Good evening! [In Arabic language]
In the last episode,
we created a parser for a B-like programming language.
It parses each function into a tree structure,
where expressions contain expressions.
Today we will focus on optimization.
As I have said before,
much in programming is actually work –
towards making the work itself easier.
The code I wrote so far –
does not single-mindedly just aim towards the end result.
Code like this, for instance, helps constructing expressions –
using much shorter code than would be otherwise necessary.
In that similar mindset, these functions I just added –
help identifying the type of the expression or identifier.
However today the video topic is optimization.
In the interest of getting this video out in reasonable time,
I am going to compromise a little bit on good programming practices.
I start by taking the list of functions out –
from inside the main program,
and moving it into a global variable.
This will simplify the rest of this episode quite a bit.
Much of the optimizations in today's episode –
concern with replacing code with simpler alternatives –
that accomplish the same outcome.
One of the most important factors,
that decide whether some code can be replaced with some other code –
is whether that code has side-effects or not.
A side-effect is when an expression produces any other outcome –
than its return value.
In this is_pure() function,
we already wrote some basic rules in episode 1,
but so far we assumed that –
any function call automatically taints the expression as inpure.
This is not necessarily the case.
Calling a pure function,
such as one that simply returns the sum of two variables,
is a pure expression.
For example, replacing two calls to the same function with one call,
or deleting the call entirely,
will not change how the program works –
assuming the same result is calculated.
We need a way to classify functions.
This is more complicated than it sounds;
the pure_fcall cannot just make the decision when it is called.
Instead, if will check a precalculated variable.
There is one variable that indicates whether the function is pure,
and another that tells –
whether we even know whether the function is pure or not.
Of course, we need a way to calculate these variables.
My language does not have any global variables,
but it has pointers.
If a function takes a pointer parameter,
and it dereferences a pointer on the left side of an assign operator,
we can assume the function has side-effects.
It causes changes outside strictly its return value.
Of course, the effect is commutative.
No, viral.
No, what's the term for that?
If the function calls another function that has side-effects,
this function, too, will have side-effects.
Because the dependency chain between functions may run in any order,
we must loop this resolving process –
until we no longer can label any function as certainly pure or impure.
To implement this function right now,
we needed a special kind of for-loop –
that iterates through all sub-expressions in an expression tree.
Here is how I defined the for_all_expr function.
It operates on the depth-first principle.
The first node to be processed will be the deepest possible child node.
After all child nodes have been processed,
only then does the parent node get processed too.
For convenience's sake,
I decided to support two kinds of functors.
Those which return a boolean value, false or true,
to indicate whether the caller found whatever it looked for,
and the processing should be stopped immediately,
and those that return nothing.
To support both conventions, a helper function is needed,
that unifies both types of functions.
If the provided functor returns nothing,
this function returns the default parameter given.
Otherwise it returns whatever the functor returns.
I am surprised that –
there is not such a function already in the standard library.
While we are at it,
let's add a function that compares two expressions –
and tells whether they are equal.
This will be very helpful later.
The first category of optimizations is called "constant folding".
We are going to walk through every single expression in the code,
and optimize them using this ConstantFolding function.
We begin by checking the type of the expression.
If the expression is, say, a negate operation,
and the parameter is an integer constant,
we can replace the negate operation with the negated integer constant.
If the expression is an equals-comparison,
and both operands are integer constants,
we can perform the comparison at compile-time –
and simply replace the expression with an integer constant,
zero or one.
The same can be done if the operands are identical pure expressions.
Actually, the name of this function is a bit of a misnomer.
This function does all sorts of simplifications.
For instance, pointer expressions can be simplified,
if an address-of operator is immediately followed by a dereference operator,
or vice versa.
If an assign-statement has the same expression on both sides,
the assign-operation is redundant –
and can be replaced with the source operand,
assuming the operand has no side effects.
If we know at compile time that a loop operation will never loop,
we can delete the entire loop statement.
Now the add-operation requires much more work.
Let's get back to that later,
because there is a certain general principle we must take care of first.
Let me show you what I mean.
This is the tree structures that the compiler generates –
when it parses an add-expression that contains four operands.
It generates three add-expressions, that each have two operands.
But the thing is, this exact same outcome –
can be accomplished with many different structures.
Some of these work only because the add-operator is commutative,
meaning the order of operations does not matter,
but the simplest possible structure is the one shown in the lower-right corner,
where we have exactly one add-operator, and four parameters.
Interestingly enough, this same optimization can be performed –
on some operators that are not commutative,
as long as you keep the order of execution unchanged.
For example the and-operator.
All of these trees perform the same sequence of operations,
but again the fourth one is the simplest one.
So for add, comma, logical or, and logical and operators,
check if any child expression is the same type as the parent expression.
For every such child that is found, adopt the grandchildren directly.
Now the add-expression may contain an assorted mixture –
of all kinds of expressions, including number literals.
Just in case there are multiple number literals in the add-group,
or maybe there is a zero there, we'll quickly sum them up.
If the sum is nonzero, we'll add it back.
While we are at it, we can also convert negations –
into a slightly more efficient format.
After all this work, there is a possibility –
that the expression has been reduced into just a single operand,
or possibly into nothing at all.
In such cases, the expression can be reduced further.
But we are only getting started!
Next let's tackle the && and || operators.
Consider this example expression.
Consider how this is evaluated.
First, "a" is checked.
If it is zero, the process stops and the && evaluates into 0.
Otherwise, "b" is checked.
If it is zero, the process stops and the && evaluates into 0.
Otherwise, one is checked.
Well, one is not zero.
So the next expression is checked.
"x" is stored into "c".
If the result is zero, the process stops and the && evaluates into 0.
Otherwise, "d" is checked.
If it is zero, the process stops and the && evaluates into 0.
Well, zero is zero.
So the process stops and && evaluates into 0.
There are two observations to be made here.
The value of "e" was never checked,
because the literal zero that preceded it –
meant that nothing that comes after it is evaluated!
Also, because of the presence of the zero,
we know the && expression always returns zero in this case.
Technically, all of these expressions that we evaluated were useless.
We can optimize the expression like this.
The literal 1 expression was deleted,
because that cannot contribute to the result in any manner.
"e" was also removed, because it is never evaluated.
"d" was removed too,
because this expression has no side-effects,
so it does not influence the outcome in any manner.
However, neither "a" nor "b" can be removed,
because their values determine –
whether the assignment expression gets executed or not.
The assignment expressions is not a pure expression,
so it cannot be deleted either.
Finally, because we already know what the && operator will return:
always a zero,
we can simply ignore the return value –
and just return a literal zero using a comma operator.
This may benefit other optimizations that come later.
The || operator works exactly the same,
except that the consequences of zero and nonzero are reversed.
So, delete all operands that cannot possibly change the outcome.
If an operand is encountered –
that shortcuts the evaluation and forces the outcome,
delete all operands that came after that operand.
Next, we tackle the comma expressions.
This is where it gets complicated,
but let's start gentle.
Comma expressions are basically sequences of operations.
If we encounter an operation –
that prevents anything after it from being executed,
such as a return statement,
the remaining operations in the comma can be deleted.
This is one particular special case that I also deal with here.
Have a look at this comma expression.
No, wait.
This one.
That's actually an optimization I am yet to write.
Here.
This is a comma expression.
A sequence of assorted operations.
Only the result of the last expression is important;
In this case it is the assignment into z.
But expressions with side-effects have to be kept too.
While the dereference of "s" is not an expression with side-effects,
and of course neither is plus operation on the far left side,
the assignment operation has side-effects, so that one has to be kept.
So, we loop through all the parameters.
Any pure expressions, except the last, will be deleted.
However, even if the expression is not pure,
its impurity may be limited.
For certain types of expressions,
we can skip over the calculation and just rob the operands.
We can also apply the exact same logic into while-loops,
as long as we are careful –
to not accidentally delete the loop condition expression.
Consider this expression: x + 3 + (y = 4)
This expression accomplishes two things:
It assigns y := 4.
And it returns a value.
What does it return?
It returns x + 7.
However, currently the code cannot optimize this as x + 7,
because the 4 is hidden inside the parenthesis-expression.
A naïve attempt would be to sum these two numeric literals,
which would produce this expression.
But this would be a blunder.
While the expression does now correctly return x + 7,
it no longer assigns y := 4.
It now assigns y := 7.
So we cannot do that.
The correct way to optimize is shown on the right.
