6 The beam_makeops script

This document describes the beam_makeops script.

6.1 Introduction

The beam_makeops Perl script is used at build-time by both the compiler and runtime system. Given a number of input files (all with the extension .tab), it will generate source files used by the Erlang compiler and by the runtime system to load and execute BEAM instructions.

Essentially those .tab files define:

• External generic BEAM instructions. They are the instructions that are known to both the compiler and the runtime system. Generic instructions are stable between releases. New generic instructions with high numbers than previous instructions can be added in major releases. The OTP 20 release has 159 external generic instructions.

• Internal generic instructions. They are known only to the runtime system and can be changed at any time without compatibility issues. They are created by transformation rules (described next).

• Rules for transforming one or more generic instructions to other generic instructions. The transformation rules allow combining, splitting, and removal of instructions, as well as shuffling operands. Because of the transformation rules, the runtime can have many internal generic instructions that are only known to runtime system.

• Specific BEAM instructions. The specific instructions are the instructions that are actually executed by the runtime system. They can be changed at any time without causing compatibility issues. The loader translates generic instructions to specific instructions. In general, for each generic instruction, there exists a family of specific instructions. The OTP 20 release has 389 specific instructions.

• The implementation of specific instructions.

Generic instructions have typed operands. Here are a few examples of operands for move/2:

{move,{atom,id},{x,5}}.
{move,{x,3},{x,0}}.
{move,{x,2},{y,1}}.

When those instructions are loaded, the loader rewrites them to specific instructions:

move_cx id 5
move_xx 3 0
move_xy 2 1

Corresponding to each generic instruction, there is a family of specific instructions. The types that an instance of a specific instruction can handle are encoded in the instruction names. For example, move_xy takes an X register number as the first operand and a Y register number as the second operand. move_cx takes a tagged Erlang term as the first operand and an X register number as the second operand.

6.2 An example: the move instruction

Using the move instruction as an example, we will give a quick tour to show the main features of beam_makeops.

In the compiler application, in the file genop.tab, there is the following line:

64: move/2

This is a definition of an external generic BEAM instruction. Most importantly it specifices that the opcode is 64. It also defines that it has two operands. The BEAM assembler will use the opcode when creating .beam files. The compiler does not really need the arity, but it will use it as an internal sanity check when assembling the BEAM code.

Let's have a look at ops.tab in erts/emulator/beam, where the specific move instructions are defined. Here are a few of them:

move x x
move x y
move c x

Each specific instructions is defined by following the name of the instruction with the types for each operand. An operand type is a single letter. For example, x means an X register, y means a Y register, and c is a "constant" (a tagged term such as an integer, an atom, or a literal).

Now let's look at the implementation of the move instruction. There are multiple files containing implementations of instructions in the erts/emulator/beam directory. The move instruction is defined in instrs.tab. It looks like this:

move(Src, Dst) {
    $Dst = $Src;
}

The implementation for an instruction largely follows the C syntax, except that the variables in the function head don't have any types. The $ before an identifier denotes a macro expansion. Thus, $Src will expand to the code to pick up the source operand for the instruction and $Dst to the code for the destination register.

We will look at the code for each specific instruction in turn. To make the code easier to understand, let's first look at the memory layout for the instruction {move,{atom,id},{x,5}}:

     +--------------------+--------------------+
I -> |                 40 |       &&lb_move_cx |
     +--------------------+--------------------+
     |                        Tagged atom 'id' |
     +--------------------+--------------------+

This example and all other examples in the document assumes a 64-bit archictecture, and furthermore that pointers to C code fit in 32 bits.

I in the BEAM virtual machine is the instruction pointer. When BEAM executes an instruction, I points to the first word of the instruction.

&&lb_move_cx is the address to C code that implements move_cx. It is stored in the lower 32 bits of the word. In the upper 32 bits is the byte offset to the X register; the register number 5 has been multiplied by the word size size 8.

In the next word the tagged atom id is stored.

With that background, we can look at the generated code for move_cx in beam_hot.h:

OpCase(move_cx):
{
  BeamInstr next_pf = BeamCodeAddr(I[2]);
  xb(BeamExtraData(I[0])) = I[1];
  I += 2;
  ASSERT(VALID_INSTR(next_pf));
  GotoPF(next_pf);
}

We will go through each line in turn.

• OpCase(move_cx): defines a label for the instruction. The OpCase() macro is defined in beam_emu.c. It will expand this line to lb_move_cx:.

• BeamInstr next_pf = BeamCodeAddr(I[2]); fetches the pointer to code for the next instruction to be executed. The BeamCodeAddr() macro extracts the pointer from the lower 32 bits of the instruction word.

• xb(BeamExtraData(I[0])) = I[1]; is the expansion of $Dst = $Src. BeamExtraData() is a macro that will extract the upper 32 bits from the instruction word. In this example, it will return 40 which is the byte offset for X register 5. The xb() macro will cast a byte pointer to an Eterm pointer and dereference it. The I[1] on the right side of the = fetches an Erlang term (the atom id in this case).

• I += 2 advances the instruction pointer to the next instruction.

• In a debug-compiled emulator, ASSERT(VALID_INSTR(next_pf)); makes sure that next_pf is a valid instruction (that is, that it points within the process_main() function in beam_emu.c).

• GotoPF(next_pf); transfers control to the next instruction.

Now let's look at the implementation of move_xx:

OpCase(move_xx):
{
  Eterm tmp_packed1 = BeamExtraData(I[0]);
  BeamInstr next_pf = BeamCodeAddr(I[1]);
  xb((tmp_packed1>>BEAM_TIGHT_SHIFT)) = xb(tmp_packed1&BEAM_TIGHT_MASK);
  I += 1;
  ASSERT(VALID_INSTR(next_pf));
  GotoPF(next_pf);
}

We will go through the lines that are new or have changed compared to move_cx.

• Eterm tmp_packed1 = BeamExtraData(I[0]); picks up both X register numbers packed into the upper 32 bits of the instruction word.

• BeamInstr next_pf = BeamCodeAddr(I[1]); pre-fetches the address of the next instruction. Note that because both X registers operands fits into the instruction word, the next instruction is in the very next word.

• xb((tmp_packed1>>BEAM_TIGHT_SHIFT)) = xb(tmp_packed1&BEAM_TIGHT_MASK); copies the source to the destination. (For a 64-bit architecture, BEAM_TIGHT_SHIFT is 16 and BEAM_TIGHT_MASK is 0xFFFF.)

