Error implementing Radix sort in C++ - c++

Question

I’m trying to implement Radix-Sort with arrays of long int.
My Algorithm has 2 inputs:
The number ’n’ of elements to be sorted
The number ‘b’ of bits per digit (So, insted of taking the last decimal number, I take the groups of ‘b’ digits, representing one digit)
But, when I try to sort the vector, I find 2 problems:
First one: It doesn’t sort the vector properly
Second one: I have implemented it for taking from the last group of bits to the first one. But it seems like it tries to sort in in the opposite direction.
Here is the code:
#define MAX_BITS sizeof(long int)*8
#define VectorL vector<long int>
struct Compare
{
int beg = 0;
int bits_per_digit = 2;
Compare(int x, int y){
beg = x;
bits_per_digit = y;
}
bool operator() (long& a, long& b){
int _begin = beg;
int _final = _begin + bits_per_digit - 1;
assert(_begin <= _final); // b==f if bits_per_digit = 1;
bitset<sizeof(long int)> _x(a), _y(b);
for(_begin; _begin <= _final; _begin++)
if(_x[_begin] != _y[_begin])
return (_x[_begin] < _y[_begin]) ? true : false;
return false;
}
};
void ALG(VectorL& nums, int n, int b)
{
assert(nums.size() == n);
assert(MAX_BITS%b == 0);
int _grupos = MAX_BITS/b;
Compare myobject(MAX_BITS,b);
for (int g = 1; g <= _grupos; g++)
{
myobject.beg -= b;
sort(nums.begin(), nums.end(), myobject);
}
}
Here’s the main:
int n=5, b=2;
VectorL nums(n);
nums[0] = 2;
nums[1] = 6;
nums[2] = 1;
nums[3] = 5;
nums[4] = 0;
ALG(nums, n, b);
And here’s the output:
Initial Vector: 2 6 1 5 0
From bit 62 to bit 63
Vector after the 1º sort: 2 6 1 5 0
From bit 60 to bit 61
Vector after the 2º sort: 2 6 1 5 0
From bit 58 to bit 59
Vector after the 3º sort: 2 6 1 5 0
From bit 56 to bit 57
Vector after the 4º sort: 2 6 1 5 0
From bit 54 to bit 55
Vector after the 5º sort: 2 6 1 5 0
From bit 52 to bit 53
Vector after the 6º sort: 2 6 1 5 0
From bit 50 to bit 51
Vector after the 7º sort: 2 6 1 5 0
From bit 48 to bit 49
Vector after the 8º sort: 2 6 1 5 0
From bit 46 to bit 47
Vector after the 9º sort: 2 6 1 5 0
From bit 44 to bit 45
Vector after the 10º sort: 2 6 1 5 0
From bit 42 to bit 43
Vector after the 11º sort: 2 6 1 5 0
From bit 40 to bit 41
Vector after the 12º sort: 2 6 1 5 0
From bit 38 to bit 39
Vector after the 13º sort: 2 6 1 5 0
From bit 36 to bit 37
Vector after the 14º sort: 2 6 1 5 0
From bit 34 to bit 35
Vector after the 15º sort: 2 6 1 5 0
From bit 32 to bit 33
Vector after the 16º sort: 2 6 1 5 0
From bit 30 to bit 31
Vector after the 17º sort: 2 6 1 5 0
From bit 28 to bit 29
Vector after the 18º sort: 2 6 1 5 0
From bit 26 to bit 27
Vector after the 19º sort: 2 6 1 5 0
From bit 24 to bit 25
Vector after the 20º sort: 2 6 1 5 0
From bit 22 to bit 23
Vector after the 21º sort: 2 6 1 5 0
From bit 20 to bit 21
Vector after the 22º sort: 2 6 1 5 0
From bit 18 to bit 19
Vector after the 23º sort: 2 6 1 5 0
From bit 16 to bit 17
Vector after the 24º sort: 2 6 1 5 0
From bit 14 to bit 15
Vector after the 25º sort: 2 6 1 5 0
From bit 12 to bit 13
Vector after the 26º sort: 2 6 1 5 0
From bit 10 to bit 11
Vector after the 27º sort: 2 6 1 5 0
From bit 8 to bit 9
Vector after the 28º sort: 2 6 1 5 0
From bit 6 to bit 7
Vector after the 29º sort: 2 6 1 5 0
From bit 4 to bit 5
Vector after the 30º sort: 2 6 1 5 0
From bit 2 to bit 3
Vector after the 31º sort: 2 1 0 6 5
From bit 0 to bit 1
Vector after the 32º sort: 0 2 6 1 5
As you can see in the output, the changes only happens in the 31st and 32nd sort (so, that means the significant bits are found in the last searchs).
Anyone can help me to find my mistake?
Thanks in advance.