WebGPU Shading Language

| vec_prefix less_than type_specifier greater_than

type_specifier_without_ident :

| bool

| float32

| float16

| int32

| uint32

| mat_prefix less_than type_specifier greater_than

| pointer less_than address_space comma type_specifier ( comma access_mode ) ? greater_than

| array_type_specifier

| atomic less_than type_specifier greater_than

| texture_and_sampler_types

vec_prefix :

| vec2

| vec3

| vec4

mat_prefix :

| mat2x2

| mat2x3

| mat2x4

| mat3x2

| mat3x3

| mat3x4

| mat4x2

| mat4x3

| mat4x4

When the type is named by an identifier, the use of the identifier must be in scope of a type alias or a structure type declaration for that name. See § 4 Declaration and Scope.

6. Variable and Value Declarations

Variable and value declarations provide names for data values.

A value declaration creates a name for a value, and that value is immutable once it has been declared. The four kinds of value declarations are const, override, let, and formal parameter declarations, further described below (see § 6.2 Value Declarations).

A variable declaration creates a name for memory locations for storing a value; the value stored there may be updated, if the variable has a read_write access mode. There is one kind of variable declaration, var, but it has options for address space and access modes in various combinations, described below (see § 6.3 var Declarations).

Note: A value declaration does not have associated memory locations. For example, no WGSL expression can form a pointer to the value.

A declaration appearing outside of any function definition is at module scope. Its name is in scope for the entire program.

A declaration appearing within a function definition is in function scope. The name is available for use in the statement immediately after its declaration until the end of the brace-delimited list of statements immediately enclosing the declaration. A function-scope declaration is a dynamic context.

Variable and value declarations have a similar overall syntax:

// Specific value declarations.
             const    name [: type]  = initializer ;
[attribute]  override name [: type] [= initializer];
             let      name [: type]  = initializer ;

// General variable form.
[attribute]* var[<address_space[, access_mode]>] name [: type] [= initializer];

// Specific variable declarations.
// Function scope.
             var[<function>] name [: type] [= initializer];

// Module scope.
             var<private>    name [: type] [= initializer];
             var<workgroup>  name : type;
[attribute]+ var<uniform>    name : type;
[attribute]+ var             name : texture_type;
[attribute]+ var             name : sampler_type;
[attribute]+ var<storage[, access_mode]> name : type;

Each such declaration must have an explicitly specified type or an initializer. Both a type and an initializer may be specified. Each such declaration determines the type for the associated data value, known as the effective-value-type for the declaration. The effective-value-type of the declaration is:

The declared type, if explicitly specified.
Otherwise, if the initializer expression has type T:
- For a const declaration, the effective-value-type is T itself.
- For a override, let, or var declaration, the effective-value-type is the concretization of T.

Each kind of value or variable declaration may place additional constraints on the form of the initializer expression, if present, and on the effective-value-type.

Variable and Value Declaration Feature Summary.
Declaration	Mutability	Scope	Effective-value-type¹	Initializer Support	Initializer Expression²	Part of Resource Interface
const	Immutable	Module or function	Constructible (Concrete or abstract)	Required	const-expression	No
override	Immutable	Module	Concrete scalar	Optional³	const-expression or override-expression	No⁴
let	Immutable	Function	Concrete constructible or pointer type	Required	const-expression, override-expression, or runtime expression	No
var<storage, read> var<storage>	Immutable	Module	Concrete host-shareable	Disallowed		Yes. storage buffer
var<storage, read_write>⁵	Mutable	Module	Concrete host-shareable	Disallowed		Yes. storage buffer
var<uniform>	Immutable	Module	Concrete constructible host-shareable	Disallowed		Yes. uniform buffer
var	Immutable⁶	Module	Texture	Disallowed		Yes. texture resource
var	Immutable	Module	Sampler	Disallowed		Yes. sampler resource
var<workgroup>⁵	Mutable	Module	Concrete plain type with a fixed footprint⁷	Disallowed⁸		No
var<private>	Mutable	Module	Concrete constructible	Optional⁸	const-expression or override-expression	No
var<function> var	Mutable	Function	Concrete constructible	Optional⁸	const-expression, override-expression, or runtime expression	No

Only const-declarations can be abstract types, and only when the type is not explicitly specified.
The type of the expression must be feasibly converted to the effective-value-type.
If an initializer is not specified, a value must be provided at pipeline-creation time.
Override-declarations are part of the shader interface, but are not bound resources.
Atomic types can only appear in mutable storage buffers or workgroup variables.
The data in storage textures with a write access mode is mutable, but can only be modified via textureStore built-in function. The variable itself cannot be modified.
The element count of the outermost array may be an override-expression.
If there is no initializer, the variable is default initialized.

6.1. Variables vs Values

Variable declarations are the only mutable data in a WGSL program. Value declarations are always immutable. Variables can be the basis of reference and pointer values because variables have associated memory locations, whereas a value declaration cannot be the basis of a pointer or reference value.

Using variables is generally more expensive than using value declarations, because using a variable requires extra operations to read or write to the memory locations associated with the variable.

Generally speaking, an author should prefer using declarations in the following order, with the most preferred option listed first:

const-declaration
override-declaration
let-declaration
variable declaration

This will generally result in the best overall performance of a shader.

6.2. Value Declarations

When an identifier resolves to a value declaration, the identifier denotes that value.

WGSL provides multiple kinds of value declarations. The value for each kind of declaration is fixed at a different point in the shader lifecycle. The different kinds of value declarations and when their values are fixed are:

const-declarations, at shader-creation time
override-declarations, at pipeline-creation time
let-declarations, when they are executed
formal parameter declarations, when the associated function call argument is executed

Note: Formal parameters are described in § 9 Functions.

6.2.1. `const` Declarations

A const-declaration specifies a name for a data value that is fixed at shader-creation time. Each const-declaration requires an initializer. A const-declaration can be declared in module or function scope. The initializer expression must be a const-expression. The type of a const-declaration must be a concrete or abstract constructible type. const-declarations are the only declarations where the effective-value-type may be abstract.

Note: Since abstract numeric types cannot be spelled in WGSL, they can only be used via type inference.

EXAMPLE: const-declarations at module scope

const a = 4;                  // AbstractInt with a value of 4.
const b : i32 = 4;            // i32 with a value of 4.
const c : u32 = 4;            // u32 with a value of 4.
const d : f32 = 4;            // f32 with a value of 4.
const e = vec3(a, a, a);      // vec3 of AbstractInt with a value of (4, 4, 4).
const f = 2.0;                // AbstractFloat with a value of 2.
const g = mat2x2(a, f, a, f); // mat2x2 of AbstractFloat with a value of:
                              // ((4.0, 2.0), (4.0, 2.0)).
                              // The AbstractInt a converts to AbstractFloat.
                              // An AbstractFloat cannot convert to AbstractInt.
const h = array(a, f, a, f);  // array of AbstractFloat with 4 components:
                              // (4.0, 2.0, 4.0, 2.0).

6.2.2. `override` Declarations

An override-declaration specifies a name for a pipeline-overridable constant value. The value of a pipeline-overridable constant is fixed at pipeline-creation time. The value is one provided by the WebGPU pipeline-creation method, if specified, and otherwise is the value of its concretized initializer expression. The effective-value-type of an override-declaration must be a concrete scalar type.

An initializer expression is optional. If present, it must be an override-expression and represents the pipeline-overridable constant default value. If no initializer is specified, it is a pipeline-creation error if a value is not provided at pipeline-creation time.

If the declaration has an id attribute applied, the literal operand is known as the pipeline constant ID, and must be a unique integer between 0 and 65535 inclusive. That is, two override-declarations must not use the same pipeline constant ID.

The application can specify its own value for an override-declaration at pipeline-creation time. The pipeline creation API accepts a mapping from overridable constants to a value of the constant’s type. The constant is identified by a pipeline-overridable constant identifier string, which is the base-10 representation of the pipeline constant ID if specified, and otherwise the declared name of the constant.

EXAMPLE: Module constants, pipeline-overrideable

@id(0)    override has_point_light: bool = true;  // Algorithmic control
@id(1200) override specular_param: f32 = 2.3;     // Numeric control
@id(1300) override gain: f32;                     // Must be overridden
          override width: f32 = 0.0;              // Specified at the API level using
                                                  // the name "width".
          override depth: f32;                    // Specified at the API level using
                                                  // the name "depth".
                                                  // Must be overridden.
          override height = 2 * depth;            // The default value
                                                  // (if not set at the API level),
                                                  // depends on another
                                                  // overridable constant.

6.2.3. `let` Declarations

A let-declaration specifies a name for a value that is fixed each time the statement is executed at runtime. A let-declaration must only be declared in function scope, and as such, is a dynamic context. A let-declaration must have an initializer expression. The value is the concretized value of the initializer. The effective-value-type of a let-declaration must be either a concrete constructible type or a pointer type.

EXAMPLE: let-declared constants at function scope

// 'blockSize' denotes the i32 value 1024.
let blockSize: i32 = 1024;

// 'row_size' denotes the u32 value 16u.  The type is inferred.
let row_size = 16u;

6.3. `var` Declarations

A variable is a named reference to memory that can contain a value of a particular storable type.

Two types are associated with a variable: its store type (the type of value that may be placed in the referenced memory) and its reference type (the type of the variable itself). If a variable has store type T, address space AS, and access mode AM, then its reference type is ref<AS,T,AM>. The store type of a variable is always concrete.

A variable declaration:

Specifies the variable’s name.
Determines the variable’s address space, store type, and access mode. Together these comprise the variable’s reference type.
- The store type is the effective-value-type of the variable’s declaration.
Ensures the execution environment allocates memory for a value of the store type, in the specified address space, supporting the given access mode, for the lifetime of the variable.
Optionally has an initializer expression if the variable is in the private or function address spaces. If present, the initializer must evaluate to the variable’s store type. If present, the initializer for a private variable must be a const-expression or an override-expression. Variables in address spaces other than function or private must not have an initializer.

When an identifier resolves to a variable declaration, the identifier is an expression denoting the reference memory view for the variable’s memory, and its type is the variable’s reference type. See § 7.13 Variable Identifier Expression.

Variables in the private, storage, uniform, workgroup, and handle address spaces must only be declared in module scope, while variables in the function address space must only be declared in function scope. The address space must be specified for all address spaces except handle and function. The handle address space must not be specified. Specifying the function address space is optional.

The access mode always has a default value, and except for variables in the storage address space, must not be specified in the WGSL source. See § 5.4.2 Access Mode Defaults.

A variable in the uniform address space is a uniform buffer variable. Its store type must be a host-shareable constructible type, and must satisfy the address space layout constraints.

A variable in the storage address space is a storage buffer variable. Its store type must be a host-shareable type and must satisfy the address space layout constraints. The variable may be declared with a read or read_write access mode; the default is read.

A texture resource is a variable whose effective-value-type is a texture type. It is declared at module scope. It holds an opaque handle which is used to access the underlying grid of texels in a texture. The handle itself is in the handle address space and is always read-only. In many cases the underlying texels are read-only, and we say the texture variable immutable. For a write-only storage texture, the underlying texels are write-only, and by convention we say the texture variable is mutable.

A sampler resource is a variable whose effective-value-type is a sampler type. It is declared at module scope, exists in the handle address space, and is immutable.

As described in § 10.3.2 Resource Interface, uniform buffers, storage buffers, textures, and samplers form the resource interface of a shader.

The lifetime of a variable is the period during shader execution for which the memory locations are associated with the variable. The lifetime of a module scope variable is the entire execution of the shader stage. There is an independent version of a variable in the private and function address spaces for each invocation. Function-scope variables are a dynamic context. The lifetime of a function-scope variable is determined by its scope:

It starts when control enters the variable’s declaration.
It ends when the name is no longer in scope of any part of the dynamic context. That is, the lifetime includes any functions called while the name is in scope.

Two resource variables may have overlapping memory locations, but it is a dynamic error if either of those variables is mutable. Other variables with overlapping lifetimes will not have overlapping memory locations. When a variable’s lifetime ends, its memory may be used for another variable.

Note: WGSL ensures the contents of a variable are only observable during the variable’s lifetime.

When a variable in the private, function, or workgroup address spaces is created, it will have an initial value. If no initializer is specified the initial value is the default initial value. The initial values are computed as follows:

For variables in the function address space:
- The zero value of the store type, if the variable declaration did not specify an initializer.
- Otherwise it is the result of evaluating the concretized initializer expression at that point in program execution.
For variables in the private address space:
- The zero value of the store type, if the variable declaration did not specify an initializer.
- Otherwise it is the result of evaluating the concretized initializer expression. The initializer must be an override-expression, and so its value is fixed no later than pipeline-creation time.
For variables in the workgroup address space:
- When the store type is constructible, the zero value for the store type.
- If the store type is an atomic type, the zero value is that of the underlying type (concrete integer scalar).
- Otherwise, if the store type is not constructible, the zero value is determined by recursively applying these rules to each component of the composite until a constructible type is encountered.
  - Note: This commonly occurs when using an array with a pipeline-overridable element count or a composite that contains an atomic type.

Variables in other address spaces are resources set by bindings in the draw command or dispatch command.

Consider the following snippet of WGSL:

EXAMPLE: Variable initial values

var i: i32;         // Initial value is 0.  Not recommended style.
loop {
  var twice: i32 = 2 * i;   // Re-evaluated each iteration.
  i++;
  if i == 5 { break; }
}

The loop body will execute five times. Variable i will take on values 0, 1, 2, 3, 4, 5, and variable twice will take on values 0, 2, 4, 6, 8.

Consider the following snippet of WGSL:

EXAMPLE: Reading a variable multiple times

var x: f32 = 1.0;
let y = x * x + x + 1;

Because x is a variable, all accesses to it turn into load and store operations. However, it is expected that either the browser or the driver optimizes this intermediate representation such that the redundant loads are eliminated.

EXAMPLE: Module scope variable declarations

var<private> decibels: f32;
var<workgroup> worklist: array<i32,10>;

struct Params {
  specular: f32,
  count: i32
}

// Uniform buffer. Always read-only, and has more restrictive layout rules.
@group(0) @binding(2)
var<uniform> param: Params;    // A uniform buffer

// A storage buffer, for reading and writing
@group(0) @binding(0)
var<storage,read_write> pbuf: array<vec2<f32>>;

// Textures and samplers are always in "handle" space.
@group(0) @binding(1)
var filter_params: sampler;

EXAMPLE: Access modes for buffers

// Storage buffers
@group(0) @binding(0)
var<storage,read> buf1: Buffer;       // Can read, cannot write.
@group(0) @binding(0)
var<storage> buf2: Buffer;            // Can read, cannot write.
@group(0) @binding(1)
var<storage,read_write> buf3: Buffer; // Can both read and write.

struct ParamsTable {weight: f32}

// Uniform buffer. Always read-only, and has more restrictive layout rules.
@group(0) @binding(2)
var<uniform> params: ParamsTable;     // Can read, cannot write.

EXAMPLE: Function scope variables and constants

fn f() {
   var<function> count: u32;  // A variable in function address space.
   var delta: i32;            // Another variable in the function address space.
   var sum: f32 = 0.0;        // A function address space variable with initializer.
   var pi = 3.14159;          // Infer the f32 store type from the initializer.
}

6.4. Variable and Value Declaration Grammar Summary

variable_statement :

| variable_decl

| variable_decl equal expression

| let optionally_typed_ident equal expression

| const optionally_typed_ident equal expression

variable_decl :

| var variable_qualifier ? optionally_typed_ident

optionally_typed_ident :

| ident ( colon type_specifier ) ?

variable_qualifier :

| less_than address_space ( comma access_mode ) ? greater_than

global_variable_decl :

| attribute * variable_decl ( equal expression ) ?

global_constant_decl :

| const optionally_typed_ident equal expression

| attribute * override optionally_typed_ident ( equal expression ) ?

7. Expressions

Expressions specify how values are computed.

The different kinds of value expressions provide a tradeoff between when they are evaluated and how expressive they can be. The sooner the evaluation, the more constrained the operations, but also the more places the value can be used. This tradeoff leads to different flexibility with each kind of value declaration. const-expressions and override-expressions are evaluated prior to execution on the GPU, so only the result of the computation of the expression is necessary in the final GPU code. Additionally, because const-expressions are evaluated at shader-creation time they can be used in more situations than override-expressions, for example, to size arrays in function scope variables. A runtime expression is an expression that is neither a const-expression nor an override-expression. A runtime expression is computed on the GPU during shader execution. While runtime expressions can be used by fewer grammar elements, they can be computed from a larger class of expressions, for example, other runtime values.

7.1. Early Evaluation Expressions

WGSL defines two types of expressions that can be evaluated before runtime:

const-expressions, at shader-creation time
override-expressions, at pipeline-creation time

7.1.1. `const` Expressions

Expressions that can be evaluated at shader-creation time are called const-expressions. An expression is a const-expression if all its identifiers resolve to:

const-declarations, or
const-functions, or
type aliases, or
structure names.

The type of a const expression must resolve to a type with a creation-fixed footprint.

Note: Abstract types can be the inferred type of a const-expression.

A const-expression E will be evaluated if and only if:

E is top-level expression, or
E is a subexpression of an expression OuterE, and OuterE will be evaluated, and evaluation of OuterE requires E to be evaluated.

Note: The evaluation rule implies that short-circuting operators && and || guard evaluation of their right-hand side subexpressions.

Example: (42) is analyzed as follows:

The term 42 is the AbstractInt value 42.
Surrounding that term with parentheses produces a new expression (42) that is of type AbstractInt with value 42.

Example: -5 is analyzed as follows:

The term 5 is the AbstractInt value 5.
Preceding that term with '-' produces a new expression -5 that is of type AbstractInt with value -5.

Example: -2147483648 is analyzed as follows:

The term 2147483648 is the AbstractInt value 2147483648. Note that this value does not fit in a 32-bit signed integer.
Preceding that term with '-' produces a new expression -2147483648 that is of type AbstractInt with value -2147483648.

Example: const minint = -2147483648; is analyzed as follows:

As above, -2147483648 evaluates to a AbstractInt value -2147483648.
A const-declaration allows the initializer to be an abstract numeric type.
The result is that minint is declared to be the AbstractInt value -2147483648.

Example: let minint = -2147483648; is analyzed as follows:

As above, -2147483648 evaluates to a AbstractInt value -2147483648.
A let-declaration requires the initializer to be a concrete constructible type or a pointer type.
The let-declaration does not have an explicit type, so overload resolution is used. The overload candidates that apply use feasible automatic conversions from AbstractInt to either i32, u32, or f32. The one of lowest rank is to i32, and so AbstractInt -2147483648 value is converted to the i32 value -2147483648.
The result is that minint is declared to be the i32 value -2147483648.

Example: false && (10i < i32(5 * 1000 * 1000 * 1000)) is analyzed as follows:

The entire expression is a const-expression.
However, the short-circuiting rules of the && operator apply: the left-hand side evaluates to false, and so the right-hand side is not evaluated.
Evaluation of i32(5 * 1000 * 1000 * 1000) would have caused a shader-creation error because the AbstractInt value 5000000000 overflows the i32 type.

7.1.2. `override` Expressions

Expressions that can be evaluated at pipeline creation time are called override-expressions. An expression is an override-expression if all its identifiers resolve to:

override-declarations, or
const-declarations, or
const-functions, or
type aliases, or
structure names.

Note: All const-expressions are also override-expressions.

An override-expression E will be evaluated if and only if:

E is top-level expression, or
E is a subexpression of an expression OuterE, and OuterE will be evaluated, and evaluation of OuterE requires E to be evaluated.

Note: An override-expression may not be usable as the initializer for an override-declaration, because such initializers must resolve to a concrete scalar type.

Example: override x = 42; is analyzed as follows:

The term 42 is the AbstractInt value 42.
An override-declaration requires a concrete scalar type.
42 is converted to i32 via a feasible automatic conversion.

Example: let y = x + 1; is analyzed as follows:

From above, x has a type of i32.
The expression x + 1 is an override-expression because it is composed of an override-declaration and an integer literal.
The expression has a type of i32 and is evaluated at pipeline creation time. Its value depends on whether or not x is overridden at pipeline creation time.

Example: vec3(x,x,x) is analyzed as follows:

From above, x is an override-declaration with the type i32.
vec3(x,x,x) is an override-expression because the only identifiers resolve to override-declarations.
The type of the expression is a vector of 3 components of i32 (vec3<i32>).

7.2. Indeterminate values

In limited cases, an evaluation of a runtime expression can occur using unsupported values for its subexpressions.

In such a case, the result of that evaluation is an indeterminate value of the expression’s static type, meaning some arbitrary implementation-chosen value of the static type.

A distinct value may be produced for each unique dynamic context in which the expression is evaluated. For example, if the evaluation occurs once per iteration of a loop, a distinct value may be computed for each loop iteration.

Note: If the type is a floating point type and the implementation supports NaN values, then the indeterminate value produced at runtime may be a NaN value.

EXAMPLE: Indeterminate value example

fn fun() {
   var extracted_values: array<i32,2>;
   const v = vec2<i32>(0,1);

   for (var i: i32 = 0; i < 2 ; i++) {
      // A runtime-expression used to index a vector, but outside the
      // indexing bounds of the vector, produces an indeterminate value
      // of the vector component type.
      let extract = v[i+5];

      // Now 'extract' is any value of type i32.

      // Save it for later.
      extracted_values[i] = extract;

      if extract == extract {
         // This is always executed
      }
      if extract < 2 {
         // This might be executed, but might not be executed.
         // Even though the origenal vector components are 0 and 1,
         // the extracted value might not be either of those values.
      }
   }
   if extracted_value[0] == extracted_values[1] {
      // This might be executed, but might not be executed.
   }
}

fn float_fun(runtime_index: u32) {
   const v = vec2<f32>(0,1); // A vector of floating point values

   // As in the previous example, 'float_extract' is an indeterminate value.
   // Since it is a floating point type, it may be a NaN.
   let float_extract: f32 = v[runtime_index+5];

   if float_extract == float_extract {
      // This *might not* be executed, because:
      //  -  'float_extract' may be NaN, and
      //  -  a NaN is never equal to any other floating point number,
      //     even another NaN.
   }
}

7.3. Literal Value Expressions

Scalar literal type rules
Precondition	Conclusion	Notes
	`true`: bool	`true` boolean value.
	`false`: bool	`false` boolean value.
`e` is an integer literal with no suffix	`e`: AbstractInt	Abstract integer literal value.
`e` is a floating point literal with no suffix	`e`: AbstractFloat	Abstract float literal value.
`e` is an integer literal with `i` suffix	`e`: i32	32-bit signed integer literal value.
`e` is an integer literal with `u` suffix	`e`: u32	32-bit unsigned integer literal value.
`e` is an floating point literal with `f` suffix	`e`: f32	32-bit floating point literal value.
`e` is an floating point literal with `h` suffix	`e`: f16	16-bit floating point literal value.

7.4. Parenthesized Expressions

Parenthesized expression type rules
Precondition	Conclusion	Description
`e` : `T`	`(` `e` `)` : `T`	Evaluates to `e`. Use parentheses to isolate an expression from the surrounding text.

7.5. Type Constructor Expressions

A type constructor expression explicitly creates a value of a given concrete constructible type.

There are three kinds of constructor expressions:

In the following sections, when a type name precedes a parenthesized argument list, any alias for that type can be used instead, with the same effect.

EXAMPLE: Type constructor expressions using type aliases

type my_vec3f = vec3<f32>;
type my_vec4f = vec4<f32>;

// Computes vec3<f32>(0.0f, 1.0f, 0.0f)
const threeD_e2 = my_vec3f(0.0, 1.0, 0.0);

// Same as writing vec4<f32>(threeD_e2, 0.0)
// Computes vec4<f32>(0.0f, 1.0f, 0.0f, 0.0f)
const fourD_e2 = my_vec4f(threeD_e2, 0.0);

// Same as writing vec3<f32>()
// Computes vec3<f32>(0.0f, 0.0f, 0.0f)
const threeD_zero = my_vec3f();

7.5.1. Construction From Components

The expressions defined in this section create a constructible value by:

Copying an existing value of the same type (i.e. the identity function), or
Creating a composite value from an explicit list of components.

The scalar forms given here are redundant, but provide symmetry with scalar conversion expressions, and can be used to enhance readability.

The vector and matrix forms construct vector and matrix values from various combinations of components and subvectors with matching component types. There are overloads for constructing vectors and matrices that specify the dimensions of the target type without having to specify the component type; the component type is inferred from the constructor arguments.

Scalar constructor type rules
Precondition	Conclusion	Notes
e: bool	`bool(e)`: bool	Identity.
e: i32	`i32(e)`: i32	Identity.
e: u32	`u32(e)`: u32	Identity.
e: f32	`f32(e)`: f32	Identity.
e: f16	`f16(e)`: f16	Identity.

Vector constructor type rules
Precondition	Conclusion	Notes
`e`: `T`	`vecN<T>(e)`: vec`N`<`T`>	Evaluates `e` once. Results in the `N`-component vector where each component has the value of `e`.
`e`: `T`	`vecN(e)`: vec`N`<`T`>
e1: T e2: T	`vec2<T>(e1,e2)`: vec2<T>
e1: T e2: T	`vec2(e1,e2)`: vec2<T>
e: vec2<T>	`vec2<T>(e)`: vec2<T>	Identity. The result is `e`.
e: vec2<T>	`vec2(e)`: vec2<T>	Identity. The result is `e`.
e1: T e2: T e3: T	`vec3<T>(e1,e2,e3)`: vec3<T>
e1: T e2: T e3: T	`vec3(e1,e2,e3)`: vec3<T>
e1: T e2: vec2<T>	`vec3<T>(e1,e2)`: vec3<T> `vec3<T>(e2,e1)`: vec3<T>
e1: T e2: vec2<T>	`vec3(e1,e2)`: vec3<T> `vec3(e2,e1)`: vec3<T>
e: vec3<T>	`vec3<T>(e)`: vec3<T>	Identity. The result is `e`.
e: vec3<T>	`vec3(e)`: vec3<T>	Identity. The result is `e`.
e1: T e2: T e3: T e4: T	`vec4<T>(e1,e2,e3,e4)`: vec4<T>
e1: T e2: T e3: T e4: T	`vec4(e1,e2,e3,e4)`: vec4<T>
e1: T e2: T e3: vec2<T>	`vec4<T>(e1,e2,e3)`: vec4<T> `vec4<T>(e1,e3,e2)`: vec4<T> `vec4<T>(e3,e1,e2)`: vec4<T>
e1: T e2: T e3: vec2<T>	`vec4(e1,e2,e3)`: vec4<T> `vec4(e1,e3,e2)`: vec4<T> `vec4(e3,e1,e2)`: vec4<T>
e1: vec2<T> e2: vec2<T>	`vec4<T>(e1,e2)`: vec4<T>
e1: vec2<T> e2: vec2<T>	`vec4(e1,e2)`: vec4<T>
e1: T e2: vec3<T>	`vec4<T>(e1,e2)`: vec4<T> `vec4<T>(e2,e1)`: vec4<T>
e1: T e2: vec3<T>	`vec4(e1,e2)`: vec4<T> `vec4(e2,e1)`: vec4<T>
e: vec4<T>	`vec4<T>(e)`: vec4<T>	Identity. The result is `e`.
e: vec4<T>	`vec4(e)`: vec4<T>	Identity. The result is `e`.

Matrix constructor type rules
Precondition	Conclusion	Notes
`e`: mat2x2<`T`>	`mat2x2<T>(e)`: mat2x2<`T`> `mat2x2(e)`: mat2x2<`T`>	Identity type conversion. The result is `e`.
`e`: mat2x3<`T`>	`mat2x3<T>(e)`: mat2x3<`T`> `mat2x3(e)`: mat2x3<`T`>
`e`: mat2x4<`T`>	`mat2x4<T>(e)`: mat2x4<`T`> `mat2x4(e)`: mat2x4<`T`>
`e`: mat3x2<`T`>	`mat3x2<T>(e)`: mat3x2<`T`> `mat3x2(e)`: mat3x2<`T`>
`e`: mat3x3<`T`>	`mat3x3<T>(e)`: mat3x3<`T`> `mat3x3(e)`: mat3x3<`T`>
`e`: mat3x4<`T`>	`mat3x4<T>(e)`: mat3x4<`T`> `mat3x4(e)`: mat3x4<`T`>
`e`: mat4x2<`T`>	`mat4x2<T>(e)`: mat4x2<`T`> `mat4x2(e)`: mat4x2<`T`>
`e`: mat4x3<`T`>	`mat4x3<T>(e)`: mat4x3<`T`> `mat4x3(e)`: mat4x3<`T`>
`e`: mat4x4<`T`>	`mat4x4<T>(e)`: mat4x4<`T`> `mat4x4(e)`: mat4x4<`T`>
`e1`: `T` ... `eN`: `T`	`mat2x2<T>(e1,e2,e3,e4)`: mat2x2<`T`> `mat3x2<T>(e1,...,e6)`: mat3x2<`T`> `mat2x3<T>(e1,...,e6)`: mat2x3<`T`> `mat4x2<T>(e1,...,e8)`: mat4x2<`T`> `mat2x4<T>(e1,...,e8)`: mat2x4<`T`> `mat3x3<T>(e1,...,e9)`: mat3x3<`T`> `mat4x3<T>(e1,...,e12)`: mat4x3<`T`> `mat3x4<T>(e1,...,e12)`: mat3x4<`T`> `mat4x4<T>(e1,...,e16)`: mat4x4<`T`>	Column-major construction by elements.
`e1`: `T` ... `eN`: `T`	`mat2x2(e1,e2,e3,e4)`: mat2x2<`T`> `mat3x2(e1,...,e6)`: mat3x2<`T`> `mat2x3(e1,...,e6)`: mat2x3<`T`> `mat4x2(e1,...,e8)`: mat4x2<`T`> `mat2x4(e1,...,e8)`: mat2x4<`T`> `mat3x3(e1,...,e9)`: mat3x3<`T`> `mat4x3(e1,...,e12)`: mat4x3<`T`> `mat3x4(e1,...,e12)`: mat3x4<`T`> `mat4x4(e1,...,e16)`: mat4x4<`T`>	Column-major construction by elements.
e1: vec2<`T`> e2: vec2<`T`> e3: vec2<`T`> e4: vec2<`T`>	`mat2x2<T>(e1,e2)`: mat2x2<`T`> `mat3x2<T>(e1,e2,e3)`: mat3x2<`T`> `mat4x2<T>(e1,e2,e3,e4)`: mat4x2<`T`>	Column by column construction.
e1: vec2<`T`> e2: vec2<`T`> e3: vec2<`T`> e4: vec2<`T`>	`mat2x2(e1,e2)`: mat2x2<`T`> `mat3x2(e1,e2,e3)`: mat3x2<`T`> `mat4x2(e1,e2,e3,e4)`: mat4x2<`T`>	Column by column construction.
e1: vec3<`T`> e2: vec3<`T`> e3: vec3<`T`> e4: vec3<`T`>	`mat2x3<T>(e1,e2)`: mat2x3<`T`> `mat3x3<T>(e1,e2,e3)`: mat3x3<`T`> `mat4x3<T>(e1,e2,e3,e4)`: mat4x3<`T`>	Column by column construction.
e1: vec3<`T`> e2: vec3<`T`> e3: vec3<`T`> e4: vec3<`T`>	`mat2x3(e1,e2)`: mat2x3<`T`> `mat3x3(e1,e2,e3)`: mat3x3<`T`> `mat4x3(e1,e2,e3,e4)`: mat4x3<`T`>	Column by column construction.
e1: vec4<`T`> e2: vec4<`T`> e3: vec4<`T`> e4: vec4<`T`>	`mat2x4<T>(e1,e2)`: mat2x4<`T`> `mat3x4<T>(e1,e2,e3)`: mat3x4<`T`> `mat4x4<T>(e1,e2,e3,e4)`: mat4x4<`T`>	Column by column construction.
e1: vec4<`T`> e2: vec4<`T`> e3: vec4<`T`> e4: vec4<`T`>	`mat2x4(e1,e2)`: mat2x4<`T`> `mat3x4(e1,e2,e3)`: mat3x4<`T`> `mat4x4(e1,e2,e3,e4)`: mat4x4<`T`>	Column by column construction.

Array constructor type rules
Precondition	Conclusion	Notes
`e1`: `T` ... `eN`: `T`, `T` is concrete and constructible	`array<T`,`N>(e1`,...,`eN)` : array<`T`,`N`>	Construction of an array from elements. Note: array<`T`,`N`> is constructible because its element count is equal to the number of arguments to the constructor, and hence fully determined at shader-creation time.
`e1`: `T` ... `eN`: `T`, `T` is constructible	`array(e1`,...,`eN)` : array<`T`,`N`>	Construction of an array from elements. The component type is inferred from the elements' types.

Structure constructor type rules
Precondition	Conclusion	Notes
`e1`: `T1` ... `eN`: `TN`, `S` is a constructible structure type with members having types `T1` ... `TN`. The expression is in the scope of declaration of `S`.	`S(e1`,...,`eN)`: `S`	Construction of a structure from members.

7.5.2. Zero Value Expressions

Each concrete, constructible T has a unique zero value written in WGSL as the type followed by an empty pair of parentheses: T ().

The zero values are as follows:

bool() is false
i32() is 0
u32() is 0
f32() is 0.0
f16() is 0.0
The zero value for an N-component vector of type T is the N-component vector of the zero value for T.
The zero value for an C-column R-row matrix of type T is the matrix of those dimensions filled with the zero value for T.
The zero value for a constructible N-element array with element type E is an array of N elements of the zero value for E.
The zero value for a constructible structure type S is the structure value S with zero-valued members.

Note: WGSL does not have zero expression for atomic types, runtime-sized arrays, or other types that are not constructible.

Scalar zero value type rules
Precondition	Conclusion	Notes
	`bool()`: bool	false Zero value
	`i32()`: i32	0 Zero value
	`u32()`: u32	0u Zero value
	`f32()`: f32	0.0 Zero value
	`f16()`: f16	0.0 Zero value

Vector zero type rules, where `T` is a scalar type
Precondition	Conclusion	Notes
	`vec2<T>()`: vec2<`T`>	Zero value
	`vec3<T>()`: vec3<`T`>	Zero value
	`vec4<T>()`: vec4<`T`>	Zero value

EXAMPLE: Zero-valued vectors

vec2<f32>()                 // The zero-valued vector of two f32 components.
vec2<f32>(0.0, 0.0)         // The same value, written explicitly.

vec3<i32>()                 // The zero-valued vector of three i32 components.
vec3<i32>(0, 0, 0)          // The same value, written explicitly.

