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                                              169
      SECTION 3.9                                                               Functions



      In addition, each type of function dictionary must include entries appropriate to
      the particular function type. The number of output values can usually be inferred
      from other attributes of the function; if not (as is always the case for type 0 and
      type 4 functions), the Range entry is required. The dimensionality of the function
      implied by the Domain and Range entries must be consistent with that implied by
      other attributes of the function.


3.9.1 Type 0 (Sampled) Functions

      Type 0 functions use a sequence of sample values (contained in a stream) to
      provide an approximation for functions whose domains and ranges are bounded.
      The samples are organized as an m-dimensional table in which each entry has n
      components.

      Sampled functions are highly general and offer reasonably accurate
      representations of arbitrary analytic functions at low expense. For example, a
      1-input sinusoidal function can be represented over the range [ 0 180 ] with an
      average error of only 1 percent, using just ten samples and linear interpolation.
      Two-input functions require significantly more samples but usually not a
      prohibitive number if the function does not have high frequency variations.

      The dimensionality of a sampled function is restricted only by implementation
      limits. However, the number of samples required to represent functions with high
      dimensionality multiplies rapidly unless the sampling resolution is very low. Also,
      the process of multilinear interpolation becomes computationally intensive if the
      number of inputs m is greater than 2. The multidimensional spline interpolation
      is even more computationally intensive.

      In addition to the entries in Table 3.35, a type 0 function dictionary includes
      those shown in Table 3.36.

      The Domain, Encode, and Size entries determine how the function’s input
      variable values are mapped into the sample table. For example, if Size is [ 21 31 ],
      the default Encode array is [ 0 20 0 30 ], which maps the entire domain into the
      full set of sample table entries. Other values of Encode may be used.

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