XMC™ MCU: Math CORDIC

This code example uses the Math CORDIC block to perform circular, hyperbolic, and logarithmic operations. The example demonstrates the blocking, non-blocking, and direct register write operations of the CORDIC block.

Requirements

• ModusToolbox™ software v3.0
• SEGGER J-Link software
• Programming language: C
• Associated parts: XMC1000 MCU parts

Supported toolchains (make variable 'TOOLCHAIN')

• GNU Arm® embedded compiler v10.3.1 (GCC_ARM) - Default value of TOOLCHAIN
• Arm® compiler v6.16 (ARM)
• IAR C/C++ compiler v9.30.1 (IAR)

Supported kits (make variable 'TARGET')

• XMC1400 boot kit (KIT_XMC14_BOOT_001) - Default value of TARGET

Hardware setup

This example uses the board's default configuration. See the kit user guide to ensure that the board is configured correctly.

Software setup

Install a terminal emulator if you do not have one. Instructions in this document use Tera Term.

Theory

The CORDIC coprocessor computes trigonometric, linear, hyperbolic, and related functions using the CORDIC algorithm. The CORDIC algorithm is a useful convergence method, which performs the mathematical operations through an iterative process. The main advantage of using this algorithm is the fast calculation speed compared to software, and high accuracy. These operations are essential in applications such as the following:

• Electric power steering and motor control: Angle computation

• Motor control: Park transformation

• Digital filtering and PI control loop:Linear operations

The X and Y data input for the CORDIC coprocessor can be sent directly in 'Qm.n' format. 'Q' is a binary fixed-point number format, where the number of integer bits (indicated by 'm') and the number of fractional bits (indicated by 'n') are specified. The 'Qm.n' format is generally used in hardware that does not have a floating-point unit.

In this code example, 'Q0.23' and 'Q1.22' formats are used:

• XMC_MATH_Q0_23_t – 1 signed bit, 0 integer bits, 23 fraction bits

• XMC_MATH_Q1_22_t – 1 signed bit, 1 integer bits, 22 fraction bits

The functions to convert the Q format to float are implemented in the code example. The theory behind the conversion is to right-shift the fractional bits to obtain the float value.

The Z input and output data also follow the same procedure for linear operations. However, for circular and hyperbolic functions, the accessible Z result data and input data are normalized. The Z input data needs to be scaled up by ((2^23)/pi). For example, if a Z input of pi/2 needs to be provided, the actual Z input that is sent to the CORDIC coprocessor is as follows:

((pi/2) * ((2^23)/pi)) = 0x400000

On the other hand, the Z result from the CORDIC block for circular and hyperbolic functions need to be scaled down by ((2^23)/pi). For example, if the CORDIC Z output is (2^23)/pi (example considered for better understanding), the actual Z result is as follows:

(((2^23)/pi) / ((2^23)/pi)) = 1

See the following for more details of the CORDIC coprocessor:

• AP32307 - Math Coprocessor application note

• XMC1000 family technical reference manuals

Using the code example

Create the project and open it using one of the following:

project-creator-cli --board-id KIT_XMC14_BOOT_001 --app-id mtb-example-xmc-math-cordic --user-app-name MathCordic --target-dir "C:/mtb_projects"

Operation

1. Connect the board to your PC using a micro-USB cable through the debug USB connector.

2. Program the board using Eclipse IDE for ModusToolbox™ software:

   1. Select the application project in the Project Explorer.

   2. In the Quick Panel, scroll down, and click <Application Name> Program (JLink).

3. Once the device is programmed, the blocking cos(), non-blocking sinh(), and ln() CORDIC operations are performed and the result is displayed on the serial terminal:

   Figure 1. Serial terminal log

   

Debugging

You can debug the example to step through the code. In the IDE, use the <Application Name> Debug (JLink) configuration in the Quick Panel. For more details, see the "Program and debug" section in the Eclipse IDE for ModusToolbox™ user guide.

Design and implementation

This code example is divided into three steps:

• Step 1: This step demonstrates the use of the CORDIC coprocessor to perform blocking operations using the cos() operation. The angle, pi/3 in this case, is first scaled up by ((2^23)/pi) because it is the input to the CORDIC Z value (check the XMC_MATH_CORDIC_Cos() implementation in xmc_math.c). The result obtained from the CORDIC block is converted from the Q0_23 format to float to obtain cos(pi/3).

• Step 2: This step demonstrates the procedure to use non-blocking CORDIC operations. Here, sinh() of pi/4 is calculated. The CORDIC interrupt is configured and enabled. The angle is again scaled up by ((2^23)/pi) and fed into the CORDIC block. Once the CORDIC operation is started, the CPU can perform other actions instead of polling such as in blocking operations. After the CORDIC operation completion, an interrupt is triggered and the result is read. The result is converted from Q1_22 format to float to obtain sinh(pi/4).

• Step 3: This step uses direct register writes to perform a natural logarithmic operation. The fundamental equation behind this process is ln(x) = 2*atanh[(x-1)/(x+1)]. Because the atanh() functionality is required, the CORDIC block is used in hyperbolic vectoring mode. The initial inputs are fed into CORDIC data registers. Setting the Start Mode to '0' ensures that the CORDIC operation starts automatically after the X data register is written. Once the operation is complete, the final result is scaled down by ((2^23)/pi) to obtain the result of ln(3).

The result of each step and debug messages are displayed on the serial terminal.

Resources and settings

The project uses a custom design.modus file because the following settings were modified in the default design.modus file.

USIC (UART) settings

USIC interrupt settings (For XMC1400 devices only)

UART Tx pin settings

UART Rx pin settings

Related resources

Other resources

Infineon provides a wealth of data at www.infineon.com to help you select the right device, and quickly and effectively integrate it into your design.

For XMC™ MCU devices, see 32-bit XMC™ industrial microcontroller based on Arm® Cortex®-M.

Document history

Document title: CE232787 – XMC™ MCU: Math CORDIC

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