# Chapter 21 Optimisation with Flambda

- 21.1 Overview
- 21.2 Command-line flags
- 21.3 Inlining
- 21.4 Specialisation
- 21.5 Default settings of parameters
- 21.6 Manual control of inlining and specialisation
- 21.7 Simplification
- 21.8 Other code motion transformations
- 21.9 Unboxing transformations
- 21.10 Removal of unused code and values
- 21.11 Other code transformations
- 21.12 Treatment of effects
- 21.13 Compilation of statically-allocated modules
- 21.14 Inhibition of optimisation
- 21.15 Use of unsafe operations
- 21.16 Glossary

## ﻿21.1 Overview

Flambda is the term used to describe a series of optimisation passes provided by the native code compilers as of OCaml 4.03.

Flambda aims to make it easier to write idiomatic OCaml code without incurring performance penalties.

To use the Flambda optimisers it is necessary to pass the -flambda option to the OCaml configure script. (There is no support for a single compiler that can operate in both Flambda and non-Flambda modes.) Code compiled with Flambda cannot be linked into the same program as code compiled without Flambda. Attempting to do this will result in a compiler error.

Whether or not a particular ocamlopt uses Flambda may be determined by invoking it with the -config option and looking for any line starting with “flambda:”. If such a line is present and says “true”, then Flambda is supported, otherwise it is not.

Flambda provides full optimisation across different compilation units, so long as the .cmx files for the dependencies of the unit currently being compiled are available. (A compilation unit corresponds to a single .ml source file.) However it does not yet act entirely as a whole-program compiler: for example, elimination of dead code across a complete set of compilation units is not supported.

Optimisation with Flambda is not currently supported when generating bytecode.

Flambda should not in general affect the semantics of existing programs. Two exceptions to this rule are: possible elimination of pure code that is being benchmarked (see section 21.14) and changes in behaviour of code using unsafe operations (see section 21.15).

Flambda does not yet optimise array or string bounds checks. Neither does it take hints for optimisation from any assertions written by the user in the code.

Consult the Glossary at the end of this chapter for definitions of technical terms used below.

## ﻿21.2 Command-line flags

The Flambda optimisers provide a variety of command-line flags that may be used to control their behaviour. Detailed descriptions of each flag are given in the referenced sections. Those sections also describe any arguments which the particular flags take.

Commonly-used options:

-O2
  Perform more optimisation than usual. Compilation times may be lengthened. (This flag is an abbreviation for a certain set of parameters described in section 21.5.)
-O3
  Perform even more optimisation than usual, possibly including unrolling of recursive functions. Compilation times may be significantly lengthened.
-Oclassic
  Make inlining decisions at the point of definition of a function rather than at the call site(s). This mirrors the behaviour of OCaml compilers not using Flambda. Compared to compilation using the new Flambda inlining heuristics (for example at -O2) it produces smaller .cmx files, shorter compilation times and code that probably runs rather slower. When using -Oclassic, only the following options described in this section are relevant: -inlining-report and -inline. If any other of the options described in this section are used, the behaviour is undefined and may cause an error in future versions of the compiler.
-inlining-report
  Emit .inlining files (one per round of optimisation) showing all of the inliner’s decisions.

Less commonly-used options:

-remove-unused-arguments
  Remove unused function arguments even when the argument is not specialised. This may have a small performance penalty. See section 21.10.3.
-unbox-closures
  Pass free variables via specialised arguments rather than closures (an optimisation for reducing allocation). See section 21.9.3. This may have a small performance penalty.

Advanced options, only needed for detailed tuning:

-inline
  The behaviour depends on whether -Oclassic is used.
  - When not in -Oclassic mode, -inline limits the total size of functions considered for inlining during any speculative inlining search. (See section 21.3.6.) Note that this parameter does not control the assessment as to whether any particular function may be inlined. Raising it to excessive amounts will not necessarily cause more functions to be inlined.
  - When in -Oclassic mode, -inline behaves as in previous versions of the compiler: it is the maximum size of function to be considered for inlining. See section 21.3.1.
-inline-toplevel
  The equivalent of -inline but used when speculative inlining starts at toplevel. See section 21.3.6. Not used in -Oclassic mode.
-inline-branch-factor
  Controls how the inliner assesses whether a code path is likely to be hot or cold. See section 21.3.5.
-inline-alloc-cost, -inline-branch-cost, -inline-call-cost
  Controls how the inliner assesses the runtime performance penalties associated with various operations. See section 21.3.5.
-inline-indirect-cost, -inline-prim-cost
  Likewise.
-inline-lifting-benefit
  Controls inlining of functors at toplevel. See section 21.3.5.
-inline-max-depth
  The maximum depth of any speculative inlining search. See section 21.3.6.
-inline-max-unroll
  The maximum depth of any unrolling of recursive functions during any speculative inlining search. See section 21.3.6.
-no-unbox-free-vars-of-closures
  Do not unbox closure variables. See section 21.9.1.
-no-unbox-specialised-args
  Do not unbox arguments to which functions have been specialised. See section 21.9.2.
-rounds
  How many rounds of optimisation to perform. See section 21.2.1.
-unbox-closures-factor
  Scaling factor for benefit calculation when using -unbox-closures. See section 21.9.3.

