# Generic State System

## Introduction

The Generic State System is a utility available in TMF to track different states over the duration of a trace. It works by first sending some or all events of the trace into a state provider, which defines the state changes for a given trace type. Once built, views and analysis modules can then query the resulting database of states (called "state history") to get information.

For example, let's suppose we have the following sequence of events in a kernel trace:

    10 s, sys_open, fd = 5, file = /home/user/myfile
    ...
    15 s, sys_read, fd = 5, size=32
    ...
    20 s, sys_close, fd = 5

Now let's say we want to implement an analysis module which will track the amount of bytes read and written to each file. Here, of course the sys_read is interesting. However, by just looking at that event, we have no information on which file is being read, only its fd (5) is known. To get the match fd5 = /home/user/myfile, we have to go back to the sys_open event which happens 5 seconds earlier.

But since we don't know exactly where this sys_open event is, we will have to go back to the very start of the trace, and look through events one by one! This is obviously not efficient, and will not scale well if we want to analyze many similar patterns, or for very large traces.

A solution in this case would be to use the state system to keep track of the amount of bytes read/written to every *filename* (instead of every file descriptor, like we get from the events). Then the module could ask the state system "what is the amount of bytes read for file "/home/user/myfile" at time 16 s", and it would return the answer "32" (assuming there is no other read than the one shown).

## High-level components

The State System infrastructure is composed of 3 parts:

- The state provider
- The central state system
- The storage backend

The state provider is the customizable part. This is where the mapping from trace events to state changes is done. This is what you want to implement for your specific trace type and analysis type. It's represented by the ITmfStateProvider interface (with a threaded implementation in AbstractTmfStateProvider, which you can extend).

The core of the state system is exposed through the ITmfStateSystem and ITmfStateSystemBuilder interfaces. The former allows only read-only access and is typically used for views doing queries. The latter also allows writing to the state history, and is typically used by the state provider.

Finally, each state system has its own separate backend. This determines how the intervals, or the "state history", are saved (in RAM, on disk, etc.) You can select the type of backend at construction time in the TmfStateSystemFactory.

## Definitions

Before we dig into how to use the state system, we should go over some useful definitions:

### Attribute

An attribute is the smallest element of the model that can be in any particular state. When we refer to the "full state", in fact it means we are interested in the state of every single attribute of the model.

### Attribute Tree

Attributes in the model can be placed in a tree-like structure, a bit like files and directories in a file system. However, note that an attribute can always have both a value and sub-attributes, so they are like files and directories at the same time. We are then able to refer to every single attribute with its path in the tree.

For example, in the attribute tree for Linux kernel traces, we use the following attributes, among others:

    |- Processes
    |    |- 1000
    |    |   |- PPID
    |    |   |- Exec_name
    |    |- 1001
    |    |   |- PPID
    |    |   |- Exec_name
    |   ...
    |- CPUs
         |- 0
         |  |- Status
         |  |- Current_pid
        ...

In this model, the attribute "Processes/1000/PPID" refers to the PPID of process with PID 1000. The attribute "CPUs/0/Status" represents the status (running, idle, etc.) of CPU 0. "Processes/1000/PPID" and "Processes/1001/PPID" are two different attribute, even though their base name is the same: the whole path is the unique identifier.

The value of each attribute can change over the duration of the trace, independently of the other ones, and independently of its position in the tree.

The tree-like organization is optional, all attributes could be at the same level. But it's possible to put them in a tree, and it helps make things clearer.

### Quark

In addition to a given path, each attribute also has a unique integer identifier, called the "quark". To continue with the file system analogy, this is like the inode number. When a new attribute is created, a new unique quark will be assigned automatically. They are assigned incrementally, so they will normally be equal to their order of creation, starting at 0.

Methods are offered to get the quark of an attribute from its path. The API methods for inserting state changes and doing queries normally use quarks instead of paths. This is to encourage users to cache the quarks and re-use them, which avoids re-walking the attribute tree over and over, which avoids unneeded hashing of strings.

### State value

The path and quark of an attribute will remain constant for the whole duration of the trace. However, the value carried by the attribute will change. The value of a specific attribute at a specific time is called the state value.

In the TMF implementation, state values can be integers, longs, doubles, or strings. There is also a "null value" type, which is used to indicate that no particular value is active for this attribute at this time, but without resorting to a 'null' reference.

