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/*
* Copyright (C) 2006-2018 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 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 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.
*/
#pragma once
#include <algorithm>
#include <climits>
#include <cmath>
#include <float.h>
#include <limits>
#include <stdint.h>
#include <stdlib.h>
#include <wtf/StdLibExtras.h>
#if OS(OPENBSD)
#include <sys/types.h>
#include <machine/ieee.h>
#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
#ifndef M_SQRT2
const double sqrtOfTwoDouble = 1.41421356237309504880;
const float sqrtOfTwoFloat = 1.41421356237309504880f;
#else
const double sqrtOfTwoDouble = M_SQRT2;
const float sqrtOfTwoFloat = static_cast<float>(M_SQRT2);
#endif
#if COMPILER(MSVC)
// Work around a bug in Win, where atan2(+-infinity, +-infinity) yields NaN instead of specific values.
extern "C" 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;
}
#define atan2(x, y) wtf_atan2(x, y)
#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> constexpr T defaultMinimumForClamp() { return std::numeric_limits<T>::min(); }
template<> constexpr float defaultMinimumForClamp() { return -std::numeric_limits<float>::max(); }
template<> constexpr double defaultMinimumForClamp() { return -std::numeric_limits<double>::max(); }
template<typename T> constexpr T defaultMaximumForClamp() { return std::numeric_limits<T>::max(); }
// Same type in and out.
template<typename TargetType, typename SourceType>
typename std::enable_if<std::is_same<TargetType, SourceType>::value, TargetType>::type
clampTo(SourceType value, TargetType min = defaultMinimumForClamp<TargetType>(), TargetType max = defaultMaximumForClamp<TargetType>())
{
if (value >= max)
return max;
if (value <= min)
return min;
return value;
}
// Floating point source.
template<typename TargetType, typename SourceType>
typename std::enable_if<!std::is_same<TargetType, SourceType>::value
&& std::is_floating_point<SourceType>::value
&& !(std::is_floating_point<TargetType>::value && sizeof(TargetType) > sizeof(SourceType)), TargetType>::type
clampTo(SourceType value, TargetType min = defaultMinimumForClamp<TargetType>(), TargetType max = defaultMaximumForClamp<TargetType>())
{
if (value >= static_cast<SourceType>(max))
return max;
if (value <= static_cast<SourceType>(min))
return min;
return static_cast<TargetType>(value);
}
template<typename TargetType, typename SourceType>
typename std::enable_if<!std::is_same<TargetType, SourceType>::value
&& std::is_floating_point<SourceType>::value
&& std::is_floating_point<TargetType>::value
&& (sizeof(TargetType) > sizeof(SourceType)), TargetType>::type
clampTo(SourceType value, TargetType min = defaultMinimumForClamp<TargetType>(), TargetType max = defaultMaximumForClamp<TargetType>())
{
TargetType convertedValue = static_cast<TargetType>(value);
if (convertedValue >= max)
return max;
if (convertedValue <= min)
return min;
return convertedValue;
}
// Source and Target have the same sign and Source is larger or equal to Target
template<typename TargetType, typename SourceType>
typename std::enable_if<!std::is_same<TargetType, SourceType>::value
&& std::numeric_limits<SourceType>::is_integer
&& std::numeric_limits<TargetType>::is_integer
&& std::numeric_limits<TargetType>::is_signed == std::numeric_limits<SourceType>::is_signed
&& sizeof(SourceType) >= sizeof(TargetType), TargetType>::type
clampTo(SourceType value, TargetType min = defaultMinimumForClamp<TargetType>(), TargetType max = defaultMaximumForClamp<TargetType>())
{
if (value >= static_cast<SourceType>(max))
return max;
if (value <= static_cast<SourceType>(min))
return min;
return static_cast<TargetType>(value);
}
// Clamping a unsigned integer to the max signed value.
