llvm-project/mlir/docs/Dialects/LLVM.md

# 'llvm' Dialect

This dialect maps [LLVM IR](https://llvm.org/docs/LangRef.html) into MLIR by
defining the corresponding operations and types. LLVM IR metadata is usually
represented as MLIR attributes, which offer additional structure verification.

We use "LLVM IR" to designate the
[intermediate representation of LLVM](https://llvm.org/docs/LangRef.html) and
"LLVM _dialect_" or "LLVM IR _dialect_" to refer to this MLIR dialect.

Unless explicitly stated otherwise, the semantics of the LLVM dialect operations
must correspond to the semantics of LLVM IR instructions and any divergence is
considered a bug. The dialect also contains auxiliary operations that smoothen
the differences in the IR structure, e.g., MLIR does not have `phi` operations
and LLVM IR does not have a `constant` operation. These auxiliary operations are
systematically prefixed with `mlir`, e.g. `llvm.mlir.constant` where `llvm.` is
the dialect namespace prefix.

[TOC]

## Dependency on LLVM IR

LLVM dialect is not expected to depend on any object that requires an
`LLVMContext`, such as an LLVM IR instruction or type. Instead, MLIR provides
thread-safe alternatives compatible with the rest of the infrastructure. The
dialect is allowed to depend on the LLVM IR objects that don't require a
context, such as data layout and triple description.

## Module Structure

IR modules use the built-in MLIR `ModuleOp` and support all its features. In
particular, modules can be named, nested and are subject to symbol visibility.
Modules can contain any operations, including LLVM functions and globals.

### Data Layout and Triple

An IR module may have an optional data layout and triple information attached
using MLIR attributes `llvm.data_layout` and `llvm.triple`, respectively. Both
are string attributes with the
[same syntax](https://llvm.org/docs/LangRef.html#data-layout) as in LLVM IR and
are verified to be correct. They can be defined as follows.

```mlir
module attributes {llvm.data_layout = "e",
                   llvm.target_triple = "aarch64-linux-android"} {
  // module contents
}
```

## Types

LLVM dialect defines a set of types that correspond to LLVM IR types. The
dialect type system is _closed_: types from other dialects are not allowed
within LLVM dialect aggregate types. This property allows for more concise
custom syntax and ensures easy translation to LLVM IR.

Similarly to other MLIR context-owned objects, the creation and manipulation of
LLVM dialect types is thread-safe.

MLIR does not support module-scoped named type declarations, e.g. `%s = type
{i32, i32}` in LLVM IR. Instead, types must be fully specified at each use,
except for recursive types where only the first reference to a named type needs
to be fully specified. MLIR type aliases are supported for top-level types, i.e.
they cannot be used inside the type due to type system closedness.

The general syntax of LLVM dialect types is `!llvm.`, followed by a type kind
identifier (e.g., `ptr` for pointer or `struct` for structure) and by an
optional list of type parameters in angle brackets. The dialect follows MLIR
style for types with nested angle brackets and keyword specifiers rather than
using different bracket styles to differentiate types. Inside angle brackets,
the `!llvm` prefix is omitted for brevity; thanks to closedness of the type
system, all types are assumed to be defined in the LLVM dialect. For example,
`!llvm.ptr<struct<packed, (i8, i32)>>` is a pointer to a packed structure type
containing an 8-bit and a 32-bit integer.

### Simple Types

The following non-parametric types are supported.

