CORDIC Intel® FPGA IP User Guide

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ID 683808
Date 1/16/2024
Public
Document Table of Contents
Document Table of Contents x
1. CORDIC IP User Guide
1. CORDIC IP User Guide x
1.1. CORDIC IP Features 1.2. CORDIC IP Device Support 1.3. CORDIC IP Functional Description 1.4. CORDIC IP Parameters 1.5. CORDIC IP Signals 1.6. Document Revision History for the CORDIC Intel FPGA IP User Guide
1.3. CORDIC IP Functional Description x
1.3.1. SinCos Function 1.3.2. Atan2 Function 1.3.3. Vector Translate Function 1.3.4. Vector Rotate Function
1. CORDIC IP User Guide

1.3.4. Vector Rotate Function

The vector rotate function takes a vector v= (x,y) T given by the two coordinates x and y and an angle a. The function produces a similarity rotation of vector v by the angle a to produce the vector v0=(x0, y0) T .
Figure 4. Vector Rotate Function

The rotation is a similarity rotation because the magnitude of the produced vector v0 is scaled up by the CORDIC specific constant K = 1.646760258121. The equations of the coordinates for vector v0 are:

  • x0 = K(xcos(a)− ysin(a))
  • y0 = K(xsin(a)+ ycos(a))

If you set the sign attribute to true for the x,y inputs for the function, the IP core restricts their range to [−1,1]. You provide the number of fractional bits. The input angle a is allowed in the range [−π,+π], and has the same number of fractional bits as the other inputs. You provide the output fractional bits and the total width of the output is w=F+3, signed.

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