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Update optimiser readme.
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@ -2,7 +2,19 @@ Note that the Yul optimiser is still in research phase. Because of that,
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the following description might not fully reflect the current or even
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planned state of the optimiser.
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## Yul Optimiser
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Table of Contents:
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- [Preprocessing](#preprocessing)
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- [Pseudo-SSA Transformation](#pseudo-ssa-transformation)
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- [Tools](#tools)
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- [Expression-Scale Simplifications](#expression-scale-simplifications)
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- [Statement-Scale Simplifications](#statement-scale-simplifications)
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- [Function Inlining](#function-inlining)
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- [Cleanup](#cleanup)
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- [Webassembly-sepcific](#webassembly-specific)
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# Yul Optimiser
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The Yul optimiser consists of several stages and components that all transform
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the AST in a semantically equivalent way. The goal is to end up either with code
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@ -12,7 +24,22 @@ optimisation steps.
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The optimiser currently follows a purely greedy strategy and does not do any
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backtracking.
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## Disambiguator
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All components of the optimiser are explained below, where
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the following transformation steps are the main components:
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- [SSA Transform](#ssa-transform)
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- [Common Subexpression Eliminator](#common-subexpression-eliminator)
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- [Expression Simplifier](#expression-simplifier)
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- [Redundant Assign Eliminator](#redundant-assign-eliminator)
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- [Full Function Inliner](#full-function-inliner)
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## Preprocessing
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The preprocessing components perform transformations to get the program
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into a certain normal form that is easier to work with. This normal
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form is kept during the rest of the optimisation process.
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### Disambiguator
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The disambiguator takes an AST and returns a fresh copy where all identifiers have
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names unique to the input AST. This is a prerequisite for all other optimiser stages.
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@ -22,16 +49,17 @@ and we can basically ignore the result of the analysis phase.
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All subsequent stages have the property that all names stay unique. This means if
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a new identifier needs to be introduced, a new unique name is generated.
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## Function Hoister
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### Function Hoister
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The function hoister moves all function definitions to the end of the topmost block. This is
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a semantically equivalent transformation as long as it is performed after the
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disambiguation stage. The reason is that moving a definition to a higher-level block cannot decrease
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its visibility and it is impossible to reference variables defined in a different function.
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The benefit of this stage is that function definitions can be looked up more easily.
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The benefit of this stage is that function definitions can be looked up more easily
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and functions can be optimised in isolation without having to traverse the AST.
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## Function Grouper
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### Function Grouper
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The function grouper has to be applied after the disambiguator and the function hoister.
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Its effect is that all topmost elements that are not function definitions are moved
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@ -41,22 +69,91 @@ After this step, a program has the following normal form:
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{ I F... }
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Where I is a block that does not contain any function definitions (not even recursively)
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Where I is a (potentially empty) block that does not contain any function definitions (not even recursively)
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and F is a list of function definitions such that no function contains a function definition.
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## Functional Inliner
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The benefit of this stage is that we always know where the list of function begins.
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The functional inliner depends on the disambiguator, the function hoister and function grouper.
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It performs function inlining such that the result of the inlining is an expression. This can
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only be done if the body of the function to be inlined has the form ``{ r := E }`` where ``r``
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is the single return value of the function, ``E`` is an expression and all arguments in the
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function call are so-called movable expressions. A movable expression is either a literal, a
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variable or a function call (or EVM opcode) which does not have side-effects and also does not
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depend on any side-effects.
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As an example, neither ``mload`` nor ``mstore`` would be allowed.
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### For Loop Init Rewriter
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## Expression Splitter
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This transformation moves the initialization part of a for-loop to before
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the loop:
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for { Init... } C { Post... } {
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Body...
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}
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is transformed to
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{
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Init...
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for {} C { Post... } {
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Body...
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}
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}
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This eases the rest of the optimisation process because we can ignore
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the complicated scoping rules of the for loop initialisation block.
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## Pseudo-SSA Transformation
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The purpose of this components is to get the program into a longer form,
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so that other components can more easily work with it. The final representation
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will be similar to a static-single-assignment (SSA) form, with the difference
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that it does not make use of explicit "phi" functions which combines the values
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from different branches of control flow because such a feature does not exist
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in the Yul language. Instead, assignments to existing variables are
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used.