##### ﻿Notes

- The set of command line flags relating to optimisation should typically be specified to be the same across an entire project. Flambda does not currently record the requested flags in the .cmx files. As such, inlining of functions from previously-compiled units will subject their code to the optimisation parameters of the unit currently being compiled, rather than those specified when they were previously compiled. It is hoped to rectify this deficiency in the future.
- Flambda-specific flags do not affect linking with the exception of affecting the optimisation of code in the startup file (containing generated functions such as currying helpers). Typically such optimisation will not be significant, so eliding such flags at link time might be reasonable.
- Flambda-specific flags are silently accepted even when the -flambda option was not provided to the configure script. (There is no means provided to change this behaviour.) This is intended to make it more straightforward to run benchmarks with and without the Flambda optimisers in effect.
- Some of the Flambda flags may be subject to change in future releases.

### ﻿21.2.1 Specification of optimisation parameters by round

Flambda operates in rounds: one round consists of a certain sequence of transformations that may then be repeated in order to achieve more satisfactory results. The number of rounds can be set manually using the -rounds parameter (although this is not necessary when using predefined optimisation levels such as with -O2 and -O3). For high optimisation the number of rounds might be set at 3 or 4.

Command-line flags that may apply per round, for example those with -cost in the name, accept arguments of the form:

n | round=n[,...]

- If the first form is used, with a single integer specified, the value will apply to all rounds.
- If the second form is used, zero-based round integers specify values which are to be used only for those rounds.

The flags -Oclassic, -O2 and -O3 are applied before all other flags, meaning that certain parameters may be overridden without having to specify every parameter usually invoked by the given optimisation level.

## ﻿21.3 Inlining

Inlining refers to the copying of the code of a function to a place where the function is called. The code of the function will be surrounded by bindings of its parameters to the corresponding arguments.

The aims of inlining are:

- to reduce the runtime overhead caused by function calls (including setting up for such calls and returning afterwards);
- to reduce instruction cache misses by expressing frequently-taken paths through the program using fewer machine instructions; and
- to reduce the amount of allocation (especially of closures).

These goals are often reached not just by inlining itself but also by other optimisations that the compiler is able to perform as a result of inlining.

When a recursive call to a function (within the definition of that function or another in the same mutually-recursive group) is inlined, the procedure is also known as unrolling. This is somewhat akin to loop peeling. For example, given the following code:

    let rec fact x =
      if x = 0 then
        1
      else
        x * fact (x - 1)

    let n = fact 4

unrolling once at the call site fact 4 produces (with the body of fact unchanged):

    let n =
      if 4 = 0 then
        1
      else
        4 * fact (4 - 1)

This simplifies to:

    let n = 4 * fact 3

Flambda provides significantly enhanced inlining capabilities relative to previous versions of the compiler.

#### ﻿Aside: when inlining is performed

Inlining is performed together with all of the other Flambda optimisation passes, that is to say, after closure conversion. This has three particular advantages over a potentially more straightforward implementation prior to closure conversion:

- It permits higher-order inlining, for example when a non-inlinable function always returns the same function yet with different environments of definition. Not all such cases are supported yet, but it is intended that such support will be improved in future.
- It is easier to integrate with cross-module optimisation, since imported information about other modules is already in the correct intermediate language.
- It becomes more straightforward to optimise closure allocations since the layout of closures does not have to be estimated in any way: it is known. Similarly, it becomes more straightforward to control which variables end up in which closures, helping to avoid closure bloat.

### ﻿21.3.1 Classic inlining heuristic

In -Oclassic mode the behaviour of the Flambda inliner mimics previous versions of the compiler. (Code may still be subject to further optimisations not performed by previous versions of the compiler: functors may be inlined, constants are lifted and unused code is eliminated all as described elsewhere in this chapter. See sections 21.3.3, 21.8.1 and 21.10. At the definition site of a function, the body of the function is measured. It will then be marked as eligible for inlining (and hence inlined at every direct call site) if:

- the measured size (in unspecified units) is smaller than that of a function call plus the argument of the -inline command-line flag; and
- the function is not recursive.

Non-Flambda versions of the compiler cannot inline functions that contain a definition of another function. However -Oclassic does permit this. Further, non-Flambda versions also cannot inline functions that are only themselves exposed as a result of a previous pass of inlining, but again this is permitted by -Oclassic. For example:

    module M : sig
      val i : int
    end = struct
      let f x =
        let g y = x + y in
        g
      let h = f 3
      let i = h 4  (* h is correctly discovered to be g and inlined *)
    end

All of this contrasts with the normal Flambda mode, that is to say without -Oclassic, where:

- the inlining decision is made at the call site; and
- recursive functions can be handled, by specialisation (see below).

The Flambda mode is described in the next section.

### ﻿21.3.2 Overview of “Flambda” inlining heuristics

The Flambda inlining heuristics, used whenever the compiler is configured for Flambda and -Oclassic was not specified, make inlining decisions at call sites. This helps in situations where the context is important. For example:

    let f b x =
      if b then
        x
      else
        ... big expression ...

    let g x = f true x

In this case, we would like to inline f into g, because a conditional jump can be eliminated and the code size should reduce. If the inlining decision has been made after the declaration of f without seeing the use, its size would have probably made it ineligible for inlining; but at the call site, its final size can be known. Further, this function should probably not be inlined systematically: if b is unknown, or indeed false, there is little benefit to trade off against a large increase in code size. In the existing non-Flambda inliner this isn’t a great problem because chains of inlining were cut off fairly quickly. However it has led to excessive use of overly-large inlining parameters such as -inline 10000.

