About Fixed-Point Numbers

  Signed Fixed-Point Numbers

  Binary Point Interpretation

  Scaling

  Quantization

  Range and Precision

  Constant Scaling for Best Precision

  Fixed-Point Data Type and Scaling Notation

  Scaled Doubles

  Example: Port Data Type Display

  About Floating-Point Numbers

  Scientific Notation

  The IEEE Format

  Range and Precision

  Exceptional Arithmetic

  Introduction

  Rounding

  Padding with Trailing Zeros

  Example: Limitations on Precision and Errors

  Example: Maximizing Precision

  Net Slope and Net Bias Precision

  Introduction

  Saturation and Wrapping

  Guard Bits

  Example: Limitations on Range

  Introduction

  Addition

  Accumulation

  Multiplication

  Gain

  Division

  Summary

  Introduction

  Parameter Conversions

  Signal Conversions

  Introduction

  Computational Units

  Addition and Subtraction

  Multiplication

  Division

  Shifts

  Introduction

  Realizations and Data Types

  Introduction

  Size Assumptions

  Operation Assumptions

  Design Rules

  Introduction

  Direct Form II

  Series Cascade Form

  Parallel Form

  Introduction to the Fixed-Point Advisor

  Best Practices for Using the Fixed-Point Advisor

  Models That Might Cause Data Type Propagation Errors

  Running the Fixed-Point Advisor

  Fixing a Task Failure

  Automatically Fixing Failures

  Batch Fixing Failures

  About This Tutorial

  Starting the Fixed-Point Advisor

  Prepare Model for Conversion

  Prepare for Data Typing and Scaling

  Perform Data Typing and Scaling

  Prepare for Code Generation

  Introduction to the Fixed-Point Tool

  Before Using the Fixed-Point Tool to Autoscale Your Simulink Model

  Best Practices for Using the Fixed-Point Tool to Autoscale Your Simulink Model

  Models That Might Cause Data Type Propagation Errors

  Opening the Fixed-Point Tool

  Understanding the Interface

  Fixed-Point Tool Workflow

  Prerequisites for Using the Fixed-Point Tool

  Running the Model to Gather a Floating-Point Benchmark

  Proposing Scaling

  Examining Results to Resolve Conflicts

  Applying Scaling

  Storing Reference Run

  Verifying New Settings

  Automatic Scaling of Simulink Signal Objects

  Opening the Demo Model

  About the Demo Model

  Simulation Setup

  Idealized Feedback Design

  Digital Controller Realization

  Before You Begin

  Initial Guess at Scaling

  Data Type Override

  Automatic Scaling

  What Is Worst-Case Error for a Lookup Table?

  Example: Square Root Function

  Introduction

  Parameters for fixpt_look1_func_approx

  Setting Function Parameters for the Lookup Table

  Example: Using errmax with Unrestricted Spacing

  Example: Using nptsmax with Unrestricted Spacing

  Example: Using errmax with Even Spacing

  Example: Using nptsmax with Even Spacing

  Example: Using errmax with Power of Two Spacing

  Example: Using nptsmax with Power of Two Spacing

  Specifying Both errmax and nptsmax

  Comparison of Example Results

  Criteria for Comparing Types of Breakpoint Spacing

  Model That Illustrates Effects of Breakpoint Spacing

  Data ROM Required for Each Lookup Table

  Determination of Out-of-Range Inputs

  How the Lookup Tables Determine Input Location

  Interpolation for Each Lookup Table

  Summary of the Effects of Breakpoint Spacing

  Introduction

  Languages

  Data Types

  Rounding Modes

  Overflow Handling

  Blocks

  Scaling

  Introduction

  External Mode

  Rapid Simulation Target

  Introduction

  Restrict Data Type Word Lengths

  Avoid Fixed-Point Scalings with Bias

  Wrap and Round to Floor or Simplest

  Limit the Use of Custom Storage Classes

  Limit the Use of Unevenly Spaced Lookup Tables

  Minimize the Variety of Similar Fixed-Point Utility Functions

  Handle Net Slope Correction

  Introduction

  Optimize Lookup Table Data

  Reduce Cumbersome Multiplications

  Optimize the Number of Multiply and Divide Operations

  Reduce Multiplies and Divides with Nonzero Bias

  Eliminate Mismatched Scaling

  Minimize Internal Conversion Issues

  Use the Most Efficient Rounding

  Optimize Net Slope Correction

  Fixed-Point Advisor Overview

  Prepare Model for Conversion Overview

  Verify model simulation settings

  Verify update diagram status

  Address unsupported blocks

  Set up signal logging

  Create simulation reference data

  Verify Fixed-Point Conversion Guidelines Overview

  Check model configuration data validity diagnostic parameters settings

  Implement logic signals as Boolean data

  Check for proper bus usage

  Simulation range checking

  Check for implicit signal resolution

  Prepare for Data Typing and Scaling Overview

  Remove output data type inheritance

  Relax input data type settings

  Verify Stateflow charts have strong data typing with Simulink

  Remove redundant specification between signal objects and blocks

  Verify hardware selection

  Specify block minimum and maximum values

  Summarize blocks with locked scaling

  Perform Data Typing and Scaling Overview

  Propose data type and scaling

  Check for numerical errors

  Analyze logged signals

  Summarize data types

  Prepare for Code Generation Overview

  Disable signal logging

  Identify blocks that generate expensive saturation and rounding code

  Identify questionable fixed-point operations

  Supported Data Types

  The Treatment of Integers

  Data Type Override

  Introduction

  Storage Containers in Simulation

  Storage Containers in Code Generation

  The Assignment of Data Type IDs

  Registering Data Types

  Setting and Getting Data Types

  Getting Information About Data Types

  Converting Data Types

  Tokens for Overflow Handling and Rounding Methods

  Overflow Logging Structure

  Introduction

  MEX-Files on UNIX

  MEX-Files on Windows

  List of Fixed-Point S-Function Examples

  Getting the Input Port Data Type

  Setting the Output Port Data Type

  Interpreting an Input Value

  Writing an Output Value

  Using the Input Data Type to Determine the Output Data Type