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An example transformation is the following:
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{
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let a := calldataload(0)
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let b := calldataload(0x20)
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if gt(a, 0) {
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b := mul(b, 0x20)
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}
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a := add(a, 1)
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sstore(a, add(b, 0x20))
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}
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When all the following transformation steps are applied, the program will look
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as follows:
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{
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let _1 := 0
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let a_1 := calldataload(_1)
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let _2 := 0x20
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let b_1 := calldataload(_2)
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let b := b_1
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let _3 := 0
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let _4 := gt(a_1, _3)
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if _4 {
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let _5 := 0x20
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let b_2 := mul(b_1, _5)
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b := b_2
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}
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let a_2 := add(a_1, 1)
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let _6 := 0x20
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let _7 := add(b, _6)
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sstore(a_2, _7)
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}
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Note that the only variable that is re-assigned in this snippet is ``b``.
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This re-assignment cannot be avoided because ``b`` has different values
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depending on the control flow. All other variables never change their
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value once they are defined. The advantage of this property is that
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variables can be freely moved around and references to them
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can be exchanged by their initial value (and vice-versa),
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as long as these values are still valid in the new context.
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Of course, the code here is far from being optimised. To the contrary, it is much
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longer. The hope is that this code will be easier to work with and furthermore,
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there are optimiser steps that undo these changes and make the code more
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compact again at the end.
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### Expression Splitter
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The expression splitter turns expressions like ``add(mload(x), mul(mload(y), 0x20))``
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into a sequence of declarations of unique variables that are assigned sub-expressions
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@ -77,19 +174,351 @@ Note that this transformation does not change the order of opcodes or function c
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It is not applied to loop conditions, because the loop control flow does not allow
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this "outlining" of the inner expressions in all cases.
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The final program should be in a form such that with the exception of loop conditions,
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function calls can only appear in the right-hand side of a variable declaration,
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assignments or expression statements and all arguments have to be constants or variables.
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The final program should be in a form such that (with the exception of loop conditions)
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function calls cannot appear nested inside expressions
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and all function call arguments have to be constants or variables.
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The benefits of this form are that it is much easier to re-order the sequence of opcodes
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and it is also easier to perform function call inlining. The drawback is that
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such code is much harder to read for humans.
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and it is also easier to perform function call inlining. Furthermore, it is simpler
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to replace individual parts of expressions or re-organize the "expression tree".
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The drawback is that such code is much harder to read for humans.
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## Expression Joiner
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### SSA Transform
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This stage tries to replace repeated assignments to
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existing variables by declarations of new variables as much as
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possible.
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The reassignments are still there, but all references to the
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reassigned variables are replaced by the newly declared variables.
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Example:
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{
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let a := 1
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mstore(a, 2)
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a := 3
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}
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is transformed to
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{
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let a_1 := 1
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let a := a_1
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mstore(a_1, 2)
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let a_3 := 3
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a := a_3
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}
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Exact semantics:
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For any variable ``a`` that is assigned to somewhere in the code
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(variables that are declared with value and never re-assigned
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are not modified) perform the following transforms:
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- replace ``let a := v`` by ``let a_i := v let a := a_i``
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- replace ``a := v`` by ``let a_i := v a := a_i``
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where ``i`` is a number such that ``a_i`` is yet unused.
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Furthermore, always record the current value of ``i`` used for ``a`` and replace each
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reference to ``a`` by ``a_i``.
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The current value mapping is cleared for a variable ``a`` at the end of each block
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in which it was assigned to and at the end of the for loop init block if it is assigned
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inside the for loop body or post block.
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After this stage, the Redundant Assign Eliminator is recommended to remove the unnecessary
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intermediate assignments.
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This stage provides best results if the Expression Splitter and the Common Subexpression Eliminator
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are run right before it, because then it does not generate excessive amounts of variables.
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On the other hand, the Common Subexpression Eliminator could be more efficient if run after the
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SSA transform.