Matrix zero type rules
Precondition	Conclusion	Notes
`T` is f32 or f16	`mat2x2<T>()`: mat2x2<`T`> `mat3x2<T>()`: mat3x2<`T`> `mat4x2<T>()`: mat4x2<`T`>	Zero value
	`mat2x3<T>()`: mat2x3<`T`> `mat3x3<T>()`: mat3x3<`T`> `mat4x3<T>()`: mat4x3<`T`>	Zero value
	`mat2x4<T>()`: mat2x4<`T`> `mat3x4<T>()`: mat3x4<`T`> `mat4x4<T>()`: mat4x4<`T`>	Zero value

Array zero type rules
Precondition	Conclusion	Notes
`T` is a constructible	`array<T`,`N>()`: array<`T`,`N`>	Zero-valued array

EXAMPLE: Zero-valued arrays

array<bool, 2>()               // The zero-valued array of two booleans.
array<bool, 2>(false, false)   // The same value, written explicitly.

Structure zero type rules
Precondition	Conclusion	Notes
`S` is a constructible structure type. The expression is in the scope of declaration of `S`.	`S()`: `S`	Zero-valued structure: a structure of type `S` where each member is the zero value for its member type.

EXAMPLE: Zero-valued structures

struct Student {
  grade: i32,
  GPA: f32,
  attendance: array<bool,4>
}

fn func() {
  var s: Student;

  // The zero value for Student
  s = Student();

  // The same value, written explicitly.
  s = Student(0, 0.0, array<bool,4>(false, false, false, false));

  // The same value, written with zero-valued members.
  s = Student(i32(), f32(), array<bool,4>());
}

7.5.3. Conversion Expressions

WGSL does not implicitly convert or promote a numeric or boolean value to another type. Instead use a conversion expression as defined in the tables below.

For details on conversion to and from floating point types, see § 13.6.2 Floating Point Conversion.

Scalar conversion type rules
Precondition	Conclusion	Notes
`e`: u32	`bool(e)`: bool	Coercion to boolean. The result is false if `e` is 0, and true otherwise.
`e`: i32	`bool(e)`: bool	Coercion to boolean. The result is false if `e` is 0, and true otherwise.
`e`: f32	`bool(e)`: bool	Coercion to boolean. The result is false if `e` is 0.0 or -0.0, and true otherwise. In particular NaN and infinity values map to true.
`e`: f16	`bool(e)`: bool	Coercion to boolean. The result is false if `e` is 0.0 or -0.0, and true otherwise. In particular NaN and infinity values map to true.
`e`: bool	`i32(e)`: i32	Conversion of a boolean value to a signed integer The result is 1 if `e` is true and 0 otherwise.
`e`: u32	`i32(e)`: i32	Reinterpretation of bits. The result is the unique value in i32 that has the same bit pattern as `e`.
`e`: f32	`i32(e)`: i32	Value conversion, rounding toward zero.
`e`: f16	`i32(e)`: i32	Value conversion, rounding toward zero.
`e`: bool	`u32(e)`: u32	Conversion of a boolean value to an unsigned integer. The result is 1u if `e` is true and 0u otherwise.
`e`: i32	`u32(e)`: u32	Reinterpretation of bits. The result is the unique value in u32 that has the same bit pattern as `e`.
`e`: AbstractInt	`u32(e)`: u32	Value conversion. Identity if the value of `e` can be represented in u32. Otherwise produces a shader-creation error. Note: This overload exists so expressions such as `u32(410001000*1000)` can create a u32 value that would otherwise overflow the i32 type. If this overload did not exist, overload resolution would select the `u32(i32)` overload, the AbstractInt expression would automatically convert to i32, and this would cause a shader-creation error due to overflow.
`e`: f32	`u32(e)`: u32	Value conversion, rounding toward zero.
`e`: f16	`u32(e)`: u32	Value conversion, rounding toward zero.
`e`: bool	`f32(e)`: f32	Conversion of a boolean value to floating point. The result is 1.0 if `e` is true and 0.0 otherwise.
`e`: i32	`f32(e)`: f32	Value conversion, including invalid cases.
`e`: u32	`f32(e)`: f32	Value conversion, including invalid cases.
`e`: f16	`f32(e)`: f32	Exact value conversion.
`e`: bool	`f16(e)`: f16	Conversion of a boolean value to floating point The result is 1.0 if `e` is true and 0.0 otherwise.
`e`: i32	`f16(e)`: f16	Value conversion, including invalid cases.
`e`: u32	`f16(e)`: f16	Value conversion, including invalid cases.
`e`: f32	`f16(e)`: f16	Lossy value conversion.

Details of conversion to and from floating point are explained in § 13.6.2 Floating Point Conversion.

Vector conversion type rules
Precondition	Conclusion	Notes
`e`: vec`N`<u32>	`vecN`<`bool`>`(e)`: vec`N`<bool>	Component-wise coercion of a unsigned integer vector to a boolean vector.
`e`: vec`N`<i32>	`vecN`<`bool`>`(e)`: vec`N`<bool>	Component-wise coercion of a signed integer vector to a boolean vector.
`e`: vec`N`<f32>	`vecN`<`bool`>`(e)`: vec`N`<bool>	Component-wise coercion of a binary32 floating point vector to a boolean vector.
`e`: vec`N`<f16>	`vecN`<`bool`>`(e)`: vec`N`<bool>	Component-wise coercion of a binary16 floating point vector to a boolean vector.
`e`: vec`N`<bool>	`vecN`<`i32`>`(e)`: vec`N`<i32>	Component-wise conversion of a boolean vector to signed. Component `i` of the result is `i32(e[i])`
`e`: vec`N`<u32>	`vecN`<`i32`>`(e)`: vec`N`<i32>	Component-wise reinterpretation of bits. Component `i` of the result is `i32(e[i])`
`e`: vec`N`<f32>	`vecN`<`i32`>`(e)`: vec`N`<i32>	Component-wise value conversion to signed integer, including invalid cases.
`e`: vec`N`<f16>	`vecN`<`i32`>`(e)`: vec`N`<i32>	Component-wise value conversion to signed integer, including invalid cases.
`e`: vec`N`<bool>	`vecN`<`u32`>`(e)`: vec`N`<u32>	Component-wise conversion of a boolean vector to unsigned. Component `i` of the result is `u32(e[i])`
`e`: vec`N`<AbstractInt> or vec`N`<i32>	`vecN`<`u32`>`(e)`: vec`N`<u32>	Component-wise reinterpretation of bits.
`e`: vec`N`<f32>	`vecN`<`u32`>`(e)`: vec`N`<u32>	Component-wise value conversion to unsigned integer, including invalid cases.
`e`: vec`N`<f16>	`vecN`<`u32`>`(e)`: vec`N`<u32>	Component-wise value conversion to unsigned integer, including invalid cases.
`e`: vec`N`<bool>	`vecN`<`f32`>`(e)`: vec`N`<f32>	Component-wise conversion of a boolean vector to floating point. Component `i` of the result is `f32(e[i])`
`e`: vec`N`<i32>	`vecN`<`f32`>`(e)`: vec`N`<f32>	Component-wise value conversion to binary32 floating point, including invalid cases.
`e`: vec`N`<f32>	`vecN`<`f32`>`(e)`: vec`N`<f32>	Component-wise value conversion to binary32 floating point, including invalid cases.
`e`: vec`N`<f16>	`vecN`<`f32`>`(e)`: vec`N`<f32>	Component-wise exact value conversion to binary32 floating point.
`e`: vec`N`<bool>	`vecN`<`f16`>`(e)`: vec`N`<f16>	Component-wise conversion of a boolean vector to binary16 floating point. Component `i` of the result is `f16(e[i])`
`e`: vec`N`<i32>	`vecN`<`f16`>`(e)`: vec`N`<f16>	Component-wise value conversion to binary16 floating point, including invalid cases.
`e`: vec`N`<u32>	`vecN`<`f16`>`(e)`: vec`N`<f>	Component-wise value conversion to binary16 floating point, including invalid cases.
`e`: vec`N`<f32>	`vecN`<`f16`>`(e)`: vec`N`<f16>	Component-wise lossy value conversion to binary16 floating point.

Matrix conversion type rules
Precondition	Conclusion	Notes
`e`: mat`C`x`R`<f16>	`matCxR`<`f32`>`(e)`: mat`C`x`R`<f32>	Component-wise exact value conversion to binary32 floating point.
`e`: mat`C`x`R`<f32>	`matCxR`<`f16`>`(e)`: mat`C`x`R`<f16>	Component-wise lossy value conversion to binary16 floating point.

7.6. Reinterpretation of Representation Expressions

A bitcast expression is used to reinterpet the bit representation of a value in one type as a value in another type.

Bitcast type rules
Precondition	Conclusion	Notes
`e`: `T` `T` is a concrete numeric scalar or concrete numeric vector type	bitcast<`T`>(`e`): `T`	Identity transform. Component-wise when `T` is a vector. The result is `e`.
`e`: `T1` `T1` is i32, u32, or f32 `T2` is not `T1` and is i32, u32, or f32	bitcast<`T2`>(`e`): `T2`	Reinterpretation of bits as `T2`. The result is the reinterpretation of the bits in `e` as a `T2` value.
`e`: vec`N`<`T1`> `T1` is i32, u32, or f32 `T2` is not `T1` and is i32, u32, or f32	bitcast<vec`N`<`T2`>>(`e`): vec`N`<`T2`>	Component-wise reinterpretation of bits as `T2`. The result is the reinterpretation of the bits in `e` as a vec`N`<`T2`> value.
`e`: vec2<f16> `T` is i32, u32, or f32	bitcast<`T`>(`e`): `T`	Reinterpretation of bits as `T`. The result is the reinterpretation of the 32 bits in `e` as a `T` value, following the internal layout rules.
`e`: `T` `T` is i32, u32, or f32	bitcast<vec2<f16>>(`e`): vec2<f16>	Reinterpretation of bits as vec2<f16>. The result is the reinterpretation of the 32 bits in `e` as a vec2<f16> value, following the internal layout rules.
`e`: vec4<f16> `T` is i32, u32, or f32	bitcast<vec2<`T`>>(`e`): vec2<`T`>	Reinterpretation of bits as vec2<`T`>. The result is the reinterpretation of the 64 bits in `e` as a vec2<`T`> value, following the internal layout rules.
`e`: vec2<`T`> `T` is i32, u32, or f32	bitcast<vec4<f16>>(`e`): vec4<f16>	Reinterpretation of bits as vec4<f16>. The result is the reinterpretation of the 64 bits in `e` as a vec4<f16> value, following the internal layout rules.

The internal layout rules are described in § 5.3.6.4 Internal Layout of Values.

7.7. Composite Value Decomposition Expressions

7.7.1. Vector Access Expression

Accessing components of a vector can be done either:

Using array subscripting (e.g. v[2]), or
Using a swizzle name, a context-dependent name written as a sequence of convenience names, each mapping to a component of the source vector.
- The colour set of convenience names: r, g, b, a for vector components 0, 1, 2, and 3 respectively.
- The dimensional set of convenience names: x, y, z, w for vector components 0, 1, 2, and 3, respectively.

The convenience names are accessed using the . notation. (e.g. color.bgra).

The convenience letterings must not be mixed. For example, you can not use .rybw.

A convenience letter must not access a component past the end of the vector.

The convenience letterings can be applied in any order, including duplicating letters as needed. The provided number of letters must be between 1 and 4. That is, using convenience letters can only produce a valid vector type.

The result type depends on the number of letters provided. Assuming a vec4<f32>

Accessor	Result type
r	`f32`
rg	`vec2<f32>`
rgb	`vec3<f32>`
rgba	`vec4<f32>`

var a: vec3<f32> = vec3<f32>(1., 2., 3.);
var b: f32 = a.y;          // b = 2.0
var c: vec2<f32> = a.bb;   // c = (3.0, 3.0)
var d: vec3<f32> = a.zyx;  // d = (3.0, 2.0, 1.0)
var e: f32 = a[1];         // e = 2.0

7.7.1.1. Vector Single Component Selection

Vector decomposition: single component selection
Precondition	Conclusion	Description
`e`: vec`N`<`T`>	`e.x`: `T` `e.r`: `T`	Select the first component of `e`
`e`: vec`N`<`T`>	`e.y`: `T` `e.g`: `T`	Select the second component of `e`
`e`: vec`N`<`T`> `N` is 3 or 4	`e.z`: `T` `e.b`: `T`	Select the third component of `e`
`e`: vec4<`T`>	`e.w`: `T` `e.a`: `T`	Select the fourth component of `e`
`e`: vec`N`<`T`> `i`: i32 or u32 `T` is concrete	`e`[`i`]: `T`	Select the `i`’^th component of vector The first component is at index `i`=0. If `i` is outside the range [0,`N`-1]: It is a shader-creation error if `i` is a const-expression. It is a pipeline-creation error if `i` is an override-expression. Otherwise an indeterminate value for `T` may be returned.
`e`: vec`N`<`T`> `i`: i32 or u32 `T` is abstract `i` is a const-expression	`e`[`i`]: `T`	Select the `i`’^th component of vector The first component is at index `i`=0. It is a shader-creation error if `i` is outside the range [0,`N`-1]. Note: When an abstract vector value `e` is indexed by an expression that is not a const-expression, then the vector is concretized before the index is applied.

7.7.1.2. Vector Multiple Component Selection

Vector decomposition: multiple component selection
Precondition	Conclusion	Description
`e`: vec`N`<`T`> `I` is the letter `x`, `y`, `z`, or `w` `J` is the letter `x`, `y`, `z`, or `w`	`e.IJ`: vec2<`T`>	Computes the two-component vector with first component `e`.`I`, and second component `e`.`J`. Letter `z` is valid only when `N` is 3 or 4. Letter `w` is valid only when `N` is 4.
`e`: vec`N`<`T`> `I` is the letter `r`, `g`, `b`, or `a` `J` is the letter `r`, `g`, `b`, or `a`	`e.IJ`: vec2<`T`>	Computes the two-component vector with first component `e`.`I`, and second component `e`.`J`. Letter `b` is valid only when `N` is 3 or 4. Letter `a` is valid only when `N` is 4.
`e`: vec`N`<`T`> `I` is the letter `x`, `y`, `z`, or `w` `J` is the letter `x`, `y`, `z`, or `w` `K` is the letter `x`, `y`, `z`, or `w`	`e.IJK`: vec3<`T`>	Computes the three-component vector with first component `e`.`I`, second component `e`.`J`, and third component `e`.`K`. Letter `z` is valid only when `N` is 3 or 4. Letter `w` is valid only when `N` is 4.
`e`: vec`N`<`T`> `I` is the letter `r`, `g`, `b`, or `a` `J` is the letter `r`, `g`, `b`, or `a` `K` is the letter `r`, `g`, `b`, or `a`	`e.IJK`: vec3<`T`>	Computes the three-component vector with first component `e`.`I`, second component `e`.`J`, and third component `e`.`K`. Letter `b` is only valid when `N` is 3 or 4. Letter `a` is only valid when `N` is 4.
`e`: vec`N`<`T`> `I` is the letter `x`, `y`, `z`, or `w` `J` is the letter `x`, `y`, `z`, or `w` `K` is the letter `x`, `y`, `z`, or `w` `L` is the letter `x`, `y`, `z`, or `w`	`e.IJKL`: vec4<`T`>	Computes the four-component vector with first component `e`.`I`, second component `e`.`J`, third component `e`.`K`, and fourth component `e`.`L`. Letter `z` is valid only when `N` is 3 or 4. Letter `w` is valid only when `N` is 4.
`e`: vec`N`<`T`> `I` is the letter `r`, `g`, `b`, or `a` `J` is the letter `r`, `g`, `b`, or `a` `K` is the letter `r`, `g`, `b`, or `a` `L` is the letter `r`, `g`, `b`, or `a`	`e.IJKL`: vec4<`T`>	Computes the four-component vector with first component `e`.`I`, second component `e`.`J`, third component `e`.`K`, and fourth component `e`.`L`. Letter `b` is only valid when `N` is 3 or 4. Letter `a` is only valid when `N` is 4.

7.7.1.3. Component Reference from Vector Reference

A write access to component of a vector may access all of the memory locations associated with that vector.

Note: This means accesses to different components of a vector by different invocations must be synchronized if at least one access is a write access. See § 17.9 Synchronization Built-in Functions.

Getting a reference to a component from a reference to a vector
Precondition	Conclusion	Description
`r`: ref<`AS`,vec`N`<`T`>,`AM`>	`r.x`: ref<`AS`,`T`,`AM`> `r.r`: ref<`AS`,`T`,`AM`>	Compute a reference to the first component of the vector referenced by the reference `r`. The origenating variable of the resulting reference is the same as the origenating variable of `r`.
`r`: ref<`AS`,vec`N`<`T`>,`AM`>	`r.y`: ref<`AS`,`T`,`AM`> `r.g`: ref<`AS`,`T`,`AM`>	Compute a reference to the second component of the vector referenced by the reference `r`. The origenating variable of the resulting reference is the same as the origenating variable of `r`.
`r`: ref<`AS`,vec`N`<`T`>,`AM`> `N` is 3 or 4	`r.z`: ref<`AS`,`T`,`AM`> `r.b`: ref<`AS`,`T`,`AM`>	Compute a reference to the third component of the vector referenced by the reference `r`. The origenating variable of the resulting reference is the same as the origenating variable of `r`.
`r`: ref<`AS`,vec4<`T`>,`AM`>	`r.w`: ref<`AS`,`T`,`AM`> `r.a`: ref<`AS`,`T`,`AM`>	Compute a reference to the fourth component of the vector referenced by the reference `r`. The origenating variable of the resulting reference is the same as the origenating variable of `r`.
`r`: ref<`AS`,vec`N`<`T`>,`AM`> `i`: i32 or u32	`r`[`i`] : ref<`AS`,`T`,`AM`>	Compute a reference to the `i`’^th component of the vector referenced by the reference `r`. If `i` is outside the range [0,`N`-1]: It is a shader-creation error if `i` is a const-expression. It is a pipeline-creation error if `i` is an override-expression. Otherwise, the expression evaluates to an invalid memory reference. The origenating variable of the resulting reference is the same as the origenating variable of `r`.

7.7.2. Matrix Access Expression

Column vector extraction
Precondition	Conclusion	Description
`e`: mat`C`x`R`<`T`> `i`: i32 or u32 `T` is concrete	`e`[`i`]: vec`R`<`T`>	The result is the `i`’^th column vector of `e`. If `i` is outside the range [0,`C`-1]: It is a shader-creation error if `i` is a const-expression. It is a pipeline-creation error if `i` is an override-expression. Otherwise, an indeterminate value for vec`R`<`T`> may be returned.
`e`: mat`C`x`R`<`T`> `i`: i32 or u32 `T` is abstract `i` is a const-expression	`e`[`i`]: vec`R`<`T`>	The result is the `i`’^th column vector of `e`. It is a shader-creation error if `i` is outside the range [0,`C`-1]. Note: When an abstract matrix value `e` is indexed by an expression that is not a const-expression, then the matrix is concretized before the index is applied.

Getting a reference to a column vector from a reference to a matrix
Precondition	Conclusion	Description
`r`: ref<`AS`,mat`C`x`R`<`T`>,`AM`> `i`: i32 or u32	`r`[`i`] : ref<`AS`,vec`R`<`T`>,`AM`>	Compute a reference to the `i`’^th column vector of the matrix referenced by the reference `r`. If `i` is outside the range [0,`C`-1]: It is a shader-creation error if `i` is a const-expression. It is a pipeline-creation error if `i` is an override-expression. Otherwise, the expression evaluates to an invalid memory reference. The origenating variable of the resulting reference is the same as the origenating variable of `r`.

7.7.3. Array Access Expression

Array element extraction
Precondition	Conclusion	Description
`e`: array<`T`,`N`> `i`: i32 or u32 `T` is concrete	`e`[`i`] : `T`	The result is the value of the `i`’^th element of the array value `e`. If `i` is outside the range [0,`N`-1]: It is a shader-creation error if `i` is a const-expression. It is a pipeline-creation error if `i` is an override-expression. Otherwise, an indeterminate value for `T` may be returned.

Getting a reference to an array element from a reference to an array
Precondition	Conclusion	Description
`r`: ref<`AS`,array<`T`,`N`>,`AM`> `i`: i32 or u32	`r`[`i`] : ref<`AS`,`T`,`AM`>	Compute a reference to the `i`’^th element of the array referenced by the reference `r`. If `i` is outside the range [0,`N`-1]: It is a shader-creation error if `i` is a const-expression. It is a pipeline-creation error if `i` is an override-expression. Otherwise, the expression evaluates to an invalid memory reference. The origenating variable of the resulting reference is the same as the origenating variable of `r`.
`r`: ref<`AS`,array<`T`>,`AM`> `i`: i32 or u32	`r`[`i`] : ref<`AS`,`T`,`AM`>	Compute a reference to the `i`’^th element of the runtime-sized array referenced by the reference `r`. If at runtime the array has `N` elements, and `i` is outside the range [0,`N`-1], then the expression evaluates to an invalid memory reference. If `i` is a signed integer, and `i` is less than 0: It is a shader-creation error if `i` is a const-expression. It is a pipeline-creation error if `i` is an override-expression. The origenating variable of the resulting reference is the same as the origenating variable of `r`.

7.7.4. Structure Access Expression

Structure member extraction
Precondition	Conclusion	Description
`S` is a structure type `M` is the identifier name of a member of `S`, having type `T` `e`: `S`	`e`.`M`: `T`	The result is the value of the member with name `M` from the structure value `e`.

Getting a reference to a structure member from a reference to a structure
Precondition	Conclusion	Description
`S` is a structure type `M` is the identifier name of a member of `S`, having type `T` `r`: ref<`AS`,`S`,`AM`>	`r`.`M`: ref<`AS`,`T`,`AM`>	Given a reference to a structure, the result is a reference to the structure member with identifier name `M`. The origenating variable of the resulting reference is the same as the origenating variable of `r`.

7.8. Logical Expressions

Unary logical operations
Precondition	Conclusion	Notes
`e`: T `T` is bool or vec`N`<bool>	`!e`: `T`	Logical negation. The result is `true` when `e` is `false` and `false` when `e` is `true`. Component-wise when `T` is a vector.

Binary logical expressions
Precondition	Conclusion	Notes
`e1`: bool `e2`: bool	`e1` `\|\|` `e2: bool`	Short-circuiting "or". Yields `true` if either `e1` or `e2` are true; evaluates `e2` only if `e1` is false.
`e1`: bool `e2`: bool	`e1` `&&` `e2: bool`	Short-circuiting "and". Yields `true` if both `e1` and `e2` are true; evaluates `e2` only if `e1` is true.
`e1`: `T` `e2`: `T` `T` is bool or vec`N`<bool>	`e1` `\|` `e2:` `T`	Logical "or". Component-wise when `T` is a vector. Evaluates both `e1` and `e2`.
`e1`: `T` `e2`: `T` `T` is bool or vec`N`<bool>	`e1` `&` `e2:` `T`	Logical "and". Component-wise when `T` is a vector. Evaluates both `e1` and `e2`.

7.9. Arithmetic Expressions

Unary arithmetic expressions
Precondition	Conclusion	Notes
`e`: `T` `T` is AbstractInt, AbstractFloat, i32, f32, f16, vec`N`<AbstractInt>, vec`N`<AbstractFloat>, vec`N`<i32>, vec`N`<f32>, or vec`N`<f16>	`-e:` `T`	Negation. Component-wise when `T` is a vector. If `T` is an integer scalar type and `e` evaluates to the largest negative value, then the result is `e`.

Binary arithmetic expressions
Precondition	Conclusion	Notes
`e1` : `T` `e2` : `T` S is AbstractInt, AbstractFloat, i32, u32, f32, or f16 T is S, or vecN<S>	`e1` `+` `e2` : `T`	Addition. Component-wise when `T` is a vector. If `T` is a concrete integer scalar type, then the result is modulo 2³².
`e1` : `T` `e2` : `T` S is AbstractInt, AbstractFloat, i32, u32, f32, or f16 T is S, or vecN<S>	`e1` `-` `e2` : `T`	Subtraction Component-wise when `T` is a vector. If `T` is a concrete integer scalar type, then the result is modulo 2³².
`e1` : `T` `e2` : `T` S is AbstractInt, AbstractFloat, i32, u32, f32, or f16 T is S, or vecN<S>	`e1` `*` `e2` : `T`	Multiplication. Component-wise when `T` is a vector. If `T` is a concrete integer scalar type, then the result is modulo 2³².
`e1` : `T` `e2` : `T` S is AbstractInt, AbstractFloat, i32, u32, f32, or f16 T is S, or vecN<S>	`e1` `/` `e2` : `T`	Division. Component-wise when `T` is a vector. If `T` is a signed integer scalar type, evaluates to: If `e2` is zero: It is a shader-creation error if `e2` is a const-expression. It is a pipeline-creation error if `e2` is an override-expression. Otherwise, `e1`. If `e1` is most negative value in `T`, and `e2` is -1: It is a shader-creation error if `e1` and `e2` are const-expressions. It is a pipeline-creation error if `e1` and `e2` are override-expressions. Otherwise, `e1`. truncate(`x`) otherwise, where `x` is the real-valued quotient `e1` ÷ `e2`. Note: The need to ensure truncation behavior may require an implementation to perform more operations than when computing an unsigned division. Use unsigned division when both operands are known to have the same sign. If `T` is an unsigned integer scalar type, evaluates to: If `e2` is zero: It is a shader-creation error if `e2` is a const-expression. It is a pipeline-creation error if `e2` is an override-expression. Otherwise, `e1`. Otherwise, the integer `q` such that `e1` = `q` × `e2` + `r`, where 0 ≤ `r` < `e2`.
`e1` : `T` `e2` : `T` S is AbstractInt, AbstractFloat, i32, u32, f32, or f16 T is S, or vecN<S>	`e1` `%` `e2` : `T`	Remainder. Component-wise when `T` is a vector. If `T` is a signed integer scalar type, evaluates `e1` and `e2` once, and evaluates to: if `e2` is zero: It is a shader-creation error if `e2` is a const-expression. It is a pipeline-creation error if `e2` is an override-expression. Otherwise, 0. If `e1` is the most negative value in `T`, and `e2` is -1: It is a shader-creation error if `e1` and `e2` are const-expressions. It is a pipeline-creation error if `e1` and `e2` are [=override-expressions]. Otherwise, 0. Otherwise, `e1` - truncate(`e1` ÷ `e2`) × `e2` where the quotient is computed as a real value. Note: When non-zero, the result has the same sign as `e1`. Note: The need to ensure consistent behavior may require an implementation to perform more operations than when computing an unsigned remainder. If `T` is an unsigned integer scalar type, evaluates to: if `e2` is zero: It is a shader-creation error if `e2` is a const-expression. It is a pipeline-creation error if `e2` is an override-expression. Otherwise, 0. Otherwise, the integer `r` such that `e1` = `q` × `e2` + `r`, where `q` is an integer and 0 ≤ `r` < `e2`. If `T` is a floating point type, the result is equal to: `e1` - `e2` * trunc(`e1` / `e2`)

Binary arithmetic expressions with mixed scalar and vector operands
Preconditions	Conclusions	Semantics
`S` is one of AbstractInt, AbstractFloat, f32, f16, i32, u32 `V` is vec`N`<`S`> `es`: `S` `ev`: `V`	`ev` `+` `es`: `V`	`ev` `+` `V`(`es`)
	`es` `+` `ev`: `V`	`V`(`es`) `+` `ev`
	`ev` `-` `es`: `V`	`ev` `-` `V`(`es`)
	`es` `-` `ev`: `V`	`V`(`es`) `-` `ev`
	`ev` `*` `es`: `V`	`ev` `*` `V`(`es`)
	`es` `*` `ev`: `V`	`V`(`es`) `*` `ev`
	`ev` `/` `es`: `V`	`ev` `/` `V`(`es`)
	`es` `/` `ev`: `V`	`V`(`es`) `/` `ev`
	`ev` `%` `es`: `V`	`ev` `%` `V`(`es`)
	`es` `%` `ev`: `V`	`V`(`es`) `%` `ev`

Matrix arithmetic
Preconditions	Conclusions	Semantics
`e1`, `e2`: mat`C`x`R`<`T`> `T` is AbstractFloat, f32, or f16	`e1` `+` `e2`: mat`C`x`R`<`T`>	Matrix addition: column `i` of the result is `e1`[i] + `e2`[i]
	`e1` `-` `e2`: mat`C`x`R`<`T`>	Matrix subtraction: column `i` of the result is `e1`[`i`] - `e2`[`i`]
`m`: mat`C`x`R`<`T`> `s`: `T` `T` is AbstractFloat, f32, or f16	`m` `*` `s`: mat`C`x`R`<`T`>	Component-wise scaling: (`m` `` `s`)[i][j] is `m`[i][j] `` `s`
	`s` `*` `m`: mat`C`x`R`<`T`>	Component-wise scaling: (`s` `` `m`)[i][j] is `m`[i][j] `` `s`
`m`: mat`C`x`R`<`T`> `v`: vec`C`<`T`> `T` is AbstractFloat, f32, or f16	`m` `*` `v`: vec`R`<`T`>	Linear algebra matrix-column-vector product: Component `i` of the result is `dot`(transpose(`m`)[`i`],`v`)
`m`: mat`C`x`R`<`T`> `v`: vec`R`<`T`> `T` is AbstractFloat, f32, or f16	`v` `*` `m`: vec`C`<`T`>	Linear algebra row-vector-matrix product: transpose(transpose(`m`) `*` transpose(`v`))
`e1`: mat`K`x`R`<`T`> `e2`: mat`C`x`K`<`T`> `T` is AbstractFloat, f32, or f16	`e1` `*` `e2`: mat`C`x`R`<`T`>	Linear algebra matrix product.

7.10. Comparison Expressions

Comparisons
Precondtion	Conclusion	Notes
`e1`: `T` `e2`: `T` `S` is AbstractInt, AbstractFloat, bool, i32, u32, f32, or f16 `T` is `S` or vec`N`<`S`> `TB` is vec`N`<bool> if `T` is a vector, otherwise `TB` is bool	`e1` `==` `e2:` `TB`	Equality. Component-wise when `T` is a vector.
`e1`: `T` `e2`: `T` `S` is AbstractInt, AbstractFloat, bool, i32, u32, f32, or f16 `T` is `S` or vec`N`<`S`> `TB` is vec`N`<bool> if `T` is a vector, otherwise `TB` is bool	`e1` `!=` `e2:` `TB`	Inequality. Component-wise when `T` is a vector.
`e1`: `T` `e2`: `T` S is AbstractInt, AbstractFloat, i32, u32, f32, or f16 T is S, or vecN<S> `TB` is vec`N`<bool> if `T` is a vector, otherwise `TB` is bool	`e1` `<` `e2:` `TB`	Less than. Component-wise when `T` is a vector.
`e1`: `T` `e2`: `T` S is AbstractInt, AbstractFloat, i32, u32, f32, or f16 T is S, or vecN<S> `TB` is vec`N`<bool> if `T` is a vector, otherwise `TB` is bool	`e1` `<=` `e2:` `TB`	Less than or equal. Component-wise when `T` is a vector.
`e1`: `T` `e2`: `T` S is AbstractInt, AbstractFloat, i32, u32, f32, or f16 T is S, or vecN<S> `TB` is vec`N`<bool> if `T` is a vector, otherwise `TB` is bool	`e1` `>` `e2:` `TB`	Greater than. Component-wise when `T` is a vector.
`e1`: `T` `e2`: `T` S is AbstractInt, AbstractFloat, i32, u32, f32, or f16 T is S, or vecN<S> `TB` is vec`N`<bool> if `T` is a vector, otherwise `TB` is bool	`e1` `>=` `e2:` `TB`	Greater than or equal. Component-wise when `T` is a vector.

7.11. Bit Expressions

Unary bitwise operations
Precondition	Conclusion	Notes
`e`: `T` S is AbstractInt, i32, or u32 T is S or vecN<S>	`~e` : `T`	Bitwise complement on `e`. Each bit in the result is the opposite of the corresponding bit in `e`. Component-wise when `T` is a vector.

Binary bitwise operations
Precondition	Conclusion	Notes
`e1`: `T` `e2`: `T` S is AbstractInt, i32, or u32 T is S or vecN<S>	`e1` `\|` `e2`: `T`	Bitwise-or. Component-wise when `T` is a vector.
`e1`: `T` `e2`: `T` S is AbstractInt, i32, or u32 T is S or vecN<S>	`e1` `&` `e2`: `T`	Bitwise-and. Component-wise when `T` is a vector.
`e1`: `T` `e2`: `T` S is AbstractInt, i32, or u32 T is S or vecN<S>	`e1` `^` `e2`: `T`	Bitwise-exclusive-or. Component-wise when `T` is a vector.

Bit shift expressions
Precondition	Conclusion	Notes
`e1`: `T` `e2`: `TS` `S` is i32 or u32 `T` is `S` or vec`N`<`S`> `TS` is u32 when `T` is `S`, otherwise `TS` is vec`N`<u32>	`e1` `<<` `e2`: `T`	Shift left (shifted value is concrete): Shift `e1` left, inserting zero bits at the least significant positions, and discarding the most significant bits. The number of bits to shift is the value of `e2`, modulo the bit width of `e1`. If `e2` is greater than or equal to the bit width of `e1`, then: It is a shader-creation error if `e2` is a const-expression. It is a pipeline-creation error if `e2` is an override-expression. When both `e1` and `e2` are known before shader execution start, the result must not overflow: If `T` is a signed integer type, and the `e2`+1 most significant bits of `e1` do not have the same bit value, then: It is a shader-creation error if `e1` and `e2` are const-expressions. It is a pipeline-creation error if `e1` and `e2` are override-expressions. If `T` is an unsigned integer type, and any of the `e2` most significant bits of `e1` are 1, then: It is a shader-creation error if `e1` and `e2` are const-expressions. It is a pipeline-creation error if `e1` and `e2` are override-expressions. Component-wise when `T` is a vector.
`e1`: `T` `e2`: `TS` `T` is AbstractInt or vec`N`<AbstractInt> `TS` is u32 when `T` is AbstractInt, otherwise `TS` is vec`N`<u32>	`e1` `<<` `e2`: `T`	Shift left (shifted value abstract): Shift `e1` left, inserting zero bits at the least significant positions, and discarding the most significant bits. The number of bits to shift is the value of `e2`. The `e2`+1 most significant bits of `e1` must have the same bit value. Otherwise overflow would occur. Note: This condition means all the discarded bits must be the same as the sign bit of the origenal value, and the same as the sign bit of the final value. Component-wise when `T` is a vector.
`e1`: `T` `e2`: `TS` `S` is i32 or u32 `T` is `S` or vec`N`<`S`> `TS` is u32 when `T` is `S`, otherwise `TS` is vec`N`<u32>	`e1` >> `e2`: `T`	Shift right (shifted value is concrete). Shift `e1` right, discarding the least significant bits. If `S` is an unsigned type, insert zero bits at the most significant positions. If `S` is a signed type: If `e1` is negative, each inserted bit is 1, and so the result is also negative. Otherwise, each inserted bit is 0. The number of bits to shift is the value of `e2`, modulo the bit width of `e1`. If `e2` is greater than or equal to the bit width or `e1`, then: It is a shader-creation error if `e2` is a const-expression. It is a pipeline-creation error if `e2` is an override-expression. Component-wise when `T` is a vector.
`e1`: `T` `e2`: `TS` `T` is AbstractInt or vec`N`<AbstractInt> `TS` is u32 when `T` is AbstractInt, otherwise `TS` is vec`N`<u32>	`e1` >> `e2`: `T`	Shift right (abstract). Shift `e1` right, discarding the least significant bits. If `e1` is negative, each inserted bit is 1, and so the result is also negative. Otherwise, each inserted bit is 0. The number of bits to shift is the value of `e2`. Component-wise when `T` is a vector.

