CORDIC Intel® FPGA IP User Guide

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ID 683808
Date 10/15/2024
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

1.3.3. Vector Translate Function

The vector translate function is an extension of the atan2 function. It outputs the magnitude of the input vector and the angle a=atan2(y,x).
Figure 3. Vector Translate Function

The function takes inputs x and y and outputs a=atan2(y, x) and M = K(x 2+y 2)0.5. M is the magnitude of the input vector v=(x,y) T , scaled by a CORDIC specific constant that converges to 1.646760258121, which is transcendental, hence has no fixed value. The functions supports two configurations, depending on the sign attribute of x and y:

  • If the inputs are signed, the formats give the allowed input range. In this configuration the output range for a is Є[− π,+π]. The output range for M depends on the input range of x and y, according with the magnitude formula.
  • If the inputs are unsigned, the IP core restricts the output value for a is in [0,+π/2]. The magnitude value still depends on the formula.
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