Trigonometry / CORDIC

Utilities for computing trigonometric functions in hardware.

class tiliqua.cordic.RectToPolarCordic(*args, src_loc_at=0, **kwargs)

Iteratively compute magnitude and phase of complex numbers.

This core uses a CORDIC (Coordinate Rotation Digital Computer) approach to convert rectangular to polar complex numbers using only shifts and adds.

This is useful for extracting power spectra from frequency-domain blocks.

Given a complex number in rectangular coordinates, this core emits:

o.payload.magnitude = S*sqrt(i.payload.real**2 + i.payload.imag**2)
o.payload.phase     = atan2(i.payload.imag, i.payload.real) / pi

S: =1 if 'magnitude_correction' is True, and =K (CORDIC gain) otherwise
Members:

  • i (In(stream.Signature(Block(CQ(shape))))) – Stream of incoming complex numbers in rectangular coordinates.

  • o (Out(stream.Signature(Block(Polar(self.internal_shape))))) – Stream of outgoing complex numbers in polar coordinates.

K = 1.646760258121

CORDIC gain constant.

__init__(shape, iterations=None, magnitude_correction=True)
shapeShape

Shape of fixed-point number to use for incoming CQ stream.

iterationsint

Number of iterations of computation. Higher is better accuracy, but requires more clock cycles. This defaults to the number of bits in the provided shape.

magnitude_correctionbool

Whether to consume an additional multiplier to correct for the CORDIC gain constant. For some applications, this is not needed and can be used to save a multiplier.