In more detail, at each call site the following procedure is followed:

- Determine whether it is clear that inlining would be beneficial without, for the moment, doing any inlining within the function itself. (The exact assessment of benefit is described below.) If so, the function is inlined.
- If inlining the function is not clearly beneficial, then inlining will be performed speculatively inside the function itself. The search for speculative inlining possibilities is controlled by two parameters: the inlining threshold and the inlining depth. (These are described in more detail below.)
  - If such speculation shows that performing some inlining inside the function would be beneficial, then such inlining is performed and the resulting function inlined at the original call site.
  - Otherwise, nothing happens.

Inlining within recursive functions of calls to other functions in the same mutually-recursive group is kept in check by an unrolling depth, described below. This ensures that functions are not unrolled to excess. (Unrolling is only enabled if -O3 optimisation level is selected and/or the -inline-max-unroll flag is passed with an argument greater than zero.)

### ﻿21.3.3 Handling of specific language constructs

#### ﻿Functors

There is nothing particular about functors that inhibits inlining compared to normal functions. To the inliner, these both look the same, except that functors are marked as such.

Applications of functors at toplevel are biased in favour of inlining. (This bias may be adjusted: see the documentation for -inline-lifting-benefit below.)

Applications of functors not at toplevel, for example in a local module inside some other expression, are treated by the inliner identically to normal function calls.

#### ﻿First-class modules

The inliner will be able to consider inlining a call to a function in a first class module if it knows which particular function is going to be called. The presence of the first-class module record that wraps the set of functions in the module does not per se inhibit inlining.

#### ﻿Objects

Method calls to objects are not at present inlined by Flambda.

### ﻿21.3.4 Inlining reports

If the -inlining-report option is provided to the compiler then a file will be emitted corresponding to each round of optimisation. For the OCaml source file basename.ml the files are named basename.round.inlining.org, with round a zero-based integer. Inside the files, which are formatted as “org mode”, will be found English prose describing the decisions that the inliner took.

### ﻿21.3.5 Assessment of inlining benefit

Inlining typically results in an increase in code size, which if left unchecked, may not only lead to grossly large executables and excessive compilation times but also a decrease in performance due to worse locality. As such, the Flambda inliner trades off the change in code size against the expected runtime performance benefit, with the benefit being computed based on the number of operations that the compiler observes may be removed as a result of inlining.

For example given the following code:

    let f b x =
      if b then
        x
      else
        ... big expression ...

    let g x = f true x

it would be observed that inlining of f would remove:

- one direct call;
- one conditional branch.

Formally, an estimate of runtime performance benefit is computed by first summing the cost of the operations that are known to be removed as a result of the inlining and subsequent simplification of the inlined body. The individual costs for the various kinds of operations may be adjusted using the various -inline-...-cost flags as follows. Costs are specified as integers. All of these flags accept a single argument describing such integers using the conventions detailed in section 21.2.1.

-inline-alloc-cost
  The cost of an allocation.
-inline-branch-cost
  The cost of a branch.
-inline-call-cost
  The cost of a direct function call.
-inline-indirect-cost
  The cost of an indirect function call.
-inline-prim-cost
  The cost of a primitive. Primitives encompass operations including arithmetic and memory access.

(Default values are described in section 21.5 below.)

The initial benefit value is then scaled by a factor that attempts to compensate for the fact that the current point in the code, if under some number of conditional branches, may be cold. (Flambda does not currently compute hot and cold paths.) The factor—the estimated probability that the inliner really is on a hot path—is calculated as 1/(1 + f)d, where f is set by -inline-branch-factor and d is the nesting depth of branches at the current point. As the inliner descends into more deeply-nested branches, the benefit of inlining thus lessens.

The resulting benefit value is known as the estimated benefit.

The change in code size is also estimated: morally speaking it should be the change in machine code size, but since that is not available to the inliner, an approximation is used.

If the estimated benefit exceeds the increase in code size then the inlined version of the function will be kept. Otherwise the function will not be inlined.

Applications of functors at toplevel will be given an additional benefit (which may be controlled by the -inline-lifting-benefit flag) to bias inlining in such situations towards keeping the inlined version.

### ﻿21.3.6 Control of speculation

As described above, there are three parameters that restrict the search for inlining opportunities during speculation:

- the inlining threshold;
- the inlining depth;
- the unrolling depth.

These parameters are ultimately bounded by the arguments provided to the corresponding command-line flags (or their default values):

- -inline (or, if the call site that triggered speculation is at toplevel, -inline-toplevel);
- -inline-max-depth;
- -inline-max-unroll.

Note in particular that -inline does not have the meaning that it has in the previous compiler or in -Oclassic mode. In both of those situations -inline was effectively some kind of basic assessment of inlining benefit. However in Flambda inlining mode it corresponds to a constraint on the search; the assessment of benefit is independent, as described above.

When speculation starts the inlining threshold starts at the value set by -inline (or -inline-toplevel if appropriate, see above). Upon making a speculative inlining decision the threshold is reduced by the code size of the function being inlined. If the threshold becomes exhausted, at or below zero, no further speculation will be performed.

The inlining depth starts at zero and is increased by one every time the inliner descends into another function. It is then decreased by one every time the inliner leaves such function. If the depth exceeds the value set by -inline-max-depth then speculation stops. This parameter is intended as a general backstop for situations where the inlining threshold does not control the search sufficiently.

