Off-by-one
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Off-by-one
An off-by-one error or off-by-one bug (known by acronyms OBOE, OBO, OB1 and OBOB) is a logic error involving the discrete equivalent of a boundary condition. It often occurs in computer programming when an iterative loop iterates one time too many or too few. This problem could arise when a programmer makes mistakes such as using "is less than or equal to" where "is less than" should have been used in a comparison, or fails to take into account that a sequence starts at zero rather than one (as with array indices in many languages). This can also occur in a mathematical context. Cases Looping over arrays Consider an array of items, and items ''m'' through ''n'' (inclusive) are to be processed. How many items are there? An intuitive answer may be ''n'' − ''m'', but that is off by one, exhibiting a fencepost error; the correct answer is (''n'' – ''m'') + 1. For this reason, ranges in computing are often represented by half-open intervals; t ...
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Fencepost Error
An off-by-one error or off-by-one bug (known by acronyms OBOE, OBO, OB1 and OBOB) is a logic error involving the discrete equivalent of a boundary condition. It often occurs in computer programming when an iterative loop iterates one time too many or too few. This problem could arise when a programmer makes mistakes such as using "is less than or equal to" where "is less than" should have been used in a comparison, or fails to take into account that a sequence starts at zero rather than one (as with array indices in many languages). This can also occur in a mathematical context. Cases Looping over arrays Consider an array of items, and items ''m'' through ''n'' (inclusive) are to be processed. How many items are there? An intuitive answer may be ''n'' − ''m'', but that is off by one, exhibiting a fencepost error; the correct answer is (''n'' – ''m'') + 1. For this reason, ranges in computing are often represented by half-open intervals; the r ...
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Computer Programming
Computer programming is the process of performing a particular computation (or more generally, accomplishing a specific computing result), usually by designing and building an executable computer program. Programming involves tasks such as analysis, generating algorithms, profiling algorithms' accuracy and resource consumption, and the implementation of algorithms (usually in a chosen programming language, commonly referred to as coding). The source code of a program is written in one or more languages that are intelligible to programmers, rather than machine code, which is directly executed by the central processing unit. The purpose of programming is to find a sequence of instructions that will automate the performance of a task (which can be as complex as an operating system) on a computer, often for solving a given problem. Proficient programming thus usually requires expertise in several different subjects, including knowledge of the application domain, specialized algori ...
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Array Data Type
In computer science, array is a data type that represents a collection of ''elements'' (value (computer science), values or variable (computer science), variables), each selected by one or more indices (identifying keys) that can be computed at Run time (program lifecycle phase), run time during program execution. Such a collection is usually called an array variable or array value.Robert W. Sebesta (2001) ''Concepts of Programming Languages''. Addison-Wesley. 4th edition (1998), 5th edition (2001), By analogy with the mathematical concepts vector (mathematics), vector and matrix (mathematics), matrix, array types with one and two indices are often called vector type and matrix type, respectively. More generally, a multidimensional array type can be called a tensor type, by anology with the physical concept, tensor. Language support for array types may include certain built-in type, built-in array data types, some syntactic constructions (''array type constructors'') that the p ...
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Zero-based Numbering
Zero-based numbering is a way of numbering in which the initial element of a sequence is assigned the index 0, rather than the index 1 as is typical in everyday ''non-mathematical'' or ''non-programming'' circumstances. Under zero-based numbering, the initial element is sometimes termed the ''zeroth'' element, rather than the ''first'' element; ''zeroth'' is a coined ordinal number corresponding to the number zero. In some cases, an object or value that does not (originally) belong to a given sequence, but which could be naturally placed before its initial element, may be termed the zeroth element. There is not wide agreement regarding the correctness of using zero as an ordinal (nor regarding the use of the term ''zeroth''), as it creates ambiguity for all subsequent elements of the sequence when lacking context. Numbering sequences starting at 0 is quite common in mathematics notation, in particular in combinatorics, though programming languages for mathematics usuall ...
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Logic Error
In computer programming, a logic error is a bug in a program that causes it to operate incorrectly, but not to terminate abnormally (or crash). A logic error produces unintended or undesired output or other behaviour, although it may not immediately be recognized as such. Logic errors occur in both compiled and interpreted languages. Unlike a program with a syntax error, a program with a logic error is a valid program in the language, though it does not behave as intended. Often the only clue to the existence of logic errors is the production of wrong solutions, though static analysis may sometimes spot them. Debugging logic errors One of the ways to find this type of error is to put out the program's variables to a file or on the screen in order to determine the error's location in code. Although this will not work in all cases, for example when calling the wrong subroutine, it is the easiest way to find the problem if the program uses the incorrect results of a bad mathem ...