-   `!llvm.bfloat` (`LLVMBFloatType`) - 16-bit “brain” floating-point value
    (7-bit significand).
-   `!llvm.half` (`LLVMHalfType`) - 16-bit floating-point value as per
    IEEE-754-2008.
-   `!llvm.float` (`LLVMFloatType`) - 32-bit floating-point value as per
    IEEE-754-2008.
-   `!llvm.double` (`LLVMDoubleType`) - 64-bit floating-point value as per
    IEEE-754-2008.
-   `!llvm.fp128` (`LLVMFP128Type`) - 128-bit floating-point value as per
    IEEE-754-2008.
-   `!llvm.x86_fp80` (`LLVMX86FP80Type`) - 80-bit floating-point value (x87).
-   `!llvm.x86_mmx` (`LLVMX86MMXType`) - value held in an MMX register on x86
    machine.
-   `!llvm.ppc_fp128` (`LLVMPPCFP128Type`) - 128-bit floating-point value (two
    64 bits).
-   `!llvm.token` (`LLVMTokenType`) - a non-inspectable value associated with an
    operation.
-   `!llvm.metadata` (`LLVMMetadataType`) - LLVM IR metadata, to be used only if
    the metadata cannot be represented as structured MLIR attributes.
-   `!llvm.void` (`LLVMVoidType`) - does not represent any value; can only
    appear in function results.

These types represent a single value (or an absence thereof in case of `void`)
and correspond to their LLVM IR counterparts.

### Parametric Types

#### Integer Types

Integer types are parametric in MLIR terminology, with their bitwidth being a
type parameter. They are expressed as follows:

```
  llvm-int-type ::= `!llvm.i` integer-literal
```

and represented internally as `LLVMIntegerType`. For example, `i1` is a 1-bit
integer type (bool) and `i32` as a 32-bit integer type.

#### Pointer Types

Pointer types specify an address in memory.

Pointer types are parametric types parameterized by the element type and the
address space. The address space is an integer, but this choice may be
reconsidered if MLIR implements named address spaces. Their syntax is as
follows:

```
  llvm-ptr-type ::= `!llvm.ptr<` llvm-type (`,` integer-literal)? `>`
```

where the optional integer literal corresponds to the memory space. Both cases
are represented by `LLVMPointerType` internally.

#### Vector Types

Vector types represent sequences of elements, typically when multiple data
elements are processed by a single instruction (SIMD). Vectors are thought of as
stored in registers and therefore vector elements can only be addressed through
constant indices.

Vector types are parameterized by the size, which may be either _fixed_ or a
multiple of some fixed size in case of _scalable_ vectors, and the element type.
Vectors cannot be nested and only 1D vectors are supported. Scalable vectors are
still considered 1D. Their syntax is as follows:

```
  llvm-vec-type ::= `!llvm.vec<` (`?` `x`)? integer-literal `x` llvm-type `>`
```

Internally, fixed vector types are represented as `LLVMFixedVectorType` and
scalable vector types are represented as `LLVMScalableVectorType`. Both classes
derive`LLVMVectorType`.

#### Array Types

Array types represent sequences of elements in memory. Unlike vectors, array
elements can be addressed with a value unknown at compile time, and can be
nested. Only 1D arrays are allowed though.

Array types are parameterized by the fixed size and the element type.
Syntactically, their representation is close to vectors:

```
  llvm-array-type ::= `!llvm.array<` integer-literal `x` llvm-type `>`
```

and are internally represented as `LLVMArrayType`.

#### Function Types

Function types represent the type of a function, i.e. its signature.

Function types are parameterized by the result type, the list of argument types
and by an optional "variadic" flag. Unlike built-in `FunctionType`, LLVM dialect
functions (`LLVMFunctionType`) always have single result, which may be
`!llvm.void` if the function does not return anything. The syntax is as follows:

```
  llvm-func-type ::= `!llvm.func<` llvm-type `(` llvm-type-list (`,` `...`)?
                     `)` `>`
```

For example,

```mlir
!llvm.func<void ()>            // a function with no arguments;
!llvm.func<i32 (float, i32)>  // a function with two arguments and a result;
!llvm.func<void (i32, ...)>   // a variadic function with at least one argument.
```

In the LLVM dialect, functions are not first-class objects and one cannot have a
value of function type. Instead, one can take the address of a function and
operate on pointers to functions.

### Structure Types

The structure type is used to represent a collection of data members together in
memory. The elements of a structure may be any type that has a size.

