Author: The Khronos® Vulkan Working Group

# Vulkan® 1.3.255 - A Specification (with all registered extensions)

The Khronos® Vulkan Working Group
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## Appendix B: Memory Model

| Note This memory model describes synchronizations provided by all implementations; however, some of the synchronizations defined require extra features to be supported by the implementation. See VkPhysicalDeviceVulkanMemoryModelFeatures.

### Agent

Operation is a general term for any task that is executed on the system.

| Note An operation is by definition something that is executed. Thus if an instruction is skipped due to control flow, it does not constitute an operation.

Each operation is executed by a particular agent. Possible agents include each shader invocation, each host thread, and each fixed-function stage of the pipeline.

### Memory Location

A memory location identifies unique storage for 8 bits of data. Memory operations access a set of memory locations consisting of one or more memory locations at a time, e.g. an operation accessing a 32-bit integer in memory would read/write a set of four memory locations. Memory operations that access whole aggregates may access any padding bytes between elements or members, but no padding bytes at the end of the aggregate. Two sets of memory locations overlap if the intersection of their sets of memory locations is non-empty. A memory operation must not affect memory at a memory location not within its set of memory locations.

Memory locations for buffers and images are explicitly allocated in VkDeviceMemory objects, and are implicitly allocated for SPIR-V variables in each shader invocation.

Variables with `Workgroup` storage class that point to a block-decorated type share a set of memory locations.

### Allocation

The values stored in newly allocated memory locations are determined by a SPIR-V variable’s initializer, if present, or else are undefined. At the time an allocation is created there have been no memory operations to any of its memory locations. The initialization is not considered to be a memory operation.

| Note For tessellation control shader output variables, a consequence of initialization not being considered a memory operation is that some implementations may need to insert a barrier between the initialization of the output variables and any reads of those variables.

### Memory Operation

For an operation A and memory location M:

- A reads M if and only if the data stored in M is an input to A.

- A writes M if and only if the data output from A is stored to M.

- A accesses M if and only if it either reads or writes (or both) M.

| Note A write whose value is the same as what was already in those memory locations is still considered to be a write and has all the same effects.

### Reference

A reference is an object that a particular agent can use to access a set of memory locations. On the host, a reference is a host virtual address. On the device, a reference is:

- The descriptor that a variable is bound to, for variables in Image, Uniform, or StorageBuffer storage classes. If the variable is an array (or array of arrays, etc.) then each element of the array may be a unique reference.

- The address range for a buffer in `PhysicalStorageBuffer` storage class, where the base of the address range is queried with vkGetBufferDeviceAddress and the length of the range is the size of the buffer.

- A single common reference for all variables with `Workgroup` storage class that point to a block-decorated type.

- The variable itself for non-block-decorated type variables in `Workgroup` storage class.

- The variable itself for variables in other storage classes.

Two memory accesses through distinct references may require availability and visibility operations as defined below.

### Program-Order

A dynamic instance of an instruction is defined in SPIR-V (https://registry.khronos.org/spir-v/specs/unified1/SPIRV.html#DynamicInstance) as a way of referring to a particular execution of a static instruction. Program-order is an ordering on dynamic instances of instructions executed by a single shader invocation:

- (Basic block): If instructions A and B are in the same basic block, and A is listed in the module before B, then the n’th dynamic instance of A is program-ordered before the n’th dynamic instance of B.

- (Branch): The dynamic instance of a branch or switch instruction is program-ordered before the dynamic instance of the OpLabel instruction to which it transfers control.

- (Call entry): The dynamic instance of an `OpFunctionCall` instruction is program-ordered before the dynamic instances of the `OpFunctionParameter` instructions and the body of the called function.

- (Call exit): The dynamic instance of the instruction following an `OpFunctionCall` instruction is program-ordered after the dynamic instance of the return instruction executed by the called function.

- (Transitive Closure): If dynamic instance A of any instruction is program-ordered before dynamic instance B of any instruction and B is program-ordered before dynamic instance C of any instruction then A is program-ordered before C.

- (Complete definition): No other dynamic instances are program-ordered.

For instructions executed on the host, the source language defines the program-order relation (e.g. as “sequenced-before”).

### Shader Call Related

Shader-call-related is an equivalence relation on invocations defined as the symmetric and transitive closure of:

- A is shader-call-related to B if A is created by an invocation repack instruction executed by B.

