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* \brief Low level math functions and compatibility wrappers
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* Johan Engelen <goejendaagh@zonnet.nl>
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* Michael G. Sloan <mgsloan@gmail.com>
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* Krzysztof Kosiński <tweenk.pl@gmail.com>
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* Copyright 2006-2009 Authors
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* This library is free software; you can redistribute it and/or
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* modify it either under the terms of the GNU Lesser General Public
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* License version 2.1 as published by the Free Software Foundation
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* (the "LGPL") or, at your option, under the terms of the Mozilla
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* Public License Version 1.1 (the "MPL"). If you do not alter this
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* notice, a recipient may use your version of this file under either
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* the MPL or the LGPL.
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* You should have received a copy of the LGPL along with this library
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* in the file COPYING-LGPL-2.1; if not, write to the Free Software
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* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
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* You should have received a copy of the MPL along with this library
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* in the file COPYING-MPL-1.1
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* The contents of this file are subject to the Mozilla Public License
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* Version 1.1 (the "License"); you may not use this file except in
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* compliance with the License. You may obtain a copy of the License at
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* http://www.mozilla.org/MPL/
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* This software is distributed on an "AS IS" basis, WITHOUT WARRANTY
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* OF ANY KIND, either express or implied. See the LGPL or the MPL for
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* the specific language governing rights and limitations.
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#ifndef LIB2GEOM_SEEN_MATH_UTILS_H
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#define LIB2GEOM_SEEN_MATH_UTILS_H
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#include <math.h> // sincos is usually only available in math.h
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#include <utility> // for std::pair
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/** @brief Sign function - indicates the sign of a numeric type.
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* Mathsy people will know this is basically the derivative of abs, except for the fact
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* that it is defined on 0.
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* @return -1 when x is negative, 1 when positive, and 0 if equal to 0. */
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template <class T> inline int sgn(const T& x) {
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return (x < 0 ? -1 : (x > 0 ? 1 : 0) );
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template <class T> inline T sqr(const T& x) {return x * x;}
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template <class T> inline T cube(const T& x) {return x * x * x;}
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/** Between function - returns true if a number x is within a range: (min < x) && (max > x).
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* The values delimiting the range and the number must have the same type.
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template <class T> inline const T& between (const T& min, const T& max, const T& x)
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{ return (min < x) && (max > x); }
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/** @brief Returns @a x rounded to the nearest multiple of \f$10^{p}\f$.
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Implemented in terms of round, i.e. we make no guarantees as to what happens if x is
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half way between two rounded numbers.
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Note: places is the number of decimal places without using scientific (e) notation, not the
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number of significant figures. This function may not be suitable for values of x whose
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magnitude is so far from 1 that one would want to use scientific (e) notation.
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places may be negative: e.g. places = -2 means rounding to a multiple of .01
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inline double decimal_round(double x, int p) {
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//TODO: possibly implement with modulus instead?
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double const multiplier = ::pow(10.0, p);
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return ::round( x * multiplier ) / multiplier;
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/** @brief Simultaneously compute a sine and a cosine of the same angle.
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* This function can be up to 2 times faster than separate computation, depending
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* on the platform. It uses the standard library function sincos() if available.
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* @param sin_ Variable that will store the sine
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* @param cos_ Variable that will store the cosine */
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inline void sincos(double angle, double &sin_, double &cos_) {
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::sincos(angle, &sin_, &cos_);
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/* Temporary fix for various misdefinitions of isnan().
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* isnan() is becoming undef'd in some .h files.
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* #include this last in your .cpp file to get it right.
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* The problem is that isnan and isfinite are part of C99 but aren't part of
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* the C++ standard (which predates C99).
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# define IS_NAN(_a) (__isnan(_a))
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#elif defined(__APPLE__) && __GNUC__ == 3
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# define IS_NAN(_a) (__isnan(_a)) /* MacOSX/Darwin definition < 10.4 */
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#elif defined(WIN32) || defined(_isnan)
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# define IS_NAN(_a) (_isnan(_a)) /* Win32 definition */
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#elif defined(isnan) || defined(__FreeBSD__) || defined(__osf__)
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# define IS_NAN(_a) (isnan(_a)) /* GNU definition */
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#elif defined (SOLARIS_2_8) && __GNUC__ == 3 && __GNUC_MINOR__ == 2
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# define IS_NAN(_a) (isnan(_a)) /* GNU definition */
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# define IS_NAN(_a) (std::isnan(_a))
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/* If the above doesn't work, then try (a != a). */
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#if defined(__isfinite)
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# define IS_FINITE(_a) (__isfinite(_a))
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#elif defined(__APPLE__) && __GNUC__ == 3
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# define IS_FINITE(_a) (__isfinite(_a)) /* MacOSX/Darwin definition < 10.4 */
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# define IS_FINITE(_a) (_isfinite(_a))
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#elif defined(isfinite)
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# define IS_FINITE(_a) (isfinite(_a))
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#elif defined(__osf__)
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# define IS_FINITE(_a) (finite(_a) && !IS_NAN(_a))
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#elif defined (SOLARIS_2_8) && __GNUC__ == 3 && __GNUC_MINOR__ == 2
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#define IS_FINITE(_a) (finite(_a) && !IS_NAN(_a))
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# define IS_FINITE(_a) (std::isfinite(_a))
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} // end namespace Geom
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#endif // LIB2GEOM_SEEN_MATH_UTILS_H
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c-file-style:"stroustrup"
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c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
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// vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:fileencoding=utf-8:textwidth=99 :
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src/2geom/math-utils.h
