Updated functions to vector format

[OmriHab]

Tested partly locally, couldn't test with BigInt because I don't have all the functions needed to compile and test.
Functions changed:

• to_string
• operator=
• operator+/-
• operator>>/<<
• operator==
• operator<

[OmriHab]

I've updated the long long compare functions to be more efficient, that instead of building unnecessary BigInt objects and calling a lot of functions, get checked straight in the function.
Also I added a conversion to 2 uint64_t's if long long is 128 bit, unlikely but adds reliability.

[faheel]

@OmriHab Thanks a lot for these changes! I have reviewed all the changes except those in functions/utility.hpp and operators/binary_arithmetic.hpp. Will review them soon.

There's a suggestion I'd like to give about non-fixed integer types. Instead of checking that their size matches 64 bits, I suggest we change all occurrences of long long to int64_t and unsigned long long to uint64_t.

[faheel]

if (magnitude != {0})

[OmriHab]

Can't do that in c++, it's possible to do if (magnitude != std::vector<uint64_t>(1,0)) but I think it's better to compare them like this.

[faheel]

This can be improved by using minimal amount of nested conditions:

if (is_negative != num.is_negative)    // signs are opposite
    return is_negative;
if (is_negative)    // both numbers are negative
    return -(*this) > -num;

// both numbers are positive
if (magnitude.size() != num.magnitude.size())
    return magnitude.size() < num.magnitude.size();

// both magnitudes have the same number of digits
// compare their digits, from MSD to LSD
for (int64_t i = magnitude.size() - 1; i >= 0; i--)
    if (magnitude[i] != num.magnitude[i])
        return magnitude[i] < num.magnitude[i];

return false;   // both numbers are equal

I've also corrected the return value when the numbers are equal.

[faheel]

You inverted the condition here. Should be:

return rhs < lhs;

[faheel]

I realised that the code for BigInt > BigInt (in the lines that follow this) can be simplified to:

return num < *this;

[faheel]

You inverted the condition here. Should be:

return rhs > lhs;

[faheel]

Lines shouldn't start with a grammar symbol (like commas and colons):

BigInt::BigInt():
        magnitude(1, 0),
        is_negative(false) { }

[faheel]

Same suggestion as above.

[faheel]

Instead of these checks at multiple places, I suggest we change all occurrences of long long to int64_t and unsigned long long to uint64_t.

[faheel]

This wouldn't work. Base conversion will need to be done. I'm working on it, so you can leave this as it previously was.

[faheel]

Please change this to <cstdint>.

[OmriHab]

Correct me if i'm wrong, would that require every reference to uint64_t to be prefixed with std::?

[OmriHab]

Because in other c++ code that I've seen they don't use the std:: prefix

[faheel]

No, you wouldn't need the std:: namespace for int64_t and uint64_t

[OmriHab]

Right, working on the fixes now, and thanks for the feedback!
This is my first OS contribution so sorry if it's a bit rusty.

[faheel]

@OmriHab Just wanted to let you know that I've been working on the conversion part (decimal string ↔ base 2⁶⁴ vector) and it's almost done. I'll push the changes in a while and you then update your PR with those. I'll also review the remaining changes in your PR once I push the changes.