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### Redundant Assign Eliminator
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The SSA transform always generates an assignment of the form ``a := a_i``, even though
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these might be unnecessary in many cases, like the following example:
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{
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let a := 1
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a := mload(a)
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a := sload(a)
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sstore(a, 1)
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}
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The SSA transform converts this snippet to the following:
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{
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let a_1 := 1
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a := a_1
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let a_2 := mload(a_1)
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a := a_2
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let a_3 := sload(a_2)
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a := a_3
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sstore(a_3, 1)
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}
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The Redundant Assign Eliminator removes all the three assignments to ``a``, because
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the value of ``a`` is not used and thus turn this
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snippet into strict SSA form:
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{
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let a_1 := 1
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let a_2 := mload(a_1)
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let a_3 := sload(a_2)
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sstore(a_3, 1)
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}
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Of course the intricate parts of determining whether an assignment is redundant or not
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are connected to joining control flow.
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The component works as follows in detail:
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The AST is traversed twice: in an information gathering step and in the
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actual removal step. During information gathering, we maintain a
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mapping from assignment statements to the three states
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"unused", "undecided" and "used" which signifies whether the assigned
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value will be used later by a reference to the variable.
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When an assignment is visited, it is added to the mapping in the "undecided" state
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(see remark about for loops below) and every other assignment to the same variable
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that is still in the "undecided" state is changed to "unused".
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When a variable is referenced, the state of any assignment to that variable still
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in the "undecided" state is changed to "used".
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At points where control flow splits, a copy
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of the mapping is handed over to each branch. At points where control flow
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joins, the two mappings coming from the two branches are combined in the following way:
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Statements that are only in one mapping or have the same state are used unchanged.
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Conflicting values are resolved in the following way:
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- "unused", "undecided" -> "undecided"
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- "unused", "used" -> "used"
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- "undecided, "used" -> "used"
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For for-loops, the condition, body and post-part are visited twice, taking
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the joining control-flow at the condition into account.
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In other words, we create three control flow paths: Zero runs of the loop,
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one run and two runs and then combine them at the end.
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Simulating a third run or even more is unnecessary, which can be seen as follows:
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A state of an assignment at the beginning of the iteration will deterministically
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result in a state of that assignment at the end of the iteration. Let this
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state mapping function be called `f`. The combination of the three different
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states `unused`, `undecided` and `used` as explained above is the `max`
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operation where `unused = 0`, `undecided = 1` and `used = 2`.
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The proper way would be to compute
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max(s, f(s), f(f(s)), f(f(f(s))), ...)
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as state after the loop. Since `f` just has a range of three different values,
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iterating it has to reach a cycle after at most three iterations,
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and thus `f(f(f(s)))` has to equal one of `s`, `f(s)`, or `f(f(s))`
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and thus
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max(s, f(s), f(f(s))) = max(s, f(s), f(f(s)), f(f(f(s))), ...).
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In summary, running the loop at most twice is enough because there are only three
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different states.
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For switch statements that have a "default"-case, there is no control-flow
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part that skips the switch.
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When a variable goes out of scope, all statements still in the "undecided"
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state are changed to "unused", unless the variable is the return
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parameter of a function - there, the state changes to "used".
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In the second traversal, all assignments that are in the "unused" state are removed.
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This step is usually run right after the SSA transform to complete
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the generation of the pseudo-SSA.
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## Tools
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### Movability
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Movability is a property of an expression. It roughly means that the expression
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is side-effect free and its evaluation only depends on the values of variables
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and the call-constant state of the environment. Most expressions are movable.
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The following parts make an expression non-movable:
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- function calls (might be relaxed in the future if all statements in the function are movable)
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- opcodes that (can) have side-effects (like ``call`` or ``selfdestruct``)
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- opcodes that read or write memory, storage or external state information
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- opcodes that depend on the current PC, memory size or returndata size
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### Dataflow Analyzer
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The Dataflow Analyzer is not an optimizer step itself but is used as a tool
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by other components. While traversing the AST, it tracks the current value of
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each variable, as long as that value is a movable expression.
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It records the variables that are part of the expression
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that is currently assigned to each other variable. Upon each assignment to
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a variable ``a``, the current stored value of ``a`` is updated and
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all stored values of all variables ``b`` are cleared whenever ``a`` is part
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of the currently stored expression for ``b``.