The unrolling depth applies to calls within the same mutually-recursive group of functions. Each time an inlining of such a call is performed the depth is incremented by one when examining the resulting body. If the depth reaches the limit set by -inline-max-unroll then speculation stops.

## ﻿21.4 Specialisation

The inliner may discover a call site to a recursive function where something is known about the arguments: for example, they may be equal to some other variables currently in scope. In this situation it may be beneficial to specialise the function to those arguments. This is done by copying the declaration of the function (and any others involved in any same mutually-recursive declaration) and noting the extra information about the arguments. The arguments augmented by this information are known as specialised arguments. In order to try to ensure that specialisation is not performed uselessly, arguments are only specialised if it can be shown that they are invariant: in other words, during the execution of the recursive function(s) themselves, the arguments never change.

Unless overridden by an attribute (see below), specialisation of a function will not be attempted if:

- the compiler is in -Oclassic mode;
- the function is not obviously recursive;
- the function is not closed.

The compiler can prove invariance of function arguments across multiple functions within a recursive group (although this has some limitations, as shown by the example below).

It should be noted that the unboxing of closures pass (see below) can introduce specialised arguments on non-recursive functions. (No other place in the compiler currently does this.)

##### ﻿Example: the well-known List.iter function

This function might be written like so:

    let rec iter f l =
      match l with
      | [] -> ()
      | h :: t ->
        f h;
        iter f t

and used like this:

    let print_int x =
      print_endline (Int.to_string x)

    let run xs =
      iter print_int (List.rev xs)

The argument f to iter is invariant so the function may be specialised:

    let run xs =
      let rec iter' f l =
        (* The compiler knows: f holds the same value as foo throughout iter'. *)
        match l with
        | [] -> ()
        | h :: t ->
          f h;
          iter' f t
      in
      iter' print_int (List.rev xs)

The compiler notes down that for the function iter’, the argument f is specialised to the constant closure print_int. This means that the body of iter’ may be simplified:

    let run xs =
      let rec iter' f l =
        (* The compiler knows: f holds the same value as foo throughout iter'. *)
        match l with
        | [] -> ()
        | h :: t ->
          print_int h;  (* this is now a direct call *)
          iter' f t
      in
      iter' print_int (List.rev xs)

The call to print_int can indeed be inlined:

    let run xs =
      let rec iter' f l =
        (* The compiler knows: f holds the same value as foo throughout iter'. *)
        match l with
        | [] -> ()
        | h :: t ->
          print_endline (Int.to_string h);
          iter' f t
      in
      iter' print_int (List.rev xs)

The unused specialised argument f may now be removed, leaving:

    let run xs =
      let rec iter' l =
        match l with
        | [] -> ()
        | h :: t ->
          print_endline (Int.to_string h);
          iter' t
      in
      iter' (List.rev xs)

##### ﻿Aside on invariant parameters.

The compiler cannot currently detect invariance in cases such as the following.

    let rec iter_swap f g l =
      match l with
      | [] -> ()
      | 0 :: t ->
        iter_swap g f l
      | h :: t ->
        f h;
        iter_swap f g t

### ﻿21.4.1 Assessment of specialisation benefit

The benefit of specialisation is assessed in a similar way as for inlining. Specialised argument information may mean that the body of the function being specialised can be simplified: the removed operations are accumulated into a benefit. This, together with the size of the duplicated (specialised) function declaration, is then assessed against the size of the call to the original function.

## ﻿21.5 Default settings of parameters

The default settings (when not using -Oclassic) are for one round of optimisation using the following parameters.

Parameter | Setting
-inline | 10
-inline-branch-factor | 0.1
-inline-alloc-cost | 7
-inline-branch-cost | 5
-inline-call-cost | 5
-inline-indirect-cost | 4
-inline-prim-cost | 3
-inline-lifting-benefit | 1300
-inline-toplevel | 160
-inline-max-depth | 1
-inline-max-unroll | 0
-unbox-closures-factor | 10

### ﻿21.5.1 Settings at -O2 optimisation level

When -O2 is specified two rounds of optimisation are performed. The first round uses the default parameters (see above). The second uses the following parameters.

Parameter | Setting
-inline | 25
-inline-branch-factor | Same as default
-inline-alloc-cost | Double the default
-inline-branch-cost | Double the default
-inline-call-cost | Double the default
-inline-indirect-cost | Double the default
-inline-prim-cost | Double the default
-inline-lifting-benefit | Same as default
-inline-toplevel | 400
-inline-max-depth | 2
-inline-max-unroll | Same as default
-unbox-closures-factor | Same as default

### ﻿21.5.2 Settings at -O3 optimisation level

When -O3 is specified three rounds of optimisation are performed. The first two rounds are as for -O2. The third round uses the following parameters.

Parameter | Setting
-inline | 50
-inline-branch-factor | Same as default
-inline-alloc-cost | Triple the default
-inline-branch-cost | Triple the default
-inline-call-cost | Triple the default
-inline-indirect-cost | Triple the default
-inline-prim-cost | Triple the default
-inline-lifting-benefit | Same as default
-inline-toplevel | 800
-inline-max-depth | 3
-inline-max-unroll | 1
-unbox-closures-factor | Same as default

## ﻿21.6 Manual control of inlining and specialisation

Should the inliner prove recalcitrant and refuse to inline a particular function, or if the observed inlining decisions are not to the programmer’s satisfaction for some other reason, inlining behaviour can be dictated by the programmer directly in the source code. One example where this might be appropriate is when the programmer, but not the compiler, knows that a particular function call is on a cold code path. It might be desirable to prevent inlining of the function so that the code size along the hot path is kept smaller, so as to increase locality.