• I += 1; advances the instruction pointer to the next instruction.

move_xy is almost identical to move_xx. The only difference is the use of the yb() macro instead of xb() to reference the destination register:

OpCase(move_xy):
{
  Eterm tmp_packed1 = BeamExtraData(I[0]);
  BeamInstr next_pf = BeamCodeAddr(I[1]);
  yb((tmp_packed1>>BEAM_TIGHT_SHIFT)) = xb(tmp_packed1&BEAM_TIGHT_MASK);
  I += 1;
  ASSERT(VALID_INSTR(next_pf));
  GotoPF(next_pf);
}

Transformation rules

Next let's look at how we can do some optimizations using transformation rules. For simple instructions such as move/2, the instruction dispatch overhead can be substantial. A simple optimization is to combine common instructions sequences to a single instruction. One such common sequence is multiple move instructions moving X registers to Y registers.

Using the following rule we can combine two move instructions to a move2 instruction:

move X1=x Y1=y | move X2=x Y2=y => move2 X1 Y1 X2 Y2

The left side of the arrow (=>) is a pattern. If the pattern matches, the matching instructions will be replaced by the instructions on the right side. Variables in a pattern must start with an uppercase letter just as in Erlang. A pattern variable may be followed = and one or more type letters to constrain the match to one of those types. The variables that are bound on the left side can be used on the right side.

We will also need to define a specific instruction and an implementation:

# In ops.tab
move2 x y x y

// In instrs.tab
move2(S1, D1, S2, D2) {
    Eterm V1, V2;
    V1 = $S1;
    V2 = $S2;
    $D1 = V1;
    $D2 = V2;
}

When the loader has found a match and replaced the matched instructions, it will match the new instructions against the transformation rules. Because of that, we can define the rule for a move3/6 instruction as follows:

move2 X1=x Y1=y X2=x Y2=y | move X3=x Y3=y => \
      move3 X1 Y1 X2 Y2 X3 Y3

(A \ before a newline can be used to break a long line for readability.)

It would also be possible to define it like this:

move X1=x Y1=y | move X2=x Y2=y | move X3=x Y3=y => \
     move3 X1 Y1 X2 Y2 X3 Y3

but in that case it must be defined before the rule for move2/4 because the first matching rule will be applied.

One must be careful not to create infinite loops. For example, if we for some reason would want to reverse the operand order for the move instruction, we must not do like this:

move Src Dst => move Dst Src

The loader would swap the operands forever. To avoid the loop, we must rename the instruction. For example:

move Src Dst => assign Dst Src

This concludes the quick tour of the features of beam_makeops.

6.3 Short overview of instruction loading

To give some background to the rest of this document, here follows a quick overview of how instructions are loaded.

• The loader reads and decodes one instruction at a time from the BEAM code and creates a generic instruction. Many transformation rules must look at multiple instructions, so the loader will keep multiple generic instructions in a linked list.

• The loader tries to apply transformation rules against the generic instructions in the linked list. If a rule matches, the matched instructions will be removed and replaced with new generic instructions constructed from the right side of the transformation.

• If a transformation rule matched, the loader applies the transformation rules again.

• If no transformation rule match, the loader will begin rewriting the first of generic instructions to a specific instruction.

• First the loader will search for a specific operation where the types for all operands match the type for the generic instruction. The first matching instruction will be selected. beam_makeops has ordered the specific instructions so that instructions with more specific operands comes before instructions with less specific operands. For example, move_nx is more specific than move_cx. If the first operand is [] (NIL), move_nx will be selected.

• Given the opcode for the selected specific instruction, the loader looks up the pointer to the C code for the instruction and stores in the code area for the module being loaded.

• The loader translates each operand to a machine word and stores it in the code area. The operand type for the selected specific instruction guides the translation. For example, if the type is e, the value of the operand is an index into an arry of external functions and will be translated to a pointer to the export entry for the function to call. If the type is x, the number of the X register will be multiplied by the word size to produce a byte offset.

• The loader runs the packing engine to pack multiple operands into a single word. The packing engine is controlled by a small program, which is a string where each character is an instruction. For example, the code to pack the operands for move_xy is "22#" (on a 64-bit machine). That program will pack the byte offsets for both registers into the same word as the pointer to C code.

6.4 Running beam_makeops

beam_makeops is found in $ERL_TOP/erts/emulator/utils. Options start with a hyphen (-). The options are followed by the name of the input files. By convention, all input files have the extension .tab, but is not enforced by beam_makeops.

The -outdir option

The option -outdir Directory specifies the output directory for the generated files. Default is the current working directory.

Running beam_makeops for the compiler

Give the option -compiler to produce output files for the compiler. The following files will be written to the output directory:

• beam_opcodes.erl - Used primarily by beam_asm and beam_diasm.

• beam_opcode.hrl - Used by beam_asm. It contains tag definitions used for encoding instruction operands.

The input file should only contain the definition of BEAMFORMATNUMBER and external generic instructions. (Everything else would be ignored.)

Running beam_makeops for the emulator

Give the option -emulator to produce output files for the emulator. The following output files will be generated in the output directory.

• beam_hot.h, beam_warm.h, beam_cold.h - Implementation of instructions. Included inside the process_main() function in beam_emu.c.

• beam_opcodes.c - Defines static data used by the loader (beam_load.c). Data about generic instructions, specific instructions (including how to pack their operands), and transformation rules are all part of this file.

• beam_opcodes.h - Miscellanous preprocessor definitions, mainly used by beam_load.c but also by beam_{hot,warm,cold}.h.

• beam_pred_funcs.h - Included by beam_load.c. Contains defines needed to call guard constraints in transformation rules.

• beam_tr_funcs.h - Included by beam_load.c. Contains defines needed to call a C function to the right of a transformation rule.

The following options can be given:

• wordsize 32|64 - Defines the word size. Default is 32.

• code-model Model - The code model as given to -mcmodel option for GCC. Default is unknown. If the code model is small (and the word size is 64 bits), beam_makeops will pack operands into the upper 32 bits of the instruction word.

• DSymbol=0|1 - Defines the value for a symbol. The symbol can be used in %if and %unless directives.

6.5 Syntax of .tab files

Comments

Any line starting with # is a comment and is ignored.

A line with // is also a comment. It is recommended to only use this style of comments in files that define implementations of instructions.

A long line can be broken into shorter lines by a placing a \ before the newline.

Variable definitions

A variable definition binds a variable to a Perl variable. It is only meaningful to add a new definition if beam_makeops is updated at the same time to use the variable. A variable definition looks this:

name=value[;]

where name is the name of a Perl variable in beam_makeops, and value is the value to be given to the variable. The line can optionally end with a ; (to avoid messing up the C indentation mode in Emacs).

