IEEE Std 1788.1-2017 pdf download – IEEE Standard for Inte rval Arithm e tic (Sim plifie d).
NOTE—Details in 6.4 of IEEE Std 1788-2015 . function Has the usual mathematical meaning of a (possibly partial, i.e., not everywhere defined) function. Synonymous with map, mapping. hull (or interval hull) The hull of a subset s of R is the tightest interval containing s. implementation When used without qualification, means a realization of an interval arithmetic conforming to the specification of this standard. inf-sup Describes a representation of an interval based on its lower and upper bounds. interval At Level 1, a (bare) interval x is a closed connected subset of R. At Level 2 a T-interval is a member of the bare interval type T, or a non-NaI member of the decorated interval type T. NOTE—Details in 4.2, 6 . interval extension At Level 1, an interval extension of a point function f is a function f from intervals to intervals such that f(x) belongs to f(x) whenever x belongs to x and f(x) is defined. It is the natural (or tightest) interval extension, if f(x) is the interval hull of the range of f over x, for all x. NOTE—Details in 4.4.4, for Level 2 interval extension, see 6.4 . decorated interval extension of f is a function from decorated intervals to decorated intervals, whose interval part is an interval extension of f, and whose decoration part propagates decorations as specified in 5.6. NOTE—Details in Clause 5 . interval vector See box. library The set of Level 1 operations (Level 1 library) or those provided by an implementation (Level 2 library). Further classification may be made into the point library, bare interval library and decorated interval library. map, mapping See function. mathematical interval of constructor The arguments of an interval constructor, if valid, define a math- ematical interval x. The actual interval returned by the constructor is the tightest interval that contains x. NOTE—Details in 6.7.5 . NaI, NaN At Level 1 NaN is the function R 0 → R with empty domain.