1 © 2013 The MathWorks, Inc.

Optimize DSP Designs and Code using Fixed-Point Designer

MathWorks Korea

이웅재 부장

Senior Application Engineer

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Agenda

Fixed-point concepts

Introducing Fixed-Point Designer

Overview of floating-point to fixed-point workflows

Workflow demos

– Simulink Based

– MATLAB Based

Code generation from fixed-point design

– C and HDL

Summery

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Real Workflow Story 1

Word Floating Point C

Use IDE or makefile

Debug using break points and watch variables in memory

Verify using File Input / File Output

Multiple teams, single location

Share Word documents, C code

TMS320C6000™

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Real Workflow Story 2

PDF MATLAB®

MATLAB Floating Point C

Floating Point C Fixed-Point C

CCS for compile – link – download

Debug: break points, watch windows

Verify using MATLAB test data

Multiple teams across the globe

Share PDF, MATLAB Code, C code

TMS320C6000™

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Design Challenges

Demand for higher performance drives increasing complexity

– 30%+ of time spent on verification

– 25%+ of design time spent on fixed-point conversion

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Introduction

Variety of Measurements & Scales

– E.g., Fahrenheit vs Celsius

– Room temperature measurement

50 – 60 deg F 10 – 15.5 deg C

– F = (C*9/5) + 32 9/5: Scaling, 32: Bias

(offset)

Characteristics of Representation in Digital

Systems

Representations in digital systems is only an

approximation of real world values

– Range: Limits of representation

– Precision: Distance between successive

numbers

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What is floating-point?

Characterized by SIGN bit, MANTISSA(Fraction) and EXPONENT IEEE

754 Single Precision format (Normalized): 32 bits word size(single)

Use of three separate fields increases both range (Exponent size) and

precision (Fraction size) of floating point numbers

Above picture from http://en.wikipedia.org/wiki/Single_precision_floating-point_format

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What is fixed-point?

Characterized by single WORD with fixed RADIX Point

Use fractional numbers without floating point

For a fixed size, trade-off between Precision and Range

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Fixed-Point Targets

Digital Signal Processors (TI, Analog Devices, etc.)

– Fixed-point DSPs are considerably less expensive than floating-point

DSPs

– Fixed-point DSPs use less power and are good for battery powered

applications

– Clock speeds for fixed-point DSPs are much higher

– Fixed word lengths

Field Programmable Gate Arrays (Xilinx, Altera, etc.)

– In fixed-point FPGA implementations every bit of increased word

length results in more silicon area used and increased power usage

– Designer can select word lengths

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Fixed Point Tradeoff

Consideration Fixed Point Floating Point

RAM and ROM consumption Small Large

Execution time Faster Slower

Hardware power consumption Low High

Embedded Hardware Cost Lower Higher

Development time Long Short

Implementation complexity More. Need to keep track of word

lengths, fractional scaling. Write

your own rounding methods and

saturation code

Less

Error Prone Harder to develop. More prone to

quantization and overflow errors

due to smaller range. More prone

to programming errors

Easier to develop

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Fixed Point Drawbacks & Solutions

Drawback

Longer development time

Solution

Using Simulation, automated verification and automated scaling tools will

shorten development time and resources

Drawback

Error prone due to implementation complexity

Solution

Using rapid prototyping, in-the-loop testing, and production code generation

helps reduce errors significantly

Drawbacks

Quantization errors due to smaller dynamic range

Solution

Quantization errors can be reduced by selecting appropriate SCALING

(position of Radix Point) and WORD SIZE (limited by Hardware)

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How Does Fixed-Point Work on my

DSP?

The chip does integer math, not fixed-point.

Fixed-point is a “do-it-yourself” world.

Addition and subtraction: – You align the binary point (using >> or <<), then add.

Multiplication: – Integer multiply, then you interpret binary point of product.

Division: – You probably can’t use /. You write a function or make a library

function call.

Sqrt: – Can’t use standard math library. You write another function.

Rounding and/or saturation: You want it? You do it.