The inliner is directed using attributes. For non-recursive functions (and one-step unrolling of recursive functions, although @unroll is more clear for this purpose) the following are supported:

@@inline always or @@inline never
  Attached to a declaration of a function or functor, these direct the inliner to either always or never inline, irrespective of the size/benefit calculation. (If the function is recursive then the body is substituted and no special action is taken for the recursive call site(s).) @@inline with no argument is equivalent to @@inline always.
@inlined always or @inlined never
  Attached to a function application, these direct the inliner likewise. These attributes at call sites override any other attribute that may be present on the corresponding declaration. @inlined with no argument is equivalent to @inlined always. @@inlined hint is equivalent to @@inline always except that it will not trigger warning 55 if the function application cannot be inlined.

For recursive functions the relevant attributes are:

@@specialise always or @@specialise never
  Attached to a declaration of a function or functor, this directs the inliner to either always or never specialise the function so long as it has appropriate contextual knowledge, irrespective of the size/benefit calculation. @@specialise with no argument is equivalent to @@specialise always.
@specialised always or @specialised never
  Attached to a function application, this directs the inliner likewise. This attribute at a call site overrides any other attribute that may be present on the corresponding declaration. (Note that the function will still only be specialised if there exist one or more invariant parameters whose values are known.) @specialised with no argument is equivalent to @specialised always.
@unrolled n
  This attribute is attached to a function application and always takes an integer argument. Each time the inliner sees the attribute it behaves as follows:
  - If n is zero or less, nothing happens.
  - Otherwise the function being called is substituted at the call site with its body having been rewritten such that any recursive calls to that function or any others in the same mutually-recursive group are annotated with the attribute unrolled(n − 1). Inlining may continue on that body.
  As such, n behaves as the “maximum depth of unrolling”.

A compiler warning will be emitted if it was found impossible to obey an annotation from an @inlined or @specialised attribute.

##### ﻿Example showing correct placement of attributes

    module F (M : sig type t end) = struct
      let[@inline never] bar x =
        x * 3

      let foo x =
        (bar [@inlined]) (42 + x)
    end [@@inline never]

    module X = F [@inlined] (struct type t = int end)

## ﻿21.7 Simplification

Simplification, which is run in conjunction with inlining, propagates information (known as approximations) about which variables hold what values at runtime. Certain relationships between variables and symbols are also tracked: for example, some variable may be known to always hold the same value as some other variable; or perhaps some variable may be known to always hold the value pointed to by some symbol.

The propagation can help to eliminate allocations in cases such as:

    let f x y =
      ...
      let p = x, y in
      ...
      ... (fst p) ... (snd p) ...

The projections from p may be replaced by uses of the variables x and y, potentially meaning that p becomes unused.

The propagation performed by the simplification pass is also important for discovering which functions flow to indirect call sites. This can enable the transformation of such call sites into direct call sites, which makes them eligible for an inlining transformation.

Note that no information is propagated about the contents of strings, even in safe-string mode, because it cannot yet be guaranteed that they are immutable throughout a given program.

## ﻿21.8 Other code motion transformations

### ﻿21.8.1 Lifting of constants

Expressions found to be constant will be lifted to symbol bindings—that is to say, they will be statically allocated in the object file—when they evaluate to boxed values. Such constants may be straightforward numeric constants, such as the floating-point number 42.0, or more complicated values such as constant closures.

Lifting of constants to toplevel reduces allocation at runtime.

The compiler aims to share constants lifted to toplevel such that there are no duplicate definitions. However if .cmx files are hidden from the compiler then maximal sharing may not be possible.

##### ﻿Notes about float arrays

The following language semantics apply specifically to constant float arrays. (By “constant float array” is meant an array consisting entirely of floating point numbers that are known at compile time. A common case is a literal such as [| 42.0; 43.0; |].

- Constant float arrays at the toplevel are mutable and never shared. (That is to say, for each such definition there is a distinct symbol in the data section of the object file pointing at the array.)
- Constant float arrays not at toplevel are mutable and are created each time the expression is evaluated. This can be thought of as an operation that takes an immutable array (which in the source code has no associated name; let us call it the initialising array) and duplicates it into a fresh mutable array.
  - If the array is of size four or less, the expression will create a fresh block and write the values into it one by one. There is no reference to the initialising array as a whole.
  - Otherwise, the initialising array is lifted out and subject to the normal constant sharing procedure; creation of the array consists of bulk copying the initialising array into a fresh value on the OCaml heap.

### ﻿21.8.2 Lifting of toplevel let bindings

Toplevel let-expressions may be lifted to symbol bindings to ensure that the corresponding bound variables are not captured by closures. If the defining expression of a given binding is found to be constant, it is bound as such (the technical term is a let-symbol binding).

Otherwise, the symbol is bound to a (statically-allocated) preallocated block containing one field. At runtime, the defining expression will be evaluated and the first field of the block filled with the resulting value. This initialise-symbol binding causes one extra indirection but ensures, by virtue of the symbol’s address being known at compile time, that uses of the value are not captured by closures.

