complete rewrite

Author: creme332

README.md

@@ -1,20 +1,63 @@
 # Criss-Cross Multiplication 
+![Badge for test workflow](https://github.com/creme332/criss-cross-algorithm/actions/workflows/test.yml/badge.svg)
 
-The criss-cross multiplication algorithm multiplies large positive integers in string format. This algorithm is nearly twice as fast as the Karatsuba algorithm when the number of digits is below 1000.
+A 50-lines algorithm for multiplying large positive integers in string format. For numbers having less than 100 digits, it outperforms the Karatsuba algorithm by as much as 50%.
 
 <img src="3x3.gif"  width="300" height="300">
 
 Read more about the algorithm in this [post](https://creme332.github.io/creamy-notes/posts/criss-cross-multiplication/).
 
+
+## Installation
+
+To install project:
+```
+git clone [email protected]:creme332/criss-cross-algorithm.git
+```
+
 ## Usage
+Import `mul.h` in your program and initialise a `Mul` object as follows:
+```cpp
+Mul Multiplier("9912", "54564");
+Multiplier.vedic(); // 540838368
+```
+
+The `Mul` class has  3 methods for multiplication:
+
+| Method         | Description                                                                                                                                                     |
+| -------------- | --------------------------------------------------------------------------------------------------------------------------------------------------------------- |
+| `basicVedic()` | A simpler and faster implementation of the criss-cross algorithm but is more limited since it uses basic arithmetic operators for addition and subtraction. |
+| `vedic()`      | A version of `basicVedic()` that uses helper functions for  adding and subtracting large string numbers.                                                        |
+| `karatsuba()`  | Uses the Karatsuba algorithm for multiplication. Algorithm uses helper functions for adding and subtracting large string numbers.                       |
+
+## Run benchmarks
+To run benchmarks:
+```
+g++ benchmarks/main.cpp benchmarks/timer.cpp src/mul.cpp -W
+./a.out
+```
+A folder `output` will be created inside the `benchmarks` folder. This new folder will contain the following files:
+
+| File name     | Content                                                                                                                                      |
+| ------------- | -------------------------------------------------------------------------------------------------------------------------------------------- |
+| `input.txt`   | A list of multiplicands and multipliers which were generated during runtime.                                                                 |
+| `time.txt`    | Each line contains 2 values representing the time taken for vedic and karatsuba algorithms respectively                                      |
+| `product.txt` | Each line contains 2 values representing the product calculated by vedic and karatsuba algorithms respectively. These values should be same. |
+
+
+## Run tests
+
+```bash
+g++ test_runner.cpp tests/tests.cpp src/mul.cpp -W
+./a.out
+```
 
 ## To-do
 
-* [ ] Use object oriented approach
-* [ ] Write tests
-* [ ] Add github workflow
-* [ ] add badges
-* [ ] Release
-* [ ] Store `sum` and `carry` as strings instead of long long data type. Then use addition and subtraction function for strings.
+* [ ] Use Google Benchmark for benchmarks
 
 ## References
+
+- [Criss cross algorithm](https://www.youtube.com/watch?v=JhGzbN5YuPo)
+- [Karatsuba algorithm](https://drawar.github.io/karatsuba-cpp/)
+- [Code for benchmarking](https://www.youtube.com/watch?v=YG4jexlSAjc&ab_channel=TheCherno)