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#ifndef INCLUDED_NJN_INTEGER
#define INCLUDED_NJN_INTEGER
/* $Id: $
* ===========================================================================
*
* PUBLIC DOMAIN NOTICE
* National Center for Biotechnology Information
*
* This software/database is a "United States Government Work" under the
* terms of the United States Copyright Act. It was written as part of
* the author's offical duties as a United States Government employee and
* thus cannot be copyrighted. This software/database is freely available
* to the public for use. The National Library of Medicine and the U.S.
* Government have not placed any restriction on its use or reproduction.
*
* Although all reasonable efforts have been taken to ensure the accuracy
* and reliability of the software and data, the NLM and the U.S.
* Government do not and cannot warrant the performance or results that
* may be obtained by using this software or data. The NLM and the U.S.
* Government disclaim all warranties, express or implied, including
* warranties of performance, merchantability or fitness for any particular
* purpose.
*
* Please cite the author in any work or product based on this material.
*
* ===========================================================================*/
/*****************************************************************************
File name: njn_integer.hpp
Author: John Spouge
Contents:
******************************************************************************/
#include "njn_ioutil.hpp"
namespace Njn {
namespace Integer {
template <class Int>
Int minimum (
Int i, // number being divided
Int j) // divisor
{
return i < j ? i : j;
}
template <class Int>
Int maximum (
Int i, // number being divided
Int j) // divisor
{
return i > j ? i : j;
}
template <class Int>
Int mod ( // Portable modular function %
Int i, // number being divided
Int j) // divisor
{
Int abs_j = j >= 0 ? j : -j;
if (j == 0)
{
Njn::IoUtil::abort ("Nks_Mod : j == 0");
}
if (i < 0)
{
Int k = (i >= 0 ? i : -i) % abs_j;
return k == 0 ? k : abs_j - k;
}
else
{
return i % abs_j;
}
}
template <class Int>
Int euclidAlgorithm ( // Euclid's algorithm returning the greatest common divisor (i, j)
Int i_,
Int j_)
{
Int abs_i = maximum <Int> (i_ >= 0 ? i_ : -i_, j_ >= 0 ? j_ : -j_);
Int abs_j = minimum <Int> (i_ >= 0 ? i_ : -i_, j_ >= 0 ? j_ : -j_);
Int remainder = 0;
while (0 < abs_j)
{
remainder = mod <Int> (abs_i, abs_j);
abs_i = abs_j;
abs_j = remainder;
}
return abs_i;
}
template <class Int, class ConstIntegerPtr>
Int euclidAlgorithmVector ( // Euclid's algorithm returning the greatest common divisor (i, j)
ConstIntegerPtr begin_,
ConstIntegerPtr end_)
{
assert (begin_ <= end_);
if (begin_ == end_) return 0;
Int gcd = *begin_;
for (ConstIntegerPtr k = begin_ + 1; k != end_; k++)
{
gcd = euclidAlgorithm (gcd, *k);
}
return gcd;
}
template <class Int>
Int minusOnePower ( // (-1)^i
Int i) // exponent
{
return mod <Int> (i, 2) == 0 ? 1 : -1;
}
template <class Real, class Int>
Real integerPower (Real x, Int n) // integer power function
{
if (x == 0.0)
{
if (n < 0)
{
Njn::IoUtil::abort ("Int::integerPower <class Real, class Int> : negative exponent of zero");
}
else if (n == 0)
{
return 1.0;
}
else
{
return 0.0;
}
}
Real y = 1.0;
Int i = 0;
for (i = n > 0 ? n : -n; i > 0 ; i /= 2)
{
if (i % 2 != 0)
{
y *= x;
}
x *= x;
}
if (n < 0)
{
y = 1.0 / y;
}
return y;
}
template <class Real, class UnsignedInteger>
Real integerPositivePower (Real x, UnsignedInteger n) // integer power function
{
if (x == 0.0)
{
if (n == 0)
{
return 1.0;
}
else
{
return 0.0;
}
}
Real y = 1.0;
UnsignedInteger i = 0;
for (i = n; i > 0 ; i /= 2)
{
if (i % 2 != 0)
{
y *= x;
}
x *= x;
}
return y;
}
template <class Int, class IntTwo>
Int intPower (Int x, IntTwo n) // integer power function
{
assert (n >= 0);
if (x == 0)
{
return n == 0 ? 1 : 0;
}
Int y = 1;
IntTwo i = 0;
for (i = n > 0 ? n : -n; i > 0 ; i /= 2)
{
if (i % 2 != 0)
{
y *= x;
}
x *= x;
}
return y;
}
}
}
#endif
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