Power very large number in C++ [closed] - c++

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Can someone with a bit of time, he could explain to me how intensify very large numbers? I'm not talking here about a ready solution, and the only explanation of how to implement the arithmetic. Ideally, it was based on the class std::string.
#edit
I read something about shifts bit, but examples were only in the form of a listing, and I want an explanation of how it works.

Answer 1

You can represent a large number as a sequence of digits in some base, and separately the sign of the number. To do arithmetic, you simply implement the algorithms you learnt at primary school to do addition, long multiplication, etc. There's more efficient algorithms (for example Karatsuba) for doing some operations, but an initial implementation could use the simpler forms.
If you really have to use std::string, you can use the first char to store the sign ('+' or '-'), and then the digits in base 10 in ascii. It's not efficient, but it's perhaps an easy way to get started, and it certainly makes printing the numbers out easy.

Answer 2

Here is something I quickly wrote when I needed (do not remember when). It is:
Buggy;
Not complete;
Arbitrarily use 3 digits per array element while it could use more;
Can clearly be improved (any kind comments are welcome^^).
However, I hope this will be somehow useful.
typedef long long int lli;
class BigInt
{
public: // Methods
BigInt(lli s) : m_nbElements(100)
{
m_number.resize(m_nbElements);
for (lli i=0; i < m_nbElements; ++i)
{
m_number[i] = s%1000;
s /= 1000;
}
}
BigInt(const std::string &str) : m_nbElements(100)
{
m_number.resize(m_nbElements);
size_t sizeStr = str.size();
int i = str.size() - 1;
int thousands = 0;
for (; i >= 2; i -= 3, ++thousands)
{
std::string subStr = str.substr(i-2, 3);
unsigned int value;
std::istringstream(subStr) >> value;
m_number[thousands] = value;
}
// Handle the "first" 1 or 2 digits
if (i >= 0)
{
std::string subStr = str.substr(0, i+1);
unsigned int value;
std::istringstream(subStr) >> value;
m_number[thousands] = value;
}
}
BigInt operator*(lli s)
{
lli temp, remainder = 0;
for (lli i=0; i < m_nbElements; ++i)
{
temp = m_number[i] * s + remainder;
m_number[i] = temp % 1000;
remainder = temp / 1000;
}
return (*this);
}
BigInt operator/(lli s)
{
lli temp, remainder = 0;
for (int i=m_nbElements-1; i >= 0; --i)
{
temp = (m_number[i] + remainder) / s;
remainder = (m_number[i] % s)*1000;
m_number[i] = temp;
}
return (*this);
}
BigInt operator-(BigInt s)
{
lli temp;
for (unsigned int i=0; i < m_nbElements; ++i)
{
temp = m_number[i] - s.m_number[i];
if (temp < 0)
{
--m_number[i+1];
temp += 1000;
}
m_number[i] = temp;
}
return (*this);
}
BigInt operator+(BigInt s)
{
lli temp, remainder = 0;
for (lli i=0; i < m_nbElements; ++i)
{
temp = m_number[i] + s.m_number[i] + remainder;
m_number[i] = temp % 1000;
remainder = temp / 1000;
}
return (*this);
}
std::string ToString()
{
std::string result = "";
bool significantDigitsFound = false;
for (int i=m_nbElements-1; i >= 0 ; --i)
{
if (!significantDigitsFound)
{
if (m_number[i] > 0)
{
std::ostringstream ss;
ss << m_number[i];
result = ss.str();
significantDigitsFound = true;
}
}
else
{
std::ostringstream ss;
ss << std::setw(3) << std::setfill( '0' ) << m_number[i];
result += ss.str();
}
}
if (result == "")
{
result = "0";
}
return result;
}
private: // Attributes
int m_nbElements;
std::vector<lli> m_number;
};