# Accelerating Execution Speed of Fixed-Point Algorithms in MATLAB & Simulink

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1 Accelerating Execution Speed of Fixed-Point Algorithms in MATLAB & Simulink 2007 The MathWorks, Inc. Houman Zarrinkoub, PhD. Product Manager Signal Processing Toolboxes

2 Outline Challenges in fixed-point signal processing Traditional design workflow Advantages of Model-Based Design workflow Introducing our integrated tools for Float-to-fixed conversion Acceleration of fixed-point simulation Automatic C code generation Demo Summary 2

3 Fixed-point signal processing applications Tasks Design and analyze fixed-point algorithms Verify fixed point implementations Hardware targets FPGA or ASIC Fixed-point DSP chip 3

4 What is fixed-point? Binary representation of data with finite number of bits Finite word length arithmetic with a fixed number of fractional digits Sign bit If signed 1 st integer bit Binary point Optimal for machine, hard for humans to program Word length (8) Number of fractional bits (3) 4

5 Why use fixed-point hardware? Advantages: Simpler circuits, smaller chip sizes Lower power consumption Lower unit cost Drawbacks: Harder to program Error-prone Device-specific and not reusable Our solution addresses all these drawbacks 5

6 Fixed-point design challenges Finite word lengths = introducing quantization error Quantization error types Overflow (overload distortion) Data beyond range of fixed-point data type Underflow (granular noise) Not enough fractional bits for exact data match 7+1=8 bit word length & 1 fractional bit Range =[ ) Step =1/2 s /2 1/4 1/8 1/16 1/32 7+1=8 bit word length & 5 fractional bits Range =[ ) Step = 1/32 6

7 Challenges in converting a design to fixed-point Goal: Ensure adherence to specifications before hardware prototyping How: properly scale input, output, and EVERY intermediate quantity Result: To minimize error propagation of EVERY variable in algorithm 7

8 Fixed-point algorithm design Traditional workflow 1. Set-up simulation flow MATLAB 2. Express your floating-point algorithm Focus on algorithmic integrity, proof of concept 3. Simulate (floating-point) iterate on algorithm trade-offs, validate against requirements 4. Convert design to fixed-point Focus of design viability based on implementation constraints 5. Simulate (fixed-point) iterate on implementation trade-offs, validate against original requirements 6. Generate code for implementation 7. Validate and verify design after deployment C/C++ 8

9 Traditional fixed-point DSP design flow Within MATLAB environment Outside MATLAB environment Floating-point M-code Floating-point C-code Fixed-point C-code Machine Assembly code Manually maintain & update multiple copies of same algorithm Compilation or hand-code 9

10 Problems with traditional fixed-point workflow Multiple truths (Copies of same algorithm) Floating-point M code Floating-point C code Fixed-point C code Error-prone design Using different tools Exchange data across tools Multiple update/test of code No standard C/C++ based fixed-point tools Floating-to-fixed-point conversion 10

11 Fixed-point algorithm design Model-based Design workflow 1. Set-up simulation flow 2. Express your floating-point algorithm Focus on algorithmic integrity, proof of concept 3. Simulate (floating-point) iterate on algorithm trade-offs, validate against requirements 4. Convert design to fixed-point Focus of design viability based on implementation constraints 5. Simulate (fixed-point) iterate on implementation trade-offs, validate against original requirements 6. Generate code for implementation 7. Validate and verify design after deployment MATLAB & Simulink 11

12 Model-based fixed-point DSP design flow Simulink Within MATLAB/Simulink environment Floating-point M-code Fixed-point M-code Fixed-point C-code Machine Assembly code Integrated elaboration streamlined MATLAB tools Automatic C code generation Compilation with Link & Target products 12

13 Advantages of Model-Based fixed-point design workflow Maintain One Truth One integrated design environment MATLAB benefit: Integrated fixed-point design tools No sacrifice of simulation speed Automatic path to implementation 13

14 How does Model-Based Design makes it faster and easier? Streamline process of converting your MATLAB algorithms to fixed-point Simulate fixed-point algorithms with large data sets at compiled- C-code speed Integrate with system-level design in Simulink Generate embeddable C code for implementation with Real- Time Workshop 14

15 Streamlined floating-to-fixed conversion: introducing Data-type override Turn on the logging mode Set data type override parameters Observe dynamic range of variables in your M-code Set the best fixed-point attributes to avoid overflow/underflow & large quantization errors 15

16 Tools for scaling a fixed-point variable Data logging Steps involved with dynamic range analysis to convert a design into fixed-point 1. Compute the range based on the min/max logs 2. Compute the integer part to fit variable within range 3. Compute the fraction length as the rest of bit budget 4. Construct the fixed-point numeric type object 16

17 Fixed-point acceleration: introducing new emlmex function Fast simulation through code generation Analogous to Simulink Accelerator Automatic generation of C-MEX function from M-function M-code confined to embedded MATLAB language subset Compile C-code execution speed (beyond 100x acceleration in MATLAB) 17

18 Integrate MATLAB design with Simulink Embedded MATLAB Function block Change parameters and run Simulink simulations from MATLAB Embedded MATLAB Function Integration of Embedded MATLAB Functions in Simulink 18

19 Automatic fixed-point C code generation Real-Time Workshop Enabled via Simulink Fixedpoint Real-Time Workshop Real-Time Workshop Embedded Coder Supports up to 32-bit fixedpoint numbers Uses only native C integer data types 19

20 Hands-on Demonstration 1. Implement the algorithm with floating-point data types in M. 2. Convert to fixed-point data types in M and run with default settings; observe scaling issues! 3. Log the full numerical range of variables (data logging and data type override) 4. Use the logged minimum and maximum values to set the fixedpoint scaling. 5. Validate the fixed-point solution interactively. 6. Convert M to MEX using EMLMEX function for fast simulation and large test-set verification. 7. Convert M to C in Simulink Embedded MATLAB Function block with RTW for embedded implementation. 20

21 New Demos in R2007a Fixed-Point Lowpass Filtering Using Embedded MATLAB MEX Fixed-Point Acceleration Fixed-Point Data Type Override, Min/Max Logging, and Scaling Floating-to-Fixed Conversion Fixed-Point Fast Fourier Transform (FFT) Fixed-Point C code generation (Simulink / RTW) 21

22 For more information Introductory fixed-point signal processing webinars (recorded) Fixed-Point Programming in MATLAB Fixed-Point Signal Processing with MATLAB and Simulink About MATLAB and Simulink signal processing products Relevant product demos User-contributed examples in MATLAB Central 22

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