File: algorithm.hpp

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/* 
   Copyright (c) Marshall Clow 2014.

   Distributed under the Boost Software License, Version 1.0. (See accompanying
   file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

 Revision history:
    2 Dec 2014 mtc First version; power
   
*/

/// \file algorithm.hpp
/// \brief Misc Algorithms
/// \author Marshall Clow
///

#ifndef BOOST_ALGORITHM_HPP
#define BOOST_ALGORITHM_HPP

#include <functional> // for plus and multiplies

#include <boost/utility/enable_if.hpp> // for boost::disable_if
#include <boost/type_traits/is_integral.hpp>

namespace boost { namespace algorithm {

template <typename T>
T identity_operation ( std::multiplies<T> ) { return T(1); }

template <typename T>
T identity_operation ( std::plus<T> ) { return T(0); }


/// \fn power ( T x, Integer n )
/// \return the value "x" raised to the power "n"
/// 
/// \param x     The value to be exponentiated
/// \param n     The exponent (must be >= 0)
///
//  \remark Taken from Knuth, The Art of Computer Programming, Volume 2:
//  Seminumerical Algorithms, Section 4.6.3
template <typename T, typename Integer>
typename boost::enable_if<boost::is_integral<Integer>, T>::type
power (T x, Integer n) {
    T y = 1; // Should be "T y{1};" 
    if (n == 0) return y;
    while (true) {
        if (n % 2 == 1) {
            y = x * y;
            if (n == 1)
                return y;
            }
        n = n / 2;
        x = x * x;
        }
    return y;
    }

/// \fn power ( T x, Integer n, Operation op )
/// \return the value "x" raised to the power "n"
/// using the operation "op".
/// 
/// \param x     The value to be exponentiated
/// \param n     The exponent (must be >= 0)
/// \param op    The operation used
///
//  \remark Taken from Knuth, The Art of Computer Programming, Volume 2:
//  Seminumerical Algorithms, Section 4.6.3
template <typename T, typename Integer, typename Operation>
typename boost::enable_if<boost::is_integral<Integer>, T>::type
power (T x, Integer n, Operation op) {
    T y = identity_operation(op);
    if (n == 0) return y;
    while (true) {
        if (n % 2 == 1) {
            y = op(x, y);
            if (n == 1)
                return y;
            }
        n = n / 2;
        x = op(x, x);
        }
    return y;
    }

}}

#endif // BOOST_ALGORITHM_HPP