math: big integer implementation

[bavernet]

Big integer structure is widely used.
But, there is no proper libraries for big integer in C/C++ languages.
If you can use the languages which support big integer structure internally, you should do that.
Or, you have to choose a library or to implement it.

For the unusual situation, it is needed to implement a big integer structure.

[bavernet]

It would better to support to convert from std::string to biginteger with a base.

[bavernet]

Addition and subtraction operations are easy to implement.
But, multiplication and division would be complicated than them.

Actually to make it work is not a problem. To make it efficient is the main issue.

Multiplication has a popular efficient algorithm named karatsuba.
Whereas, I think that there is no known algorithms for division operation.

I have to survey it

• Long division: https://en.wikipedia.org/wiki/Long_division
• Polynomial long division: https://dawoum.ddns.net/wiki/Polynomial_long_division
• Euclidean division: https://dawoum.ddns.net/wiki/Polynomial_greatest_common_divisor#Euclidean_division
• Faster integer division for embedded hardware: https://www.robotshop.com/community/forum/t/conquer-the-divide-faster-integer-division/4905
• gmplib: https://gmplib.org/manual/Divide-and-Conquer-Division