In my previous blog post Understanding the Stack I mentioned that “RealWorld tokens disappear” in the generated code. This is not entirely accurate. Simon Marlow gives a very brief explanation of this on the old glasgow-haskell-users mailing list. In this blog post we will explore this in more depth and hopefully come to a better understanding of the RealWorld , though perhaps not of the real world.

In order to make some points a bit easier to illustrate, we will be using a 32-bit version of ghc; and since there are no 32-bit builds of ghc for OSX later than version 7.4.2, that’s what we’ll use for most of this blog post.

Warmup exercise

Consider

# :: () -> Int # constant_Int() # _ = 1234 # constant_Int

This compiles to the following C-- code:

1234 ; R1 = 4 ; Sp = Sp + 0 ]) (); jump (I32[Sp +]) ();

On x86 architectures all Haskell function arguments are passed through the stack (on x86-64 the first few arguments are passed through registers). That means that on entry to constant_Int# the top of the stack contains the () argument, which we discard and pop off the stack by incrementing the stack pointer Sp . (I will explain why I am introducing this unused argument towards the end of this blog post.)

Since 1234# is already in weak head normal form we simply call the continuation on the top of the stack with #1234 as the first argument. If you followed along in the previous blog post this will all be old hat to you.

Heap allocation

What happens if we use a boxed integer instead?

constant_Int :: () -> Int () = 1234 constant_Int _

If we compare the STG code for constant_Int# and constant_Int we see that the only difference is indeed that constant_Int must box its argument:

= \r [ds_sf9] I # [ 1234 ]; constant_Int\r [ds_sf9]]; # = \r [ds_sfb] 1234 ; constant_Int\r [ds_sfb]

This means however that we must create a heap object, and hence the C-- is significantly more complicated:

chJ: 8 ; Hp = Hp + if (Hp > I32[BaseReg + 92 ]) goto chO; (Hp > I32[BaseReg +])chO; 4 ] = I#_con_info; I32[Hp -] = I#_con_info; 0 ] = 1234 ; I32[Hp +] = 3 ; R1 = Hp - 4 ; Sp = Sp + 0 ]) (); jump (I32[Sp +]) (); chM: R1 = constant_Int_closure; 4 ]) (); jump (I32[BaseReg -]) (); chO: 116 ] = 8 ; I32[BaseReg +] = goto chM; chM;

The function starts with a heap overflow check. This works in much the same way as the stack overflow check that we discussed previously, so we will ignore it for the sake of this blog post, and omit heap and stack overflow checks from further code samples.

The interesting code happens after we conclude that the heap is okay. Every heap object consists of a code pointer followed by a payload. In this case, the code pointer is the one for the I# constructor, and the payload is 1234 .

Since I# 1234 is already in weak head normal form, we don’t need to evaluate it any further, and we can call the continuation on the stack with the address of the heap object we just constructed as its argument. Incidentally, if you are confused by the Hp - 3 , think of it as Hp - 4 + 1 instead; Hp - 4 is the address of the code pointer (the start of the heap object); the + 1 is pointer tagging at work again.

(Incidentally, ghc will “preallocate” small integers, so that when you write, say, 1 instead of 1234 it doesn’t actually create a new heap object but gives you a reference to a cached Int instead.)

Larger types

What happens if we move from Int to Double ?

# :: () -> Double # constant_Double() # _ = 1234.0 ## constant_Double constant_Double :: () -> Double () = 1234.0 constant_Double _

The C-- code for constant_Double is

F64[BaseReg + 56] = 1234.0 :: W64; Sp = Sp + 4; jump (I32[Sp + 0]) ();

Since a Double is 64-bits it cannot be passed through the 32-bit register R1 / esi . On 32-bit machines ghc passes Double values through a “virtual register”. Virtual registers are just memory locations; BaseReg ( ebx on x86 ) is the address of the first of them. (On x86-64 architectures ghc will use the SSE registers for Double s.)

