Sethi–Ullman algorithm: Difference between revisions

Revision as of 16:36, 9 February 2023

Latest revision as of 15:13, 24 February 2025

(5 intermediate revisions by 3 users not shown)

Line 1:

{{Short description|Algorithm for minimising register usage}}

In [[computer science]], the '''Sethi–Ullman algorithm''' is an [[algorithm]] named after [[Ravi Sethi]] and [[Jeffrey D. Ullman]], its inventors, for translating [[abstract syntax tree]]s into [[machine code]] that uses as few [[Processor register|registers]] as possible.

Line 8 ⟶ 9:

# Traverse the [[abstract syntax tree]] in pre- or postorder

## For every leaf node, if it is a non-constant leaf nodeleft-child, assign a 1 (i.e. 1 register is needed to hold the variable/field/etc.), ifotherwise itassign isa the0 left(it child of its parent else assignis a 0.non-constant Forright child everyor constant leaf node (RHS of an operation – literals, values), assign a 0).

## For every non-leaf node ''n'', assignif the numberleft ofand registers needed to evaluate the respectiveright subtrees ofrespectively ''n''.need Ifdifferent the numbernumbers of registers needed in the left subtree (''l'') areand not equal to the number of registers needed in the right subtree (''r''), thethen number of registers needed for the current nodeassign max(''nl'' is max(l, r). If ''l == r''), thenotherwise the number of registers needed for the current node isassign ''r'' + 1.

# To emit code, if the subtrees need different numbers of registers, evaluate the subtree needing the most registers first (since the register needed to save the result of one subtree may make the other one [[Register spilling|spill]]), otherwise the order is irrelevant.

# Code emission

## If the number of registers needed to compute the left subtree of node ''n'' is bigger than the number of registers for the right subtree, then the left subtree is evaluated first (since it may be possible that the one more register needed by the right subtree to save the result makes the left subtree [[Register spilling|spill]]). If the right subtree needs more registers than the left subtree, the right subtree is evaluated first accordingly. If both subtrees need an equal number of registers, then the order of evaluation is irrelevant.

===Example===

For an arithmetic expression <math>a = (b + c + f * g) * (d + 3)</math>, the [[abstract syntax tree]] looks like this:

=