A comma expression is created between the = and + operations,
and the right-hand side of the assign expression is duplicated.
This way,
other optimizations will eventually convert this expression like this.
The result is exactly what we wanted in the first place:
y := 4, and then x + 7 is calculated and this value is the result.
However!
If the right-hand side of the assign expression has side-effects,
the optimization I proposed here would be a mistake,
because it causes the expression to be evaluated twice.
This is what must be done instead.
The result of the side-effect expression is assigned into a temporary variable,
and that temporary variable can be then copied –
as many times as necessary.
The next operation is fascinating.
Consider this example expression: z := the sum of x++ and y++.
The parser generates this complicated tree for this expression.
There are two comma expressions,
and the sum of these comma expressions is assigned into z.
This is what we can convert it into.
Two things have happened here.
First, the comma expressions from the inside of the outer sum expression –
have been extracted, so that only the last components –
of the comma expressions are retained in the sum.
Then, the assign into z is moved inside the comma expression.
This produces an overall much flatter tree structure than we started with.
Where there were six nested levels of expressions before,
there are now at most three,
yet it still behaves exactly the same as before.
We can also do the same operation –
for the first element in && and || expressions,
as long as we only operate on the first element.
We begin by scanning the parameter list –
backwards from the end anchor, until we find a comma expression.
This delimits the parameters into two sections.
The first section will be processed.
If there is a comma expression,
its parameters will be moved into the outer comma expression,
except for the last one.
If something was moved,
then this expression is replaced with a comma –
where the original expression is its last item.
However,
for anything except the last parameter in the first section,
the expression is moved into a temporary variable –
and that temporary variable s put in its place.
This ensures the unchanging of the evaluation order –
of different expressions.
Now if we take these rules for the "if" expression,
and try to apply it to the "while" expression verbatim,
we will produce incorrect behavior.
In the original expression, x gets incremented on each loop,
but in this modified form, x gets incremented only once,
before the loop.
Here is how it must be corrected.
The parts that were extracted –
from inside the loop to the outside of the loop –
must be replicated at the end of the loop.
Yes, this optimization may actually make the code longer.
But it has to be done,
if we wish to enable certain other optimizations to work.
Now you may have noticed that –
this optimization function does not necessarily bring out –
the best possible result immediately.
It may have to be run multiple times.
We will simply run this loop as long –
as running the optimization for one of the functions –
produces any changes to the structure.
I created a couple of testcases to make sure this works as intended.
In this layout, on the top you can see the original code.
On the left, what the parser produced for this code,
and on its right side, how it was optimized.
This first example shows how powerful the add-expression flattener is.
You can also see it calculated the sum of 4 + 7 at compile time,
despite them being in separate sub-expressions.
In the second example I modified the numbers so that their sum is zero.
You can see the integer literal is completely absent –
from the optimized output,
because adding zero to something would not accomplish anything.
The third example experiments with the negation operations.
The original expression contains five negations,
but the optimized expression contains only four.
You can verify this on pen and paper,
if you don't believe this optimization was correct.
The simple removal of two consecutive neg-operations seems to work alright.
An odd number of neg-operations still retains one, as it should.
Pairs of address-of and dereference operations get reduced, too.
This is one of the tests for the comma reducer.
Ignore the first two functions;
they are just artificial examples –
of pure and impure functions for the sake of the test.
The actual test function contains a sequence of five statements,
plus the implicit return statement.
As we can see, the optimizer detected all the pure expressions –
and deleted them.
The last expression in the list is kept, even though it is pure,
because it is returned as the function return value.
This testcase has three functions.
In the top example, x is stored into x.
Somehow it gets optimized into nothing.
How come?
Let's look at the middle function first.
x is stored into x, and then it is returned.
Storing a variable into itself –
gets optimized into just the variable itself.
Now, when we look back at the first function,
we can guess what happened.
First, the self-assignment got optimized as just the variable.
Then, the variable was removed,
because it was a pure expression in a comma statement.
The assignment was not a pure expression,
but the variable alone was pure.
So it got removed.
Only the return statement remains.
In the third function,
the left-hand side and the right-hand side –
of the assign expression are not identical,
so the assignment was not removed.
However, the source operand was duplicated for the return value.
And here it seems there is actually a bug in my design!
