QBE Intermediate Language

Table of Contents

  1. Basic Concepts
  2. Types
  3. Constants
  4. Linkage
  5. Definitions
  6. Control
  7. Instructions
  8. Instructions Index

1. Basic Concepts

The intermediate language (IL) is a higher-level language than the machine's assembly language. It smoothes most of the irregularities of the underlying hardware and allows an infinite number of temporaries to be used. This higher abstraction level allows frontend programmers to focus on language design issues.

Input Files

The intermediate language is provided to QBE as text. Usually, one file is generated per each compilation unit from the frontend input language. An IL file is a sequence of Definitions for data, functions, and types. Once processed by QBE, the resulting file can be assembled and linked using a standard toolchain (e.g., GNU binutils).

Here is a complete "Hello World" IL file which defines a function that prints to the screen. Since the string is not a first class object (only the pointer is) it is defined outside the function's body. Comments start with a # character and finish with the end of the line.

# Define the string constant.
data $str = { b "hello world", b 0 }

export function w $main() {
@start
        # Call the puts function with $str as argument.
        %r =w call $puts(l $str)
        ret 0
}

If you have read the LLVM language reference, you might recognize the example above. In comparison, QBE makes a much lighter use of types and the syntax is terser.

BNF Notation

The language syntax is vaporously described in the sections below using BNF syntax. The different BNF constructs used are listed below.

Sigils

The intermediate language makes heavy use of sigils, all user-defined names are prefixed with a sigil. This is to avoid keyword conflicts, and also to quickly spot the scope and nature of identifiers.

In this BNF syntax, we use ?IDENT to designate an identifier starting with the sigil ?.

Spacing

NL := '\n'+

Individual tokens in IL files must be separated by one or more spacing characters. Both spaces and tabs are recognized as spacing characters. In data and type definitions, newlines may also be used as spaces to prevent overly long lines. When exactly one of two consecutive tokens is a symbol (for example , or = or {), spacing may be omitted.

2. Types

Simple Types

BASETY := 'w' | 'l' | 's' | 'd'  # Base types
EXTTY  := BASETY    | 'b' | 'h'  # Extended types

The IL makes minimal use of types. By design, the types used are restricted to what is necessary for unambiguous compilation to machine code and C interfacing. Unlike LLVM, QBE is not using types as a means to safety; they are only here for semantic purposes.

The four base types are w (word), l (long), s (single), and d (double), they stand respectively for 32-bit and 64-bit integers, and 32-bit and 64-bit floating-point numbers. There are no pointer types available; pointers are typed by an integer type sufficiently wide to represent all memory addresses (e.g., l on 64-bit architectures). Temporaries in the IL can only have a basic type.

Extended types contain base types plus b (byte) and h (half word), respectively for 8-bit and 16-bit integers. They are used in Aggregate Types and Data definitions.

For C interfacing, the IL also provides user-defined aggregate types. The syntax used to designate them is :foo. Details about their definition are given in the Aggregate Types section.

Subtyping

The IL has a minimal subtyping feature, for integer types only. Any value of type l can be used in a w context. In that case, only the 32 least significant bits of the word value are used.

Make note that it is the opposite of the usual subtyping on integers (in C, we can safely use an int where a long is expected). A long value cannot be used in word context. The rationale is that a word can be signed or unsigned, so extending it to a long could be done in two ways, either by zero-extension, or by sign-extension.

3. Constants

CONST :=
    ['-'] NUMBER  # Decimal integer
  | 's_' FP       # Single-precision float
  | 'd_' FP       # Double-precision float
  | $IDENT        # Global symbol

Throughout the IL, constants are specified with a unified syntax and semantics. Constants are immediates, meaning that they can be used directly in instructions; there is no need for a "load constant" instruction.

The representation of integers is two's complement. Floating-point numbers are represented using the single-precision and double-precision formats of the IEEE 754 standard.

Constants specify a sequence of bits and are untyped. They are always parsed as 64-bit blobs. Depending on the context surrounding a constant, only some of its bits are used. For example, in the program below, the two variables defined have the same value since the first operand of the subtraction is a word (32-bit) context.

%x =w sub -1, 0
%y =w sub 4294967295, 0

Because specifying floating-point constants by their bits makes the code less readable, syntactic sugar is provided to express them. Standard scientific notation is prefixed with s_ and d_ for single and double precision numbers respectively. Once again, the following example defines twice the same double-precision constant.

