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+/**
+ * \file
+ * \brief Low level math functions and compatibility wrappers
+ *//*
+ * Authors:
+ *   Johan Engelen <goejendaagh@zonnet.nl>
+ *   Michael G. Sloan <mgsloan@gmail.com>
+ *   Krzysztof Kosiński <tweenk.pl@gmail.com>
+ * Copyright 2006-2009 Authors
+ *
+ * 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., 59 Temple Place, Suite 330, Boston, MA 02111-1307 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
+ * http://www.mozilla.org/MPL/
+ *
+ * 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.
+ *
+ */
+
+#ifndef LIB2GEOM_SEEN_MATH_UTILS_H
+#define LIB2GEOM_SEEN_MATH_UTILS_H
+
+#include <math.h> // sincos is usually only available in math.h
+#include <array>
+#include <cmath>
+#include <utility> // for std::pair
+#include <boost/math/special_functions/fpclassify.hpp>
+
+namespace Geom {
+
+/** @brief Sign function - indicates the sign of a numeric type.
+ * Mathsy people will know this is basically the derivative of abs, except for the fact
+ * that it is defined on 0.
+ * @return -1 when x is negative, 1 when positive, and 0 if equal to 0. */
+template <class T> inline int sgn(const T& x) {
+    return (x < 0 ? -1 : (x > 0 ? 1 : 0) );
+// can we 'optimize' this with:
+//    return ( (T(0) < x) - (x < T(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: (min < x) && (max > x).
+ * 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); }
+
+/** @brief Returns @a x rounded to the nearest multiple of \f$10^{p}\f$.
+
+    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 x, int p) {
+    //TODO: possibly implement with modulus instead?
+    double const multiplier = ::pow(10.0, p);
+    return ::round( x * multiplier ) / multiplier;
+}
+
+/** @brief Simultaneously compute a sine and a cosine of the same angle.
+ * This function can be up to 2 times faster than separate computation, depending
+ * on the platform. It uses the standard library function sincos() if available.
+ * @param angle Angle
+ * @param sin_ Variable that will store the sine
+ * @param cos_ Variable that will store the cosine */
+inline void sincos(double angle, double &sin_, double &cos_) {
+#ifdef HAVE_SINCOS
+    ::sincos(angle, &sin_, &cos_);
+#else
+    sin_ = ::sin(angle);
+    cos_ = ::cos(angle);
+#endif
+}
+
+/** @brief Scale the doubles in the passed array to make them "reasonably large".
+ *
+ * All doubles in the passed array will get scaled by the same power of 2 (which is
+ * a lossless operation) in such a way that their geometric average gets closer to 1.
+ *
+ * @tparam N The size of the passed array.
+ * @param[in,out] values The doubles to be rescaled in place.
+ * @return The exponent in the power of two by which the doubles got scaled.
+ */
+template <size_t N>
+inline int rescale_homogenous(std::array<double, N> &values)
+{
+    if constexpr (N == 0) {
+        return 0;
+    }
+    std::array<int, N> exponents;
+    std::array<double, N> mantissas;
+    int average = 0;
+    for (size_t i = 0; i < N; i++) {
+        mantissas[i] = std::frexp(values[i], &exponents[i]);
+        average += exponents[i];
+    }
+    average /= (int)N;
+    for (size_t i = 0; i < N; i++) {
+        values[i] = std::ldexp(mantissas[i], exponents[i] - average);
+    }
+    return -average;
+}
+
+} // end namespace Geom
+
+#endif // LIB2GEOM_SEEN_MATH_UTILS_H
+
+/*
+  Local Variables:
+  mode:c++
+  c-file-style:"stroustrup"
+  c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
+  indent-tabs-mode:nil
+  fill-column:99
+  End:
+*/
+// vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:fileencoding=utf-8:textwidth=99 :