Any other type of value could be used, as long as the backend knows how to store it.

Note that the TMF implementation also forces every attribute to always carry the same type of state value. This is to make it simpler for views, so they can expect that an attribute will always use a given type, without having to check every single time. Null values are an exception, they are always allowed for all attributes, since they can safely be "unboxed" into all types.

### State change

A state change is the element that is inserted in the state system. It consists of:

- a timestamp (the time at which the state change occurs)
- an attribute (the attribute whose value will change)
- a state value (the new value that the attribute will carry)

It's not an object per se in the TMF implementation (it's represented by a function call in the state provider). Typically, the state provider will insert zero, one or more state changes for every trace event, depending on its event type, payload, etc.

Note, we use "timestamp" here, but it's in fact a generic term that could be referred to as "index". For example, if a given trace type has no notion of timestamp, the event rank could be used.

In the TMF implementation, the timestamp is a long (64-bit integer).

### State interval

State changes are inserted into the state system, but state intervals are the objects that come out on the other side. Those are stocked in the storage backend. A state interval represents a "state" of an attribute we want to track. When doing queries on the state system, intervals are what is returned. The components of a state interval are:

- Start time
- End time
- State value
- Quark

The start and end times represent the time range of the state. The state value is the same as the state value in the state change that started this interval. The interval also keeps a reference to its quark, although you normally know your quark in advance when you do queries.

### State history

The state history is the name of the container for all the intervals created by the state system. The exact implementation (how the intervals are stored) is determined by the storage backend that is used.

Some backends will use a state history that is persistent on disk, others do not. When loading a trace, if a history file is available and the backend supports it, it will be loaded right away, skipping the need to go through another construction phase.

### Construction phase

Before we can query a state system, we need to build the state history first. To do so, trace events are sent one-by-one through the state provider, which in turn sends state changes to the central component, which then creates intervals and stores them in the backend. This is called the construction phase.

Note that the state system needs to receive its events into chronological order. This phase will end once the end of the trace is reached.

Also note that it is possible to query the state system while it is being build. Any timestamp between the start of the trace and the current end time of the state system (available with ITmfStateSystem#getCurrentEndTime()) is a valid timestamp that can be queried.

### Queries

As mentioned previously, when doing queries on the state system, the returned objects will be state intervals. In most cases it's the state *value* we are interested in, but since the backend has to instantiate the interval object anyway, there is no additional cost to return the interval instead. This way we also get the start and end times of the state "for free".

There are two types of queries that can be done on the state system:

#### Full queries

A full query means that we want to retrieve the whole state of the model for one given timestamp. As we remember, this means "the state of every single attribute in the model". As parameter we only need to pass the timestamp (see the API methods below). The return value will be an array of intervals, where the offset in the array represents the quark of each attribute.

#### Single queries

In other cases, we might only be interested in the state of one particular attribute at one given timestamp. For these cases it's better to use a single query. For a single query, we need to pass both a timestamp and a quark in parameter. The return value will be a single interval, representing the state that this particular attribute was at that time.

Single queries are typically faster than full queries (but once again, this depends on the backend that is used), but not by much. Even if you only want the state of say 10 attributes out of 200, it could be faster to use a full query and only read the ones you need. Single queries should be used for cases where you only want one attribute per timestamp (for example, if you follow the state of the same attribute over a time range).

#### 2D queries

2D queries are useful and more efficient than the previous two when querying several attributes at multiple time stamps. This type of query returns an iterable of the intervals matching the queried attributes and that overlap the queried time range or one of the queried time stamps. It is more efficient because it batches the queries and searches the backend for all the desired intervals in a single pass. The returned iterable is lazily evaluated, so it can be interrupted in an intermediate state at no cost. This type of query is recommended for querying backends to populate views where a subset of attributes are queried on a sampled time range. The returned iterable is not ordered to limit overhead.

## Relevant interfaces/classes

This section will describe the public interface and classes that can be used if you want to use the state system.

### Main classes in org.eclipse.tracecompass.tmf.core.statesystem

#### ITmfStateProvider / AbstractTmfStateProvider

ITmfStateProvider is the interface you have to implement to define your state provider. This is where most of the work has to be done to use a state system for a custom trace type or analysis type.

