pwl_sel :
A selectable piecewise-linear (PWL) function for xreal-typed signals

The pwl_sel primitive computes a piecewise-linear (PWL) function of an xreal-type input in, which can be selected from a set of multiple PWL 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.

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 PWL functions to select from. Each PWL 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 PWL functions. First, the parameter indices is an integer-type array that lists the indices of the PWL 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 PWL 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, in1_0, out1_0, in2_0, out2_0, ...     // PWL function with index 'indices[0]'
              N1, in1_1, out1_1, in2_1, out2_1, ...     // PWL function with index 'indices[1]'
              ...
              Ni, in1_i, out1_i, in2_i, out2_i, ...     // PWL function with index 'indices[i]'
              ...
           }

Each set of data values describing a single PWL function starts with the number of PWL data points (Ni), followed by a list of (input, output) pairs: in1_i, out1_i, in2_i, out2_i, …. When the PWL function describes a constant function, use Ni of 0 followed by a single output value, i.e. 0, out1_i. Otherwise, Ni must be at least 2.

For illustration, the following example describes two PWL functions with index 0 and 1, respectively. The PWL function with index 0 is described with 3 data points, outputting 10*|x| when the input x satisfies |x| < 1 and outputting 10.0 otherwise. The PWL function with index 1 is described with 0 data points, outputting a constant value of 0.0.

    indices = '{0, 1}
    data = '{3, -1.0, 10.0, 0.0, 0.0, 1.0, 10.0, 0, 0.0}

When the parameter indices does not list a complete set of indices, the undefined PWL 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 PWL data points (Ni) and list the PWL data points 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 = [3, -1.0, 10.0, 0.0, 0.0, 1.0, 10.0, 0, 0.0]

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
width_sel	integer	1	None	width of selection bits
indices	int array	‘{0}	None	list of function indices
data	real array	‘{-1.0,-1.0,1.0,1.0}	None	list of function data
filename	string	“”	None	parameter definition file