%x =d add d_0, d_-1
%y =d add d_0, -4616189618054758400

Global symbols can also be used directly as constants; they will be resolved and turned into actual numeric constants by the linker.

4. Linkage

LINKAGE :=
    'export' [NL]
  | 'section' SECNAME [NL]
  | 'section' SECNAME SECFLAGS [NL]

SECNAME  := '"' .... '"'
SECFLAGS := '"' .... '"'

Function and data definitions (see below) can specify linkage information to be passed to the assembler and eventually to the linker.

The export linkage flag marks the defined item as visible outside the current file's scope. If absent, the symbol can only be referred to locally. Functions compiled by QBE and called from C need to be exported.

A section flag can be specified to tell the linker to put the defined item in a certain section. The use of the section flag is platform dependent and we refer the user to the documentation of their assembler and linker for relevant information.

section ".init_array"
data $.init.f = { l $f }

The section flag can be used to add function pointers to a global initialization list, as depicted above. Note that some platforms provide a BSS section that can be used to minimize the footprint of uniformly zeroed data. When this section is available, QBE will automatically make use of it and no section flag is required.

The section and export linkage flags should each appear at most once in a definition. If multiple occurrences are present, QBE is free to use any.

5. Definitions

Definitions are the essential components of an IL file. They can define three types of objects: aggregate types, data, and functions. Aggregate types are never exported and do not compile to any code. Data and function definitions have file scope and are mutually recursive (even across IL files). Their visibility can be controlled using linkage flags.

Aggregate Types

TYPEDEF :=
    # Regular type
    'type' :IDENT '=' ['align' NUMBER]
    '{'
        ( SUBTY [NUMBER] ),
    '}'
  | # Opaque type
    'type' :IDENT '=' 'align' NUMBER '{' NUMBER '}'

SUBTY := EXTTY | :IDENT

Aggregate type definitions start with the type keyword. They have file scope, but types must be defined before being referenced. The inner structure of a type is expressed by a comma-separated list of types enclosed in curly braces.

type :fourfloats = { s, s, d, d }

For ease of IL generation, a trailing comma is tolerated by the parser. In case many items of the same type are sequenced (like in a C array), the shorter array syntax can be used.

type :abyteandmanywords = { b, w 100 }

By default, the alignment of an aggregate type is the maximum alignment of its members. The alignment can be explicitly specified by the programmer.

type :cryptovector = align 16 { w 4 }

Opaque types are used when the inner structure of an aggregate cannot be specified; the alignment for opaque types is mandatory. They are defined simply by enclosing their size between curly braces.

type :opaque = align 16 { 32 }

Data

DATADEF :=
    LINKAGE*
    'data' $IDENT '=' ['align' NUMBER]
    '{'
        ( EXTTY DATAITEM+
        | 'z'   NUMBER ),
    '}'

DATAITEM :=
    $IDENT ['+' NUMBER]  # Symbol and offset
  |  '"' ... '"'         # String
  |  CONST               # Constant

Data definitions express objects that will be emitted in the compiled file. Their visibility and location in the compiled artifact are controlled with linkage flags described in the Linkage section.

They define a global identifier (starting with the sigil $), that will contain a pointer to the object specified by the definition.

Objects are described by a sequence of fields that start with a type letter. This letter can either be an extended type, or the z letter. If the letter used is an extended type, the data item following specifies the bits to be stored in the field. When several data items follow a letter, they initialize multiple fields of the same size.

The members of a struct will be packed. This means that padding has to be emitted by the frontend when necessary. Alignment of the whole data objects can be manually specified, and when no alignment is provided, the maximum alignment from the platform is used.

When the z letter is used the number following indicates the size of the field; the contents of the field are zero initialized. It can be used to add padding between fields or zero-initialize big arrays.

Here are various examples of data definitions.

# Three 32-bit values 1, 2, and 3
# followed by a 0 byte.
data $a = { w 1 2 3, b 0 }

# A thousand bytes 0 initialized.
data $b = { z 1000 }

# An object containing two 64-bit
# fields, one with all bits sets and the
# other containing a pointer to the
# object itself.
data $c = { l -1, l $c }

Functions

FUNCDEF :=
    LINKAGE*
    'function' [ABITY] $IDENT '(' (PARAM), ')' [NL]
    '{' NL
        BLOCK+
    '}'

PARAM :=
    ABITY %IDENT  # Regular parameter
  | 'env' %IDENT  # Environment parameter (first)
  | '...'         # Variadic marker (last)

ABITY := BASETY | :IDENT

Function definitions contain the actual code to emit in the compiled file. They define a global symbol that contains a pointer to the function code. This pointer can be used in call instructions or stored in memory.