### Shader Call Order

Shader-call-order is a partial order on dynamic instances of instructions executed by invocations that are shader-call-related:

- (Program order): If dynamic instance A is program-ordered before B, then A is shader-call-ordered before B.

- (Shader call entry): If A is a dynamic instance of an invocation repack instruction and B is a dynamic instance executed by an invocation that is created by A, then A is shader-call-ordered before B.

- (Shader call exit): If A is a dynamic instance of an invocation repack instruction, B is the next dynamic instance executed by the same invocation, and C is a dynamic instance executed by an invocation that is created by A, then C is shader-call-ordered before B.

- (Transitive closure): If A is shader-call-ordered-before B and B is shader-call-ordered-before C, then A is shader-call-ordered-before C.

- (Complete definition): No other dynamic instances are shader-call-ordered.

### Scope

Atomic and barrier instructions include scopes which identify sets of shader invocations that must obey the requested ordering and atomicity rules of the operation, as defined below.

The various scopes are described in detail in the Shaders chapter.

### Atomic Operation

An atomic operation on the device is any SPIR-V operation whose name begins with `OpAtomic`. An atomic operation on the host is any operation performed with an std::atomic typed object.

Each atomic operation has a memory scope and a semantics. Informally, the scope determines which other agents it is atomic with respect to, and the semantics constrains its ordering against other memory accesses. Device atomic operations have explicit scopes and semantics. Each host atomic operation implicitly uses the `CrossDevice` scope, and uses a memory semantics equivalent to a C++ std::memory_order value of relaxed, acquire, release, acq_rel, or seq_cst.

Two atomic operations A and B are potentially-mutually-ordered if and only if all of the following are true:

- They access the same set of memory locations.

- They use the same reference.

- A is in the instance of B’s memory scope.

- B is in the instance of A’s memory scope.

- A and B are not the same operation (irreflexive).

Two atomic operations A and B are mutually-ordered if and only if they are potentially-mutually-ordered and any of the following are true:

- A and B are both device operations.

- A and B are both host operations.

- A is a device operation, B is a host operation, and the implementation supports concurrent host- and device-atomics.

| Note If two atomic operations are not mutually-ordered, and if their sets of memory locations overlap, then each must be synchronized against the other as if they were non-atomic operations.

### Scoped Modification Order

For a given atomic write A, all atomic writes that are mutually-ordered with A occur in an order known as A’s scoped modification order. A’s scoped modification order relates no other operations.

| Note Invocations outside the instance of A’s memory scope may observe the values at A’s set of memory locations becoming visible to it in an order that disagrees with the scoped modification order.

| Note It is valid to have non-atomic operations or atomics in a different scope instance to the same set of memory locations, as long as they are synchronized against each other as if they were non-atomic (if they are not, it is treated as a data race). That means this definition of A’s scoped modification order could include atomic operations that occur much later, after intervening non-atomics. That is a bit non-intuitive, but it helps to keep this definition simple and non-circular.

### Memory Semantics

Non-atomic memory operations, by default, may be observed by one agent in a different order than they were written by another agent.

Atomics and some synchronization operations include memory semantics, which are flags that constrain the order in which other memory accesses (including non-atomic memory accesses and availability and visibility operations) performed by the same agent can be observed by other agents, or can observe accesses by other agents.

Device instructions that include semantics are `OpAtomic*`, `OpControlBarrier`, `OpMemoryBarrier`, and `OpMemoryNamedBarrier`. Host instructions that include semantics are some std::atomic methods and memory fences.

SPIR-V supports the following memory semantics:

- Relaxed: No constraints on order of other memory accesses.

- Acquire: A memory read with this semantic performs an acquire operation. A memory barrier with this semantic is an acquire barrier.

- Release: A memory write with this semantic performs a release operation. A memory barrier with this semantic is a release barrier.

- AcquireRelease: A memory read-modify-write operation with this semantic performs both an acquire operation and a release operation, and inherits the limitations on ordering from both of those operations. A memory barrier with this semantic is both a release and acquire barrier.

| Note SPIR-V does not support “consume” semantics on the device.

The memory semantics operand also includes storage class semantics which indicate which storage classes are constrained by the synchronization. SPIR-V storage class semantics include:

- UniformMemory

- WorkgroupMemory

- ImageMemory

- OutputMemory

Each SPIR-V memory operation accesses a single storage class. Semantics in synchronization operations can include a combination of storage classes.