The code for constant_Double is similar to the code for constant_Int , except that it must allocate 12 bytes, rather than 8, for the heap object:

12 ; Hp = Hp + 8 ] = D#_con_info; I32[Hp -] = D#_con_info; 4 ] = 1234.0 :: W64; F64[Hp -] =:: W64; 7 ; R1 = Hp - 4 ; Sp = Sp + 0 ]) (); jump (I32[Sp +]) ();

Functions

So far we considered only constants (modulo that extra argument of type () ). Let’s consider some simple functions next:

# :: Int # -> Int # want_Int # x = x want_Int

translates to

0 ]; R1 = I32[Sp +]; 4 ; Sp = Sp + 0 ]) (); jump (I32[Sp +]) ();

Since any Int# is by definition already in weak head normal form, the argument to want_Int# must already be in weak head normal form and hence we can just pop that Int# off the stack and pass it to the continuation through register R1 . The situation for Double# is comparable, except that as before we need to use a different register, and pop two words off the stack rather than one. That is,

# :: Double # -> Double # want_Double # x = x want_Double

translates to

56 ] = F64[Sp + 0 ]; F64[BaseReg +] = F64[Sp +]; 8 ; Sp = Sp + 0 ]) (); jump (I32[Sp +]) ();

The translation for Int is different.

want_Int :: Int -> Int = x want_Int x

Since we don’t know if x is in weak head normal form yet, we cannot call the continuation; instead, we must enter x itself:

R1 = I32 [ Sp + 0 ]; ]; Sp = Sp + 4 ; R1 = R1 & ( - 4 ); ); I32 [ R1 ] (); jump] ();

Remember from the previous blog post that when we enter a closure the address of the closure must be in register R1 , in case the closure needs to lookup any free variables. So, we pop off the address of the closure from the stack, load it into R1 , mask out any pointer tagging bits, and enter the closure. It will be the responsibility of the closure to eventually call the continuation on the stack once it reaches weak head normal form.

The translation of

want_Double :: Double -> Double = x want_Double x

is precisely identical; indeed, both are identical to the translation of

id :: a -> a id x = x

That’s the point of boxing, of course: every argument has the same shape, and hence we can universally quantify over any non-primitive type. Incidentally, this is precisely why Int# and Double# have kind # rather than kind * : it means you cannot apply a polymorphic function such as id to an argument of a primitive type.

Calling known functions

We saw how we can define functions; how do we call them? Consider

# :: () -> Int # call_the_want_Int() # _ = want_Int # 1234 # call_the_want_Intwant_Int

This translates to

0 ] = 1234 ; I32[Sp +] = jump want_Int#_info ();

This couldn’t be simpler. We overwrite the top of the stack (which contains the () argument that we are ignoring) with the argument for want_Int# , and then jump to the code for want_Int# .

For want_Double# the situation is slightly more complicated.

# :: () -> Double # call_the_want_Double() # _ = want_Double # 1234.0 ## call_the_want_Doublewant_Double

Since the Double is two words, we have to grow the stack by one word (and deal with a potential stack overflow, which we omit again):

4 ] = 1234.0 :: W64; F64[Sp -] =:: W64; 4 ; Sp = Sp - jump want_Double#_info ();

To call a function with a boxed Int or Double we have to create the heap object. For instance,

call_the_want_Int :: () -> Int () = want_Int 1234 call_the_want_Int _want_Int

translates to

Hp = Hp + 8 ; I32 [ Hp - 4 ] = I # _con_info; _con_info; I32 [ Hp + 0 ] = 1234 ; I32 [ Sp + 0 ] = Hp - 3 ; jump want_Int_info ();

No real surprises here. We create the heap object, push the address of the newly created heap object onto the stack, and call want_Int_info . The same happens when we call want_Double , except of course that we need to create a larger heap object (12 bytes rather than 8).

