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5 0 obj << /Limits [(Actinium) (Astatine)] /Names [ (Actinium) 25 0 R (Aluminum) 26 0 R (Americium) 27 0 R (Antimony) 28 0 R (Argon) 29 0 R (Arsenic) 30 0 R (Astatine) 31 0 R ] >> endobj 24 0 obj << /Limits [(Xenon) (Zirconium)] /Names [ (Xenon) 129 0 R (Ytterbium) 130 0 R (Yttrium) 131 0 R (Zinc) 132 0 R (Zirconium) 133 0 R ] >> endobj 25 0 obj 89 endobj 133 0 obj 40 endobj

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A number tree is similar to a name tree (see Section 384, Name Trees ), except that its keys are integers instead of strings, sorted in ascending numerical order The entries in the leaf (or root) nodes containing the key-value pairs are named Nums instead of Names as in a name tree Table 325 shows the entries in a number tree s node dictionaries

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TABLE 325 Entries in a number tree node dictionary

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(Root and intermediate nodes only; required in intermediate nodes; present in the root node if and only if Nums is not present) An array of indirect references to the immediate children of this node The children may be intermediate or leaf nodes (Root and leaf nodes only; required in leaf nodes; present in the root node if and only if Kids is not present) An array of the form

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[key1 value1 key2 value2 keyn valuen ]

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Nums

array

where each keyi is an integer and the corresponding valuei is an indirect reference to the object associated with that key The keys are sorted in numerical order, analogously to the arrangement of keys in a name tree as described in Section 384, Name Trees

Limits

array

(Intermediate and leaf nodes only; required) An array of two integers, specifying the (numerically) least and greatest keys included in the Nums array of a leaf node or in the Nums arrays of any leaf nodes that are descendants of an intermediate node

39 Functions

PDF is not a programming language, and a PDF le is not a program; however, PDF does provide several types of function object (PDF 12) that represent parameterized classes of functions, including mathematical formulas and sampled representations with arbitrary resolution Functions are used in various ways in PDF: device-dependent rasterization information for high-quality printing (halftone spot functions and transfer functions), color transform functions for certain color spaces, and speci cation of colors as a function of position for smooth shadings Functions in PDF represent static, self-contained numerical transformations A function to add two numbers has two input values and one output value: f ( x0 , x1 ) = x0 + x1 Similarly, a function that computes the arithmetic and geometric mean of two numbers could be viewed as a function of two input values and two output values: x0 + x1 f ( x 0 , x 1 ) = ---------------- , 2 x0 x1

S E CTIO N 3 9

Functions

In general, a function can take any number (m) of input values and produce any number (n) of output values: f ( x0 , , xm 1 ) = y0 , , yn 1 In PDF functions, all the input values and all the output values are numbers, and functions have no side effects Each function de nition includes a domain, the set of legal values for the input Some types of functions also de ne a range, the set of legal values for the output Input values passed to the function are clipped to the domain, and output values produced by the function are clipped to the range For example, suppose the function f (x) = x + 2 is de ned with a domain of [ 1 1] If the function is called with the input value 6, that value is replaced with the nearest value in the de ned domain, 1, before the function is evaluated; the resulting output value is therefore 3 Similarly, if the function f ( x0 , x1 ) = 3 x0 + x1 is de ned with a range of [0 100], and if the input values 6 and 4 are passed to the function (and are within its domain), then the output value produced by the function, 14, is replaced with 0, the nearest value in the de ned range A function object may be a dictionary or a stream, depending on the type of function; the term function dictionary will be used generically in this section to refer to either a dictionary object or the dictionary portion of a stream object A function dictionary speci es the function s representation, the set of attributes that parameterize that representation, and the additional data needed by that representation Four types of function are available, as indicated by the dictionary s FunctionType entry: