Programming Digital Systems

Numerical Methods

David Mayerich

Scalable Tissue Imaging and Modeling (STIM) Laboratory

Department of Electrical and Computer Engineering

Cullen College of Engineering

University of Houston

David Mayerich

STIM Laboratory, University of Houston

C/C++ Development Tools

Compiling and linking

Using gcc, Visual Studio, and secure shell (SSH)

David Mayerich

STIM Laboratory, University of Houston

C/C++

David Mayerich

STIM Laboratory, University of Houston

executable

linker

object code

compiler

preprocessor

opengl

ntdll

kernel32

msvcrt

dynamic
libraries

eigen3

glm

boost

static
libraries

glm.h

iostream

eigen3.h

opengl.h

header
files

source code

Compilers

GNU Compiler collection (gcc/g++)
Clang/LLVM (clang/clang++)
- Open source compiler on all major operating systems
- Strong support for recent C/C++ language standards
Microsoft Visual C++ (msvc/cl)
- Proprietary compiler only available for Windows
- Poor support for C++ 26, decent support for C++ 23
- Integrated UI/debugging tools
Intel oneAPI C++ Compiler (icpx/icx)
- Proprietary compiler available for all major operating systems
- Poor support for C++ 26, good support for C++ 23
- Excellent benchmark/optimization performance, especially with their math libraries

David Mayerich

STIM Laboratory, University of Houston

Operating Systems - Recommendations

David Mayerich

STIM Laboratory, University of Houston

Visual C++, GNU, Clang, oneAPI

Visual Studio:

Easy to install
Provides good debugging and profiling tools
Very hard to start a project from scratch

GNU C/C++

More difficult to install (use MinGW)
Need an IDE (CLion, Dev-C++)

Consider using VS with Intel's oneAPI compiler. Install VS (be sure to click C/C++), then oneAPI.

GNU, Xcode/Clang, oneAPI

GNU C/C++:

Install using homebrew
Very easy to start/use
Select your IDE: CLion, VS Code, Code::Blocks, Eclipse

Xcode/Clang:

Default compiler, uses Clang
Can't use CUDA (uses Metal)

Recommend installing GNU because std::thread support is a little spotty. Can't use CUDA on your system so you'll have to use a server with GNU anyway.

GNU, Clang, oneAPI

GNU C/C++:

Install via package manager
Very easy to start/use
Select your IDE: CLion, VS Code, Code::Blocks, Eclipse

Intel oneAPI:

Installation will link GNU
Generally better benchmarking performance

I prefer CLion with either GNU or oneAPI - usually GNU on workstations and oneAPI on servers.

Windows

macOS

Linux

Working with Good Source Code

David Mayerich

STIM Laboratory, University of Houston

source repository

source code
data
documentation
test code
build scripts

source repository

source code
data
documentation
test code
build scripts

build

executable

build directory

Makefiles
VS project
data files

generate

pull

version control
(Git, Subversion)

local development system/workstation

Source Code Repository

myproject

```
CMakeLists.txt
```

src/

```
main_func.cpp
```
```
other-funcs.cpp
```
```
myproject.h
```

```
data/
```
- ```
image.jpg
```
- ```
spreadsheet.csv
```
```
docs/
```
- ```
Doxyfile
```

David Mayerich

STIM Laboratory, University of Houston

Put everything needed to build your project from scratch in here
Keep this directory structured
Make your project easy to build
- CMakeLists.txt - CMake script describes how to build the project
- Doxyfile - Doxygen script generates documentation
Create a separate "build" directory that holds binary files
- You should be able to work from different computers by sharing ONLY the source repository

Build Systems

Compiler/Linker require:
- source files to be compiled
- header files for any external libraries
- static library locations for linking
When multiple compilers are used (ex. C and CUDA)
- source files are passed to a CUDA compiler nvcc
- CUDA-related source is stripped and compiled into object code
- remaining source is passed to the C/C++ compiler
- all object code files are linked at the end
Anyway, this all gets very complicated and you shouldn't do it manually