Multiple arguments

Conceptually speaking Haskell does not have functions of multiple arguments. Instead, a function such as

## :: Int # -> Double # -> Int # want_ID ## x y = x +# double2Int # y want_IDx ydouble2Int

with two arguments is thought of as a function of a single argument of type Int# , which returns a new function, that takes an argument of type Double# and returns an Int# . The compiler does not implement that literally, however, as that would be much too slow. Instead, a function such as want_ID## really does take two arguments, both of which are on the stack (or in registers on architectures where that is possible); want_ID## gets compiled to

0 ] + %MO_FS_Conv_W64_W32(F64[Sp + 4 ]); R1 = I32[Sp +] + %MO_FS_Conv_W64_W32(F64[Sp +]); 12 ; Sp = Sp + 0 ]) (); jump (I32[Sp +]) ();

We add together the Int# and Double# on the stack, store the result in R1 , pop them off the stack and call the continuation. Similarly, when we call a function of multiple arguments, we push all arguments to the stack before jumping to the function entry code:

## :: () -> Int # call_the_want_ID() ## _ = want_ID ## 1234 # 1234.0 ## call_the_want_IDwant_ID

translates to

4 ] = 1234.0 :: W64; F64[Sp -] =:: W64; 8 ] = 1234 ; I32[Sp -] = 8 ; Sp = Sp - jump want_ID##_info ();

Calling unknown functions

In the previous section we knew precisely what function we were calling. Things are more difficult if we don’t:

# :: ( Int # -> a) -> a call_some_want_Inta) # f = f 1234 # call_some_want_Int

The reason that this is more difficult is that we do not know how many arguments f takes. If it takes just one, then we can call f in precisely the same way that we were calling want_Int# previously. But what if f takes more than one argument? In that case we must construct a PAP heap object to record the partial application of f . Clearly, the shape of this heap object must depend on the arguments that we have supplied: for an Int# the size of the payload must be one word, for a Double# it must be two, and so on.

We must also deal with the case that f is already such a PAP object. In that case, we must check if we now have all the arguments necessary to call f ; if so, we can call f as we did before; if not, we must construct a new PAP object collecting the previously supplied arguments and the arguments we are supplying now.

Finally, if we are providing multiple arguments, we must deal with the case that f actually takes fewer arguments than we are providing and returns a new PAP object. In that case, we must provide all the arguments that f needs, call f , and then continue with the PAP object that f returns.

Rather than generating code to deal with all these possibilities at every call-to-unknown-function site, ghc delegates this to a bunch of specialized functions which are part of the RTS. The compilation of call_some_want_Int# therefore looks deceptively simple:

0 ]; R1 = I32[Sp +]; 0 ] = 1234 ; I32[Sp +] = jump stg_ap_n_fast ();

stg_ap_n_fast deals with the application of an unknown function to a single Int# ; hence the _n in the name. It finds out how many arguments f has (by looking at the pointer tags, or failing that at the info table for f ), and deals with all the cases that mentioned above (as well as a bunch of others; we haven’t shown the full picture here). To call stg_ap_n_fast we pop the function argument ( f ) off the stack and store it in R1 and then push the argument that we want to provide to f onto the stack.

The case for Double#

# :: ( Double # -> a) -> a call_some_want_Doublea) # f = f 1234.0 ## call_some_want_Double

is very similar, except that we need to grow the stack by one word, and use stg_ap_d_fast instead ( d for Double# ):

0 ]; R1 = I32[Sp +]; 4 ] = 1234.0 :: W64; F64[Sp -] =:: W64; 4 ; Sp = Sp - jump stg_ap_d_fast ();

Finally, for non-primitive arguments there is a generic stg_ap_p_fast ( p for pointer);

call_some_want_Int :: ( Int -> a) -> a a) = f 1234 call_some_want_Int f

translates to

8 ; Hp = Hp + 4 ] = I#_con_info; I32[Hp -] = I#_con_info; 0 ] = 1234 ; I32[Hp +] = 0 ]; R1 = I32[Sp +]; 0 ] = Hp - 3 ; I32[Sp +] = Hp - jump stg_ap_p_fast ();

No real surprises here; we construct the heap object and call stg_ap_p_fast .