The type given right before the function name is the return type of the function. All return values of this function must have this return type. If the return type is missing, the function cannot return any value.

The parameter list is a comma separated list of temporary names prefixed by types. The types are used to correctly implement C compatibility. When an argument has an aggregate type, a pointer to the aggregate is passed by the caller. In the example below, we have to use a load instruction to get the value of the first (and only) member of the struct.

type :one = { w }

function w $getone(:one %p) {
@start
        %val =w loadw %p
        ret %val
}

If the parameter list ends with ..., the function is a variadic function: it can accept a variable number of arguments. To access the extra arguments provided by the caller, use the vastart and vaarg instructions described in the Variadic section.

Optionally, the parameter list can start with an environment parameter env %e. This special parameter is a 64-bit integer temporary (i.e., of type l). If the function does not use its environment parameter, callers can safely omit it. This parameter is invisible to a C caller: for example, the function

export function w $add(env %e, w %a, w %b) {
@start
        %c =w add %a, %b
        ret %c
}

must be given the C prototype int add(int, int). The intended use of this feature is to pass the environment pointer of closures while retaining a very good compatibility with C. The Call section explains how to pass an environment parameter.

Since global symbols are defined mutually recursive, there is no need for function declarations: a function can be referenced before its definition. Similarly, functions from other modules can be used without previous declaration. All the type information is provided in the call instructions.

The syntax and semantics for the body of functions are described in the Control section.

6. Control

The IL represents programs as textual transcriptions of control flow graphs. The control flow is serialized as a sequence of blocks of straight-line code which are connected using jump instructions.

Blocks

BLOCK :=
    @IDENT NL     # Block label
    ( PHI NL )*   # Phi instructions
    ( INST NL )*  # Regular instructions
    JUMP NL       # Jump or return

All blocks have a name that is specified by a label at their beginning. Then follows a sequence of instructions that have "fall-through" flow. Finally one jump terminates the block. The jump can either transfer control to another block of the same function or return; jumps are described further below.

The first block in a function must not be the target of any jump in the program. If a jump to the function start is needed, the frontend must insert an empty prelude block at the beginning of the function.

When one block jumps to the next block in the IL file, it is not necessary to write the jump instruction, it will be automatically added by the parser. For example the start block in the example below jumps directly to the loop block.

function $loop() {
@start
@loop
        %x =w phi @start 100, @loop %x1
        %x1 =w sub %x, 1
        jnz %x1, @loop, @end
@end
        ret
}

Jumps

JUMP :=
    'jmp' @IDENT               # Unconditional
  | 'jnz' VAL, @IDENT, @IDENT  # Conditional
  | 'ret' [VAL]                # Return

A jump instruction ends every block and transfers the control to another program location. The target of a jump must never be the first block in a function. The three kinds of jumps available are described in the following list.

  1. Unconditional jump.

    Simply jumps to another block of the same function.

  2. Conditional jump.

    When its word argument is non-zero, it jumps to its first label argument; otherwise it jumps to the other label. The argument must be of word type; because of subtyping a long argument can be passed, but only its least significant 32 bits will be compared to 0.

  3. Function return.

    Terminates the execution of the current function, optionally returning a value to the caller. The value returned must be of the type given in the function prototype. If the function prototype does not specify a return type, no return value can be used.

7. Instructions

Instructions are the smallest piece of code in the IL, they form the body of Blocks. The IL uses a three-address code, which means that one instruction computes an operation between two operands and assigns the result to a third one.

An instruction has both a name and a return type, this return type is a base type that defines the size of the instruction's result. The type of the arguments can be unambiguously inferred using the instruction name and the return type. For example, for all arithmetic instructions, the type of the arguments is the same as the return type. The two additions below are valid if %y is a word or a long (because of Subtyping).

%x =w add 0, %y
%z =w add %x, %x

Some instructions, like comparisons and memory loads have operand types that differ from their return types. For instance, two floating points can be compared to give a word result (0 if the comparison succeeds, 1 if it fails).

%c =w cgts %a, %b

In the example above, both operands have to have single type. This is made explicit by the instruction suffix.

