AN5325_ 基于STM32CubeG4软件包开始使用CORDIC加速器的应用手册.pdf

Introduction

This document applies to STM32CubeG4 MCU Package, for use with STM32G4 Series microcontrollers.

The CORDIC is a hardware accelerator designed to speed up the calculation of certain mathematical functions, notably

trigonometric and hyperbolic, compared to a software implementation.

The accelerator is particularly useful in motor control and related applications, where algorithms require frequent and rapid

conversions between rectangular (x, y) and angular (amplitude, phase) co-ordinates.

This application note describes how the CORDIC accelerator works on STM32G4 Series microcontrollers, its capabilities and

limitations, and evaluates the speed of execution for certain calculations compared with equivalent software implementations.

The example code to accompany this application note is included in the STM32CubeG4 MCU Package available on

www.st.com

1 General information

The STM32CubeG4 MCU Package runs on STM32G4 Series microncontrollers, based on Arm

®

Cortex

®

-M4

processors.

2 CORDIC introduction

Cordic (coordinate rotation digital computer) is a low-cost successive approximation algorithm for evaluating

trigonometric and hyperbolic functions.

and sine of

This is illustrated in Figure 1 for an angle of 60 deg. The vector undergoes a scaling by 1/0.61

(~1.65) over the course of the calculation.

q

Inversely, the angle of a vector [x, y] is determined by rotating 0.61[x, y] through successively decreasing angles

to obtain the unit vector [1, 0]. The cumulative sum of the rotation angles gives the angle of the original vector,

corresponding to arctangent (y/x).

The CORDIC algorithm can also be used for calculating hyperbolic functions (sinh, cosh, atanh) by replacing the

circular rotations by hyperbolic angles tanh

-1

(2

-j

) (j = 1, 2, 3...), see Figure 2. CORDIC hyperbolic mode operation.

The natural logarithm is a special case of the inverse hyperbolic tangent, obtained from the identity:

CORDIC also calculates √(cosh

2

t - sinh

2

Additional functions are calculated from the above using appropriate identities:

tanh x =

x = log

10

The CORDIC algorithm lends itself to hardware implementation since there are no multiplications involved (the

fixed scaling factor A is pre-loaded). Only add and shift operations are performed. This also means that it is

ideally suited to integer arithmetic.

3

2.1 Limitations

In circular mode, the CORDIC converges for all angles in the range -π to π radians. The use of fixed point

representation means that input and output values must be in the range -1 to +1. Input angles in radians must be

multiplied by 1/π and output angles must be multiplied by π to convert back to radians.

The modulus must be in the range 0 to 1, whether converting from polar to rectangular or rectangular to polar.

This means that phase(1.0, 1.0) gives false results since the modulus (√2) is out of range and saturates the

CORDIC engine, even if only the phase is needed.

In hyperbolic mode, x = cosh t being defined only for x ≥ 1, all inputs and outputs are divided by 2 to remain in the

j

angle |tanh

j tends to infinity, the sum of |δt

j

| tends to 1.118:

j = 1

∞

tanh

−1

2

= 1.118