Structure types are represented in a single dedicated class
mlir::LLVM::LLVMStructType. Internally, the struct type stores a (potentially
empty) name, a (potentially empty) list of contained types and a bitmask
indicating whether the struct is named, opaque, packed or uninitialized.
Structure types that don't have a name are referred to as _literal_ structs.
Such structures are uniquely identified by their contents. _Identified_ structs
on the other hand are uniquely identified by the name.

#### Identified Structure Types

Identified structure types are uniqued using their name in a given context.
Attempting to construct an identified structure with the same name a structure
that already exists in the context *will result in the existing structure being
returned*. **MLIR does not auto-rename identified structs in case of name
conflicts** because there is no naming scope equivalent to a module in LLVM IR
since MLIR modules can be arbitrarily nested.

Programmatically, identified structures can be constructed in an _uninitialized_
state. In this case, they are given a name but the body must be set up by a
later call, using MLIR's type mutation mechanism. Such uninitialized types can
be used in type construction, but must be eventually initialized for IR to be
valid. This mechanism allows for constructing _recursive_ or mutually referring
structure types: an uninitialized type can be used in its own initialization.

Once the type is initialized, its body cannot be changed anymore. Any further
attempts to modify the body will fail and return failure to the caller _unless
the type is initialized with the exact same body_. Type initialization is
thread-safe; however, if a concurrent thread initializes the type before the
current thread, the initialization may return failure.

The syntax for identified structure types is as follows.

```
llvm-ident-struct-type ::= `!llvm.struct<` string-literal, `opaque` `>`
                         | `!llvm.struct<` string-literal, `packed`?
                            `(` llvm-type-or-ref-list  `)` `>`
llvm-type-or-ref-list ::= <maybe empty comma-separated list of llvm-type-or-ref>
llvm-type-or-ref ::= <any llvm type>
                   | `!llvm.struct<` string-literal >
```

The body of the identified struct is printed in full unless the it is
transitively contained in the same struct. In the latter case, only the
identifier is printed. For example, the structure containing the pointer to
itself is represented as `!llvm.struct<"A", (ptr<"A">)>`, and the structure `A`
containing two pointers to the structure `B` containing a pointer to the
structure `A` is represented as `!llvm.struct<"A", (ptr<"B", (ptr<"A">)>,
ptr<"B", (ptr<"A">))>`. Note that the structure `B` is "unrolled" for both
elements. _A structure with the same name but different body is a syntax error._
**The user must ensure structure name uniqueness across all modules processed in
a given MLIR context.** Stucture names are arbitrary string literals and may
include, e.g., spaces and keywords.

Identified structs may be _opaque_. In this case, the body is unknown but the
structure type is considered _initialized_ and is valid in the IR.

#### Literal Structure Types

Literal structures are uniqued according to the list of elements they contain,
and can optionally be packed. The syntax for such structs is as follows.

```
llvm-literal-struct-type ::= `!llvm.struct<` `packed`? `(` llvm-type-list `)`
                             `>`
llvm-type-list ::= <maybe empty comma-separated list of llvm types w/o `!llvm`>
```

Literal structs cannot be recursive, but can contain other structs. Therefore,
they must be constructed in a single step with the entire list of contained
elements provided.

#### Examples of Structure Types

```mlir
!llvm.struct<>                  // NOT allowed
!llvm.struct<()>                // empty, literal
!llvm.struct<(i32)>             // literal
!llvm.struct<(struct<(i32)>)>   // struct containing a struct
!llvm.struct<packed (i8, i32)>  // packed struct
!llvm.struct<"a">               // recursive reference, only allowed within
                                // another struct, NOT allowed at top level
!llvm.struct<"a", ptr<struct<"a">>>  // supported example of recursive reference
!llvm.struct<"a", ()>           // empty, named (necessary to differentiate from
                                // recursive reference)
!llvm.struct<"a", opaque>       // opaque, named
!llvm.struct<"a", (i32)>        // named
!llvm.struct<"a", packed (i8, i32)>  // named, packed
```

### Unsupported Types

LLVM IR `label` type does not have a counterpart in the LLVM dialect since, in
MLIR, blocks are not values and don't need a type.

