Sethi–Ullman Algorithm
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Sethi–Ullman Algorithm
In computer science, the Sethi–Ullman algorithm is an algorithm named after Ravi Sethi and Jeffrey D. Ullman, its inventors, for translating abstract syntax trees into machine code that uses as few registers as possible. Overview When 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 spilled to memory and then restored. The Sethi–Ullman algorithm (also known as Sethi–Ullman numbering) produces code which needs the fewest instructions possible as well as the fewest storage references (under the assumption that at the most commutativity and associativity apply to the operators ...
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Computer Science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical disciplines (including the design and implementation of Computer architecture, hardware and Computer programming, software). Computer science is generally considered an area of research, academic research and distinct from computer programming. Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of computational problem, problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and for preventing Vulnerability (computing), security vulnerabilities. Computer graphics (computer science), Computer graphics and computational geometry address the generation of images. Progr ...
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Register Allocation
In compiler optimization, register allocation is the process of assigning local automatic variables and expression results to a limited number of processor registers. Register allocation can happen over a basic block (''local register allocation''), over a whole function/ procedure (''global register allocation''), or across function boundaries traversed via call-graph (''interprocedural register allocation''). When done per function/procedure the calling convention may require insertion of save/restore around each call-site. Context Principle {, class="wikitable floatright" , + Different number of scalar registers in the most common architectures , - ! Architecture ! scope="col" , 32 bits ! scope="col" , 64 bits , - ! scope="row" , ARM , 15 , 31 , - ! scope="row" , Intel x86 , 8 , 16 , - ! scope="row" , MIPS , 32 , 32 , - ! scope="row" , POWER/PowerPC , 32 , 32 , - ! scope="row" , RISC-V , 16/32 , 32 , - ! scope="row" , SP ...
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Journal Of The Association For Computing Machinery
The ''Journal of the ACM'' is a peer-reviewed scientific journal covering computer science in general, especially theoretical aspects. It is an official journal of the Association for Computing Machinery. Its current editor-in-chief is Venkatesan Guruswami. The journal was established in 1954 and "computer scientists universally hold the ''Journal of the ACM'' in high esteem". See also * ''Communications of the ACM ''Communications of the ACM'' is the monthly journal of the Association for Computing Machinery (ACM). It was established in 1958, with Saul Rosen as its first managing editor. It is sent to all ACM members. Articles are intended for readers with ...'' References External links * Publications established in 1954 Computer science journals Association for Computing Machinery academic journals Bimonthly journals English-language journals {{compu-journal-stub ...
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Ershov Number
Ershov numbers, named after Andrey Petrovich Yershov, are used in code optimization to minimize the amount of register allocations. Ershov numbers can be used in methods to optimally select registers when there is only one expression in a code block. Given an expression E = E1 ''op'' E2 the goal is to generate code so as to either minimize the number of registers used, or, if an insufficient number of registers is available, to minimize the number of nonregister temporaries required. Definition The Ershov number ''n'' of a node in given expression tree is defined as follows: # Every leaf has ''n'' = 1. # For a node with one child, ''n'' is the same as child's. # For a node with two children, ''n'' is defined as: : n = \begin max(child_1, child_2) & child_1 \ne child_2 \\ child_1 + 1 & child_1 = child_2 \end The Ershov number of a node represents the minimum number of registers required to evaluate the subexpression whose root is that node. The idea is that we evaluate the ...
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Strahler Number
In mathematics, the Strahler number or Horton–Strahler number of a mathematical tree is a numerical measure of its branching complexity. These numbers were first developed in hydrology by and ; in this application, they are referred to as the Strahler stream order and are used to define stream size based on a hierarchy of tributaries. They also arise in the analysis of L-systems and of hierarchical biological structures such as (biological) trees and animal respiratory and circulatory systems, in register allocation for compilation of high-level programming languages and in the analysis of social networks. Alternative stream ordering systems have been developed by Shreve and Hodgkinson et al.Hodgkinson, J.H., McLoughlin, S. & Cox, M.E. 2006. The influence of structural grain on drainage in a metamorphic sub-catchment: Laceys Creek, southeast Queensland, Australia. Geomorphology, 81: 394–407. A statistical comparison of Strahler and Shreve systems, together with an analysis of ...