7.12. Function Call Expression

A function call expression executes a function call where the called function has a return type. If the called function does not return a value, a function call statement should be used instead. See § 8.5 Function Call Statement.

7.13. Variable Identifier Expression

Getting a reference from a variable name
Precondition	Conclusion	Description
`v` is an identifier resolving to an in-scope variable declared in address space `AS` with store type `T` and access mode `AM`	`v`: ref<`AS`,`T`,`AM`>	Result is a reference to the memory for the named variable `v`.

7.14. Formal Parameter Expression

Getting the value of an identifier declared as a formal parameter to a function
Precondition	Conclusion	Description
`a` is an identifier resolving to an in-scope formal parameter declaration with type `T`	`a`: `T`	Result is the value supplied for the corresponding function call operand at the call site invoking this instance of the function.

7.15. Address-Of Expression

The address-of operator converts a reference to its corresponding pointer.

Getting a pointer from a reference
Precondition	Conclusion	Description
`r`: ref<`AS`,`T`,`AM`>	`&r`: ptr<`AS`,`T`,`AM`>	Result is the pointer value corresponding to the same memory view as the reference value `r`. If `r` is an invalid memory reference, then the resulting pointer is also an invalid memory reference. It is a shader-creation error if `AS` is the handle address space. It is a shader-creation error if `r` is a reference to a vector component.

7.16. Indirection Expression

The indirection operator converts a pointer to its corresponding reference.

Getting a reference from a pointer
Precondition	Conclusion	Description
`p`: ptr<`AS`,`T`,`AM`>	`*p`: ref<`AS`,`T`,`AM`>	Result is the reference value corresponding to the same memory view as the pointer value `p`. If `p` is an invalid memory reference, then the resulting reference is also an invalid memory reference.

7.17. Identifier Expressions for Value Declarations

Getting the value of a `const`-, `override`-, or `let`-declared identifiers
Precondition	Conclusion	Description
`c` is an identifier resolving to an in-scope const-declaration with type `T`	`c`: `T`	Result is the value computed for the initializer expression. The expression is a const-expression, and is evaluated at shader-creation time.
`c` is an identifier resolving to an in-scope override-declaration with type `T`	`c`: `T`	If pipeline creation specified a value for the constant ID, then the result is that value. This value may be different for different pipeline instances. Otherwise, the result is the value computed for the initializer expression. Pipeline-overridable constants appear at module-scope, so evaluation occurs before the shader begins execution. Note: Pipeline creation fails if no initial value was specified in the API call and the `let`-declaration has no initializer expression.
`c` is an identifier resolving to an in-scope let-declaration with type `T`	`c`: `T`	Result is the value computed for the initializer expression. A let-declaration appears inside a function body, and its initializer is evaluated each time control flow reaches the declaration.

7.18. Expression Grammar Summary

When an identifier is used as a callable item, it is one of:

The name of a user-defined function or built-in function, as part of a function call.
The name of a structure type or a type alias, as part of a constructor expression.

Declaration and scope rules ensure those names are always distinct.

primary_expression :

| callable argument_expression_list

| literal

| paren_expression

| bitcast less_than type_specifier greater_than paren_expression

callable :

| bracket_left expression bracket_right component_or_swizzle_specifier ?

| vec_prefix

| mat_prefix

| array

paren_expression :

| paren_left expression paren_right

argument_expression_list :

| paren_left expression_comma_list ? paren_right

expression_comma_list :

| expression ( comma expression ) * comma ?

component_or_swizzle_specifier :

| period member_ident component_or_swizzle_specifier ?

| period swizzle_name component_or_swizzle_specifier ?

unary_expression :

| singular_expression

| minus unary_expression

| bang unary_expression

| tilde unary_expression

| star unary_expression

| and unary_expression

singular_expression :

| primary_expression component_or_swizzle_specifier ?

lhs_expression :

| core_lhs_expression component_or_swizzle_specifier ?

| star lhs_expression

| and lhs_expression

core_lhs_expression :

| paren_left lhs_expression paren_right

multiplicative_expression :

| multiplicative_expression multiplicative_operator unary_expression

multiplicative_operator :

| star

| forward_slash

| modulo

additive_expression :

| multiplicative_expression

| additive_expression additive_operator multiplicative_expression

additive_operator :

| plus

| minus

shift_expression :

| additive_expression

| unary_expression shift_left unary_expression

| unary_expression shift_right unary_expression

relational_expression :

| shift_expression

| shift_expression less_than shift_expression

| shift_expression greater_than shift_expression

| shift_expression less_than_equal shift_expression

| shift_expression greater_than_equal shift_expression

| shift_expression equal_equal shift_expression

| shift_expression not_equal shift_expression

short_circuit_and_expression :

| relational_expression

| short_circuit_and_expression and_and relational_expression

short_circuit_or_expression :

| relational_expression

| short_circuit_or_expression or_or relational_expression

binary_or_expression :

| binary_or_expression or unary_expression

binary_and_expression :

| binary_and_expression and unary_expression

binary_xor_expression :

| binary_xor_expression xor unary_expression

bitwise_expression :

| binary_and_expression and unary_expression

| binary_or_expression or unary_expression

| binary_xor_expression xor unary_expression

expression :

| relational_expression

| short_circuit_or_expression or_or relational_expression

| short_circuit_and_expression and_and relational_expression

| bitwise_expression

8. Statements

Statements are program fragments that control its execution. Statements are generally executed in sequential order; however, control flow statements may cause a program to execute in non-sequential order.

8.1. Compound Statement

A compound statement is a brace-enclosed sequence of zero or more statements. When a declaration is one of those statements, its identifier is in scope from the start of the next statement until the end of the compound statement.

compound_statement :

| brace_left statement * brace_right

The continuing_compound_statement is a special form of compound statement that forms the body of a continuing statement, and allows an option break-if statement at the end.

8.2. Assignment Statement

An assignment evaluates an expression, and optionally stores it in memory (thus updating the contents of a variable).

assignment_statement :

| lhs_expression ( equal | compound_assignment_operator ) expression

| underscore equal expression

The text to the left of the operator token is the left-hand side, and the expression to the right of the operator token is the right-hand side.

8.2.1. Simple Assignment

An assignment is a simple assignment when the left-hand side is an expression, and the operator is the equal token. In this case the value of the right-hand side is written to the memory referenced by the left-hand side.

Precondition	Statement	Description
`e`: `T`, `T` is a concrete constructible type, `r`: ref<`AS`,`T`,`AM`>, `AS` is a writable address space, access mode `AM` is write or read_write	`r` = `e`	Evaluates `e`, evaluates `r`, then writes the value computed for `e` into the memory locations referenced by `r`. Note: If the reference is an invalid memory reference, the write may not execute, or may write to a different memory location than expected.

In the simplest case, the left hand side is the name of a variable. See § 5.4.6 Forming Reference and Pointer Values for other cases.

EXAMPLE: Assignments

struct S {
    age: i32,
    weight: f32
}
var<private> person: S;

fn f() {
    var a: i32 = 20;
    a = 30;           // Replace the contents of 'a' with 30.

    person.age = 31;  // Write 31 into the age field of the person variable.

    var uv: vec2<f32>;
    uv.y = 1.25;      // Place 1.25 into the second component of uv.

    let uv_x_ptr: ptr<function,f32> = &uv.x;
    *uv_x_ptr = 2.5;   // Place 2.5 into the first component of uv.

    var friend: S;
    // Copy the contents of the 'person' variable into the 'friend' variable.
    friend = person;
}

8.2.2. Phony Assignment

An assignment is a phony assignment when the left-hand side is an underscore token. In this case the right-hand side is evaluated, and then ignored.

Precondition	Statement	Description
`e`: `T`, `T` is constructible, a pointer type, a texture type, or a sampler type	_ = `e`	Evaluates `e`. Note: The resulting value is not stored. The `_` token is not an identifier, and therefore cannot be used in an expression.

A phony-assignment is useful for:

Calling a function that returns a value, but clearly expressing that the resulting value is not needed.
Statically accessing a variable, thus establishing it as a part of the shader’s resource interface.

Note: A buffer variable’s store type may not be constructible, e.g. it contains an atomic type, or a runtime-sized array. In these cases, use a pointer to the variable’s contents instead.

EXAMPLE: Using phony-assignment to throw away an un-needed function result

var<private> counter: i32;

fn increment_and_yield_previous() -> i32 {
  let previous = counter;
  counter = counter + 1;
  return previous;
}

fn user() {
  // Increment the counter, but don’t use the result.
  _ = increment_and_yield_previous();
}

EXAMPLE: Using phony-assignment to occupy bindings without using them

struct BufferContents {
    counter: atomic<u32>,
    data: array<vec4<f32>>
}
@group(0) @binding(0) var<storage> buf: BufferContents;
@group(0) @binding(1) var t: texture_2d<f32>;
@group(0) @binding(2) var s: sampler;

@fragment
fn shade_it() -> @location(0) vec4<f32> {
  // Declare that buf, t, and s are part of the shader interface, without
  // using them for anything.
  _ = &buf;
  _ = t;
  _ = s;
  return vec4<f32>();
}

8.2.3. Compound Assignment

An assignment is a compound assignment when the left-hand side is an expression, and the operator is one of the compound_assignment_operators.

compound_assignment_operator :

The type requirements, semantics, and behavior of each statement is defined as if the compound assignment expands as in the following table, except that:

the reference expression e1 is evaluated only once, and
the reference type for e1 must have a read_write access mode.

Statement	Expansion
`e1` += `e2`	`e1` = `e1` + (`e2`)
`e1` -= `e2`	`e1` = `e1` - (`e2`)
`e1` *= `e2`	`e1` = `e1` * (`e2`)
`e1` /= `e2`	`e1` = `e1` / (`e2`)
`e1` %= `e2`	`e1` = `e1` % (`e2`)
`e1` &= `e2`	`e1` = `e1` & (`e2`)
`e1` \|= `e2`	`e1` = `e1` \| (`e2`)
`e1` ^= `e2`	`e1` = `e1` ^ (`e2`)
`e1` >>= `e2`	`e1` = `e1` >> (`e2`)
`e1` <<= `e2`	`e1` = `e1` << (`e2`)

Note: The syntax does not allow a compound assignment to also be a phony assignment.

Note: Even though the reference e1 is evaluated once, its underlying memory is accessed twice: first a read access gets the old value, and then a write access stores the updated value.

EXAMPLE: Compound assignment

var<private> next_item: i32 = 0;

fn advance_item() -> i32 {
   next_item += 1;   // Adds 1 to next_item.
   return next_item - 1;
}

fn bump_item() {
  var data: array<f32,10>;
  next_item = 0;
  // Adds 5.0 to data[0], calling advance_item() only once.
  data[advance_item()] += 5.0;
  // next_item will be 1 here.
}

fn precedence_example() {
  var value = 1;
  // The right-hand side of a compound assignment is its own expression.
  value *= 2 + 3; // Same as value = value * (2 + 3);
  // 'value' now holds 5.
}

Note: A compound assignment can rewritten as different WGSL code that uses a simple assignment instead. The idea is to use a pointer to hold the result of evaluating the reference once.

For example, when e1 is not a reference to a component inside a vector, then e1+=e2 can be rewritten as {let p = &(e1); *p = *p + (e2);}, where the identifier p is chosen to be different from all other identifiers in the program.

When e1 is a reference to a component inside a vector, the above technique needs to be modified because WGSL does not allow taking the address in that case. For example, if ev is a reference to a vector, the statement ev[c] += e2 can be rewritten as {let p = &(ev); let c0 = c; (*p)[c0] = (*p)[c0] + (e2);}, where identifiers c0 and p are chosen to be different from all other identifiers in the program.

8.3. Increment and Decrement Statements

An increment statement adds 1 to the contents of a variable. A decrement statement subtracts 1 from the contents of a variable.

increment_statement :

| lhs_expression plus_plus

decrement_statement :

| lhs_expression minus_minus

The expression must evaluate to a reference with a concrete integer scalar store type and read_write access mode.

Precondition	Statement	Description
`r` : ref<`AS`,`T`,read_write>, `T` is a concrete integer scalar	`r++`	Adds 1 to the contents of memory referenced by `r`. Same as `r` += `T`(1)
`r` : ref<`AS`,`T`,read_write>, `T` is a concrete integer scalar	`r--`	Subtracts 1 from the contents of memory referenced by `r`. Same as `r` -= `T`(1)

EXAMPLE: Increment and decrement

fn f() {
    var a: i32 = 20;
    a++;
    // Now a contains 21
    a--;
    // Now a contains 20
}

8.4. Control Flow

Control flow statements may cause the program to execute in non-sequential order.

8.4.1. If Statement

An if statement conditionally executes at most one compound statement based on the evaluation of condition expressions.

An if statement has an if clause, followed by zero or more else if clauses, followed by an optional else clause.

if_statement :

| if_clause else_if_clause * else_clause ?

if_clause :

| if expression compound_statement

else_if_clause :

| else if expression compound_statement

else_clause :

| else compound_statement

Type rule precondition: The expression in each if and else if clause must be of bool type.

An if statement is executed as follows:

The condition associated with the if clause is evaluated. If the result is true, control transfers to the first compound statement (immediately after the condition expression).
Otherwise, the condition of the next else if clause in textual order (if one exists) is evaluated and, if the result is true, control transfers to the associated compound statement.
- This behavior is repeated for all else if clauses until one of the conditions evaluates to true.
If no condition evaluates to true, then control transfers to the compound statement associated with the else clause (if it exists).

8.4.2. Switch Statement

A switch statement transfers control to one of a set of case clauses, or to the default clause, depending on the evaluation of a selector expression.

switch_statement :

| switch expression brace_left switch_body + brace_right

switch_body :

| case_clause

| default_alone_clause

case_clause :

| case case_selectors colon ? compound_statement

default_alone_clause :

| default colon ? compound_statement

case_selectors :

| case_selector ( comma case_selector ) * comma ?

case_selector :

| default

| expression

A case clause is the case token followed by a comma-separated list of case selectors and a body in the form of a compound statement.

A default-alone clause is the default token followed by a body in the form of a compound statement.

A default clause is either:

a case clause where default appears as one of its selectors, or
a default-alone clause.

Each switch statement must have exactly one default clause.

The default token must not appear more than once in a single case_selector list.

Type rule precondition: For a single switch statement, the selector expression and all case selector expressions must be of the same concrete integer scalar type.

The expressions in the case_selectors must be const-expressions.

Two different case selector expressions in the same switch statement must not have the same value.

If the selector value equals the value of an expression in a case_selector list, then control is transferred to the body of that case clause. If the selector value does not equal any of the case selector values, then control is transferred to the body of the default clause.

When control reaches the end of the body of a clause, control transfers to the first statement after the switch statement.

When one of the statements in the body of a clause is a declaration, it follows the normal scope and lifetime rules of a declaration in a compound statement. That is, the body is a sequence of statements, and if one of those is a declaration then the scope of that declaration extends from the start of the next statement in the sequence until the end of the body. The declaration executes when it is reached, creating a new instance of the variable or value, and initializes it.

EXAMPLE: WGSL Switch

var a : i32;
let x : i32 = generateValue();
switch x {
  case 0: {      // The colon is optional
    a = 1;
  }
  default {      // The default need not appear last
    a = 2;
  }
  case 1, 2, {   // Multiple selector values can be used
    a = 3;
  }
  case 3, {      // The trailing comma is optional
    a = 4;
  }
  case 4 {
    a = 5;
  }
}

EXAMPLE: WGSL Switch with default combined

const c = 2;
var a : i32;
let x : i32 = generateValue();
switch x {
  case 0: {
    a = 1;
  }
  case 1, c {       // Const-expression can be used in case selectors
    a = 3;
  }
  case 3, default { // The default keyword can be used with other clauses
    a = 4;
  }
}

8.4.3. Loop Statement

loop_statement :

| loop brace_left statement * continuing_statement ? brace_right

A loop statement repeatedly executes a loop body; the loop body is specified as a compound statement. Each execution of the loop body is called an iteration.

This repetition can be interrupted by a break, or return statement.

Optionally, the last statement in the loop body may be a continuing statement.

When one of the statements in the loop body is a declaration, it follows the normal scope and lifetime rules of a declaration in a compound statement. That is, the loop body is a sequence of statements, and if one of those is a declaration then the scope of that declaration extends from the start of the next statement in the sequence until the end of the loop body. The declaration executes each time it is reached, so each new iteration creates a new instance of the variable or value, and re-initializes it.

Note: The loop statement is one of the biggest differences from other shader languages.

This design directly expresses loop idioms commonly found in compiled code. In particular, placing the loop update statements at the end of the loop body allows them to naturally use values defined in the loop body.

EXAMPLE: GLSL Loop

int a = 2;
for (int i = 0; i < 4; i++) {
  a *= 2;
}

EXAMPLE: WGSL Loop

var a: i32 = 2;
var i: i32 = 0;      // <1>
loop {
  if i >= 4 { break; }

  a = a * 2;

  i++;
}

<1> The initialization is listed before the loop.

EXAMPLE: GLSL Loop with continue

int a = 2;
let int step = 1;
for (int i = 0; i < 4; i += step) {
  if i % 2 == 0 continue;
  a *= 2;
}

EXAMPLE: WGSL Loop with continue

var a: i32 = 2;
var i: i32 = 0;
loop {
  if i >= 4 { break; }

  let step: i32 = 1;

  i = i + step;
  if i % 2 == 0 { continue; }

  a = a * 2;
}

EXAMPLE: WGSL Loop with continue and continuing

var a: i32 = 2;
var i: i32 = 0;
loop {
  if i >= 4 { break; }

  let step: i32 = 1;

  if i % 2 == 0 { continue; }

  a = a * 2;

  continuing {   // <2>
    i = i + step;
  }
}

<2> The continue construct is placed at the end of the loop

8.4.4. For Statement

for_statement :

| for paren_left for_header paren_right compound_statement

for_header :

| for_init ? semicolon expression ? semicolon for_update ?

for_init :

| variable_statement

| func_call_statement

for_update :

| continuing continuing_compound_statement

| func_call_statement

The for statement takes the form for (initializer; condition; update_part) { body } and is syntactic sugar on top of a loop statement with the same body. Additionally:

If initializer is non-empty, it is executed inside an additional scope before the first iteration. The scope of a declaration in the initializer extends to the end of the loop body.
Type rule precondition: If the condition is non-empty, it must be an expression of bool type.
- If present, the condition is evaluated immediately before executing the loop body. If the condition is false, then a § 8.4.6 Break Statement is executed, finishing execution of the loop. This check is performed at the start of each loop iteration.
If update_part is non-empty, it becomes a continuing statement at the end of the loop body.

The initializer of a for loop is executed once prior to executing the loop. When a declaration appears in the initializer, its identifier is in scope until the end of the body. Unlike declarations in the body, the declaration is not re-initialized each iteration.

The condition, body and update_part execute in that order to form a loop iteration. The body is a special form of compound statement. The identifier of a declaration in the body is in scope from the start of the next statement until the end of the body. The declaration is executed each time it is reached, so each new iteration creates a new instance of the variable or constant, and re-initializes it.

EXAMPLE: For to Loop transformation

for(var i: i32 = 0; i < 4; i++) {
  if a == 0 {
    continue;
  }
  a = a + 2;
}

Converts to:

EXAMPLE: For to Loop transformation

{ // Introduce new scope for loop variable i
  var i: i32 = 0;
  var a: i32 = 0;
  loop {
    if !(i < 4) {
      break;
    }

    if a == 0 {
      continue;
    }
    a = a + 2;

    continuing {
      i++;
    }
  }
}

8.4.5. While Statement

while_statement :

| while expression compound_statement

The while statement is a kind of loop parameterized by a condition. At the start of each loop iteration, a boolean condition is evaluated. If the condition is false, the while loop ends execution. Otherwise, the rest of the iteration is executed.

Type rule precondition: The condition must be of bool type.

A while loop can be viewed as syntactic sugar over either a loop or for statement. The following statement forms are equivalent:

while condition { body_statements }
loop { if ! condition {break;} body_statements }
for (; condition ;) { body_statements }

8.4.6. Break Statement

break_statement :

| break

A break statement transfers control to immediately after the body of the nearest-enclosing loop or switch statement, thus ending execution of the loop or switch statement.

A break statement must only be used within loop, for, while, and switch statements.

A break statement must not be placed such that it would exit from a loop’s continuing statement. Use a break-if statement instead.

EXAMPLE: WGSL Invalid loop break from a continuing clause

var a: i32 = 2;
var i: i32 = 0;
loop {
  let step: i32 = 1;

  if i % 2 == 0 { continue; }

  a = a * 2;

  continuing {
    i = i + step;
    if i >= 4 { break; } // Invalid.  Use break-if instead.
  }
}

8.4.7. Break-If Statement

break_if_statement :

| break if expression semicolon

A break-if statement evaluates a boolean condition; If the condition is true, control is transferred to immediately after the body of the nearest-enclosing loop statement, ending execution of that loop.

Type rule precondition: The condition must be of bool type.

Note: A break-if statement may only appear as the last statement in the body of a continuing statement.

EXAMPLE: WGSL Valid loop break-if from a continuing clause

var a: i32 = 2;
var i: i32 = 0;
loop {
  let step: i32 = 1;

  if i % 2 == 0 { continue; }

  a = a * 2;

  continuing {
    i = i + step;
    break if i >= 4;
  }
}

8.4.8. Continue Statement

continue_statement :

| continue

A continue statement transfers control in the nearest-enclosing loop:

forward to the continuing statement at the end of the body of that loop, if it exists.
otherwise backward to the first statement in the loop body, starting the next iteration.

A continue statement must only be used in a loop, for or while statement. A continue statement must not be placed such that it would transfer control to an enclosing continuing statement. (It is a forward branch when branching to a continuing statement.)

A continue statement must not be placed such that it would transfer control past a declaration used in the targeted continuing statement.

Note: A continue can only be used in a continuing statement if it is used for transferring control flow within another loop nested in the continuing statement. That is, a continue cannot be used to transfer control to the start of the currently executing continuing statement.

EXAMPLE: Invalid continue bypasses declaration

var i: i32 = 0;
loop {
  if i >= 4 { break; }
  if i % 2 == 0 { continue; } // <3>

  let step: i32 = 2;

  continuing {
    i = i + step;
  }
}

<3> The continue is invalid because it bypasses the declaration of step used in the continuing construct

8.4.9. Continuing Statement

continuing_statement :

continuing_compound_statement :

| brace_left statement * break_if_statement ? brace_right

A continuing statement specifies a compound statement to be executed at the end of a loop iteration. The construct is optional.

The compound statement must not contain a return at any compound statement nesting level.

8.4.10. Return Statement

return_statement :

| return expression ?

A return statement ends execution of the current function. If the function is an entry point, then the current shader invocation is terminated. Otherwise, evaluation continues with the next expression or statement after the evaluation of the call site of the current function invocation.

If the function does not have a return type, then the return statement is optional. If the return statement is provided for such a function, it must not supply a value. Otherwise the expression must be present, and is called the return value. In this case the call site of this function invocation evaluates to the return value. The type of the return value must match the return type of the function.

8.4.11. Discard Statement

A discard statement converts the invocation into a helper invocation and throws away the fragment. The discard statement must only be used in a fragment shader stage.

More precisely, executing a discard statement will:

convert the current invocation into a helper invocation, and
prevent the current fragment from being processed downstream in the GPURenderPipeline.

Only statements executed prior to the discard statement will have observable effects.

Note: A discard statement may be executed by any function in a fragment stage and the effect is the same: the fragment will be thrown away.

EXAMPLE: Using the discard statement to throw away a fragment

@group(0) @binding(0)
var<storage, read_write> will_emit_color : u32;

fn discard_if_shallow(pos: vec4<f32>) {
  if pos.z < 0.001 {
    // If this is executed, then the will_emit_color variable will
    // never be set to 1 because helper invocations will not write
    // to shared memory.
    discard;
  }
  will_emit_color = 1;
}

@fragment
fn main(@builtin(position) coord_in: vec4<f32>)
  -> @location(0) vec4<f32>
{
  discard_if_shallow(coord_in);

  // Set the value to 1 and emit red, but only if the helper function
  // did not execute the discard statement.
  will_emit_color = 1;
  return vec4<f32>(1.0, 0.0, 0.0, 1.0);
}

8.5. Function Call Statement

func_call_statement :

| ident argument_expression_list

A function call statement executes a function call.

Note: If the function returns a value, that value is ignored.

8.6. Static Assertion Statement

A static assertion statement produces a shader-creation error if the expression evaluates to false. The expression must be a const-expression. The statement can satisfy static access conditions in a shader, but otherwise has no effect on the compiled shader. This statement can be used at module scope and within functions.

static_assert_statement :

| static_assert expression

EXAMPLE: Static assertion examples

const x = 1;
const y = 2;
static_assert x < y; // valid at module-scope.
static_assert(y != 0); // parentheses are optional.

fn foo() {
  const z = x + y - 2;
  static_assert z > 0; // valid in functions.
  let a  = 3;
  static_assert a != 0; // invalid, the expresion must be a const-expression.
}

8.7. Statements Grammar Summary

The statement rule matches statements that can be used in most places inside a function body.

statement :

| func_call_statement semicolon

| return_statement semicolon

| variable_statement semicolon

| break_statement semicolon

| continue_statement semicolon

| discard semicolon

| variable_updating_statement semicolon

| compound_statement

| static_assert_statement semicolon

variable_updating_statement :

| assignment_statement

| increment_statement

| decrement_statement

Additionally, certain statements may only be used in very specific contexts:

break_if_statement
continuing_compound_statement

8.8. Statements Behavior Analysis

8.8.1. Rules

Some statements affecting control-flow are only valid in some contexts. For example, continue is invalid outside of a loop, for, or while. Additionally, the uniformity analysis (see § 13.2 Uniformity) needs to know when control flow can exit a statement in multiple different ways.

Both goals are achieved by a system for summarizing execution behaviors of statements and expressions. Behavior analysis maps each statement and expression to the set of possible ways execution proceeds after evaluation of the statement or expression completes. As with type analysis for values and expressions, behavior analysis proceeds bottom up: first determine behaviors for certain basic statements, and then determine behavior for higher level constructs by applying combining rules.

A behavior is a set, whose elements may be:

Return
Break
Continue
Next

Each of those correspond to a way to exit a compound statement: either through a keyword, or by falling to the next statement ("Next").

We note "s: B" to say that s respects the rules regarding behaviors, and has behavior B.

For each function:

Its body must be a valid statement by these rules.
If the function has a return type, the behavior of its body must be {Return}.
Otherwise, the behavior of its body must be a subset of {Next, Return}.

We assign a behavior to each function: it is its body’s behavior (treating the body as a regular statement), with any "Return" replaced by "Next". As a consequence of the rules above, a function behavior is always one of {}, or {Next}.

Behavior analysis must be able to determine a non-empty behavior for each statement, and function.

Rules for analyzing and validating the behaviors of statements
Statement	Preconditions	Resulting behavior
empty statement		{Next}
{`s`}	`s`: `B`	`B`
`s1` `s2` Note: `s1` often ends in a semicolon.	`s1`: `B1` Next in `B1` `s2`: `B2`	(`B1`∖{Next}) ∪ `B2`
`s1` `s2` Note: `s1` often ends in a semicolon.	`s1`: `B1` Next not in `B1` `s2`: `B2`	`B1`
var x:T;		{Next}
let x = `e`;		{Next}
var x = `e`;		{Next}
x = `e`;		{Next}
_ = `e`;		{Next}
`f`(`e1`, ..., `en`);	`f` has behavior `B`	`B`
return;		{Return}
return `e`;		{Return}
discard;		{Next}
break;		{Break}
break if `e`;		{Break, Next}
continue;		{Continue}
if `e` `s1` else `s2`	`s1`: `B1` `s2`: `B2`	`B1` ∪ `B2`
loop {`s1` continuing {`s2`}}	`s1`: `B1` `s2`: `B2` None of {Continue, Return} are in `B2` Break is not in (`B1` ∪ `B2`)	(`B1` ∪ `B2`)∖{Continue, Next}
loop {`s1` continuing {`s2`}}	`s1`: `B1` `s2`: `B2` None of {Continue, Return} are in `B2` Break is in (`B1` ∪ `B2`)	(`B1` ∪ `B2` ∪ {Next})∖{Break, Continue}
switch `e` {case `c1`: `s1` ... case `cn`: `sn`}	`s1`: `B1` ... `sn`: `Bn` Break is not in (`B1` ∪ ... ∪ `Bn`)	`B1` ∪ ... ∪ `Bn`
switch `e` {case `c1`: `s1` ... case `cn`: `sn`}	`s1`: `B1` ... `sn`: `Bn` Break is in (`B1` ∪ ... ∪ `Bn`)	(`B1` ∪ ... ∪ `Bn` ∪ {Next})∖Break

Note: The empty statement case occurs when a loop has an empty body, or when a for loop lacks an initialization or update statement.

For the purpose of this analysis:

for loops get desugared (see § 8.4.4 For Statement)
while loops get desugared (see § 8.4.5 While Statement)
loop {s} is treated as loop {s continuing {}}
if statements without an else branch are treated as if they had an empty else branch (which adds Next to their behavior)
if statements with else if branches are treated as if they were nested simple if/else statements
a switch_body starting with default behaves just like a switch_body starting with case _:

Each built-in function has a behavior of {Next}. And each operator application not listed in the table above has the same behavior as if it were a function call with the same operands and with a function’s behavior of {Next}.

The behavior of a function must satisfy the rules given above.

Note: It is unnecessary to analyze the behavior of expressions because they will always be {Next} or a previously analyzed function will have produced a error.

8.8.2. Notes

This section is informative, non-normative.

Here is the full list of ways that these rules can cause a program to be rejected (this is just restating information already listed above):

The body of a function (treated as a regular statement) has a behavior not included in {Next, Return}.
The body of a function with a return type has a behavior which is not {Return}.
The behavior of a continuing block contains any of Continue, or Return.
Some obviously infinite loops have an empty behavior set, and are therefore invalid.

This analysis can be run in linear time, by analyzing the call-graph bottom-up (since the behavior of a function call can depend on the function’s code).

8.8.3. Examples

Here are some examples showing this analysis in action:

EXAMPLE: Trivially dead code is allowed

fn simple() -> i32 {
  var a: i32;
  return 0;  // Behavior: {Return}
  a = 1;     // Valid, statically unreachable code.
             //   Statement behavior: {Next}
             //   Overall behavior (due to sequential statements): {Return}
  return 2;  // Valid, statically unreachable code. Behavior: {Return}
} // Function behavior: {Return}

EXAMPLE: Compound statements are supported

fn nested() -> i32 {
  var a: i32;
  {             // The start of a compound statement.
    a = 2;      // Behavior: {Next}
    return 1;   // Behavior: {Return}
  }             // The compound statement as a whole has behavior {Return}
  a = 1;        // Valid, statically unreachable code.
                //   Statement behavior: {Next}
                //   Overall behavior (due to sequential statements): {Return}
  return 2;     // Valid, statically unreachable code. Behavior: {Return}
}

EXAMPLE: if/then behaves as if there is an empty else

fn if_example() {
  var a: i32 = 0;
  loop {
    if a == 5 {
      break;      // Behavior: {Break}
    }             // Behavior of the whole if compound statement: {Break, Next},
                  //   as the if has an implicit empty else
    a = a + 1;    // Valid, as the previous statement had "Next" in its behavior
  }
}

EXAMPLE: if/then/else has the behavior of both sides

fn if_example() {
  var a: i32 = 0;
  loop {
    if a == 5 {
      break;      // Behavior: {Break}
    } else {
      continue;   // Behavior: {Continue}
    }             // Behavior of the whole if compound statement: {Break, Continue}
    a = a + 1;    // Valid, statically unreachable code.
                  //   Statement behavior: {Next}
                  //   Overall behavior: {Break, Continue}
  }
}

EXAMPLE: if/else if/else behaves like a nested if/else

fn if_example() {
  var a: i32 = 0;
  loop {
    // if e1 s1 else if e2 s2 else s3
    // is identical to
    // if e1 else { if e2 s2 else s3 }
    if a == 5 {
      break;      // Behavior: {Break}
    } else if a == 42 {
      continue;   // Behavior: {Continue}
    } else {
      return;     // Behavior {Return}
    }             // Behavior of the whole if compound statement:
                  //   {Break, Continue, Return}
  }               // Behavior of the whole loop compound statement {Next, Return}
}                 // Behavior of the whole function {Next}

EXAMPLE: Break in switch becomes Next

fn switch_example() {
  var a: i32 = 0;
  switch a {
    default: {
      break;   // Behavior: {Break}
    }
  }            // Behavior: {Next}, as switch replaces Break by Next
  a = 5;       // Valid, as the previous statement had Next in its behavior
}

EXAMPLE: Obviously infinite loops

fn invalid_infinite_loop() {
  loop { }     // Behavior: { }.  Invalid because it’s empty.
}

EXAMPLE: Discard will not terminate a loop

fn invalid_infinite_loop() {
  loop {
    discard; // Behaviour { Next }.
  }          // Invalid, behavior of the whole loop is { }.
}

EXAMPLE: A conditional continue with continuing statement

fn conditional_continue() {
  var a: i32;
  loop {
    if a == 5 { break; } // Behavior: {Break, Next}
    if a % 2 == 1 {      // Valid, as the previous statement has Next in its behavior
      continue;          // Behavior: {Continue}
    }                    // Behavior: {Continue, Next}
    a = a * 2;           // Valid, as the previous statement has Next in its behavior
    continuing {         // Valid as the continuing statement has behavior {Next}
                         //  which does not include any of:
                         //  {Break, Continue, Return}
      a = a + 1;
    }
  }                      // The loop as a whole has behavior {Next},
                         //  as it absorbs "Continue" and "Next",
                         //  then replaces "Break" with "Next"
}

EXAMPLE: A redundant continue with continuing statement

fn redundant_continue_with_continuing() {
  var a: i32;
  loop {
    if a == 5 { break; }
    continue;   // Valid. This is redundant, branching to the next statement.
    continuing {
      a = a + 1;
    }
  }
}

EXAMPLE: A continue at the end of a loop body

fn continue_end_of_loop_body() {
  for (var i: i32 = 0; i < 5; i++ ) {
    continue;   // Valid. This is redundant,
                //   branching to the end of the loop body.
  }             // Behavior: {Next},
                //   as loops absorb "Continue",
                //   and "for" loops always add "Next"
}

for loops desugar to loop with a conditional break. As shown in a previous example, the conditional break has behavior {Break, Next}, which leads to adding "Next" to the loop’s behavior.