For first-time users, it's recommended to extend AbstractTmfStateProvider instead. This class takes care of all the initialization mumbo-jumbo, and also runs the event handler in a separate thread. You will only need to implement eventHandle, which is the call-back that will be called for every event in the trace.

For an example, you can look at StatsStateProvider in the TMF tree, or at the small example below.

#### TmfStateSystemFactory

Once you have defined your state provider, you need to tell your trace type to build a state system with this provider during its initialization. This consists of overriding TmfTrace#buildStateSystems() and in there of calling the method in TmfStateSystemFactory that corresponds to the storage backend you want to use (see the section Comparison of state system backends).

You will have to pass in parameter the state provider you want to use, which you should have defined already. Each backend can also ask for more configuration information.

You must then call registerStateSystem(id, statesystem) to make your state system visible to the trace objects and the views. The ID can be any string of your choosing. To access this particular state system, the views or modules will need to use this ID.

Also, don't forget to call super.buildStateSystems() in your implementation, unless you know for sure you want to skip the state providers built by the super-classes.

You can look at how LttngKernelTrace does it for an example. It could also be possible to build a state system only under certain conditions (like only if the trace contains certain event types).

#### ITmfStateSystem

ITmfStateSystem is the main interface through which views or analysis modules will access the state system. It offers a read-only view of the state system, which means that no states can be inserted, and no attributes can be created. Calling TmfTrace#getStateSystems().get(id) will return you a ITmfStateSystem view of the requested state system. The main methods of interest are:

##### getQuarkAbsolute()/getQuarkRelative()

Those are the basic quark-getting methods. The goal of the state system is to return the state values of given attributes at given timestamps. As we've seen earlier, attributes can be described with a file-system-like path. The goal of these methods is to convert from the path representation of the attribute to its quark.

Since quarks are created on-the-fly, there is no guarantee that the same attributes will have the same quark for two traces of the same type. The views should always query their quarks when dealing with a new trace or a new state provider. Beyond that however, quarks should be cached and reused as much as possible, to avoid potentially costly string re-hashing.

getQuarkAbsolute() takes a variable amount of Strings in parameter, which represent the full path to the attribute. Some of them can be constants, some can come programmatically, often from the event's fields.

getQuarkRelative() is to be used when you already know the quark of a certain attribute, and want to access on of its sub-attributes. Its first parameter is the origin quark, followed by a String varagrs which represent the relative path to the final attribute.

These two methods will throw an AttributeNotFoundException if trying to access an attribute that does not exist in the model.

These methods also imply that the view has the knowledge of how the attribute tree is organized. This should be a reasonable hypothesis, since the same analysis plugin will normally ship both the state provider and the view, and they will have been written by the same person. In other cases, it's possible to use getSubAttributes() to explore the organization of the attribute tree first.

##### optQuarkAbsolute()/optQuarkRelative()

These two methods are similar to their counterparts getQuarkAbsolute() and getQuarkRelative(). The only difference is that if the referenced attribute does not exist, the value ITmfStateSystem#INVALID_ATTRIBUTE (-2) is returned instead of throwing an exception.

These methods should be used when the presence of the referenced attribute is known to be optional, to avoid the performance cost of generating exceptions.

##### getQuarks()

This method (with or without a starting node quark) takes an attribute path array which may contain wildcard "*" or parent ".." elements, and returns the list of matching attribute quarks. If no matching attribute is found, an empty list is returned.

##### waitUntilBuilt()

This is a simple method used to block the caller until the construction phase of this state system is done. If the view prefers to wait until all information is available before starting to do queries (to get all known attributes right away, for example), this is the guy to call.

##### queryFullState()

This is the method to do full queries. As mentioned earlier, you only need to pass a target timestamp in parameter. It will return a List of state intervals, in which the offset corresponds to the attribute quark. This will represent the complete state of the model at the requested time.

##### querySingleState()

The method to do single queries. You pass in parameter both a timestamp and an attribute quark. This will return the single state matching this timestamp/attribute pair.

Other methods are available, you are encouraged to read their Javadoc and see if they can be potentially useful.

#### ITmfStateSystemBuilder

ITmfStateSystemBuilder is the read-write interface to the state system. It extends ITmfStateSystem itself, so all its methods are available. It then adds methods that can be used to write to the state system, either by creating new attributes of inserting state changes.

