Digging deeper in SSA

September 20, 2018 · by Björn Gustavsson .

This blog post continues the exploration of the new SSA-based intermediate representation through multiple examples. Make sure to read the Introduction to SSA if you missed it.

Calling a BIF that may fail

The first example calls a guard BIF that may fail with an exception:

element_body(T) ->
    element(2, T).

The (optimized) SSA code looks like this:

function blog:element_body(_0) {
0:
  %% blog.erl:5
  _1 = bif:element literal 2, _0
  @ssa_bool = succeeded _1
  br @ssa_bool, label 3, label 1

3:
  ret _1

1:
  @ssa_ret = call remote (literal erlang):(literal error)/1, literal badarg
  ret @ssa_ret
}

Let’s go through the code a few lines at a time:

  %% blog.erl:5
  _1 = bif:element literal 2, _0
  @ssa_bool = succeeded _1

The bif:element instruction calls the guard BIF element/2, assigning the value to the variable _1 if the call is successful.

What if the call is not successful?

The succeeded _1 instruction tests whether the previous instruction assigning to _1 was successful. true will be assigned to @ssa_bool if the second element of the tuple was successfully fetched from the tuple, and false will be assigned otherwise.

  br @ssa_bool, label 3, label 1

The br instruction tests whether @ssa_bool is true. If true, execution continues at block 3, which returns the value of the second element from the tuple. If false, execution continues at block 1.

It was mentioned in the previous blog post that block 1 is a special block that the SSA code generator always emits. In the previous examples, it was never referenced and therefore removed by one of the optimization passes.

In this example, it is used as the target when the call to element/2 fails.

The BEAM code generator treats references to block 1 specially. Here follows the BEAM code for the function. As usual, I have omitted the function header.

  %% Block 0.
  {line,[{location,"blog.erl",5}]}.
  {bif,element,{f,0},[{integer,2},{x,0}],{x,0}}.
  return.

Note that no code has been generated for block 1.

The line instructions gives the file name and line number of the source file. It will be used in the stack backtrace if the following instruction fails.

The bif instruction calls the given guard BIF, element/2 in this case. The {f,0} operand gives the action to take if the element/2 fails. The number 0 is a special case, meaning that a badarg exception should be raised if the call of element/2 fails.

A failing BIF call in a guard

In the next example, element/2 is called in a guard:

element_guard(T) when element(2, T) =:= true ->
    ok;
element_guard(_) ->
    error.

The SSA code looks like this:

function blog:element_guard(_0) {
0:
  %% blog.erl:7
  _1 = bif:element literal 2, _0
  @ssa_bool = succeeded _1
  br @ssa_bool, label 4, label 3

4:
  @ssa_bool:5 = bif:'=:=' _1, literal true
  br @ssa_bool:5, label 6, label 3

6:
  ret literal ok

3:
  ret literal error
}

The first two instructions in block 0 are the same as in the previous example. The br instruction has different labels, though. The failure label refers to block 3, which returns the value error. The success label continues execution at block 4.

4:
  @ssa_bool:5 = bif:'=:=' _1, literal true
  br @ssa_bool:5, label 6, label 3

Block 4 is the translation of =:= true part of the Erlang code. If the second element in the tuple is equal to true, execution continues at block 6, which returns the value ok. Otherwise execution continues at block 3, which returns the value error.

Here is the BEAM code:

  {bif,element,{f,5},[{integer,2},{x,0}],{x,0}}.
  {test,is_eq_exact,{f,5},[{x,0},{atom,true}]}.
  {move,{atom,ok},{x,0}}.
  return.
{label,5}.
  {move,{atom,error},{x,0}}.
  return.

In the bif instruction, {f,5} means that execution should continue at label 5 if the element/2 call fails. Otherwise execution will continue at the next instruction.

Our first case

Here is the next example:

case1(X) ->
    case X of
        1 -> a;
        2 -> b;
        _ -> c
    end.

Translated to SSA code:

function blog:case1(_0) {
0:
  switch _0, label 3, [ { literal 2, label 5 }, { literal 1, label 4 } ]

4:
  ret literal a

5:
  ret literal b

3:
  ret literal c
}

The switch instruction is a multi-way branch to one of any number of other blocks, based on the value of a variable. In this example, it branches based on the value of the variable _0. If _0 is equal to 2, execution continues at block 5. If _0 is equal to 1, execution continues at block 4. If the value is not equal to any of the values in the switch list, execution continues at the block referred to by the failure label, in this example block 3.