David Mayerich

STIM Laboratory, University of Houston

Build Automation

Automation tools create a build system for your desired compiler and IDE
Find external libraries and header files
Pass the appropriate parameters to the compiler/linker
May also create an IDE
Multiple options
CMake has flaws but is the closest to an industry standard

David Mayerich

STIM Laboratory, University of Houston

Current Standards:

CMake - most popular, bad scripting

cmake.org

Premake - better scripting (Lua)

premake.github.io

Meson - fast for large projects

mesonbuild.com

CMake Scripts (CMakeLists.txt)

The CMakeLists.txt file is a script describing:
- what is required to build the project
- how to build the project
- what will be created as a result
The project will be created in the build directory
If anything goes wrong, you can always delete the build directory and re-run CMake

David Mayerich

STIM Laboratory, University of Houston

# specify the CMake version required
cmake_minimum_required(VERSION 3.0)

# create a name for this project
project(myproject)

# "glob" is a term for combining files
file(GLOB_RECURSE SOURCE src/*.cpp src/*.h)
file(GLOB_RECURSE DATA data/*)

# copy data files to the build directory
file(COPY ${DATA} DESTINATION .)

# create an executable from the source code
add_executable(myexe ${SOURCE})

Using CMake

Pull the repository:
git clone https://github.com/name/repo.git
Create your build environment
- from your source directory:
  cmake -B /path/to/build
- from anywhere else:
  cmake -B /path/to/build -S /path/to/source
Compile your project (depends on IDE/compiler)
- Visual Studio: click "build"
- GNU:
  cd /path/to/build
  make

David Mayerich

STIM Laboratory, University of Houston

CMake GUI (cmake-gui)

C/C++

David Mayerich

STIM Laboratory, University of Houston

executable

linker

object code

compiler

preprocessor

opengl

ntdll

kernel32

msvcrt

dynamic
libraries

eigen3

glm

boost

static
libraries

glm.h

iostream

eigen3.h

opengl.h

header
files

source code

Download libraries
Compile them if necessary
Tell the build system where to find them

Package Managers

Automate installing, updating, and removing software
This can include software like:
- static and dynamic libraries
- executable programs
- source code and documentation
Linux package managers vary with distribution
- aptitude (apt), Red Hat (rpm), pacman, snapcraft (snap)
macOS: homebrew

David Mayerich

STIM Laboratory, University of Houston

Windows doesn't have one BUT
vcpkg is cross-platform
- https://vcpkg.io
- Downloads and builds libraries locally
- Integrates with CMake

vcpkg

Clone vcpkg as a Git repository:
git clone https://github.com/microsoft/vcpkg.git
Run the build script (generates a vcpkg executable for your system)
cd vcpkg
./bootstrap-vcpkg.bat (Windows)
or
./bootstrap-vcpkg.sh (Linux, macOS)
Install libraries
./vcpkg install glfw3
./vcpkg install glm
...

David Mayerich

STIM Laboratory, University of Houston

Development Tools Summary

Create a source repository
- Organize your code using directories
Use a version tool (probably git)
- Organize revisions, undo mistakes
- Work on multiple updates
Make your repository redundant
- Dropbox, GitHub, Syncthing, etc.
- Easy to transfer code between computers

David Mayerich

STIM Laboratory, University of Houston

Create a CMakeLists.txt script
Generate the project
Edit source code
Compile/Run
Add libraries as needed

Data Types

Standards

Registers and Promotion

Integers and Overflow

David Mayerich

STIM Laboratory, University of Houston

Standards

Languages and data types are standardized
- ISO: International Organization for Standardization
- IEC: International Electrotechnical Commission
Most recent standards:
- C23 (published ISO/IEC 9899:2024)
- C++23 (published ISO/IEC 14882:2024)
- C26 and C++26 are currently working drafts
Available standards depend on what compiler you're using
- g++, Visual Studio, Clang, and Xcode all have good support for C++23
- g++, Clang, and Xcode have some support for upcoming features in C++26

