| 1 | /* |
| 2 | * Copyright (C) 2006-2018 Apple Inc. All rights reserved. |
| 3 | * |
| 4 | * Redistribution and use in source and binary forms, with or without |
| 5 | * modification, are permitted provided that the following conditions |
| 6 | * are met: |
| 7 | * 1. Redistributions of source code must retain the above copyright |
| 8 | * notice, this list of conditions and the following disclaimer. |
| 9 | * 2. Redistributions in binary form must reproduce the above copyright |
| 10 | * notice, this list of conditions and the following disclaimer in the |
| 11 | * documentation and/or other materials provided with the distribution. |
| 12 | * |
| 13 | * THIS SOFTWARE IS PROVIDED BY APPLE INC. ``AS IS'' AND ANY |
| 14 | * EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| 15 | * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR |
| 16 | * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL APPLE INC. OR |
| 17 | * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, |
| 18 | * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, |
| 19 | * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR |
| 20 | * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY |
| 21 | * OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT |
| 22 | * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE |
| 23 | * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
| 24 | */ |
| 25 | |
| 26 | #pragma once |
| 27 | |
| 28 | #include <algorithm> |
| 29 | #include <climits> |
| 30 | #include <cmath> |
| 31 | #include <float.h> |
| 32 | #include <limits> |
| 33 | #include <stdint.h> |
| 34 | #include <stdlib.h> |
| 35 | #include <wtf/StdLibExtras.h> |
| 36 | |
| 37 | #if OS(OPENBSD) |
| 38 | #include <sys/types.h> |
| 39 | #include <machine/ieee.h> |
| 40 | #endif |
| 41 | |
| 42 | #ifndef M_PI |
| 43 | const double piDouble = 3.14159265358979323846; |
| 44 | const float piFloat = 3.14159265358979323846f; |
| 45 | #else |
| 46 | const double piDouble = M_PI; |
| 47 | const float piFloat = static_cast<float>(M_PI); |
| 48 | #endif |
| 49 | |
| 50 | #ifndef M_PI_2 |
| 51 | const double piOverTwoDouble = 1.57079632679489661923; |
| 52 | const float piOverTwoFloat = 1.57079632679489661923f; |
| 53 | #else |
| 54 | const double piOverTwoDouble = M_PI_2; |
| 55 | const float piOverTwoFloat = static_cast<float>(M_PI_2); |
| 56 | #endif |
| 57 | |
| 58 | #ifndef M_PI_4 |
| 59 | const double piOverFourDouble = 0.785398163397448309616; |
| 60 | const float piOverFourFloat = 0.785398163397448309616f; |
| 61 | #else |
| 62 | const double piOverFourDouble = M_PI_4; |
| 63 | const float piOverFourFloat = static_cast<float>(M_PI_4); |
| 64 | #endif |
| 65 | |
| 66 | #ifndef M_SQRT2 |
| 67 | const double sqrtOfTwoDouble = 1.41421356237309504880; |
| 68 | const float sqrtOfTwoFloat = 1.41421356237309504880f; |
| 69 | #else |
| 70 | const double sqrtOfTwoDouble = M_SQRT2; |
| 71 | const float sqrtOfTwoFloat = static_cast<float>(M_SQRT2); |
| 72 | #endif |
| 73 | |
| 74 | #if COMPILER(MSVC) |
| 75 | |
| 76 | // Work around a bug in Win, where atan2(+-infinity, +-infinity) yields NaN instead of specific values. |
| 77 | extern "C" inline double wtf_atan2(double x, double y) |
| 78 | { |
| 79 | double posInf = std::numeric_limits<double>::infinity(); |
| 80 | double negInf = -std::numeric_limits<double>::infinity(); |
| 81 | double nan = std::numeric_limits<double>::quiet_NaN(); |
| 82 | |
| 83 | double result = nan; |
| 84 | |
| 85 | if (x == posInf && y == posInf) |
| 86 | result = piOverFourDouble; |
| 87 | else if (x == posInf && y == negInf) |
| 88 | result = 3 * piOverFourDouble; |
| 89 | else if (x == negInf && y == posInf) |
| 90 | result = -piOverFourDouble; |
| 91 | else if (x == negInf && y == negInf) |
| 92 | result = -3 * piOverFourDouble; |
| 93 | else |
| 94 | result = ::atan2(x, y); |
| 95 | |
| 96 | return result; |
| 97 | } |
| 98 | |
| 99 | #define atan2(x, y) wtf_atan2(x, y) |
| 100 | |
| 101 | #endif // COMPILER(MSVC) |
| 102 | |
| 103 | inline double deg2rad(double d) { return d * piDouble / 180.0; } |
| 104 | inline double rad2deg(double r) { return r * 180.0 / piDouble; } |
| 105 | inline double deg2grad(double d) { return d * 400.0 / 360.0; } |
| 106 | inline double grad2deg(double g) { return g * 360.0 / 400.0; } |
| 107 | inline double turn2deg(double t) { return t * 360.0; } |