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At control-flow joins, knowledge about variables is cleared if they have or would be assigned
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in any of the control-flow paths. For instance, upon entering a
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for loop, all variables are cleared that will be assigned during the
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body or the post block.
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## Expression-Scale Simplifications
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These simplification passes change expressions and replace them by equivalent
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and hopefully simpler expressions.
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### Common Subexpression Eliminator
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This step uses the Dataflow Analyzer and replaces subexpressions that
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syntactically match the current value of a variable by a reference to
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that variable. This is an equivalence transform because such subexpressions have
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to be movable.
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All subexpressions that are identifiers themselves are replaced by their
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current value if the value is an identifier.
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The combination of the two rules above allow to compute a local value
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numbering, which means that if two variables have the same
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value, one of them will always be unused. The Unused Pruner or the
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Redundant Assign Eliminator will then be able to fully eliminate such
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variables.
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This step is especially efficient if the expression splitter is run
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before. If the code is in pseudo-SSA form,
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the values of variables are available for a longer time and thus we
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have a higher chance of expressions to be replaceable.
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The expression simplifier will be able to perform better replacements
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if the common subexpression eliminator was run right before it.
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### Expression Simplifier
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The Expression Simplifier uses the Dataflow Analyzer and makes use
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of a list of equivalence transforms on expressions like ``X + 0 -> X``
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to simplify the code.
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It tries to match patterns like ``X + 0`` on each subexpression.
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During the matching procedure, it resolves variables to their currently
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assigned expressions to be able to match more deeply nested patterns
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even when the code is in pseudo-SSA form.
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Some of the patterns like ``X - X -> 0`` can only be applied as long
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as the expression ``X`` is movable, because otherwise it would remove its potential side-effects.
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Since variable references are always movable, even if their current
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value might not be, the Expression Simplifier is again more powerful
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in split or pseudo-SSA form.
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## Statement-Scale Simplifications
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### Unused Pruner
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This step removes the definitions of all functions that are never referenced.
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It also removes the declaration of variables that are never referenced.
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If the declaration assigns a value that is not movable, the expression is retained,
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but its value is discarded.
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All movable expression statements (expressions that are not assigned) are removed.
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### Structural Simplifier
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This is a general step that performs various kinds of simplifications on
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a structural level:
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- replace if statement with empty body by ``pop(condition)``
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- replace if statement with true condition by its body
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- remove if statement with false condition
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- turn switch with single case into if
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- replace switch with only default case by ``pop(expression)`` and body
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- replace switch with literal expression by matching case body
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- replace for loop with false condition by its initialization part
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This component uses the Dataflow Analyzer.
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### Equivalent Function Combiner
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If two functions are syntactically equivalent, while allowing variable
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renaming but not any re-ordering, then any reference to one of the
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functions is replaced by the other.
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The actual removal of the function is performed by the Unused Pruner.
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### Block Flattener
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This stage eliminates nested blocks by inserting the statement in the
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inner block at the appropriate place in the outer block:
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{
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let x := 2
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{
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let y := 3
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mstore(x, y)
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}
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}
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is transformed to
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{
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let x := 2
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let y := 3
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mstore(x, y)
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}
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As long as the code is disambiguated, this does not cause a problem because
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the scopes of variables can only grow.
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## Function Inlining
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||||
### Functional Inliner
|
||||
|
||||
The functional inliner performs restricted function inlining. In particular,
|
||||
the result of this inlining is always a single expression. This can
|
||||
only be done if the function to be inlined has the form ``function f(...) -> r { r := E }`` where
|
||||
``E`` is an expression that does not reference ``r`` and all arguments in the
|
||||
function call are movable expressions. The function call is directly replaced
|
||||
by ``E``, substituting the function call arguments. Because this can cause the
|
||||
function call arguments to be duplicated, removed or re-ordered, they have
|
||||
to be movable.
|
||||
|
||||
### Full Function Inliner
|
||||
|
||||
The Full Function Inliner replaces certain calls of certain functions
|
||||
by the function's body. This is not very helpful in most cases, because
|
||||
it just increases the code size but does not have a benefit. Furthermore,
|
||||
code is usually very expensive and we would often rather have shorter
|
||||
code than more efficient code. In same cases, though, inlining a function
|
||||
can have positive effects on subsequent optimizer steps. This is the case
|
||||
if one of the function arguments is a constant, for example.