Here follows a description of the variables that are defined.

BEAM_FORMAT_NUMBER

genop.tab has the following definition:

BEAM_FORMAT_NUMBER=0

It defines the version of the instruction set (which will be included in the code header in the BEAM code). Theoretically, the version could be bumped, and all instructions changed. In practice, we would have two support two instruction sets in the runtime system for at least two releases, so it will probably never happen in practice.

GC_REGEXP

In macros.tab, there is a definition of GC_REGEXP. It will be described in a later section.

Directives

There are directives to classify specific instructions depending on how frequently used they are:

• %hot - Implementation will be placed in beam_hot.h. Frequently executed instructions.

• %warm - Implementation will be placed in beam_warm.h. Binary syntax instructions.

• %cold - Implementation will be placed in beam_cold.h. Trace instructions and infrequently used instructions.

Default is %hot. The directives will be applied to declarations of the specific instruction that follow. Here is an example:

%cold
is_number f? xy
%hot

Conditional compilation directives

The %if directive includes a range of lines if a condition is true. For example:

%if ARCH_64
i_bs_get_integer_32 x f? x
%endif

The specific instruction i_bs_get_integer_32 will only be defined on a 64-bit machine.

The condition can be inverted by using %unless instead of %if:

%unless NO_FPE_SIGNALS
fcheckerror p => i_fcheckerror
i_fcheckerror
fclearerror
%endif

It is also possible to add an %else clause:

%if ARCH_64
BS_SAFE_MUL(A, B, Fail, Dst) {
    Uint64 res = ($A) * ($B);
    if (res / $B != $A) {
        $Fail;
    }
    $Dst = res;
}
%else
BS_SAFE_MUL(A, B, Fail, Dst) {
    Uint64 res = (Uint64)($A) * (Uint64)($B);
    if ((res >> (8*sizeof(Uint))) != 0) {
        $Fail;
    }
    $Dst = res;
}
%endif

Symbols that are defined in directives

The following symbols are always defined.

• ARCH_64 - is 1 for a 64-bit machine, and 0 otherwise.
• ARCH_32 - is 1 for 32-bit machine, and 1 otherwise.

The Makefile for building the emulator currently defines the following symbols by using the -D option on the command line for beam_makeops.

• NO_FPE_SIGNALS - 1 if FPE signals are not enable in runtime system, 0 otherwise.
• USE_VM_PROBES - 1 if the runtime system is compiled to use VM probes (support for dtrace or systemtap), 0 otherwise.

Defining external generic instructions

External generic BEAM instructions are known to both the compiler and the runtime system. They remain stable between releases. A new major release may add more external generic instructions, but must not change the semantics for a previously defined instruction.

The syntax for an external generic instruction is as follows:

opcode: [-]name/arity

opcode is an integer greater than or equal to 1.

name is an identifier starting with a lowercase letter. arity is an integer denoting the number of operands.

name can optionally be preceded by - to indicate that it has been obsoleted. The compiler is not allowed to generate BEAM files that use obsolete instructions and the loader will refuse to load BEAM files that use obsolete instructions.

It only makes sense to define external generic instructions in the file genop.tab in lib/compiler/src, because the compiler must know about them in order to use them.

New instructions must be added at the end of the file, with higher numbers than the previous instructions.

Defining internal generic instructions

Internal generic instructions are known only to the runtime system and can be changed at any time without compatibility issues.

There are two ways to define internal generic instructions:

• Implicitly when a specific instruction is defined. This is by far the most common way. Whenever a specific instruction is created, beam_makeops automatically creates an internal generic instruction if it does not previously exist.

• Explicitly. This is necessary only when a generic instruction does not have any corresponding specific instruction.

The syntax for an internal generic instruction is as follows:

name/arity

name is an identifier starting with a lowercase letter. arity is an integer denoting the number of operands.

About generic instructions in general

Each generic instruction has an opcode. The opcode is an integer, greater than or equal to 1. For an external generic instruction, it must be explicitly given genop.tab, while internal generic instructions are automatically numbered by beam_makeops.

The identity of a generic instruction is its name combined with its arity. That means that it is allowed to define two distinct generic instructions having the same name but with different arities. For example:

move_window/5
move_window/6

Each operand of a generic instruction is tagged with its type. A generic instruction can have one of the following types:

• x - X register.

• y - Y register.

• l - Floating point register number.

• i - Tagged literal integer.

• a - Tagged literal atom.

• n - NIL ([], the empty list).

• q - Literal that don't fit in a word, that is an object stored on the heap such as a list or tuple. Any heap object type is supported, even types that don't have real literals such as external references.

• f - Non-zero failure label.

• p - Zero failure label.

• u - Untagged integer that fits in a machine word. It is used for many different purposes, such as the number of live registers in test_heap/2, as a reference to the export for call_ext/2, and as the flags operand for binary syntax instructions. When the generic instruction is translated to a specific instruction, the type for the operand in the specific operation will tell the loader how to treat the operand.

• o - Overflow. If the value for an u operand does not fit in a machine word, the type of the operand will be changed to o (with no associated value). Currently only used internally in the loader in the guard constraint function binary_too_big().

• v - Arity value. Only used internally in the loader.

Defining specific instructions

The specific instructions are known only to the runtime system and are the instructions that are actually executed. They can be changed at any time without causing compatibility issues.

A specific instruction can have at most 6 operands.

A specific instruction is defined by first giving its name followed by the types for each operand. For example:

move x y

Internally, for example in the generated code and in the output from the BEAM disassembler, the instruction move x y will be called move_xy.

The name for a specific instruction is an identifier starting with a lowercase letter. A type is an lowercase or uppercase letter.

All specific instructions with a given name must have the same number of operands. That is, the following is not allowed:

move x x
move x y x y

Here follows the type letters that more or less directly corresponds to the types for generic instructions.

• x - X register. Will be loaded as a byte offset to the X register relative to the base of X register array. (Can be packed with other operands.)

• y - Y register. Will be loaded as a byte offset to the Y register relative to the stack frame. (Can be packed with other operands.)

• r - X register 0. An implicit operand that will not be stored in the loaded code.

• l - Floating point register number. (Can be packed with other operands.)

• i - Tagged literal integer (a SMALL that will fit in one word).

• a - Tagged atom.

• n - NIL or the empty list. (Will not be stored in the loaded code.)

• q - Tagged CONS or BOXED pointer. That is, a term such as a list or tuple. Any heap object type is supported, even types that don't have real literals such as external references.

• f - Failure label (non-zero). The target for a branch or call instruction.