It should be noted that the blocks corresponding to initialise-symbol bindings are kept alive forever, by virtue of them occurring in a static table of GC roots within the object file. This extended lifetime of expressions may on occasion be surprising. If it is desired to create some non-constant value (for example when writing GC tests) that does not have this extended lifetime, then it may be created and used inside a function, with the application point of that function (perhaps at toplevel)—or indeed the function declaration itself—marked as to never be inlined. This technique prevents lifting of the definition of the value in question (assuming of course that it is not constant).

## ﻿21.9 Unboxing transformations

The transformations in this section relate to the splitting apart of boxed (that is to say, non-immediate) values. They are largely intended to reduce allocation, which tends to result in a runtime performance profile with lower variance and smaller tails.

### ﻿21.9.1 Unboxing of closure variables

This transformation is enabled unless -no-unbox-free-vars-of-closures is provided.

Variables that appear in closure environments may themselves be boxed values. As such, they may be split into further closure variables, each of which corresponds to some projection from the original closure variable(s). This transformation is called unboxing of closure variables or unboxing of free variables of closures. It is only applied when there is reasonable certainty that there are no uses of the boxed free variable itself within the corresponding function bodies.

##### ﻿Example:

In the following code, the compiler observes that the closure returned from the function f contains a variable pair (free in the body of f) that may be split into two separate variables.

    let f x0 x1 =
      let pair = x0, x1 in
      Printf.printf "foo\n";
      fun y ->
        fst pair + snd pair + y

After some simplification one obtains:

    let f x0 x1 =
      let pair_0 = x0 in
      let pair_1 = x1 in
      Printf.printf "foo\n";
      fun y ->
        pair_0 + pair_1 + y

and then:

    let f x0 x1 =
      Printf.printf "foo\n";
      fun y ->
        x0 + x1 + y

The allocation of the pair has been eliminated.

This transformation does not operate if it would cause the closure to contain more than twice as many closure variables as it did beforehand.

### ﻿21.9.2 Unboxing of specialised arguments

This transformation is enabled unless -no-unbox-specialised-args is provided.

It may become the case during compilation that one or more invariant arguments to a function become specialised to a particular value. When such values are themselves boxed the corresponding specialised arguments may be split into more specialised arguments corresponding to the projections out of the boxed value that occur within the function body. This transformation is called unboxing of specialised arguments. It is only applied when there is reasonable certainty that the boxed argument itself is unused within the function.

If the function in question is involved in a recursive group then unboxing of specialised arguments may be immediately replicated across the group based on the dataflow between invariant arguments.

##### ﻿Example:

Having been given the following code, the compiler will inline loop into f, and then observe inv being invariant and always the pair formed by adding 42 and 43 to the argument x of the function f.

    let rec loop inv xs =
      match xs with
      | [] -> fst inv + snd inv
      | x::xs -> x + loop2 xs inv
    and loop2 ys inv =
      match ys with
      | [] -> 4
      | y::ys -> y - loop inv ys

    let f x =
      Printf.printf "%d\n" (loop (x + 42, x + 43) [1; 2; 3])

Since the functions have sufficiently few arguments, more specialised arguments will be added. After some simplification one obtains:

    let f x =
      let rec loop' xs inv_0 inv_1 =
        match xs with
        | [] -> inv_0 + inv_1
        | x::xs -> x + loop2' xs inv_0 inv_1
      and loop2' ys inv_0 inv_1 =
        match ys with
        | [] -> 4
        | y::ys -> y - loop' ys inv_0 inv_1
      in
      Printf.printf "%d\n" (loop' [1; 2; 3] (x + 42) (x + 43))

The allocation of the pair within f has been removed. (Since the two closures for loop’ and loop2’ are constant they will also be lifted to toplevel with no runtime allocation penalty. This would also happen without having run the transformation to unbox specialise arguments.)

The transformation to unbox specialised arguments never introduces extra allocation.

The transformation will not unbox arguments if it would result in the original function having sufficiently many arguments so as to inhibit tail-call optimisation.

The transformation is implemented by creating a wrapper function that accepts the original arguments. Meanwhile, the original function is renamed and extra arguments are added corresponding to the unboxed specialised arguments; this new function is called from the wrapper. The wrapper will then be inlined at direct call sites. Indeed, all call sites will be direct unless -unbox-closures is being used, since they will have been generated by the compiler when originally specialising the function. (In the case of -unbox-closures other functions may appear with specialised arguments; in this case there may be indirect calls and these will incur a small penalty owing to having to bounce through the wrapper. The technique of direct call surrogates used for -unbox-closures is not used by the transformation to unbox specialised arguments.)

### ﻿21.9.3 Unboxing of closures

This transformation is not enabled by default. It may be enabled using the -unbox-closures flag.

The transformation replaces closure variables by specialised arguments. The aim is to cause more closures to become closed. It is particularly applicable, as a means of reducing allocation, where the function concerned cannot be inlined or specialised. For example, some non-recursive function might be too large to inline; or some recursive function might offer no opportunities for specialisation perhaps because its only argument is one of type unit.

At present there may be a small penalty in terms of actual runtime performance when this transformation is enabled, although more stable performance may be obtained due to reduced allocation. It is recommended that developers experiment to determine whether the option is beneficial for their code. (It is expected that in the future it will be possible for the performance degradation to be removed.)

