Computing Fixed-Point Square Roots and Their Reciprocals Using Goldschmidt Algorithm

Michael Morris June 14, 2020
Introduction

A well known algorithm for computing square roots by iteration is provided by the Newton-Raphson Algorithm. The algorithm determines the square root using iteration until the root has been determined to some user-defined level of accuracy. The method is easily derived. First, describe a number in terms of its square root:

$$ a = y ^ {2} ,$$

where $y = \sqrt{a}$. The value of the $\sqrt{a}$ can be written as $y = y_0 + \epsilon$, where $y_0$ is the value of the square root and...


Cutting a Path Forward

David Days April 4, 20183 comments
Introduction

As a newcomer to the community, I thought I would start off by introducing myself, and give a little information about what has drawn me to start working with FPGAs.

My day job is as a professional software developer:  Figure out what people want; figure out how to make it happen (if possible); and then wrangle code, databases, networks, and servers into giving the correct responses or actions as necessary.

By night, however, I've been working on my...


An absolute position encoder VHDL core

Fabien Le Mentec November 11, 2015
Introduction

Let's consider motorized systems controlled by electronics. A closed loop architecture looks like this:

The following components are involved:

  • the motor itself (DC, stepper ...),
  • the controller, in charge of computing position according to the whole system state,
  • the driver board in charge of generating signals and power for the motor,
  • the position encoder, the subject of this post.

Most of the time, there is a difference between the position the system...


An absolute position encoder VHDL core

Fabien Le Mentec November 11, 2015
Introduction

Let's consider motorized systems controlled by electronics. A closed loop architecture looks like this:

The following components are involved:

  • the motor itself (DC, stepper ...),
  • the controller, in charge of computing position according to the whole system state,
  • the driver board in charge of generating signals and power for the motor,
  • the position encoder, the subject of this post.

Most of the time, there is a difference between the position the system...


Cutting a Path Forward

David Days April 4, 20183 comments
Introduction

As a newcomer to the community, I thought I would start off by introducing myself, and give a little information about what has drawn me to start working with FPGAs.

My day job is as a professional software developer:  Figure out what people want; figure out how to make it happen (if possible); and then wrangle code, databases, networks, and servers into giving the correct responses or actions as necessary.

By night, however, I've been working on my...


Computing Fixed-Point Square Roots and Their Reciprocals Using Goldschmidt Algorithm

Michael Morris June 14, 2020
Introduction

A well known algorithm for computing square roots by iteration is provided by the Newton-Raphson Algorithm. The algorithm determines the square root using iteration until the root has been determined to some user-defined level of accuracy. The method is easily derived. First, describe a number in terms of its square root:

$$ a = y ^ {2} ,$$

where $y = \sqrt{a}$. The value of the $\sqrt{a}$ can be written as $y = y_0 + \epsilon$, where $y_0$ is the value of the square root and...