• p - The 0 failure label, meaning that an exception should be raised if the instruction fails. (Will not be stored in the loaded code.)

• c - Any literal term; that is, immediate literals such as SMALL, and CONS or BOXED pointers to literals. (Can be used where the operand in the generic instruction has one of the types i, a, n, or q.)

The types that follow do a type test of the operand at runtime; thus, they are generally more expensive in terms of runtime than the types described earlier. However, those operand types are needed to avoid a combinatorial explosion in the number of specific instructions and overall code size of process_main().

• s - Tagged source: X register, Y register, or a literal term. The tag will be tested at runtime to retrieve the value from an X register, a Y register, or simply use the value as a tagged Erlang term. (Implementation note: An X register is tagged as a pid, and a Y register as a port. Therefore the literal term must not contain a port or pid.)

• S - Tagged source register (X or Y). The tag will be tested at runtime to retrieve the value from an X register or a Y register. Slighly cheaper than s.

• d - Tagged destination register (X or Y). The tag will be tested at runtime to set up a pointer to the destination register. If the instrution performs a garbarge collection, it must use the $REFRESH_GEN_DEST() macro to refresh the pointer before storing to it (there are more details about that in a later section).

• j - A failure label (combination of f and p). If the branch target 0, an exception will be raised if instruction fails, otherwise control will be transfered to the target address.

The types that follows are all applied to an operand that has the u type.

• t - An untagged integer that will fit in 12 bits (0-4096). It can be packed with other operands in a word. Most often used as the number of live registers in instructions such as test_heap.

• I - An untagged integer that will fit in 32 bits. It can be packed with other operands in a word on a 64-bit system.

• W - Untagged integer or pointer. Not possible to pack with other operands.

• e - Pointer to an export entry. Use by call instructions that call other modules, such as call_ext.

• L - A label. Only used by the label/1 instruction.

• b - Pointer to BIF. Used by instructions that BIFs, such as call_bif.

• A - A tagged arityvalue. Used in instructions that test the arity of a tuple.

• P - A byte offset into a tuple.

• Q - A byte offset into the stack. Used for updating the frame pointer register. Can be packed with other operands.

When the loader translates a generic instruction a specific instruction, it will choose the most specific instruction that will fit the types. Consider the following two instructions:

move c x
move n x

The c operand can encode any literal value, including NIL. The n operand only works for NIL. If we have the generic instruction {move,nil,{x,1}}, the loader will translate it to move_nx 1 because move n x is more specific. move_nx could be slightly faster or smaller (depending on the architecture), because the [] is not stored explicitly as an operand.

Syntactic sugar for specific instructions

It is possible to specify more than one type letter for each operand. Here is an example:

move cxy xy

This is syntactic sugar for:

move c x
move c y
move x x
move x y
move y x
move y y

Note the difference between move c xy and move c d. Note that move c xy is equivalent to the following two definitions:

move c x
move c y

On the other hand, move c d is a single instruction. At runtime, the d operand will be tested to see whether it refers to an X register or a Y register, and a pointer to the register will be set up.

The '?' type modifier

The character ? can be added to the end of an operand to indicate that the operand will not be used every time the instruction is executed. For example:

allocate_heap t I t?
is_eq_exact f? x xy

In allocate_heap, the last operand is the number of live registers. It will only be used if there is not enough heap space and a garbage collection must be performed.

In is_eq_exact, the failure address (the first operand) will only be used if the two register operands are not equal.

Knowing that an operand is not always used can improve how packing is done for some instructions.

For the allocate_heap instruction, without the ? the packing would be done like this:

     +--------------------+--------------------+
I -> |       Stack needed | &&lb_allocate_heap +
     +--------------------+--------------------+
     |        Heap needed | Live registers     +
     +--------------------+--------------------+

"Stack needed" and "Heap needed" are always used, but they are in different words. Thus, at runtime the allocate_heap instruction must read both words from memory even though it will not always use "Live registers".

With the ?, the operands will be packed like this:

     +--------------------+--------------------+
I -> |     Live registers | &&lb_allocate_heap +
     +--------------------+--------------------+
     |        Heap needed |       Stack needed +
     +--------------------+--------------------+

Now "Stack needed" and "Heap needed" are in the same word.

Defining transformation rules

Transformation rules are used to rewrite generic instructions to other generic instructions. The transformations rules are applied repeatedly until no rule match. At that point, the first instruction in the resulting instruction sequence will be converted to a specific instruction and added to the code for the module being loaded. Then the transformation rules for the remaining instructions are run in the same way.

A rule is recognized by its right-pointer arrow: =>. To the left of the arrow is one or more instruction patterns, separated by |. To the right of the arrow is zero or more instructions, separated by |. If the instructions from the BEAM code matches the instruction patterns on the left side, they will be replaced with instructions on the right side (or removed if there are no instructions on the right).

Defining instruction patterns

We will start looking at the patterns on the left side of the arrow.

A pattern for an instruction consists of its name, followed by a pattern for each of its operands. The operand patterns are separated by spaces.

The simplest possible pattern is a variable. Just like in Erlang, a variable must begin with an uppercase letter. If the same variable is used in multiple operands, the pattern will only match if the operands are equal. For example:

move Same Same =>

This pattern will match if the operands for move are the same. If the pattern match, the instruction will be removed. (That used to be an actual rule a long time ago when the compiler would occasionally produce instructions such as {move,{x,2},{x,2}}.)

Variables that have been bound on the left side can be used on the right side. For example, this rule will rewrite all move instructions to assign instructions with the operands swapped:

move Src Dst => assign Dst Src

If we only want to match operands of a certain type, we can use a type constraint. A type constraint consists of one or more lowercase letters, each specifying a type. For example:

is_integer Fail an => jump Fail

The second operand pattern, an, will match if the second operand is either an atom or NIL (the empty list). In case of a match, the is_integer/2 instruction will be replaced with a jump/1 instruction.

An operand pattern can bind a variable and constrain the type at the same time by following the variable with a = and the constraint. For example:

is_eq_exact Fail=f R=xy C=q => i_is_eq_exact_literal Fail R C

Here the is_eq_exact instruction is replaced with a specialized instruction that only compares literals, but only if the first operand is a register and the second operand is a literal.

Further constraining patterns

In addition to specifying a type letter, the actual value for the type can be specified. For example:

move C=c x==1 => move_x1 C

Here the second operand of move is constrained to be X register 1.

When specifying an atom constraint, the atom is written as it would be in the C source code. That is, it needs an am_ prefix, and it must be listed in atom.names. For example:

is_boolean Fail=f a==am_true =>
is_boolean Fail=f a==am_false =>

There are several constraints available for testing whether a call is to a BIF or a function.