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Frame Pointer
In computer science, a call stack is a stack data structure that stores information about the active subroutines of a computer program. This kind of stack is also known as an execution stack, program stack, control stack, run-time stack, or machine stack, and is often shortened to just "the stack". Although maintenance of the call stack is important for the proper functioning of most software, the details are normally hidden and automatic in high-level programming languages. Many computer instruction sets provide special instructions for manipulating stacks. A call stack is used for several related purposes, but the main reason for having one is to keep track of the point to which each active subroutine should return control when it finishes executing. An active subroutine is one that has been called, but is yet to complete execution, after which control should be handed back to the point of call. Such activations of subroutines may be nested to any level (recursive as a special ...
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Linear Interpolation
In mathematics, linear interpolation is a method of curve fitting using linear polynomials to construct new data points within the range of a discrete set of known data points. Linear interpolation between two known points If the two known points are given by the coordinates (x_0,y_0) and (x_1,y_1), the linear interpolant is the straight line between these points. For a value in the interval (x_0, x_1), the value along the straight line is given from the equation of slopes \frac = \frac, which can be derived geometrically from the figure on the right. It is a special case of polynomial interpolation with . Solving this equation for , which is the unknown value at , gives \begin y &= y_0 + (x-x_0)\frac \\ &= \frac + \frac\\ &= \frac \\ &= \frac, \end which is the formula for linear interpolation in the interval (x_0,x_1). Outside this interval, the formula is identical to linear extrapolation. This formula can also be understood as a weighted average. The weights are inv ...
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C Standard Library
The C standard library or libc is the standard library for the C programming language, as specified in the ISO C standard.ISO/IEC (2018). '' ISO/IEC 9899:2018(E): Programming Languages - C §7'' Starting from the original ANSI C standard, it was developed at the same time as the C library POSIX specification, which is a superset of it. Since ANSI C was adopted by the International Organization for Standardization, the C standard library is also called the ISO C library. The C standard library provides macros, type definitions and functions for tasks such as string handling, mathematical computations, input/output processing, memory management, and several other operating system services. Application programming interface Header files The application programming interface (API) of the C standard library is declared in a number of header files. Each header file contains one or more function declarations, data type definitions, and macros. After a long period of stabi ...
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Strcat
The C programming language has a set of functions implementing operations on strings (character strings and byte strings) in its standard library. Various operations, such as copying, concatenation, tokenization and searching are supported. For character strings, the standard library uses the convention that strings are null-terminated: a string of characters is represented as an array of elements, the last of which is a character (with numeric value 0). The only support for strings in the programming language proper is that the compiler translates quoted string constants into null-terminated strings. Definitions A string is defined as a contiguous sequence of code units terminated by the first zero code unit (often called the ''NUL'' code unit). This means a string cannot contain the zero code unit, as the first one seen marks the end of the string. The ''length'' of a string is the number of code units before the zero code unit. The memory occupied by a string is always ...
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Endianness
In computing, endianness, also known as byte sex, is the order or sequence of bytes of a word of digital data in computer memory. Endianness is primarily expressed as big-endian (BE) or little-endian (LE). A big-endian system stores the most significant byte of a word at the smallest memory address and the least significant byte at the largest. A little-endian system, in contrast, stores the least-significant byte at the smallest address. Bi-endianness is a feature supported by numerous computer architectures that feature switchable endianness in data fetches and stores or for instruction fetches. Other orderings are generically called middle-endian or mixed-endian. Endianness may also be used to describe the order in which the bits are transmitted over a communication channel, e.g., big-endian in a communications channel transmits the most significant bits first. Bit-endianness is seldom used in other contexts. Etymology Danny Cohen introduced the terms ''big-endian'' a ...
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Rounding Error
A roundoff error, also called rounding error, is the difference between the result produced by a given algorithm using exact arithmetic and the result produced by the same algorithm using finite-precision, rounded arithmetic. Rounding errors are due to inexactness in the representation of real numbers and the arithmetic operations done with them. This is a form of quantization error. When using approximation equations or algorithms, especially when using finitely many digits to represent real numbers (which in theory have infinitely many digits), one of the goals of numerical analysis is to estimate computation errors. Computation errors, also called numerical errors, include both truncation errors and roundoff errors. When a sequence of calculations with an input involving any roundoff error are made, errors may accumulate, sometimes dominating the calculation. In ill-conditioned problems, significant error may accumulate. In short, there are two major facets of roundoff errors i ...
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Boundary-value Analysis
Boundary-value analysis is a software testing technique in which tests are designed to include representatives of boundary values in a range. The idea comes from the boundary. Given that we have a set of test vectors to test the system, a topology can be defined on that set. Those inputs which belong to the same equivalence class as defined by the equivalence partitioning theory would constitute the basis. Given that the basis sets are neighbors, there would exist a boundary between them. The test vectors on either side of the boundary are called boundary values. In practice this would require that the test vectors can be ordered, and that the individual parameters follows some kind of order (either partial order or total order). Formal definition Formally the boundary values can be defined as below: :Let the set of the test vectors be . :Let's assume that there is an ordering relation defined over them, as . :Let be two equivalent classes. :Assume that test vector and . :If ...
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