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Control Flow Graph
In computer science, a control-flow graph (CFG) is a representation, using graph notation, of all paths that might be traversed through a program during its execution. The control-flow graph was conceived by Frances E. Allen, who noted that Reese T. Prosser used boolean connectivity matrices for flow analysis before. The CFG is essential to many compiler optimizations and static-analysis tools. Definition In a control-flow graph each node in the graph represents a basic block, i.e. a straight-line sequence of code with a single entry point and a single exit point, where no branches or jumps occur within the block. Basic blocks start with jump targets and end with jumps or branch instructions. Directed edges are used to represent jumps in the control flow. There are, in most presentations, two specially designated blocks: the ''entry block'', through which control enters into the flow graph, and the ''exit block'', through which all control flow leaves. Because of its co ...
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Some Types Of Control Flow Graphs
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Exception Handling
In computing and computer programming, exception handling is the process of responding to the occurrence of ''exceptions'' – anomalous or exceptional conditions requiring special processing – during the execution of a program. In general, an exception breaks the normal flow of execution and executes a pre-registered ''exception handler''; the details of how this is done depend on whether it is a hardware or software exception and how the software exception is implemented. Exceptions are defined by different layers of a computer system, and the typical layers are CPU-defined interrupts, operating system (OS)-defined signals, programming language-defined exceptions. Each layer requires different ways of exception handling although they may be interrelated, e.g. a CPU interrupt could be turned into an OS signal. Some exceptions, especially hardware ones, may be handled so gracefully that execution can resume where it was interrupted. Definition The definition of an excep ...
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Depth-first Search
Depth-first search (DFS) is an algorithm for traversing or searching tree or graph data structures. The algorithm starts at the root node (selecting some arbitrary node as the root node in the case of a graph) and explores as far as possible along each branch before backtracking. Extra memory, usually a stack, is needed to keep track of the nodes discovered so far along a specified branch which helps in backtracking of the graph. A version of depth-first search was investigated in the 19th century by French mathematician Charles Pierre Trémaux as a strategy for solving mazes. Properties The time and space analysis of DFS differs according to its application area. In theoretical computer science, DFS is typically used to traverse an entire graph, and takes time where , V, is the number of vertices and , E, the number of edges. This is linear in the size of the graph. In these applications it also uses space O(, V, ) in the worst case to store the stack of vertices on t ...
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Lengauer–Tarjan's Algorithm
In computer science, a node of a control-flow graph dominates a node if every path from the ''entry node'' to must go through . Notationally, this is written as (or sometimes ). By definition, every node dominates itself. There are a number of related concepts: * A node ''strictly dominates'' a node if dominates and does not equal . * The ''immediate dominator'' or idom of a node is the unique node that strictly dominates but does not strictly dominate any other node that strictly dominates . Every node reachable from the entry node has an immediate dominator (except the entry node). * The ''dominance frontier'' of a node is the set of all nodes such that dominates an immediate predecessor of , but does not strictly dominate . It is the set of nodes where 's dominance stops. * A ''dominator tree'' is a tree where each node's children are those nodes it immediately dominates. The start node is the root of the tree. History Dominance was first introduced by Re ...
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Jump Threading
In computing, jump threading is a compiler optimization of one jump directly to a second jump. If the second condition is a subset or inverse of the first, it can be eliminated, or threaded through the first jump. This is easily done in a single pass through the program, following acyclic chained jumps until the compiler arrives at a fixed point. Benefits The primary benefit of jump threading is the reduction of the amount of dynamically executed jumps. This makes way for further optimizations as there is a decrease in the number of conditionals, which will improve performance. On average one can expect 2-3 instructions being omitted as a result from a successful removal of a runtime branch. Examples The following pseudocode demonstrates when a jump may be threaded. 10. a = SomeNumber(); 20. IF a > 10 GOTO 50 ... 50. IF a > 0 GOTO 100 ... The jump on line 50 will always be taken if the jump on line 20 is taken. Therefore, for as long as line 100 is within ...
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Constant Folding
Constant folding and constant propagation are related compiler optimizations used by many modern compilers. An advanced form of constant propagation known as sparse conditional constant propagation can more accurately propagate constants and simultaneously remove dead code. Constant folding Constant folding is the process of recognizing and evaluating constant expressions at compile time rather than computing them at runtime. Terms in constant expressions are typically simple literals, such as the integer literal 2, but they may also be variables whose values are known at compile time. Consider the statement: i = 320 * 200 * 32; Most compilers would not actually generate two multiply instructions and a store for this statement. Instead, they identify constructs such as these and substitute the computed values at compile time (in this case, 2,048,000). Constant folding can make use of arithmetic identities. If x is numeric, the value of 0 * x is zero even if the compiler ...
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Halting Problem
In computability theory (computer science), computability theory, the halting problem is the problem of determining, from a description of an arbitrary computer program and an input, whether the program will finish running, or continue to run forever. The halting problem is ''Undecidable problem, undecidable'', meaning that no general algorithm exists that solves the halting problem for all possible program–input pairs. The problem comes up often in discussions of computability since it demonstrates that some functions are mathematically Definable set, definable but not Computable function, computable. A key part of the formal statement of the problem is a mathematical definition of a computer and program, usually via a Turing machine. The proof then shows, for any program that might determine whether programs halt, that a "pathological" program exists for which makes an incorrect determination. Specifically, is the program that, when called with some input, passes its own s ...
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Infinite Loop
In computer programming, an infinite loop (or endless loop) is a sequence of instructions that, as written, will continue endlessly, unless an external intervention occurs, such as turning off power via a switch or pulling a plug. It may be intentional. There is no general algorithm to determine whether a computer program contains an infinite loop or not; this is the halting problem. Overview This differs from "a type of computer program that runs the same instructions continuously until it is either stopped or interrupted". Consider the following pseudocode: how_many = 0 while is_there_more_data() do how_many = how_many + 1 end display "the number of items counted = " how_many ''The same instructions'' were run ''continuously until it was stopped or interrupted'' . . . by the ''FALSE'' returned at some point by the function ''is_there_more_data''. By contrast, the following loop will not end by itself: birds = 1 fish = 2 while birds + fish > 1 do birds = 3 - bird ...
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Unreachable Code
In computer programming, unreachable code is part of the source code of a program which can never be executed because there exists no control flow path to the code from the rest of the program. Unreachable code is sometimes also called ''dead code'', although dead code may also refer to code that is executed but has no effect on the output of a program. Unreachable code is generally considered undesirable for several reasons: * It uses memory unnecessarily * It can cause unnecessary use of the CPU's instruction cache ** This can also decrease data locality * Time and effort may be spent testing, maintaining and documenting code which is never used ** Sometimes an automated test is the only thing using the code. Unreachable code can have some legitimate uses, like providing a library of functions for calling or jumping to manually via a debugger while the program is halted after a breakpoint. This is particularly useful for examining and pretty-printing the internal state of th ...
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