Source/wtf/MathExtras.h

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This source file includes following definitions.
wtf_ceil
round
roundf
llround
llroundf
lround
lroundf
trunc
log2
log2f
nextafter
nextafterf
copysign
wtf_atan2
wtf_fmod
wtf_pow
lrint
deg2rad
rad2deg
deg2grad
grad2deg
turn2deg
deg2turn
rad2grad
grad2rad
deg2rad
rad2deg
deg2grad
grad2deg
turn2deg
deg2turn
rad2grad
grad2rad
defaultMinimumForClamp
defaultMinimumForClamp
defaultMinimumForClamp
defaultMaximumForClamp
clampTo
clampToInteger
clampToUnsigned
clampToFloat
clampToPositiveInteger
clampToInteger
clampToInteger
isWithinIntRange
doubleToInteger
/*
 * Copyright (C) 2006, 2007, 2008, 2009, 2010 Apple Inc. All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY APPLE COMPUTER, INC. ``AS IS'' AND ANY
 * EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
 * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL APPLE COMPUTER, INC. OR
 * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
 * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
 * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
 * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
 * OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
 * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */

#ifndef WTF_MathExtras_h
#define WTF_MathExtras_h

#include "wtf/CPU.h"
#include <cmath>
#include <limits>

#if COMPILER(MSVC)
#include "wtf/Assertions.h"
#include <stdint.h>
#endif

#if OS(OPENBSD)
#include <sys/types.h>
#include <machine/ieee.h>
#endif

const double piDouble = M_PI;
const float piFloat = static_cast<float>(M_PI);

const double piOverTwoDouble = M_PI_2;
const float piOverTwoFloat = static_cast<float>(M_PI_2);

const double piOverFourDouble = M_PI_4;
const float piOverFourFloat = static_cast<float>(M_PI_4);

const double twoPiDouble = piDouble * 2.0;
const float twoPiFloat = piFloat * 2.0f;

#if OS(MACOSX)

// Work around a bug in the Mac OS X libc where ceil(-0.1) return +0.
inline double wtf_ceil(double x) { return copysign(ceil(x), x); }

#define ceil(x) wtf_ceil(x)

#endif

#if OS(OPENBSD)

namespace std {

#ifndef isfinite
inline bool isfinite(double x) { return finite(x); }
#endif
#ifndef signbit
inline bool signbit(double x) { struct ieee_double *p = (struct ieee_double *)&x; return p->dbl_sign; }
#endif

} // namespace std

#endif

#if COMPILER(MSVC) && (_MSC_VER < 1800)

// We must not do 'num + 0.5' or 'num - 0.5' because they can cause precision loss.
static double round(double num)
{
    double integer = ceil(num);
    if (num > 0)
        return integer - num > 0.5 ? integer - 1.0 : integer;
    return integer - num >= 0.5 ? integer - 1.0 : integer;
}
static float roundf(float num)
{
    float integer = ceilf(num);
    if (num > 0)
        return integer - num > 0.5f ? integer - 1.0f : integer;
    return integer - num >= 0.5f ? integer - 1.0f : integer;
}
inline long long llround(double num) { return static_cast<long long>(round(num)); }
inline long long llroundf(float num) { return static_cast<long long>(roundf(num)); }
inline long lround(double num) { return static_cast<long>(round(num)); }
inline long lroundf(float num) { return static_cast<long>(roundf(num)); }
inline double trunc(double num) { return num > 0 ? floor(num) : ceil(num); }

#endif

#if OS(ANDROID) || COMPILER(MSVC)
// ANDROID and MSVC's math.h does not currently supply log2 or log2f.
inline double log2(double num)
{
    // This constant is roughly M_LN2, which is not provided by default on Windows and Android.
    return log(num) / 0.693147180559945309417232121458176568;
}

inline float log2f(float num)
{
    // This constant is roughly M_LN2, which is not provided by default on Windows and Android.
    return logf(num) / 0.693147180559945309417232121458176568f;
}
#endif

#if COMPILER(MSVC)

// VS2013 has most of the math functions now, but we still need to work
// around various differences in behavior of Inf.

