number_tests.hpp

#ifndef PASTELSYS_NUMBER_TESTS_HPP
#define PASTELSYS_NUMBER_TESTS_HPP

#include "pastel/sys/math/number_tests.h"
#include "pastel/sys/ensure.h"

namespace Pastel
{

    template <typename Integer>
    bool isPowerOfTwo(const Integer& that)
    {
        PENSURE_OP(that, >=, 0);

        // ==>
        // Suppose 'that' is a power of two.
        // Then its binary representation is
        // of the form
        //
        //         0...010....0
        //
        // Subtracting one gives
        //
        //      0...001....1
        //
        // and therefore the logical AND
        // gives zero.

        // <==
        // Suppose 'that' is not a power of two.
        // Then its binary representation is
        // either of the form
        //
        //     x...10..00
        //
        // or
        //
        //     x...1
        //
        // In the first case, subtracting one
        // gives
        //
        //     x...01...1
        //
        // Since 'that' is not a power of two,
        // the x-part is non-zero, and remains
        // the same. Therefore the logical AND
        // is non-zero.
        //
        // In the second case, subtracting one
        // gives
        //
        //     x...0
        //
        // With the same justification as above,
        // the logical AND is non-zero.

        return zero(that & (that - 1));
    }

}

#endif