`bit::vector` — Binary Shift Operators

We have methods to perform binary left and right shifts for the elements in a bit-vector — shifting in zeros as needed.

1constexpr bit::vector &operator<<=(std::size_t p);
2constexpr bit::vector &operator>>=(std::size_t p);

3constexpr bit::vector operator<<(std::size_t p) const;
4constexpr bit::vector operator>>(std::size_t p) const;

1: Left-shift the elements of this bit-vector p places.
2: Right-shift the elements of this bit-vector p places.
3: Returns a bit-vector that is this one left shifted by p places
4: Returns a bit-vector that is this one right shifted by p places

The first two methods are destructive (i.e., operate in-place) and return a reference to *this, so can be chained with other calls.

Like most things in the bit library, the methods operate on the elements of the bit-vector in vector-order. So if \(v\) is our bit-vector \[ v = \left[v_0, v_1, \ldots, v_{n-2}, v_{n-1} \right], \] then left shifting pushes out the element \(v_0\) and pushes in a new zero element on the right: \[ v \ll 1 = \left[v_1, \ldots, v_{n-2}, v_{n-1}, 0 \right]. \] Similarly, right shifting pushes out the element \(v_{n-1}\) and pushes in a new zero element on the left: \[ v \gg 1 = \left[0, v_0, v_1, \ldots, v_{n-2}, \right]. \]

Thus, right shifts are equivalent to left shifts, considering the elements in bit-order. Similarly, the left shifts are equivalent to right shifts, considering the elements in bit-order.

Example

#include <bit/bit.h>
int main()
{
    auto v = bit::vector<>::ones(12);

    std::cout << "Left shift:\n";
    std::cout << "v:        " << v         << '\n';
    std::cout << "v << 1:   " << (v << 1)  << '\n';
    std::cout << "v << 4:   " << (v << 4)  << '\n';
    std::cout << "v << 9:   " << (v << 9)  << '\n';
    std::cout << "v << 13:  " << (v << 13) << '\n';
    std::cout << '\n';

    std::cout << "Right shift:\n";
    std::cout << "v:        " << v         << '\n';
    std::cout << "v >> 1:   " << (v >> 1)  << '\n';
    std::cout << "v >> 4:   " << (v >> 4)  << '\n';
    std::cout << "v >> 9:   " << (v >> 9)  << '\n';
    std::cout << "v >> 13:  " << (v >> 13) << '\n';
    std::cout << '\n';
}

Output

Left shift:
v:        [1 1 1 1 1 1 1 1 1 1 1 1]
v << 1:   [1 1 1 1 1 1 1 1 1 1 1 0]
v << 4:   [1 1 1 1 1 1 1 1 0 0 0 0]
v << 9:   [1 1 1 0 0 0 0 0 0 0 0 0]
v << 13:  [0 0 0 0 0 0 0 0 0 0 0 0]

Right shift:
v:        [1 1 1 1 1 1 1 1 1 1 1 1]
v >> 1:   [0 1 1 1 1 1 1 1 1 1 1 1]
v >> 4:   [0 0 0 0 1 1 1 1 1 1 1 1]
v >> 9:   [0 0 0 0 0 0 0 0 0 1 1 1]
v >> 13:  [0 0 0 0 0 0 0 0 0 0 0 0]

See Also