The BEAM code looks like this:

  {select_val,{x,0},{f,10},{list,[{integer,2},{f,9},{integer,1},{f,8}]}}.
{label,8}.
  {move,{atom,a},{x,0}}.
  return.
{label,9}.
  {move,{atom,b},{x,0}}.
  return.
{label,10}.
  {move,{atom,c},{x,0}}.
  return.

Terminators

As mentioned in the previous blog post, the last instruction in a block is called a terminator. A terminator either returns from the function or transfers control to another block. With the introduction of switch, the terminator story is complete. To summarize, a block can end in one of the following terminators:

  • ret to return a value from the function.

  • br to either branch to another block (one-way branch), or branch to one of two possible other blocks based on a variable (two-way branch).

  • switch to branch to one of any number of other blocks.

Another case

Here is a slightly different example:

case2(X) ->
    case X of
        1 -> a;
        2 -> b;
        3 -> c
    end.

In this case, X must be one of the integers 1, 2, or 3. Otherwise, there will be a {case_clause,X} exception. Here is the SSA code:

function blog:case2(_0) {
0:
  switch _0, label 3, [ { literal 3, label 6 }, { literal 2, label 5 }, { literal 1, label 4 } ]

4:
  ret literal a

5:
  ret literal b

6:
  ret literal c

3:
  _2 = put_tuple literal case_clause, _0

  %% blog.erl:20
  @ssa_ret:7 = call remote (literal erlang):(literal error)/1, _2
  ret @ssa_ret:7
}

The failure label for the switch is 3. Block 3 builds the {case_clause,X} tuple and calls erlang:error/1.

Here is the BEAM code:

  {select_val,{x,0},
              {f,16},
              {list,[{integer,3},
                     {f,15},
                     {integer,2},
                     {f,14},
                     {integer,1},
                     {f,13}]}}.
{label,13}.
  {move,{atom,a},{x,0}}.
  return.
{label,14}.
  {move,{atom,b},{x,0}}.
  return.
{label,15}.
  {move,{atom,c},{x,0}}.
  return.
{label,16}.
  {line,[{location,"blog.erl",20}]}.
  {case_end,{x,0}}.

The case_end instruction is an optimization to save space. It is shorter than the equivalent:

  {test_heap,3,1}.
  {put_tuple2,{x,0},{list,[{atom,case_clause},{x,0}]}}.
  {line,[{location,"blog.erl",20}]}.
  {call_ext_only,1,{extfunc,erlang,error,1}}.

(The put_tuple2 instruction was introduced in #1947: Introduce a put_tuple2 instruction, which was recently merged to master.)

Our final case

It’s time to address the kind of case similar to what was teased at the end of the previous blog post.

In this example, the variable Y will be assigned different values in each clause of the case:

case3a(X) ->
    case X of
        zero ->
            Y = 0;
        something ->
            Y = X;
        _ ->
            Y = no_idea
    end,
    {ok,Y}.

Perhaps a more common way to write this case would be:

case3b(X) ->
    Y = case X of
            zero -> 0;
            something -> X;
            _ -> no_idea
        end,
    {ok,Y}.

In either case, the problem remains. Static Single Assignment means that each variable can only be given a value once. So how can this example be translated to SSA code?

Here follows the SSA code for case3a/1. The SSA code for case3b/1 is almost identical except for variable naming.

function blog:case3a(_0) {
0:
  switch _0, label 4, [ { literal something, label 6 }, { literal zero, label 5 } ]

5:
  br label 3

6:
  br label 3

4:
  br label 3

3:
  Y = phi { literal no_idea, 4 }, { literal 0, 5 }, { _0, 6 }
  _7 = put_tuple literal ok, Y
  ret _7
}

Let’s jump right to the interesting (and confusing) part of the code:

3:
  Y = phi { literal no_idea, 4 }, { literal 0, 5 }, { _0, 6 }

Clearly, Y is only given a value once, so the SSA property is preserved.

That’s good, but exactly what is the value that is being assigned?

The name of the instruction is phi, which is the name of the Greek letter φ. Having an unusual name, the instruction deserves to have unusual operands, too. Each operand is a pair, the first element in the pair being a value and the second element a block number of a predecessor block. The value of the phi node will be one of the values from one the pairs. But from which pair? That depends on the number of the previous block that branched to the phi instruction.