The types of instructions are described below using a short type string. A type string specifies all the valid return types an instruction can have, its arity, and the type of its arguments depending on its return type.

Type strings begin with acceptable return types, then follows, in parentheses, the possible types for the arguments. If the N-th return type of the type string is used for an instruction, the arguments must use the N-th type listed for them in the type string. When an instruction does not have a return type, the type string only contains the types of the arguments.

The following abbreviations are used.

For example, consider the type string wl(F), it mentions that the instruction has only one argument and that if the return type used is long, the argument must be of type double.

Arithmetic and Bits

The base arithmetic instructions in the first bullet are available for all types, integers and floating points.

When div is used with word or long return type, the arguments are treated as signed. The unsigned integral division is available as udiv instruction. When the result of a division is not an integer, it is truncated towards zero.

The signed and unsigned remainder operations are available as rem and urem. The sign of the remainder is the same as the one of the dividend. Its magnitude is smaller than the divisor one. These two instructions and udiv are only available with integer arguments and result.

Bitwise OR, AND, and XOR operations are available for both integer types. Logical operations of typical programming languages can be implemented using Comparisons and Jumps.

Shift instructions sar, shr, and shl, shift right or left their first operand by the amount from the second operand. The shifting amount is taken modulo the size of the result type. Shifting right can either preserve the sign of the value (using sar), or fill the newly freed bits with zeroes (using shr). Shifting left always fills the freed bits with zeroes.

Remark that an arithmetic shift right (sar) is only equivalent to a division by a power of two for non-negative numbers. This is because the shift right "truncates" towards minus infinity, while the division truncates towards zero.

Memory

The following example makes use some of the memory instructions. Pointers are stored in long temporaries.

%A0 =l alloc4 8      # stack allocate an array A of 2 words
%A1 =l add %A0, 4
storew 43,  %A0      # A[0] <- 43
storew 255, %A1      # A[1] <- 255
%v1 =w loadw  %A0    # %v1 <- A[0] as word
%v2 =w loadsb %A1    # %v2 <- A[1] as signed byte
%v3 =w add %v1, %v2  # %v3 is 42 here

Comparisons

Comparison instructions return an integer value (either a word or a long), and compare values of arbitrary types. The returned value is 1 if the two operands satisfy the comparison relation, or 0 otherwise. The names of comparisons respect a standard naming scheme in three parts.

  1. All comparisons start with the letter c.
  2. Then comes a comparison type. The following types are available for integer comparisons:

    • eq for equality
    • ne for inequality
    • sle for signed lower or equal
    • slt for signed lower
    • sge for signed greater or equal
    • sgt for signed greater
    • ule for unsigned lower or equal
    • ult for unsigned lower
    • uge for unsigned greater or equal
    • ugt for unsigned greater

    Floating point comparisons use one of these types:

    • eq for equality
    • ne for inequality
    • le for lower or equal
    • lt for lower
    • ge for greater or equal
    • gt for greater
    • o for ordered (no operand is a NaN)
    • uo for unordered (at least one operand is a NaN)

    Because floating point types always have a sign bit, all the comparisons available are signed.

  3. Finally, the instruction name is terminated with a basic type suffix precising the type of the operands to be compared.

For example, cod (I(dd,dd)) compares two double-precision floating point numbers and returns 1 if the two floating points are not NaNs, or 0 otherwise. The csltw (I(ww,ww)) instruction compares two words representing signed numbers and returns 1 when the first argument is smaller than the second one.

Conversions

Conversion operations change the representation of a value, possibly modifying it if the target type cannot hold the value of the source type. Conversions can extend the precision of a temporary (e.g., from signed 8-bit to 32-bit), or convert a floating point into an integer and vice versa.

Extending the precision of a temporary is done using the ext family of instructions. Because QBE types do not specify the signedness (like in LLVM), extension instructions exist to sign-extend and zero-extend a value. For example, extsb takes a word argument and sign-extends the 8 least-significant bits to a full word or long, depending on the return type.

The instructions exts (extend single) and truncd (truncate double) are provided to change the precision of a floating point value. When the double argument of truncd cannot be represented as a single-precision floating point, it is truncated towards zero.

Converting between signed integers and floating points is done using stosi (single to signed integer), stoui (single to unsigned integer, dtosi (double to signed integer), dtoui (double to unsigned integer), swtof (signed word to float), uwtof (unsigned word to float), sltof (signed long to float) and ultof (unsigned long to float).