It is normally reserved for the state provider and should not be visible to external components. However it will be available in AbstractTmfStateProvider, in the field 'ss'. That way you can call ss.modifyAttribute() etc. in your state provider to write to the state.

The main methods of interest are:

##### getQuark*AndAdd()

getQuarkAbsoluteAndAdd() and getQuarkRelativeAndAdd() work exactly like their non-AndAdd counterparts in ITmfStateSystem. The difference is that the -AndAdd versions will not throw any exception: if the requested attribute path does not exist in the system, it will be created, and its newly-assigned quark will be returned.

When in a state provider, the -AndAdd version should normally be used (unless you know for sure the attribute already exist and don't want to create it otherwise). This means that there is no need to define the whole attribute tree in advance, the attributes will be created on-demand.

##### modifyAttribute()

This is the main state-change-insertion method. As was explained before, a state change is defined by a timestamp, an attribute and an object representing the value of this state. Those three elements need to be passed to modifyAttribute as parameters.

Other state change insertion methods are available (increment-, push-, pop- and removeAttribute()), but those are simply convenience wrappers around modifyAttribute(). Check their Javadoc for more information.

##### closeHistory()

When the construction phase is done, do not forget to call closeHistory() to tell the backend that no more intervals will be received. Depending on the backend type, it might have to save files, close descriptors, etc. This ensures that a persistent file can then be re-used when the trace is opened again.

If you use the AbstractTmfStateProvider, it will call closeHistory() automatically when it reaches the end of the trace.

### Other relevant interfaces

#### ITmfStateValue

This is the interface used to represent state values. Those are used when inserting state changes in the provider, and is also part of the state intervals obtained when doing queries.

The abstract TmfStateValue class contains the factory methods to create new state values of either int, long, double or string types. To retrieve the real object inside the state value, one can use the .unbox* methods.

Note: Do not instantiate null values manually, use TmfStateValue.nullValue()

#### ITmfStateInterval

This is the interface to represent the state intervals, which are stored in the state history backend, and are returned when doing state system queries. A very simple implementation is available in TmfStateInterval. Its methods should be self-descriptive.

### Exceptions

The following exceptions, found in o.e.t.statesystem.core.exceptions, are related to state system activities.

#### AttributeNotFoundException

This is thrown by getQuarkRelative() and getQuarkAbsolute() (but not by the -AndAdd versions!) when passing an attribute path that is not present in the state system. This is to ensure that no new attribute is created when using these versions of the methods.

Views can expect some attributes to be present, but they should handle these exceptions for when the attributes end up not being in the state system (perhaps this particular trace didn't have a certain type of events, etc.)

#### StateValueTypeException

This exception will be thrown when trying to unbox a state value into a type different than its own. You should always check with ITmfStateValue#getType() beforehand if you are not sure about the type of a given state value.

#### TimeRangeException

This exception is thrown when trying to do a query on the state system for a timestamp that is outside of its range. To be safe, you should check with ITmfStateSystem#getStartTime() and #getCurrentEndTime() for the current valid range of the state system. This is especially important when doing queries on a state system that is currently being built.

#### StateSystemDisposedException

This exception is thrown when trying to access a state system that has been disposed, with its dispose() method. This can potentially happen at shutdown, since Eclipse is not always consistent with the order in which the components are closed.

## Comparison of state system backends

As we have seen in section High-level components, the state system needs a storage backend to save the intervals. Different implementations are available when building your state system from TmfStateSystemFactory.

Do not confuse full/single queries with full/partial history! All backend types should be able to handle any type of queries defined in the ITmfStateSystem API, unless noted otherwise.

### Full history

Available with TmfStateSystemFactory#newFullHistory(). The full history uses a History Tree data structure, which is an optimized structure store state intervals on disk. Once built, it can respond to queries in a log(n) manner.

You need to specify a file at creation time, which will be the container for the history tree. Once it's completely built, it will remain on disk (until you delete the trace from the project). This way it can be reused from one session to another, which makes subsequent loading time much faster.

This the backend used by the LTTng kernel plugin. It offers good scalability and performance, even at extreme sizes (it's been tested with traces of sizes up to 500 GB). Its main downside is the amount of disk space required: since every single interval is written to disk, the size of the history file can quite easily reach and even surpass the size of the trace itself.

### Null history

Available with TmfStateSystemFactory#newNullHistory(). As its name implies the null history is in fact an absence of state history. All its query methods will return null (see the Javadoc in NullBackend).