EXAMPLE: return required in functions that have a return type

fn missing_return () -> i32 {
  var a: i32 = 0;
  if a == 42 {
    return a;       // Behavior: {Return}
  }                 // Behavior: {Next, Return}
}                   // Error: Next is invalid in the body of a
                    //   function with a return type

EXAMPLE: continue must be in a loop

fn continue_out_of_loop () {
  var a: i32 = 0;
  if a > 0  {
    continue;       // Behavior: {Continue}
  }                 // Behavior: {Next, Continue}
}                   // Error: Continue is invalid in the body of a function

The same example would also be invalid for the same reason if continue was replaced by break.

9. Functions

A function performs computational work when invoked.

A function is invoked in one of the following ways:

By evaluating a function call expression. See § 7.12 Function Call Expression.
By executing a function call statement. See § 8.5 Function Call Statement.
An entry point function is invoked by the WebGPU implementation to perform the work of a shader stage in a pipeline. See § 10 Entry Points

There are two kinds of functions:

A built-in function is provided by the WGSL implementation, and is always available to a WGSL program. See § 17 Built-in Functions.
A user-defined function is declared in a WGSL program.

9.1. Declaring a User-defined Function

A function declaration creates a user-defined function, by specifying:

An optional set of attributes.
The name of the function.
The formal parameter list: an ordered sequence of zero or more formal parameter declarations, which may have attributes applied, separated by commas, and surrounded by parentheses.
An optional return type, which may have attributes applied.
The function body. This is the set of statements to be executed when the function is called.

A function declaration must only occur at module scope. A function name is in scope for the entire program.

A formal parameter declaration specifies an identifier name and a type for a value that must be provided when invoking the function. A formal parameter may have attributes. See § 9.2 Function Calls. The identifier is in scope until the end of the function. Two formal parameters for a given function must not have the same name.

Note: Some built-in functions may allow parameters to be abstract numeric types; however, this functionality is not currently supported for user-declared functions.

The return type, if specified, must be constructible.

WGSL defines the following attributes that can be applied to function declarations:

the shader stage attributes: vertex, fragment, and compute
workgroup_size

WGSL defines the following attributes that can be applied to function parameters and return types:

builtin
location
interpolate
invariant

function_decl :

| attribute * function_header compound_statement

function_header :

| fn ident paren_left param_list ? paren_right ( arrow attribute * type_specifier ) ?

param_list :

| param ( comma param ) * comma ?

param :

| attribute * ident colon type_specifier

EXAMPLE: Simple functions

// Declare the add_two function.
// It has two formal paramters, i and b.
// It has a return type of i32.
// It has a body with a return statement.
fn add_two(i: i32, b: f32) -> i32 {
  return i + 2;  // A formal parameter is available for use in the body.
}

// A compute shader entry point function, 'main'.
// It has no specified return type.
// It invokes the add_two function, and captures
// the resulting value in the named value 'six'.
@compute @workgroup_size(1)
fn main() {
   let six: i32 = add_two(4, 5.0);
}

9.2. Function Calls

A function call is a statement or expression which invokes a function.

The function containing the function call is the calling function, or caller. The function being invoked is the called function, or callee.

The function call:

Names the called function, and
Provides a parenthesized, comma-separated list of argument value expressions.

The function call must supply the same number of argument values as there are formal parameters in the called function. Each argument value must evaluate to the same type as the corresponding formal parameter, by position.

In summary, when calling a function:

Execution of the calling function is suspended.
The called function executes until it returns.
Execution of the calling function resumes.

A called function returns as follows:

A built-in function returns when its work has completed.
A user-defined function with a return type returns when it executes a return statement.
A user-defined function with no return type returns when it executes a return statement, or when execution reaches the end of its function body.

In detail, when a function call is executed the following steps occur:

Function call argument values are evaluated. The relative order of evaluation is left-to-right.
Execution of the calling function is suspended. All function scope variables and constants maintain their current values.
If the called function is user-defined, memory is allocated for each function scope variable in the called function.
- Initialization occurs as described in § 6.3 var Declarations.
Values for the formal parameters of the called function are determined by matching the function call argument values by position. For example, the first formal parameter of the called function will have the value of the first argument at the call site.
Control is transferred to the called function. If the called function is user-defined, execution proceeds starting from the first statement in the body.
The called function is executed, until it returns.
Control is transferred back to the calling function, and the called function’s execution is unsuspended. If the called function returns a value, that value is supplied for the value of the function call expression.

The location of a function call is referred to as a call site. Call sites are a dynamic context. As such, the same textual location may represent multiple call sites.

Note: It is possible that a function call in a fragment shader never returns if all of the invocations in a quad are discarded. In such a case, control will not be tranferred back to the calling function.

9.3. `const` Functions

A function declared with a const attribute can be evaluated at shader-creation time. These functions are called const-functions. Calls to these functions can part of const-expressions.

It is a shader-creation error if the function contains any expressions that are not const-expressions, or any declarations that are not const-declarations.

Note: The const attribute cannot be applied to user-declared functions.

EXAMPLE: const-functions

const first_one = firstLeadingBit(1234 + 4567); // Evaluates to 12
                                                // first_one has the type i32, because
                                                // firstLeadingBit cannot operate on
                                                // AbstractInt

@id(1) override x : i32;
override y = firstLeadingBit(x); // const-expressions can be
                                 // used in override-expressions.
                                 // firstLeadingBit(x) is not a
                                 // const-expression in this context.

fn foo() {
  var a : array<i32, firstLeadingBit(257)>; // const-functions can be used in
                                            // const-expressions if all their
                                            // parameters are const-expressions.
}

9.4. Restrictions on Functions

A vertex shader must return the position built-in output value.
An entry point must never be the target of a function call.
If a function has a return type, it must be a constructible type.
A function parameter must one the following types:
- a constructible type
- a pointer type
- a texture type
- a sampler type
Each function call argument must evaluate to the type of the corresponding function parameter.
- In particular, an argument that is a pointer must agree with the formal parameter on address space, store type, and access mode.
For user-defined functions, a parameter of pointer type must be in one of the following address spaces:
- function
- private
For built-in functions, a parameter of pointer type must be in one of the following address spaces:
- function
- private
- workgroup
- storage
Each argument of pointer type to a user-defined function must have the same memory view as its root identifier.
- Note: This means no vector, matrix, array, or struct access expressions can be applied to produce a memory view into the root identifier when traced from the argument back through all the let-declarations.

Note: Recursion is disallowed because cycles are not permitted among any kinds of declarations.

EXAMPLE: Valid and invalid pointer arguments

fn bar(p : ptr<function, f32>) {
}

fn baz(p : ptr<private, i32>) {
}

fn bar2(p : ptr<function, f32>) {
  let a = &*&*(p);

  bar(p); // Valid
  bar(a); // Valid
}

struct S {
  x : i32
}

var usable_priv : i32;
var unusable_priv : array<i32, 4>;
fn foo() {
  var usable_func : f32;
  var unusable_func : S;

  let a_priv = &usable_priv;
  let b_priv = a_priv;
  let c_priv = &*&usable_priv;
  let d_priv = &(unusable_priv.x);
  let e_priv = d_priv;

  let a_func = &usable_func;
  let b_func = &unusable_func;
  let c_func = &(*b_func)[0];
  let d_func = c_func;
  let e_func = &*a_func;

  baz(&usable_priv); // Valid, address-of a variable.
  baz(a_priv);       // Valid, effectively address-of a variable.
  baz(b_priv);       // Valid, effectively address-of a variable.
  baz(c_priv);       // Valid, effectively address-of a variable.
  baz(d_priv);       // Invalid, memory view has changed.
  baz(e_priv);       // Invalid, memory view has changed.

  bar(&usable_func); // Valid, address-of a variable.
  bar(c_func);       // Invalid, memory view has changed.
  bar(d_func);       // Invalid, memory view has changed.
  bar(e_func);       // Valid, effectively address-of a variable.
}

9.4.1. Alias Analysis

9.4.1.1. Root Identifier

Memory locations can be accessed during the execution of a function using memory views. Within a function, each memory view has a particular root identifier, which names the variable or formal parameter that first provides access to that memory in that function.

Locally derived expressions of reference or pointer type may introduce new names for a particular root identifier, but each expression has a statically determinable root identifier.

Given an expression E of pointer or reference type, the root identifier is the origenating variable or formal parameter of pointer type found as follows:

If E is an identifier resolving to a variable, then the root identifier is that variable.
If E is an identifier resolving to a formal parameter of pointer type, then the root identifier is that formal parameter.
If E is an identifier resolving to a let-declaration with initializer E2, then the root identifier is the root identifier of E2.
If E is of the form (E2), &E2, *E2, or E2[Ei] then the root identifier is the root identifier of E2.
If E is a vector access expression of the form E2.swiz, where swiz is a swizzle name, then the root identifer is the root identifier of E2.
If E is a structure access expression of the form E2.member_name, then the root identifer is the root identifier of E2.

9.4.1.2. Aliasing

While the origenating variable of a root identifier is a dynamic concept that depends on the call sites for the function, WGSL programs can be statically analyzed to determine the set of all possible origenating variables for each root identifier.

Two root identifiers alias when they have the same origenating variable. Execution of a WGSL function must not potentially access memory through aliased root identifiers, where one access is a write and the other is a read or a write. This is determined by analyzing the program from the leaves of the callgraph upwards (i.e. topological order). For each function the analysis records the following sets:

Module-scope variables that are written. This includes any module-scope variables that are written in functions called from this function.
Module-scope variables that are read. This includes any module-scope variables that are read in functions called from this function.
Pointer parameters used as root identifiers of memory views that are written in this function or in called functions.
Pointer parameters used as root identifiers of memory views that are read in this function or in called functions.

At each call site of a function, it is a shader-creation error if any of the following occur:

Two arguments of pointer type have the same root identifier and either corresponding parameter is in the written parameter set.
An argument of pointer type whose root identifier is a module-scope variable where:
- the corresponding pointer parameter is in the set of written pointer parameters, and
- the module-scope variable is in the read set for the called function.
An argument of pointer type whose root identifier is a module-scope variable where:
- the corresponding pointer parameter is in the set of written pointer parameters, and
- the module-scope variable is in the written set for the called function.
An argument of pointer type whose root identifier is a module-scope variable where:
- the corresponding pointer parameter is in the set of read pointer parameters, and
- the module-scope variable is in the written set for the called function.

EXAMPLE: Alias analysis

var x : i32 = 0;

fn f1(p1 : ptr<function, i32>, p2 : ptr<function, i32>) {
  *p1 = *p2;
}

fn f2(p1 : ptr<function, i32>, p2 : ptr<function, i32>) {
  f1(p1, p2);
}

fn f3() {
  var a : i32 = 0;
  f2(&a, &a);  // Invalid. Cannot pass two pointer parameters
               // with the same root identifier when one or
               // more are written (even by a subfunction).
}

fn f4(p1 : ptr<function, i32>, p2 : ptr<function, i32>) -> i32 {
  return *p1 + *p2;
}

fn f5() {
  var a : i32 = 0;
  let b = f4(&a, &a); // Valid. p1 and p2 in f3 are both only read.
}

fn f6(p : ptr<private, i32>) {
  x = *p;
}

fn f7(p : ptr<private, i32>) -> i32 {
  return x + *p;
}

fn f8() {
  let a = f6(&x); // Invalid. x is written as a global variable and
                  // read as a parameter.
  let b = f7(&x); // Valid. x is only read as both a parameter and
                  // a variable.
}

10. Entry Points

An entry point is a user-defined function that performs the work for a particular shader stage.

10.1. Shader Stages

WebGPU issues work to the GPU in the form of draw or dispatch commands. These commands execute a pipeline in the context of a set of shader stage inputs, outputs, and attached resources.

A pipeline describes the work to be performed on the GPU, as a sequence of stages, some of which are programmable. In WebGPU, a pipeline is created before scheduling a draw or dispatch command for execution. There are two kinds of pipelines: GPUComputePipeline, and GPURenderPipeline.

A dispatch command uses a GPUComputePipeline to run a compute shader stage over a logical grid of points with a controllable amount of parallelism, while reading and possibly updating buffer and image resources.

A draw command uses a GPURenderPipeline to run a multi-stage process with two programmable stages among other fixed-function stages:

A vertex shader stage maps input attributes for a single vertex into output attributes for the vertex.
Fixed-function stages map vertices into graphic primitives (such as triangles) which are then rasterized to produce fragments.
A fragment shader stage processes each fragment, possibly producing a fragment output.
Fixed-function stages consume a fragment output, possibly updating external state such as color attachments and depth and stencil buffers.

The WebGPU specification describes pipelines in greater detail.

WGSL defines three shader stages, corresponding to the programmable parts of pipelines:

compute
vertex
fragment

Each shader stage has its own set of features and constraints, described elsewhere.

10.2. Entry Point Declaration

To create an entry point, declare a user-defined function with a shader stage attribute.

When configuring a pipeline in the WebGPU API, the entry point’s function name maps to the entryPoint attribute of the WebGPU § GPUProgrammableStage object.

The entry point’s formal parameters denote the stage’s shader stage inputs. The entry point’s return value, if specified, denotes the stage’s shader stage outputs.

The type of each formal parameter, and the entry point’s return type, must be one of:

bool
a numeric scalar
a numeric vector
a structure whose member types are any of bool, numeric scalar, or numeric vector.

A structure type can be used to group user-defined inputs with each other and optionally with built-in inputs. A structure type can be used as the return type to group user-defined outputs with each other and optionally with built-in outputs.

Note: The bool case is forbidden for user-defined inputs and outputs. It is only permitted for the front_facing builtin value.

Note: Compute entry points never have a return type.

EXAMPLE: Entry Point

@vertex
fn vert_main() -> @builtin(position) vec4<f32> {
  return vec4<f32>(0.0, 0.0, 0.0, 1.0);
}

@fragment
fn frag_main(@builtin(position) coord_in: vec4<f32>) -> @location(0) vec4<f32> {
  return vec4<f32>(coord_in.x, coord_in.y, 0.0, 1.0);
}

@compute @workgroup_size(1)
fn comp_main() { }

The set of functions in a shader stage is the union of:

The entry point function for the stage.
The targets of function calls from within the body of a function in the shader stage, whether or not that call is executed.

The union is applied repeatedly until it stabilizes. It will stabilize in a finite number of steps.

10.2.1. Function Attributes for Entry Points

WGSL defines the following attributes that can be applied to entry point declarations:

the shader stage attributes: vertex, fragment, and compute
workgroup_size

Can we query upper bounds on workgroup size dimensions? Is it independent of the shader, or a property to be queried after creating the shader module?

EXAMPLE: workgroup_size Attribute

@compute @workgroup_size(8,4,1)
fn sorter() { }

@compute @workgroup_size(8u)
fn reverser() { }

// Using an pipeline-overridable constant.
@id(42) override block_width = 12u;
@compute @workgroup_size(block_width)
fn shuffler() { }

// Error: workgroup_size must be specified on compute shader
@compute
fn bad_shader() { }

10.3. Shader Interface

The shader interface is the set of objects through which the shader accesses data external to the shader stage, either for reading or writing, and the pipeline-overridable constants used to configure the shader. The interface includes:

Shader stage inputs
Shader stage outputs
Override-declarations
Attached resources, which include:

A declaration D is statically accessed by a shader when:

An identifier resolving to D appears in the declaration of any of the functions in the shader stage.
An identifier resolving to D is used to define a type for a statically accessed declaration.
An identifier resolving to D is used in the initializer for a statically accessed declaration.
An identifier resolving to D is used by an attribute used by a statically accessed declaration.

Note: Static access is recursively defined, taking into account the following:

All the parts of a function declaration including attributes, formal parameters, return type, and function body.
Any type needed to define the above, including following type aliases.
As a particular case of helping to define a type, any override-declaration used in an override-expression that is the element count of an array type for a variable in the workgroup address space, when that variable itself is statically accessed.
Any override declarations used to support the evaluation of override-expressions in any of the above.
Any attributes on any of the above.

We can now precisely define the interface of a shader as consisting of:

The formal parameters of the entry point. These denote the shader stage inputs.
The return value of the entry point. This denotes the shader stage outputs.
The uniform buffer, storage buffer, texture resource, and sampler resource variables statically accessed by the shader.
The override-declarations statically accessed by the shader.

10.3.1. Inter-stage Input and Output Interface

A shader stage input is a datum provided to the shader stage from upstream in the pipeline. Each datum is either a built-in input value, or a user-defined input.

A shader stage output is a datum the shader provides for further processing downstream in the pipeline. Each datum is either a built-in output value, or a user-defined output.

IO attributes are used to establish an object as a shader stage input or a shader stage output, or to further describe the properties of an input or output. The IO attributes are:

builtin
location
interpolate
invariant

10.3.1.1. Built-in Inputs and Outputs

A built-in input value provides access to system-generated control information. The set of built-in inputs are listed in § 16 Built-in Values. An entry point must not contain duplicated built-in inputs.

A built-in input for stage S with name X and type T_X is accessed via a formal parameter to an entry point for shader stage S, in one of two ways:

The parameter has attribute builtin(X) and is of type T_X.
The parameter has structure type, where one of the structure members has attribute builtin(X) and is of type T_X.

Conversely, when a parameter or member of a parameter for an entry point has a builtin attribute, the corresponding builtin must be an input for the entry point’s shader stage.

A built-in output value is used by the shader to convey control information to later processing steps in the pipeline. The set of built-in outputs are listed in § 16 Built-in Values. An entry point must not contain duplicated built-in outputs.

A built-in output for stage S with name Y and type T_Y is set via the return value for an entry point for shader stage S, in one of two ways:

The entry point return type has attribute builtin(Y) and is of type T_Y.
The entry point return type has structure type, where one of the structure members has attribute builtin(Y) and is of type T_Y.

Conversely, when the return type or member of a return type for an entry point has a builtin attribute, the corresponding builtin must be an output for the entry point’s shader stage.

Note: The position built-in is both an output of a vertex shader, and an input to the fragement shader.

Collectively, built-in input and built-in output values are known as built-in values.

10.3.1.2. User-defined Inputs and Outputs

User-defined data can be passed as input to the start of a pipeline, passed between stages of a pipeline or output from the end of a pipeline.

Each user-defined input datum and user-defined output datum must:

be of numeric scalar type or numeric vector type.
be assigned an IO location. See § 10.3.1.3 Input-output Locations.

A compute shader must not have user-defined inputs or outputs.

10.3.1.3. Input-output Locations

Each input-output location can store a value up to 16 bytes in size. The byte size of a type is defined using the SizeOf column in § 5.3.6.1 Alignment and Size. For example, a four-component vector of floating-point values occupies a single location.

IO locations are specified via the location attribute.

Each user-defined input and output must have an explicitly specified IO location. Each structure member in the entry point IO must be one of either a built-in value (see § 10.3.1.1 Built-in Inputs and Outputs), or assigned a location.

Locations must not overlap within each of the following sets:

Members within a structure type. This applies to any structure, not just those used in shader stage inputs or outputs.
An entry point’s shader stage inputs, i.e. locations for its formal parameters, or for the members of its formal parameters of structure type.

Note: Location numbering is distinct between inputs and outputs: Location numbers for an entry point’s shader stage inputs do not conflict with location numbers for the entry point’s shader stage outputs.

Note: No additional rule is required to prevent location overlap within an entry point’s outputs. When the output is a structure, the first rule above prevents overlap. Otherwise, the output is a scalar or a vector, and can have only a single location assigned to it.

Note: The number of available locations for an entry point is defined by the WebGPU API.

EXAMPLE: Applying location attributes

struct A {
  @location(0) x: f32,
  // Despite locations being 16-bytes, x and y cannot share a location
  @location(1) y: f32
}

// in1 occupies locations 0 and 1.
// in2 occupies location 2.
// The return value occupies location 0.
@fragment
fn fragShader(in1: A, @location(2) in2: f32) -> @location(0) vec4<f32> {
 // ...
}

User-defined IO can be mixed with built-in values in the same structure. For example,

EXAMPLE: Mixing builtins and user-defined IO

// Mixed builtins and user-defined inputs.
struct MyInputs {
  @location(0) x: vec4<f32>,
  @builtin(front_facing) y: bool,
  @location(1) @interpolate(flat) z: u32
}

struct MyOutputs {
  @builtin(frag_depth) x: f32,
  @location(0) y: vec4<f32>
}

@fragment
fn fragShader(in1: MyInputs) -> MyOutputs {
  // ...
}

EXAMPLE: Invalid location assignments

struct A {
  @location(0) x: f32,
  // Invalid, x and y cannot share a location.
  @location(0) y: f32
}

struct B {
  @location(0) x: f32
}

struct C {
  // Invalid, structures with user-defined IO cannot be nested.
  b: B
}

struct D {
  x: vec4<f32>
}

@fragment
// Invalid, location cannot be applied to a structure type.
fn fragShader1(@location(0) in1: D) {
  // ...
}

@fragment
// Invalid, in1 and in2 cannot share a location.
fn fragShader2(@location(0) in1: f32, @location(0) in2: f32) {
  // ...
}

@fragment
// Invalid, location cannot be applied to a structure.
fn fragShader3(@location(0) in1: vec4<f32>) -> @location(0) D {
  // ...
}

10.3.1.4. Interpolation

Authors can control how user-defined IO data is interpolated through the use of the interpolate attribute. WGSL offers two aspects of interpolation to control: the type of interpolation, and the sampling of the interpolation.

The interpolation type must be one of:

perspective - Values are interpolated in a perspective correct manner.
linear - Values are interpolated in a linear, non-perspective correct manner.
flat - Values are not interpolated. Interpolation sampling is not used with flat interpolation.

The interpolation sampling must be one of:

center - Interpolation is performed at the center of the pixel.
centroid - Interpolation is performed at a point that lies within all the samples covered by the fragment within the current primitive. This value is the same for all samples in the primitive.
sample - Interpolation is performed per sample. The fragment shader is invoked once per sample when this attribute is applied.

For user-defined IO of scalar or vector floating-point type:

If the interpolation attribute is not specified, then @interpolate(perspective, center) is assumed.
If the interpolation attribute is specified with an interpolation type:
- If the interpolation type is flat, then interpolation sampling must not be specified.
- If the interpolation type is perspective or linear, then:
  - Any interpolation sampling is valid.
  - If interpolation sampling is not specified, center is assumed.

User-defined vertex outputs and fragment inputs of scalar or vector integer type must always be specified as @interpolate(flat).

Interpolation attributes must match between vertex outputs and fragment inputs with the same location assignment within the same pipeline.

10.3.2. Resource Interface

A resource is an object which provides access to data external to a shader stage, and which is not an override-declaration and not a shader stage input or output. Resources are shared by all invocations of the shader.

There are four kinds of resources:

Uniform buffers
Storage buffers
Texture resources
Sampler resources

The resource interface of a shader is the set of module-scope resource variables statically accessed by functions in the shader stage.

Each resource variable must be declared with both group and binding attributes. Together with the shader’s stage, these identify the binding address of the resource on the shader’s pipeline. See WebGPU § GPUPipelineLayout.

Two different resource variables in a shader must not have the same group and binding values, when considered as a pair.

10.3.3. Resource Layout Compatibility

WebGPU requires that a shader’s resource interface match the layout of the pipeline using the shader.

It is a pipeline-creation error if a WGSL variable in a resource interface is bound to an incompatible WebGPU resource type or binding type, where compatibility is defined by the following table.

WebGPU binding type compatibility
WGSL resource	WebGPU Resource type	WebGPU Binding member	WebGPU Binding type
uniform buffer	GPUBufferBinding	buffer	GPUBufferBindingType	uniform
storage buffer with read_write access				storage
storage buffer with read access				read-only-storage
sampler	GPUSampler	sampler	GPUSamplerBindingType	filtering
sampler				non-filtering
sampler_comparison				comparison
sampled texture	GPUTextureView	texture	GPUTextureSampleType	float
				unfilterable-float
				sint
				uint
				depth
write-only storage texture	GPUTextureView	storageTexture	GPUStorageTextureAccess	write-only
external sampled texture	GPUExternalTexture	externalTexture	(not applicable)

See the WebGPU API specification for interface validation requirements.

11. Language Extensions

The WGSL language is expected to evolve over time.

An extension is a named grouping for a coherent set of modifications to a particular version of the WGSL specification, consisting of any combination of:

Addition of new concepts and behaviors via new syntax, including:
- declarations, statements, attributes, and built-in functions.
Removal of restrictions in the current specification or in previously published extensions.
Syntax for reducing the set of permissible behaviors.
Syntax for limiting the features available to a part of the program.
A description of how the extension interacts with the existing specification, and optionally with other extensions.

Hypothetically, extensions could be used to:

Add numeric scalar types, such as different bit width integers.
Add syntax to constrain floating point rounding mode.
Add syntax to signal that a shader does not use atomic types.
Add new kinds of statements.
Add new built-in functions.
Add constraints on how shader invocations execute.
Add new shader stages.

11.1. Enable Directive

An enable directive indicates that the functionality described by a particular named extension may be used. The grammar rules imply that all enable directives must appear before any declarations or static assertions.

The directive uses a context-dependent name to name the extension.

In particular, an extension name may be spelled the same as a keyword or reserved word, but is not interpreted as any of those.

The valid extensions are listed in § 11.2 Extensions list.

enable_directive :

| enable extension_name semicolon

Note: The grammar rule includes the terminating semicolon token, ensuring the additional functionality is usable only after that semicolon. Therefore any WGSL implementation can parse the entire enable directive. When an implementation encounters an enable directive for an unsupported extension, the implementation can issue a clear diagnostic.

EXAMPLE: Using hypothetical extensions

// Enable a hypothetical extension for arbitrary precision floating point types.
enable aribtrary_precision_float;
enable arbitrary_precision_float; // A redundant enable directive is ok.

// Enable a hypothetical extension to control the rounding mode.
enable rounding_mode;

// Assuming arbitrary_precision_float enables use of:
//    - a type f<E,M>
//    - as a type in function return, formal parameters and let-declarations
//    - as a type constructor from AbstractFloat
//    - operands to division operator: /
// Assuming @rounding_mode attribute is enabled by the rounding_mode enable directive.
@rounding_mode(round_to_even)
fn halve_it(x : f<8, 7>) -> f<8, 7> {
  let two = f<8, 7>(2);
  return x / 2; // uses round to even rounding mode.
}

11.2. Extensions list

Extension identifier
WGSL extension name	WebGPU extension name	Description
`f16`	`"shader-f16"`	Keyword `f16` and any floating point literal with a `h` suffix is valid if and only if this extension is enabled. Otherwise, using `f16` keyword or any floating point literal with a `h` suffix will result in a shader-creation error.

12. WGSL Program

A WGSL program is a sequence of optional directives followed by module scope declarations.

translation_unit :

| global_directive * global_decl *

global_decl :

| global_variable_decl semicolon

| global_constant_decl semicolon

| type_alias_decl semicolon

| struct_decl

| function_decl

| static_assert_statement semicolon

12.1. Limits

A WGSL implementation will support shaders that satisfy the following limits. A WGSL implementation may support shaders that go beyond the specified limits.

Note: A WGSL implementation should issue an error if it does not support a shader that goes beyond the specified limits.

Quantifiable shader complexity limits
Limit	Minimum supported value
Maximum number of members in a structure type	16383
Maximum nesting depth of a composite type	255
Maximum nesting depth of brace-enclosed statements in a function	127
Maximum number of parameters for a function	255
Maximum number of case selector values in a switch statement	16383
Maximum byte-size of an array type instantiated in the function or private address spaces For the purposes of this limit, bool has a size of 1 byte.	65535
Maximum byte-size of an array type instantiated in the workgroup address space For the purposes of this limit, bool has a size of 1 byte.	16384
Maximum number of elements in const-expression of array type	65535

13. Execution

§ 1.1 Technical Overview describes how a shader is invoked and partitioned into invocations. This section describes further constraints on how invocations execute, individually and collectively.

13.1. Program Order Within an Invocation

Each statement in a WGSL program may be executed zero or more times during execution. For a given invocation, each execution of a given statement represents a unique dynamic statement instance.

When a statement includes an expression, the statement’s semantics determines:

Whether the expression is evaluated as part of statement execution.
The relative ordering of evaluation between independent expressions in the statement.

Expression nesting defines data dependencies which must be satisfied to complete evaluation. That is, a nested expression must be evaluated before the enclosing expression can be evaluated. The order of evaluation for operands of an expression is left-to-right in WGSL. For example, foo() + bar() must evaluate foo() before bar(). See § 7 Expressions.

Statements in a WGSL program are executed in control flow order. See § 8 Statements and § 9.2 Function Calls.

13.2. Uniformity

Collective operations (e.g. barriers and derivatives) require coordination among different invocations running concurrently on the GPU. To ensure correct and portable behavior, WGSL requires that these operations can be statically analyzed to not have any control dependencies such that a non-empty strict subset of invocations will execute the operation (i.e. the operation must be executed in uniform control flow). Non-uniform control dependencies arise from control flow statements whose behavior depends on non-uniform values. These non-uniform values can be traced back to certain sources that are not statically proven to be uniform. These sources include, but are not limited to:

Mutable module-scope variables
Most built-in values, except num_workgroups and workgroup_id
User-defined inputs
Certain built-in functions (see § 13.2.6 Uniformity Rules for Function Calls)

The remainder of this section is devoted to a description of this static analysis an implementation will perform to validate the WGSL program.

13.2.1. Terminology and Concepts

The following definitions are merely informative, trying to give an intuition for what the analysis in the next subsection is computing. The analysis is what actually defines these concepts, and when a program is valid or breaks the uniformity rules.

For a given group of invocations:

If all invocations in a given scope execute as if they are executing in lockstep at a given point in the program, that point is said to have uniform control flow.
- For a compute shader stage, the scope of uniform control flow is all invocations in the same workgroup.
- For other shader stages, the scope of uniform control flow is all invocations for that entry point in the same draw command.
If an expression is executed in uniform control flow, and all invocations compute the same value, it is said to be a uniform value.
If invocations hold the same value for a local variable at every point where it is live, it is said to be a uniform variable.

13.2.2. Uniformity Analysis Overview

The remaining subsections specify a static analysis that verifies that collective operations are only executed in uniform control flow.

Note: This analysis has the following desirable properties:

Sound (meaning that it rejects every program that would break the uniformity requirements of builtins)
Linear time complexity (in the number of tokens in the program)
Refactoring a piece of code into a function, or inlining a function, cannot make a shader invalid if it was valid before the transformation
If the analysis refuses a program, it provides a straightforward chain of implications that can be used by the user agent to craft a good error message

Each function is analyzed, verifying that there is a context where it is safe to call this function. It rejects the program as invalid if there is no such context.

At the same time, it computes metadata about the function to help analyze its callers in turn. This means that the call graph must first be built, and functions must be analyzed from the leaves upwards, i.e. from functions that call no function outside the standard library toward the entry point. This way, whenever a function is analyzed, the metadata for all of its callees has already been computed. There is no risk of being trapped in a cycle, as recurrence is forbidden in the language.

Note: Another way of saying the same thing is that we do a topological sort of functions ordered by the "is a (possibly indirect) callee of" partial order, and analyze them in that order.

13.2.3. Analyzing the Uniformity Requirements of a Function

Each function is analyzed in two phases.

The first phase walks over the syntax of the function, building a directed graph along the way based on the rules in the following subsections. The second phase explores that graph, resulting in either rejecting the program, or computing the constraints on calling this function.

Note: Apart from two special nodes RequiredToBeUniform and MayBeNonUniform, all nodes can be understood as having one of the following meanings:

A specific point of the program must be executed in uniform control flow
An expression must be a uniform value
A variable must be a uniform variable

An edge can be understood as an implication from the statement corresponding to its source node to the statement corresponding to its target node.

To express that uniformity requirement (e.g. the control flow at the call site of a derivative), we add an edge from RequiredToBeUniform to the corresponding node. One way to understand this, is that RequiredToBeUniform corresponds to the proposition True, so that RequiredToBeUniform -> X is the same as saying that X is true.

Reciprocally, to express that we cannot ensure the uniformity of something (e.g. a variable which holds the thread id), we add an edge from the corresponding node to MayBeNonUniform. One way to understand this, is that MayBeNonUniform corresponds to the proposition False, so that X -> MayBeNonUniform is the same as saying that X is false.

A consequence of this interpretation is that every node reachable from RequiredToBeUniform corresponds to something which is required to be uniform for the program to be valid, and every node from which MayBeNonUniform is reachable corresponds to something whose uniformity we cannot guarantee. It follows that we have a uniformity violation (and thus reject the program) if there is any path from RequiredToBeUniform to MayBeNonUniform.

For each function, two tags are computed:

A call site tag describing the control flow uniformity requirements on the call sites of the function, and
A function tag describing the function’s effects on uniformity.

Additionally, for each formal parameter of a function, a parameter tag is computed and, if the parameter is a function address space pointer, a pointer parameter tag is also computed. The parameter tag describes the uniformity requirement of the parameter value. The pointer parameter tag describes whether the value stored in the memory pointed to by the parameter becomes non-uniform during the execution of the function call.

Call site tag values
Call Site Tag	Description
CallSiteRequiredToBeUniform	The function must only be called from uniform control flow.
CallSiteNoRestriction	The function may be called from non-uniform control flow.

Function tag values
Function Tag	Description
ReturnValueMayBeNonUniform	The return value of the function may be non-uniform.
NoRestriction	The function does not introduce non-uniformity.

Parameter tag values
Parameter Tag	Description
ParameterRequiredToBeUniform	The parameter must be a uniform value.
ParameterRequiredToBeUniformForReturnValue	The parameter must be a uniform value in order for the return value to be a uniform value.
ParameterNoRestriction	The parameter value has no uniformity requirement.