| 108 | inline double deg2turn(double d) { return d / 360.0; } |
| 109 | inline double rad2grad(double r) { return r * 200.0 / piDouble; } |
| 110 | inline double grad2rad(double g) { return g * piDouble / 200.0; } |
| 111 | |
| 112 | inline float deg2rad(float d) { return d * piFloat / 180.0f; } |
| 113 | inline float rad2deg(float r) { return r * 180.0f / piFloat; } |
| 114 | inline float deg2grad(float d) { return d * 400.0f / 360.0f; } |
| 115 | inline float grad2deg(float g) { return g * 360.0f / 400.0f; } |
| 116 | inline float turn2deg(float t) { return t * 360.0f; } |
| 117 | inline float deg2turn(float d) { return d / 360.0f; } |
| 118 | inline float rad2grad(float r) { return r * 200.0f / piFloat; } |
| 119 | inline float grad2rad(float g) { return g * piFloat / 200.0f; } |
| 120 | |
| 121 | // std::numeric_limits<T>::min() returns the smallest positive value for floating point types |
| 122 | template<typename T> constexpr T defaultMinimumForClamp() { return std::numeric_limits<T>::min(); } |
| 123 | template<> constexpr float defaultMinimumForClamp() { return -std::numeric_limits<float>::max(); } |
| 124 | template<> constexpr double defaultMinimumForClamp() { return -std::numeric_limits<double>::max(); } |
| 125 | template<typename T> constexpr T defaultMaximumForClamp() { return std::numeric_limits<T>::max(); } |
| 126 | |
| 127 | // Same type in and out. |
| 128 | template<typename TargetType, typename SourceType> |
| 129 | typename std::enable_if<std::is_same<TargetType, SourceType>::value, TargetType>::type |
| 130 | clampTo(SourceType value, TargetType min = defaultMinimumForClamp<TargetType>(), TargetType max = defaultMaximumForClamp<TargetType>()) |
| 131 | { |
| 132 | if (value >= max) |
| 133 | return max; |
| 134 | if (value <= min) |
| 135 | return min; |
| 136 | return value; |
| 137 | } |
| 138 | |
| 139 | // Floating point source. |
| 140 | template<typename TargetType, typename SourceType> |
| 141 | typename std::enable_if<!std::is_same<TargetType, SourceType>::value |
| 142 | && std::is_floating_point<SourceType>::value |
| 143 | && !(std::is_floating_point<TargetType>::value && sizeof(TargetType) > sizeof(SourceType)), TargetType>::type |
| 144 | clampTo(SourceType value, TargetType min = defaultMinimumForClamp<TargetType>(), TargetType max = defaultMaximumForClamp<TargetType>()) |
| 145 | { |
| 146 | if (value >= static_cast<SourceType>(max)) |
| 147 | return max; |
| 148 | if (value <= static_cast<SourceType>(min)) |
| 149 | return min; |
| 150 | return static_cast<TargetType>(value); |
| 151 | } |
| 152 | |
| 153 | template<typename TargetType, typename SourceType> |
| 154 | typename std::enable_if<!std::is_same<TargetType, SourceType>::value |
| 155 | && std::is_floating_point<SourceType>::value |
| 156 | && std::is_floating_point<TargetType>::value |
| 157 | && (sizeof(TargetType) > sizeof(SourceType)), TargetType>::type |
| 158 | clampTo(SourceType value, TargetType min = defaultMinimumForClamp<TargetType>(), TargetType max = defaultMaximumForClamp<TargetType>()) |
| 159 | { |
| 160 | TargetType convertedValue = static_cast<TargetType>(value); |
| 161 | if (convertedValue >= max) |
| 162 | return max; |
| 163 | if (convertedValue <= min) |
| 164 | return min; |
| 165 | return convertedValue; |
| 166 | } |
| 167 | |
| 168 | // Source and Target have the same sign and Source is larger or equal to Target |
| 169 | template<typename TargetType, typename SourceType> |
| 170 | typename std::enable_if<!std::is_same<TargetType, SourceType>::value |
| 171 | && std::numeric_limits<SourceType>::is_integer |
| 172 | && std::numeric_limits<TargetType>::is_integer |
| 173 | && std::numeric_limits<TargetType>::is_signed == std::numeric_limits<SourceType>::is_signed |
| 174 | && sizeof(SourceType) >= sizeof(TargetType), TargetType>::type |
| 175 | clampTo(SourceType value, TargetType min = defaultMinimumForClamp<TargetType>(), TargetType max = defaultMaximumForClamp<TargetType>()) |
| 176 | { |
| 177 | if (value >= static_cast<SourceType>(max)) |
| 178 | return max; |
| 179 | if (value <= static_cast<SourceType>(min)) |
| 180 | return min; |
| 181 | return static_cast<TargetType>(value); |
| 182 | } |
| 183 | |
| 184 | // Clamping a unsigned integer to the max signed value. |
| 185 | template<typename TargetType, typename SourceType> |
| 186 | typename std::enable_if<!std::is_same<TargetType, SourceType>::value |