The UniformMemory storage class semantic applies to accesses to memory in the PhysicalStorageBuffer, `ShaderRecordBufferKHR`, Uniform and StorageBuffer storage classes. The WorkgroupMemory storage class semantic applies to accesses to memory in the Workgroup storage class. The ImageMemory storage class semantic applies to accesses to memory in the Image storage class. The OutputMemory storage class semantic applies to accesses to memory in the Output storage class.

| Note Informally, these constraints limit how memory operations can be reordered, and these limits apply not only to the order of accesses as performed in the agent that executes the instruction, but also to the order the effects of writes become visible to all other agents within the same instance of the instruction’s memory scope.

| Note Release and acquire operations in different threads can act as synchronization operations, to guarantee that writes that happened before the release are visible after the acquire. (This is not a formal definition, just an Informative forward reference.)

| Note The OutputMemory storage class semantic is only useful in tessellation control shaders, which is the only execution model where output variables are shared between invocations.

The memory semantics operand can also include availability and visibility flags, which apply availability and visibility operations as described in availability and visibility. The availability/visibility flags are:

- MakeAvailable: Semantics must be Release or AcquireRelease. Performs an availability operation before the release operation or barrier.

- MakeVisible: Semantics must be Acquire or AcquireRelease. Performs a visibility operation after the acquire operation or barrier.

The specifics of these operations are defined in Availability and Visibility Semantics.

Host atomic operations may support a different list of memory semantics and synchronization operations, depending on the host architecture and source language.

### Release Sequence

After an atomic operation A performs a release operation on a set of memory locations M, the release sequence headed by A is the longest continuous subsequence of A’s scoped modification order that consists of:

- the atomic operation A as its first element

- atomic read-modify-write operations on M by any agent

| Note The atomics in the last bullet must be mutually-ordered with A by virtue of being in A’s scoped modification order.

| Note This intentionally omits “atomic writes to M performed by the same agent that performed A”, which is present in the corresponding C++ definition.

### Synchronizes-With

Synchronizes-with is a relation between operations, where each operation is either an atomic operation or a memory barrier (aka fence on the host).

If A and B are atomic operations, then A synchronizes-with B if and only if all of the following are true:

- A performs a release operation

- B performs an acquire operation

- A and B are mutually-ordered

- B reads a value written by A or by an operation in the release sequence headed by A

`OpControlBarrier`, `OpMemoryBarrier`, and `OpMemoryNamedBarrier` are memory barrier instructions in SPIR-V.

If A is a release barrier and B is an atomic operation that performs an acquire operation, then A synchronizes-with B if and only if all of the following are true:

- there exists an atomic write X (with any memory semantics)

- A is program-ordered before X

- X and B are mutually-ordered

- B reads a value written by X or by an operation in the release sequence headed by X

  - If X is relaxed, it is still considered to head a hypothetical release sequence for this rule

- A and B are in the instance of each other’s memory scopes

- X’s storage class is in A’s semantics.

If A is an atomic operation that performs a release operation and B is an acquire barrier, then A synchronizes-with B if and only if all of the following are true:

- there exists an atomic read X (with any memory semantics)

- X is program-ordered before B

- X and A are mutually-ordered

- X reads a value written by A or by an operation in the release sequence headed by A

- A and B are in the instance of each other’s memory scopes

- X’s storage class is in B’s semantics.

If A is a release barrier and B is an acquire barrier, then A synchronizes-with B if all of the following are true:

- there exists an atomic write X (with any memory semantics)

- A is program-ordered before X

- there exists an atomic read Y (with any memory semantics)

- Y is program-ordered before B

- X and Y are mutually-ordered

- Y reads the value written by X or by an operation in the release sequence headed by X

  - If X is relaxed, it is still considered to head a hypothetical release sequence for this rule

- A and B are in the instance of each other’s memory scopes

- X’s and Y’s storage class is in A’s and B’s semantics.

  - NOTE: X and Y must have the same storage class, because they are mutually ordered.