template<typename TargetType, typename SourceType>
typename std::enable_if<!std::is_same<TargetType, SourceType>::value
&& std::numeric_limits<SourceType>::is_integer
&& std::numeric_limits<TargetType>::is_integer
&& std::numeric_limits<TargetType>::is_signed
&& !std::numeric_limits<SourceType>::is_signed
&& sizeof(SourceType) >= sizeof(TargetType), TargetType>::type
clampTo(SourceType value)
{
TargetType max = std::numeric_limits<TargetType>::max();
if (value >= static_cast<SourceType>(max))
return max;
return static_cast<TargetType>(value);
}
// Clamping a signed integer into a valid unsigned integer.
template<typename TargetType, typename SourceType>
typename std::enable_if<!std::is_same<TargetType, SourceType>::value
&& std::numeric_limits<SourceType>::is_integer
&& std::numeric_limits<TargetType>::is_integer
&& !std::numeric_limits<TargetType>::is_signed
&& std::numeric_limits<SourceType>::is_signed
&& sizeof(SourceType) == sizeof(TargetType), TargetType>::type
clampTo(SourceType value)
{
if (value < 0)
return 0;
return static_cast<TargetType>(value);
}
template<typename TargetType, typename SourceType>
typename std::enable_if<!std::is_same<TargetType, SourceType>::value
&& std::numeric_limits<SourceType>::is_integer
&& std::numeric_limits<TargetType>::is_integer
&& !std::numeric_limits<TargetType>::is_signed
&& std::numeric_limits<SourceType>::is_signed
&& (sizeof(SourceType) > sizeof(TargetType)), TargetType>::type
clampTo(SourceType value)
{
if (value < 0)
return 0;
TargetType max = std::numeric_limits<TargetType>::max();
if (value >= static_cast<SourceType>(max))
return max;
return static_cast<TargetType>(value);
}
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);
}
template<typename T>
inline int clampToInteger(T x)
{
static_assert(std::numeric_limits<T>::is_integer, "T must be an integer.");
const T intMax = static_cast<unsigned>(std::numeric_limits<int>::max());
if (x >= intMax)
return std::numeric_limits<int>::max();
return static_cast<int>(x);
}
// Explicitly accept 64bit result when clamping double value.
// Keep in mind that double can only represent 53bit integer precisely.
template<typename T> constexpr T clampToAccepting64(double value, T min = defaultMinimumForClamp<T>(), T max = defaultMaximumForClamp<T>())
{
return (value >= static_cast<double>(max)) ? max : ((value <= static_cast<double>(min)) ? min : static_cast<T>(value));
}
inline bool isWithinIntRange(float x)
{
return x > static_cast<float>(std::numeric_limits<int>::min()) && x < static_cast<float>(std::numeric_limits<int>::max());
}
inline float normalizedFloat(float value)
{
if (value > 0 && value < std::numeric_limits<float>::min())
return std::numeric_limits<float>::min();
if (value < 0 && value > -std::numeric_limits<float>::min())
return -std::numeric_limits<float>::min();
return value;
}
template<typename T> constexpr bool hasOneBitSet(T value)
{
return !((value - 1) & value) && value;
}
template<typename T> constexpr bool hasZeroOrOneBitsSet(T value)
{
return !((value - 1) & value);
}
template<typename T> constexpr bool hasTwoOrMoreBitsSet(T value)
{
return !hasZeroOrOneBitsSet(value);
}
template<typename T> inline T divideRoundedUp(T a, T b)
{
return (a + b - 1) / b;
}
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);
}
template<typename T> inline bool isNotZeroAndOrdered(T value)
{
return value > 0.0 || value < 0.0;
}
template<typename T> inline bool isZeroOrUnordered(T value)
{
return !isNotZeroAndOrdered(value);
}
template<typename T> inline bool isGreaterThanNonZeroPowerOfTwo(T value, unsigned power)
{
// The crazy way of testing of index >= 2 ** power
// (where I use ** to denote pow()).
