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| 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 instructions as possible.
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| ==Overview==
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| When [[code generation (compiler)|generating code]] for arithmetic expressions, the [[compiler]] has to decide which is the best way to translate the expression in terms of number of instructions used as well as number of registers needed to evaluate a certain subtree. Especially in the case that free registers are scarce, the [[order of evaluation]] can be important to the length of the generated code, because different orderings may lead to larger or smaller numbers of intermediate values being [[register allocation|spilled]] to memory and then restored. The Sethi–Ullman algorithm (also known as '''Sethi–Ullman numbering''') fulfills the property of producing code which needs the least number of instructions possible as well as the least number of storage references (under the assumption that at the most [[commutativity]] and [[associativity]] apply to the operators used, but distributive laws i.e. <math>a * b + a * c = a * (b + c)</math> do not hold). Please note that the algorithm succeeds as well if neither [[commutativity]] nor [[associativity]] hold for the expressions used, and therefore arithmetic transformations can not be applied.
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| ==Simple Sethi–Ullman algorithm==
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| The '''simple Sethi–Ullman algorithm''' works as follows (for a [[RISC|load-store architecture]]):
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| # Traverse the [[abstract syntax tree]] in pre- or postorder
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| ## For every non-constant leaf node, assign a 1 (i.e. 1 register is needed to hold the variable/field/etc.). For every constant leaf node (RHS of an operation – literals, values), assign a 0.
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| ## For every non-leaf node ''n'', assign the number of registers needed to evaluate the respective subtrees of ''n''. If the number of registers needed in the left subtree (''l'') are not equal to the number of registers needed in the right subtree (''r''), the number of registers needed for the current node ''n'' is max(l, r). If ''l == r'', then the number of registers needed for the current node is l + 1.
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| # Code emission
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| ## 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 equal as much registers, then the order of evaluation is irrelevant.
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| ===Example===
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| For an arithmetic expression <math>a = (b + c+ f * g) * (d + 3)</math>, the [[abstract syntax tree]] looks like this:
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| =
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| / \
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| a *
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| / \
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| / \
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| + +
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| / \ / \
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| / \ d 3
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| + *
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| / \ / \
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| b c f g
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| To continue with the algorithm, we need only to examine the arithmetic expression <math>(b + c + f * g) * (d + 3)</math>, i.e. we only have to look at the right subtree of the assignment '=':
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| *
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| / \
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| / \
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| + +
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| / \ / \
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| / \ d 3
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| + *
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| / \ / \
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| b c f g
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| Now we start traversing the tree (in preorder for now), assigning the number of registers needed to evaluate each subtree (note that the last summand in the expression <math>(b + c + f * g) * (d + 3)</math> is a constant):
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| *<sub>'''2'''</sub>
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| / \
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| / \
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| +<sub>'''2'''</sub> +<sub>'''1'''</sub>
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| / \ / \
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| / \ d<sub>'''1'''</sub> 3<sub>'''0'''</sub>
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| +<sub>'''1'''</sub> *<sub>'''1'''</sub>
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| / \ / \
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| b<sub>'''1'''</sub> c<sub>'''0'''</sub>f<sub>'''1'''</sub> g<sub>'''0'''</sub>
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| From this tree it can be seen that we need 2 registers to compute the left subtree of the '*', but only 1 register to compute the right subtree. Nodes 'c' and 'g' do not need registers for the following reasons: If T is a tree leaf, then the number of registers to evaluate T is either 1 or 0 depending whether T is a left or a right subtree(since an operation such as add R1, A can handle the right component A directly without storing it into a register). Therefore we shall start to emit code for the left subtree first, because we might run into the situation that we only have 2 registers left to compute the whole expression. If we now computed the right subtree first (which needs only 1 register), we would then need a register to hold the result of the right subtree while computing the left subtree (which would still need 2 registers), therefore needing 3 registers concurrently. Computing the left subtree first needs 2 registers, but the result can be stored in 1, and since the right subtree needs only 1 register to compute, the evaluation of the expression can do with only 2 registers left.
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| ==Advanced Sethi–Ullman algorithm==
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| In an advanced version of the '''Sethi–Ullman algorithm''', the arithmetic expressions are first transformed, exploiting the algebraic properties of the operators used.
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| ==See also==
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| *[[Strahler number]], the minimum number of registers needed to evaluate an expression without any external storage
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| ==References==
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| *{{citation|title=The Generation of Optimal Code for Arithmetic Expressions|first1=Ravi|last1=Sethi|author1-link=Ravi Sethi|first2=Jeffrey D.|last2=Ullman|author2-link=Jeffrey D. Ullman|journal=[[Journal of the Association for Computing Machinery]]|volume=17|issue=4|year=1970|pages=715–728|doi=10.1145/321607.321620}}.
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| ==External links==
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| *[http://lambda.uta.edu/cse5317/fall02/notes/node40.html Code Generation for Trees]
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| {{DEFAULTSORT:Sethi-Ullman algorithm}}
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| [[Category:Compiler construction]]
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| [[Category:Graph algorithms]]
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Whenever you registry gets cluttered up with a great deal of junk you don't utilize, the PC usually run slower. Therefore it's prudent which you regularly receive your registry cleaned.
Registry cleaning is significant considering the registry could get crowded and messy when it is actually left unchecked. False entries send the operating program trying to find files and directories that have long ago been deleted. This takes time and uses precious resources. So, a slowdown inevitably occurs. It is particularly noticeable whenever we multitask.
Chrome enables customizing itself by applying range of themes available online. If you had lately applied a theme that no longer works correctly, it results in Chrome crash on Windows 7. It is suggested to set the authentic theme.
Many tuneup utilities s let you to download their product for free, thus you can scan the computer yourself. That means you are able to see how many mistakes it finds, where it finds them, plus how it can fix them. A remarkable registry cleaner may remove the registry problems, and optimize plus accelerate the PC, with little effort on your piece.
Reinstall Windows 7 - If nothing appears to function, reinstall Windows 7 with the installation disc that came with all the pack. Kindly backup or restore all a information to a flash drive or another hard drive/CD etc. before performing the reinstallation.
To accelerate a computer, we just have to be capable to get rid of all these junk files, permitting the computer to obtain what it wants, when it wants. Luckily, there's a tool that enables you to do this conveniently plus swiftly. It's a tool called a 'registry cleaner'.
By changing the method you employ the web we can have access more of the precious bandwidth. This usually eventually provide you a quicker surfing experience. Here is a link to 3 techniques to personalize a PC speed online.