|
||||
|
||||
During inlining, a heuristic is used to tell if the function call
|
||||
should be inlined or not.
|
||||
The current heuristic does not inline into "large" functions unless
|
||||
the called function is tiny. Functions that are only used once
|
||||
are inlined, as well as medium-sized functions, while function
|
||||
calls with constant arguments allow slightly larger functions.
|
||||
|
||||
|
||||
In the future, we might want to have a backtracking component
|
||||
that, instead of inlining a function right away, only specializes it,
|
||||
which means that a copy of the function is generated where
|
||||
a certain parameter is always replaced by a constant. After that,
|
||||
we can run the optimizer on this specialized function. If it
|
||||
results in heavy gains, the specialized function is kept,
|
||||
otherwise the original function is used instead.
|
||||
|
||||
## Cleanup
|
||||
|
||||
The cleanup is performed at the end of the optimizer run. It tries
|
||||
to combine split expressions into deeply nested ones again and also
|
||||
improves the "compilability" for stack machines by eliminating
|
||||
variables as much as possible.
|
||||
|
||||
### Expression Joiner
|
||||
|
||||
This is the opposite operation of the expression splitter. It turns a sequence of
|
||||
variable declarations that have exactly one reference into a complex expression.
|
||||
This stage again fully preserves the order of function calls and opcode executions.
|
||||
This stage fully preserves the order of function calls and opcode executions.
|
||||
It does not make use of any information concerning the commutability of opcodes;
|
||||
if moving the value of a variable to its place of use would change the order
|
||||
of any function call or opcode execution, the transformation is not performed.
|
||||
@ -97,23 +526,69 @@ of any function call or opcode execution, the transformation is not performed.
|
||||
Note that the component will not move the assigned value of a variable assignment
|
||||
or a variable that is referenced more than once.
|
||||
|
||||
## Common Subexpression Eliminator
|
||||
The snippet ``let x := add(0, 2) let y := mul(x, mload(2))`` is not transformed,
|
||||
because it would cause the order of the call to the opcodes ``add`` and
|
||||
``mload`` to be swapped - even though this would not make a difference
|
||||
because ``add`` is movable.
|
||||
|
||||
This step replaces a subexpression by the value of a pre-existing variable
|
||||
that currently has the same value (only if the value is movable), based
|
||||
on a syntactic comparison.
|
||||
When reordering opcodes like that, variable references and literals are ignored.
|
||||
Because of that, the snippet ``let x := add(0, 2) let y := mul(x, 3)`` is
|
||||
transformed to ``let y := mul(add(0, 2), 3)``, even though the ``add`` opcode
|
||||
would be executed after the evaluation of the literal ``3``.
|
||||
|
||||
This can be used to compute a local value numbering, especially if the
|
||||
expression splitter is used before.
|
||||
### SSA Reverser
|
||||
|
||||
The expression simplifier will be able to perform better replacements
|
||||
if the common subexpression eliminator was run right before it.
|
||||
This is a tiny step that helps in reversing the effects of the SSA transform
|
||||
if it is combined with the Common Subexpression Eliminator and the
|
||||
Unused Pruner.
|
||||
|
||||
Prerequisites: Disambiguator
|
||||
The SSA form we generate is detrimental to code generation on the EVM and
|
||||
WebAssembly alike because it generates many local variables. It would
|
||||
be better to just re-use existing variables with assignments instead of
|
||||
fresh variable declarations.
|
||||
|
||||
## Full Function Inliner
|
||||
The SSA transform rewrites
|
||||
|
||||
## Rematerialisation
|
||||
a := E
|
||||
mstore(a, 1)
|
||||
|
||||
to
|
||||
|
||||
let a_1 := E
|
||||
a := a_1
|
||||
mstore(a_1, 1)
|
||||
|
||||
The problem is that instead of ``a``, the variable ``a_1`` is used
|
||||
whenever ``a`` was referenced. The SSA transform changes statements
|
||||
of this form by just swapping out the declaration and the assignment. The above
|
||||
snippet is turned into
|
||||
|
||||
a := E
|
||||
let a_1 := a
|
||||
mstore(a_1, 1)
|
||||
|
||||
This is a very simple equivalence transform, but when we now run the
|
||||
Common Subexpression Eliminator, it will replace all occurrences of ``a_1``
|
||||
by ``a`` (until ``a`` is re-assigned). The Unused Pruner will then
|
||||
eliminate the variable ``a_1`` altogether and thus fully reverse the
|
||||
SSA transform.