##### ﻿Simple example:

In the following code (which might typically occur when g is too large to inline) the value of x would usually be communicated to the application of the + function via the closure of g.

    let f x =
      let g y =
        x + y
      in
      (g [@inlined never]) 42

Unboxing of the closure causes the value for x inside g to be passed as an argument to g rather than through its closure. This means that the closure of g becomes constant and may be lifted to toplevel, eliminating the runtime allocation.

The transformation is implemented by adding a new wrapper function in the manner of that used when unboxing specialised arguments. The closure variables are still free in the wrapper, but the intention is that when the wrapper is inlined at direct call sites, the relevant values are passed directly to the main function via the new specialised arguments.

Adding such a wrapper will penalise indirect calls to the function (which might exist in arbitrary places; remember that this transformation is not for example applied only on functions the compiler has produced as a result of specialisation) since such calls will bounce through the wrapper. To mitigate this, if a function is small enough when weighed up against the number of free variables being removed, it will be duplicated by the transformation to obtain two versions: the original (used for indirect calls, since we can do no better) and the wrapper/rewritten function pair as described in the previous paragraph. The wrapper/rewritten function pair will only be used at direct call sites of the function. (The wrapper in this case is known as a direct call surrogate, since it takes the place of another function—the unchanged version used for indirect calls—at direct call sites.)

The -unbox-closures-factor command line flag, which takes an integer, may be used to adjust the point at which a function is deemed large enough to be ineligible for duplication. The benefit of duplication is scaled by the integer before being evaluated against the size.

##### ﻿Harder example:

In the following code, there are two closure variables that would typically cause closure allocations. One is called fv and occurs inside the function baz; the other is called z and occurs inside the function bar. In this toy (yet sophisticated) example we again use an attribute to simulate the typical situation where the first argument of baz is too large to inline.

    let foo c =
      let rec bar zs fv =
        match zs with
        | [] -> []
        | z::zs ->
          let rec baz f = function
            | [] -> []
            | a::l -> let r = fv + ((f [@inlined never]) a) in r :: baz f l
          in
          (map2 (fun y -> z + y) [z; 2; 3; 4]) @ bar zs fv
      in
      Printf.printf "%d" (List.length (bar [1; 2; 3; 4] c))

The code resulting from applying -O3 -unbox-closures to this code passes the free variables via function arguments in order to eliminate all closure allocation in this example (aside from any that might be performed inside printf).

## ﻿21.10 Removal of unused code and values

### ﻿21.10.1 Removal of redundant let expressions

The simplification pass removes unused let bindings so long as their corresponding defining expressions have “no effects”. See the section “Treatment of effects” below for the precise definition of this term.

### ﻿21.10.2 Removal of redundant program constructs

This transformation is analogous to the removal of let-expressions whose defining expressions have no effects. It operates instead on symbol bindings, removing those that have no effects.

### ﻿21.10.3 Removal of unused arguments

This transformation is only enabled by default for specialised arguments. It may be enabled for all arguments using the -remove-unused-arguments flag.

The pass analyses functions to determine which arguments are unused. Removal is effected by creating a wrapper function, which will be inlined at every direct call site, that accepts the original arguments and then discards the unused ones before calling the original function. As a consequence, this transformation may be detrimental if the original function is usually indirectly called, since such calls will now bounce through the wrapper. (The technique of direct call surrogates used to reduce this penalty during unboxing of closure variables (see above) does not yet apply to the pass that removes unused arguments.)

### ﻿21.10.4 Removal of unused closure variables

This transformation performs an analysis across the whole compilation unit to determine whether there exist closure variables that are never used. Such closure variables are then eliminated. (Note that this has to be a whole-unit analysis because a projection of a closure variable from some particular closure may have propagated to an arbitrary location within the code due to inlining.)

## ﻿21.11 Other code transformations

### ﻿21.11.1 Transformation of non-escaping references into mutable variables

Flambda performs a simple analysis analogous to that performed elsewhere in the compiler that can transform refs into mutable variables that may then be held in registers (or on the stack as appropriate) rather than being allocated on the OCaml heap. This only happens so long as the reference concerned can be shown to not escape from its defining scope.

### ﻿21.11.2 Substitution of closure variables for specialised arguments

This transformation discovers closure variables that are known to be equal to specialised arguments. Such closure variables are replaced by the specialised arguments; the closure variables may then be removed by the “removal of unused closure variables” pass (see below).

## ﻿21.12 Treatment of effects

The Flambda optimisers classify expressions in order to determine whether an expression:

- does not need to be evaluated at all; and/or
- may be duplicated.

This is done by forming judgements on the effects and the coeffects that might be performed were the expression to be executed. Effects talk about how the expression might affect the world; coeffects talk about how the world might affect the expression.

Effects are classified as follows:

No effects:
  The expression does not change the observable state of the world. For example, it must not write to any mutable storage, call arbitrary external functions or change control flow (e.g. by raising an exception). Note that allocation is not classed as having “no effects” (see below).
  - It is assumed in the compiler that expressions with no effects, whose results are not used, may be eliminated. (This typically happens where the expression in question is the defining expression of a let; in such cases the let-expression will be eliminated.) It is further assumed that such expressions with no effects may be duplicated (and thus possibly executed more than once).
  - Exceptions arising from allocation points, for example “out of memory” or exceptions propagated from finalizers or signal handlers, are treated as “effects out of the ether” and thus ignored for our determination here of effectfulness. The same goes for floating point operations that may cause hardware traps on some platforms.
Only generative effects:
  The expression does not change the observable state of the world save for possibly affecting the state of the garbage collector by performing an allocation. Expressions that only have generative effects and whose results are unused may be eliminated by the compiler. However, unlike expressions with “no effects”, such expressions will never be eligible for duplication.
Arbitrary effects:
  All other expressions.