If A is a release barrier, B is an acquire barrier, and C is a control barrier (where A can equal C, and B can equal C), then A synchronizes-with B if all of the following are true:

- A is program-ordered before (or equals) C

- C is program-ordered before (or equals) B

- A and B are in the instance of each other’s memory scopes

- A and B are in the instance of C’s execution scope

| Note This is similar to the barrier-barrier synchronization above, but with a control barrier filling the role of the relaxed atomics.

Let F be an ordering of fragment shader invocations, such that invocation F1 is ordered before invocation F2 if and only if F1 and F2 overlap as described in Fragment Shader Interlock and F1 executes the interlocked code before F2.

If A is an `OpEndInvocationInterlockEXT` instruction and B is an `OpBeginInvocationInterlockEXT` instruction, then A synchronizes-with B if the agent that executes A is ordered before the agent that executes B in F. A and B are both considered to have `FragmentInterlock` memory scope and semantics of UniformMemory and ImageMemory, and A is considered to have Release semantics and B is considered to have Acquire semantics.

| Note `OpBeginInvocationInterlockEXT` and `OpBeginInvocationInterlockEXT` do not perform implicit availability or visibility operations. Usually, shaders using fragment shader interlock will declare the relevant resources as `coherent` to get implicit per-instruction availability and visibility operations.

If A is a release barrier and B is an acquire barrier, then A synchronizes-with B if all of the following are true:

- A is shader-call-ordered-before B

- A and B are in the instance of each other’s memory scopes

No other release and acquire barriers synchronize-with each other.

### System-Synchronizes-With

System-synchronizes-with is a relation between arbitrary operations on the device or host. Certain operations system-synchronize-with each other, which informally means the first operation occurs before the second and that the synchronization is performed without using application-visible memory accesses.

If there is an execution dependency between two operations A and B, then the operation in the first synchronization scope system-synchronizes-with the operation in the second synchronization scope.

| Note This covers all Vulkan synchronization primitives, including device operations executing before a synchronization primitive is signaled, wait operations happening before subsequent device operations, signal operations happening before host operations that wait on them, and host operations happening before vkQueueSubmit. The list is spread throughout the synchronization chapter, and is not repeated here.

System-synchronizes-with implicitly includes all storage class semantics and has `CrossDevice` scope.

If A system-synchronizes-with B, we also say A is system-synchronized-before B and B is system-synchronized-after A.

### Private vs. Non-Private

By default, non-atomic memory operations are treated as private, meaning such a memory operation is not intended to be used for communication with other agents. Memory operations with the NonPrivatePointer/NonPrivateTexel bit set are treated as non-private, and are intended to be used for communication with other agents.

More precisely, for private memory operations to be Location-Ordered between distinct agents requires using system-synchronizes-with rather than shader-based synchronization. Non-private memory operations still obey program-order.

Atomic operations are always considered non-private.

### Inter-Thread-Happens-Before

Let SC be a non-empty set of storage class semantics. Then (using template syntax) operation A inter-thread-happens-before<SC> operation B if and only if any of the following is true:

- A system-synchronizes-with B

- A synchronizes-with B, and both A and B have all of SC in their semantics

- A is an operation on memory in a storage class in SC or that has all of SC in its semantics, B is a release barrier or release atomic with all of SC in its semantics, and A is program-ordered before B

- A is an acquire barrier or acquire atomic with all of SC in its semantics, B is an operation on memory in a storage class in SC or that has all of SC in its semantics, and A is program-ordered before B

- A and B are both host operations and A inter-thread-happens-before B as defined in the host language specification

- A inter-thread-happens-before<SC> some X and X inter-thread-happens-before<SC> B

### Happens-Before

Operation A happens-before operation B if and only if any of the following is true:

- A is program-ordered before B

- A inter-thread-happens-before<SC> B for some set of storage classes SC

Happens-after is defined similarly.

| Note Unlike C++, happens-before is not always sufficient for a write to be visible to a read. Additional availability and visibility operations may be required for writes to be visible-to other memory accesses.

| Note Happens-before is not transitive, but each of program-order and inter-thread-happens-before<SC> are transitive. These can be thought of as covering the “single-threaded” case and the “multi-threaded” case, and it is not necessary (and not valid) to form chains between the two.

### Availability and Visibility

Availability and visibility are states of a write operation, which (informally) track how far the write has permeated the system, i.e. which agents and references are able to observe the write. Availability state is per memory domain. Visibility state is per (agent,reference) pair. Availability and visibility states are per-memory location for each write.