If you pass, say, number eight, as a parameter to this function,
you would expect that the function returns nine.
But the "optimized" version first increments the variable once,
and then increments it again when returning,
so it actually returns ten instead of nine!
This is a bug that must be fixed!
Let's make a note about that.
This is why we test.
Here is another example of the comma optimization.
Here, this function contains two return statements.
The second return statement can never be reached,
so the optimizer deleted it.
The function always returns 100.
In this example we have two while-loops.
The first while-loop will never run,
because the loop condition is known at compile-time to be false.
So it was deleted.
The second while-loop, on the other hand,
never terminates.
It is an infinite loop.
So any code that comes after that is dead code;
it can never be reached.
So the rest of the code was deleted by the optimizer.
Then we have the && sequence.
This is exactly the same example as earlier at 9:21 in this video.
The one was deleted, because it cannot change the result.
The zero was deleted, because it forces the result.
The "e" was deleted, because it would never be evaluated –
because of the zero.
This is the || version.
Here, because the compiler knows at compile-time –
that this || expression will always match because of the 1-literal,
it made that assignment into x explicit rather than conditional.
This function does two postincrements.
There is nothing too interesting about this test,
other than that the optimized tree is a great deal simpler than the original one.
The optimizer did not notice –
that the value of "x" is never used after it is incremented,
and technically it could delete the whole addition,
but that's all right:
I didn't write that kind of optimization yet.
We will get to that topic in the third or fourth episode.
This is almost the same as the previous one,
except now we have a function call instead of an addition.
There is something weird here.
Notice the function call?
It seems to have created a temporary variable,
stored a function pointer into that variable,
and then called the function indirectly at the end.
This is not incorrect behavior, but it is certainly odd,
and very likely a pessimization.
I will have to fix that.
This is the optimization –
that I explained in great detail at 14:11 in this video.
The assign expression is flattened out –
in order to make the add-expression optimizable…
But something is wrong here.
The compiler has created a temporary variable –
for the number three literal,
and this blocks the optimizer –
from performing the very purpose it was designed to do.
I will have to fix this too!
The problem with the last two tests –
was that the compiler created temporary variables –
for simple expressions that were effectively compile-time constants.
The is_pure() function is not enough to detect these situations.
We need a second classification method –
that determines whether an expression conveys a compile-time constant.
A compile-time constant is a number literal –
or a string literal, or a function identifier,
or any simple expression –
that consists of only compile-time constants.
We can immediately use this function to simplify some existing code.
So here!
This is the loop –
that hoists sub-expressions out from parents –
and replaces them with temporaries.
We will just simply check that –
if the expression is a compile-time constant,
the hoisting is not performed.
Done.
Then there was that problem with the x+1 assignment going wrong.
This is easiest to fix here, when checking for the self-assignment.
In short,
if the target expression is also used in the source expression,
a temporary variable will be created,
and that temporary variable will be referred to –
in each location in the source expression.
Then, it no longer matters if the temporary variable gets duplicated.
Now let's get back to test 7.
This is how it changed.
The +1 expression still gets duplicated, but the function does not change;
a bug is not introduced, which is the most important thing.
It would be nice,
if the whole source expression did not have to be duplicated —
it really does not need to be duplicated —
but no optimizer is perfect.
If I copied the target expression instead of the source expression,
that plus-seven optimization would be impossible.
Speaking of that.
This is what happens when the source expression is not duplicated properly,
but dubious temporary variables are created.
And we fixed that.
Now, it gets optimized properly as was originally intended,
thanks to the compile-time constant detection.
Technically that assignment into a temporary variable –
is unnecessary here, but it does not hurt.
In the next episode –
we will deal with a whole new category of optimizations –
that makes all these temporary variables not matter in the least.
We will create a register-based intermediate language –
that is one step closer to actual machine code.
Subscribe to my channel and click the bell icon –
to make sure you won't miss one episode!
As always, thank you for all your support.
In case you have questions,
make sure you first check the video description,
the links in the video description; and the top-fiveish comments —
to make sure your question has not been already answered twenty times.
I do appreciate and heartily welcome all of your comments,
thumbsups, shares, and so on,
but it will make things faster for you –
if you just spent ten seconds –
looking first whether your question has already been answered.
Have a most pleasant and fulfilling day!
See you again! [In Arabic language]
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