return !!((value >> 1) >> (power - 1));
}
template<typename T> constexpr bool isLessThan(const T& a, const T& b) { return a < b; }
template<typename T> constexpr bool isLessThanEqual(const T& a, const T& b) { return a <= b; }
template<typename T> constexpr bool isGreaterThan(const T& a, const T& b) { return a > b; }
template<typename T> constexpr bool isGreaterThanEqual(const T& a, const T& b) { return a >= b; }
#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;
}
template<typename T> constexpr unsigned countOfBits = sizeof(T) * CHAR_BIT;
template<typename T> constexpr unsigned countOfMagnitudeBits = countOfBits<T> - std::is_signed_v<T>;
constexpr float powerOfTwo(unsigned e)
{
float p = 1;
while (e--)
p *= 2;
return p;
}
template<typename T> constexpr float maxPlusOne = powerOfTwo(countOfMagnitudeBits<T>);
// 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), maxPlusOne<unsigned long long>);
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
constexpr 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;
}
constexpr unsigned maskForSize(unsigned size)
{
if (!size)
return 0;
return roundUpToPowerOfTwo(size) - 1;
}
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;
}
inline unsigned fastLog2(uint64_t value)
{
unsigned high = static_cast<unsigned>(value >> 32);
if (high)
return fastLog2(high) + 32;
return fastLog2(static_cast<unsigned>(value));
}
template <typename T>
inline typename std::enable_if<std::is_floating_point<T>::value, T>::type safeFPDivision(T u, T v)
{
// Protect against overflow / underflow.
if (v < 1 && u > v * std::numeric_limits<T>::max())
return std::numeric_limits<T>::max();
if (v > 1 && u < v * std::numeric_limits<T>::min())
return 0;
return u / v;
}
// Floating point numbers comparison:
// u is "essentially equal" [1][2] to v if: | u - v | / |u| <= e and | u - v | / |v| <= e
//
// [1] Knuth, D. E. "Accuracy of Floating Point Arithmetic." The Art of Computer Programming. 3rd ed. Vol. 2.
// Boston: Addison-Wesley, 1998. 229-45.
// [2] http://www.boost.org/doc/libs/1_34_0/libs/test/doc/components/test_tools/floating_point_comparison.html
template <typename T>
inline typename std::enable_if<std::is_floating_point<T>::value, bool>::type areEssentiallyEqual(T u, T v, T epsilon = std::numeric_limits<T>::epsilon())
{
if (u == v)
return true;
const T delta = std::abs(u - v);
return safeFPDivision(delta, std::abs(u)) <= epsilon && safeFPDivision(delta, std::abs(v)) <= epsilon;
}
// Match behavior of Math.min, where NaN is returned if either argument is NaN.
template <typename T>
inline typename std::enable_if<std::is_floating_point<T>::value, T>::type nanPropagatingMin(T a, T b)
{
return std::isnan(a) || std::isnan(b) ? std::numeric_limits<T>::quiet_NaN() : std::min(a, b);
}
// Match behavior of Math.max, where NaN is returned if either argument is NaN.
template <typename T>
inline typename std::enable_if<std::is_floating_point<T>::value, T>::type nanPropagatingMax(T a, T b)
{
return std::isnan(a) || std::isnan(b) ? std::numeric_limits<T>::quiet_NaN() : std::max(a, b);
}
inline bool isIntegral(float value)
{
return static_cast<int>(value) == value;
}
template<typename T>
inline void incrementWithSaturation(T& value)
{
if (value != std::numeric_limits<T>::max())
value++;
}
template<typename T>
inline T leftShiftWithSaturation(T value, unsigned shiftAmount, T max = std::numeric_limits<T>::max())
{
T result = value << shiftAmount;
// We will have saturated if shifting right doesn't recover the original value.
if (result >> shiftAmount != value)
return max;
if (result > max)
return max;
return result;
}
// Check if two ranges overlap assuming that neither range is empty.
template<typename T>
inline bool nonEmptyRangesOverlap(T leftMin, T leftMax, T rightMin, T rightMax)
{
ASSERT(leftMin < leftMax);
ASSERT(rightMin < rightMax);
return leftMax > rightMin && rightMax > leftMin;
}
// Pass ranges with the min being inclusive and the max being exclusive. For example, this should
// return false:
//
// rangesOverlap(0, 8, 8, 16)
template<typename T>
inline bool rangesOverlap(T leftMin, T leftMax, T rightMin, T rightMax)
{
ASSERT(leftMin <= leftMax);
ASSERT(rightMin <= rightMax);
// Empty ranges interfere with nothing.