Memory domains are named according to the agents whose memory accesses use the domain. Domains used by shader invocations are organized hierarchically into multiple smaller memory domains which correspond to the different scopes. Each memory domain is considered the dual of a scope, and vice versa. The memory domains defined in Vulkan include:

- host - accessible by host agents

- device - accessible by all device agents for a particular device

- shader - accessible by shader agents for a particular device, corresponding to the `Device` scope

- queue family instance - accessible by shader agents in a single queue family, corresponding to the `QueueFamily` scope.

- fragment interlock instance - accessible by fragment shader agents that overlap, corresponding to the `FragmentInterlock` scope.

- shader call instance - accessible by shader agents that are shader-call-related, corresponding to the `ShaderCallKHR` scope.

- workgroup instance - accessible by shader agents in the same workgroup, corresponding to the `Workgroup` scope.

- subgroup instance - accessible by shader agents in the same subgroup, corresponding to the `Subgroup` scope.

The memory domains are nested in the order listed above, except for shader call instance domain, with memory domains later in the list nested in the domains earlier in the list. The shader call instance domain is at an implementation-dependent location in the list, and is nested according to that location. The shader call instance domain is not broader than the queue family instance domain.

| Note Memory domains do not correspond to storage classes or device-local and host-local VkDeviceMemory allocations, rather they indicate whether a write can be made visible only to agents in the same subgroup, same workgroup, overlapping fragment shader invocation, shader-call-related ray tracing invocation, in any shader invocation, or anywhere on the device, or host. The shader, queue family instance, fragment interlock instance, shader call instance, workgroup instance, and subgroup instance domains are only used for shader-based availability/visibility operations, in other cases writes can be made available from/visible to the shader via the device domain.

Availability operations, visibility operations, and memory domain operations alter the state of the write operations that happen-before them, and which are included in their source scope to be available or visible to their destination scope.

- For an availability operation, the source scope is a set of (agent,reference,memory location) tuples, and the destination scope is a set of memory domains.

- For a memory domain operation, the source scope is a memory domain and the destination scope is a memory domain.

- For a visibility operation, the source scope is a set of memory domains and the destination scope is a set of (agent,reference,memory location) tuples.

How the scopes are determined depends on the specific operation. Availability and memory domain operations expand the set of memory domains to which the write is available. Visibility operations expand the set of (agent,reference,memory location) tuples to which the write is visible.

Recall that availability and visibility states are per-memory location, and let W be a write operation to one or more locations performed by agent A via reference R. Let L be one of the locations written. (W,L) (the write W to L), is initially not available to any memory domain and only visible to (A,R,L). An availability operation AV that happens-after W and that includes (A,R,L) in its source scope makes (W,L) available to the memory domains in its destination scope.

A memory domain operation DOM that happens-after AV and for which (W,L) is available in the source scope makes (W,L) available in the destination memory domain.

A visibility operation VIS that happens-after AV (or DOM) and for which (W,L) is available in any domain in the source scope makes (W,L) visible to all (agent,reference,L) tuples included in its destination scope.

If write W2 happens-after W, and their sets of memory locations overlap, then W will not be available/visible to all agents/references for those memory locations that overlap (and future AV/DOM/VIS ops cannot revive W’s write to those locations).

Availability, memory domain, and visibility operations are treated like other non-atomic memory accesses for the purpose of memory semantics, meaning they can be ordered by release-acquire sequences or memory barriers.

An availability chain is a sequence of availability operations to increasingly broad memory domains, where element N+1 of the chain is performed in the dual scope instance of the destination memory domain of element N and element N happens-before element N+1. An example is an availability operation with destination scope of the workgroup instance domain that happens-before an availability operation to the shader domain performed by an invocation in the same workgroup. An availability chain AVC that happens-after W and that includes (A,R,L) in the source scope makes (W,L) available to the memory domains in its final destination scope. An availability chain with a single element is just the availability operation.

Similarly, a visibility chain is a sequence of visibility operations from increasingly narrow memory domains, where element N of the chain is performed in the dual scope instance of the source memory domain of element N+1 and element N happens-before element N+1. An example is a visibility operation with source scope of the shader domain that happens-before a visibility operation with source scope of the workgroup instance domain performed by an invocation in the same workgroup. A visibility chain VISC that happens-after AVC (or DOM) and for which (W,L) is available in any domain in the source scope makes (W,L) visible to all (agent,reference,L) tuples included in its final destination scope. A visibility chain with a single element is just the visibility operation.

