GnashNumeric.h

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// GnashNumeric.h: vaguely useful mathematical functions.
// 
//   Copyright (C) 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012
//   Free Software Foundation, Inc
// 
// This program is free software; you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation; either version 3 of the License, or
// (at your option) any later version.
// 
// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.
// 
// You should have received a copy of the GNU General Public License
// along with this program; if not, write to the Free Software
// Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA
//

#ifndef GNASH_NUMERIC_H
#define GNASH_NUMERIC_H

#ifdef HAVE_CONFIG_H
# include "gnashconfig.h"
#endif

#ifdef SOLARIS_HOST
# include <ieeefp.h> // for finite()
#endif

#include <cassert>
#include <cmath>
#include <algorithm>
#include <cstdint>
#include <limits>
#include <type_traits>

namespace gnash {

// Using a possible built-in pi constant M_PI, which is not in
// the C++ standard, has no greate advantage, so we will use this
// one. Make it as accurate as you like.
static const double PI = 3.14159265358979323846;

inline bool
isFinite(double d)
{
#if defined(HAVE_FINITE) && !defined(HAVE_ISFINITE)
    return (finite(d));
#else
    // Put using namespace std; here if you have to
    // put it anywhere.
    using namespace std;
    return (isfinite(d));
#endif
}

template <typename T>
inline
bool
isNaN(const T& num)
{
    static_assert(std::is_floating_point<T>::value,
        "isNaN() is only meaningful for floating point types.");
    return num != num;
}

inline double
infinite_to_zero(double x)
{
    return isFinite(x) ? x : 0.0;
}

template <typename T>
inline T
clamp(T i, T min, T max)
{
    assert(min <= max);
    return std::max<T>(min, std::min<T>(i, max));
}

template<typename T>
inline T
lerp(T a, T b, T f)
{
    return (b - a) * f + a;
}

inline int
frnd(float f) 
{
    return static_cast<int>(f + 0.5f);
}

inline double
twipsToPixels(int i) 
{ 
    return i / 20.0;
}

template<size_t Factor>
std::int32_t
truncateWithFactor(double a)
{
    // If a is NaN, then this function would return -NAN, which when cast to
    // int32, converts to zero on x86*, but converts to -1 on ARM. The
    // behaviour is undefined according to ISO-IEC 14882:2003 4.9.1.
    if (isNaN(a)) {
        return 0;
    }

    const double factor = static_cast<double>(Factor);

    // This truncates large values without relying on undefined behaviour.
    // For very large values of 'a' it is noticeably slower than the UB
    // version (due to fmod), but should always be legal behaviour. For
    // ordinary values (within ±1.07374e+08 pixels) it is comparable to
    // the UB version for speed. Because values outside the limit are
    // extremely rare, using this safe version has no implications for
    // performance under normal circumstances.
    static const double upperUnsignedLimit =
                std::numeric_limits<std::uint32_t>::max() + 1.0;
    static const double upperSignedLimit =
                std::numeric_limits<std::int32_t>::max() / factor;
    static const double lowerSignedLimit =
                std::numeric_limits<std::int32_t>::min() / factor;

    if (a >= lowerSignedLimit && a <= upperSignedLimit) {
        return a * Factor;
    }

    // This slow truncation happens only in very unlikely cases.
    return a >= 0 ?
        static_cast<std::uint32_t>(
                std::fmod(a * factor, upperUnsignedLimit))
        : 
        -static_cast<std::uint32_t>(
                std::fmod(-a * factor, upperUnsignedLimit));
}

// truncate when overflow occurs.
inline std::int32_t
pixelsToTwips(double a)
{
    return truncateWithFactor<20>(a);
}

} // namespace gnash

#endif