Multiple arguments, again

What happens if we call an unknown function with multiple arguments?

call_some_want_II :: ( Int -> Int -> a) -> a a) = f 1234 5678 call_some_want_II f

This is really no different from supplying just one argument; we still have to deal with the same set of possibilities; the only difference is that we now need a payload for two pointers. This is created by stg_ap_pp_fast :

16 ; Hp = Hp + 12 ] = I#_con_info; I32[Hp -] = I#_con_info; 8 ] = 5678 ; I32[Hp -] = 4 ] = I#_con_info; I32[Hp -] = I#_con_info; 0 ] = 1234 ; I32[Hp +] = 0 ]; R1 = I32[Sp +]; 0 ] = Hp - 11 ; I32[Sp +] = Hp - 4 ] = Hp - 3 ; I32[Sp -] = Hp - 4 ; Sp = Sp - jump stg_ap_pp_fast ();

We construct two heap objects for the two boxed integers, and then call stg_ap_pp_fast .

If at this point you are wondering “how many variations on stg_ap_XYZ_fast are there?” congratulate yourself, you are paying attention :) Clearly, there cannot be a version of this function for every possible number and type of argument, as there are infinitely many such combinations. Instead, the RTS only contains versions for the most common combinations. For example, there is no version for calling a function with two Int# arguments. So what does

## :: ( Int # -> Int # -> a) -> a call_some_want_IIa) ## f = f 1234 # 5678 # call_some_want_II

compile to?

0 ]; R1 = I32[Sp +]; 0 ] = 5678 ; I32[Sp +] = 4 ] = I32[Lstg_ap_n_info$non_lazy_ptr]; I32[Sp -] = I32[Lstg_ap_n_info$non_lazy_ptr]; 8 ] = 1234 ; I32[Sp -] = 8 ; Sp = Sp - jump stg_ap_n_fast ();

Let’s consider carefully what’s going on here:

We call stg_ap_n_fast (with a single n ) with 1234 on the top of the stack. stg_ap_n_fast will notice that f has (at least) two arguments, and can therefore not yet be called. Instead, it creates a PAP object containing just 1234 (and the address of f ). After it has created the PAP object, it then calls the continuation on the top of the stack (after the argument). This continuation happens to be stg_ap_n_info , which is the “continuation wrapper” of stg_ap_n . This in turn will pop the next argument off the stack ( 5678 ) and the process repeats.

In this way any non-standard version of stg_ap_XYZ can be simulated with a chain of standard stg_ap_XYZ functions.

RealWorld tokens

The main points to take away from all of the above are

Different kinds of primitive types may have different sizes; one word for Int# , two for Double# (on a 32-bit machine).

Different kinds of primitive types are passed through different kinds of registers; Int# through the standard registers, Double# through a virtual register (on x86 ) or through the SSE registers (on x86-64 ).

Of course, both Int# and Double# can also be passed through the stack, in which case Int# takes up one word, and Double# takes up two.

Similarly, the size of heap objects varies depending on the size of the primitive types.

Finally, when calling unknown functions we need different kinds of stg_ap_XYZ functions to deal with different kinds of primitive types.

So what does all this have to do with the RealWorld tokens that I promised at the start we would look at? Well, the RealWorld tokens have type State# RealWorld , which is yet another primitive type … of size 0. So let us retrace our steps and consider the same examples that we considered for Int# and Double# , but now look at the corresponding translation for State# RealWorld .

We first considered the construction of a constant:

# :: () -> State # RealWorld constant_State() # _ = realWorld # constant_StaterealWorld

This translates to

4 ; Sp = Sp + 0 ]) (); jump (I32[Sp +]) ();

All we need to do is pop the () argument off the stack and call the continuation; since a State# RealWorld type has size zero, we don’t need any register at all to store it!

