Criss-Cross Multiplication

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%.

Read more about the algorithm in this post.

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:

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

g++ test_runner.cpp tests/tests.cpp src/mul.cpp -W
./a.out

To-do

• Use Google Benchmark for benchmarks

References

• Criss cross algorithm
• Karatsuba algorithm
• Code for benchmarking