IEEE Std 1788.1 pdf free download

IEEE Std 1788.1 pdf free download.Interval Arithmetic (Simplified).
expression A symbolic form 1ISC(l to (lefiIW a function. Au arithmetic expression is one whose operations are all arithmetic operations.
NOTE Details in Clause 6 of IEEE Std 1788-2015.
fma Fused multiply—add operation that computes x x y + z.
FTIA, FTDIA For a real function f defined by an aritinnetic expression:
The Fiii idaiiient al Tlworeni of Interval Arithinwt,ie (FTI A) gives relations l)etweetl the result y of evaluat i tig the expression in interval mode over an input box and the behavior of f on the box. The basic property is that y cotitaijis the range of f over the box: various extra conditions can give extra conclusions, such as that f is continuous on the box.
— The Fundamental Theorem of Decorated Interval Arithmetic (FTDIA) describes how evaluating the cxpressioui in decorated iiiterval iuiode enables the various conditions of the FTIA to be verified. iiiaking the corresponding conclusions computable.
NOTE—Details in 6.4 of IEEE Std 1788-2015.
function I las the usual mathematical meaning of a (pos.sihlv partial, i.e., not everywhere defined) function. Siioiinious with map. mapping.
hull (or interval hull) The hull of a subset s of R is the tightest interval containing s. implementatioti Vhieii used without qualification, titeans a realization of all interval arithniet Ic conforming
to the specification of this standard.
inf-sup Describes a representation of an interval based on its lower and upper hounds.
interval At Level 1, a (bare) interval x is a closed connected sul)set of . At Level 2 a T—interval is a
member of the bare interval type T, or a non-Nal member of the decorated interval type T.
NOTE Details in 1.2, 6.
interval extension At Level 1, an interval extension of a 1)01111 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 iii
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 iuiiplementation (Level 2 library). Further classification may be Ina(le into the point library, hare interval library and (lecorated interval library.
map, mapping See function.
mathematical interval of constructor The arguments of an interval constructor, if valid, define a mathemnatical interval x. The actual interval returned by time constructor is the tightest interval that contains x. NOTE Details in 6.7.5.
An implementation makes the decoration system available by providing: a decorated version of each interval extension of an arithmetic operation, of each interval constructor, and of some other operations; and various auxiliary functions, e.g.， to extract the interval and decoration parts, and to apply a standard initial decoration to an interval. The decoration system is specified here at a mathematical level, with the finite- precision aspects presented in Clause 6. Subclauuses 5.2, 5.3, and 5.4 give the basic concepts; 5.5 and 5.6 define how intervals are given an initial decoration, and how decorations are bound to library interval arithmetic operations to give correct propagation through expressions; 5.7 is about non-arithmetic operations.
IEEE Std 1788.1  pdf download.