Operation on Unlimited Digits containing Number

Hello...

I'm writing a C++ program to find the definite integration of any function. For this purpose, I need to deal with numbers having infinitely small values such as those having decimal places around 100-500 places, I know its not simple.

Could anyone help me write a program which could store such weird numbers in variables(no matter static or dynamic) and perform some basic mathematical operations(add, subtract, multiply) with them.

Thanks...
There's no point in reinventing the wheel, especially if you're trying to invent a nano cogwheel in the stone age.
See http://gmplib.org/
I'd suggest writing an interface to a CAS such as Maxima or Wolfram Mathematica. It would be far simpler and you'd get exact results, rather than numerical approximations.
In the case of Maxima, this would involve starting Maxima in a separate process, then opening a socket to it, then sending commands and getting back results
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