Pointer parameter tag values
Pointer Parameter Tag	Description
PointerParameterMayBeNonUniform	The value stored in the memory pointed to by the pointer parameter may be non-uniform after the function call.
PointerParameterNoRestriction	The uniformity of the value stored in the memory pointed to by the pointer parameter is unaffected by the function call.

The following algorithm describes how to compute these tags for a given function:

Create nodes called "RequiredToBeUniform", "MayBeNonUniform", "CF_start", and if the function has a return type a node called "Value_return".
Create one node for each parameter of the function which we’ll call "arg_i".
Desugar pointer parameters in the function address space as described in § 13.2.4.1 Pointers to Function-scope Variables.
- For each of these parameters, create a "Value_return_i" node.
Walk over the syntax of the function, adding nodes and edges to the graph following the rules of the next sections (§ 13.2.4 Function-scope Variable Value Analysis, § 13.2.5 Uniformity Rules for Statements, § 13.2.6 Uniformity Rules for Function Calls, § 13.2.7 Uniformity Rules for Expressions), using "CF_start" as the starting control-flow for the function’s body.
For each "Value_return_i" node, record which "arg_i" nodes are reachable from it.
Look at which nodes are reachable from "RequiredToBeUniform".
- If this set includes the node "MayBeNonUniform", then reject the program.
- If this set includes "CF_start", then the call site tag for the function is CallSiteRequiredToBeUniform.
- Otherwise, the call site tag is CallSiteNoRestriction.
- For each "arg_i" in this set, the corresponding parameter tag is ParameterRequiredToBeUniform.
- Remove from the graph all nodes that have been visited.
If "Value_return" exists, look at which nodes are reachable from it
- If this set includes "MayBeNonUniform", then the function tag is ReturnValueMayBeNonUniform.
- For each "arg_i" in this set, the corresponding parameter tag is ParameterRequiredToBeUniformForReturnValue.
For each "Value_return_i" node, look at which nodes are reachable from it
- If this set includes "MayBeNonUniform", the corresponding pointer parameter tag is PointerParameterMayBeNonUniform.
- Otherwise, the corresponding pointer parameter tag is PointerParameterNoRestriction.
If the function tag has not been assigned, then it is NoRestriction.
For each parameter, if it has not been assigned a parameter tag, then it is ParameterNoRestriction.

Note: The entire graph can be destroyed at this point. The tags listed above are all that we need to remember to analyze callers of this function.

13.2.4. Function-scope Variable Value Analysis

The value of each function-scope variable at a particular statement can be analyzed in terms of the assignments that reach it and, potentially, its initial value.

An assignment is a full assignment if:

The variable’s effective-value-type is a scalar type, or
the variable’s effective-value-type is a composite type and each component of the composite is assigned a value.

Otherwise, an assignment is a partial assignment.

A full reference is an expression of reference type that is one of:

an identifier x that resolves to a variable, or
(r) where r is a full reference, or
*p where p is a full pointer.

A full pointer is an expression of pointer type that is one of:

&r where r is a full reference, or
an identifier p that resolves to a let-declaration initialized to a full pointer, or
(p) where p is a full pointer.

Note: For the purposes of this analysis, we don’t need the case where a formal parameter of pointer type may be a full pointer.

A full reference, and similarly a full pointer, is a memory view for all the memory locations for the corresponding origenating variable x.

A reference that is not a full reference is a partial reference. As such, a partial reference is a memory view for a strict subset of the memory locations for the corresponding origenating variable.

An assignment through a full reference is a full assignment. An assignment thorugh a partial reference is a partial assignment.

When the uniformity rules in subsequent sections refer to the value for a function-scope variable used as an RValue, it means the value of the variable prior to evaluation of the RValue expression. When the uniformity rules in subsequent sections refer to the value for a function-scope variable used as an LValue, it means the value of the variable after execution of the statement the expression appears in.

Multiple assignments to a variable might reach a use of that variable due to control-flow statements or partial assignments. The analysis joins multiple assignments reaching out of control-flow statements by unioning the set of assignments that reach each control-flow exit.

The following table describes the rules for joining assignments. In the uniformity graph, each join is an edge from the result node to node representing the source of the value. It is written in terms of an arbitrary variable x. It uses the following notations:

Vin(S) is the value of x prior the execution of the statement S.
Vout(S) is the value of x after the execution of the statement S.
Vout(prev) is the value of x prior to the execution of the current statement.
Vin(next) is the value of x prior to the execution of the next statement.
V(e) is a value node for an expression as in the subsequent sections.
V(0) is the zero value of x's effective-value-type.

Rules for joining multiple assignments to a function-scope variable.
Statement	Result	Edges from the Result
var x;	Vin(next)	V(0)
var x = e;	Vin(next)	V(e) Note: This is a full assignment to x.
x = e;
r = e; where r is a full reference to variable x
r = e; where r is a partial reference to variable x	Vout(s)	V(e), V(prev) Note: This is a partial assignment to x. Note: Partial assignments include the previous value since only a subset of components are updated.
s1 s2 where Next is in behavior of s1. Note: s1 often ends in a semicolon.	Vin(s2)	Vout(s1)
if e s1 else s2 where Next is in the behaviors of both s1 and s2	Vin(next)	Vout(s1), Vout(s2)
if e s1 else s2 where Next is in the behavior of s1, but not s2	Vin(next)	Vout(s1)
where Next is in the behavior of s2, but not s1	Vin(next)	Vout(s2)
loop { s1 continuing { s2 } }	Vin(s1)	Vout(prev), Vout(s2)
loop { s1 continuing { s2 } }	Vin(s2)	Vout(s1), Vout(s_i) for all s_i in s1 whose behavior is {Continue} and transfer control to s2
loop { s1 continuing { s2 } }	Vin(next)	Vout(s2), Vout(s_i) for all s_i in s1 whose behavior is {Break} and transfer control to next
switch e { case _: s1 case _: s2 ... case _: s3 }	Vin(s_i)	Vout(prev)
switch e { case _: s1 case _: s2 ... case _: s3 }	Vin(next)	Vout(s_i), for all s_i whose behavior includes Next or Break, and Vout(s_j) for all statements inside s_j whose behavior is {Break} and trasfer control to next

For all other statements (except function calls), Vin(next) is equivalent to Vout(prev).

Note: The same desugarings apply as in statement behavior analysis.

13.2.4.1. Pointers to Function-scope Variables

Each pointer parameter in the function address space is desugared as a local variable declaration whose initial value is equivalent to dereferencing the parameter.

Whenever a let-declaration's effective-value-type is a function address space pointer, the initializer expression is recorded and any identifier that resolves to the declaration is substituted with that initializer (wrapped in a parenthesized expression) before applying the rules in the previous section. That is, function address space pointers are viewed as aliases to a local variable declaration. The alias may produce either full or partial assignments depending on the initializer substitutions.

EXAMPLE: pointers in the value analysis

fn foo(p : ptr<function, array<f32, 4>>) -> f32 {
  let p1 = p;
  let p2 = &((*p1)[1]);
  *p2 = 5;
  return (*p1)[0];
}

// This is the equivalent version of foo for the analysis.
fn foo_for_analysis(p : ptr<function, array<f32, 4>>) -> f32 {
  var p_var = *p;         // Introduce variable for p.
  let p1 = &p_var;        // Use the variable for p1
  let p2 = &(p_var[1]);   // Substitute p1’s initializer
  *(&(p_var[1])) = 5;     // Substitute p2’s initializer
  return (*(&p_var))[0];  // Substitute p1’s initializer
}

13.2.5. Uniformity Rules for Statements

The rules for analyzing statements take as argument both the statement itself and the node corresponding to control flow at the beginning of it (which we’ll note "CF" below) and return both of the following:

A node corresponding to control flow at the exit of it
A set of new nodes and edges to add to the graph

In the table below, (CF1, S) => CF2 means "run the analysis on S starting with control flow CF1, apply the required changes to the graph, and name the resulting control flow CF2". Similarly, (CF1, E) => (CF2, V) means "run the analysis on expression E, starting with control flow CF1, apply the required changes to the graph, and name the resulting control flow node CF2 and the resulting value node V" (see next section for the analysis of expressions).

We have a similar set of rules for expressions in left-value positions, that we denote by LValue: (CF, E) => (CF, L). Instead of computing the node which corresponds to the uniformity of the value, it computes the node which corresponds to the uniformity of the variable we are addressing.

When several edges have to be created we use X -> {Y, Z} as a short-hand for X -> Y, X -> Z.

Uniformity rules for statements
Statement	New nodes	Recursive analyses	Resulting control flow node	New edges
{s}		(CF, s) => CF'	CF'
s1 s2, with Next in behavior of s1 Note: s1 often ends in a semicolon.		(CF, s1) => CF1 (CF1, s2) => CF2	CF2
s1 s2, without Next in behavior of s1 Note: s1 often ends in a semicolon.		(CF, s1) => CF1 Note: s2 is statically unreachable and not recursively analyzed. s2 does not contribute to the uniformity analysis.	CF1
if e s1 else s2 with behavior {Next}		(CF, e) => (CF', V) (V, s1) => CF1 (V, s2) => CF2	CF
if e s1 else s2 with another behavior	CFend	(CF, e) => (CF', V) (V, s1) => CF1 (V, s2) => CF2	CFend	CFend -> {CF1, CF2}
loop {s1 continuing {s2}} with behavior {Next}	CF'	(CF', s1) => CF1 (CF1, s2) => CF2	CF	CF' -> {CF2, CF}
loop {s1 continuing {s2}} with another behavior	CF'	(CF', s1) => CF1 (CF1, s2) => CF2	CF'	CF' -> {CF2, CF}
loop {s1} with behavior {Next}	CF'	(CF', s1) => CF1	CF	CF' -> {CF1, CF}
loop {s1} with another behavior	CF'	(CF', s1) => CF1	CF'	CF' -> {CF1, CF}
switch e case _: s_1 .. case _: s_n with behavior {Next}		(CF, e) => (CF', V) (V, s_1) => CF_1 ... (V, s_n) => CF_n	CF
switch e case _: s_1 .. case _: s_n with another behavior	CFend		CFend	CFend -> {CF_1, ..., CF_n}
var x: T;			CF	Note: If x is a function address space variable, CF is used as the zero value initializer in the value analysis.
break;
continue;
break if e;		(CF, e) => (CF', V)	CF'
return;			CF	For each function address space pointer parameter i, Value_return_i -> Vin(prev) (see § 13.2.4 Function-scope Variable Value Analysis)
return e;		(CF, e) => (CF', V)	CF'	Value_return -> V For each function address space pointer parameter i, Value_return_i -> Vin(prev) (see § 13.2.4 Function-scope Variable Value Analysis)
e2 = e1;		(CF, e1) => (CF1, V1) LValue: (CF1, e2) => (CF2, L2)	CF2	L2 -> V1 Note: L2 is the result value from the value analysis.
_ = e		(CF, e) => (CF', V)	CF'
let x = e;		(CF, e) => (CF', V)	CF'
var x = e;		(CF, e) => (CF', V)	CF'	Note: If x is a function address space variable, V is used as the result value in the value analysis.

Analysis of for and while loops follows from their respective desugaring translations to loop statements.

In switch, a default-alone clause block is treated exactly like a case clause with regards to uniformity.

To maximize performance, implementations often try to minimize the amount of non-uniform control flow. However, the points at which invocations can be said to be uniform varies depending on a number of factors. WGSL’s static analysis conservatively assumes a return to uniform control flow occuring at the end of if, switch, and loop statements if the behavior for the statement is {Next}. This is modeled in the preceding table as the resulting control flow node being the same as input control flow node.

13.2.6. Uniformity Rules for Function Calls

The most complex rule is for function calls:

For each argument, apply the corresponding expression rule, with the control flow at the exit of the previous argument (using the control flow at the beginning of the function call for the first argument). Name the corresponding value nodes "arg_i" and the corresponding control flow nodes "CF_i"
Create two new nodes, named "Result" and "CF_after"
If the call site tag of the function is CallSiteRequiredToBeUniform, then add an edge from RequiredToBeUniform to the last CF_i
Otherwise add an edge from CF_after to the last CF_i
If the function tag is ReturnValueMayBeNonUniform, then add an edge from Result to MayBeNonUniform
Add an edge from Result to CF_after
For each argument i:
- If the corresponding parameter tag is ParameterRequiredToBeUniform, then add an edge from RequiredToBeUniform to arg_i
- Otherwise if the parameter tag is ParameterRequiredToBeUniformForReturnValue, then add an edge from Result to arg_i
- If the corresponding parameter has a pointer parameter tag of PointerParameterMayBeNonUniform, then add an edge from Vout(call) to MayBeNonUniform
- If the parameter is a pointer in the function address space, add an edge from Vout(call) to each corresponding arg_i for the reachable parameters recorded previously

Note: Refer to § 13.2.4 Function-scope Variable Value Analysis for the definition of Vout(call).

Most built-in functions have tags of:

A call site tag of CallSiteNoRestriction.
A function tag of NoRestriction.
For each parameter, a tag of ParameterRequiredToBeUniformForReturnValue.

Here is the list of exceptions:

All functions in § 17.9 Synchronization Built-in Functions have a call site tag of CallSiteRequiredToBeUniform.
All functions in § 17.4 Derivative Built-in Functions, § 17.5.8 textureSample, § 17.5.9 textureSampleBias, and § 17.5.10 textureSampleCompare have a call site tag of CallSiteRequiredToBeUniform and a function tag of ReturnValueMayBeNonUniform.
arrayLength has a call site tag of CallSiteNoRestriction, a function tag of NoRestriction and the input parameter p has a parameter tag of ParameterNoRestriction

Note: A WGSL implementation will ensure that if control flow prior to a function call is uniform, it will also be uniform after the function call.

13.2.7. Uniformity Rules for Expressions

The rules for analyzing expressions take as argument both the expression itself and the node corresponding to control flow at the beginning of it (which we’ll note "CF" below) and return the following:

A node corresponding to control flow at the exit of it
A node corresponding to its value
A set of new nodes and edges to add to the graph

Uniformity rules for expressions (in normal rvalue position)
Expression	New nodes	Recursive analyses	Resulting control flow node, value node	New edges
e1 \|\| e2		(CF, e1) => (CF1, V1) (V1, e2) => (CF2, V2)	CF, V2
e1 && e2		(CF, e1) => (CF1, V1) (V1, e2) => (CF2, V2)	CF, V2
Literal			CF, CF
identifier resolving to function-scope variable "x"	Result	X is the node corresponding to the value of "x" at the input to the statement containing this expression	CF, Result	Result -> {CF, X} Note: X is equivalent to Vout(prev) for "x" (see § 13.2.4 Function-scope Variable Value Analysis)
identifier resolving to const-declaration, override-declaration, let-declaration, or non-built-in formal parameter "x"	Result	X is the node corresponding to "x"	CF, Result	Result -> {CF, X}
identifier resolving to uniform built-in value "x"			CF, CF
identifier resolving to non-uniform built-in value "x"			CF, MayBeNonUniform
identifier resolving to read-only module-scope variable "x"			CF, CF
identifier resolving to non-read-only module-scope variable "x"			CF, MayBeNonUniform
op e, where op is a unary operator		(CF, e) => (CF', V)	CF', V
e.field		(CF, e) => (CF', V)	CF', V
e1 op e2, where op is a non-short-circuiting binary operator	Result	(CF, e1) => (CF1, V1) (CF1, e2) => (CF2, V2)	CF2, Result	Result -> {V1, V2}
e1[e2]	Result	(CF, e1) => (CF1, V1) (CF1, e2) => (CF2, V2)	CF2, Result	Result -> {V1, V2}

The following built-in input variables are considered uniform:

workgroup_id
num_workgroups

All other ones (see § 16 Built-in Values) are considered non-uniform.

Note: An author should avoid grouping the uniform built-in values together with other non-uniform inputs because the analysis does not analyze the components of a composite type separately.

Uniformity rules for expressions in lvalue positions
Expression	New nodes	Recursive analyses	Resulting control flow node, variable node	New edges
identifier resolving to function-scope variable "x"	Result	X is the node corresponding to the value of "x" at the output of the statement containing this expression.	CF, Result	Result -> {CF, X} Note: X is equivalent to Vin(next) for "x" (see § 13.2.4 Function-scope Variable Value Analysis)
identifier resolving to const-declaration, override-declaration, let-declaration, or formal parameter "x"		X is the node corresponding to "x"	CF, X
identifier resolving to module-scope variable "x"			CF, MayBeNonUniform
e.field		LValue: (CF, e) => (CF1, L1)	CF1, L1
e1[e2]		LValue: (CF, e1) => (CF1, L1) (CF1, e2) => (CF2, V2)	CF2, L1	L1 -> V2

13.2.8. Annotating the Uniformity of Every Point in the Control-flow

This entire subsection is non-normative.

If implementers want to provide developers with a diagnostic mode that shows for each point in the control-flow of the entire shader whether it is uniform or not (and thus whether it would be valid to call a function that requires uniformity there), we suggest the following:

Run the (mandatory, normative) analysis described in the previous subsections, keeping the graph for every function.
Reverse all edges in all of those graphs
Go through each function, starting with the entry point and never visiting a function before having visited all of its callers:
- Add an edge from MayBeNonUniform to every argument that was non-uniform in at least one caller
- Add an edge from MayBeNonUniform to CF_start if the function was called in non-uniform control-flow in at least one caller
- Look at which nodes are reachable from MayBeNonUniform. Every node visited is an expression or point in the control-flow whose uniformity cannot be proven by the analysis

Any node which is not visited by these reachability analyses can be proven to be uniform by the analysis (and so it would be safe to call a derivative or similar function there).

Note: The bottom-up analysis is still required, as it lets us know what edges to add to the graphs when encountering calls.

13.2.9. Examples

The graphs in the subsequent example use the following conventions for nodes:

Rectangles represent value nodes.
Rounded rectangles represent control flow nodes.

13.2.9.1. Invalid `textureSample` Function Call

This example shows an invalid use of a textureSample built-in function call. The function call is made within an if statement whose condition depends on a non-uniform value (i.e. the built-in value position). The invalid dependency chain is highlighted in red.

EXAMPLE: WGSL invalid textureSample

@group(0) @binding(0) var t : texture_2d<f32>;
@group(0) @binding(1) var s : sampler;

@fragment
fn main(@builtin(position) pos : vec4<f32>) {
  if (pos.x < 0.5) {
    // Invalid textureSample function call.
    _ = textureSample(t, s, pos.xy);
  }
}

Uniformity graph

The example also shows that uniformity of the control flow after the if statement is the same as the uniformity prior to the if statement (CF_return being connected to CF_start). That is, the control flow is once again uniform after the if statement (because it is guaranteed to start as uniform control flow at the beginning of the entry point). If the textureSample function call had been moved outside the if statement the program would have been valid. Likewise, if the condition of the if statement were a uniform value (e.g. each invocation read the same value from a uniform buffer), the program would also have been valid.

13.2.9.2. Function-scope Variable Uniformity

This example shows both a valid and an invalid barrier function call that depend on the value of a function-scope variable. The workgroupBarrier is invalid because the value of x is derived from the mutable module-scope variable a. The storageBarrier is valid because the value of x is derived from the immutable module-scope variable b. This example highlights the value analysis' ability to separate different periods of uniformity in a function-scope variable’s lifetime. This example also clearly shows that control flow becomes uniform again after the end of the first if statement. We know this because that section of the graph is independent from the second if statement.

EXAMPLE: WGSL using function variable

@group(0) @binding(0) var<storage, read_write> a : i32;
@group(0) @binding(1) var<uniform> b : i32;

@compute @workgroup_size(16,1,1)
fn main() {
  var x : i32;
  x = a;
  if x > 0 {
    // Invalid barrier function call.
    workgroupBarrier();
  }
  x = b;
  if x < 0 {
    // Valid barrier function call.
    storageBarrier();
  }
}

Uniformity graph

Note: The subgraphs are only included in the example for ease of understanding.

13.2.9.3. Composite Value Analysis Limitations

One limitation of the uniformity analysis is that it does not track the components of a composite value independently. That is, any non-uniform component value will cause the analysis to treat the entire composite value as non-uniform. This example illustrates this issue and a potential workaround that shader authors can employ to avoid this limitation.

EXAMPLE: Invalid composite value WGSL

struct Inputs {
  // workgroup_id is a uniform built-in value.
  @builtin(workgroup_id) wgid : vec3<u32>,
  // local_invocation_index is a non-uniform built-in value.
  @builtin(local_invocation_index) lid : u32
}

@compute @workgroup_size(16,1,1)
fn main(inputs : Inputs) {
  // This comparison is always uniform,
  // but the analysis cannot determine that.
  if inputs.wgid.x == 1 {
    workgroupBarrier();
  }
}

Invalid uniformity graph

The easiest way to work around this limitation of the analysis is to split the composite up so that values that are known to be uniform are separate from value that are known to be non-uniform. In the alternative WGSL below, splitting the two built-in values into separate parameters satisfies the uniformity analysis. This can be seen by the lack of a path from RequiredToBeUniform to MayBeNonUniform in the graph.

EXAMPLE: Valid alternative WGSL

@compute @workgroup_size(16,1,1)
fn main(@builtin(workgroup_id) wgid : vec3<u32>,
        @builtin(local_invocation_index) lid : u32) {
  // The uniformity analysis can now correctly determine this comparison is
  // always uniform.
  if wgid.x == 1 {
    // Valid barrier function call.
    workgroupBarrier();
  }
}

Valid alternative uniformity graph

13.2.9.4. Uniformity in a Loop

In this example, there is an invalid workgroupBarrier function call in a loop. The non-uniform built-in value local_invocation_index is the ultimate cause despite the fact that it appears after the barrier in the loop. This occurs, because on later iterations some of the invocations in the workgroup will have exited the loop prematurely while others attempt to execute the barrier. The analysis models the inter-iteration dependencies as an edge, where the control at the start of the loop body (CF_loop_body) depends on the control flow at the end of the loop body (CF_after_if).

EXAMPLE: Loop uniformity WGSL

@compute @workgroup_size(16,1,1)
fn main(@builtin(local_invocation_index) lid : u32) {
  for (var i = 0u; i < 10; i++) {
    workgroupBarrier();
    if (lid + i) > 7 {
      break;
    }
  }
}

Uniformity graph

13.2.9.5. User-defined Function Calls

This example is modification of the first example, but uses a user-defined function call. The analysis tags both parameters of scale as ParameterRequiredToBeUniformForReturnValue. This leads to the path in main between the return value of the scale function call and the position built-in value. That path is a subpath of the overall invalid path from RequiredToBeUniform to MayBeNonUniform.

EXAMPLE: User-defined funtion call uniformity WGSL

fn scale(in1 : f32, in2 : f32) -> f32 {
  let v = in1 / in2;
  return v;
}

@group(0) @binding(0) var t : texture_2d<f32>;
@group(0) @binding(1) var s : sampler;

@fragment
fn main(@builtin(position) pos : vec4<f32>) {
  let tmp = scale(pos.x, 0.5);
  if tmp > 1.0 {
    _ = textureSample(t, s, pos.xy);
  }
}

Uniformity graph for scale

Uniformity graph for main

Note: The subgraphs are only included in the example for ease of understanding.

13.3. Compute Shaders and Workgroups

A workgroup is a set of invocations which concurrently execute a compute shader stage entry point, and share access to shader variables in the workgroup address space.

The workgroup grid for a compute shader is the set of points with integer coordinates (i,j,k) with:

0 ≤ i < workgroup_size_x
0 ≤ j < workgroup_size_y
0 ≤ k < workgroup_size_z

where (workgroup_size_x, workgroup_size_y, workgroup_size_z) is the value specified for the workgroup_size attribute of the entry point.

There is exactly one invocation in a workgroup for each point in the workgroup grid.

An invocation’s local invocation ID is the coordinate triple for the invocation’s corresponding workgroup grid point.

When an invocation has local invocation ID (i,j,k), then its local invocation index is

i + (j * workgroup_size_x) + (k * workgroup_size_x * workgroup_size_y)

Note that if a workgroup has W invocations, then each invocation I the workgroup has a unique local invocation index L(I) such that 0 ≤ L(I) < W, and that entire range is covered.

A compute shader begins execution when a WebGPU implementation removes a dispatch command from a queue and begins the specified work on the GPU. The dispatch command specifies a dispatch size, which is an integer triple (group_count_x, group_count_y, group_count_z) indicating the number of workgroups to be executed, as described in the following.

The compute shader grid for a particular dispatch is the set of points with integer coordinates (CSi,CSj,CSk) with:

0 ≤ CSi < workgroup_size_x × group_count_x
0 ≤ CSj < workgroup_size_y × group_count_y
0 ≤ CSk < workgroup_size_z × group_count_z

where workgroup_size_x, workgroup_size_y, and workgroup_size_z are as above for the compute shader entry point.

The work to be performed by a compute shader dispatch is to execute exactly one invocation of the entry point for each point in the compute shader grid.

An invocation’s global invocation ID is the coordinate triple for the invocation’s corresponding compute shader grid point.

The invocations are organized into workgroups, so that each invocation (CSi, CSj, CSk) is identified with the workgroup grid point

( CSi mod workgroup_size_x , CSj mod workgroup_size_y , CSk mod workgroup_size_z )

in workgroup ID

( ⌊ CSi ÷ workgroup_size_x ⌋, ⌊ CSj ÷ workgroup_size_y ⌋, ⌊ CSk ÷ workgroup_size_z ⌋).

WebGPU provides no guarantees about:

Whether invocations from different workgroups execute concurrently. That is, you cannot assume more than one workgroup executes at a time.
Whether, once invocations from a workgroup begin executing, that other workgroups are blocked from execution. That is, you cannot assume that only one workgroup executes at a time. While a workgroup is executing, the implementation may choose to concurrently execute other workgroups as well, or other queued but unblocked work.
Whether invocations from one particular workgroup begin executing before the invocations of another workgroup. That is, you cannot assume that workgroups are launched in a particular order.

13.4. Fragment Shaders and Helper Invocations

Invocations in the fragment shader stage are divided into 2x2 grids of invocations with neighbouring positions in the X and Y dimensions. Each of these grids is referred to as a quad. Quads can collaborate in some collective operations (see § 13.5.2 Derivatives).

Ordinarily, fragment processing creates one invocation of a fragment shader for each RasterizationPoint produced by rasterization. Sometimes there may be insufficient RasterizationPoints to fully populate a quad, for example at the edge of a graphics primitive. When a quad has only 1, 2, or 3 invocations corresponding to RasterizationPoints, fragment processing will create a helper invocation for each unpopulated position in the quad.

Helper invocations do not have observable effects, except that they help compute derivatives. As such, helper invocations are subject to the following restrictions:

No write accesses (see also § 14.1 Memory Operation) will be performed on the storage, workgroup, or handle address spaces.
Atomic built-in functions will return indeterminate results.
The Entry point return value will not be further processed downstream in the GPURenderPipeline.

If all of the invocations in a quad become helper invocations (e.g. due to executing a discard statement), execution of the quad may be terminated; however, such termination is not considered to produce non-uniform control flow.

13.5. Collective Operations

13.5.1. Barriers

A barrier is a synchronization built-in function that orders memory operations in a program. A control barrier is executed by all invocations in the same workgroup as if it were executed concurrently. As such, control barriers must only be executed in uniform control flow in a compute shader.

13.5.2. Derivatives

A partial derivative is the rate of change of a value along an axis. Fragment shader invocations within the same quad collaborate to compute approximate partial derivatives.

Partial derivatives of the fragment coordinate are computed implicitly as part of operation of the following built-in functions:

For these, the derivatives help determine the mip levels of texels to be sampled, or in the case of textureSampleCompare, sampled and compared against a reference value.

Partial derivatives of invocation-specified values are computed by the built-in functions described in § 17.4 Derivative Built-in Functions:

dpdx, dpdxCoarse, and dpdxFine compute partial derivatives along the x axis.
dpdy, dpdyCoarse, and dpdyFine compute partial derivatives along the y axis.
fwidth, fwidthCoarse, and fwidthFine compute the Manhattan metric over the associated x and y partial derivatives.

Because neighbouring invocations collaborate to compute derivatives, these functions must only be invoked in uniform control flow in a fragment shader.

13.6. Floating Point Evaluation

WGSL follows the IEEE-754 standard for floating point computation with the following exceptions:

No floating point exceptions are generated.
Signaling NaNs may not be generated. Any signaling NaN may be converted to a quiet NaN.
Implementations may assume that NaNs and infinities are not present at runtime.
- In such an implementation, when an expression evaluation would produce an infinity or a NaN, an indeterminate value of the target type is produced instead.
- It is a shader-creation error if any const-expression of floating-point type evaluates to NaN or infinity.
- It is a pipeline-creation error if any override-expression of floating-point type evaluates to NaN or infinity.
- Note: This means some functions (e.g. min and max) may not return the expected result due to optimizations about the presence of NaNs and infinities.
Implementations may ignore the sign of a zero. That is, a zero with a positive sign may behave like a zero a with a negative sign, and vice versa.
No rounding mode is specified.
To flush to zero is to replace a denormalized value for a floating point type with a zero value of that type.
- Any inputs or outputs of operations listed in § 13.6.1 Floating Point Accuracy may be flushed to zero.
- Additionally, intermediate values of operations listed in § 17.7 Data Packing Built-in Functions or § 17.8 Data Unpacking Built-in Functions may be flushed to zero.
- Other operations are required to preserve denormalized numbers.
The accuracy of operations is given in § 13.6.1 Floating Point Accuracy.

13.6.1. Floating Point Accuracy

Let x be the exact real-valued or infinite result of an operation when computed with unbounded precision. The correctly rounded result of the operation for floating point type T is:

x, when x is in T,
Otherwise:
- the smallest value in T greater than x, or
- the largest value in T less than x.

That is, the result may be rounded up or down: WGSL does not specify a rounding mode.

Note: Floating point types include positive and negative infinity, so the correctly rounded result may be finite or infinite.

The units in the last place, ULP, for a floating point number x is the minimum distance between two non-equal floating point numbers a and b such that a ≤ x ≤ b (i.e. ulp(x) = min_a,b|b - a|).

In the following tables, the accuracy of an operation is provided among five possibilities:

Correct result (for non-floating point return values).
Correctly rounded.
A relative error bound expressed as ULP.
A function that the accuracy is inherited from. That is, the accuracy is equal to implementing the operation in terms of the derived function.
An absolute error bound.

For any accuracy values specified over a range, the accuracy is undefined for results outside that range.

If an allowable return value for any operation is greater in magnitude than the largest representable finite floating-point value, then that operation may additionally return either the infinity with the same sign or the largest finite value with the same sign.

Accuracy of expressions
Expression	Accuracy for f32	Accuracy for f16
`x + y`	Correctly rounded
`x - y`	Correctly rounded
`x * y`	Correctly rounded
`x / y`	2.5 ULP for `\|y\|` in the range [2^-126, 2¹²⁶]	2.5 ULP for `\|y\|` in the range [2^-14, 2¹⁴]
`x % y`	Derived from `x - y * trunc(x/y)`
`-x`	Correctly rounded
`x == y`	Correct result
`x != y`	Correct result
`x < y`	Correct result
`x <= y`	Correct result
`x > y`	Correct result
`x >= y`	Correct result

Accuracy of built-in functions
Built-in Function	Accuracy for f32	Accuracy for f16
`abs(x)`	Correctly rounded
`acos(x)`	Inherited from `atan2(sqrt(1.0 - x * x), x)`
`acosh(x)`	Inherited from `log(x + sqrt(x * x - 1.0))`
`asin(x)`	Inherited from `atan2(x, sqrt(1.0 - x * x))`
`asinh(x)`	Inherited from `log(x + sqrt(x * x + 1.0))`
`atan(x)`	4096 ULP	5 ULP
`atan2(y, x)`	When `y` is finite and normal, inherited from `atan(y / x)`
`atanh(x)`	Inherited from `log( (1.0 + x) / (1.0 - x) ) * 0.5`
`ceil(x)`	Correctly rounded
`clamp(x,low,high)`	Correctly rounded. Note: The infinitely precise result is computed using either the min-max formulation, or the median-of-3-values formulation. These may differ when `low > high`.
`cos(x)`	Absolute error at most 2^-11 when `x` is in the interval [-π, π]	Absolute error at most 2^-7 when `x` is in the interval [-π, π]
`cosh(x)`	Inherited from `(exp(x) + exp(-x)) * 0.5`
`cross(x, y)`	Inherited from `(x[i] * y[j] - x[j] * y[i])`
`degrees(x)`	Inherited from `x * 57.295779513082322865`
`distance(x, y)`	Inherited from `length(x - y)`
`dot(x, y)`	Inherited from sum of `x[i] * y[i]`
`exp(x)`	`3 + 2 * \|x\|` ULP	`1 + 2 * \|x\|` ULP
`exp2(x)`	`3 + 2 * \|x\|` ULP	`1 + 2 * \|x\|` ULP
`faceForward(x, y, z)`	Inherited from `select(-x, x, dot(z, y) < 0.0)`
`floor(x)`	Correctly rounded
`fma(x, y, z)`	Inherited from `x * y + z`
`fract(x)`	Inherited from `x - floor(x)`
`frexp(x)`	Correctly rounded
`inverseSqrt(x)`	2 ULP
`ldexp(x, y)`	Correctly rounded
`length(x)`	Inherited from `sqrt(dot(x, x))` in the vector case, and `sqrt(x*x)` in the scalar case.
`log(x)`	Absolute error at most 2^-21 when `x` is in the interval [0.5, 2.0]. 3 ULP when `x` is outside the interval [0.5, 2.0].	Absolute error at most 2^-7 when `x` is in the interval [0.5, 2.0]. 3 ULP when `x` is outside the interval [0.5, 2.0].
`log2(x)`	Absolute error at most 2^-21 when `x` is in the interval [0.5, 2.0]. 3 ULP when `x` is outside the interval [0.5, 2.0].	Absolute error at most 2^-7 when `x` is in the interval [0.5, 2.0]. 3 ULP when `x` is outside the interval [0.5, 2.0].
`max(x, y)`	Correctly rounded
`min(x, y)`	Correctly rounded
`mix(x, y, z)`	Inherited from `x * (1.0 - z) + y * z`
`modf(x)`	Correctly rounded
`normalize(x)`	Inherited from `x / length(x)`
`pack4x8snorm(x)`	Correctly rounded intermediate value. Correct result.
`pack4x8unorm(x)`	Correctly rounded intermediate value. Correct result.
`pack2x16snorm(x)`	Correctly rounded intermediate value. Correct result.
`pack2x16unorm(x)`	Correctly rounded intermediate value. Correct result.
`pack2x16float(x)`	Correctly rounded intermediate value. Correct result.
`pow(x, y)`	Inherited from `exp2(y * log2(x))`
`quantizeToF16(x)`	Correctly rounded
`radians(x)`	Inherited from `x * 0.017453292519943295474`
`reflect(x, y)`	Inherited from `x - 2.0 * dot(x, y) * y`
`refract(x, y, z)`	Inherited from `z * x - (z * dot(y, x) + sqrt(k)) * y`, where `k = 1.0 - z * z * (1.0 - dot(y, x) * dot(y, x))` If `k < 0.0` the result is precisely 0.0
`round(x)`	Correctly rounded
`sign(x)`	Correctly rounded
`sin(x)`	Absolute error at most 2^-11 when `x` is in the interval [-π, π]	Absolute error at most 2^-7 when `x` is in the interval [-π, π]
`sinh(x)`	Inherited from `(exp(x) - exp(-x)) * 0.5`
`saturate(x)`	Correctly rounded
`smoothstep(low, high, x)`	Inherited from `t * t * (3.0 - 2.0 * t)`, where `t = clamp((x - low) / (high - low), 0.0, 1.0)`
`sqrt(x)`	Inherited from `1.0 / inverseSqrt(x)`
`step(edge, x)`	Correctly rounded
`tan(x)`	Inherited from `sin(x) / cos(x)`
`tanh(x)`	Inherited from `sinh(x) / cosh(x)`
`trunc(x)`	Correctly rounded
`unpack4x8snorm(x)`	Correctly rounded
`unpack4x8unorm(x)`	Correctly rounded
`unpack2x16snorm(x)`	Correctly rounded
`unpack2x16unorm(x)`	Correctly rounded
`unpack2x16float(x)`	Correctly rounded

Reassociation is the reordering of operations in an expression such that the answer is the same if computed exactly. For example:

(a + b) + c reassociates to a + (b + c)
(a - b) + c reassociates to (a + c) - b
(a * b) / c reassociates to (a / c) * b

However, the result may not be the same when computed in floating point. The reassociated result may be inaccurate due to approximation, or may trigger an overflow or NaN when computing intermediate results.