The constraint u$is_bif will test whether the given operand refers to a BIF. For example:

call_ext u Bif=u$is_bif => call_bif Bif
call_ext u Func         => i_call_ext Func

The call_ext instruction can be used to call functions written in Erlang as well as BIFs (or more properly called SNIFs). The u$is_bif constraint will match if the operand refers to a BIF (that is, if it is listed in the file bif.tab). Note that u$is_bif should only be applied to operands that are known to contain an index to the import table chunk in the BEAM file (such operands have the type b or e in the corresponding specific instruction). If applied to other u operands, it will at best return a nonsense result.

The u$is_not_bif constraint matches if the operand does not refer to a BIF (not listed in bif.tab). For example:

move S X0=x==0 | line Loc | call_ext_last Ar Func=u$is_not_bif D => \
     move S X0 | call_ext_last Ar Func D

The u$bif:Module:Name/Arity constraint tests whether the given operand refers to a specific BIF. Note that Module:Name/Arity must be an existing BIF defined in bif.tab, or there will be a compilation error. It is useful when a call to a specific BIF should be replaced with an instruction as in this example:

gc_bif2 Fail Live u$bif:erlang:splus/2 S1 S2 Dst => \
     gen_plus Fail Live S1 S2 Dst

Here the call to the GC BIF '+'/2 will be replaced with the instruction gen_plus/5. Note that the same name as used in the C source code must be used for the BIF, which in this case is splus. It is defined like this in bit.tab:

ubif erlang:'+'/2 splus_2

The u$func:Module:Name/Arity will test whether the given operand is a a specific function. Here is an example:

bif1 Fail u$func:erlang:is_constant/1 Src Dst => too_old_compiler

is_constant/1 used to be a BIF a long time ago. The transformation replaces the call with the too_old_compiler instruction which will produce a nicer error message than the default error would be for a missing guard BIF.

Type constraints allowed in patterns

Here are all type letters that are allowed on the left side of a transformation rule.

• u - An untagged integer that fits in a machine word.

• x - X register.

• y - Y register.

• l - Floating point register number.

• i - Tagged literal integer.

• a - Tagged literal atom.

• n - NIL ([], the empty list).

• q - Literals that don't fit in a word, such as list or tuples.

• f - Non-zero failure label.

• p - The zero failure label.

• j - Any label. Equivalent to fp.

• c - Any literal term. Equivalent to ainq.

• s - X register, Y register, or any literal term. Equivalent to xyc.

• d - X or Y register. Equivalent to xy. (In a pattern d will match both source and destination registers. As an operand in a specific instruction, it must only be used for a destination register.)

• o - Overflow. An untagged integer that does not fit in a machine word.

Guard constraints

If the constraints described so far is not enough, additional constraints can be written in C in beam_load.c and be called as a guard function on the left side of the transformation. If the guard function returns a non-zero value, the matching of the rule will continue, otherwise the match will fail. For example:

ensure_map Lit=q | literal_is_map(Lit) =>

The guard test literal_is_map/1 tests whether the given literal is a map. If the literal is a map, the instruction is unnecessary and can be removed.

It is outside the scope for this document to describe in detail how such guard functions are written, but for the curious here is the implementation of literal_is_map():

static int
literal_is_map(LoaderState* stp, GenOpArg Lit)
{
    Eterm term;

    ASSERT(Lit.type == TAG_q);
    term = stp->literals[Lit.val].term;
    return is_map(term);
}

Handling instruction with variable number of operands

Some instructions, such as select_val/3, essentially has a variable number of operands. Such instructions have a {list,[...]} operand as their last operand in the BEAM assembly code. For example:

{select_val,{x,0},
            {f,1},
            {list,[{atom,b},{f,4},{atom,a},{f,5}]}}.

The loader will convert a {list,[...]} operand to an u operand whose value is the number of elements in the list, followed by each element in the list. The instruction above would be translated to the following generic instruction:

{select_val,{x,0},{f,1},{u,4},{atom,b},{f,4},{atom,a},{f,5}}

To match a variable number of arguments we need to use the special operand type * like this:

select_val Src=aiq Fail=f Size=u List=* => \
    i_const_select_val Src Fail Size List

This transformation renames a select_val/3 instruction with a constant source operand to i_const_select_val/3.

Constructing new instructions on the right side

The most common operand on the right side is a variable that was bound while matching the left side. For example:

trim N Remaining => i_trim N

An operand can also be a type letter to construct an operand of that type. Each type has a default value. For example, the type x has the default value 1023, which is the highest X register. That makes x on the right side a convenient shortcut for a temporary X register. For example:

is_number Fail Literal=q => move Literal x | is_number Fail x

If the second operand for is_number/2 is a literal, it will be moved to X register 1023. Then is_number/2 will test whether the value stored in X register 1023 is a number.

This kind of transformation is useful when it is rare that an operand can be anything else but a register. In the case of is_number/2, the second operand is always a register unless the compiler optimizations have been disabled.

If the default value is not suitable, the type letter can be followed by = and a value. Most types take an integer value. The value for an atom is written the same way as in the C source code. For example, the atom false is written as am_false. The atom must be listed in atom.names.

Here is an example showing how values can be specified:

bs_put_utf32 Fail=j Flags=u Src=s => \
    i_bs_validate_unicode Fail Src | \
    bs_put_integer Fail i=32 u=1 Flags Src

Type letters on the right side

Here follows all types that are allowed to be used in operands for instructions being constructed on the right side of a transformation rule.

• u - Construct an untagged integer. The default value is 0.

• x - X register. The default value is 1023. That makes x convenient to use as a temporary X register.

• y - Y register. The default value is 0.

• l - Foating point register number. The default value is 0.

• i - Tagged literal integer. The default value is 0.

• a - Tagged atom. The default value is the empty atom (am_Empty).

• n - NIL ([], the empty list).

Function call on the right side

Transformations that are not possible to describe with the rule language as described here can be written as a C function in beam_load.c and called from the right side of a transformation. The left side of the transformation will perform the match and bind operands to variables. The variables can then be passed to a generator function on the right side. For example:

bif2 Fail=j u$bif:erlang:element/2 Index=s Tuple=xy Dst=d => \
    gen_element(Jump, Index, Tuple, Dst)

This transformation rule matches a call to the BIF element/2. The operands will be captured and the function gen_element() will be called.

gen_element() will produce one of two instructions depending on Index. If Index is an integer in the range from 1 up to the maximum tuple size, the instruction i_fast_element/2 will be produced, otherwise the instruction i_element/4 will be produced. The corresponding specific instructions are:

i_fast_element xy j? I d
i_element xy j? s d

The i_fast_element/2 instruction is faster because the tuple is already an untagged integer. It also knows that the index is at least 1, so it does not have to test for that. The i_element/4 instruction will have to fetch the index from a register, test that it is an integer, and untag the integer.