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Register Spilling
In compiler optimization, register allocation is the process of assigning local automatic variables and expression results to a limited number of processor registers. Register allocation can happen over a basic block (''local register allocation''), over a whole function/ procedure (''global register allocation''), or across function boundaries traversed via call-graph (''interprocedural register allocation''). When done per function/procedure the calling convention may require insertion of save/restore around each call-site. Context Principle {, class="wikitable floatright" , + Different number of scalar registers in the most common architectures , - ! Architecture ! scope="col" , 32 bits ! scope="col" , 64 bits , - ! scope="row" , ARM , 15 , 31 , - ! scope="row" , Intel x86 , 8 , 16 , - ! scope="row" , MIPS , 32 , 32 , - ! scope="row" , POWER/PowerPC , 32 , 32 , - ! scope="row" , RISC-V , 16/32 , 32 , - ! scope="row" , SP ...
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Associativity
In mathematics, the associative property is a property of some binary operations, which means that rearranging the parentheses in an expression will not change the result. In propositional logic, associativity is a valid rule of replacement for expressions in logical proofs. Within an expression containing two or more occurrences in a row of the same associative operator, the order in which the operations are performed does not matter as long as the sequence of the operands is not changed. That is (after rewriting the expression with parentheses and in infix notation if necessary), rearranging the parentheses in such an expression will not change its value. Consider the following equations: \begin (2 + 3) + 4 &= 2 + (3 + 4) = 9 \,\\ 2 \times (3 \times 4) &= (2 \times 3) \times 4 = 24 . \end Even though the parentheses were rearranged on each line, the values of the expressions were not altered. Since this holds true when performing addition and multiplication on any real ...
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Commutativity
In mathematics, a binary operation is commutative if changing the order of the operands does not change the result. It is a fundamental property of many binary operations, and many mathematical proofs depend on it. Most familiar as the name of the property that says something like or , the property can also be used in more advanced settings. The name is needed because there are operations, such as division and subtraction, that do not have it (for example, ); such operations are ''not'' commutative, and so are referred to as ''noncommutative operations''. The idea that simple operations, such as the multiplication and addition of numbers, are commutative was for many years implicitly assumed. Thus, this property was not named until the 19th century, when mathematics started to become formalized. A similar property exists for binary relations; a binary relation is said to be symmetric if the relation applies regardless of the order of its operands; for example, equality is s ...
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Order Of Evaluation
Order, ORDER or Orders may refer to: * Categorization, the process in which ideas and objects are recognized, differentiated, and understood * Heterarchy, a system of organization wherein the elements have the potential to be ranked a number of different ways * Hierarchy, an arrangement of items that are represented as being "above", "below", or "at the same level as" one another * an action or inaction that must be obeyed, mandated by someone in authority People * Orders (surname) Arts, entertainment, and media * ''Order'' (album), a 2009 album by Maroon * "Order", a 2016 song from ''Brand New Maid'' by Band-Maid * ''Orders'' (1974 film), a 1974 film by Michel Brault * ''Orders'', a 2010 film by Brian Christopher * ''Orders'', a 2017 film by Eric Marsh and Andrew Stasiulis * ''Jed & Order'', a 2022 film by Jedman Business * Blanket order, purchase order to allow multiple delivery dates over a period of time * Money order or postal order, a financial instrument usually intende ...
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Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can perform automated deductions (referred to as automated reasoning) and use mathematical and logical tests to divert the code execution through various routes (referred to as automated decision-making). Using human characteristics as descriptors of machines in metaphorical ways was already practiced by Alan Turing with terms such as "memory", "search" and "stimulus". In contrast, a Heuristic (computer science), heuristic is an approach to problem solving that may not be fully specified or may not guarantee correct or optimal results, especially in problem domains where there is no well-defined correct or optimal result. As an effective method, an algorithm ca ...
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Compiler
In computing, a compiler is a computer program that translates computer code written in one programming language (the ''source'' language) into another language (the ''target'' language). The name "compiler" is primarily used for programs that translate source code from a high-level programming language to a low-level programming language (e.g. assembly language, object code, or machine code) to create an executable program. Compilers: Principles, Techniques, and Tools by Alfred V. Aho, Ravi Sethi, Jeffrey D. Ullman - Second Edition, 2007 There are many different types of compilers which produce output in different useful forms. A ''cross-compiler'' produces code for a different CPU or operating system than the one on which the cross-compiler itself runs. A ''bootstrap compiler'' is often a temporary compiler, used for compiling a more permanent or better optimised compiler for a language. Related software include, a program that translates from a low-level language to a h ...
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