Addition, Multiplication of Very Long Integers

Well, I am posting an article after a long gap. When i was reading a C++ Programming, i came across a programme that was showing using of very long integers. It was quiet good and that impressed me and made me write the same in C#.

The purpose of the article is to be able to build a class that allows any C# programmer to use very long integer related functionalities like addition and multiplication. I have implement it using operator overloading. While reading in C++ and while analyzing the programme to write in C#, i came to a conclusion, that using operator overloading makes the performance ease and it is very easy to understand the code and functionality in certain cases.

In computer programming, operator overloading (less commonly known as operator ad-hoc polymorphism) is a specific case of polymorphism in which some or all of operators like +, =, or == have different implementations depending on the types of their arguments. Sometimes the overloadings are defined by the language; sometimes the programmer can implement support for new types. Operator overloading is claimed to be useful because it allows the developer to program using notation “closer to the target domain” and allows user-defined types a similar level of syntactic support as types built into the language. It can easily be emulated using function calls; for an example, consider the integers a, b, c:

In a language that supports operator overloading, and assuming the ‘*’ operator has higher precedence than ‘+’, this is effectively a more concise way of writing:

All unary and binary operators have pre-defined implementations, that are automatically available in any expressions. In addition to this pre-defined implementations, user defined implementations can also be introduced in C#. The mechanism of giving a special meaning to a standard C# operator with respect to a user defined data type such as classes or structures is known as operator overloading. Remember that it is not possible to overload all operators in C#. The following table shows the operators and their overloadability in C#.

Operators Overloadability

+, -, *, /, %, &, |, <<, >> All C# binary operators can be overloaded.

+, -, !, ~, ++, –, true, false All C# unary operators can be overloaded.

==, !=, <, >, <= , >= All relational operators can be overloaded,
but only as pairs.

&&, || They can’t be overloaded

() (Conversion operator) They can’t be overloaded

+=, -=, *=, /=, %= These compound assignment operators can be
overloaded. But in C#, these operators are
automatically overloaded when the respective
binary operator is overloaded.

=, . , ?:, ->, new, is, as, size of These operators can’t be overloaded

In C#, a special function called operator function is used for overloading purpose. These special function or method must be public and static. They can take only value arguments.The ref and out parameters are not allowed as arguments to operator functions. The general form of an operator function is as follows.

public static return_type operator op (argument list)
Where the op is the operator to be overloaded and operator is the required keyword. For overloading the unary operators, there is only one argument and for overloading a binary operator there are two arguments. Remember that at least one of the arguments must be a user-defined type such as class or struct type.

Overloading Unary Operators – the general form of operator function for unary operators is as follows.public static return_type operator op (Type t){// Statements}Where Type must be a class or struct.The return type can be any type except void for unary operators like +,~, ! and dot (.). but the return type must be the type of ‘Type’ for ++and o remember that the true and false operators can be overloaded only as pairs. The compilation error occurs if a class declares one of these operators without declaring the other.

Operating overloading allows us to pass different variable types to the same function and produce different results. In this article i have given the low-down on operator overloading in C#.Operator overloading is common-place among many efficient C# programmers. It allows you to use the same function name, but as different functions.

In this article I have shown exactly what operator overloading is, and how you can get it to work for you in C#.

Inside Logic

First the very long numbers are inputted as string. Then each characters in the string are converted as integers. The same is done for the another input string. Now the digits are added and is stored in a separate character array. Adn finally this character array is converted as string, which the exact output that we need.

Here also the same logic. But here we add some extra functionalities like multiplying a single digit, multiplying with 10.

Here we acheive factorial as a recursive calling of multiplication. We can find factorial of number upto 250 (!Wow).

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