It is outside the scope of this document to describe in detail how generator functions are written, but for the curious, here is the implementation of gen_element():

static GenOp*
gen_element(LoaderState* stp, GenOpArg Fail,
   GenOpArg Index, GenOpArg Tuple, GenOpArg Dst)
{
    GenOp* op;

    NEW_GENOP(stp, op);
    op->arity = 4;
    op->next = NULL;

    if (Index.type == TAG_i && Index.val > 0 &&
       Index.val <= ERTS_MAX_TUPLE_SIZE &&
       (Tuple.type == TAG_x || Tuple.type == TAG_y)) {
        op->op = genop_i_fast_element_4;
        op->a[0] = Tuple;
        op->a[1] = Fail;
        op->a[2].type = TAG_u;
        op->a[2].val = Index.val;
        op->a[3] = Dst;
    } else {
        op->op = genop_i_element_4;
        op->a[0] = Tuple;
        op->a[1] = Fail;
        op->a[2] = Index;
        op->a[3] = Dst;
    }

    return op;
}

Defining the implementation

The actual implementation of instructions are also defined in .tab files processed by beam_makeops. For practical reasons, instruction definitions are stored in several files, at the time of writing in the following files:

bif_instrs.tab
arith_instrs.tab
bs_instrs.tab
float_instrs.tab
instrs.tab
map_instrs.tab
msg_instrs.tab
select_instrs.tab
trace_instrs.tab

There is also a file that only contains macro definitions:

macros.tab

The syntax of each file is similar to C code. In fact, most of the contents is C code, interspersed with macro invocations.

To allow Emacs to auto-indent the code, each file starts with the following line:

// -*- c -*-

To avoid messing up the indentation, all comments are written as C++ style comments (//) instead of #. Note that a comment must start at the beginning of a line.

The meat of an instruction definition file are macro definitions. We have seen this macro definition before:

move(Src, Dst) {
    $Dst = $Src;
}

A macro definitions must start at the beginning of the line (no spaces allowed), the opening curly bracket must be on the same line, and the finishing curly bracket must be at the beginning of a line. It is recommended that the macro body is properly indented.

As a convention, the macro arguments in the head all start with an uppercase letter. In the body, the macro arguments can be expanded by preceding them with $.

A macro definition whose name and arity matches a family of specific instructions is assumed to be the implementation of that instruction.

A macro can also be invoked from within another macro. For example, move_deallocate_return/2 avoids repeating code by invoking $deallocate_return() as a macro:

move_deallocate_return(Src, Deallocate) {
    x(0) = $Src;
    $deallocate_return($Deallocate);
}

Here is the definition of deallocate_return/1:

deallocate_return(Deallocate) {
    //| -no_next
    int words_to_pop = $Deallocate;
    SET_I((BeamInstr *) cp_val(*E));
    E = ADD_BYTE_OFFSET(E, words_to_pop);
    CHECK_TERM(x(0));
    DispatchReturn;
}

The expanded code for move_deallocate_return will look this:

OpCase(move_deallocate_return_cQ):
{
  x(0) = I[1];
  do {
    int words_to_pop = Qb(BeamExtraData(I[0]));
    SET_I((BeamInstr *) cp_val(*E));
    E = ADD_BYTE_OFFSET(E, words_to_pop);
    CHECK_TERM(x(0));
    DispatchReturn;
  } while (0);
}

When expanding macros, beam_makeops wraps the expansion in a do/while wrapper unless beam_makeops can clearly see that no wrapper is needed. In this case, the wrapper is needed.

Note that arguments for macros cannot be complex expressions, because the arguments are split on ,. For example, the following would not work because beam_makeops would split the expression into two arguments:

$deallocate_return(get_deallocation(y, $Deallocate));

Code generation directives

Within macro definitions, // comments are in general not treated specially. They will be copied to the file with the generated code along with the rest of code in the body.

However, there is an exception. Within a macro definition, a line that starts with whitespace followed by //| is treated specially. The rest of the line is assumed to contain directives to control code generation.

Currently, two code generation directives are recognized:

• -no_prefetch
• -no_next

The -no_prefetch directive

To see what -no_prefetch does, let's first look at the default code generation. Here is the code generated for move_cx:

OpCase(move_cx):
{
  BeamInstr next_pf = BeamCodeAddr(I[2]);
  xb(BeamExtraData(I[0])) = I[1];
  I += 2;
  ASSERT(VALID_INSTR(next_pf));
  GotoPF(next_pf);
}

Note that the very first thing done is to fetch the address to the next instruction. The reason is that it usually improves performance.

Just as a demonstration, we can add a -no_prefetch directive to the move/2 instruction:

move(Src, Dst) {
    //| -no_prefetch
    $Dst = $Src;
}

We can see that the prefetch is no longer done:

OpCase(move_cx):
{
  xb(BeamExtraData(I[0])) = I[1];
  I += 2;
  ASSERT(VALID_INSTR(*I));
  Goto(*I);
}

When would we want to turn off the prefetch in practice?

In instructions that will not always execute the next instruction. For example:

is_atom(Fail, Src) {
    if (is_not_atom($Src)) {
        $FAIL($Fail);
    }
}

// From macros.tab
FAIL(Fail) {
    //| -no_prefetch
    $SET_I_REL($Fail);
    Goto(*I);
}

is_atom/2 may either execute the next instruction (if the second operand is an atom) or branch to the failure label.

The generated code looks like this:

OpCase(is_atom_fx):
{
  if (is_not_atom(xb(I[1]))) {
    ASSERT(VALID_INSTR(*(I + (fb(BeamExtraData(I[0]))) + 0)));
    I += fb(BeamExtraData(I[0])) + 0;;
    Goto(*I);;
  }
  I += 2;
  ASSERT(VALID_INSTR(*I));
  Goto(*I);
}

The -no_next directive

Next we will look at when the -no_next directive can be used. Here is the jump/1 instruction:

jump(Fail) {
    $JUMP($Fail);
}

// From macros.tab
JUMP(Fail) {
    //| -no_next
    $SET_I_REL($Fail);
    Goto(*I);
}

The generated code looks like this:

OpCase(jump_f):
{
  ASSERT(VALID_INSTR(*(I + (fb(BeamExtraData(I[0]))) + 0)));
  I += fb(BeamExtraData(I[0])) + 0;;
  Goto(*I);;
}

If we remove the -no_next directive, the code would look like this:

OpCase(jump_f):
{
  BeamInstr next_pf = BeamCodeAddr(I[1]);
  ASSERT(VALID_INSTR(*(I + (fb(BeamExtraData(I[0]))) + 0)));
  I += fb(BeamExtraData(I[0])) + 0;;
  Goto(*I);;
  I += 1;
  ASSERT(VALID_INSTR(next_pf));
  GotoPF(next_pf);
}

In the end, the C compiler will probably optimize this code to the same native code as the first version, but the first version is certainly much easier to read for human readers.