|
||||
|
||||
### Stack Compressor
|
||||
|
||||
One problem that makes code generation for the Ethereum Virtual Machine
|
||||
hard is the fact that there is a hard limit of 16 slots for reaching
|
||||
down the expression stack. This more or less translates to a limit
|
||||
of 16 local variables. The stack compressor takes Yul code and
|
||||
compiles it to EVM bytecode. Whenever the stack difference is too
|
||||
large, it records the function this happened in.
|
||||
|
||||
For each function that caused such a problem, the Rematerialiser
|
||||
is called with a special request to aggressively eliminate specific
|
||||
variables sorted by the cost of their values.
|
||||
|
||||
On failure, this procedure is repeated multiple times.
|
||||
|
||||
### Rematerialiser
|
||||
|
||||
The rematerialisation stage tries to replace variable references by the expression that
|
||||
was last assigned to the variable. This is of course only beneficial if this expression
|
||||
@ -123,31 +598,10 @@ point of use. The main benefit of this stage is that it can save stack slots if
|
||||
leads to a variable being eliminated completely (see below), but it can also
|
||||
save a DUP opcode on the EVM if the expression is very cheap.
|
||||
|
||||
The algorithm only allows movable expressions (see above for a definition) in this case.
|
||||
Expressions that contain other variables are also disallowed if one of those variables
|
||||
have been assigned to in the meantime. This is also not applied to variables where
|
||||
assignment and use span across loops and conditionals.
|
||||
|
||||
## Unused Definition Pruner
|
||||
|
||||
If a variable or function is not referenced, it is removed from the code.
|
||||
If there are two assignments to a variable where the first one is a movable expression
|
||||
and the variable is not used between the two assignments (and the second is not inside
|
||||
a loop or conditional, the first one is not inside), the first assignment is removed.
|
||||
|
||||
This step also removes movable expression statements.
|
||||
|
||||
|
||||
## Function Unifier
|
||||
|
||||
## Expression Simplifier
|
||||
|
||||
This step can only be applied for the EVM-flavoured dialect of Yul. It applies
|
||||
simple rules like ``x + 0 == x`` to simplify expressions.
|
||||
|
||||
## Ineffective Statement Remover
|
||||
|
||||
This step removes statements that have no side-effects.
|
||||
The Rematerialiser uses the Dataflow Analyzer to track the current values of variables,
|
||||
which are always movable.
|
||||
If the value is very cheap or the variable was explicitly requested to be eliminated,
|
||||
the variable reference is replaced by its current value.
|
||||
|
||||
## WebAssembly specific
|
||||
|
||||
|
@ -34,7 +34,7 @@ namespace yul
|
||||
* - turn switch with single case into if
|
||||
* - replace switch with only default case with pop(expression) and body
|
||||
* - replace switch with const expr with matching case body
|
||||
* - remove for with false condition
|
||||
* - replace for with false condition by its initialization part
|
||||
*
|
||||
* Prerequisites: Disambiguator
|
||||
*
|
||||
|
@ -64,8 +64,8 @@ void UnusedPruner::operator()(Block& _block)
|
||||
{
|
||||
VariableDeclaration& varDecl = boost::get<VariableDeclaration>(statement);
|
||||
// Multi-variable declarations are special. We can only remove it
|
||||
// if all vairables are unused and the right-hand-side is either
|
||||
// movable or it return a single value. In the latter case, we
|
||||
// if all variables are unused and the right-hand-side is either
|
||||
// movable or it returns a single value. In the latter case, we
|
||||
// replace `let a := f()` by `pop(f())` (in pure Yul, this will be
|
||||
// `drop(f())`).
|
||||
if (boost::algorithm::none_of(
|
||||
|
Loading…
Reference in New Issue
Block a user