#if _MSC_VER < 1800

namespace std {

inline bool isinf(double num) { return !_finite(num) && !_isnan(num); }
inline bool isnan(double num) { return !!_isnan(num); }
inline bool isfinite(double x) { return _finite(x); }
inline bool signbit(double num) { return _copysign(1.0, num) < 0; }

} // namespace std

inline double nextafter(double x, double y) { return _nextafter(x, y); }
inline float nextafterf(float x, float y) { return x > y ? x - FLT_EPSILON : x + FLT_EPSILON; }

inline double copysign(double x, double y) { return _copysign(x, y); }

#endif // _MSC_VER

// Work around a bug in Win, where atan2(+-infinity, +-infinity) yields NaN instead of specific values.
inline double wtf_atan2(double x, double y)
{
    double posInf = std::numeric_limits<double>::infinity();
    double negInf = -std::numeric_limits<double>::infinity();
    double nan = std::numeric_limits<double>::quiet_NaN();

    double result = nan;

    if (x == posInf && y == posInf)
        result = piOverFourDouble;
    else if (x == posInf && y == negInf)
        result = 3 * piOverFourDouble;
    else if (x == negInf && y == posInf)
        result = -piOverFourDouble;
    else if (x == negInf && y == negInf)
        result = -3 * piOverFourDouble;
    else
        result = ::atan2(x, y);

    return result;
}

// Work around a bug in the Microsoft CRT, where fmod(x, +-infinity) yields NaN instead of x.
inline double wtf_fmod(double x, double y) { return (!std::isinf(x) && std::isinf(y)) ? x : fmod(x, y); }

// Work around a bug in the Microsoft CRT, where pow(NaN, 0) yields NaN instead of 1.
inline double wtf_pow(double x, double y) { return y == 0 ? 1 : pow(x, y); }

#define atan2(x, y) wtf_atan2(x, y)
#define fmod(x, y) wtf_fmod(x, y)
#define pow(x, y) wtf_pow(x, y)

#if _MSC_VER < 1800

// MSVC's math functions do not bring lrint.
inline long int lrint(double flt)
{
    int64_t intgr;
#if CPU(X86)
    __asm {
        fld flt
        fistp intgr
    };
#else
    ASSERT(std::isfinite(flt));
    double rounded = round(flt);
    intgr = static_cast<int64_t>(rounded);
    // If the fractional part is exactly 0.5, we need to check whether
    // the rounded result is even. If it is not we need to add 1 to
    // negative values and subtract one from positive values.
    if ((fabs(intgr - flt) == 0.5) & intgr)
        intgr -= ((intgr >> 62) | 1); // 1 with the sign of result, i.e. -1 or 1.
#endif
    return static_cast<long int>(intgr);
}

#endif // _MSC_VER

#endif // COMPILER(MSVC)

inline double deg2rad(double d)  { return d * piDouble / 180.0; }
inline double rad2deg(double r)  { return r * 180.0 / piDouble; }
inline double deg2grad(double d) { return d * 400.0 / 360.0; }
inline double grad2deg(double g) { return g * 360.0 / 400.0; }
inline double turn2deg(double t) { return t * 360.0; }
inline double deg2turn(double d) { return d / 360.0; }
inline double rad2grad(double r) { return r * 200.0 / piDouble; }
inline double grad2rad(double g) { return g * piDouble / 200.0; }

inline float deg2rad(float d)  { return d * piFloat / 180.0f; }
inline float rad2deg(float r)  { return r * 180.0f / piFloat; }
inline float deg2grad(float d) { return d * 400.0f / 360.0f; }
inline float grad2deg(float g) { return g * 360.0f / 400.0f; }
inline float turn2deg(float t) { return t * 360.0f; }
inline float deg2turn(float d) { return d / 360.0f; }
inline float rad2grad(float r) { return r * 200.0f / piFloat; }
inline float grad2rad(float g) { return g * piFloat / 200.0f; }