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Example: Fixed-Point C implementation

void differentialEq( void ) { /* Implements a fixed point first order difference equation */ int Prod; long Accum; static short lastVal=0; short a=0x7eb8; // 0.99 in s16,15 short oneminusa=0x0148; // .01 in s16,15 short temp; Prod = gAlg_in1 * gAlg_in1; temp = Prod >> 15; Accum = a*lastVal + oneminusa*temp; gAlg_out1 = (short)(Accum >> 15); lastVal = gAlg_out1; }

No saturation or rounding

Convert variables to integer types

Keep track of binary point location

Need lots of comments to

understand code

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Unified Fixed-Point Toolbox

and Simulink Fixed Point

Products

Supports MATLAB and

Simulink workflows

Simulink

Fixed Point

Fixed-Point

Designer

Fixed-Point

Toolbox

Introducing Fixed-Point Designer

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3 Tools for Converting a Design to Fixed Point

Instrumented Code Generation Report for MATLAB

Requires: Fixed-Point Designer

Works on: MATLAB Code

MATLAB Function Blocks

Fixed-Point Conversion Tool for MATLAB

Requires: Fixed-Point Designer

MATLAB Coder

Works on: MATLAB Code

Fixed-Point Tool for Simulink

Requires: Fixed-Point Designer

Simulink

Works on: Simulink Blocks

Stateflow Charts

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Simulink Workflow for Fixed Point Design

Are results

satisfactory?

No Yes

Prepare for fixed

point conversion

Collect Range

Information

Propose Data Types

Apply Data Types

Compare Result

Existing model (Floating-Point /

Fixed-Point)

Generate

Code

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Prepare your model for fixed-point conversion

by using Fixed-Point Advisor

Select a task in the listed order.

Run the task.

• If passed, move to the next task.

• If failed, fix the error, run the task again, and

move to the next task.

• If there is a warning,

• If important, take the recommended

action(s), run the task again and move

on to the next task when the issue is

resolved.

• If not critical, ignore the warning and

move to the next task.

Return to Fixed-Point Tool.

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Workflow Demo 1: Envelop Detector

Fixed-Point Tool in Simulink

Logging to capture dynamic range of signals

Data Type Override to switch between floating- and fixed-point data types

Auto-scale to set fractional precision based on recorded dynamic range

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MATLAB Workflow for Fixed Point Design

Are results

satisfactory?

No Yes

Prepare for

fixed-point

conversion

Collect Range

Information

Type Proposal

Generate fixed point

MATLAB code

Test Numerics

Existing Code (Floating-Point)

Generate

Code

Existing Stimulus (Floating-Point)

Make Project

Set Input Type

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Workflow Demo 2: Kalman Filter

Fixed-Point Conversion Tool in MATLAB

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Code Generation for Fixed-Point

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Benefit of using both C/HDL auto code

generation tools

Separation between Design and Implementation

Target Devices can be chosen at the final stage.

Software and Hardware Partitioning can be

easily made.

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Code Generation Products for C/C++

MATLAB® Coder™

Automatically generate C and C++ from

MATLAB code

Simulink® Coder™

Automatically generate C and C++ from

Simulink models and Stateflow charts

Embedded Coder™

Automatically generate C and C++

optimized for embedded systems

Simulink

Coder

Embedded Coder

MATLAB Coder

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Code Generation Products for VHDL/Verilog

MATLAB® Coder™

Automatically generate C and C++ from

MATLAB code

MATLAB Coder

HDL Coder HDL Coder™

Automatically generate VHDL or Verilog

from MATLAB code and Simulink Model

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Simple example: C Code

fiCodeGen7.c fixedCodeGen_Y.Result = (int16_T)((fixedCodeGen_U.In1 << 2) + fixedCodeGen_U.In2) * fixedCodeGen_U.In3;

fiCodeGen7.h /* External Input*/ typedef struct { int8_T In1; int16_T In2; int8_T In3; } ExternalInputs_fixedCodeGen; /* External Output*/ typedef struct { int32_T Result; } ExternalOutputs_fixedCodeGen;

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Simple example: HDL Code (vhdl case)

Entity Part

Architecture Body Part

Synthesis Result (Precision RTL)

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Supports automated code generation to C or HDL

Code Generation Demo: LPF

Simulink workflow

C/C++ HDL

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Code Generation Demo: LPF

MATLAB workflow

C/C++

HDL

MATLAB Code

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Summary

MATLAB/Simulink

Algorithm Design

FPGA ASIC FPGA ASIC

VHDL/Verilog

Gen

FPGA ASIC

Simulink Coder

MCU DSP

C/C++

Fixed Point Designer

Fixed-Point Conversion

Gen

Number System Concepts

Fixed-Point Designer

Conversion Workflow

– MATLAB/Simulink

Code generation

– C and HDL

Gen

Gen

Embedded Coder HDL Coder

MATLAB Coder