# SystemC Code Generation for Bisection Algorithm

You can generate SystemC™ code from a MATLAB® design that implements a bisection algorithm to calculate the square root of a number in fixed-point notation.

### MATLAB Design

First, set up the `sqrt` model.

```mlhdlc_demo_setup('sqrt'); % Design Sqrt design_name = 'mlhdlc_sqrt'; % Test Bench for Sqrt testbench_name = 'mlhdlc_sqrt_tb'; ```

Review the `sqrt` design

```dbtype(design_name) ```
```1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 2 % MATLAB design: Pipelined Bisection Square root algorithm 3 % 4 % Introduction: 5 % 6 % Implement SQRT by the bisection algorithm in a pipeline, for unsigned fixed 7 % point numbers (also why you don't need to run fixed-point conversion for this design). 8 % The demo illustrates the usage of a pipelined implementation for numerical algorithms. 9 % 10 % Key Design pattern covered in this example: 11 % (1) State of the bisection algorithm is maintained with persistent variables 12 % (2) Stages of the bisection algorithm are implemented in a pipeline 13 % (3) Code is written in a parameterized fashion, i.e. word-length independent, to work for any size fi-type 14 % 15 % Ref. 1. R. W. Hamming, "Numerical Methods for Scientists and Engineers," 2nd, Ed, pp 67-69. ISBN-13: 978-0486652412. 16 % 2. Bisection method, http://en.wikipedia.org/wiki/Bisection_method, (accessed 02/18/13). 17 % 18 19 % Copyright 2013-2015 The MathWorks, Inc. 20 21 %#codegen 22 function [y,z] = mlhdlc_sqrt( x ) 23 persistent sqrt_pipe 24 persistent in_pipe 25 if isempty(sqrt_pipe) 26 sqrt_pipe = fi(zeros(1,x.WordLength),numerictype(x)); 27 in_pipe = fi(zeros(1,x.WordLength),numerictype(x)); 28 end 29 30 % Extract the outputs from pipeline 31 y = sqrt_pipe(x.WordLength); 32 z = in_pipe(x.WordLength); 33 34 % for analysis purposes you can calculate the error between the fixed-point bisection routine and the floating point result. 35 %Q = [double(y).^2, double(z)]; 36 %[Q, diff(Q)] 37 38 % work the pipeline 39 for itr = x.WordLength-1:-1:1 40 % move pipeline forward 41 in_pipe(itr+1) = in_pipe(itr); 42 % guess the bits of the square-root solution from MSB to the LSB of word length 43 sqrt_pipe(itr+1) = guess_and_update( sqrt_pipe(itr), in_pipe(itr+1), itr ); 44 end 45 46 %% Prime the pipeline 47 % with new input and the guess 48 in_pipe(1) = x; 49 sqrt_pipe(1) = guess_and_update( fi(0,numerictype(x)), x, 1 ); 50 51 %% optionally print state of the pipeline 52 %disp('************** State of Pipeline **********************') 53 %double([in_pipe; sqrt_pipe]) 54 55 return 56 end 57 58 % Guess the bits of the square-root solution from MSB to the LSB in 59 % a binary search-fashion. 60 function update = guess_and_update( prev_guess, x, stage ) 61 % Key step of the bisection algorithm is to set the bits 62 guess = bitset( prev_guess, x.WordLength - stage + 1); 63 % compare if the set bit is a candidate solution to retain or clear it 64 if ( guess*guess <= x ) 65 update = guess; 66 else 67 update = prev_guess; 68 end 69 return 70 end ```

### Simulate the Design

It is a best practice to simulate the design with the test bench prior to code generation to check for run-time errors.