if (leftMin == leftMax)
return false;
if (rightMin == rightMax)
return false;
return nonEmptyRangesOverlap(leftMin, leftMax, rightMin, rightMax);
}
template<typename VectorType, typename RandomFunc>
void shuffleVector(VectorType& vector, size_t size, const RandomFunc& randomFunc)
{
for (size_t i = 0; i + 1 < size; ++i)
std::swap(vector[i], vector[i + randomFunc(size - i)]);
}
template<typename VectorType, typename RandomFunc>
void shuffleVector(VectorType& vector, const RandomFunc& randomFunc)
{
shuffleVector(vector, vector.size(), randomFunc);
}
template <typename T>
constexpr unsigned clzConstexpr(T value)
{
constexpr unsigned bitSize = countOfBits<T>;
using UT = typename std::make_unsigned<T>::type;
UT uValue = value;
unsigned zeroCount = 0;
for (int i = bitSize - 1; i >= 0; i--) {
if (uValue >> i)
break;
zeroCount++;
}
return zeroCount;
}
template<typename T>
inline unsigned clz(T value)
{
constexpr unsigned bitSize = countOfBits<T>;
using UT = typename std::make_unsigned<T>::type;
UT uValue = value;
#if COMPILER(GCC_COMPATIBLE)
constexpr unsigned bitSize64 = countOfBits<uint64_t>;
if (uValue)
return __builtin_clzll(uValue) - (bitSize64 - bitSize);
return bitSize;
#elif COMPILER(MSVC) && !CPU(X86)
// Visual Studio 2008 or upper have __lzcnt, but we can't detect Intel AVX at compile time.
// So we use bit-scan-reverse operation to calculate clz.
// _BitScanReverse64 is defined in X86_64 and ARM in MSVC supported environments.
unsigned long ret = 0;
if (_BitScanReverse64(&ret, uValue))
return bitSize - 1 - ret;
return bitSize;
#else
UNUSED_PARAM(bitSize);
UNUSED_PARAM(uValue);
return clzConstexpr(value);
#endif
}
template <typename T>
constexpr unsigned ctzConstexpr(T value)
{
constexpr unsigned bitSize = countOfBits<T>;
using UT = typename std::make_unsigned<T>::type;
UT uValue = value;
unsigned zeroCount = 0;
for (unsigned i = 0; i < bitSize; i++) {
if (uValue & 1)
break;
zeroCount++;
uValue >>= 1;
}
return zeroCount;
}
template<typename T>
inline unsigned ctz(T value)
{
constexpr unsigned bitSize = countOfBits<T>;
using UT = typename std::make_unsigned<T>::type;
UT uValue = value;
#if COMPILER(GCC_COMPATIBLE)
if (uValue)
return __builtin_ctzll(uValue);
return bitSize;
#elif COMPILER(MSVC) && !CPU(X86)
unsigned long ret = 0;
if (_BitScanForward64(&ret, uValue))
return ret;
return bitSize;
#else
UNUSED_PARAM(bitSize);
UNUSED_PARAM(uValue);
return ctzConstexpr(value);
#endif
}
template<typename T>
inline unsigned getLSBSet(T t)
{
ASSERT(t);
return ctz(t);
}
template<typename T>
constexpr unsigned getLSBSetConstexpr(T t)
{
ASSERT_UNDER_CONSTEXPR_CONTEXT(t);
return ctzConstexpr(t);
}
template<typename T>
inline unsigned getMSBSet(T t)
{
constexpr unsigned bitSize = countOfBits<T>;
ASSERT(t);
return bitSize - 1 - clz(t);
}
template<typename T>
constexpr unsigned getMSBSetConstexpr(T t)
{
constexpr unsigned bitSize = countOfBits<T>;
ASSERT_UNDER_CONSTEXPR_CONTEXT(t);
return bitSize - 1 - clzConstexpr(t);
}
template<typename T> unsigned log2(T value) { return getMSBSet(value); }
template<typename T> constexpr unsigned log2Constexpr(T value) { return getMSBSetConstexpr(value); }
} // namespace WTF
using WTF::shuffleVector;
using WTF::clz;
using WTF::ctz;
using WTF::getLSBSet;
using WTF::getMSBSet;