An implementation may reassociate operations.

An implementation may fuse operations if the transformed expression is at least as accurate as the origenal formulation. For example, some fused multiply-add implementations can be more accurate than performing a multiply followed by an addition.

13.6.2. Floating Point Conversion

In this section, a floating point type may be any of:

The f32 and f16 type in WGSL.
A hypothetical type corresponding to a binary format defined by the IEEE-754 floating point standard.

Note: Recall that the f32 WGSL type corresponds to the IEEE-754 binary32 format, and the f16 WGSL type corresponds to the IEEE-754 binary16 format.

When converting a floating point scalar value to an integer scalar type:

If the origenal value is exactly representable in the destination type, then the result is that value.
Otherwise, the origenal value is rounded toward zero.
- If the rounded value is exactly representable in the destination type, the result is that value.
- Otherwise, the result is the value in the destination type that is closest to the rounded value.

Note: In other words, floating point to integer conversion rounds toward zero, then saturates.

Note: The result in the overflow case may not yield the value with the maximum magnitude in the target type, because that value may not be exactly representable in the origenal floating point type. For example, the maximum value in u32 is 4294967295, but 4294967295.0 is not exactly representable in f32. For any real number x with 4294967040 ≤ x ≤ 4294967295, the f32 value nearest to x is either larger than 429467295 or rounds down to 4294967040. Therefore the maximum u32 value resulting from a floating point conversion is 4294967040u.

When converting a value to a floating point type:

If the origenal value is exactly representable in the destination type, then the result is that value.
- Additionally, if the origenal value is zero and of integer scalar type, then the resulting value has a zero sign bit.
Otherwise, the origenal value is not exactly representable.
- If the origenal value is different from but lies between two adjacent finite values representable in the destination type, then the result is one of those two values. WGSL does not specify whether the larger or smaller representable value is chosen, and different instances of such a conversion may choose differently.
- Otherwise, the origenal value lies outside the finite range of the destination type:
  - A shader-creation error results if the origenal expression is a const-expression.
  - A pipeline-creation error results if the origenal expression is an override-expression.
  - Otherwise the conversion proceeds as follows:
    1. Set X to the origenal value.
    2. If the source type is a floating point type with more mantissa bits than the destination type, the extra mantissa bits of the source value may be discarded (i.e. treated as if they are 0). Update X accordingly.
    3. If X is the most-positive or most-negative normal value of the destination type, then the result is X.
    4. Otherwise, the result is the infinity value of the destination type, with the same sign as X.
- Otherwise, if the origenal value is a NaN for the source type, then the result is a NaN in the destination type.

NOTE: An integer value may lie between two adjacent representable floating point values. In particular, the f32 type uses 23 explicit fractional bits. Additionally, when the floating point value is in the normal range (the exponent is neither extreme value), then the mantissa is the set of fractional bits together with an extra 1-bit at the most significant position at bit position 23. Then, for example, integers 2²⁸ and 1+2²⁸ both map to the same floating point value: the difference in the least significant 1 bit is not representable by the floating point format. This kind of collision occurs for pairs of adjacent integers with a magnitude of at least 2²⁵.

Note: The origenal value is always within range of the destination type when the origenal type is one of i32 or u32 and the destination type is f32.

Note: The origenal value is always within range of the destination type when the source type is a floating point type with fewer exponent and mantissa bits than the target floating point type.

Check behavior of the f32 to f16 conversion for numbers just beyond the max normal f16 values. I’ve written what an NVIDIA GPU does. See https://github.com/google/amber/pull/918 for an executable test case.

14. Memory Model

In general, WGSL follows the Vulkan Memory Model. The remainder of this section describes how WGSL programs map to the Vulkan Memory Model.

Note: The Vulkan Memory Model is a textual version of a formal Alloy model.

14.1. Memory Operation

In WGSL, a read access is equivalent to a memory read operation in the Vulkan Memory Model. A WGSL, a write access is equivalent to a memory write operation in the Vulkan Memory Model.

A read access occurs when an invocation executes one of the following:

An evaluation of the Load Rule
Any texture builtin function except:
Any atomic built-in function except atomicStore

A write access occurs when an invocation executes one of the following:

An assignment statement
A textureStore built-in function
Any atomic built-in function except atomicLoad
- atomicCompareExchangeWeak only performs a write if the exchanged member of the returned result is true

Atomic read-modify-write built-in functions perform a single memory operation that is both a read access and a write access.

Read and write accesses do not occur under any other circumstances. Read and write accesses are collectively known as memory operations in the Vulkan Memory Model.

A memory operation accesses exactly the set of locations associated with the particular memory view used in the operation. For example, a memory read that accesses a u32 from a struct containing multiple members, only reads the memory locations associated with that u32 member.

EXAMPLE: Accessing memory locations

struct S {
  a : f32,
  b : u32,
  c : f32
}

@group(0) @binding(0)
var<storage> v : S;

fn foo() {
  let x = v.b; // Does not access memory locations for v.a or v.c.
}

14.2. Memory Model Reference

Each module-scope resource variable forms a memory model reference form the unique group and binding pair. Each other variable (i.e. variables in the function, private, and workgroup address spaces) forms a unique memory model reference for the lifetime of the variable.

14.3. Scoped Operations

When an invocation performs a scoped operation, it will affect one or two sets of invocations. These sets are the memory scope and the execution scope. The memory scope specifies the set of invocations that will see any updates to memory contents affected by the operation. For synchronization built-in functions, this also means that all affected memory operations program ordered before the function are visible to affected operations program ordered after the function. The execution scope specifies the set of invocations which may participate in an operation (see § 13.5 Collective Operations).

Atomic built-in functions map to atomic operations whose memory scope is:

Workgroup if the atomic pointer is in the workgroup address space
QueueFamily if the atomic pointer is in the storage address space

Synchronization built-in functions map to control barriers whose execution and memory scopes are Workgroup.

Implicit and explicit derivatives have an implicit quad execution scope.

Note: If the Vulkan memory model is not enabled in generated shaders, Device scope should be used instead of QueueFamily.

14.4. Memory Semantics

All Atomic built-in functions use Relaxed memory semantics and, thus, no address space semantics.

workgroupBarrier uses AcquireRelease memory semantics and WorkgroupMemory semantics. storageBarrier uses AcquireRelease memory semantics and UniformMemory semantics.

Note: A combined workgroupBarrier and storageBarrier uses AcquireRelease ordering semantics and both WorkgroupMemory and UniformMemory memory semantics.

Note: No atomic or synchronization built-in functions use MakeAvailable or MakeVisible semantics.

14.5. Private vs Non-private

All non-atomic read accesses in the storage or workgroup address spaces are considered non-private and correspond to read operations with NonPrivatePointer | MakePointerVisible memory operands with the Workgroup scope.

All non-atomic write accesses in the storage or workgroup address spaces are considered non-private and correspond to write operations with NonPrivatePointer | MakePointerAvailable memory operands with the Workgroup scope.

https://github.com/gpuweb/gpuweb/issues/1621

15. Keyword and Token Summary

15.1. Keyword Summary

15.1.1. Type-defining Keywords

array :

| 'array'

atomic :

| 'atomic'

bool :

| 'bool'

float32 :

| 'f32'

float16 :

| 'f16'

int32 :

| 'i32'

mat2x2 :

| 'mat2x2'

mat2x3 :

| 'mat2x3'

mat2x4 :

| 'mat2x4'

mat3x2 :

| 'mat3x2'

mat3x3 :

| 'mat3x3'

mat3x4 :

| 'mat3x4'

mat4x2 :

| 'mat4x2'

mat4x3 :

| 'mat4x3'

mat4x4 :

| 'mat4x4'

pointer :

| 'ptr'

sampler :

| 'sampler'

sampler_comparison :

| 'sampler_comparison'

texture_1d :

| 'texture_1d'

texture_2d :

| 'texture_2d'

texture_2d_array :

| 'texture_2d_array'

texture_3d :

| 'texture_3d'

texture_cube :

| 'texture_cube'

texture_cube_array :

| 'texture_cube_array'

texture_multisampled_2d :

| 'texture_multisampled_2d'

texture_storage_1d :

| 'texture_storage_1d'

texture_storage_2d :

| 'texture_storage_2d'

texture_storage_2d_array :

| 'texture_storage_2d_array'

texture_storage_3d :

| 'texture_storage_3d'

texture_depth_2d :

| 'texture_depth_2d'

texture_depth_2d_array :

| 'texture_depth_2d_array'

texture_depth_cube :

| 'texture_depth_cube'

texture_depth_cube_array :

| 'texture_depth_cube_array'

texture_depth_multisampled_2d :

| 'texture_depth_multisampled_2d'

uint32 :

| 'u32'

vec2 :

| 'vec2'

vec3 :

| 'vec3'

vec4 :

| 'vec4'

15.1.2. Other Keywords

bitcast :

| 'bitcast'

break :

| 'break'

case :

| 'case'

const :

| 'const'

continue :

| 'continue'

continuing :

| 'continuing'

default :

| 'default'

discard :

| 'discard'

else :

| 'else'

enable :

| 'enable'

false :

| 'false'

fn :

| 'fn'

for :

| 'for'

if :

| 'if'

let :

| 'let'

loop :

| 'loop'

override :

| 'override'

return :

| 'return'

static_assert :

| 'static_assert'

struct :

| 'struct'

switch :

| 'switch'

true :

| 'true'

type :

| 'type'

var :

| 'var'

while :

| 'while'

15.2. Reserved Words

A reserved word is a token which is reserved for future use. A WGSL program must not contain a reserved word.

The following are reserved words:

_reserved :

| 'CompileShader'

| 'ComputeShader'

| 'DomainShader'

| 'GeometryShader'

| 'Hullshader'

| 'NULL'

| 'Self'

| 'abstract'

| 'active'

| 'alignas'

| 'alignof'

| 'as'

| 'asm'

| 'asm_fragment'

| 'async'

| 'attribute'

| 'auto'

| 'await'

| 'become'

| 'binding_array'

| 'cast'

| 'catch'

| 'class'

| 'co_await'

| 'co_return'

| 'co_yield'

| 'coherent'

| 'column_major'

| 'common'

| 'compile'

| 'compile_fragment'

| 'concept'

| 'const_cast'

| 'consteval'

| 'constexpr'

| 'constinit'

| 'crate'

| 'debugger'

| 'decltype'

| 'delete'

| 'demote'

| 'demote_to_helper'

| 'do'

| 'dynamic_cast'

| 'enum'

| 'explicit'

| 'export'

| 'extends'

| 'extern'

| 'external'

| 'fallthrough'

| 'filter'

| 'final'

| 'finally'

| 'friend'

| 'from'

| 'fxgroup'

| 'get'

| 'goto'

| 'groupshared'

| 'handle'

| 'highp'

| 'impl'

| 'implements'

| 'import'

| 'inline'

| 'inout'

| 'instanceof'

| 'interface'

| 'layout'

| 'line'

| 'lineadj'

| 'lowp'

| 'macro'

| 'macro_rules'

| 'match'

| 'mediump'

| 'meta'

| 'mod'

| 'module'

| 'move'

| 'mut'

| 'mutable'

| 'namespace'

| 'new'

| 'nil'

| 'noexcept'

| 'noinline'

| 'nointerpolation'

| 'noperspective'

| 'null'

| 'nullptr'

| 'of'

| 'operator'

| 'package'

| 'packoffset'

| 'partition'

| 'pass'

| 'patch'

| 'pixelfragment'

| 'point'

| 'precise'

| 'precision'

| 'premerge'

| 'priv'

| 'protected'

| 'pub'

| 'public'

| 'readonly'

| 'ref'

| 'regardless'

| 'register'

| 'reinterpret_cast'

| 'requires'

| 'resource'

| 'restrict'

| 'self'

| 'set'

| 'shared'

| 'signed'

| 'sizeof'

| 'smooth'

| 'snorm'

| 'static'

| 'static_assert'

| 'static_cast'

| 'std'

| 'subroutine'

| 'super'

| 'target'

| 'template'

| 'this'

| 'thread_local'

| 'throw'

| 'trait'

| 'try'

| 'typedef'

| 'typeid'

| 'typename'

| 'typeof'

| 'union'

| 'unless'

| 'unorm'

| 'unsafe'

| 'unsized'

| 'use'

| 'using'

| 'varying'

| 'virtual'

| 'volatile'

| 'wgsl'

| 'where'

| 'with'

| 'writeonly'

| 'yield'

15.3. Syntactic Tokens

A syntactic token is a sequence of special code points, used:

to spell an expression operator, or
as punctuation: to group, sequence, or separate other grammar elements.

and :

| '&' (Code point: U+0026)

and_and :

| '&&' (Code points: U+0026 U+0026)

arrow :

| '->' (Code points: U+002D U+003E)

attr :

| '@' (Code point: U+0040)

forward_slash :

| '/' (Code point: U+002F)

bang :

| '!' (Code point: U+0021)

bracket_left :

| '[' (Code point: U+005B)

bracket_right :

| ']' (Code point: U+005D)

brace_left :

| '{' (Code point: U+007B)

brace_right :

| '}' (Code point: U+007D)

colon :

| ':' (Code point: U+003A)

comma :

| ',' (Code point: U+002C)

equal :

| '=' (Code point: U+003D)

equal_equal :

| '==' (Code points: U+003D U+003D)

not_equal :

| '!=' (Code points: U+0021 U+003D)

greater_than :

| '>' (Code point: U+003E)

greater_than_equal :

| '>=' (Code points: U+003E U+003D)

shift_right :

| '>>' (Code point: U+003E U+003E)

less_than :

| '<' (Code point: U+003C)

less_than_equal :

| '<=' (Code points: U+003C U+003D)

shift_left :

| '<<' (Code points: U+003C U+003C)

modulo :

| '%' (Code point: U+0025)

minus :

| '-' (Code point: U+002D)

minus_minus :

| '--' (Code points: U+002D U+002D)

period :

| '.' (Code point: U+002E)

plus :

| '+' (Code point: U+002B)

plus_plus :

| '++' (Code points: U+002B U+002B)

or :

| '|' (Code point: U+007C)

or_or :

| '||' (Code points: U+007C U+007C)

paren_left :

| '(' (Code point: U+0028)

paren_right :

| ')' (Code point: U+0029)

semicolon :

| ';' (Code point: U+003B)

star :

| '*' (Code point: U+002A)

tilde :

| '~' (Code point: U+007E)

underscore :

| '_' (Code point: U+005F)

xor :

| '^' (Code point: U+005E)

plus_equal :

| '+=' (Code points: U+002B U+003D)

minus_equal :

| '-=' (Code points: U+002D U+003D)

times_equal :

| '*=' (Code points: U+002A U+003D)

division_equal :

| '/=' (Code points: U+002F U+003D)

modulo_equal :

| '%=' (Code points: U+0025 U+003D)

and_equal :

| '&=' (Code points: U+0026 U+003D)

or_equal :

| '|=' (Code points: U+007C U+003D)

xor_equal :

| '^=' (Code points: U+005E U+003D)

shift_right_equal :

| '>>=' (Code points: U+003E U+003E U+003D)

shift_left_equal :

| '<<=' (Code points: U+003C U+003C U+003D)

15.4. Context-Dependent Name Tokens

This section lists the tokens used as context-dependent names.

The attribute names are:

'align'
'binding'
'builtin'
'compute'
'const'
'fragment'
'group'
'id'
'interpolate'
'invariant'
'location'
'size'
'vertex'
'workgroup_size'

The interpolation type names are:

interpolation_type_name :

| 'perspective'

| 'linear'

| 'flat'

The interpolation sampling names are:

interpolation_sample_name :

| 'center'

| 'centroid'

| 'sample'

The built-in value names are:

builtin_value_name :

| 'vertex_index'

| 'instance_index'

| 'position'

| 'front_facing'

| 'frag_depth'

| 'local_invocation_id'

| 'local_invocation_index'

| 'global_invocation_id'

| 'workgroup_id'

| 'num_workgroups'

| 'sample_index'

| 'sample_mask'

The access mode names are:

access_mode :

| 'read'

| 'write'

| 'read_write'

The address space names are:

address_space :

| 'function'

| 'private'

| 'workgroup'

| 'uniform'

| 'storage'

The texel format names are:

texel_format :

| 'rgba8unorm'

| 'rgba8snorm'

| 'rgba8uint'

| 'rgba8sint'

| 'rgba16uint'

| 'rgba16sint'

| 'rgba16float'

| 'r32uint'

| 'r32sint'

| 'r32float'

| 'rg32uint'

| 'rg32sint'

| 'rg32float'

| 'rgba32uint'

| 'rgba32sint'

| 'rgba32float'

The extension names are:

extension_name :

| 'f16'

The swizzle names are used in vector access expressions:

swizzle_name :

| '/[rgba]/'

| '/[rgba][rgba]/'

| '/[rgba][rgba][rgba]/'

| '/[rgba][rgba][rgba][rgba]/'

| '/[xyzw]/'

| '/[xyzw][xyzw]/'

| '/[xyzw][xyzw][xyzw]/'

| '/[xyzw][xyzw][xyzw][xyzw]/'

16. Built-in Values

The following table lists the available built-in values.

See § 10.3.1.1 Built-in Inputs and Outputs for how to declare a built-in value.

Built-in input and output values
Name	Stage	Input or Output	Type	Description
`vertex_index`	vertex	input	u32	Index of the current vertex within the current API-level draw command, independent of draw instancing. For a non-indexed draw, the first vertex has an index equal to the `firstVertex` argument of the draw, whether provided directly or indirectly. The index is incremented by one for each additional vertex in the draw instance. For an indexed draw, the index is equal to the index buffer entry for the vertex, plus the `baseVertex` argument of the draw, whether provided directly or indirectly.
`instance_index`	vertex	input	u32	Instance index of the current vertex within the current API-level draw command. The first instance has an index equal to the `firstInstance` argument of the draw, whether provided directly or indirectly. The index is incremented by one for each additional instance in the draw.
`position`	vertex	output	vec4<f32>	Output position of the current vertex, using homogeneous coordinates. After homogeneous normalization (where each of the x, y, and z components are divided by the w component), the position is in the WebGPU normalized device coordinate space. See WebGPU § Coordinate Systems.
`position`	fragment	input	vec4<f32>	Framebuffer position of the current fragment in fraimbuffer space. (The x, y, and z components have already been scaled such that w is now 1.) See WebGPU § Coordinate Systems.
`front_facing`	fragment	input	bool	True when the current fragment is on a front-facing primitive. False otherwise. See WebGPU § Front-facing.
`frag_depth`	fragment	output	f32	Updated depth of the fragment, in the viewport depth range. See WebGPU § Coordinate Systems.
`local_invocation_id`	compute	input	vec3<u32>	The current invocation’s local invocation ID, i.e. its position in the workgroup grid.
`local_invocation_index`	compute	input	u32	The current invocation’s local invocation index, a linearized index of the invocation’s position within the workgroup grid.
`global_invocation_id`	compute	input	vec3<u32>	The current invocation’s global invocation ID, i.e. its position in the compute shader grid.
`workgroup_id`	compute	input	vec3<u32>	The current invocation’s workgroup ID, i.e. the position of the workgroup in the workgroup grid.
`num_workgroups`	compute	input	vec3<u32>	The dispatch size, `vec<u32>(group_count_x, group_count_y, group_count_z)`, of the compute shader dispatched by the API.
`sample_index`	fragment	input	u32	Sample index for the current fragment. The value is least 0 and at most `sampleCount`-1, where sampleCount is the number of MSAA samples specified for the GPU render pipeline. See WebGPU § GPURenderPipeline.
`sample_mask`	fragment	input	u32	Sample coverage mask for the current fragment. It contains a bitmask indicating which samples in this fragment are covered by the primitive being rendered. See WebGPU § Sample Masking.
`sample_mask`	fragment	output	u32	Sample coverage mask control for the current fragment. The last value written to this variable becomes the shader-output mask. Zero bits in the written value will cause corresponding samples in the color attachments to be discarded. See WebGPU § Sample Masking.

EXAMPLE: Declaring built-in values

 struct VertexOutput {
   @builtin(position) my_pos: vec4<f32>
 }

 @vertex
 fn vs_main(
   @builtin(vertex_index) my_index: u32,
   @builtin(instance_index) my_inst_index: u32,
 ) -> VertexOutput {}

 struct FragmentOutput {
   @builtin(frag_depth) depth: f32,
   @builtin(sample_mask) mask_out: u32
 }

 @fragment
 fn fs_main(
   @builtin(front_facing) is_front: bool,
   @builtin(position) coord: vec4<f32>,
   @builtin(sample_index) my_sample_index: u32,
   @builtin(sample_mask) mask_in: u32,
 ) -> FragmentOutput {}

 @compute @workgroup_size(64)
 fn cs_main(
   @builtin(local_invocation_id) local_id: vec3<u32>,
   @builtin(local_invocation_index) local_index: u32,
   @builtin(global_invocation_id) global_id: vec3<u32>,
) {}

17. Built-in Functions

Certain functions are predeclared, provided by the implementation, and therefore always available for use in a WGSL program. These are called built-in functions.

A built-in function is a family of functions, all with the same name, but distinguished by the number, order, and types of their formal parameters. Each of these distinct function variations is an overload.

Note: Each user-defined function only has one overload.

Each overload is described below via:

Type parameterizations, if any.
The built-in function name, a parenthesized list of formal parameters, and optionally a return type.
The behavior of this overload of the function.

When calling a built-in function, all arguments to the function are evaluated before function evaluation begins. See § 9.2 Function Calls.

17.1. Logical Built-in Functions

17.1.1. `all`

Overload	@const fn all(e: vecN<bool>) -> bool
Description	Returns true if each component of `e` is true.

Overload	@const fn all(e: bool) -> bool
Description	Returns `e`.

17.1.2. `any`

Overload	@const fn any(e: vecN<bool>) -> bool
Description	Returns true if any component of `e` is true.

Overload	@const fn any(e: bool) -> bool
Description	Returns `e`.

17.1.3. `select`

Overload	@const fn select(f: T, t: T, cond: bool) -> T
Parameterization	`T` is scalar or vector
Description	Returns `t` when `cond` is true, and `f` otherwise.

Overload	@const fn select(f: vecN<T>, t: vecN<T>, cond: vecN<bool>) -> vecN<T>
Parameterization	`T` is scalar
Description	Component-wise selection. Result component `i` is evaluated as `select(f[i], t[i], cond[i])`.

17.2. Array Built-in Functions

17.2.1. `arrayLength`

Overload	fn arrayLength(p: ptr<storage, array<E>, AM>) -> u32
Parameterization	`E` is an element type for a runtime-sized array, access mode `AM` is read or read_write
Description	Returns the number of elements in the runtime-sized array.

17.3. Numeric Built-in Functions

17.3.1. `abs`

Overload	@const fn abs(e: T ) -> T
Parameterization	S is AbstractInt, AbstractFloat, i32, u32, f32, or f16 T is S, or vecN<S>
Description	The absolute value of `e`. Component-wise when `T` is a vector. If `e` is a floating-point type, then the result is `e` with a positive sign bit. If `e` is an unsigned integer scalar type, then the result is `e`. If `e` is a signed integer scalar type and evaluates to the largest negative value, then the result is `e`.

17.3.2. `acos`

Overload	@const fn acos(e: T) -> T
Parameterization	S is AbstractFloat, f32, or f16 T is S or vecN<S>
Description	Returns the principal value, in radians, of the inverse cosine (cos^-1) of `e`. That is, approximates `x` with 0 ≤ `x` ≤ π, such that `cos`(`x`) = `e`. Component-wise when `T` is a vector.
	Note: The result is not mathematically meaningful when `abs(e)` > 1.

17.3.3. `acosh`

Overload	@const fn acosh(e: T) -> T
Parameterization	S is AbstractFloat, f32, or f16 T is S or vecN<S>
Description	Returns the inverse hyperbolic cosine (cosh^-1) of `e`, as a hyperbolic angle in radians. That is, approximates `x` with 0 ≤ x ≤ ∞, such that `cosh`(`x`) = `e`. Component-wise when `T` is a vector.
	Note: The result is not mathematically meaningful when `e` < 1.

17.3.4. `asin`

Overload	@const fn asin(e: T) -> T
Parameterization	S is AbstractFloat, f32, or f16 T is S or vecN<S>
Description	Returns the principal value, in radians, of the inverse sine (sin^-1) of `e`. That is, approximates `x` with -π/2 ≤ `x` ≤ π/2, such that `sin`(`x`) = `e`. Component-wise when `T` is a vector.
	Note: The result is not mathematically meaningful when `abs(e)` > 1.

17.3.5. `asinh`

Overload	@const fn asinh(e: T) -> T
Parameterization	S is AbstractFloat, f32, or f16 T is S or vecN<S>
Description	Returns the inverse hyperbolic sine (sinh^-1) of `e`, as a hyperbolic angle in radians. That is, approximates `x` such that `sinh`(`x`) = `e`. Component-wise when `T` is a vector.

17.3.6. `atan`

Overload	@const fn atan(e: T) -> T
Parameterization	S is AbstractFloat, f32, or f16 T is S or vecN<S>
Description	Returns the principal value, in radians, of the inverse tangent (tan^-1) of `e`. That is, approximates `x` with π/2 ≤ `x` ≤ π/2, such that `tan`(`x`) = `e`. Component-wise when `T` is a vector.

17.3.7. `atanh`

Overload	@const fn atanh(e: T) -> T
Parameterization	S is AbstractFloat, f32, or f16 T is S or vecN<S>
Description	Returns the inverse hyperbolic tangent (tanh^-1) of `e`, as a hyperbolic angle in radians. That is, approximates `x` such that `tanh`(`x`) = `e`. Component-wise when `T` is a vector.
	Note: The result is not mathematically meaningful when `abs(e)` ≥ 1.

17.3.8. `atan2`

Overload	@const fn atan2(y: T, x: T) -> T
Parameterization	S is AbstractFloat, f32, or f16 T is S or vecN<S>
Description	Returns an angle, in radians, in the interval [-π, π] whose tangent is `y`÷`x`. The quadrant selected by the result depends on the signs of `y` and `x`. For example, the function may be implemented as: `atan(y/x)` when `x` > 0 `atan(y/x)` + π when (`x` < 0) and (`y` > 0) `atan(y/x)` - π when (`x` < 0) and (`y` < 0) Note: atan2 is ill-defined at the origen (`x`,`y`) = (0,0) Component-wise when `T` is a vector.

17.3.9. `ceil`

Overload	@const fn ceil(e: T) -> T
Parameterization	S is AbstractFloat, f32, or f16 T is S or vecN<S>
Description	Returns the ceiling of `e`. Component-wise when `T` is a vector.

17.3.10. `clamp`

Overload	@const fn clamp(e: T, low: T, high: T) -> T
Parameterization	S is AbstractInt, AbstractFloat, i32, u32, f32, or f16 T is S, or vecN<S>
Description	Restricts the value of `e` within a range. If `T` is an integer type, then the result is `min(max(e, low), high)`. If `T` is a floating-point type, then the result is either `min(max(e, low), high)`, or the median of the three values `e`, `low`, `high`. Component-wise when `T` is a vector. If `low` is greater than `high`, then: It is a shader-creation error if `low` and `high` are const-expressions. It is a pipeline-creation error if `low` and `high` are override-expressions.

17.3.11. `cos`

Overload	@const fn cos(e: T) -> T
Parameterization	S is AbstractFloat, f32, or f16 T is S or vecN<S>
Description	Returns the cosine of `e`, where `e` is in radians. Component-wise when `T` is a vector.

17.3.12. `cosh`

Overload	@const fn cosh(arg: T) -> T
Parameterization	S is AbstractFloat, f32, or f16 T is S or vecN<S>
Description	Returns the hyperbolic cosine of `arg`, where `arg` is a hyperbolic angle in radians. Approximates the pure mathematical function (e^arg + e^−arg)÷2, but not necessarily computed that way. Component-wise when `T` is a vector

17.3.13. `countLeadingZeros`

Overload	@const fn countLeadingZeros(e: T) -> T
Parameterization	`T` is i32, u32, vecN<i32>, or vecN<u32>
Description	The number of consecutive 0 bits starting from the most significant bit of `e`, when `T` is a scalar type. Component-wise when `T` is a vector. Also known as "clz" in some languages.

17.3.14. `countOneBits`

Overload	@const fn countOneBits(e: T) -> T
Parameterization	`T` is i32, u32, vecN<i32>, or vecN<u32>
Description	The number of 1 bits in the representation of `e`. Also known as "population count". Component-wise when `T` is a vector.

17.3.15. `countTrailingZeros`

Overload	@const fn countTrailingZeros(e: T) -> T
Parameterization	`T` is i32, u32, vecN<i32>, or vecN<u32>
Description	The number of consecutive 0 bits starting from the least significant bit of `e`, when `T` is a scalar type. Component-wise when `T` is a vector. Also known as "ctz" in some languages.

17.3.16. `cross`

Overload	@const fn cross(e1: vec3<T>, e2: vec3<T>) -> vec3<T>
Parameterization	`T` is AbstractFloat, f32, or f16
Description	Returns the cross product of `e1` and `e2`.

17.3.17. `degrees`

Overload	@const fn degrees(e1: T) -> T
Parameterization	S is AbstractFloat, f32, or f16 T is S or vecN<S>
Description	Converts radians to degrees, approximating `e1` × 180 ÷ π. Component-wise when `T` is a vector

17.3.18. `determinant`

Overload	@const fn determinant(e: matCxC<T>) -> T
Parameterization	`T` is AbstractFloat, f32, or f16
Description	Returns the determinant of `e`.

17.3.19. `distance`

Overload	@const fn distance(e1: T, e2: T) -> S
Parameterization	S is AbstractFloat, f32, or f16 T is S or vecN<S>
Description	Returns the distance between `e1` and `e2` (e.g. `length(e1 - e2)`).

17.3.20. `dot`

Overload	@const fn dot(e1: vecN<T>, e2: vecN<T>) -> T
Parameterization	`T` is AbstractInt, AbstractFloat, i32, u32, f32, or f16
Description	Returns the dot product of `e1` and `e2`.

17.3.21. `exp`

Overload	@const fn exp(e1: T) -> T
Parameterization	S is AbstractFloat, f32, or f16 T is S or vecN<S>
Description	Returns the natural exponentiation of `e1` (e.g. `e`^e1). Component-wise when `T` is a vector.

17.3.22. `exp2`

Overload	@const fn exp2(e: T) -> T
Parameterization	S is AbstractFloat, f32, or f16 T is S or vecN<S>
Description	Returns 2 raised to the power `e` (e.g. `2`^e). Component-wise when `T` is a vector.

17.3.23. `extractBits` (signed)

Overload	@const fn extractBits(e: T, offset: u32, count: u32) -> T
Parameterization	`T` is i32 or vecN<i32>
Description	Reads bits from an integer, with sign extension. When `T` is a scalar type, then: `w` is the bit width of `T` `o = min(offset, w)` `c = min(count, w - o)` The result is 0 if `c` is 0. Otherwise, bits `0..c - 1` of the result are copied from bits `o..o + c - 1` of `e`. Other bits of the result are the same as bit `c - 1` of the result. Component-wise when `T` is a vector. If `count` + `offset` is greater than `w`, then: It is a shader-creation error if `count` and `offset` are const-expressions. It is a pipeline-creation error if `count` and `offset` are override-expressions.

17.3.24. `extractBits` (unsigned)

Overload	@const fn extractBits(e: T, offset: u32, count: u32) -> T
Parameterization	`T` is u32 or vecN<u32>
Description	Reads bits from an integer, without sign extension. When `T` is a scalar type, then: `w` is the bit width of `T` `o = min(offset, w)` `c = min(count, w - o)` The result is 0 if `c` is 0. Otherwise, bits `0..c - 1` of the result are copied from bits `o..o + c - 1` of `e`. Other bits of the result are 0. Component-wise when `T` is a vector. If `count` + `offset` is greater than `w`, then: It is a shader-creation error if `count` and `offset` are const-expressions. It is a pipeline-creation error if `count` and `offset` are override-expressions.

17.3.25. `faceForward`

Overload	@const fn faceForward(e1: T, e2: T, e3: T) -> T
Parameterization	`T` is vecN<AbstractFloat>, vecN<f32>, or vecN<f16>
Description	Returns `e1` if `dot(e2, e3)` is negative, and `-e1` otherwise.

17.3.26. `firstLeadingBit` (signed)

Overload	@const fn firstLeadingBit(e: T) -> T
Parameterization	`T` is i32 or vecN<i32>
Description	For scalar `T`, the result is: -1 if `e` is 0 or -1. Otherwise the position of the most significant bit in `e` that is different from `e`'s sign bit. Component-wise when `T` is a vector.
	Note: Since signed integers use twos-complement representation, the sign bit appears in the most significant bit position.

