Newton's method implemented in C

This program is an implementation of Newton's method, a numeric method for computing the root of a function, in the C programming language. It demonstrates the implementation of a compiler frontend, analysis of the resulting syntax tree, a compiler backend to generate bytecode and a virtual machine to execute the code.

The entire project was inteded as a learning exercise for myself and I am releasing the source code to the public for others to learn from it. The focus of the project was simplicity and clean code, so don't expect a GUI, complex operations or any features that would detract from the main focus.

Building

A makefile is included with the project, to build navigate to the source folder and type on of the following into your terminal:

make
make release

The release target will apply compiler optimisations, while the default target does not, it is intended for debugging where we don't want the compiler to alter our code.

The makefile was written for the clang compiler, if you want to use a different compiler you have to re-assign the CC variable:

make release CC=gcc

To clean up the build directory use the clean target:

make clean

You can also run the clang static analyser, both of the spellings below are valid:

make analyze
make analyse

There are no dependencies, other than a C11-compliant compiler with support for variable-sized arrays. You can refer to the makefile for more details if you wish, it is a very simple makefile.

Runnig

The program is a command-line application and all information is passed as arguments. Here is the syntax:

newton function guess

Where function is a string representing the function and guess is a string that represents the starting value for the method. There is no need to specify a derivative function, the program will compute it.

A more verbose way of calling the program is this:

newton --f function --g guess [--p]

The optional --p flage makes the program print every step of the iteration (if you are not familiar with syntax notation, the brackets indicate something optional, you don't actually type them).

Legal function syntax

The program is pretty clever about its input and will insert implicit operators, i.e. 5x will be understood to mean 5 * x. Here is an overview of known symbols and functions:

Symbol	Meaning
( [	Opening parethesis
) ]	Closing parethesis
x	Variable x
+	Addition
-	Negation or Subtraction, depending on context
*	Multiplication
/	Division
^	Power
exp	Exponential function
ln	Natural logarithm
sin	Sine
cos	Cosine
tan	Tangent
pi	Constant number π
e	Constant number e

Both types of parantheses can be used interchangably, one can even close the other. It's just an aesthetic difference.

Square roots can be entered using a power via the following rule:

$$\sqrt[b]{a} = a^{\frac{1}{b}}$$

Numbers can be entered as either integers or decimal numbers, it does not matter, they always get converted to double-precision floating point numbers.

Further reading

There is an in-depth documentation on the working of the program in the Docs directory. If you want to read the source code you will find everything documented using Doxygen comments. To generate a Doxygen documentation use the doxyfile in the Docs directory.

License

The MIT License (MIT)

Copyright (c) 2015 "HiPhish"

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.