Macros in the macros.tab file

The file macros.tab contains many useful macros. When implementing new instructions it is good practice to look through macros.tab to see if any of existing macros can be used rather than re-inventing the wheel.

We will describe a few of the most useful macros here.

The GC_REGEXP definition

The following line defines a regular expression that will recognize a call to a function that does a garbage collection:

GC_REGEXP=erts_garbage_collect|erts_gc|GcBifFunction;

The purpose is that beam_makeops can verify that an instruction that does a garbage collection and has an d operand uses the $REFRESH_GEN_DEST() macro.

If you need to define a new function that does garbage collection, you should give it the prefix erts_gc_. If that is not possible you should update the regular expression so that it will match your new function.

FAIL(Fail)

Branch to $Fail. Will suppress prefetch (-no_prefetch). Typical use:

is_nonempty_list(Fail, Src) {
    if (is_not_list($Src)) {
        $FAIL($Fail);
    }
}

JUMP(Fail)

Branch to $Fail. Suppresses generation of dispatch of the next instruction (-no_next). Typical use:

jump(Fail) {
    $JUMP($Fail);
}

GC_TEST(NeedStack, NeedHeap, Live)

$GC_TEST(NeedStack, NeedHeap, Live) tests that given amount of stack space and heap space is available. If not it will do a garbage collection. Typical use:

test_heap(Nh, Live) {
    $GC_TEST(0, $Nh, $Live);
}

AH(NeedStack, NeedHeap, Live)

AH(NeedStack, NeedHeap, Live) allocates a stack frame and optionally additional heap space.

Pre-defined macros and variables

beam_makeops defines several built-in macros and pre-bound variables.

The NEXT_INSTRUCTION pre-bound variable

The NEXT_INSTRUCTION is a pre-bound variable that is available in all instructions. It expands to the address of the next instruction.

Here is an example:

i_call(CallDest) {
    SET_CP(c_p, $NEXT_INSTRUCTION);
    $DISPATCH_REL($CallDest);
}

When calling a function, the return address is first stored in c_p->cp (using the SET_CP() macro defined in beam_emu.c), and then control is transferred to the callee. Here is the generated code:

OpCase(i_call_f):
{
  SET_CP(c_p, I+1);
  ASSERT(VALID_INSTR(*(I + (fb(BeamExtraData(I[0]))) + 0)));
  I += fb(BeamExtraData(I[0])) + 0;;
  DTRACE_LOCAL_CALL(c_p, erts_code_to_codemfa(I));
  Dispatch();;
}

We can see that that $NEXT_INSTRUCTION has been expanded to I+1. That makes sense since the size of the i_call_f/1 instruction is one word.

The IP_ADJUSTMENT pre-bound variable

$IP_ADJUSTMENT is usually 0. In a few combined instructions (described below) it can be non-zero. It is used like this in macros.tab:

SET_I_REL(Offset) {
    ASSERT(VALID_INSTR(*(I + ($Offset) + $IP_ADJUSTMENT)));
    I += $Offset + $IP_ADJUSTMENT;
}

Avoid using IP_ADJUSTMENT directly. Use SET_I_REL() or one of the macros that invoke such as FAIL() or JUMP() defined in macros.tab.

Pre-defined macro functions

The IF() macro

$IF(Expr, IfTrue, IfFalse) evaluates Expr, which must be a valid Perl expression (which for simple numeric expressions have the same syntax as C). If Expr evaluates to 0, the entire IF() expression will be replaced with IfFalse, otherwise it will be replaced with IfTrue.

See the description of OPERAND_POSITION() for an example.

The OPERAND_POSITION() macro

$OPERAND_POSITION(Expr) returns the position for Expr, if Expr is an operand that is not packed. The first operand is at position 1.

Returns 0 otherwise.

This macro could be used like this in order to share code:

FAIL(Fail) {
    //| -no_prefetch
    $IF($OPERAND_POSITION($Fail) == 1 && $IP_ADJUSTMENT == 0,
        goto common_jump,
        $DO_JUMP($Fail));
}

DO_JUMP(Fail) {
    $SET_I_REL($Fail);
    Goto(*I));
}

// In beam_emu.c:
common_jump:
   I += I[1];
   Goto(*I));

The $REFRESH_GEN_DEST() macro

When a specific instruction has a d operand, early during execution of the instruction, a pointer will be initialized to point to the X or Y register in question.

If there is a garbage collection before the result is stored, the stack will move and if the d operand refered to a Y register, the pointer will no longer be valid. (Y registers are stored on the stack.)

In those circumstances, $REFRESH_GEN_DEST() must be invoked to set up the pointer again. beam_makeops will notice if there is a call to a function that does a garbage collection and $REFRESH_GEN_DEST() is not called.

Here is a complete example. The new_map instruction is defined like this:

new_map d t I

It is implemented like this:

new_map(Dst, Live, N) {
    Eterm res;

    HEAVY_SWAPOUT;
    res = erts_gc_new_map(c_p, reg, $Live, $N, $NEXT_INSTRUCTION);
    HEAVY_SWAPIN;
    $REFRESH_GEN_DEST();
    $Dst = res;
    $NEXT($NEXT_INSTRUCTION+$N);
}

If we have forgotten the $REFRESH_GEN_DEST() there would be a message similar to this:

pointer to destination register is invalid after GC -- use $REFRESH_GEN_DEST()
... from the body of new_map at beam/map_instrs.tab(30)

Combined instructions

Problem: For frequently executed instructions we want to use "fast" operands types such as x and y, as opposed to s or S. To avoid an explosion in code size, we want to share most of the implementation between the instructions. Here are the specific instructions for i_increment/5:

i_increment r W t d
i_increment x W t d
i_increment y W t d

The i_increment instruction is implemented like this:

i_increment(Source, IncrementVal, Live, Dst) {
    Eterm increment_reg_source = $Source;
    Eterm increment_val = $IncrementVal;
    Uint live;
    Eterm result;

    if (ERTS_LIKELY(is_small(increment_reg_val))) {
        Sint i = signed_val(increment_reg_val) + increment_val;
        if (ERTS_LIKELY(IS_SSMALL(i))) {
            $Dst = make_small(i);
            $NEXT0();
        }
    }
    live = $Live;
    HEAVY_SWAPOUT;
    reg[live] = increment_reg_val;
    reg[live+1] = make_small(increment_val);
    result = erts_gc_mixed_plus(c_p, reg, live);
    HEAVY_SWAPIN;
    ERTS_HOLE_CHECK(c_p);
    if (ERTS_LIKELY(is_value(result))) {
        $REFRESH_GEN_DEST();
        $Dst = result;
        $NEXT0();
    }
    ASSERT(c_p->freason != BADMATCH || is_value(c_p->fvalue));
    goto find_func_info;
}

There will be three almost identical copies of the code. Given the size of the code, that could be too high cost to pay.

To avoid the three copies of the code, we could use only one specific instruction:

i_increment S W t d

(The same implementation as above will work.)

That reduces the code size, but is slower because S means that there will be extra code to test whether the operand refers to an X register or a Y register.

Solution: We can use "combined instructions". Combined instructions are combined from instruction fragments. The bulk of the code can be shared.

Here we will show how i_increment can be implemented as a combined instruction. We will show each individual fragment first, and then show how to connect them together. First we will need a variable that we can store the value fetched from the register in:

increment.head() {
    Eterm increment_reg_val;
}

The name increment is the name of the group that the fragment belongs to. Note that it does not need to have the same name as the instruction. The group name is followed by . and the name of the fragment. The name head is pre-defined. The code in it will be placed at the beginning of a block, so that all fragments in the group can access it.

Next we define the fragment that will pick up the value from the register from the first operand:

increment.fetch(Src) {
    increment_reg_val = $Src;
}

We call this fragment fetch. This fragment will be duplicated three times, one for each value of the first operand (r, x, and y).

Next we define the main part of the code that do the actual incrementing.

increment.execute(IncrementVal, Live, Dst) {
    Eterm increment_val = $IncrementVal;
    Uint live;
    Eterm result;

    if (ERTS_LIKELY(is_small(increment_reg_val))) {
        Sint i = signed_val(increment_reg_val) + increment_val;
        if (ERTS_LIKELY(IS_SSMALL(i))) {
            $Dst = make_small(i);
            $NEXT0();
        }
    }
    live = $Live;
    HEAVY_SWAPOUT;
    reg[live] = increment_reg_val;
    reg[live+1] = make_small(increment_val);
    result = erts_gc_mixed_plus(c_p, reg, live);
    HEAVY_SWAPIN;
    ERTS_HOLE_CHECK(c_p);
    if (ERTS_LIKELY(is_value(result))) {
        $REFRESH_GEN_DEST();
        $Dst = result;
        $NEXT0();
    }
    ASSERT(c_p->freason != BADMATCH || is_value(c_p->fvalue));
    goto find_func_info;
}

We call this fragment execute. It will handle the three remaining operands (W t d). There will only be one copy of this fragment.

Now that we have defined the fragments, we need to inform beam_makeops how they should be connected:

i_increment := increment.fetch.execute;

To the left of the := is the name of the specific instruction that should be implemented by the fragments, in this case i_increment. To the right of := is the name of the group with the fragments, followed by a .. Then the name of the fragments in the group are listed in the order they should be executed. Note that the head fragment is not listed.

The line ends in ; (to avoid messing up the indentation in Emacs).

(Note that in practice the := line is usually placed before the fragments.)

The generated code looks like this:

{
  Eterm increment_reg_val;
  OpCase(i_increment_rWtd):
  {
    increment_reg_val = r(0);
  }
  goto increment__execute;

  OpCase(i_increment_xWtd):
  {
    increment_reg_val = xb(BeamExtraData(I[0]));
  }
  goto increment__execute;

  OpCase(i_increment_yWtd):
  {
    increment_reg_val = yb(BeamExtraData(I[0]));
  }
  goto increment__execute;

  increment__execute:
  {
    // Here follows the code from increment.execute()
    .
    .
    .
}

Some notes about combined instructions

The operands that are different must be at the beginning of the instruction. All operands in the last fragment must have the same operands in all variants of the specific instruction.

As an example, the following specific instructions cannot be implemented as a combined instruction:

i_times j? t x x d
i_times j? t x y d
i_times j? t s s d

We would have to change the order of the operands so that the two operands that are different are placed first:

i_times x x j? t d
i_times x y j? t d
i_times s s j? t d

We can then define:

i_times := times.fetch.execute;

times.head {
    Eterm op1, op2;
}

times.fetch(Src1, Src2) {
    op1 = $Src1;
    op2 = $Src2;
}

times.execute(Fail, Live, Dst) {
    // Multiply op1 and op2.
    .
    .
    .
}

Several instructions can share a group. As an example, the following instructions have different names, but in the end they all create a binary. The last two operands are common for all of them:

i_bs_init_fail       xy j? t? x
i_bs_init_fail_heap s I j? t? x
i_bs_init                W t? x
i_bs_init_heap         W I t? x

The instructions are defined like this (formatted with extra spaces for clarity):

i_bs_init_fail_heap := bs_init . fail_heap . verify . execute;
i_bs_init_fail      := bs_init . fail      . verify . execute;
i_bs_init           := bs_init .           .  plain . execute;
i_bs_init_heap      := bs_init .               heap . execute;

Note that the first two instruction have three fragments, while the other two only have two fragments. Here are the fragments:

bs_init_bits.head() {
    Eterm num_bits_term;
    Uint num_bits;
    Uint alloc;
}

bs_init_bits.plain(NumBits) {
    num_bits = $NumBits;
    alloc = 0;
}

bs_init_bits.heap(NumBits, Alloc) {
    num_bits = $NumBits;
    alloc = $Alloc;
}

bs_init_bits.fail(NumBitsTerm) {
    num_bits_term = $NumBitsTerm;
    alloc = 0;
}

bs_init_bits.fail_heap(NumBitsTerm, Alloc) {
    num_bits_term = $NumBitsTerm;
    alloc = $Alloc;
}

bs_init_bits.verify(Fail) {
    // Verify the num_bits_term, fail using $FAIL
    // if there is a problem.
.
.
.
}

bs_init_bits.execute(Live, Dst) {
   // Long complicated code to a create a binary.
   .
   .
   .
}

The full definitions of those instructions can be found in bs_instrs.tab. The generated code can be found in beam_warm.h.