## Operations

All operations in the LLVM IR dialect have a custom form in MLIR. The mnemonic
of an operation is that used in LLVM IR prefixed with "`llvm.`".

### LLVM functions

MLIR functions are defined by an operation that is not built into the IR itself.
The LLVM IR dialect provides an `llvm.func` operation to define functions
compatible with LLVM IR. These functions have wrapped LLVM IR function type but
use MLIR syntax to express it. They are required to have exactly one result
type. LLVM function operation is intended to capture additional properties of
LLVM functions, such as linkage and calling convention, that may be modeled
differently by the built-in MLIR function.

```mlir
// The type of @bar is !llvm<"i64 (i64)">
llvm.func @bar(%arg0: !llvm.i64) -> !llvm.i64 {
  llvm.return %arg0 : !llvm.i64
}

// Type type of @foo is !llvm<"void (i64)">
// !llvm.void type is omitted
llvm.func @foo(%arg0: !llvm.i64) {
  llvm.return
}

// A function with `internal` linkage.
llvm.func internal @internal_func() {
  llvm.return
}

```

#### Attribute pass-through

An LLVM IR dialect function provides a mechanism to forward function-level
attributes to LLVM IR using the `passthrough` attribute. This is an array
attribute containing either string attributes or array attributes. In the former
case, the value of the string is interpreted as the name of LLVM IR function
attribute. In the latter case, the array is expected to contain exactly two
string attributes, the first corresponding to the name of LLVM IR function
attribute, and the second corresponding to its value. Note that even integer
LLVM IR function attributes have their value represented in the string form.

Example:

```mlir
llvm.func @func() attributes {
  passthrough = ["noinline",           // value-less attribute
                 ["alignstack", "4"],  // integer attribute with value
                 ["other", "attr"]]    // attribute unknown to LLVM
} {
  llvm.return
}
```

If the attribute is not known to LLVM IR, it will be attached as a string
attribute.

#### Linkage

An LLVM IR dialect function has a linkage attribute derived from LLVM IR
[linkage types](https://llvm.org/docs/LangRef.html#linkage-types). Linkage is
specified by the same keyword as in LLVM IR and is located between `llvm.func`
and the symbol name. If no linkage keyword is present, `external` linkage is
assumed by default.

### LLVM IR operations

The following operations are currently supported. The semantics of these
operations corresponds to the semantics of the similarly-named LLVM IR
instructions.

#### Integer binary arithmetic operations

Take two arguments of wrapped LLVM IR integer type, produce one value of the
same type.

-   `add`
-   `sub`
-   `mul`
-   `udiv`
-   `sdiv`
-   `urem`
-   `srem`

Examples:

```mlir
// Integer addition.
%0 = llvm.add %a, %b : !llvm.i32

// Unsigned integer division.
%1 = llvm.udiv %a, %b : !llvm.i32
```

#### Floating point binary arithmetic operations

Take two arguments of wrapped LLVM IR floating point type, produce one value of
the same type.

-   `fadd`
-   `fsub`
-   `fmul`
-   `fdiv`
-   `frem`

Examples:

```mlir
// Float addition.
%0 = llvm.fadd %a, %b : !llvm.float

// Float division.
%1 = llvm.fdiv %a, %b : !llvm.float
```

#### Memory-related operations

-   `<r> = alloca <size> x <type>`
-   `<r> = getelementptr <address>[<index> (, <index>)+]`
-   `<r> = load <address>`
-   `store <value>, <address>`

In these operations, `<size>` must be a value of wrapped LLVM IR integer type,
`<address>` must be a value of wrapped LLVM IR pointer type, and `<value>` must
be a value of wrapped LLVM IR type that corresponds to the pointer type of
`<address>`.

The `index` operands are integer values whose semantics is identical to the
non-pointer arguments of LLVM IR's `getelementptr`.