// std::numeric_limits<T>::min() returns the smallest positive value for floating point types
template<typename T> inline T defaultMinimumForClamp() { return std::numeric_limits<T>::min(); }
template<> inline float defaultMinimumForClamp() { return -std::numeric_limits<float>::max(); }
template<> inline double defaultMinimumForClamp() { return -std::numeric_limits<double>::max(); }
template<typename T> inline T defaultMaximumForClamp() { return std::numeric_limits<T>::max(); }

template<typename T> inline T clampTo(double value, T min = defaultMinimumForClamp<T>(), T max = defaultMaximumForClamp<T>())
{
    if (value >= static_cast<double>(max))
        return max;
    if (value <= static_cast<double>(min))
        return min;
    return static_cast<T>(value);
}
template<> inline long long int clampTo(double, long long int, long long int); // clampTo does not support long long ints.

inline int clampToInteger(double value)
{
    return clampTo<int>(value);
}

inline unsigned clampToUnsigned(double value)
{
    return clampTo<unsigned>(value);
}

inline float clampToFloat(double value)
{
    return clampTo<float>(value);
}

inline int clampToPositiveInteger(double value)
{
    return clampTo<int>(value, 0);
}

inline int clampToInteger(float value)
{
    return clampTo<int>(value);
}

inline int clampToInteger(unsigned x)
{
    const unsigned intMax = static_cast<unsigned>(std::numeric_limits<int>::max());

    if (x >= intMax)
        return std::numeric_limits<int>::max();
    return static_cast<int>(x);
}

inline bool isWithinIntRange(float x)
{
    return x > static_cast<float>(std::numeric_limits<int>::min()) && x < static_cast<float>(std::numeric_limits<int>::max());
}

#ifndef UINT64_C
#if COMPILER(MSVC)
#define UINT64_C(c) c ## ui64
#else
#define UINT64_C(c) c ## ull
#endif
#endif

// Calculate d % 2^{64}.
inline void doubleToInteger(double d, unsigned long long& value)
{
    if (std::isnan(d) || std::isinf(d))
        value = 0;
    else {
        // -2^{64} < fmodValue < 2^{64}.
        double fmodValue = fmod(trunc(d), std::numeric_limits<unsigned long long>::max() + 1.0);
        if (fmodValue >= 0) {
            // 0 <= fmodValue < 2^{64}.
            // 0 <= value < 2^{64}. This cast causes no loss.
            value = static_cast<unsigned long long>(fmodValue);
        } else {
            // -2^{64} < fmodValue < 0.
            // 0 < fmodValueInUnsignedLongLong < 2^{64}. This cast causes no loss.
            unsigned long long fmodValueInUnsignedLongLong = static_cast<unsigned long long>(-fmodValue);
            // -1 < (std::numeric_limits<unsigned long long>::max() - fmodValueInUnsignedLongLong) < 2^{64} - 1.
            // 0 < value < 2^{64}.
            value = std::numeric_limits<unsigned long long>::max() - fmodValueInUnsignedLongLong + 1;
        }
    }
}

namespace WTF {

inline unsigned fastLog2(unsigned i)
{
    unsigned log2 = 0;
    if (i & (i - 1))
        log2 += 1;
    if (i >> 16)
        log2 += 16, i >>= 16;
    if (i >> 8)
        log2 += 8, i >>= 8;
    if (i >> 4)
        log2 += 4, i >>= 4;
    if (i >> 2)
        log2 += 2, i >>= 2;
    if (i >> 1)
        log2 += 1;
    return log2;
}

} // namespace WTF

#endif // #ifndef WTF_MathExtras_h
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root/Source/wtf/MathExtras.h

INCLUDED FROM

DEFINITIONS
