Divider (`divider_s`)

Divides two integer values together.

Design

Divides two short values together generating a quotient and a remainder. The division method can be selected from: truncated (C/C++ standard method), and floored (Python // operator).

The mathematical representation of the implementation is given in (103).

(103)\[z[n] = \left \lfloor \frac{x[n]}{y[n]} \right \rfloor\]

(104)\[r[n] = {x[n]} \space \mathbf{mod} \space {y[n]}\]

In (103) and (104)

\(x[n]\) and \(y[n]\) are the input values.

\(z[n]\) is the output values.

\(r[n]\) is the remainder values.

In (103), all outputs are converted to integer representations.

A block diagram representation of the implementation is given in Figure 143:.

Block diagram outlining divider implementation. — Figure 143: Divider implementation.

Interface

<?xml version="1.0"?>
<componentspec>
  <property name="method" type="enum" initial="true" writable="false" enums="floor,truncate" default="truncate"
    description="Division definition to use"/>
  <port name="input" producer="false" protocol="short_timed_sample-prot"/>
  <port name="denominator" producer="false" protocol="short_timed_sample-prot"/>
  <port name="output" producer="true" optional="true" protocol="short_timed_sample-prot"/>
  <port name="remainder" producer="true" optional="true" protocol="short_timed_sample-prot"/>
</componentspec>

Ports

Inputs:

input: Numerator samples port.
- Protocol: short_timed_sample-prot
- Optional: False
denominator: Denominator samples port.
- Protocol: short_timed_sample-prot
- Optional: False

Outputs:

output: Quotient samples port.
- Protocol: short_timed_sample-prot
- Optional: True
remainder: Remainder samples port.
- Protocol: short_timed_sample-prot
- Optional: True

Opcode Handling

Division is only applied to the sample opcode messages. All other opcode messages received on input are passed through this component to both output ports. All messages with a non-sample opcode received on denominator are discarded.

Sample message lengths received on input are preserved on the output. Sample message lengths received on denominator are ignored.

Properties

method: Division definition to use.
- Type: enum
  - Allowed values: ['floor', 'truncate']
- Access:
  - Parameter: False
  - Writable: False
  - Initial: True
  - Volatile: False
- Default value: truncate

Implementations

divider_s (HDL)

Non pipelined HDL short divider implementation.
divider_s (RCC)

RCC short divider implementation.

Example Application

<?xml version="1.0"?>
<application done="file_write">
  <instance component="ocpi.core.file_read" name="numerator">
    <property name="filename" value="input.bin"/>
  </instance>
  <instance component="ocpi.core.file_read" name="denominator">
    <property name="filename" value="denominator.bin"/>
  </instance>
  <instance component="ocpi.comp.sdr.math.divider_s" name="divider">
    <property name="method" value="truncate"/>
  </instance>
  <instance component="ocpi.core.file_write" name="quotient">
    <property name="filename" value="output.bin"/>
  </instance>
  <instance component="ocpi.core.file_write" name="remainder">
    <property name="filename" value="remainder.bin"/>
  </instance>
  <connection>
    <port instance="numerator" name="output"/>
    <port instance="divider" name="input"/>
  </connection>
  <connection>
    <port instance="denominator" name="output"/>
    <port instance="divider" name="denominator"/>
  </connection>
  <connection>
    <port instance="divider" name="output"/>
    <port instance="quotient" name="input"/>
  </connection>
  <connection>
    <port instance="divider" name="remainder"/>
    <port instance="remainder" name="input"/>
  </connection>
</application>

Dependencies

The dependencies to other elements in OpenCPI are:

Divider primitive

Protocol interface delay primitive v2

There is also a dependency on:

ieee.std_logic_1164

ieee.numeric_std

Limitations

Limitations of divider_s are:

In order to keep compatibility between HDL and RCC, division by zero does not raise any exceptions, but instead returns the following:
- If division method is floor: 0 or -1 on the Quotient port (depending upon the sign of input), and input is passed as the remainder.
- If division method is truncate: 1 or -1 on the Quotient port (depending upon the sign of input), and input is passed as the remainder.

Testing

Tested platforms: None

Component testing not completed.

Divider (divider_s)