### Availability, Visibility, and Domain Operations

The following operations generate availability, visibility, and domain operations. When multiple availability/visibility/domain operations are described, they are system-synchronized-with each other in the order listed.

An operation that performs a memory dependency generates:

- If the source access mask includes `VK_ACCESS_HOST_WRITE_BIT`, then the dependency includes a memory domain operation from host domain to device domain.

- An availability operation with source scope of all writes in the first access scope of the dependency and a destination scope of the device domain.

- A visibility operation with source scope of the device domain and destination scope of the second access scope of the dependency.

- If the destination access mask includes `VK_ACCESS_HOST_READ_BIT` or `VK_ACCESS_HOST_WRITE_BIT`, then the dependency includes a memory domain operation from device domain to host domain.

vkFlushMappedMemoryRanges performs an availability operation, with a source scope of (agents,references) = (all host threads, all mapped memory ranges passed to the command), and destination scope of the host domain.

vkInvalidateMappedMemoryRanges performs a visibility operation, with a source scope of the host domain and a destination scope of (agents,references) = (all host threads, all mapped memory ranges passed to the command).

vkQueueSubmit performs a memory domain operation from host to device, and a visibility operation with source scope of the device domain and destination scope of all agents and references on the device.

### Availability and Visibility Semantics

A memory barrier or atomic operation via agent A that includes MakeAvailable in its semantics performs an availability operation whose source scope includes agent A and all references in the storage classes in that instruction’s storage class semantics, and all memory locations, and whose destination scope is a set of memory domains selected as specified below. The implicit availability operation is program-ordered between the barrier or atomic and all other operations program-ordered before the barrier or atomic.

A memory barrier or atomic operation via agent A that includes MakeVisible in its semantics performs a visibility operation whose source scope is a set of memory domains selected as specified below, and whose destination scope includes agent A and all references in the storage classes in that instruction’s storage class semantics, and all memory locations. The implicit visibility operation is program-ordered between the barrier or atomic and all other operations program-ordered after the barrier or atomic.

The memory domains are selected based on the memory scope of the instruction as follows:

- `Device` scope uses the shader domain

- `QueueFamily` scope uses the queue family instance domain

- `FragmentInterlock` scope uses the fragment interlock instance domain

- `ShaderCallKHR` scope uses the shader call instance domain

- `Workgroup` scope uses the workgroup instance domain

- `Subgroup` uses the subgroup instance domain

- `Invocation` perform no availability/visibility operations.

When an availability operation performed by an agent A includes a memory domain D in its destination scope, where D corresponds to scope instance S, it also includes the memory domains that correspond to each smaller scope instance S' that is a subset of S and that includes A. Similarly for visibility operations.

### Per-Instruction Availability and Visibility Semantics

A memory write instruction that includes MakePointerAvailable, or an image write instruction that includes MakeTexelAvailable, performs an availability operation whose source scope includes the agent and reference used to perform the write and the memory locations written by the instruction, and whose destination scope is a set of memory domains selected by the Scope operand specified in Availability and Visibility Semantics. The implicit availability operation is program-ordered between the write and all other operations program-ordered after the write.

A memory read instruction that includes MakePointerVisible, or an image read instruction that includes MakeTexelVisible, performs a visibility operation whose source scope is a set of memory domains selected by the Scope operand as specified in Availability and Visibility Semantics, and whose destination scope includes the agent and reference used to perform the read and the memory locations read by the instruction. The implicit visibility operation is program-ordered between read and all other operations program-ordered before the read.

| Note Although reads with per-instruction visibility only perform visibility ops from the shader or fragment interlock instance or shader call instance or workgroup instance or subgroup instance domain, they will also see writes that were made visible via the device domain, i.e. those writes previously performed by non-shader agents and made visible via API commands.

| Note It is expected that all invocations in a subgroup execute on the same processor with the same path to memory, and thus availability and visibility operations with subgroup scope can be expected to be “free”.

### Location-Ordered

Let X and Y be memory accesses to overlapping sets of memory locations M, where X != Y. Let (AX,RX) be the agent and reference used for X, and (AY,RY) be the agent and reference used for Y. For now, let “→” denote happens-before and “→rcpo” denote the reflexive closure of program-ordered before.