Obviously, no file is required, and almost no memory space is used.

It's meant to be used in cases where you are not interested in past states, but only in the "ongoing" one. It can also be useful for debugging and benchmarking.

### In-memory history

Available with TmfStateSystemFactory#newInMemHistory(). This is a simple wrapper using a TreeSet to store all state intervals in memory. The implementation at the moment is quite simple, it will perform a binary search on entries when doing queries to find the ones that match.

The advantage of this method is that it's very quick to build and query, since all the information resides in memory. However, you are limited to 2^31 entries (roughly 2 billions), and depending on your state provider and trace type, that can happen really fast!

There are no safeguards, so if you bust the limit you will end up with ArrayOutOfBoundsException's everywhere. If your trace or state history can be arbitrarily big, it's probably safer to use a Full History instead.

### Partial history

Available with TmfStateSystemFactory#newPartialHistory(). The partial history is a more advanced form of the full history. Instead of writing all state intervals to disk like with the full history, we only write a small fraction of them, and go back to read the trace to recreate the states in-between.

It has a big advantage over a full history in terms of disk space usage. It's very possible to reduce the history tree file size by a factor of 1000, while keeping query times within a factor of two. Its main downside comes from the fact that you cannot do efficient single queries with it (they are implemented by doing full queries underneath).

This makes it a poor choice for views like the Control Flow view, where you do a lot of range queries and single queries. However, it is a perfect fit for cases like statistics, where you usually do full queries already, and you store lots of small states which are very easy to "compress".

However, it can't really be used until bug 409630 is fixed.

## State System Operations

TmfStateSystemOperations is a static class that implements additional statistical operations that can be performed on attributes of the state system.

These operations require that the attribute be one of the numerical values (int, long or double).

The speed of these operations can be greatly improved for large data sets if the attribute was inserted in the state system as a mipmap attribute. Refer to the Mipmap feature section.

##### queryRangeMax()

This method returns the maximum numerical value of an attribute in the specified time range. The attribute must be of type int, long or double. Null values are ignored. The returned value will be of the same state value type as the base attribute, or a null value if there is no state interval stored in the given time range.

##### queryRangeMin()

This method returns the minimum numerical value of an attribute in the specified time range. The attribute must be of type int, long or double. Null values are ignored. The returned value will be of the same state value type as the base attribute, or a null value if there is no state interval stored in the given time range.

##### queryRangeAverage()

This method returns the average numerical value of an attribute in the specified time range. The attribute must be of type int, long or double. Each state interval value is weighted according to time. Null values are counted as zero. The returned value will be a double primitive, which will be zero if there is no state interval stored in the given time range.

## Code example

Here is a small example of code that will use the state system. For this example, let's assume we want to track the state of all the CPUs in a LTTng kernel trace. To do so, we will watch for the "sched_switch" event in the state provider, and will update an attribute indicating if the associated CPU should be set to "running" or "idle".

We will use an attribute tree that looks like this:

    CPUs
     |--0
     |  |--Status
     |
     |--1
     |  |--Status
     |
     |  2
     |  |--Status
    ...

The second-level attributes will be named from the information available in the trace events. Only the "Status" attributes will carry a state value (this means we could have just used "1", "2", "3",... directly, but we'll do it in a tree for the example's sake).

Also, we will use integer state values to represent "running" or "idle", instead of saving the strings that would get repeated every time. This will help in reducing the size of the history file.

First we will define a state provider in MyStateProvider. Then, we define an analysis module that takes care of creating the state provider. The analysis module will also contain code that can query the state system.

### State Provider

    import java.util.Objects;

    import org.eclipse.jdt.annotation.NonNull;
    import org.eclipse.tracecompass.statesystem.core.ITmfStateSystemBuilder;
    import org.eclipse.tracecompass.tmf.core.event.ITmfEvent;
    import org.eclipse.tracecompass.tmf.core.event.aspect.TmfCpuAspect;
    import org.eclipse.tracecompass.tmf.core.statesystem.AbstractTmfStateProvider;
    import org.eclipse.tracecompass.tmf.core.statesystem.ITmfStateProvider;
    import org.eclipse.tracecompass.tmf.core.trace.ITmfTrace;
    import org.eclipse.tracecompass.tmf.core.trace.TmfTraceUtils;

