/* * 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); #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) && (_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); } // 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) // 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 // 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