David Mayerich

STIM Laboratory, University of Houston

Specifying Data Types

All values are stored in memory as a series of binary bits
A processor has to know how to process a given set of bits
C/C++ is compiled directly into processor instructions, so variable types have to be known at compile time
Data types follow IOS and IEC standards:

David Mayerich

STIM Laboratory, University of Houston

Integer Types

char - smallest addressable unit
(minimum 8-bit)
int - minimum 16 bits
(32-bit on most desktops)
can be specified as signed or unsigned
size_t - memory location
(64-bit on 64-bit systems)

Fractional Types

float - 32-bit decimal
IEEE 754 standard
double - 64-bit decimal
IEEE 754 standard

Type Resolution (C/C++)

Operations between the same type returns a value of that type
All operations must be between the same data type
Operations attempted between different types result in promotion of the lowest
Different types can be enforced by casting

David Mayerich

STIM Laboratory, University of Houston

int a = 2;
int b = 3;
int c = a * b;			//c is 6
int d = b / a;			//d is 1, why?

int x = 2;
float y = 1.6;
float z = x & y;		//z is 3.2

float w = x * (int) y;	// w = 2
int k = x * y;			// k = 3

Promotion

In general, data types are promoted from less information to more information
Sometimes that's ambiguous: 64-bit integers are promoted to 32-bit floats

David Mayerich

STIM Laboratory, University of Houston

64-bit long double

64-bit double

32-bit float

64-bit unsigned long long

64-bit long long

32-bit unsigned long

32-bit long

32-bit unsigned int

32-bit int

16-bit short

16-bit unsigned short

8-bit char

Modulus Operation

Modulus (or mod) is a binary operator commonly used in numerical computing
The mod operation (% in C/C++) returns the remainder of a division:

David Mayerich

STIM Laboratory, University of Houston

int a = 15;
int b = 4;
int x = a % b;		// x is 3

int c = 3;
int y = a % c;		// y is 0

Limits of Integers

Allocated registers have specified bit limits
A char is usually 8 bits
- signed char is limited to the range \([-128, 127]\)
- unsigned char is limited to the range \([0, 255]\)
What happens when these limits are exceeded?

David Mayerich

STIM Laboratory, University of Houston

unsigned char b = 254;
unsigned char y = b + 5;	// wraps around to 3
							// 254 -> 255 -> 0 -> 1 -> 2 -> 3
signed char a = 127;
signed char x = a + 1;		// undefined

Overflow as a Modulus

An unsigned overflow is defined as "wrapping around"
This is a modulus operation based on the \(n\)-bit register size:

David Mayerich

STIM Laboratory, University of Houston

y = b \text{ mod } 2^n

unsigned char b = 254;		// char is 8 bits
unsigned char y = b + 5;	// y = 3
							// 254 + 5 = 259
                            // 259 % 2^8
                            // 259 % 256 = 3

This can be helpful since a modulus operation is slow

Memory Allocation

Stack vs. Heap

Dynamic Allocation

Multidimensional Arrays

David Mayerich

STIM Laboratory, University of Houston

Memory Allocation

stack vs. heap
A stack is a data structure that is very fast at removing stuff added last
Basic allocations happen on the stack:

David Mayerich

STIM Laboratory, University of Houston

int a = 12;
int b = 300;
float x = 3.14;
float y[3];

float* z = (float*) malloc(sizeof(float) * 3);

previous allocations

a = 12

b = 300

x = 3.14

y[0]

y[1]

y[2]

z*

z[0]

z[1]

z[2]

heap

Practical Stack vs. Heap Allocation

The stack is fast - resets with scope:

David Mayerich

STIM Laboratory, University of Houston

int N = 100;
float z = 0.0;
for(int i = 0; i < N; i++) {
	float x = sin( a[i] );
    float y = cos( b[i] );
    z = x * y;
}

The stack has a limited size (stack overflow)
The heap is slower to allocate/free

previous allocations

N = 100

z = 0.0

i = 0

Dynamic Allocation

DO NOT use variables in static allocations:
- Not supported in recent versions of the C standard
- Can result in a stack overflow

David Mayerich

STIM Laboratory, University of Houston

DO use dynamic allocation:

int n;
scanf("size of array: %d", n);
float A[n];

float* A = (float*) malloc( n * sizeof(float));

OR (using C++):

float* A = new float[n];

Segmentation Faults

David Mayerich

STIM Laboratory, University of Houston

int N = 2000;
//.....
double* x;
x = (double*) malloc(N * sizeof(double));
x[2000] = 3.14159;		// possible segmentation fault

Heap Memory

Case 1 - allocation is contiguous in memory

Case 2 - allocation is not contiguous in memory

A[6] overwrites B[0]
(no error reported)

segmentation fault

A[0]

B[0]

A[0]

B[0]

Multidimensional Arrays

Stack allocation for 2D arrays:

David Mayerich

STIM Laboratory, University of Houston

Heap allocation for indirect addressing:

double A[20][20];
A[7][3] = 7.0 * 3.0;

int M = 20;		int N = 20;
//.....
double** A;
A = (double**) malloc(M * sizeof(double*));
for(int i = 0; i < M; i++) {
	A[i] = (double*) malloc(N * sizeof(double));
}
A[7][3] = 7.0 * 3.0;

A[N][0]

A[N][1]

A[N][N-1]

A[1][0]

A[1][1]

A[1][N-1]

double*

double**

A

double

\vdots

Multidimensional Arrays

Indirect addressing is slower
- requires following a pointer in the heap
- difficult to cache
Heap allocation for direct addressing:

David Mayerich

STIM Laboratory, University of Houston

int M = 20;		int N = 20;
//.....
double* A;
A = (double*) malloc(M * N * sizeof(double*));
A[7 * N + 3] = 7.0 * 3.0;

integer math is fast

A

A[0]

A[1*M+0]

A[1*M+2]

A[(N-1)*M+0]

Higher Dimensions

Three dimensions \((x, y, z)\):

David Mayerich

STIM Laboratory, University of Houston

int X = 20;		int Y = 30;		int Z = 10;

float* A = (float*) malloc(X * Y * Z * sizeof(float));

// access (7, 8, 9):
A[9 * X * Y + 8 * X + 7] = 7.0f * 3.0f;

Discussion

I created a repository that should be a good starting point for programming projects using several useful libraries
https://github.com/STIM-Lab/helloworld
This provides a good opportunity to make sure you have the tools available for development
Compile this code and run it on Tuxedo (tuxedo.ee.e.uh.edu)
I've heavily commented the code to explain what each step does (including the CMakeLists.txt script)
Upload a screenshot to Canvas when you get it working

David Mayerich

STIM Laboratory, University of Houston

A.3 Programming Digital Systems

By STIM Laboratory

A.3 Programming Digital Systems

STIM Laboratory

stim.ee.uh.edu

Programming Digital Systems

Numerical Methods

David Mayerich

C/C++ Development Tools

C/C++

Compilers

Operating Systems - Recommendations

Working with Good Source Code

Source Code Repository

Build Systems

Build Automation

CMake Scripts (CMakeLists.txt)

Using CMake

C/C++

Package Managers

vcpkg

Development Tools Summary

Data Types

Standards

Specifying Data Types

Type Resolution (C/C++)

Promotion

Modulus Operation

Limits of Integers

Overflow as a Modulus

Memory Allocation

Memory Allocation

Practical Stack vs. Heap Allocation

Dynamic Allocation

Segmentation Faults

Multidimensional Arrays

Multidimensional Arrays

Higher Dimensions

Discussion

A.3 Programming Digital Systems

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