
    3  40  40  20  10

    In the example above, distance 0 to 2 is 20, 2 to 3 is 20, but 0 to 3 is 40.
    The kernel will always match with the shortest associativity domain possible,
    and we're attempting to retain the previous established relations between the
    nodes. This means that a distance equal to 20 between nodes 0 and 2 and the
    same distance 20 between nodes 2 and 3 will cause the distance between 0 and 3
    to also be 20.

# Legacy (5.1 and older) pseries NUMA mechanics

In short, we can summarize the NUMA distances seem in pseries Linux guests, using QEMU up to 5.1, as follows:

- local distance, i.e. the distance of the resource to its own NUMA node: 10

- if it’s a NVLink GPU device, distance: 80

- every other resource, distance: 40

The way the pseries Linux guest calculates NUMA distances has a direct effect on what QEMU users can expect when doing NUMA tuning. As of QEMU 5.1, this is the default ibm,associativity-reference-points being used in the pseries machine:

ibm,associativity-reference-points = {0x4, 0x4, 0x2}

The first and second level are equal, 0x4, and a third one was added in commit a6030d7e0b35 exclusively for NVLink GPUs support. This means that regardless of how the ibm,associativity properties are being created in the device tree, the pseries Linux guest will only recognize three scenarios as far as NUMA distance goes:

- if the resources belongs to the same first NUMA level = 10

- second level is skipped since it’s equal to the first

- all resources that aren’t a NVLink GPU, it is guaranteed that they will belong to the same third NUMA level, having distance = 40

- for NVLink GPUs, distance = 80 from everything else

This also means that user input in QEMU command line does not change the NUMA distancing inside the guest for the pseries machine.