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+/*
+ * 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 <algorithm>
+#include <cmath>
+#include <float.h>
+#include <limits>
+#include <stdint.h>
+#include <stdlib.h>
+#include <wtf/StdLibExtras.h>
+
+#if OS(SOLARIS)
+#include <ieeefp.h>
+#endif
+
+#if OS(OPENBSD)
+#include <sys/types.h>
+#include <machine/ieee.h>
+#endif
+
+#if OS(QNX)
+// FIXME: Look into a way to have cmath import its functions into both the standard and global
+// namespace. For now, we include math.h since the QNX cmath header only imports its functions
+// into the standard namespace.
+#include <math.h>
+// These macros from math.h conflict with the real functions in the std namespace.
+#undef signbit
+#undef isnan
+#undef isinf
+#undef isfinite
+#endif
+
+#ifndef M_PI
+const double piDouble = 3.14159265358979323846;
+const float piFloat = 3.14159265358979323846f;
+#else
+const double piDouble = M_PI;
+const float piFloat = static_cast<float>(M_PI);
+#endif
+
+#ifndef M_PI_2
+const double piOverTwoDouble = 1.57079632679489661923;
+const float piOverTwoFloat = 1.57079632679489661923f;
+#else
+const double piOverTwoDouble = M_PI_2;
+const float piOverTwoFloat = static_cast<float>(M_PI_2);
+#endif
+
+#ifndef M_PI_4
+const double piOverFourDouble = 0.785398163397448309616;
+const float piOverFourFloat = 0.785398163397448309616f;
+#else
+const double piOverFourDouble = M_PI_4;
+const float piOverFourFloat = static_cast<float>(M_PI_4);
+#endif
+
+#if OS(DARWIN)
+
+// 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(SOLARIS)
+
+namespace std {
+
+#ifndef isfinite
+inline bool isfinite(double x) { return finite(x) && !isnand(x); }
+#endif
+#ifndef signbit
+inline bool signbit(double x) { return copysign(1.0, x) < 0; }
+#endif
+#ifndef isinf
+inline bool isinf(double x) { return !finite(x) && !isnand(x); }
+#endif
+
+} // namespace std
+
+#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)
+
+// 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 COMPILER(GCC) && OS(QNX)
+// The stdlib on QNX doesn't contain long abs(long). See PR #104666.
+inline long long abs(long num) { return labs(num); }
+#endif
+
+#if COMPILER(MSVC)
+// 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.
+ return log(num) / 0.693147180559945309417232121458176568;
+}
+
+inline float log2f(float num)
+{
+ // This constant is roughly M_LN2, which is not provided by default on Windows.
+ return logf(num) / 0.693147180559945309417232121458176568f;
+}
+#endif
+
+#if COMPILER(MSVC)
+// The 64bit version of abs() is already defined in stdlib.h which comes with VC10
+#if COMPILER(MSVC9_OR_LOWER)
+inline long long abs(long long num) { return _abs64(num); }
+#endif
+
+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 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());
+}
+
+template<typename T> inline bool hasOneBitSet(T value)
+{
+ return !((value - 1) & value) && value;
+}
+
+template<typename T> inline bool hasZeroOrOneBitsSet(T value)
+{
+ return !((value - 1) & value);
+}
+
+template<typename T> inline bool hasTwoOrMoreBitsSet(T value)
+{
+ return !hasZeroOrOneBitsSet(value);
+}
+
+template <typename T> inline unsigned getLSBSet(T value)
+{
+ unsigned result = 0;
+
+ while (value >>= 1)
+ ++result;
+
+ return result;
+}
+
+template<typename T> inline T timesThreePlusOneDividedByTwo(T value)
+{
+ // Mathematically equivalent to:
+ // (value * 3 + 1) / 2;
+ // or:
+ // (unsigned)ceil(value * 1.5));
+ // This form is not prone to internal overflow.
+ return value + (value >> 1) + (value & 1);
+}
+
+#ifndef UINT64_C
+#if COMPILER(MSVC)
+#define UINT64_C(c) c ## ui64
+#else
+#define UINT64_C(c) c ## ull
+#endif
+#endif
+
+#if COMPILER(MINGW64) && (!defined(__MINGW64_VERSION_RC) || __MINGW64_VERSION_RC < 1)
+inline double wtf_pow(double x, double y)
+{
+ // MinGW-w64 has a custom implementation for pow.
+ // This handles certain special cases that are different.
+ if ((x == 0.0 || std::isinf(x)) && std::isfinite(y)) {
+ double f;
+ if (modf(y, &f) != 0.0)
+ return ((x == 0.0) ^ (y > 0.0)) ? std::numeric_limits<double>::infinity() : 0.0;
+ }
+
+ if (x == 2.0) {
+ int yInt = static_cast<int>(y);
+ if (y == yInt)
+ return ldexp(1.0, yInt);
+ }
+
+ return pow(x, y);
+}
+#define pow(x, y) wtf_pow(x, y)
+#endif // COMPILER(MINGW64) && (!defined(__MINGW64_VERSION_RC) || __MINGW64_VERSION_RC < 1)
+
+
+// decompose 'number' to its sign, exponent, and mantissa components.
+// The result is interpreted as:
+// (sign ? -1 : 1) * pow(2, exponent) * (mantissa / (1 << 52))
+inline void decomposeDouble(double number, bool& sign, int32_t& exponent, uint64_t& mantissa)
+{
+ ASSERT(std::isfinite(number));
+
+ sign = std::signbit(number);
+
+ uint64_t bits = WTF::bitwise_cast<uint64_t>(number);
+ exponent = (static_cast<int32_t>(bits >> 52) & 0x7ff) - 0x3ff;
+ mantissa = bits & 0xFFFFFFFFFFFFFull;
+
+ // Check for zero/denormal values; if so, adjust the exponent,
+ // if not insert the implicit, omitted leading 1 bit.
+ if (exponent == -0x3ff)
+ exponent = mantissa ? -0x3fe : 0;
+ else
+ mantissa |= 0x10000000000000ull;
+}
+
+// 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 {
+
+// From http://graphics.stanford.edu/~seander/bithacks.html#RoundUpPowerOf2
+inline uint32_t roundUpToPowerOfTwo(uint32_t v)
+{
+ v--;
+ v |= v >> 1;
+ v |= v >> 2;
+ v |= v >> 4;
+ v |= v >> 8;
+ v |= v >> 16;
+ v++;
+ return v;
+}
+
+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