```mlhdlc_sqrt_tb ```
```Iter = 01| Input = 0.000| Output = 0000000000 (0.00) | actual = 0.000000 | abserror = 0.000000 Iter = 02| Input = 0.000| Output = 0000000000 (0.00) | actual = 0.000000 | abserror = 0.000000 Iter = 03| Input = 0.000| Output = 0000000000 (0.00) | actual = 0.000000 | abserror = 0.000000 Iter = 04| Input = 0.000| Output = 0000000000 (0.00) | actual = 0.000000 | abserror = 0.000000 Iter = 05| Input = 0.000| Output = 0000000000 (0.00) | actual = 0.000000 | abserror = 0.000000 Iter = 06| Input = 0.000| Output = 0000000000 (0.00) | actual = 0.000000 | abserror = 0.000000 Iter = 07| Input = 0.000| Output = 0000000000 (0.00) | actual = 0.000000 | abserror = 0.000000 Iter = 08| Input = 0.000| Output = 0000000000 (0.00) | actual = 0.000000 | abserror = 0.000000 Iter = 09| Input = 0.000| Output = 0000000000 (0.00) | actual = 0.000000 | abserror = 0.000000 Iter = 10| Input = 0.000| Output = 0000000000 (0.00) | actual = 0.000000 | abserror = 0.000000 Iter = 11| Input = 4.625| Output = 0000010000 (2.00) | actual = 2.150581 | abserror = 0.150581 Iter = 12| Input = 12.500| Output = 0000011100 (3.50) | actual = 3.535534 | abserror = 0.035534 Iter = 13| Input = 16.250| Output = 0000100000 (4.00) | actual = 4.031129 | abserror = 0.031129 Iter = 14| Input = 18.125| Output = 0000100010 (4.25) | actual = 4.257347 | abserror = 0.007347 Iter = 15| Input = 20.125| Output = 0000100010 (4.25) | actual = 4.486090 | abserror = 0.236090 Iter = 16| Input = 21.875| Output = 0000100100 (4.50) | actual = 4.677072 | abserror = 0.177072 Iter = 17| Input = 35.625| Output = 0000101110 (5.75) | actual = 5.968668 | abserror = 0.218668 Iter = 18| Input = 50.250| Output = 0000111000 (7.00) | actual = 7.088723 | abserror = 0.088723 Iter = 19| Input = 54.000| Output = 0000111010 (7.25) | actual = 7.348469 | abserror = 0.098469 Iter = 20| Input = 62.125| Output = 0000111110 (7.75) | actual = 7.881941 | abserror = 0.131941 Iter = 21| Input = 70.000| Output = 0001000010 (8.25) | actual = 8.366600 | abserror = 0.116600 Iter = 22| Input = 81.000| Output = 0001001000 (9.00) | actual = 9.000000 | abserror = 0.000000 Iter = 23| Input = 83.875| Output = 0001001000 (9.00) | actual = 9.158330 | abserror = 0.158330 Iter = 24| Input = 83.875| Output = 0001001000 (9.00) | actual = 9.158330 | abserror = 0.158330 Iter = 25| Input = 86.875| Output = 0001001010 (9.25) | actual = 9.320676 | abserror = 0.070676 Iter = 26| Input = 95.125| Output = 0001001110 (9.75) | actual = 9.753205 | abserror = 0.003205 Iter = 27| Input = 97.000| Output = 0001001110 (9.75) | actual = 9.848858 | abserror = 0.098858 Iter = 28| Input = 101.375| Output = 0001010000 (10.00) | actual = 10.068515 | abserror = 0.068515 Iter = 29| Input = 102.375| Output = 0001010000 (10.00) | actual = 10.118053 | abserror = 0.118053 Iter = 30| Input = 104.250| Output = 0001010000 (10.00) | actual = 10.210289 | abserror = 0.210289 ```

### Create HDL Coder™ Project

Create an HDL Coder project.

```coder -hdlcoder -new mlhdlc_sqrt_prj ```

Add the file `mlhdlc_sqrt.m` to the project as the MATLAB Function. Add the file `mlhdlc_sqrt_tb.m` as the MATLAB Test Bench.

### SystemC Code Generation

This design is already in fixed point and suitable for SystemC code generation. You do not need to run floating point to fixed point conversion on this design.

To generate SystemC code from the MATLAB design:

1. At the MATLAB command line, set up the path for SystemC code generation by using the function `hdlsetuphlstoolpath`.