isl (integer set library) is a portable C

library A library is a collection of Book, books, and possibly other Document, materials and Media (communication), media, that is accessible for use by its members and members of allied institutions. Libraries provide physical (hard copies) or electron ...

for manipulating sets and relations of

integer An integer is the number zero (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...). The negations or additive inverses of the positive natural numbers are referred to as negative in ...

points bounded by

linear In mathematics, the term ''linear'' is used in two distinct senses for two different properties: * linearity of a '' function'' (or '' mapping''); * linearity of a '' polynomial''. An example of a linear function is the function defined by f(x) ...

constraints Constraint may refer to: * Constraint (computer-aided design), a demarcation of geometrical characteristics between two or more entities or solid modeling bodies * Constraint (mathematics), a condition of an optimization problem that the solution m ...

. The following operations are supported: *

intersection In mathematics, the intersection of two or more objects is another object consisting of everything that is contained in all of the objects simultaneously. For example, in Euclidean geometry, when two lines in a plane are not parallel, their ...

, union,

set difference In set theory, the complement of a set , often denoted by A^c (or ), is the set of elements not in . When all elements in the universe, i.e. all elements under consideration, are considered to be members of a given set , the absolute complement ...

emptiness Emptiness as a human condition is a sense of generalized boredom, social alienation, nihilism, and apathy. Feelings of emptiness often accompany dysthymia, depression (mood), depression, loneliness, anhedonia, wiktionary:despair, despair, or o ...

check *

convex hull In geometry, the convex hull, convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined either as the intersection of all convex sets containing a given subset of a Euclidean space, ...

* (integer)

affine hull In mathematics, the affine hull or affine span of a set ''S'' in Euclidean space R''n'' is the smallest affine set containing ''S'', or equivalently, the intersection of all affine sets containing ''S''. Here, an ''affine set'' may be defined as ...

* integer

projection Projection or projections may refer to: Physics * Projection (physics), the action/process of light, heat, or sound reflecting from a surface to another in a different direction * The display of images by a projector Optics, graphics, and carto ...

* computing the lexicographic minimum using parametric integer programming * coalescing * parametric

vertex enumeration In mathematics, the vertex enumeration problem for a polytope, a polyhedral cell complex, a hyperplane arrangement, or some other object of discrete geometry, is the problem of determination of the object's vertices given some formal representatio ...

It also includes an ILP solver based on generalized

basis Basis is a term used in mathematics, finance, science, and other contexts to refer to foundational concepts, valuation measures, or organizational names; here, it may refer to: Finance and accounting * Adjusted basis, the net cost of an asse ...

reduction,

transitive closure In mathematics, the transitive closure of a homogeneous binary relation on a set (mathematics), set is the smallest Relation (mathematics), relation on that contains and is Transitive relation, transitive. For finite sets, "smallest" can be ...

s on

maps A map is a symbolic depiction of interrelationships, commonly spatial, between things within a space. A map may be annotated with text and graphics. Like any graphic, a map may be fixed to paper or other durable media, or may be displayed on ...

(which may encode

infinite graph This is a glossary of graph theory. Graph theory is the study of graphs, systems of nodes or vertices connected in pairs by lines or edges. Symbols A B ...

s),

dependence analysis In compiler theory, dependence analysis produces execution-order constraints between statements/instructions. Broadly speaking, a statement ''S2'' depends on ''S1'' if ''S1'' must be executed before ''S2''. Broadly, there are two classes of depend ...

and bounds on

piecewise In mathematics, a piecewise function (also called a piecewise-defined function, a hybrid function, or a function defined by cases) is a function whose domain is partitioned into several intervals ("subdomains") on which the function may be ...

step-polynomials. All computations are performed in exact integer arithmetic using GMP or imath. Many

program analysis In computer science, program analysis is the process of analyzing the behavior of computer programs regarding a property such as correctness, robustness, safety and liveness. Program analysis focuses on two major areas: program optimization an ...

techniques are based on integer set manipulations. The integers typically represent iterations of a loop nest or elements of an

array An array is a systematic arrangement of similar objects, usually in rows and columns. Things called an array include: {{TOC right Music * In twelve-tone and serial composition, the presentation of simultaneous twelve-tone sets such that the ...

. isl uses parametric

integer programming An integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers. In many settings the term refers to integer linear programming (ILP), in which the objective ...

to obtain an explicit representation in terms of integer divisions. It is used as backend polyhedral library in the GCC Graphite framework and in the

LLVM LLVM, also called LLVM Core, is a target-independent optimizer and code generator. It can be used to develop a Compiler#Front end, frontend for any programming language and a Compiler#Back end, backend for any instruction set architecture. LLVM i ...

br>Polly framework
ref> for

loop optimization In compiler theory, loop optimization is the process of increasing execution speed and reducing the overheads associated with loops. It plays an important role in improving cache performance and making effective use of parallel processing capa ...

References

{{reflist

External links

Official ISL web site

ISL source repository

Integer sets and relations: from high-level modeling to low-level implementation (Sven Verdoolaege)
Computer arithmetic C (programming language) libraries Numerical libraries Free software programmed in C Software using the MIT license

See also

References

External links