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PL/I (Programming Language One, pronounced and sometimes written PL/1) is a procedural, imperative computer programming language developed and published by IBM. It is designed for scientific, engineering, business and system programming. It has been used by academic, commercial and industrial organizations since it was introduced in the 1960s, and is still used. PL/I's main domains are data processing, numerical computation, scientific computing, and system programming. It supports recursion, structured programming, linked data structure handling, fixed-point, floating-point, complex, character string handling, and bit string handling. The language syntax is English-like and suited for describing complex data formats with a wide set of functions available to verify and manipulate them. Early history In the 1950s and early 1960s, business and scientific users programmed for different computer hardware using different programming languages. Business users were movi ...
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Procedural Programming
Procedural programming is a programming paradigm, derived from imperative programming, based on the concept of the '' procedure call''. Procedures (a type of routine or subroutine) simply contain a series of computational steps to be carried out. Any given procedure might be called at any point during a program's execution, including by other procedures or itself. The first major procedural programming languages appeared circa 1957–1964, including Fortran, ALGOL, COBOL, PL/I and BASIC. Pascal and C were published circa 1970–1972. Computer processors provide hardware support for procedural programming through a stack register and instructions for calling procedures and returning from them. Hardware support for other types of programming is possible, but no attempt was commercially successful (for example Lisp machines or Java processors). Procedures and modularity Modularity is generally desirable, especially in large, complicated programs. Inputs are usu ...
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Numerical Computation
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts. Current growth in computing power has enabled the use of more complex numerical analysis, providing detailed and realistic mathematical models in science and engineering. Examples of numerical analysis include: ordinary differential equations as found in celestial mechanics (predicting the motions of planets, stars and galaxies), numerical linear algebra in data analysis, and stochastic differential equations and Markov chains for simulating living cells in medicine and b ...
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GEORGE (programming Language)
GEORGE (General Order Generator) is a programming language invented by Charles Leonard Hamblin in 1957. It was designed around a push-down pop-up stack for arithmetic operations, and employed reverse Polish notation. The language included loops, subroutines, conditionals, vector Vector most often refers to: *Euclidean vector, a quantity with a magnitude and a direction *Vector (epidemiology), an agent that carries and transmits an infectious pathogen into another living organism Vector may also refer to: Mathematic ...s, and matrices. Algebraic expressions were written in reverse Polish notation; thus, a + b was written a b +, and similarly for the other arithmetic operations of subtraction, multiplication, and division. The algebraic expression ax^2 + bx + c was written a x dup × × b x × + c +, where 'dup' meant 'duplicate the value'. Following the reverse Polish form, an assignment statement to evaluate the formula y = ax^2 + bx + c was written as a x dup × × ...
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ALGOL
ALGOL (; short for "Algorithmic Language") is a family of imperative computer programming languages originally developed in 1958. ALGOL heavily influenced many other languages and was the standard method for algorithm description used by the Association for Computing Machinery (ACM) in textbooks and academic sources for more than thirty years. In the sense that the syntax of most modern languages is "Algol-like", it was arguably more influential than three other high-level programming languages among which it was roughly contemporary: FORTRAN, Lisp, and COBOL. It was designed to avoid some of the perceived problems with FORTRAN and eventually gave rise to many other programming languages, including PL/I, Simula, BCPL, B, Pascal, and C. ALGOL introduced code blocks and the begin...end pairs for delimiting them. It was also the first language implementing nested function definitions with lexical scope. Moreover, it was the first programming language which gave detailed ...
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COMTRAN
COMTRAN (COMmercial TRANslator) is an early programming language developed at IBM. It was intended as the business programming equivalent of the scientific programming language FORTRAN (FORmula TRANslator). It served as one of the forerunners to the COBOL language. Developed by Bob Bemer Robert William Bemer (February 8, 1920 – June 22, 2004) was a computer scientist best known for his work at IBM during the late 1950s and early 1960s. Early life and education Born in Sault Ste. Marie, Michigan, Bemer graduated from Cranbr ..., in 1957, the language was the first to feature the programming language element known as a picture clause. Contributions to COBOL Several elements of COMTRAN were incorporated into COBOL: * Picture clause. *Paragraphing: dividing code into paragraphs (with line breaks not significant). *Paragraph names. Assigning names to paragraphs, and jumps ('s) are to a paragraph name, not to a line number. * clause on file input operations. *Figurative ...
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Autocoder
Autocoder is any of a group of assemblers for a number of IBM computers of the 1950s and 1960s. The first Autocoders appear to have been the earliest assemblers to provide a macro facility. Terminology Both ''autocoder'', and the unrelated '' autocode'', a term of the same era used in the UK for languages of a higher level, derive from the phrase '' automatic coding''. This referred generally to programs which eased the burden of producing the numeric machine language codes of programs. "Autocoding" is seen occasionally, and can refer to any kind of programming system. In some circles "autocoder" could be used generically to refer to what is now called a macro-assembler. History The first Autocoders were released in 1955 for the IBM 702, and in 1956 for the almost compatible IBM 705. They were designed by Roy Goldfinger who earlier had worked on New York University's (NYU) NYAP assembler. These machines were variable word length commercial machines, as were many of the c ...