Examples:

```mlir
// Allocate an array of 4 floats on stack
%c4 = llvm.mlir.constant(4) : !llvm.i64
%0 = llvm.alloca %c4 x !llvm.float : (!llvm.i64) -> !llvm<"float*">

// Get the second element of the array (note 0-based indexing).
%c1 = llvm.mlir.constant(1) : !llvm.i64
%1 = llvm.getelementptr %0[%c1] : (!llvm<"float*">, !llvm.i64)
                                   -> !llvm<"float*">

// Store a constant into this element.
%cf = llvm.mlir.constant(42.0 : f32) : !llvm.float
llvm.store %cf, %1 : !llvm<"float*">

// Load the value from this element.
%3 = llvm.load %1 : !llvm<"float*">
```

#### Operations on values of aggregate type.

-   `<value> = extractvalue <struct>[<index> (, <index>)+]`
-   `<struct> = insertvalue <value>, <struct>[<index> (, <index>)+]`

In these operations, `<struct>` must be a value of wrapped LLVM IR structure
type and `<value>` must be a value that corresponds to one of the (nested)
structure element types.

Note the use of integer literals to designate subscripts, which is made possible
by `extractvalue` and `insertvalue` must have constant subscripts. Internally,
they are modeled as array attributes.

Examples:

```mlir
// Get the value third element of the second element of a structure.
%0 = llvm.extractvalue %s[1, 2] : !llvm<"{i32, {i1, i8, i16}">

// Insert the value to the third element of the second element of a structure.
// Note that this returns a new structure-typed value.
%1 = llvm.insertvalue %0, %s[1, 2] : !llvm<"{i32, {i1, i8, i16}">
```

#### Terminator operations.

Branch operations:

-   `br [<successor>(<operands>)]`
-   `cond_br <condition> [<true-successor>(<true-operands>),`
    `<false-successor>(<false-operands>)]`

In order to comply with MLIR design, branch operations in the LLVM IR dialect
pass arguments to basic blocks. Successors must be valid block MLIR identifiers
and operand lists for each of them must have the same types as the arguments of
the respective blocks. `<condition>` must be a wrapped LLVM IR `i1` type.

Since LLVM IR uses the name of the predecessor basic block to identify the
sources of a PHI node, it is invalid for two entries of the PHI node to indicate
different values coming from the same block. Therefore, `cond_br` in the LLVM IR
dialect disallows its successors to be the same block _if_ this block has
arguments.

Examples:

```mlir
// Branch without arguments.
^bb0:
  llvm.br ^bb0

// Branch and pass arguments.
^bb1(%arg: !llvm.i32):
  llvm.br ^bb1(%arg : !llvm.i32)

// Conditionally branch and pass arguments to one of the blocks.
llvm.cond_br %cond, ^bb0, %bb1(%arg : !llvm.i32)

// It's okay to use the same block without arguments, but probably useless.
llvm.cond_br %cond, ^bb0, ^bb0

// ERROR: Passing different arguments to the same block in a conditional branch.
llvm.cond_br %cond, ^bb1(%0 : !llvm.i32), ^bb1(%1 : !llvm.i32)

```

Call operations:

-   `<r> = call(<operands>)`
-   `call(<operands>)`

In LLVM IR, functions may return either 0 or 1 value. LLVM IR dialect implements
this behavior by providing a variadic `call` operation for 0- and 1-result
functions. Even though MLIR supports multi-result functions, LLVM IR dialect
disallows them.

The `call` instruction supports both direct and indirect calls. Direct calls
start with a function name (`@`-prefixed) and indirect calls start with an SSA
value (`%`-prefixed). The direct callee, if present, is stored as a function
attribute `callee`. The trailing type of the instruction is always the MLIR
function type, which may be different from the indirect callee that has the
wrapped LLVM IR function type.

