| /* |
| * 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 double turn2grad(double t) { return t * 400; } |
| inline double grad2turn(double g) { return g / 400; } |
| |
| 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; } |
| inline float turn2grad(float t) { return t * 400; } |
| inline float grad2turn(float g) { return g / 400; } |
| |
| // 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()); |
| } |
| |
| static size_t greatestCommonDivisor(size_t a, size_t b) |
| { |
| return b ? greatestCommonDivisor(b, a % b) : a; |
| } |
| |
| inline size_t lowestCommonMultiple(size_t a, size_t b) |
| { |
| return a && b ? a / greatestCommonDivisor(a, b) * b : 0; |
| } |
| |
| #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 |