If D1 and D2 are different memory domains, then let DOM(D1,D2) be a memory domain operation from D1 to D2. Otherwise, let DOM(D,D) be a placeholder such that X→DOM(D,D)→Y if and only if X→Y.

X is location-ordered before Y for a location L in M if and only if any of the following is true:

- AX == AY and RX == RY and X→Y

  - NOTE: this case means no availability/visibility ops are required when it is the same (agent,reference).

- X is a read, both X and Y are non-private, and X→Y

- X is a read, and X (transitively) system-synchronizes with Y

- If RX == RY and AX and AY access a common memory domain D (e.g. are in the same workgroup instance if D is the workgroup instance domain), and both X and Y are non-private:

  - X is a write, Y is a write, AVC(AX,RX,D,L) is an availability chain making (X,L) available to domain D, and X→rcpoAVC(AX,RX,D,L)→Y

  - X is a write, Y is a read, AVC(AX,RX,D,L) is an availability chain making (X,L) available to domain D, VISC(AY,RY,D,L) is a visibility chain making writes to L available in domain D visible to Y, and X→rcpoAVC(AX,RX,D,L)→VISC(AY,RY,D,L)→rcpoY

  - If VkPhysicalDeviceVulkanMemoryModelFeatures::`vulkanMemoryModelAvailabilityVisibilityChains` is `VK_FALSE`, then AVC and VISC must each only have a single element in the chain, in each sub-bullet above.

- Let DX and DY each be either the device domain or the host domain, depending on whether AX and AY execute on the device or host:

  - X is a write and Y is a write, and X→AV(AX,RX,DX,L)→DOM(DX,DY)→Y

  - X is a write and Y is a read, and X→AV(AX,RX,DX,L)→DOM(DX,DY)→VIS(AY,RY,DY,L)→Y

| Note The final bullet (synchronization through device/host domain) requires API-level synchronization operations, since the device/host domains are not accessible via shader instructions. And “device domain” is not to be confused with “device scope”, which synchronizes through the “shader domain”.

### Data Race

Let X and Y be operations that access overlapping sets of memory locations M, where X != Y, and at least one of X and Y is a write, and X and Y are not mutually-ordered atomic operations. If there does not exist a location-ordered relation between X and Y for each location in M, then there is a data race.

Applications must ensure that no data races occur during the execution of their application.

| Note Data races can only occur due to instructions that are actually executed. For example, an instruction skipped due to control flow must not contribute to a data race.

### Visible-To

Let X be a write and Y be a read whose sets of memory locations overlap, and let M be the set of memory locations that overlap. Let M2 be a non-empty subset of M. Then X is visible-to Y for memory locations M2 if and only if all of the following are true:

- X is location-ordered before Y for each location L in M2.

- There does not exist another write Z to any location L in M2 such that X is location-ordered before Z for location L and Z is location-ordered before Y for location L.

If X is visible-to Y, then Y reads the value written by X for locations M2.

| Note It is possible for there to be a write between X and Y that overwrites a subset of the memory locations, but the remaining memory locations (M2) will still be visible-to Y.

### Acyclicity

Reads-from is a relation between operations, where the first operation is a write, the second operation is a read, and the second operation reads the value written by the first operation. From-reads is a relation between operations, where the first operation is a read, the second operation is a write, and the first operation reads a value written earlier than the second operation in the second operation’s scoped modification order (or the first operation reads from the initial value, and the second operation is any write to the same locations).

Then the implementation must guarantee that no cycles exist in the union of the following relations:

- location-ordered

- scoped modification order (over all atomic writes)

- reads-from

- from-reads

| Note This is a “consistency” axiom, which informally guarantees that sequences of operations cannot violate causality.

#### Scoped Modification Order Coherence

Let A and B be mutually-ordered atomic operations, where A is location-ordered before B. Then the following rules are a consequence of acyclicity:

- If A and B are both reads and A does not read the initial value, then the write that A takes its value from must be earlier in its own scoped modification order than (or the same as) the write that B takes its value from (no cycles between location-order, reads-from, and from-reads).

- If A is a read and B is a write and A does not read the initial value, then A must take its value from a write earlier than B in B’s scoped modification order (no cycles between location-order, scope modification order, and reads-from).