Examples:

```mlir
// Direct call without arguments and with one result.
%0 = llvm.call @foo() : () -> (!llvm.float)

// Direct call with arguments and without a result.
llvm.call @bar(%0) : (!llvm.float) -> ()

// Indirect call with an argument and without a result.
llvm.call %1(%0) : (!llvm.float) -> ()
```

#### Miscellaneous operations.

Integer comparisons: `icmp "predicate" <lhs>, <rhs>`. The following predicate
values are supported:

-   `eq` - equality comparison;
-   `ne` - inequality comparison;
-   `slt` - signed less-than comparison
-   `sle` - signed less-than-or-equal comparison
-   `sgt` - signed greater-than comparison
-   `sge` - signed greater-than-or-equal comparison
-   `ult` - unsigned less-than comparison
-   `ule` - unsigned less-than-or-equal comparison
-   `ugt` - unsigned greater-than comparison
-   `uge` - unsigned greater-than-or-equal comparison

Bitwise reinterpretation: `bitcast <value>`.

Selection: `select <condition>, <lhs>, <rhs>`.

### Auxiliary MLIR Operations for Constants and Globals

LLVM IR has broad support for first-class constants, which is not the case for
MLIR. Instead, constants are defined in MLIR as regular SSA values produced by
operations with specific traits. The LLVM dialect provides a set of operations
that model LLVM IR constants. These operations do not correspond to LLVM IR
instructions and are therefore prefixed with `llvm.mlir`.

Inline constants can be created by `llvm.mlir.constant`, which currently
supports integer, float, string or elements attributes (constant structs are not
currently supported). LLVM IR constant expressions are expected to be
constructed as sequences of regular operations on SSA values produced by
`llvm.mlir.constant`. Additionally, MLIR provides semantically-charged
operations `llvm.mlir.undef` and `llvm.mlir.null` for the corresponding
constants.

LLVM IR globals can be defined using `llvm.mlir.global` at the module level,
except for functions that are defined with `llvm.func`. Globals, both variables
and functions, can be accessed by taking their address with the
`llvm.mlir.addressof` operation, which produces a pointer to the named global,
unlike the `llvm.mlir.constant` that produces the value of the same type as the
constant.

#### `llvm.mlir.addressof`

Creates an SSA value containing a pointer to a global variable or constant
defined by `llvm.mlir.global`. The global value can be defined after its first
referenced. If the global value is a constant, storing into it is not allowed.

Examples:

```mlir
func @foo() {
  // Get the address of a global variable.
  %0 = llvm.mlir.addressof @const : !llvm<"i32*">

  // Use it as a regular pointer.
  %1 = llvm.load %0 : !llvm<"i32*">

  // Get the address of a function.
  %2 = llvm.mlir.addressof @foo : !llvm<"void ()*">

  // The function address can be used for indirect calls.
  llvm.call %2() : () -> ()
}

// Define the global.
llvm.mlir.global @const(42 : i32) : !llvm.i32
```

#### `llvm.mlir.constant`

Unlike LLVM IR, MLIR does not have first-class constant values. Therefore, all
constants must be created as SSA values before being used in other operations.
`llvm.mlir.constant` creates such values for scalars and vectors. It has a
mandatory `value` attribute, which may be an integer, floating point attribute;
dense or sparse attribute containing integers or floats. The type of the
attribute is one of the corresponding MLIR builtin types. It may be omitted for
`i64` and `f64` types that are implied. The operation produces a new SSA value
of the specified LLVM IR dialect type. The type of that value _must_ correspond
to the attribute type converted to LLVM IR.

Examples:

```mlir
// Integer constant, internal i32 is mandatory
%0 = llvm.mlir.constant(42 : i32) : !llvm.i32

// It's okay to omit i64.
%1 = llvm.mlir.constant(42) : !llvm.i64

// Floating point constant.
%2 = llvm.mlir.constant(42.0 : f32) : !llvm.float

// Splat dense vector constant.
%3 = llvm.mlir.constant(dense<1.0> : vector<4xf32>) : !llvm<"<4 x float>">
```

#### `llvm.mlir.global`

Since MLIR allows for arbitrary operations to be present at the top level,
global variables are defined using the `llvm.mlir.global` operation. Both global
constants and variables can be defined, and the value may also be initialized in
both cases.