The translation of

# :: () -> State # RealWorld call_the_want_State() # _ = want_State # realWorld # call_the_want_Statewant_StaterealWorld

is

4 ; Sp = Sp + jump want_State#_info ();

and finally the translation of

# :: ( State # RealWorld -> a) -> a call_some_want_Statea) # f = f realWorld # call_some_want_Statef realWorld

is

R1 = I32 [ Sp + 0 ]; ]; Sp = Sp + 4 ; jump stg_ap_v_fast ();

The v here stands for “void”, and here we finally see a trace of a RealWorld token in the compiled code: we are applying a function to a primitive type of type void; admittedly, this is something of size zero, but it’s still somehow here. Note that stg_ap_v_fast must still deal with all the possible cases (exact number of arguments, too many arguments, too few arguments) that we mentioned above, despite the fact that we are providing no arguments at all.

Proxy#

In the case of RealWorld and the IO monad this doesn’t really matter most of the time. Usually when we repeatedly call an unknown IO function we are providing an argument (think mapM , for instance), and the STG runtime provides specialized versions of stg_ap_XYZ_fast for a function that takes one, two, or three pointers and a single void argument, in which case the additional void parameter does not introduce any additional overhead of the indirection through stg_ap . But it is good to be aware that the runtime cost is not quite zero when writing highly performance critical code.

However, as we start to do more and more type level programming in Haskell, we increasingly need to explicitly pass type variables around. For this reason ghc 7.8 introduces a new primitive type

Proxy # :: * -> #

with a single “constructor”

# :: Proxy # a proxy

The sole purpose of a Proxy# argument is to instantiate a type variable. It is used heavily for instance in the new ghc extension for overloaded records. This isn’t a blog post about type level programming—quite the opposite :)—so we will just consider a completely contrived example, along the same lines of the other examples that we considered so far:

# :: ( Proxy # a -> Proxy # b -> Proxy # c call_some_want_Proxies -> (a, b, c) -> (c, b, a)) (a, b, c)(c, b, a)) -> (a, b, c) -> (c, b, a) (a, b, c)(c, b, a) # f tup = f proxy # proxy # proxy # tup call_some_want_Proxiesf tupf proxyproxyproxytup

Although a Proxy# argument takes up no memory, they do play a role when calling an unknown function, as we have seen. The above function call translates to

R1 = P32[Sp]; 12 ] = stg_ap_v_info; I32[Sp -] = stg_ap_v_info; 8 ] = stg_ap_v_info; I32[Sp -] = stg_ap_v_info; 4 ] = stg_ap_v_info; I32[Sp -] = stg_ap_v_info; I32[Sp] = stg_ap_p_info; 12 ; Sp = Sp - 24 , res: 0 , upd: 4 ; call stg_ap_v_fast(R1) args:, res:, upd:

Note the stack that we set up here: we apply the function to a single “void” argument; then when that is done, we apply it to the next, and again to the third, and only then we apply it to a “pointer” argument (the actual tuple). The use of Proxy# thus does incur a runtime cost. Of course, one could envision various ways in which ghc could be improved to alleviate this cost; the simplest of which would be to introduce some more stg_ap_XYZ variations targeted at void arguments.

For now, if this really matters it is faster to use a single Proxy# argument, and make sure that it is the last argument so that we can take advantage of the specialized stg_ap functions which were introduced for the IO monad:

# :: ((a, b, c) -> Proxy # (a, b, c) -> (c, b, a)) fast_call_some_want_Proxies((a, b, c)(a, b, c)(c, b, a)) -> (a, b, c) -> (c, b, a) (a, b, c)(c, b, a) # f tup = f tup proxy # fast_call_some_want_Proxiesf tupf tup proxy

compiles to just

R1 = P32[Sp]; Sp = Sp + 4; call stg_ap_pv_fast(R1) args: 8, res: 0, upd: 4;

What is I#_con_info ?