    /**
     * An example of a simple state provider for a simple state system analysis
     *
     * @author Alexandre Montplaisir
     * @author Geneviève Bastien
     */
    public class ExampleStateProvider extends AbstractTmfStateProvider {

        private static final @NonNull String PROVIDER_ID = "org.eclipse.tracecompass.examples.state.provider"; //$NON-NLS-1$
        private static final int VERSION = 0;

        /**
         * Constructor
         *
         * @param trace
         *            The trace for this state provider
         */
        public ExampleStateProvider(@NonNull ITmfTrace trace) {
            super(trace, PROVIDER_ID);
        }

        @Override
        public int getVersion() {
            return VERSION;
        }

        @Override
        public @NonNull ITmfStateProvider getNewInstance() {
            return new ExampleStateProvider(getTrace());
        }

        @Override
        protected void eventHandle(ITmfEvent event) {

            /**
             * Do what needs to be done with this event, here is an example that
             * updates the CPU state and TID after a sched_switch
             */
            if (event.getName().equals("sched_switch")) { //$NON-NLS-1$

                final long ts = event.getTimestamp().getValue();
                Long nextTid = event.getContent().getFieldValue(Long.class, "next_tid"); //$NON-NLS-1$
                Integer cpu = TmfTraceUtils.resolveIntEventAspectOfClassForEvent(event.getTrace(), TmfCpuAspect.class, event);
                if (cpu == null || nextTid == null) {
                    return;
                }

                ITmfStateSystemBuilder ss = Objects.requireNonNull(getStateSystemBuilder());
                int quark = ss.getQuarkAbsoluteAndAdd("CPUs", String.valueOf(cpu)); //$NON-NLS-1$

                // The status attribute has an integer value
                int statusQuark = ss.getQuarkRelativeAndAdd(quark, "Status"); //$NON-NLS-1$
                Integer value = (nextTid > 0 ? 1 : 0);
                ss.modifyAttribute(ts, value, statusQuark);

                // The main quark contains the tid of the running thread
                ss.modifyAttribute(ts, nextTid, quark);
            }
        }

    }

### Analysis module definition

    import java.util.Objects;

    import org.eclipse.jdt.annotation.NonNull;
    import org.eclipse.tracecompass.tmf.core.statesystem.ITmfStateProvider;
    import org.eclipse.tracecompass.tmf.core.statesystem.TmfStateSystemAnalysisModule;

    /**
     * An example of a simple state system analysis module.
     *
     * @author Geneviève Bastien
     */
    public class ExampleStateSystemAnalysisModule extends TmfStateSystemAnalysisModule {

        /**
         * Module ID
         */
        public static final String ID = "org.eclipse.tracecompass.examples.state.system.module"; //$NON-NLS-1$

        @Override
        protected @NonNull ITmfStateProvider createStateProvider() {
            return new ExampleStateProvider(Objects.requireNonNull(getTrace()));
        }

    }

## Mipmap feature

The mipmap feature allows attributes to be inserted into the state system with additional computations performed to automatically store sub-attributes that can later be used for statistical operations. The mipmap has a resolution which represents the number of state attribute changes that are used to compute the value at the next mipmap level.

The supported mipmap features are: max, min, and average. Each one of these features requires that the base attribute be a numerical state value (int, long or double). An attribute can be mipmapped for one or more of the features at the same time.

To use a mipmapped attribute in queries, call the corresponding methods of the static class TmfStateSystemOperations.

### AbstractTmfMipmapStateProvider

AbstractTmfMipmapStateProvider is an abstract provider class that allows adding features to a specific attribute into a mipmap tree. It extends AbstractTmfStateProvider.

If a provider wants to add mipmapped attributes to its tree, it must extend AbstractTmfMipmapStateProvider and call modifyMipmapAttribute() in the event handler, specifying one or more mipmap features to compute. Then the structure of the attribute tree will be:

    |- <attribute>
    |   |- <mipmapFeature> (min/max/avg)
    |   |   |- 1
    |   |   |- 2
    |   |   |- 3
    |   |  ...
    |   |   |- n (maximum mipmap level)
    |   |- <mipmapFeature> (min/max/avg)
    |   |   |- 1
    |   |   |- 2
    |   |   |- 3
    |   |  ...
    |   |   |- n (maximum mipmap level)
    |  ...