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Cordic Compute Unit Documentation

Documentation of the main cordic compute Unit.

Verilog Model:

  • rtl/cordic.v
    • incl/cordic_if.svh
    • incl/types.svh

Test Benches

  • tb/testbench.sv
    • tb/core_test.sv

Module Interface

Module Interface defined in file incl/cordic_if.svh.

Parameters

  • p_WIDTH : bus width of the architecture, default 32.

Ports

Defined in interface cordic_if.core.

Port name Direction Width Description
xPrev Input p_WIDTH Previous (input) x value
yPrev Input p_WIDTH Previous (input) y value
zPrev Input p_WIDTH Previous (input) angle value
rotationDir Input 1 0 for anti-clockwise, 1 for clockwise rotation
rotationSystem Input 1 0 for hyperbolic, 1 for circular
rotationAngle Input p_WIDTH Angle we are rotating with (from LUT)
shiftAmount Input p_LOG2_WIDTH Shift amount in current iteration
xResult Output p_WIDTH Output x value
yResult Output p_WIDTH Output y value
zResult Output p_WIDTH Output angle
xOverflow Output 1 Did x addition lead to overflow?
yOverflow Output 1 Did y addition lead to overflow?
zOverflow Output 1 Did z addition lead to overflow?

CORDIC core defintion

xPrev and yPrev are shifted to the right with sign extension by shiftAmount. Let these by xShifted and yShifted.

deltaX, deltaY and deltaZ define the change in x, y and z from xPrev, yPrev and zPrev to xResult, yResult and zResult. I.e,

xResult = xPrev + deltaX
yResult = yPrev + deltaY
zResult = zPrev + deltaZ

The following table decides the magnitude of change (or delta)

Delta variable Magnitude of change
deltaX xShifted (xPrev >>> shiftAmount)
deltaY yShifted (yPrev >>> shiftAmount)
deltaZ rotationAngle

The sign of deltaX, deltaY and deltaZ depend on direction of rotation and rotation system. The following table documents this

rotationSystem rotationDir deltaX deltaY deltaZ
Hyperbolic (1) - (0) - - +
Hyperbolic (1) + (1) + + -
Circular (1) - (0) + - +
Circular (1) + (1) - + -

So, effectively, these are the equations for the results (and for CORDIC rotations) :

rotationSystem rotationDir xResult yResult zResult
Hyperbolic (1) - (0) xPrev - (xPrev >>> shiftAmount) yPrev - (yPrev >>> shiftAmount) zPrev + rotationAngle
Hyperbolic (1) + (1) xPrev + (xPrev >>> shiftAmount) yPrev + (yPrev >>> shiftAmount) zPrev - rotationAngle
Circular (1) - (0) xPrev + (xPrev >>> shiftAmount) yPrev + (yPrev >>> shiftAmount) zPrev - rotationAngle
Circular (1) + (1) xPrev - (xPrev >>> shiftAmount) yPrev - (yPrev >>> shiftAmount) zPrev + rotationAngle

Each of these additions can overflow, and if they do, they are reported using active high signals, xOverflow, yOverflow and zOverflow

Controlling the CORDIC core

The CORDIC core is a purely combinational unit that does the computation and the controller / sequencer gives appropriate control inputs to the CORDIC. These are the important points for controlling the CORDIC core.

Inputs to the controller

  • Initial x value
  • Initial y value
  • Initiail angle (z) value
  • Hyperbolic / circular rotation system?
  • Rotation / vectoring mode?
  • Number of iterations

Control logic

Port Name How to initialize? On each iteration?
xPrev Set required input = xResult
yPrev Set required input = yResult
zPrev Set required input = zResult
rotationDir rotation or vectoring condition rotation or vectoring condition
rotationSystem Hyperbolic / Circular Hyperbolic / Circular (should not change)
rotationAngle Look up from table Look up from table
shiftAmount 0 for circ, 1 for hyp = shiftAmount + 1

Limitations

Maximum rotation angle (for both rotation and vectoring) is :

Rotation system Maximum /minimum rotation angle
Circular +/- 100 degrees
Hyperbolic +/- 60 degrees

Also, for rotations, abs(x) < abs(y) and x < 0 (abs is short for absolute / magnitude)