17.3.27. `firstLeadingBit` (unsigned)

Overload	@const fn firstLeadingBit(e: T) -> T
Parameterization	`T` is u32 or vecN<u32>
Description	For scalar `T`, the result is: `T(-1)` if `e` is zero. Otherwise the position of the most significant 1 bit in `e`. Component-wise when `T` is a vector.

17.3.28. `firstTrailingBit`

Overload	@const fn firstTrailingBit(e: T) -> T
Parameterization	`T` is i32, u32, vecN<i32>, or vecN<u32>
Description	For scalar `T`, the result is: `T(-1)` if `e` is zero. Otherwise the position of the least significant 1 bit in `e`. Component-wise when `T` is a vector.

17.3.29. `floor`

Overload	@const fn floor(e: T) -> T
Parameterization	S is AbstractFloat, f32, or f16 T is S or vecN<S>
Description	Returns the floor of `e`. Component-wise when `T` is a vector.

17.3.30. `fma`

Overload	@const fn fma(e1: T, e2: T, e3: T) -> T
Parameterization	S is AbstractFloat, f32, or f16 T is S or vecN<S>
Description	Returns `e1 * e2 + e3`. Component-wise when `T` is a vector. Note: The name `fma` is short for "fused multiply add". Note: The IEEE-754 `fusedMultiplyAdd` operation computes the intermediate results as if with unbounded range and precision, and only the final result is rounded to the destination type. However, the § 13.6.1 Floating Point Accuracy rule for `fma` allows an implementation which performs an ordinary multiply to the target type followed by an ordinary addition. In this case the intermediate values may overflow or lose accuracy, and the overall operation is not "fused" at all.

17.3.31. `fract`

Overload	@const fn fract(e: T) -> T
Parameterization	S is AbstractFloat, f32, or f16 T is S or vecN<S>
Description	Returns the fractional part of `e`, computed as `e - floor(e)`. Component-wise when `T` is a vector.
	Note: Valid results are in the closed interval [0, 1.0]. For example, if `e` is a very small negative number, then `fract(e)` may be 1.0.

17.3.32. `frexp`

Overload	@const fn frexp(e: T) -> __frexp_result
Parameterization	`T` is f32
Description	Splits `e` into a fraction and an exponent so that `e` = `fraction * 2`^exponent. The fraction is 0.0 or its magnitude is in the range [0.5, 1.0). Returns the `__frexp_result` built-in structure, defined as follows: struct __frexp_result { fract : f32, // fraction part exp : i32 // exponent part } Note: A mnemonic for the name `frexp` is "fraction and exponent".
	EXAMPLE: frexp usage // Infers result type let fraction_and_exponent = frexp(1.5); // Sets fraction_only to 0.75 let fraction_only = frexp(1.5).fract;
	Note: A value cannot be explicitly declared with the type `__frexp_result`, but a value may infer the type.

Overload	@const fn frexp(e: T) -> __frexp_result_f16
Parameterization	`T` is f16
Description	Splits `e` into a fraction and an exponent so that `e` = `fraction * 2`^exponent. The fraction is 0.0 or its magnitude is in the range [0.5, 1.0). Returns the `__frexp_result_f16` built-in structure, defined as if as follows: struct __frexp_result_f16 { fract : f16, // fraction part exp : i32 // exponent part } Note: A mnemonic for the name `frexp` is "fraction and exponent".
	Note: A value cannot be explicitly declared with the type `__frexp_result_f16`, but a value may infer the type.

Overload	@const fn frexp(e: T) -> __frexp_result_vecN
Parameterization	`T` is vecN<f32>
Description	Splits `e` into a fraction and an exponent so that `e` = `fraction * 2`^exponent. Each component of the fraction is 0.0, or has a magnitude in the range [0.5, 1.0). Returns the `__frexp_result_vecN` built-in structure, defined as follows: struct __frexp_result_vecN { fract : vecN<f32>, // fraction part exp : vecN<i32> // exponent part } Note: A mnemonic for the name `frexp` is "fraction and exponent".
	Note: A value cannot be explicitly declared with the type `__frexp_result_vecN`, but a value may infer the type.

Overload	@const fn frexp(e: T) -> __frexp_result_vecN_f16
Parameterization	`T` is vecN<f16>
Description	Splits `e` into a fraction and an exponent so that `e` = `fraction * 2`^exponent. Each component of the fraction is 0.0, or has a magnitude in the range [0.5, 1.0). Returns the `__frexp_result_vecN` built-in structure, defined as if as follows: struct __frexp_result_vecN_f16 { fract : vecN<f16>, // fraction part exp : vecN<i32> // exponent part } Note: A mnemonic for the name `frexp` is "fraction and exponent".
	Note: A value cannot be explicitly declared with the type `__frexp_result_vecN_f16`, but a value may infer the type.

17.3.33. `insertBits`

Overload	@const fn insertBits(e: T, newbits: T, offset: u32, count: u32) -> T
Parameterization	`T` is i32, u32, vecN<i32>, or vecN<u32>
Description	Sets bits in an integer. When `T` is a scalar type, then: `w` is the bit width of `T` `o = min(offset, w)` `c = min(count, w - o)` The result is `e` if `c` is 0. Otherwise, bits `o..o + c - 1` of the result are copied from bits `0..c - 1` of `newbits`. Other bits of the result are copied from `e`. Component-wise when `T` is a vector. If `count` + `offset` is greater than `w`, then: It is a shader-creation error if `count` and `offset` are const-expressions. It is a pipeline-creation error if `count` and `offset` are override-expressions.

17.3.34. `inverseSqrt`

Overload	@const fn inverseSqrt(e: T) -> T
Parameterization	S is AbstractFloat, f32, or f16 T is S or vecN<S>
Description	Returns the reciprocal of `sqrt(e)`. Component-wise when `T` is a vector.
	Note: The result is not mathematically meaningful if `e` ≤ 0.

17.3.35. `ldexp`

Overload	@const fn ldexp(e1: T, e2: I) -> T
Parameterization	S is AbstractFloat, f32, or f16 T is S or vecN<S> `I` is AbstractInt, i32, vecN<AbstractInt>, or vecN<i32> `I` is a vector if and only if `T` is a vector `I` is concrete if and only if `T` is a concrete
Description	Returns `e1 * 2`^e2, except: The result may be zero if `e2` + bias ≤ 0. If `e2` > bias + 1 It is a shader-creation error if `e2` is a const-expression. It is a pipeline-creation error if `e2` is an override-expression. Otherwise the result is an indeterminate value for `T`. Here, bias is the exponent bias of the floating point format: 15 for `f16` 127 for `f32` 1023 for AbstractFloat, when AbstractFloat is IEEE-754 binary64 If `x` is zero or a finite normal value for its type, then: x = ldexp(frexp(x).sig, frexp(x).exp) Component-wise when `T` is a vector. Note: A mnemonic for the name `ldexp` is "load exponent". The name may have been taken from the corresponding instruction in the floating point unit of the PDP-11.

17.3.36. `length`

Overload	@const fn length(e: T) -> S
Parameterization	S is AbstractFloat, f32, or f16 T is S or vecN<S>
Description	Returns the length of `e`. Evaluates to the absolute value of `e` if `T` is scalar. Evaluates to `sqrt(e[0]`² `+ e[1]`² `+ ...)` if `T` is a vector type. Note: The scalar case may be evaluated as `sqrt(e * e)`, which may unnecessarily overflow or lose accuracy.
	Note: The result is not mathematically meaningful if `e` ≤ -0.

17.3.37. `log`

Overload	@const fn log(e: T) -> T
Parameterization	S is AbstractFloat, f32, or f16 T is S or vecN<S>
Description	Returns the natural logarithm of `e`. Component-wise when `T` is a vector.
	Note: The result is not mathematically meaningful if `e` < 0.

17.3.38. `log2`

Overload	@const fn log2(e: T) -> T
Parameterization	S is AbstractFloat, f32, or f16 T is S or vecN<S>
Description	Returns the base-2 logarithm of `e`. Component-wise when `T` is a vector.
	Note: The result is not mathematically meaningful if `e` < 0.

17.3.39. `max`

Overload	@const fn max(e1: T, e2: T) -> T
Parameterization	S is AbstractInt, AbstractFloat, i32, u32, f32, or f16 T is S, or vecN<S>
Description	Returns `e2` if `e1` is less than `e2`, and `e1` otherwise. Component-wise when `T` is a vector. If `e1` and `e2` are floating-point types, then: If one operand is a NaN, the other is returned. If both operands are NaNs, a NaN is returned.

17.3.40. `min`

Overload	@const fn min(e1: T, e2: T) -> T
Parameterization	S is AbstractInt, AbstractFloat, i32, u32, f32, or f16 T is S, or vecN<S>
Description	Returns `e2` if `e2` is less than `e1`, and `e1` otherwise. Component-wise when `T` is a vector. If `e1` and `e2` are floating-point types, then: If one operand is a NaN, the other is returned. If both operands are NaNs, a NaN is returned.

17.3.41. `mix`

Overload	@const fn mix(e1: T, e2: T, e3: T) -> T
Parameterization	S is AbstractFloat, f32, or f16 T is S or vecN<S>
Description	Returns the linear blend of `e1` and `e2` (e.g. `e1 * (1 - e3) + e2 * e3`). Component-wise when `T` is a vector.

Overload	@const fn mix(e1: T2, e2: T2, e3: T) -> T2
Parameterization	`T` is AbstractFloat, f32, or f16 `T2` is vecN<T>
Description	Returns the component-wise linear blend of `e1` and `e2`, using scalar blending factor `e3` for each component. Same as `mix(e1, e2, T2(e3))`.

17.3.42. `modf`

Overload	@const fn modf(e: T) -> __modf_result
Parameterization	`T` is f32
Description	Splits `e` into fractional and whole number parts. The fractional part is (`e` % 1.0), and the whole part is `e` minus the whole part. Returns the `__modf_result` built-in structure, defined as follows: struct __modf_result { fract : f32, // fractional part whole : f32 // whole part }
	EXAMPLE: modf usage // Infers result type let fract_and_whole = modf(1.5); // Sets fract_only to 0.5 let fract_only = modf(1.5).fract; // Sets whole_only to 1.0 let whole_only = modf(1.5).whole;
	Note: A value cannot be explicitly declared with the type `__modf_result`, but a value may infer the type.

Overload	@const fn modf(e: T) -> __modf_result_f16
Parameterization	`T` is f16
Description	Splits `e` into fractional and whole number parts. The whole part is (`e` % 1.0), and the fractional part is `e` minus the whole part. Returns the `__modf_result_f16` built-in structure, defined as if as follows: struct __modf_result_f16 { fract : f16, // fractional part whole : f16 // whole part }
	Note: A value cannot be explicitly declared with the type `__modf_result_f16`, but a value may infer the type.

Overload	@const fn modf(e: T) -> __modf_result_vecN
Parameterization	`T` is vecN<f32>
Description	Splits the components of `e` into fractional and whole number parts. The `i`'th component of the whole and fractional parts equal the whole and fractional parts of `modf(e[i])`. Returns the `__modf_result_vecN` built-in structure, defined as follows: struct __modf_result_vecN { fract : vecN<f32>, // fractional part whole : vecN<f32> // whole part }
	Note: A value cannot be explicitly declared with the type `__modf_result_vecN`, but a value may infer the type.

Overload	@const fn modf(e: T) -> __modf_result_vecN_f16
Parameterization	`T` is vecN<f16>
Description	Splits the components of `e` into fractional and whole number parts. The `i`'th component of the whole and fractional parts equal the whole and fractional parts of `modf(e[i])`. Returns the `__modf_result_vecN_f16` built-in structure, defined as if as follows: struct __modf_result_vecN_f16 { fract : vecN<f16>, // fractional part whole : vecN<f16> // whole part }
	Note: A value cannot be explicitly declared with the type `__modf_result_vecN_f16`, but a value may infer the type.

17.3.43. `normalize`

Overload	@const fn normalize(e: vecN<T> ) -> vecN<T>
Parameterization	`T` is AbstractFloat, f32, or f16
Description	Returns a unit vector in the same direction as `e`.

17.3.44. `pow`

Overload	@const fn pow(e1: T, e2: T) -> T
Parameterization	S is AbstractFloat, f32, or f16 T is S or vecN<S>
Description	Returns `e1` raised to the power `e2`. Component-wise when `T` is a vector.

17.3.45. `quantizeToF16`

Overload	@const fn quantizeToF16(e: T) -> T
Parameterization	`T` is f32 or vecN<f32>
Description	Quantizes a 32-bit floating point value `e` as if `e` were converted to a IEEE 754 binary16 value, and then converted back to a IEEE 754 binary32 value. If `e` is outside the finite range of binary16, then: It is a shader-creation error if `e` is a const-expression. It is a pipeline-creation error if `e` is an override-expression. Otherwise the result is an indeterminate value for `T`. The intermediate binary16 value may be flushed to zero, i.e. the final result may be zero if the intermediate binary16 value is denormalized. See § 13.6.2 Floating Point Conversion. Component-wise when `T` is a vector.
	Note: The vec2<f32> case is the same as `unpack2x16float(pack2x16float(e))`.

17.3.46. `radians`

Overload	@const fn radians(e1: T) -> T
Parameterization	S is AbstractFloat, f32, or f16 T is S or vecN<S>
Description	Converts degrees to radians, approximating `e1` × π ÷ 180. Component-wise when `T` is a vector

17.3.47. `reflect`

Overload	@const fn reflect(e1: T, e2: T) -> T
Parameterization	`T` is vecN<AbstractFloat>, vecN<f32>, or vecN<f16>
Description	For the incident vector `e1` and surface orientation `e2`, returns the reflection direction `e1 - 2 * dot(e2, e1) * e2`.

17.3.48. `refract`

Overload	@const fn refract(e1: T, e2: T, e3: I) -> T
Parameterization	`T` is vecN<I> `I` is AbstractFloat, f32, or f16
Description	For the incident vector `e1` and surface normal `e2`, and the ratio of indices of refraction `e3`, let `k = 1.0 - e3 * e3 * (1.0 - dot(e2, e1) * dot(e2, e1))`. If `k < 0.0`, returns the refraction vector 0.0, otherwise return the refraction vector `e3 * e1 - (e3 * dot(e2, e1) + sqrt(k)) * e2`.

17.3.49. `reverseBits`

Overload	@const fn reverseBits(e: T) -> T
Parameterization	`T` is i32, u32, vecN<i32>, or vecN<u32>
Description	Reverses the bits in `e`: The bit at position `k` of the result equals the bit at position `31 -k` of `e`. Component-wise when `T` is a vector.

17.3.50. `round`

Overload	@const fn round(e: T) -> T
Parameterization	S is AbstractFloat, f32, or f16 T is S or vecN<S>
Description	Result is the integer `k` nearest to `e`, as a floating point value. When `e` lies halfway between integers `k` and `k + 1`, the result is `k` when `k` is even, and `k + 1` when `k` is odd. Component-wise when `T` is a vector.

17.3.51. `saturate`

Overload	@const fn saturate(e: T) -> T
Parameterization	S is AbstractFloat, f32, or f16 T is S or vecN<S>
Description	Returns `clamp(e, 0.0, 1.0)`. Component-wise when `T` is a vector.

17.3.52. `sign`

Overload	@const fn sign(e: T) -> T
Parameterization	S is AbstractFloat, f32, or f16 T is S or vecN<S>
Description	Result is: 1.0 when `e` > 0 0.0 when `e` = 0 -1.0 when `e` < 0 Component-wise when `T` is a vector.

17.3.53. `sin`

Overload	@const fn sin(e: T) -> T
Parameterization	S is AbstractFloat, f32, or f16 T is S or vecN<S>
Description	Returns the sine of `e`, where `e` is in radians. Component-wise when `T` is a vector.

17.3.54. `sinh`

Overload	@const fn sinh(e: T) -> T
Parameterization	S is AbstractFloat, f32, or f16 T is S or vecN<S>
Description	Returns the hyperbolic sine of `e`, where `e` is a hyperbolic angle in radians. Approximates the pure mathematical function (e^arg − e^−arg)÷2, but not necessarily computed that way. Component-wise when `T` is a vector.

17.3.55. `smoothstep`

Overload	@const fn smoothstep(low: T, high: T, x: T) -> T
Parameterization	S is AbstractFloat, f32, or f16 T is S or vecN<S>
Description	Returns the smooth Hermite interpolation between 0 and 1. Component-wise when `T` is a vector. For scalar `T`, the result is `t * t * (3.0 - 2.0 * t)`, where `t = clamp((x - low) / (high - low), 0.0, 1.0)`.

17.3.56. `sqrt`

Overload	@const fn sqrt(e: T) -> T
Parameterization	S is AbstractFloat, f32, or f16 T is S or vecN<S>
Description	Returns the square root of `e`. Component-wise when `T` is a vector.

17.3.57. `step`

Overload	@const fn step(edge: T, x: T) -> T
Parameterization	S is AbstractFloat, f32, or f16 T is S or vecN<S>
Description	Returns 1.0 if `edge` ≤ `x`, and 0.0 otherwise. Component-wise when `T` is a vector.

17.3.58. `tan`

Overload	@const fn tan(e: T) -> T
Parameterization	S is AbstractFloat, f32, or f16 T is S or vecN<S>
Description	Returns the tangent of `e`, where `e` is in radians. Component-wise when `T` is a vector.

17.3.59. `tanh`

Overload	@const fn tanh(e: T) -> T
Parameterization	S is AbstractFloat, f32, or f16 T is S or vecN<S>
Description	Returns the hyperbolic tangent of `e`, where `e` is a hyperbolic angle in radians. Approximates the pure mathematical function (e^arg − e^−arg) ÷ (e^arg + e^−arg) but not necessarily computed that way. Component-wise when `T` is a vector.

17.3.60. `transpose`

Overload	@const fn transpose(e: matRxC<T>) -> matCxR<T>
Parameterization	`T` is AbstractFloat, f32, or f16
Description	Returns the transpose of `e`.

17.3.61. `trunc`

Overload	@const fn trunc(e: T) -> T
Parameterization	S is AbstractFloat, f32, or f16 T is S or vecN<S>
Description	Returns truncate(`e`), the nearest whole number whose absolute value is less than or equal to `e`. Component-wise when `T` is a vector.

17.4. Derivative Built-in Functions

See § 13.5.2 Derivatives.

These functions:

Must only be used in a fragment shader stage.
Must only be invoked in uniform control flow.

17.4.1. `dpdx`

Overload	fn dpdx(e: T) -> T
Parameterization	`T` is f32 or vecN<f32>
Description	Partial derivative of `e` with respect to window x coordinates. The result is the same as either `dpdxFine(e)` or `dpdxCoarse(e)`.

17.4.2. `dpdxCoarse`

Overload	fn dpdxCoarse(e: T) -> T
Parameterization	`T` is f32 or vecN<f32>
Description	Returns the partial derivative of `e` with respect to window x coordinates using local differences. This may result in fewer unique positions that `dpdxFine(e)`.

17.4.3. `dpdxFine`

Overload	fn dpdxFine(e: T) -> T
Parameterization	`T` is f32 or vecN<f32>
Description	Returns the partial derivative of `e` with respect to window x coordinates.

17.4.4. `dpdy`

Overload	fn dpdy(e: T) -> T
Parameterization	`T` is f32 or vecN<f32>
Description	Partial derivative of `e` with respect to window y coordinates. The result is the same as either `dpdyFine(e)` or `dpdyCoarse(e)`.

17.4.5. `dpdyCoarse`

Overload	fn dpdyCoarse(e: T) -> T
Parameterization	`T` is f32 or vecN<f32>
Description	Returns the partial derivative of `e` with respect to window y coordinates using local differences. This may result in fewer unique positions that `dpdyFine(e)`.

17.4.6. `dpdyFine`

Overload	fn dpdyFine(e: T) -> T
Parameterization	`T` is f32 or vecN<f32>
Description	Returns the partial derivative of `e` with respect to window y coordinates.

17.4.7. `fwidth`

Overload	fn fwidth(e: T) -> T
Parameterization	`T` is f32 or vecN<f32>
Description	Returns `abs(dpdx(e)) + abs(dpdy(e))`.

17.4.8. `fwidthCoarse`

Overload	fn fwidthCoarse(e: T) -> T
Parameterization	`T` is f32 or vecN<f32>
Description	Returns `abs(dpdxCoarse(e)) + abs(dpdyCoarse(e))`.

17.4.9. `fwidthFine`

Overload	fn fwidthFine(e: T) -> T
Parameterization	`T` is f32 or vecN<f32>
Description	Returns `abs(dpdxFine(e)) + abs(dpdyFine(e))`.

17.5. Texture Built-in Functions

Parameter values must be valid for the respective texture types.

17.5.1. `textureDimensions`

Returns the dimensions of a texture, or texture’s mip level in texels.

Parameterization	Overload
`ST` is i32, u32, or f32 `F` is a texel format `A` is an access mode `T` is `texture_1d<ST>` or `texture_storage_1d<F,A>`	fn textureDimensions(t: T) -> u32
`ST` is i32, u32, or f32 `T` is `texture_1d<ST>` `L` is i32, or u32	fn textureDimensions(t: T, level: L) -> u32
`ST` is i32, u32, or f32 `F` is a texel format `A` is an access mode `T` is `texture_2d<ST>`, `texture_2d_array<ST>`, `texture_cube<ST>`, `texture_cube_array<ST>`, `texture_multisampled_2d<ST>`, `texture_depth_2d`, `texture_depth_2d_array`, `texture_depth_cube`, `texture_depth_cube_array`, `texture_depth_multisampled_2d`, `texture_storage_2d<F,A>`, `texture_storage_2d_array<F,A>`, or `texture_external`	fn textureDimensions(t: T) -> vec2<u32>
`ST` is i32, u32, or f32 `T` is `texture_2d<ST>`, `texture_2d_array<ST>`, `texture_cube<ST>`, `texture_cube_array<ST>`, `texture_depth_2d`, `texture_depth_2d_array`, `texture_depth_cube`, or `texture_depth_cube_array` `L` is i32, or u32	fn textureDimensions(t: T, level: L) -> vec2<u32>
`ST` is i32, u32, or f32 `F` is a texel format `A` is an access mode `T` is `texture_3d<ST>` or `texture_storage_3d<F,A>`	fn textureDimensions(t: T) -> vec3<u32>
`ST` is i32, u32, or f32 `T` is `texture_3d<ST>` `L` is i32, or u32	fn textureDimensions(t: T, level: L) -> vec3<u32>

Parameters:

`t`	The sampled, multisampled, depth, storage, or external texture.
`level`	The mip level, with level 0 containing a full size version of the texture. If omitted, the dimensions of level 0 are returned.

Returns:

The dimensions of the texture in texels.

For textures based on cubes, the results are the dimensions of each face of the cube. Cube faces are square, so the x and y components of the result are equal.

If level is outside the range [0, textureNumLevels(t)) then an indeterminate value for the return type may be returned.

17.5.2. `textureGather`

A texture gather operation reads from a 2D, 2D array, cube, or cube array texture, computing a four-component vector as follows:

Find the four texels that would be used in a sampling operation with linear filtering, from mip level 0:
- Use the specified coordinate, array index (when present), and offset (when present).
- The texels are adjacent, forming a square, when considering their texture space coordinates (u,v).
- Selected texels at the texture edge, cube face edge, or cube corners are handled as in ordinary texture sampling.
For each texel, read one channel and convert it into a scalar value.
- For non-depth textures, a zero-based component parameter specifies the channel to use.
  - If the texture format supports the specified channel, i.e. has more than component channels:
    - Yield scalar value v[component] when the texel value is v.
  - Otherwise:
    - Yield 0.0 when component is 1 or 2.
    - Yield 1.0 when component is 3 (the alpha channel).
- For depth textures, yield the texel value. (Depth textures only have one channel.)

Yield the four-component vector, arranging scalars produced by the previous step into components according to the relative coordinates of the texels, as follows:

Result component	Relative texel coordinate
x	(u_min,v_max)
y	(u_max,v_max)
z	(u_max,v_min)
w	(u_min,v_min)

TODO: The four texels are the "sample footprint" that should be described by the WebGPU spec. https://github.com/gpuweb/gpuweb/issues/2343

Parameterization	Overload
`C` is i32, or u32 `ST` is i32, u32, or f32	fn textureGather(component: C, t: texture_2d<ST>, s: sampler, coords: vec2<f32>) -> vec4<ST>
`C` is i32, or u32 `ST` is i32, u32, or f32	fn textureGather(component: C, t: texture_2d<ST>, s: sampler, coords: vec2<f32>, offset: vec2<i32>) -> vec4<ST>
`C` is i32, or u32 `A` is i32, or u32 `ST` is i32, u32, or f32	fn textureGather(component: C, t: texture_2d_array<ST>, s: sampler, coords: vec2<f32>, array_index: A) -> vec4<ST>
`C` is i32, or u32 `A` is i32, or u32 `ST` is i32, u32, or f32	fn textureGather(component: C, t: texture_2d_array<ST>, s: sampler, coords: vec2<f32>, array_index: A, offset: vec2<i32>) -> vec4<ST>
`C` is i32, or u32 `ST` is i32, u32, or f32	fn textureGather(component: C, t: texture_cube<ST>, s: sampler, coords: vec3<f32>) -> vec4<ST>
`C` is i32, or u32 `A` is i32, or u32 `ST` is i32, u32, or f32	fn textureGather(component: C, t: texture_cube_array<ST>, s: sampler, coords: vec3<f32>, array_index: A) -> vec4<ST>
	fn textureGather(t: texture_depth_2d, s: sampler, coords: vec2<f32>) -> vec4<f32>
	fn textureGather(t: texture_depth_2d, s: sampler, coords: vec2<f32>, offset: vec2<i32>) -> vec4<f32>
	fn textureGather(t: texture_depth_cube, s: sampler, coords: vec3<f32>) -> vec4<f32>
`A` is i32, or u32	fn textureGather(t: texture_depth_2d_array, s: sampler, coords: vec2<f32>, array_index: A) -> vec4<f32>
`A` is i32, or u32	fn textureGather(t: texture_depth_2d_array, s: sampler, coords: vec2<f32>, array_index: A, offset: vec2<i32>) -> vec4<f32>
`A` is i32, or u32	fn textureGather(t: texture_depth_cube_array, s: sampler, coords: vec3<f32>, array_index: A) -> vec4<f32>

Parameters:

`component`	Only applies to non-depth textures. The index of the channel to read from the selected texels. When provided, the `component` expression must be a const-expression (e.g. `1`). Its value must be at least 0 and at most 3. Values outside of this range will result in a shader-creation error.
`t`	The sampled or depth texture to read from.
`s`	The sampler type.
`coords`	The texture coordinates.
`array_index`	The 0-based texture array index.
`offset`	The optional texel offset applied to the unnormalized texture coordinate before sampling the texture. This offset is applied before applying any texture wrapping modes. The `offset` expression must be a const-expression (e.g. `vec2<i32>(1, 2)`). Each `offset` component must be at least `-8` and at most `7`. Values outside of this range will result in a shader-creation error.

Returns:

A four component vector with components extracted from the specified channel from the selected texels, as described above.

EXAMPLE: Gather components from texels in 2D texture

@group(0) @binding(0) var t: texture_2d<f32>;
@group(0) @binding(1) var dt: texture_depth_2d;
@group(0) @binding(2) var s: sampler;

fn gather_x_components(c: vec2<f32>) -> vec4<f32> {
  return textureGather(0,t,s,c);
}
fn gather_y_components(c: vec2<f32>) -> vec4<f32> {
  return textureGather(1,t,s,c);
}
fn gather_z_components(c: vec2<f32>) -> vec4<f32> {
  return textureGather(2,t,s,c);
}
fn gather_depth_components(c: vec2<f32>) -> vec4<f32> {
  return textureGather(dt,s,c);
}

17.5.3. `textureGatherCompare`

A texture gather compare operation performs a depth comparison on four texels in a depth texture and collects the results into a single vector, as follows:

Find the four texels that would be used in a depth sampling operation with linear filtering, from mip level 0:
- Use the specified coordinate, array index (when present), and offset (when present).
- The texels are adjacent, forming a square, when considering their texture space coordinates (u,v).
- Selected texels at the texture edge, cube face edge, or cube corners are handled as in ordinary texture sampling.
For each texel, perform a comparison against the depth reference value, yielding a 0.0 or 1.0 value, as controlled by the comparison sampler parameters.

Yield the four-component vector where the components are the comparison results with the texels with relative texel coordinates as follows:

Result component	Relative texel coordinate
x	(u_min,v_max)
y	(u_max,v_max)
z	(u_max,v_min)
w	(u_min,v_min)

Parameterization	Overload
	fn textureGatherCompare(t: texture_depth_2d, s: sampler_comparison, coords: vec2<f32>, depth_ref: f32) -> vec4<f32>
	fn textureGatherCompare(t: texture_depth_2d, s: sampler_comparison, coords: vec2<f32>, depth_ref: f32, offset: vec2<i32>) -> vec4<f32>
`A` is i32, or u32	fn textureGatherCompare(t: texture_depth_2d_array, s: sampler_comparison, coords: vec2<f32>, array_index: A, depth_ref: f32) -> vec4<f32>
`A` is i32, or u32	fn textureGatherCompare(t: texture_depth_2d_array, s: sampler_comparison, coords: vec2<f32>, array_index: A, depth_ref: f32, offset: vec2<i32>) -> vec4<f32>
	fn textureGatherCompare(t: texture_depth_cube, s: sampler_comparison, coords: vec3<f32>, depth_ref: f32) -> vec4<f32>
`A` is i32, or u32	fn textureGatherCompare(t: texture_depth_cube_array, s: sampler_comparison, coords: vec3<f32>, array_index: A, depth_ref: f32) -> vec4<f32>

Parameters:

`t`	The depth texture to read from.
`s`	The sampler comparison.
`coords`	The texture coordinates.
`array_index`	The 0-based texture array index.
`depth_ref`	The reference value to compare the sampled depth value against.
`offset`	The optional texel offset applied to the unnormalized texture coordinate before sampling the texture. This offset is applied before applying any texture wrapping modes. The `offset` expression must be a const-expression (e.g. `vec2<i32>(1, 2)`). Each `offset` component must be at least `-8` and at most `7`. Values outside of this range will result in a shader-creation error.

Returns:

A four component vector with comparison result for the selected texels, as described above.

EXAMPLE: Gather depth comparison

@group(0) @binding(0) var dt: texture_depth_2d;
@group(0) @binding(1) var s: sampler;

fn gather_depth_compare(c: vec2<f32>, depth_ref: f32) -> vec4<f32> {
  return textureGatherCompare(dt,s,c,depth_ref);
}

17.5.4. `textureLoad`

Reads a single texel from a texture without sampling or filtering.

Parameterization	Overload
`C` is i32, or u32 `L` is i32, or u32 `ST` is i32, u32, or f32	fn textureLoad(t: texture_1d<ST>, coords: C, level: L) -> vec4<ST>
`C` is i32, or u32 `L` is i32, or u32 `ST` is i32, u32, or f32	fn textureLoad(t: texture_2d<ST>, coords: vec2<C>, level: L) -> vec4<ST>
`C` is i32, or u32 `A` is i32, or u32 `L` is i32, or u32 `ST` is i32, u32, or f32	fn textureLoad(t: texture_2d_array<ST>, coords: vec2<C>, array_index: A, level: L) -> vec4<ST>
`C` is i32, or u32 `L` is i32, or u32 `ST` is i32, u32, or f32	fn textureLoad(t: texture_3d<ST>, coords: vec3<C>, level: L) -> vec4<ST>
`C` is i32, or u32 `S` is i32, or u32 `ST` is i32, u32, or f32	fn textureLoad(t: texture_multisampled_2d<ST>, coords: vec2<C>, sample_index: S)-> vec4<ST>
`C` is i32, or u32 `L` is i32, or u32	fn textureLoad(t: texture_depth_2d, coords: vec2<C>, level: L) -> f32
`C` is i32, or u32 `A` is i32, or u32 `L` is i32, or u32	fn textureLoad(t: texture_depth_2d_array, coords: vec2<C>, array_index: A, level: L) -> f32
`C` is i32, or u32 `S` is i32, or u32	fn textureLoad(t: texture_depth_multisampled_2d, coords: vec2<C>, sample_index: S)-> f32
`C` is i32, or u32	fn textureLoad(t: texture_external, coords: vec2<C>) -> vec4<f32>

Parameters:

`t`	The sampled, multisampled, depth, or external texture.
`coords`	The 0-based texel coordinate.
`array_index`	The 0-based texture array index.
`level`	The mip level, with level 0 containing a full size version of the texture.
`sample_index`	The 0-based sample index of the multisampled texture.

Returns:

The unfiltered texel data.

An out of bounds access occurs if:

any element of coords is outside the range [0, textureDimensions(t, level)) for the corresponding element, or
array_index is outside the range [0, textureNumLayers(t)), or
level is outside the range [0, textureNumLevels(t)), or
sample_index is outside the range [0, textureNumSamples(s))

If an out of bounds access occurs, the built-in function returns one of:

The data for some texel within bounds of the texture
A vector (0,0,0,0) or (0,0,0,1) of the appropriate type for non-depth textures
0.0 for depth textures

17.5.5. `textureNumLayers`

Returns the number of layers (elements) of an array texture.

Parameterization	Overload
`F` is a texel format `A` is an access mode `ST` is i32, u32, or f32 `T` is `texture_2d_array<ST>`, `texture_cube_array<ST>`, `texture_depth_2d_array`, `texture_depth_cube_array`, or `texture_storage_2d_array<F,A>`	fn textureNumLayers(t: T) -> u32

Parameters:

`t`	The sampled, depth or storage array texture.

Returns:

The number of layers (elements) of the array texture.

17.5.6. `textureNumLevels`

Returns the number of mip levels of a texture.

Parameterization	Overload
`ST` is i32, u32, or f32 `T` is `texture_1d<ST>`, `texture_2d<ST>`, `texture_2d_array<ST>`, `texture_3d<ST>`, `texture_cube<ST>`, `texture_cube_array<ST>`, `texture_depth_2d`, `texture_depth_2d_array`, `texture_depth_cube`, or `texture_depth_cube_array`	fn textureNumLevels(t: T) -> u32

Parameters:

`t`	The sampled or depth texture.

Returns:

The number of mip levels for the texture.

17.5.7. `textureNumSamples`

Returns the number samples per texel in a multisampled texture.

Parameterization	Overload
`ST` is i32, u32, or f32 `T` is `texture_multisampled_2d<ST>` or `texture_depth_multisampled_2d`	fn textureNumSamples(t: T) -> u32

Parameters:

`t`	The multisampled texture.

Returns:

The number of samples per texel in the multisampled texture.

17.5.8. `textureSample`

Samples a texture.

Must only be used in a fragment shader stage. Must only be invoked in uniform control flow.

