poly_sel :
A selectable polynomial function for xreal-typed signals

The poly_sel primitive computes a polynomial function of xreal-typed inputs in, which can be selected from a set of multiple polynomial functions by a wire-type selection signal sel. With this primitive, one can describe a nonlinear DC transfer function that varies with a set of digital input values. The poly_sel primitive supports up to three inputs, of which number is specified by the parameter num_in.

With the width of the input sel equal to k, as specified by the parameter width_sel, the primitive can have up to 2^k polynomial functions to select from. Each polynomial function is indexed by an integer ranging from 0 to 2^k-1, which corresponds to the unsigned integer value of the input sel[k-1:0].

The parameters indices and data together describe the set of polynomial functions. First, the parameter indices is an integer-type array that lists the indices of the polynomial functions in the order that they are defined by the parameter data. The indices may be listed in an arbitrary order and may not span a complete set, but each index must be within the range of 0~2^k-1. For example, ‘{0, 3, 1} is possible when k=2. The special value of ‘{-1} is equivalent to a complete set of indices listed as ‘{0, 1, 2, …, 2^k-1}.

On the other hand, the parameter data is a real-type array defining each of the polynomial functions of which indices are listed in the parameter indices using a concatenated set of data values formatted as below (for the number of indices > 1):

    data = '{ N0, C0_0, C1_0, C2_0, ...         // polynomial function with index 'indices[0]'
              N1, C0_1, C1_1, C2_1, ...         // polynomial function with index 'indices[1]'
              ...
              Ni, C0_i, C1_i, C2_i, ...         // polynomial function with index 'indices[i]'
              ...
           }

Each set of data values describing a single polynomial function starts with the number of coefficients (Ni), followed by a list of coefficient values: C0_i, C1_i, C2_i, …. This set of Ni coefficients describes a polynomial function in the same way that the parameter data does for the poly_func primitive.

For a single-input polynomial (num_in = 1):

    out = C0_i + C1_i*in + C2*in^2 + C3_i*in^3 + C4_i*in^4 + ...

For a two-input polynomial (num_in = 2):

    out = C0_i + C1_i*in[1] + C2_i*in[0] +
          C3_i*in[1]^2 + C4_i*in[1]*in[0] + C5_i*in[0]^2 +
          C6_i*in[1]^3 + C7_i*in[1]^2*in[0] + C8_i*in[1]*in[0]^2 + C9_i*in[0]^3 +
          C10_i*in[1]^4 + ...

For a three-input polynomial (num_in = 3):

    out = C0_i + C1_i*in[2] + C2_i*in[1] + C3_i*in[0] +
          C4_i*in[2]^2 + C5_i*in[2]*in[1] + C6_i*in[2]*in[0] +
          C7_i*in[1]^2 + C8_i*in[1]*in[0] + C9_i*in[0]^2 +
          C10_i*in[2]^3 + C11_i*in[2]^2*in[1] + C12_i*in[2]^2*in[0] + C13_i*in[2]*in[1]^2 + C14_i*in[2]*in[1]*in[0] +
          C15_i*in[2]*in[0]^2 + C16_i*in[1]^3 + C17_i*in[1]^2*in[0] + C18_i*in[1]*in[0]^2 + C19_i*in[0]^3 +
          C20_i*in[2]^4 + ...

For illustration, the following example describes two single-input polynomial functions with index 0 and 1, respectively. The polynomial function with index 0 computes x-1 for the input x while the polynomial function with index 1 computes (x-1)^2.

    indices = '{0, 1}
    data = '{2, -1.0, 1.0, 3, 1.0, -2.0, 1.0}

When the parameter indices does not list a complete set of indices, the undefined polynomial functions are assumed to be a constant function outputting 0.0. When the parameter indices has only one index, the parameter data must omit the number of coefficients (Ni) and list the coefficients only.

When the parameter filename is defined, the primitive reads the named file that defines the parameter values in Python format. For the above example, the values of the parameters indices and data can be defined within a file as below:

    indices = [0, 1]
    data = [2, -1.0, 1.0, 3, 1.0, -2.0, 1.0]

NOTE: this primitive adds a unit timestep delay from its input to output for synchronization.

Input/Output Terminals

Name	I/O	Type	Description
out	output	xreal	output signal
in	input	xreal	input signal
sel	input	wire	selection signal (binary-coded)

Parameters

Name	Type	Default	Unit	Description
num_in	integer	1	None	number of inputs
width_sel	integer	1	None	width of selection bits
indices	int array	‘{0}	None	list of function indices
data	real array	‘{0.0}	None	list of function data
filename	string	“”	None	parameter definition file

poly_sel :A selectable polynomial function for xreal-typed signals

poly_sel :
A selectable polynomial function for xreal-typed signals