There are two forms of initialization syntax. Simple constants that can be
represented as MLIR attributes can be given in-line:

```mlir
llvm.mlir.global @variable(32.0 : f32) : !llvm.float
```

This initialization and type syntax is similar to `llvm.mlir.constant` and may
use two types: one for MLIR attribute and another for the LLVM value. These
types must be compatible.

More complex constants that cannot be represented as MLIR attributes can be
given in an initializer region:

```mlir
// This global is initialized with the equivalent of:
//   i32* getelementptr (i32* @g2, i32 2)
llvm.mlir.global constant @int_gep() : !llvm<"i32*"> {
  %0 = llvm.mlir.addressof @g2 : !llvm<"i32*">
  %1 = llvm.mlir.constant(2 : i32) : !llvm.i32
  %2 = llvm.getelementptr %0[%1] : (!llvm<"i32*">, !llvm.i32) -> !llvm<"i32*">
  // The initializer region must end with `llvm.return`.
  llvm.return %2 : !llvm<"i32*">
}
```

Only one of the initializer attribute or initializer region may be provided.

`llvm.mlir.global` must appear at top-level of the enclosing module. It uses an
@-identifier for its value, which will be uniqued by the module with respect to
other @-identifiers in it.

Examples:

```mlir
// Global values use @-identifiers.
llvm.mlir.global constant @cst(42 : i32) : !llvm.i32

// Non-constant values must also be initialized.
llvm.mlir.global @variable(32.0 : f32) : !llvm.float

// Strings are expected to be of wrapped LLVM i8 array type and do not
// automatically include the trailing zero.
llvm.mlir.global @string("abc") : !llvm<"[3 x i8]">

// For strings globals, the trailing type may be omitted.
llvm.mlir.global constant @no_trailing_type("foo bar")

// A complex initializer is constructed with an initializer region.
llvm.mlir.global constant @int_gep() : !llvm<"i32*"> {
  %0 = llvm.mlir.addressof @g2 : !llvm<"i32*">
  %1 = llvm.mlir.constant(2 : i32) : !llvm.i32
  %2 = llvm.getelementptr %0[%1] : (!llvm<"i32*">, !llvm.i32) -> !llvm<"i32*">
  llvm.return %2 : !llvm<"i32*">
}
```

Similarly to functions, globals have a linkage attribute. In the custom syntax,
this attribute is placed between `llvm.mlir.global` and the optional `constant`
keyword. If the attribute is omitted, `external` linkage is assumed by default.

Examples:

```mlir
// A constant with internal linkage will not participate in linking.
llvm.mlir.global internal constant @cst(42 : i32) : !llvm.i32

// By default, "external" linkage is assumed and the global participates in
// symbol resolution at link-time.
llvm.mlir.global @glob(0 : f32) : !llvm.float
```

#### `llvm.mlir.null`

Unlike LLVM IR, MLIR does not have first-class null pointers. They must be
explicitly created as SSA values using `llvm.mlir.null`. This operation has
no operands or attributes, and returns a null value of a wrapped LLVM IR
pointer type.

Examples:

```mlir
// Null pointer to i8 value.
%0 = llvm.mlir.null : !llvm<"i8*">

// Null pointer to a function with signature void() value.
%1 = llvm.mlir.null : !llvm<"void()*">
```

#### `llvm.mlir.undef`

Unlike LLVM IR, MLIR does not have first-class undefined values. Such values
must be created as SSA values using `llvm.mlir.undef`. This operation has no
operands or attributes. It creates an undefined value of the specified LLVM IR
dialect type wrapping an LLVM IR structure type.

Example:

```mlir
// Create a structure with a 32-bit integer followed by a float.
%0 = llvm.mlir.undef : !llvm<"{i32, float}">
```