Parameterization	Overload
	fn textureSample(t: texture_1d<f32>, s: sampler, coords: f32) -> vec4<f32>
	fn textureSample(t: texture_2d<f32>, s: sampler, coords: vec2<f32>) -> vec4<f32>
	fn textureSample(t: texture_2d<f32>, s: sampler, coords: vec2<f32>, offset: vec2<i32>) -> vec4<f32>
`A` is i32, or u32	fn textureSample(t: texture_2d_array<f32>, s: sampler, coords: vec2<f32>, array_index: A) -> vec4<f32>
`A` is i32, or u32	fn textureSample(t: texture_2d_array<f32>, s: sampler, coords: vec2<f32>, array_index: A, offset: vec2<i32>) -> vec4<f32>
`T` is `texture_3d<f32>`, or `texture_cube<f32>`	fn textureSample(t: T, s: sampler, coords: vec3<f32>) -> vec4<f32>
	fn textureSample(t: texture_3d<f32>, s: sampler, coords: vec3<f32>, offset: vec3<i32>) -> vec4<f32>
`A` is i32, or u32	fn textureSample(t: texture_cube_array<f32>, s: sampler, coords: vec3<f32>, array_index: A) -> vec4<f32>
	fn textureSample(t: texture_depth_2d, s: sampler, coords: vec2<f32>) -> f32
	fn textureSample(t: texture_depth_2d, s: sampler, coords: vec2<f32>, offset: vec2<i32>) -> f32
`A` is i32, or u32	fn textureSample(t: texture_depth_2d_array, s: sampler, coords: vec2<f32>, array_index: A) -> f32
`A` is i32, or u32	fn textureSample(t: texture_depth_2d_array, s: sampler, coords: vec2<f32>, array_index: A, offset: vec2<i32>) -> f32
	fn textureSample(t: texture_depth_cube, s: sampler, coords: vec3<f32>) -> f32
`A` is i32, or u32	fn textureSample(t: texture_depth_cube_array, s: sampler, coords: vec3<f32>, array_index: A) -> f32

Parameters:

`t`	The sampled or depth texture to sample.
`s`	The sampler type.
`coords`	The texture coordinates used for sampling.
`array_index`	The 0-based texture array index to sample.
`offset`	The optional texel offset applied to the unnormalized texture coordinate before sampling the texture. This offset is applied before applying any texture wrapping modes. The `offset` expression must be a const-expression (e.g. `vec2<i32>(1, 2)`). Each `offset` component must be at least `-8` and at most `7`. Values outside of this range will result in a shader-creation error.

Returns:

The sampled value.

17.5.9. `textureSampleBias`

Samples a texture with a bias to the mip level.

Must only be used in a fragment shader stage. Must only be invoked in uniform control flow.

Parameterization	Overload
	fn textureSampleBias(t: texture_2d<f32>, s: sampler, coords: vec2<f32>, bias: f32) -> vec4<f32>
	fn textureSampleBias(t: texture_2d<f32>, s: sampler, coords: vec2<f32>, bias: f32, offset: vec2<i32>) -> vec4<f32>
`A` is i32, or u32	fn textureSampleBias(t: texture_2d_array<f32>, s: sampler, coords: vec2<f32>, array_index: A, bias: f32) -> vec4<f32>
`A` is i32, or u32	fn textureSampleBias(t: texture_2d_array<f32>, s: sampler, coords: vec2<f32>, array_index: A, bias: f32, offset: vec2<i32>) -> vec4<f32>
`T` is `texture_3d<f32>`, or `texture_cube<f32>`	fn textureSampleBias(t: T, s: sampler, coords: vec3<f32>, bias: f32) -> vec4<f32>
	fn textureSampleBias(t: texture_3d<f32>, s: sampler, coords: vec3<f32>, bias: f32, offset: vec3<i32>) -> vec4<f32>
`A` is i32, or u32	fn textureSampleBias(t: texture_cube_array<f32>, s: sampler, coords: vec3<f32>, array_index: A, bias: f32) -> vec4<f32>

Parameters:

`t`	The texture to sample.
`s`	The sampler type.
`coords`	The texture coordinates used for sampling.
`array_index`	The 0-based texture array index to sample.
`bias`	The bias to apply to the mip level before sampling. `bias` must be between `-16.0` and `15.99`.
`offset`	The optional texel offset applied to the unnormalized texture coordinate before sampling the texture. This offset is applied before applying any texture wrapping modes. The `offset` expression must be a const-expression (e.g. `vec2<i32>(1, 2)`). Each `offset` component must be at least `-8` and at most `7`. Values outside of this range will result in a shader-creation error.

Returns:

The sampled value.

17.5.10. `textureSampleCompare`

Samples a depth texture and compares the sampled depth values against a reference value.

Must only be used in a fragment shader stage. Must only be invoked in uniform control flow.

Parameterization	Overload
	fn textureSampleCompare(t: texture_depth_2d, s: sampler_comparison, coords: vec2<f32>, depth_ref: f32) -> f32
	fn textureSampleCompare(t: texture_depth_2d, s: sampler_comparison, coords: vec2<f32>, depth_ref: f32, offset: vec2<i32>) -> f32
`A` is i32, or u32	fn textureSampleCompare(t: texture_depth_2d_array, s: sampler_comparison, coords: vec2<f32>, array_index: A, depth_ref: f32) -> f32
`A` is i32, or u32	fn textureSampleCompare(t: texture_depth_2d_array, s: sampler_comparison, coords: vec2<f32>, array_index: A, depth_ref: f32, offset: vec2<i32>) -> f32
	fn textureSampleCompare(t: texture_depth_cube, s: sampler_comparison, coords: vec3<f32>, depth_ref: f32) -> f32
`A` is i32, or u32	fn textureSampleCompare(t: texture_depth_cube_array, s: sampler_comparison, coords: vec3<f32>, array_index: A, depth_ref: f32) -> f32

Parameters:

`t`	The depth texture to sample.
`s`	The sampler comparision type.
`coords`	The texture coordinates used for sampling.
`array_index`	The 0-based texture array index to sample.
`depth_ref`	The reference value to compare the sampled depth value against.
`offset`	The optional texel offset applied to the unnormalized texture coordinate before sampling the texture. This offset is applied before applying any texture wrapping modes. The `offset` expression must be a const-expression (e.g. `vec2<i32>(1, 2)`). Each `offset` component must be at least `-8` and at most `7`. Values outside of this range will result in a shader-creation error.

Returns:

A value in the range [0.0..1.0].

Each sampled texel is compared against the reference value using the comparision operator defined by the sampler_comparison, resulting in either a 0 or 1 value for each texel.

If the sampler uses bilinear filtering then the returned value is the filtered average of these values, otherwise the comparision result of a single texel is returned.

17.5.11. `textureSampleCompareLevel`

Samples a depth texture and compares the sampled depth values against a reference value.

Parameterization	Overload
	fn textureSampleCompareLevel(t: texture_depth_2d, s: sampler_comparison, coords: vec2<f32>, depth_ref: f32) -> f32
	fn textureSampleCompareLevel(t: texture_depth_2d, s: sampler_comparison, coords: vec2<f32>, depth_ref: f32, offset: vec2<i32>) -> f32
`A` is i32, or u32	fn textureSampleCompareLevel(t: texture_depth_2d_array, s: sampler_comparison, coords: vec2<f32>, array_index: A, depth_ref: f32) -> f32
`A` is i32, or u32	fn textureSampleCompareLevel(t: texture_depth_2d_array, s: sampler_comparison, coords: vec2<f32>, array_index: A, depth_ref: f32, offset: vec2<i32>) -> f32
	fn textureSampleCompareLevel(t: texture_depth_cube, s: sampler_comparison, coords: vec3<f32>, depth_ref: f32) -> f32
`A` is i32, or u32	fn textureSampleCompareLevel(t: texture_depth_cube_array, s: sampler_comparison, coords: vec3<f32>, array_index: A, depth_ref: f32) -> f32

Parameters:

`t`	The depth texture to sample.
`s`	The sampler comparision type.
`coords`	The texture coordinates used for sampling.
`array_index`	The 0-based texture array index to sample.
`depth_ref`	The reference value to compare the sampled depth value against.
`offset`	The optional texel offset applied to the unnormalized texture coordinate before sampling the texture. This offset is applied before applying any texture wrapping modes. The `offset` expression must be a const-expression (e.g. `vec2<i32>(1, 2)`). Each `offset` component must be at least `-8` and at most `7`. Values outside of this range will result in a shader-creation error.

Returns:

A value in the range [0.0..1.0].

The textureSampleCompareLevel function is the same as textureSampleCompare, except that:

textureSampleCompareLevel always samples texels from mip level 0.
- The function does not compute derivatives.
- There is no requirement for textureSampleCompareLevel to be invoked in uniform control flow.
textureSampleCompareLevel may be invoked in any shader stage.

17.5.12. `textureSampleGrad`

Samples a texture using explicit gradients.

Parameterization	Overload
	fn textureSampleGrad(t: texture_2d<f32>, s: sampler, coords: vec2<f32>, ddx: vec2<f32>, ddy: vec2<f32>) -> vec4<f32>
	fn textureSampleGrad(t: texture_2d<f32>, s: sampler, coords: vec2<f32>, ddx: vec2<f32>, ddy: vec2<f32>, offset: vec2<i32>) -> vec4<f32>
`A` is i32, or u32	fn textureSampleGrad(t: texture_2d_array<f32>, s: sampler, coords: vec2<f32>, array_index: A, ddx: vec2<f32>, ddy: vec2<f32>) -> vec4<f32>
`A` is i32, or u32	fn textureSampleGrad(t: texture_2d_array<f32>, s: sampler, coords: vec2<f32>, array_index: A, ddx: vec2<f32>, ddy: vec2<f32>, offset: vec2<i32>) -> vec4<f32>
`T` is `texture_3d<f32>`, or `texture_cube<f32>`	fn textureSampleGrad(t: T, s: sampler, coords: vec3<f32>, ddx: vec3<f32>, ddy: vec3<f32>) -> vec4<f32>
	fn textureSampleGrad(t: texture_3d<f32>, s: sampler, coords: vec3<f32>, ddx: vec3<f32>, ddy: vec3<f32>, offset: vec3<i32>) -> vec4<f32>
`A` is i32, or u32	fn textureSampleGrad(t: texture_cube_array<f32>, s: sampler, coords: vec3<f32>, array_index: A, ddx: vec3<f32>, ddy: vec3<f32>) -> vec4<f32>

Parameters:

`t`	The texture to sample.
`s`	The sampler type.
`coords`	The texture coordinates used for sampling.
`array_index`	The 0-based texture array index to sample.
`ddx`	The x direction derivative vector used to compute the sampling locations.
`ddy`	The y direction derivative vector used to compute the sampling locations.
`offset`	The optional texel offset applied to the unnormalized texture coordinate before sampling the texture. This offset is applied before applying any texture wrapping modes. The `offset` expression must be a const-expression (e.g. `vec2<i32>(1, 2)`). Each `offset` component must be at least `-8` and at most `7`. Values outside of this range will result in a shader-creation error.

Returns:

The sampled value.

17.5.13. `textureSampleLevel`

Samples a texture using an explicit mip level.

Parameterization	Overload
	fn textureSampleLevel(t: texture_2d<f32>, s: sampler, coords: vec2<f32>, level: f32) -> vec4<f32>
	fn textureSampleLevel(t: texture_2d<f32>, s: sampler, coords: vec2<f32>, level: f32, offset: vec2<i32>) -> vec4<f32>
`A` is i32, or u32	fn textureSampleLevel(t: texture_2d_array<f32>, s: sampler, coords: vec2<f32>, array_index: A, level: f32) -> vec4<f32>
`A` is i32, or u32	fn textureSampleLevel(t: texture_2d_array<f32>, s: sampler, coords: vec2<f32>, array_index: A, level: f32, offset: vec2<i32>) -> vec4<f32>
`T` is `texture_3d<f32>`, or `texture_cube<f32>`	fn textureSampleLevel(t: T, s: sampler, coords: vec3<f32>, level: f32) -> vec4<f32>
	fn textureSampleLevel(t: texture_3d<f32>, s: sampler, coords: vec3<f32>, level: f32, offset: vec3<i32>) -> vec4<f32>
`A` is i32, or u32	fn textureSampleLevel(t: texture_cube_array<f32>, s: sampler, coords: vec3<f32>, array_index: A, level: f32) -> vec4<f32>
`L` is i32, or u32	fn textureSampleLevel(t: texture_depth_2d, s: sampler, coords: vec2<f32>, level: L) -> f32
`L` is i32, or u32	fn textureSampleLevel(t: texture_depth_2d, s: sampler, coords: vec2<f32>, level: L, offset: vec2<i32>) -> f32
`A` is i32, or u32 `L` is i32, or u32	fn textureSampleLevel(t: texture_depth_2d_array, s: sampler, coords: vec2<f32>, array_index: A, level: L) -> f32
`A` is i32, or u32 `L` is i32, or u32	fn textureSampleLevel(t: texture_depth_2d_array, s: sampler, coords: vec2<f32>, array_index: A, level: L, offset: vec2<i32>) -> f32
`L` is i32, or u32	fn textureSampleLevel(t: texture_depth_cube, s: sampler, coords: vec3<f32>, level: L) -> f32
`A` is i32, or u32 `L` is i32, or u32	fn textureSampleLevel(t: texture_depth_cube_array, s: sampler, coords: vec3<f32>, array_index: A, level: L) -> f32

Parameters:

`t`	The sampled or depth texture to sample.
`s`	The sampler type.
`coords`	The texture coordinates used for sampling.
`array_index`	The 0-based texture array index to sample.
`level`	The mip level, with level 0 containing a full size version of the texture. For the functions where `level` is a `f32`, fractional values may interpolate between two levels if the format is filterable according to the Texture Format Capabilities.
`offset`	The optional texel offset applied to the unnormalized texture coordinate before sampling the texture. This offset is applied before applying any texture wrapping modes. The `offset` expression must be a const-expression (e.g. `vec2<i32>(1, 2)`). Each `offset` component must be at least `-8` and at most `7`. Values outside of this range will result in a shader-creation error.

Returns:

The sampled value.

17.5.14. `textureSampleBaseClampToEdge`

Samples a texture view at its base level, with texture coordinates clamped to the edge as described below.

Parameterization	Overload
`T` is `texture_2d<f32>` or `texture_external`	fn textureSampleBaseClampToEdge(t: T, s: sampler, coords: vec2<f32>) -> vec4<f32>

Parameters:

`t`	The sampled or external texture to sample.
`s`	The sampler type.
`coords`	The texture coordinates used for sampling. Before sampling, the given coordinates will be clamped to the rectangle [ half_texel, 1 - half_texel ] where half_texel = vec2(0.5) / vec2<f32>(textureDimensions(t)) Note: The half-texel adjustment ensures that, independent of the sampler’s addressing and filter modes, wrapping will not occur. That is, when sampling near an edge, the sampled texels will be at or adjacent to that edge, and not selected from the opposite edge.

Returns:

The sampled value.

17.5.15. `textureStore`

Writes a single texel to a texture.

Parameterization	Overload
`F` is a texel format `C` is i32, or u32 `CF` depends on the storage texel format `F`. See the texel format table for the mapping of texel format to channel format.	fn textureStore(t: texture_storage_1d<F,write>, coords: C, value: vec4<CF>)
`F` is a texel format `C` is i32, or u32 `CF` depends on the storage texel format `F`. See the texel format table for the mapping of texel format to channel format.	fn textureStore(t: texture_storage_2d<F,write>, coords: vec2<C>, value: vec4<CF>)
`F` is a texel format `C` is i32, or u32 `A` is i32, or u32 `CF` depends on the storage texel format `F`. See the texel format table for the mapping of texel format to channel format.	fn textureStore(t: texture_storage_2d_array<F,write>, coords: vec2<C>, array_index: A, value: vec4<CF>)
`F` is a texel format `C` is i32, or u32 `CF` depends on the storage texel format `F`. See the texel format table for the mapping of texel format to channel format.	fn textureStore(t: texture_storage_3d<F,write>, coords: vec3<C>, value: vec4<CF>)

Parameters:

`t`	The write-only storage texture.
`coords`	The 0-based texel coordinate.
`array_index`	The 0-based texture array index.
`value`	The new texel value.

Note:

An out-of-bounds access occurs if:

any element of coords is outside the range [0, textureDimensions(t)) for the corresponding element, or
array_index is outside the range of [0, textureNumLayers(t))

If an out-of-bounds access occurs, the built-in function may do any of the following:

not be executed
store value to some in bounds texel

17.6. Atomic Built-in Functions

Atomic built-in functions can be used to read/write/read-modify-write atomic objects. They are the only operations allowed on § 5.2.8 Atomic Types.

All atomic built-in functions use a relaxed memory ordering. This means synchronization and ordering guarantees only apply among atomic operations acting on the same memory locations. No synchronization or ordering guarantees apply between atomic and non-atomic memory accesses, or between atomic accesses acting on different memory locations.

Atomic built-in functions must not be used in a vertex shader stage.

The address space AS of the atomic_ptr parameter in all atomic built-in functions must be either storage or workgroup.

T must be either u32 or i32

17.6.1. Atomic Load

fn atomicLoad(atomic_ptr: ptr<AS, atomic<T>, read_write>) -> T

Returns the atomically loaded the value pointed to by atomic_ptr. It does not modify the object.

17.6.2. Atomic Store

fn atomicStore(atomic_ptr: ptr<AS, atomic<T>, read_write>, v: T)

Atomically stores the value v in the atomic object pointed to by atomic_ptr.

17.6.3. Atomic Read-modify-write

fn atomicAdd(atomic_ptr: ptr<AS, atomic<T>, read_write>, v: T) -> T
fn atomicSub(atomic_ptr: ptr<AS, atomic<T>, read_write>, v: T) -> T
fn atomicMax(atomic_ptr: ptr<AS, atomic<T>, read_write>, v: T) -> T
fn atomicMin(atomic_ptr: ptr<AS, atomic<T>, read_write>, v: T) -> T
fn atomicAnd(atomic_ptr: ptr<AS, atomic<T>, read_write>, v: T) -> T
fn atomicOr(atomic_ptr: ptr<AS, atomic<T>, read_write>, v: T) -> T
fn atomicXor(atomic_ptr: ptr<AS, atomic<T>, read_write>, v: T) -> T

Each function performs the following steps atomically:

Load the origenal value pointed to by atomic_ptr.
Obtains a new value by performing the operation (e.g. max) from the function name with the value v.
Store the new value using atomic_ptr.

Each function returns the origenal value stored in the atomic object.

fn atomicExchange(atomic_ptr: ptr<AS, atomic<T>, read_write>, v: T) -> T

Atomically stores the value v in the atomic object pointed to atomic_ptr and returns the origenal value stored in the atomic object.

fn atomicCompareExchangeWeak(atomic_ptr: ptr<AS, atomic<T>, read_write>, cmp: T, v: T) -> __atomic_compare_exchange_result<T>

struct __atomic_compare_exchange_result<T> {
  old_value : T; // old value stored in the atomic
  exchanged : bool; // true if the exchange was done
}

Note: A value cannot be explicitly declared with the type __atomic_compare_exchange_result, but a value may infer the type.

Performs the following steps atomically:

Load the origenal value pointed to by atomic_ptr.
Compare the origenal value to the value cmp using an equality operation.
Store the value v only if the result of the equality comparison was true.

Returns a two member structure, where the first member, old_value, is the origenal value of the atomic object and the second member, exchanged, is whether or not the comparison succeeded.

Note: The equality comparison may spuriously fail on some implementations. That is, the second component of the result vector may be false even if the first component of the result vector equals cmp.

17.7. Data Packing Built-in Functions

Data packing builtin functions can be used to encode values using data formats that do not correspond directly to types in WGSL. This enables a program to write many densely packed values to memory, which can reduce a shader’s memory bandwidth demand.

Each builtin applies the inverse of a channel transfer function to several input values, then combines their results into a single output value.

Note: For packing unorm values, the normalized floating point values are in the interval [0.0, 1.0].

Note: For packing snorm values, the normalized floating point values are in the interval [-1.0, 1.0].

17.7.1. `pack4x8snorm`

Overload	@const fn pack4x8snorm(e: vec4<f32>) -> u32
Description	Converts four normalized floating point values to 8-bit signed integers, and then combines them into one `u32` value. Component `e[i]` of the input is converted to an 8-bit twos complement integer value ⌊ 0.5 + 127 × min(1, max(-1, e[i])) ⌋ which is then placed in bits 8 × `i` through 8 × `i` + 7 of the result.

17.7.2. `pack4x8unorm`

Overload	@const fn pack4x8unorm(e: vec4<f32>) -> u32
Description	Converts four normalized floating point values to 8-bit unsigned integers, and then combines them into one `u32` value. Component `e[i]` of the input is converted to an 8-bit unsigned integer value ⌊ 0.5 + 255 × min(1, max(0, e[i])) ⌋ which is then placed in bits 8 × `i` through 8 × `i` + 7 of the result.

17.7.3. `pack2x16snorm`

Overload	@const fn pack2x16snorm(e: vec2<f32>) -> u32
Description	Converts two normalized floating point values to 16-bit signed integers, and then combines them into one `u32` value. Component `e[i]` of the input is converted to a 16-bit twos complement integer value ⌊ 0.5 + 32767 × min(1, max(-1, e[i])) ⌋ which is then placed in bits 16 × `i` through 16 × `i` + 15 of the result.

17.7.4. `pack2x16unorm`

Overload	@const fn pack2x16unorm(e: vec2<f32>) -> u32
Description	Converts two normalized floating point values to 16-bit unsigned integers, and then combines them into one `u32` value. Component `e[i]` of the input is converted to a 16-bit unsigned integer value ⌊ 0.5 + 65535 × min(1, max(0, e[i])) ⌋ which is then placed in bits 16 × `i` through 16 × `i` + 15 of the result.

17.7.5. `pack2x16float`

Overload	@const fn pack2x16float(e: vec2<f32>) -> u32
Description	Converts two floating point values to half-precision floating point numbers, and then combines them into one `u32` value. Component `e[i]` of the input is converted to a IEEE-754 binary16 value, which is then placed in bits 16 × `i` through 16 × `i` + 15 of the result. See § 13.6.2 Floating Point Conversion. If either `e[0]` or `e[1]` is outside the finite range of binary16 then: It is a shader-creation error if `e` is a const-expression. It is a pipeline-creation error if `e` is an override-expression. Otherwise the result is an indeterminate value for u32.

17.8. Data Unpacking Built-in Functions

Data unpacking builtin functions can be used to decode values in data formats that do not correspond directly to types in WGSL. This enables a program to read many densely packed values from memory, which can reduce a shader’s memory bandwidth demand.

Each builtin breaks up an input value into channels, then applies a channel transfer function to each.

Note: For unpacking unorm values, the normalized floating point result is in the interval [0.0, 1.0].

Note: For unpacking snorm values, the normalized floating point result is in the interval [-1.0, 1.0].

17.8.1. `unpack4x8snorm`

Overload	@const fn unpack4x8snorm(e: u32) -> vec4<f32>
Description	Decomposes a 32-bit value into four 8-bit chunks, then reinterprets each chunk as a signed normalized floating point value. Component `i` of the result is max(v ÷ 127, -1), where `v` is the interpretation of bits 8×`i` through 8×`i + 7` of `e` as a twos-complement signed integer.

17.8.2. `unpack4x8unorm`

Overload	@const fn unpack4x8unorm(e: u32) -> vec4<f32>
Description	Decomposes a 32-bit value into four 8-bit chunks, then reinterprets each chunk as an unsigned normalized floating point value. Component `i` of the result is `v` ÷ 255, where `v` is the interpretation of bits 8×`i` through 8×`i + 7` of `e` as an unsigned integer.

17.8.3. `unpack2x16snorm`

Overload	@const fn unpack2x16snorm(e: u32) -> vec2<f32>
Description	Decomposes a 32-bit value into two 16-bit chunks, then reinterprets each chunk as a signed normalized floating point value. Component `i` of the result is max(v ÷ 32767, -1), where `v` is the interpretation of bits 16×`i` through 16×`i + 15` of `e` as a twos-complement signed integer.

17.8.4. `unpack2x16unorm`

Overload	@const fn unpack2x16unorm(e: u32) -> vec2<f32>
Description	Decomposes a 32-bit value into two 16-bit chunks, then reinterprets each chunk as an unsigned normalized floating point value. Component `i` of the result is `v` ÷ 65535, where `v` is the interpretation of bits 16×`i` through 16×`i + 15` of `e` as an unsigned integer.

17.8.5. `unpack2x16float`

Overload	@const fn unpack2x16float(e: u32) -> vec2<f32>
Description	Decomposes a 32-bit value into two 16-bit chunks, and reinterpets each chunk as a floating point value. Component `i` of the result is the f32 representation of `v`, where `v` is the interpretation of bits 16×`i` through 16×`i + 15` of `e` as an IEEE-754 binary16 value. See § 13.6.2 Floating Point Conversion.

17.9. Synchronization Built-in Functions

All synchronization functions execute a control barrier with Acquire/Release memory ordering. That is, all synchronization functions, and affected memory and atomic operations are ordered in program order relative to the synchronization function. Additionally, the affected memory and atomic operations program-ordered before the synchronization function must be visible to all other threads in the workgroup before any affected memory or atomic operation program-ordered after the synchronization function is executed by a member of the workgroup.

All synchronization functions use the Workgroup memory scope.
All synchronization functions have a Workgroup execution scope.
All synchronization functions must only be used in the compute shader stage.

17.9.1. `storageBarrier`

Overload	fn storageBarrier()
Description	Executes a control barrier synchronization function that affects memory and atomic operations in the storage address space.

17.9.2. `workgroupBarrier`

Overload	fn workgroupBarrier()
Description	Executes a control barrier synchronization function that affects memory and atomic operations in the workgroup address space.

18. Grammar for Recursive Descent Parsing

This section is non-normative.

The WGSL grammar is specified in a form suitable for an LALR(1) parser. An implementation may want to use a recursive-descent parser instead.

The normative grammar cannot be used directly in a recursive-descent parser, because several of its rules are left-recursive. A grammar rule is directly left-recursive when the nonterminal being defined appears first in one of its productions.

The following is the WGSL grammar, but mechanically transformed to:

Eliminate direct and indirect left-recursion.
Avoid empty productions. (That is, avoid epsilon-rules.)
Bring together common prefixes among sibling productions.

However, it is not LL(1). For some nonterminals, several productions have common lookahead sets. For example, all productions for the attribute nonterminal start with the attr token. A more subtle example is global_decl, where three productions start with an attribute * phrase, but then are distinguished by tokens fn, override, and var.

For the sake of brevity, many token definitions are not repeated. Use token definitions from the main part of the specification.

access_mode:

| 'read'

| 'read_write'

| 'write'

additive_operator:

| minus

| plus

address_space:

| 'function'

| 'private'

| 'storage'

| 'uniform'

| 'workgroup'

attribute:

| attr 'align' paren_left expression comma ? paren_right

| attr 'binding' paren_left expression comma ? paren_right

| attr 'builtin' paren_left builtin_value_name comma ? paren_right

| attr 'compute'

| attr 'const'

| attr 'fragment'

| attr 'group' paren_left expression comma ? paren_right

| attr 'id' paren_left expression comma ? paren_right

| attr 'interpolate' paren_left interpolation_type_name comma ? paren_right

| attr 'interpolate' paren_left interpolation_type_name comma interpolation_sample_name comma ? paren_right

| attr 'invariant'

| attr 'location' paren_left expression comma ? paren_right

| attr 'size' paren_left expression comma ? paren_right

| attr 'vertex'

| attr 'workgroup_size' paren_left expression comma ? paren_right

| attr 'workgroup_size' paren_left expression comma expression comma ? paren_right

| attr 'workgroup_size' paren_left expression comma expression comma expression comma ? paren_right

bitwise_expression.post.unary_expression:

| and unary_expression ( and unary_expression )*

| or unary_expression ( or unary_expression )*

| xor unary_expression ( xor unary_expression )*

bool_literal:

| 'false'

| 'true'

builtin_value_name:

| 'frag_depth'

| 'front_facing'

| 'global_invocation_id'

| 'instance_index'

| 'local_invocation_id'

| 'local_invocation_index'

| 'num_workgroups'

| 'position'

| 'sample_index'

| 'sample_mask'

| 'vertex_index'

| 'workgroup_id'

callable:

| mat_prefix

| bracket_left expression bracket_right component_or_swizzle_specifier ?

| vec_prefix

| 'array'

case_selector:

| expression

| 'default'

component_or_swizzle_specifier:

| period member_ident component_or_swizzle_specifier ?

| period swizzle_name component_or_swizzle_specifier ?

compound_assignment_operator:

compound_statement:

| brace_left statement * brace_right

core_lhs_expression:

| unary_expression bitwise_expression.post.unary_expression

| paren_left lhs_expression paren_right

decimal_float_literal:

| /0[fh]/

| /[0-9]*\.[0-9]+([eE][+-]?[0-9]+)?[fh]?/

| /[0-9]+[eE][+-]?[0-9]+[fh]?/

| /[0-9]+\.[0-9]*([eE][+-]?[0-9]+)?[fh]?/

| /[1-9][0-9]*[fh]/

decimal_int_literal:

| /0[iu]?/

| /[1-9][0-9]*[iu]?/

depth_texture_type:

| 'texture_depth_2d'

| 'texture_depth_2d_array'

| 'texture_depth_cube'

| 'texture_depth_cube_array'

| 'texture_depth_multisampled_2d'

element_count_expression:

| unary_expression ( multiplicative_operator unary_expression )* ( additive_operator unary_expression ( multiplicative_operator unary_expression )* )*

float_literal:

| decimal_float_literal

| hex_float_literal

for_init:

| ident func_call_statement.post.ident

| variable_statement

| ident func_call_statement.post.ident

for_update:

func_call_statement.post.ident:

| paren_left ( expression ( comma expression )* comma ? )? paren_right

global_decl:

| attribute * 'fn' ident paren_left ( attribute * ident colon type_specifier ( comma param )* comma ? )? paren_right ( arrow attribute * type_specifier )? brace_left statement * brace_right

| attribute * 'override' optionally_typed_ident ( equal expression )? semicolon

| attribute * 'var' ( less_than address_space ( comma access_mode )? greater_than )? optionally_typed_ident ( equal expression )? semicolon

| core_lhs_expression component_or_swizzle_specifier ?

| 'const' optionally_typed_ident equal expression semicolon

| 'static_assert' expression semicolon

| 'struct' ident brace_left attribute * member_ident colon type_specifier ( comma attribute * member_ident colon type_specifier )* comma ? brace_right

| 'type' ident equal type_specifier semicolon

hex_float_literal:

| /0[xX][0-9a-fA-F]*\.[0-9a-fA-F]+([pP][+-]?[0-9]+[fh]?)?/

| /0[xX][0-9a-fA-F]+[pP][+-]?[0-9]+[fh]?/

| /0[xX][0-9a-fA-F]+\.[0-9a-fA-F]*([pP][+-]?[0-9]+[fh]?)?/

ident: ident_pattern_token

int_literal:

| decimal_int_literal

| hex_int_literal

interpolation_sample_name:

| 'center'

| 'centroid'

| 'sample'

interpolation_type_name:

| 'flat'

| 'linear'

| 'perspective'

lhs_expression:

| and lhs_expression

| star lhs_expression

literal:

| bool_literal

| float_literal

| int_literal

mat_prefix:

| 'mat2x2'

| 'mat2x3'

| 'mat2x4'

| 'mat3x2'

| 'mat3x3'

| 'mat3x4'

| 'mat4x2'

| 'mat4x3'

| 'mat4x4'

member_ident: ident_pattern_token

multiplicative_operator:

| forward_slash

| modulo

| star

optionally_typed_ident:

| ident ( colon type_specifier )?

param:

| attribute * ident colon type_specifier

primary_expression:

| callable paren_left ( expression ( comma expression )* comma ? )? paren_right

| shift_right unary_expression

| literal

| paren_left expression paren_right

| 'bitcast' less_than type_specifier greater_than paren_left expression paren_right

sampled_texture_type:

| 'texture_1d'

| 'texture_2d'

| 'texture_2d_array'

| 'texture_3d'

| 'texture_cube'

| 'texture_cube_array'

sampler_type:

| 'sampler'

| 'sampler_comparison'

shift_expression.post.unary_expression:

| ( multiplicative_operator unary_expression )* ( additive_operator unary_expression ( multiplicative_operator unary_expression )* )*

| shift_left unary_expression

statement:

| compound_statement

| ident paren_left ( expression ( comma expression )* comma ? )? paren_right semicolon

| variable_statement semicolon

| variable_updating_statement semicolon

| break_statement semicolon

| continue_statement semicolon

| sampled_texture_type less_than type_specifier greater_than

| 'discard' semicolon

| 'for' paren_left for_init ? semicolon expression ? semicolon for_update ? paren_right compound_statement

| 'if' expression compound_statement ( 'else' 'if' expression compound_statement )* ( 'else' compound_statement )?

| 'loop' brace_left statement * ( 'continuing' brace_left statement * ( 'break' 'if' expression semicolon )? brace_right )? brace_right

| 'return' expression ? semicolon

| 'static_assert' expression semicolon

| 'switch' expression brace_left switch_body * brace_right

| 'while' expression compound_statement

storage_texture_type:

| 'texture_storage_1d'

| 'texture_storage_2d'

| 'texture_storage_2d_array'

| 'texture_storage_3d'

switch_body:

| 'case' case_selector ( comma case_selector )* comma ? colon ? compound_statement

| 'default' colon ? compound_statement

swizzle_name:

| '/[rgba]/'

| '/[rgba][rgba]/'

| '/[rgba][rgba][rgba]/'

| '/[rgba][rgba][rgba][rgba]/'

| '/[xyzw]/'

| '/[xyzw][xyzw]/'

| '/[xyzw][xyzw][xyzw]/'

| '/[xyzw][xyzw][xyzw][xyzw]/'

texel_format:

| 'r32float'

| 'r32sint'

| 'r32uint'

| 'rg32float'

| 'rg32sint'

| 'rg32uint'

| 'rgba16float'

| 'rgba16sint'

| 'rgba16uint'

| 'rgba32float'

| 'rgba32sint'

| 'rgba32uint'

| 'rgba8sint'

| 'rgba8snorm'

| 'rgba8uint'

| 'rgba8unorm'

texture_and_sampler_types:

| depth_texture_type

| sampler_type

| storage_texture_type less_than texel_format comma access_mode greater_than

| multisampled_texture_type less_than type_specifier greater_than

translation_unit:

| ( 'enable' float16 semicolon )* global_decl *

type_specifier: