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/** Various utility functions.
 * Copyright 2007 Johan Engelen <>
 * Copyright 2006 Michael G. Sloan <>
 * This library is free software; you can redistribute it and/or
 * modify it either under the terms of the GNU Lesser General Public
 * License version 2.1 as published by the Free Software Foundation
 * (the "LGPL") or, at your option, under the terms of the Mozilla
 * Public License Version 1.1 (the "MPL"). If you do not alter this
 * notice, a recipient may use your version of this file under either
 * the MPL or the LGPL.
 * You should have received a copy of the LGPL along with this library
 * in the file COPYING-LGPL-2.1; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
 * You should have received a copy of the MPL along with this library
 * in the file COPYING-MPL-1.1
 * The contents of this file are subject to the Mozilla Public License
 * Version 1.1 (the "License"); you may not use this file except in
 * compliance with the License. You may obtain a copy of the License at
 * This software is distributed on an "AS IS" basis, WITHOUT WARRANTY
 * OF ANY KIND, either express or implied. See the LGPL or the MPL for
 * the specific language governing rights and limitations.

#include <cmath>

namespace Geom {

// proper logical xor
inline bool logical_xor (bool a, bool b) { return (a || b) && !(a && b); }

/** Sign function - indicates the sign of a numeric type.  -1 indicates negative, 1 indicates
 *  positive, and 0 indicates, well, 0.  Mathsy people will know this is basically the derivative
 *  of abs, except for the fact that it is defined on 0.

template <class T> inline int sgn(const T& x) {return (x < 0 ? -1 : (x > 0 ? 1 : 0) );}

template <class T> inline T sqr(const T& x) {return x * x;}
template <class T> inline T cube(const T& x) {return x * x * x;}

/** Between function - returns true if a number x is within a range. The values delimiting the
 *  range and the number must have the same type.

template <class T> inline const T& between (const T& min, const T& max, const T& x)
    { return min < x && max > x; }

/** Returns x rounded to the nearest integer.  It is unspecified what happens
 *  if x is half way between two integers: we may in future use rint/round
 *  on platforms that have them.

inline double round(double const x) { return std::floor(x + .5); }

/** Returns x rounded to the nearest \a places decimal places.

    Implemented in terms of round, i.e. we make no guarantees as to what happens if x is
    half way between two rounded numbers.
    Note: places is the number of decimal places without using scientific (e) notation, not the
    number of significant figures.  This function may not be suitable for values of x whose
    magnitude is so far from 1 that one would want to use scientific (e) notation.

    places may be negative: e.g. places = -2 means rounding to a multiple of .01

inline double decimal_round(double const x, int const places) {
    //TODO: possibly implement with modulus instead?
    double const multiplier = std::pow(10.0, places);
    return round( x * multiplier ) / multiplier;