We saw that the heap object header for boxed integers is I#_con_info . You might be wondering what exactly is at that code pointer address. We can fire up lldb (or gdb ) and find out:

(lldb) disassemble -n ghczmprim_GHCziTypes_Izh_con_info ghczmprim_GHCziTypes_Izh_con_info: Main` 0x68398 ] : incl %esi Main[incl %esi 0x68399 ] : jmpl *(%ebp) Main[jmpl *(%ebp)

ghczmprim_GHCziTypes_Izh is the Z-encoding for ghc-prim_GHC.Types.I# ; zm for minus, zh for hash, and zi for dot (“the dot on the i”). So what does the code do? Well, the code pointer associated with every heap object is the code that reduces that heap object to normal form (this what we mean by “entering a closure”). Since a constructor application already is in normal form, there is almost nothing to do, so we just call the continuation on the stack ( jmpl ).

The only complication is due to pointer tagging, once again. Remember that when we evaluate a closure, R1 (mapped to esi on x86 architectures) points to the address of the closure. If we entered the closure that means the pointer wasn’t tagged yet, or we ignored the tag bits (for whatever reason); we make sure to tag it by calling incl before calling the continuation so that we don’t unnecessarily enter the closure again.

## Info tables

The discussion of constant_Int above assumed that the “tables next to code” optimization is enabled (which is most of the time). With this optimization enabled the code pointer for a closure also doubles as a pointer to the info table for the closure. The info table for a closure contains information such as the constructor tag (which constructor of a data type is this?), the size of the payload and the types of its elements (int, float, pointer etc) for garbage collection purposes, the static reference table (used for garbage collection of CAFs), profiling information, etc. The info table is located just before the closure entry code in memory.

When the optimization is not enabled the heap object header is a pointer to the info table, which in turn contains a field for the entry code. This means that in order to enter a closure an additional indirection is necessary.

Allocation in STG

I have often seen claims that the only place where heap allocation occurs in STG code is in let expressions (for instance, on StackOverflow and on cvs-ghc). This is not entirely accurate, as we saw when we looked at constant_Int . See cgExpr in compiler/codeGen/StgCmmExpr in the ghc sources, and in particular function cgConApp under “tail calls”.

Boxing state

We don’t normally box State# objects, but we could:

data State a = State # ( State # a) a) constant_State :: () -> State RealWorld () = State # realWorld # constant_State _realWorld

The translation of constant_State is however a bit surprising:

8 ; Hp = Hp + if (Hp > I32[BaseReg + 92 ]) goto cm8; (Hp > I32[BaseReg +])cm8; 4 ] = State#_con_info; I32[Hp -] = State#_con_info; 3 ; R1 = Hp - 4 ; Sp = Sp + 0 ]) (); jump (I32[Sp +]) ();

This creates a heap object with a one-word payload, which is subseqeuently left unused. The reason is that every heap object must be at least two words, so that there is enough room to overwrite it with a forwarding pointer during garbage collection. Thanks to rwbarton on reddit for pointing this out!

That strange () argument

Many of the examples we looked at had an additional () argument:

# :: () -> Int # call_the_want_Int() # _ = want_Int # 1234 # call_the_want_Intwant_Int

What is the purpose of this argument? Well, first of all, a top-level binding to a primitive type (something of kind # ) is not allowed; this is illegal Haskell:

# :: Int # -- Not legal Haskell caf_the_want_Int # = want_Int # 1234 # caf_the_want_Intwant_Int

But even for examples where it would be legal we want to avoid it for the sake of this blog post. Consider

caf_the_want_Int :: Int = want_Int 1234 caf_the_want_Intwant_Int

The difference between call_the_want_Int and caf_the_want_Int is that the latter is a CAF or “constant applicative form”; ghc must ensure that caf_the_want_Int is reduced to weak head normal form only once in the execution of the program. CAFs are a large topic in their own right; another blog post, perhaps (for now, some interesting links are this Stack overflow question and ghc ticket #917, answer from Simon Peyton-Jones about how CAFs are garbage collected, and the entry on the ghc wiki). If you are feeling brave, take a look at the generated code for caf_the_want_Int .