| Developer(s) | Bruno Haible and Richard B. Kreckel |
|---|---|
| Stable release | 1.3.7 / January 22, 2024 |
| Written in | C++11 |
| Operating system | Cross-platform |
| Type | Mathematical software |
| License | GPL |
| Website | https://www.ginac.de/CLN/ |
Class Library for Numbers (CLN) is a free library for arbitrary precision arithmetic. It operates on signed integers, rational numbers, floating point numbers, complex numbers, modular numbers, and univariate polynomials. Its implementation programming language is C++.
CLN uses object oriented techniques and operator overloading to achieve a natural algebraic syntax: The sum x of two variables a and b is written as x = a + b, as opposed to the function sum(&x, a, b).
CLN uses class inheritance to model the natural subsets of the available number types: E.g. the integer class is a subtype of the rational class, just as the integer numbers are a subset of the rational numbers. The complex numbers and all its subtypes behave exactly like the types of numbers known to the Common Lisp language, giving CLN another meaning: it becomes an abbreviation of Common Lisp Numbers. Due to this, CLN can be and is used for implementations of Common Lisp, other interpreted languages, or computer algebra systems.
The implementation is efficient. It can be configured to use the GNU Multi-Precision Library as kernel for speed-critical inner loops and implements advanced algorithms like Schönhage–Strassen multiplication, binary splitting [1] for computing certain mathematical constants and others. All CLN objects are either immediate or reference counted, providing for non-interruptive garbage collection with no burden on the main application.
Common Lisp (CL) is a dialect of the Lisp programming language, published in American National Standards Institute (ANSI) standard document ANSI INCITS 226-1994 (S2018). The Common Lisp HyperSpec, a hyperlinked HTML version, has been derived from the ANSI Common Lisp standard.
An integer is the number zero (0), a positive natural number or a negative integer. The negative numbers are the additive inverses of the corresponding positive numbers. The set of all integers is often denoted by the boldface Z or blackboard bold .
Scheme is a dialect of the Lisp family of programming languages. Scheme was created during the 1970s at the MIT Computer Science and Artificial Intelligence Laboratory and released by its developers, Guy L. Steele and Gerald Jay Sussman, via a series of memos now known as the Lambda Papers. It was the first dialect of Lisp to choose lexical scope and the first to require implementations to perform tail-call optimization, giving stronger support for functional programming and associated techniques such as recursive algorithms. It was also one of the first programming languages to support first-class continuations. It had a significant influence on the effort that led to the development of Common Lisp.
In computer science and computer programming, a data type is a collection or grouping of data values, usually specified by a set of possible values, a set of allowed operations on these values, and/or a representation of these values as machine types. A data type specification in a program constrains the possible values that an expression, such as a variable or a function call, might take. On literal data, it tells the compiler or interpreter how the programmer intends to use the data. Most programming languages support basic data types of integer numbers, floating-point numbers, characters and Booleans.
In computer programming, a type system is a logical system comprising a set of rules that assigns a property called a type to every term. Usually the terms are various language constructs of a computer program, such as variables, expressions, functions, or modules. A type system dictates the operations that can be performed on a term. For variables, the type system determines the allowed values of that term. Type systems formalize and enforce the otherwise implicit categories the programmer uses for algebraic data types, data structures, or other components.
In computer science, a set is an abstract data type that can store unique values, without any particular order. It is a computer implementation of the mathematical concept of a finite set. Unlike most other collection types, rather than retrieving a specific element from a set, one typically tests a value for membership in a set.
In programming language theory and type theory, polymorphism is the use of a single symbol to represent multiple different types.
In computer science, primitive data types are a set of basic data types from which all other data types are constructed. Specifically it often refers to the limited set of data representations in use by a particular processor, which all compiled programs must use. Most processors support a similar set of primitive data types, although the specific representations vary. More generally, "primitive data types" may refer to the standard data types built into a programming language. Data types which are not primitive are referred to as derived or composite.
GNU Multiple Precision Arithmetic Library (GMP) is a free library for arbitrary-precision arithmetic, operating on signed integers, rational numbers, and floating-point numbers. There are no practical limits to the precision except the ones implied by the available memory (operands may be of up to 232−1 bits on 32-bit machines and 237 bits on 64-bit machines). GMP has a rich set of functions, and the functions have a regular interface. The basic interface is for C, but wrappers exist for other languages, including Ada, C++, C#, Julia, .NET, OCaml, Perl, PHP, Python, R, Ruby, and Rust. Prior to 2008, Kaffe, a Java virtual machine, used GMP to support Java built-in arbitrary precision arithmetic. Shortly after, GMP support was added to GNU Classpath.
In Scheme and in Lisp dialects inspired by it, the numerical tower is a set of data types that represent numbers and a logic for their hierarchical organisation.
Many programming language type systems support subtyping. For instance, if the type Cat is a subtype of Animal, then an expression of type Cat should be substitutable wherever an expression of type Animal is used.
In computer science, object composition and object aggregation are closely related ways to combine objects or data types into more complex ones. In conversation the distinction between composition and aggregation is often ignored. Common kinds of compositions are objects used in object-oriented programming, tagged unions, sets, sequences, and various graph structures. Object compositions relate to, but are not the same as, data structures.
In object-oriented programming, inheritance is the mechanism of basing an object or class upon another object or class, retaining similar implementation. Also defined as deriving new classes from existing ones such as super class or base class and then forming them into a hierarchy of classes. In most class-based object-oriented languages like C++, an object created through inheritance, a "child object", acquires all the properties and behaviors of the "parent object", with the exception of: constructors, destructors, overloaded operators and friend functions of the base class. Inheritance allows programmers to create classes that are built upon existing classes, to specify a new implementation while maintaining the same behaviors, to reuse code and to independently extend original software via public classes and interfaces. The relationships of objects or classes through inheritance give rise to a directed acyclic graph.
In many programming languages, map is a higher-order function that applies a given function to each element of a collection, e.g. a list or set, returning the results in a collection of the same type. It is often called apply-to-all when considered in functional form.
This article compares a large number of programming languages by tabulating their data types, their expression, statement, and declaration syntax, and some common operating-system interfaces.
In mathematics, a real number is a number that can be used to measure a continuous one-dimensional quantity such as a distance, duration or temperature. Here, continuous means that pairs of values can have arbitrarily small differences. Every real number can be almost uniquely represented by an infinite decimal expansion.
Some programming languages provide a complex data type for complex number storage and arithmetic as a built-in (primitive) data type.
Some programming languages provide a built-in (primitive) rational data type to represent rational numbers like 1/3 and -11/17 without rounding, and to do arithmetic on them. Examples are the ratio type of Common Lisp, and analogous types provided by most languages for algebraic computation, such as Mathematica and Maple. Many languages that do not have a built-in rational type still provide it as a library-defined type.
In mathematics and computer science, computer algebra, also called symbolic computation or algebraic computation, is a scientific area that refers to the study and development of algorithms and software for manipulating mathematical expressions and other mathematical objects. Although computer algebra could be considered a subfield of scientific computing, they are generally considered as distinct fields because scientific computing is usually based on numerical computation with approximate floating point numbers, while symbolic computation emphasizes exact computation with expressions containing variables that have no given value and are manipulated as symbols.
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