atan2

Compute four-quadrant arctangent

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Libraries:
Motor Control Blockset / Controls / Math Transforms
Motor Control Blockset HDL Support / Controls / Math Transforms

Description

The atan2 block performs the four-quadrant arctangent on two real numbers.

Equations

This equation describes how the block computes the four-quadrant arctangent (θ).

$$Theta=\text{atan2}(A,B)=\{\begin{array}{l}\arctan \left(\frac{A}{B}\right)\text{ if B>0,}\\ \arctan \left(\frac{A}{B}\right)+\pi \text{ if B<0 and A}\ge \text{0,}\\ \arctan \left(\frac{A}{B}\right)-\pi \text{ if B<0 and A<0,}\\ +\frac{\pi }{2}\text{ if B=0 and A>0, }\\ -\frac{\pi }{2}\text{ if B=0 and A<0,}\\ undefined\text{ if B=0 and A=0}\text{.}\end{array}$$

where:

$$-\pi <Theta\le \pi \text{ (Radians)}$$

Ports

Input

A — y-coordinate value (real number)

scalar

Real number on the y-axis that you provide as input to the block.

Data Types: single | double | fixed point

B — x-coordinate value (real number)

scalar

Real number on the x-axis that you provide as input to the block.

Data Types: single | double | fixed point

Output

θ — Angle represented by arctangent

scalar

Angle represented by arctangent. This is the angle made by a vector from the origin to a specified point (x,y) with the positive x-axis.

Data Types: single | double | fixed point

The following figure shows the representation of input values A, B, and arctangent on the x-y coordinate plane.

Parameters

Approximation method — Type of approximation used for atan2 computation

None (default) | CORDIC | Lookup

Type of approximation that the block uses for atan2 computation:

• None — The block does not use any approximation.

• CORDIC — The block uses the approximation based on coordinate rotation digital computer (CORDIC) algorithm.

• Lookup — The block uses the lookup table based approximation.

Note

When you use the block for code generation:

• None option works better with single data type.

• CORDIC option works better for FPGA deployment.

• Lookup option works better with fixed-point data type.

Output unit — Unit of output values

Radians (default) | PerUnit

Unit of the output values.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

HDL Code Generation

Generate VHDL, Verilog and SystemVerilog code for FPGA and ASIC designs using HDL Coder™.

HDL Coder™ provides additional configuration options that affect HDL implementation and synthesized logic.

HDL Architecture

This block has one default HDL architecture.

HDL Block Properties

ConstrainedOutputPipeline	Number of registers to place at the outputs by moving existing delays within your design. Distributed pipelining does not redistribute these registers. The default is 0. For more details, see ConstrainedOutputPipeline (HDL Coder).
InputPipeline	Number of input pipeline stages to insert in the generated code. Distributed pipelining and constrained output pipelining can move these registers. The default is 0. For more details, see InputPipeline (HDL Coder).
OutputPipeline	Number of output pipeline stages to insert in the generated code. Distributed pipelining and constrained output pipelining can move these registers. The default is 0. For more details, see OutputPipeline (HDL Coder).
SharingFactor	Number of functionally equivalent resources to map to a single shared resource. The default is 0. See also Resource Sharing (HDL Coder).

Restriction

If you run third-party (3p) simulation, the block may show a minor mismatch (of the order 1e-7) in the simulation results because of an internal trigonometric function that uses the floating point datatype.

Fixed-Point Conversion
Design and simulate fixed-point systems using Fixed-Point Designer™.

Version History

Introduced in R2020a