- If A is a write and B is a read, then B must take its value from A or a write later than A in A’s scoped modification order (no cycles between location-order, scoped modification order, and from-reads).

- If A and B are both writes, then A must be earlier than B in A’s scoped modification order (no cycles between location-order and scoped modification order).

- If A is a write and B is a read-modify-write and B reads the value written by A, then B comes immediately after A in A’s scoped modification order (no cycles between scoped modification order and from-reads).

### Shader I/O

If a shader invocation A in a shader stage other than `Vertex` performs a memory read operation X from an object in storage class `CallableDataKHR`, `IncomingCallableDataKHR`, `RayPayloadKHR`, `HitAttributeKHR`, `IncomingRayPayloadKHR`, or `Input`, then X is system-synchronized-after all writes to the corresponding `CallableDataKHR`, `IncomingCallableDataKHR`, `RayPayloadKHR`, `HitAttributeKHR`, `IncomingRayPayloadKHR`, or `Output` storage variable(s) in the shader invocation(s) that contribute to generating invocation A, and those writes are all visible-to X.

| Note It is not necessary for the upstream shader invocations to have completed execution, they only need to have generated the output that is being read.

### Deallocation

A call to vkFreeMemory must happen-after all memory operations on all memory locations in that VkDeviceMemory object.

| Note Normally, device memory operations in a given queue are synchronized with vkFreeMemory by having a host thread wait on a fence signalled by that queue, and the wait happens-before the call to vkFreeMemory on the host.

The deallocation of SPIR-V variables is managed by the system and happens-after all operations on those variables.

### Descriptions (Informative)

This subsection offers more easily understandable consequences of the memory model for app/compiler developers.

Let SC be the storage class(es) specified by a release or acquire operation or barrier.

- An atomic write with release semantics must not be reordered against any read or write to SC that is program-ordered before it (regardless of the storage class the atomic is in).

- An atomic read with acquire semantics must not be reordered against any read or write to SC that is program-ordered after it (regardless of the storage class the atomic is in).

- Any write to SC program-ordered after a release barrier must not be reordered against any read or write to SC program-ordered before that barrier.

- Any read from SC program-ordered before an acquire barrier must not be reordered against any read or write to SC program-ordered after the barrier.

A control barrier (even if it has no memory semantics) must not be reordered against any memory barriers.

This memory model allows memory accesses with and without availability and visibility operations, as well as atomic operations, all to be performed on the same memory location. This is critical to allow it to reason about memory that is reused in multiple ways, e.g. across the lifetime of different shader invocations or draw calls. While GLSL (and legacy SPIR-V) applies the “coherent” decoration to variables (for historical reasons), this model treats each memory access instruction as having optional implicit availability/visibility operations. GLSL to SPIR-V compilers should map all (non-atomic) operations on a coherent variable to Make{Pointer,Texel}{Available}{Visible} flags in this model.

Atomic operations implicitly have availability/visibility operations, and the scope of those operations is taken from the atomic operation’s scope.

### Tessellation Output Ordering

For SPIR-V that uses the Vulkan Memory Model, the `OutputMemory` storage class is used to synchronize accesses to tessellation control output variables. For legacy SPIR-V that does not enable the Vulkan Memory Model via `OpMemoryModel`, tessellation outputs can be ordered using a control barrier with no particular memory scope or semantics, as defined below.

Let X and Y be memory operations performed by shader invocations AX and AY. Operation X is tessellation-output-ordered before operation Y if and only if all of the following are true:

- There is a dynamic instance of an `OpControlBarrier` instruction C such that X is program-ordered before C in AX and C is program-ordered before Y in AY.

- AX and AY are in the same instance of C’s execution scope.

If shader invocations AX and AY in the `TessellationControl` execution model execute memory operations X and Y, respectively, on the `Output` storage class, and X is tessellation-output-ordered before Y with a scope of `Workgroup`, then X is location-ordered before Y, and if X is a write and Y is a read then X is visible-to Y.

### Cooperative Matrix Memory Access

For each dynamic instance of a cooperative matrix load or store instruction (`OpCooperativeMatrixLoadNV` or `OpCooperativeMatrixStoreNV`), a single implementation-dependent invocation within the instance of the matrix’s scope performs a non-atomic load or store (respectively) to each memory location that is defined to be accessed by the instruction.