There is a single classification for coeffects:

No coeffects:
  The expression does not observe the effects (in the sense described above) of other expressions. For example, it must not read from any mutable storage or call arbitrary external functions.

It is assumed in the compiler that, subject to data dependencies, expressions with neither effects nor coeffects may be reordered with respect to other expressions.

## ﻿21.13 Compilation of statically-allocated modules

Compilation of modules that are able to be statically allocated (for example, the module corresponding to an entire compilation unit, as opposed to a first class module dependent on values computed at runtime) initially follows the strategy used for bytecode. A sequence of let-bindings, which may be interspersed with arbitrary effects, surrounds a record creation that becomes the module block. The Flambda-specific transformation follows: these bindings are lifted to toplevel symbols, as described above.

## ﻿21.14 Inhibition of optimisation

Especially when writing benchmarking suites that run non-side-effecting algorithms in loops, it may be found that the optimiser entirely elides the code being benchmarked. This behaviour can be prevented by using the Sys.opaque_identity function (which indeed behaves as a normal OCaml function and does not possess any “magic” semantics). The documentation of the Sys module should be consulted for further details.

## ﻿21.15 Use of unsafe operations

The behaviour of the Flambda simplification pass means that certain unsafe operations, which may without Flambda or when using previous versions of the compiler be safe, must not be used. This specifically refers to functions found in the Obj module.

In particular, it is forbidden to change any value (for example using Obj.set_field or Obj.set_tag) that is not mutable. (Values returned from C stubs are always treated as mutable.) The compiler will emit warning 59 if it detects such a write—but it cannot warn in all cases. Here is an example of code that will trigger the warning:

    let f x =
      let a = 42, x in
      (Obj.magic a : int ref) := 1;
      fst a

The reason this is unsafe is because the simplification pass believes that fst a holds the value 42; and indeed it must, unless type soundness has been broken via unsafe operations.

If it must be the case that code has to be written that triggers warning 59, but the code is known to actually be correct (for some definition of correct), then Sys.opaque_identity may be used to wrap the value before unsafe operations are performed upon it. Great care must be taken when doing this to ensure that the opacity is added at the correct place. It must be emphasised that this use of Sys.opaque_identity is only for exceptional cases. It should not be used in normal code or to try to guide the optimiser.

As an example, this code will return the integer 1:

    let f x =
      let a = Sys.opaque_identity (42, x) in
      (Obj.magic a : int ref) := 1;
      fst a

However the following code will still return 42:

    let f x =
      let a = 42, x in
      Sys.opaque_identity (Obj.magic a : int ref) := 1;
      fst a

High levels of inlining performed by Flambda may expose bugs in code thought previously to be correct. Take care, for example, not to add type annotations that claim some mutable value is always immediate if it might be possible for an unsafe operation to update it to a boxed value.

## ﻿21.16 Glossary

The following terminology is used in this chapter of the manual.

Call site
  See direct call site and indirect call site below.
Closed function
  A function whose body has no free variables except its parameters and any to which are bound other functions within the same (possibly mutually-recursive) declaration.
Closure
  The runtime representation of a function. This includes pointers to the code of the function together with the values of any variables that are used in the body of the function but actually defined outside of the function, in the enclosing scope. The values of such variables, collectively known as the environment, are required because the function may be invoked from a place where the original bindings of such variables are no longer in scope. A group of possibly mutually-recursive functions defined using let rec all share a single closure. (Note to developers: in the Flambda source code a closure always corresponds to a single function; a set of closures refers to a group of such.)
Closure variable
  A member of the environment held within the closure of a given function.
Constant
  Some entity (typically an expression) the value of which is known by the compiler at compile time. Constantness may be explicit from the source code or inferred by the Flambda optimisers.
Constant closure
  A closure that is statically allocated in an object file. It is almost always the case that the environment portion of such a closure is empty.
Defining expression
  The expression e in let x = e in e’.
Direct call site
  A place in a program’s code where a function is called and it is known at compile time which function it will always be.
Indirect call site
  A place in a program’s code where a function is called but is not known to be a direct call site.
Program
  A collection of symbol bindings forming the definition of a single compilation unit (i.e. .cmx file).
Specialised argument
  An argument to a function that is known to always hold a particular value at runtime. These are introduced by the inliner when specialising recursive functions; and the unbox-closures pass. (See section 21.4.)
Symbol
  A name referencing a particular place in an object file or executable image. At that particular place will be some constant value. Symbols may be examined using operating system-specific tools (for example objdump on Linux).
Symbol binding
  Analogous to a let-expression but working at the level of symbols defined in the object file. The address of a symbol is fixed, but it may be bound to both constant and non-constant expressions.
Toplevel
  An expression in the current program which is not enclosed within any function declaration.
Variable
  A named entity to which some OCaml value is bound by a let expression, pattern-matching construction, or similar.