To make that somewhat clearer, let’s look at all operands:

  • { literal no_idea, 4 }: If the number of block that executed br label 3 was 4, the value of the phi instruction will be the value in this pair, that is, the atom no_idea. The failure label for the switch instruction is 4, so this pair will be chosen when _0 does not match any of the values in the switch list.

  • { literal 0, 5 }: If the number of block that executed br label 3 was 5, the value of the phi instruction will be the integer 0. The switch instruction will transfer control to block 5 if the value of _0 is the atom zero.

  • { _0, 6 }: Finally, if _0 is the atom something, the switch will transfer control to block 6, which will transfer control to block 3. The value of the phi instruction will be the value of the variable _0.

The concept of phi instructions probably feels a bit strange at first sight (and at second sight), and one might also think they must be terribly inefficient.

Leaving the strangeness aside, let’s talk about the efficiency. phi instructions is a fiction convenient for representing and optimizing the code. When translating to BEAM code, the phi instructions are eliminated.

Here follows an example that is not SSA code, because it assigns the variable Y three times, but gives an idea how the phi instruction is eliminated:

%% Not SSA code!
function blog:case3a(_0) {
0:
  switch _0, label 4, [ { literal something, label 6 }, { literal zero, label 5 } ]

5:
  Y := literal 0
  br label 3

6:
  Y := _0
  br label 3

4:
  Y := no_idea
  br label 3

3:
  _7 = put_tuple literal ok, Y
  ret _7
}

The BEAM code generator (beam_ssa_codegen) does a similar rewrite during code generation.

Here is the unoptimized BEAM code, slightly edited for clarity:

%% Block 0.
{select_val,{x,0},
            {f,53},
            {list,[{atom,something},{f,55},{atom,zero},{f,57}]}}.

%% Block 5.
{label,57}.
  {move,{integer,0},{x,0}}.
  {jump,{f,59}}.

%% Block 6.
{label,55}.
  %% The result is already in {x,0}.
  {jump,{f,59}}.

%% Block 4.
{label,53}.
  {move,{atom,no_idea},{x,0}}.
  {jump,{f,59}}.

%% Block 3.
{label,59}.
   {test_heap,3,1}.
   {put_tuple2,{x,0},{list,[{atom,ok},{x,0}]}}.
   return.

Here is the final BEAM code after some more optimizations:

{label,18}.
  {select_val,{x,0},
              {f,20},
              {list,[{atom,something},{f,21},{atom,zero},{f,19}]}}.
{label,19}.
  {move,{integer,0},{x,0}}.
  {jump,{f,21}}.
{label,20}.
  {move,{atom,no_idea},{x,0}}.
{label,21}.
  {test_heap,3,1}.
  {put_tuple2,{x,0},{list,[{atom,ok},{x,0}]}}.
  return.

The cold case

Here is the example from the end of the previous blog post:

bar(X) ->
    case X of
        none ->
            Y = 0;
        _ ->
            Y = X
    end,
    Y + 1.

And here is the SSA code:

function blog:bar(_0) {
0:
  @ssa_bool = bif:'=:=' _0, literal none
  br @ssa_bool, label 5, label 4

5:
  br label 3

4:
  br label 3

3:
  Y = phi { _0, 4 }, { literal 0, 5 }

  %% blog.erl:52
  _6 = bif:'+' Y, literal 1
  @ssa_bool:6 = succeeded _6
  br @ssa_bool:6, label 7, label 1

7:
  ret _6

1:
  @ssa_ret = call remote (literal erlang):(literal error)/1, literal badarg
  ret @ssa_ret
}

It is left as an exercise to the reader to read and understand the code.

Here is the BEAM code:

{label,28}.
  {test,is_eq_exact,{f,29},[{x,0},{atom,none}]}.
  {move,{integer,0},{x,0}}.
{label,29}.
  {line,[{location,"blog.erl",52}]}.
  {gc_bif,'+',{f,0},1,[{x,0},{integer,1}],{x,0}}.
  return.

The gc_bif instruction calls a guard BIF that might need to do a garbage collection. Since integers can be of essentially unlimited size in Erlang, the result of + might not fit in a word. The 1 following {f,0} is the number of registers that must be preserved; in this case, only {x,0}.