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Bit String
A bit array (also known as bitmask, bit map, bit set, bit string, or bit vector) is an array data structure that compactly stores bits. It can be used to implement a simple set data structure. A bit array is effective at exploiting bit-level parallelism in hardware to perform operations quickly. A typical bit array stores ''kw'' bits, where ''w'' is the number of bits in the unit of storage, such as a byte or word, and ''k'' is some nonnegative integer. If ''w'' does not divide the number of bits to be stored, some space is wasted due to internal fragmentation. Definition A bit array is a mapping from some domain (almost always a range of integers) to values in the set . The values can be interpreted as dark/light, absent/present, locked/unlocked, valid/invalid, et cetera. The point is that there are only two possible values, so they can be stored in one bit. As with other arrays, the access to a single bit can be managed by applying an index to the array. Assuming its size ...
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String (computer Science)
In computer programming, a string is traditionally a sequence of characters, either as a literal constant or as some kind of variable. The latter may allow its elements to be mutated and the length changed, or it may be fixed (after creation). A string is generally considered as a data type and is often implemented as an array data structure of bytes (or words) that stores a sequence of elements, typically characters, using some character encoding. ''String'' may also denote more general arrays or other sequence (or list) data types and structures. Depending on the programming language and precise data type used, a variable declared to be a string may either cause storage in memory to be statically allocated for a predetermined maximum length or employ dynamic allocation to allow it to hold a variable number of elements. When a string appears literally in source code, it is known as a string literal or an anonymous string. In formal languages, which are used in mathemati ...
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Complex Arithmetic
In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the form a + bi, where and are real numbers. Because no real number satisfies the above equation, was called an imaginary number by René Descartes. For the complex number a+bi, is called the , and is called the . The set of complex numbers is denoted by either of the symbols \mathbb C or . Despite the historical nomenclature "imaginary", complex numbers are regarded in the mathematical sciences as just as "real" as the real numbers and are fundamental in many aspects of the scientific description of the natural world. Complex numbers allow solutions to all polynomial equations, even those that have no solutions in real numbers. More precisely, the fundamental theorem of algebra asserts that every non-constant polynomial equation with re ...
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Floating-point
In computing, floating-point arithmetic (FP) is arithmetic that represents real numbers approximately, using an integer with a fixed precision, called the significand, scaled by an integer exponent of a fixed base. For example, 12.345 can be represented as a base-ten floating-point number: 12.345 = \underbrace_\text \times \underbrace_\text\!\!\!\!\!\!^ In practice, most floating-point systems use base two, though base ten ( decimal floating point) is also common. The term ''floating point'' refers to the fact that the number's radix point can "float" anywhere to the left, right, or between the significant digits of the number. This position is indicated by the exponent, so floating point can be considered a form of scientific notation. A floating-point system can be used to represent, with a fixed number of digits, numbers of very different orders of magnitude — such as the number of meters between galaxies or between protons in an atom. For this reason, floating-p ...
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Fixed-point Arithmetic
In computing, fixed-point is a method of representing fractional (non-integer) numbers by storing a fixed number of digits of their fractional part. Dollar amounts, for example, are often stored with exactly two fractional digits, representing the cents (1/100 of dollar). More generally, the term may refer to representing fractional values as integer multiples of some fixed small unit, e.g. a fractional amount of hours as an integer multiple of ten-minute intervals. Fixed-point number representation is often contrasted to the more complicated and computationally demanding floating-point representation. In the fixed-point representation, the fraction is often expressed in the same number base as the integer part, but using negative powers of the base ''b''. The most common variants are decimal (base 10) and binary (base 2). The latter is commonly known also as binary scaling. Thus, if ''n'' fraction digits are stored, the value will always be an integer multiple of ''b ...
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Linked Data Structure
In computer science, a linked data structure is a data structure which consists of a set of data records ('' nodes'') linked together and organized by references (''links'' or ''pointers''). The link between data can also be called a connector. In linked data structures, the links are usually treated as special data types that can only be dereferenced or compared for equality. Linked data structures are thus contrasted with arrays and other data structures that require performing arithmetic operations on pointers. This distinction holds even when the nodes are actually implemented as elements of a single array, and the references are actually array indices: as long as no arithmetic is done on those indices, the data structure is essentially a linked one. Linking can be done in two ways using dynamic allocation and using array index linking. Linked data structures include linked lists, search trees, expression trees, and many other widely used data structures. They are also ...
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