Because of Subtyping, there is no need to have an instruction to lower the precision of an integer temporary.

Cast and Copy

The cast and copy instructions return the bits of their argument verbatim. However a cast will change an integer into a floating point of the same width and vice versa.

Casts can be used to make bitwise operations on the representation of floating point numbers. For example the following program will compute the opposite of the single-precision floating point number %f into %rs.

%b0 =w cast %f
%b1 =w xor 2147483648, %b0  # flip the msb
%rs =s cast %b1

Call

CALL := [%IDENT '=' ABITY] 'call' VAL '(' (ARG), ')'

ARG :=
    ABITY VAL  # Regular argument
  | 'env' VAL  # Environment argument (first)
  | '...'      # Variadic marker

ABITY := BASETY | :IDENT

The call instruction is special in several ways. It is not a three-address instruction and requires the type of all its arguments to be given. Also, the return type can be either a base type or an aggregate type. These specifics are required to compile calls with C compatibility (i.e., to respect the ABI).

When an aggregate type is used as argument type or return type, the value respectively passed or returned needs to be a pointer to a memory location holding the value. This is because aggregate types are not first-class citizens of the IL.

Unless the called function does not return a value, a return temporary must be specified, even if it is never used afterwards.

An environment parameter can be passed as first argument using the env keyword. The passed value must be a 64-bit integer. If the called function does not expect an environment parameter, it will be safely discarded. See the Functions section for more information about environment parameters.

When the called function is variadic, there must be a ... marker separating the named and variadic arguments.

Variadic

The vastart and vaarg instructions provide a portable way to access the extra parameters of a variadic function.

The vastart instruction initializes a variable argument list used to access the extra parameters of the enclosing variadic function. It is safe to call it multiple times.

The vaarg instruction fetches the next argument from a variable argument list. It is currently limited to fetching arguments that have a base type. This instruction is essentially effectful: calling it twice in a row will return two consecutive arguments from the argument list.

Both instructions take a pointer to a variable argument list as sole argument. The size and alignment of variable argument lists depend on the target used. However, it is possible to conservatively use the maximum size and alignment required by all the targets.

type :valist = align 8 { 24 }  # For amd64_sysv
type :valist = align 8 { 32 }  # For arm64
type :valist = align 8 { 8 }   # For rv64

The following example defines a variadic function adding its first three arguments.

function s $add3(s %a, ...) {
@start
        %ap =l alloc8 32
        vastart %ap
        %r =s call $vadd(s %a, l %ap)
        ret %r
}

function s $vadd(s %a, l %ap) {
@start
        %b =s vaarg %ap
        %c =s vaarg %ap
        %d =s add %a, %b
        %e =s add %d, %c
        ret %e
}

Phi

PHI := %IDENT '=' BASETY 'phi' ( @IDENT VAL ),

First and foremost, phi instructions are NOT necessary when writing a frontend to QBE. One solution to avoid having to deal with SSA form is to use stack allocated variables for all source program variables and perform assignments and lookups using Memory operations. This is what LLVM users typically do.

Another solution is to simply emit code that is not in SSA form! Contrary to LLVM, QBE is able to fixup programs not in SSA form without requiring the boilerplate of loading and storing in memory. For example, the following program will be correctly compiled by QBE.

@start
        %x =w copy 100
        %s =w copy 0
@loop
        %s =w add %s, %x
        %x =w sub %x, 1
        jnz %x, @loop, @end
@end
        ret %s

Now, if you want to know what phi instructions are and how to use them in QBE, you can read the following.

Phi instructions are specific to SSA form. In SSA form values can only be assigned once, without phi instructions, this requirement is too strong to represent many programs. For example consider the following C program.

int f(int x) {
        int y;
        if (x)
                y = 1;
        else
                y = 2;
        return y;
}

The variable y is assigned twice, the solution to translate it in SSA form is to insert a phi instruction.

@ifstmt
        jnz %x, @ift, @iff
@ift
        jmp @retstmt
@iff
        jmp @retstmt
@retstmt
        %y =w phi @ift 1, @iff 2
        ret %y

Phi instructions return one of their arguments depending on where the control came from. In the example, %y is set to 1 if the @ift branch is taken, or it is set to 2 otherwise.

An important remark about phi instructions is that QBE assumes that if a variable is defined by a phi it respects all the SSA invariants. So it is critical to not use phi instructions unless you know exactly what you are doing.

8. Instructions Index