| 187 | && std::numeric_limits<SourceType>::is_integer |
| 188 | && std::numeric_limits<TargetType>::is_integer |
| 189 | && std::numeric_limits<TargetType>::is_signed |
| 190 | && !std::numeric_limits<SourceType>::is_signed |
| 191 | && sizeof(SourceType) >= sizeof(TargetType), TargetType>::type |
| 192 | clampTo(SourceType value) |
| 193 | { |
| 194 | TargetType max = std::numeric_limits<TargetType>::max(); |
| 195 | if (value >= static_cast<SourceType>(max)) |
| 196 | return max; |
| 197 | return static_cast<TargetType>(value); |
| 198 | } |
| 199 | |
| 200 | // Clamping a signed integer into a valid unsigned integer. |
| 201 | template<typename TargetType, typename SourceType> |
| 202 | typename std::enable_if<!std::is_same<TargetType, SourceType>::value |
| 203 | && std::numeric_limits<SourceType>::is_integer |
| 204 | && std::numeric_limits<TargetType>::is_integer |
| 205 | && !std::numeric_limits<TargetType>::is_signed |
| 206 | && std::numeric_limits<SourceType>::is_signed |
| 207 | && sizeof(SourceType) == sizeof(TargetType), TargetType>::type |
| 208 | clampTo(SourceType value) |
| 209 | { |
| 210 | if (value < 0) |
| 211 | return 0; |
| 212 | return static_cast<TargetType>(value); |
| 213 | } |
| 214 | |
| 215 | template<typename TargetType, typename SourceType> |
| 216 | typename std::enable_if<!std::is_same<TargetType, SourceType>::value |
| 217 | && std::numeric_limits<SourceType>::is_integer |
| 218 | && std::numeric_limits<TargetType>::is_integer |
| 219 | && !std::numeric_limits<TargetType>::is_signed |
| 220 | && std::numeric_limits<SourceType>::is_signed |
| 221 | && (sizeof(SourceType) > sizeof(TargetType)), TargetType>::type |
| 222 | clampTo(SourceType value) |
| 223 | { |
| 224 | if (value < 0) |
| 225 | return 0; |
| 226 | TargetType max = std::numeric_limits<TargetType>::max(); |
| 227 | if (value >= static_cast<SourceType>(max)) |
| 228 | return max; |
| 229 | return static_cast<TargetType>(value); |
| 230 | } |
| 231 | |
| 232 | inline int clampToInteger(double value) |
| 233 | { |
| 234 | return clampTo<int>(value); |
| 235 | } |
| 236 | |
| 237 | inline unsigned clampToUnsigned(double value) |
| 238 | { |
| 239 | return clampTo<unsigned>(value); |
| 240 | } |
| 241 | |
| 242 | inline float clampToFloat(double value) |
| 243 | { |
| 244 | return clampTo<float>(value); |
| 245 | } |
| 246 | |
| 247 | inline int clampToPositiveInteger(double value) |
| 248 | { |
| 249 | return clampTo<int>(value, 0); |
| 250 | } |
| 251 | |
| 252 | inline int clampToInteger(float value) |
| 253 | { |
| 254 | return clampTo<int>(value); |
| 255 | } |
| 256 | |
| 257 | template<typename T> |
| 258 | inline int clampToInteger(T x) |
| 259 | { |
| 260 | static_assert(std::numeric_limits<T>::is_integer, "T must be an integer." ); |
| 261 | |
| 262 | const T intMax = static_cast<unsigned>(std::numeric_limits<int>::max()); |
| 263 | |
| 264 | if (x >= intMax) |
| 265 | return std::numeric_limits<int>::max(); |
| 266 | return static_cast<int>(x); |
| 267 | } |
| 268 | |
| 269 | // Explicitly accept 64bit result when clamping double value. |
| 270 | // Keep in mind that double can only represent 53bit integer precisely. |
| 271 | template<typename T> constexpr T clampToAccepting64(double value, T min = defaultMinimumForClamp<T>(), T max = defaultMaximumForClamp<T>()) |
| 272 | { |
| 273 | return (value >= static_cast<double>(max)) ? max : ((value <= static_cast<double>(min)) ? min : static_cast<T>(value)); |
| 274 | } |
| 275 | |
| 276 | inline bool isWithinIntRange(float x) |
| 277 | { |
| 278 | return x > static_cast<float>(std::numeric_limits<int>::min()) && x < static_cast<float>(std::numeric_limits<int>::max()); |
| 279 | } |
| 280 | |
| 281 | inline float normalizedFloat(float value) |
| 282 | { |
| 283 | if (value > 0 && value < std::numeric_limits<float>::min()) |
| 284 | return std::numeric_limits<float>::min(); |
| 285 | if (value < 0 && value > -std::numeric_limits<float>::min()) |
| 286 | return -std::numeric_limits<float>::min(); |
| 287 | return value; |
| 288 | } |
| 289 | |
| 290 | template<typename T> constexpr bool hasOneBitSet(T value) |
| 291 | { |
| 292 | return !((value - 1) & value) && value; |
| 293 | } |
| 294 | |
| 295 | template<typename T> constexpr bool hasZeroOrOneBitsSet(T value) |
| 296 | { |
| 297 | return !((value - 1) & value); |
| 298 | } |
| 299 | |
| 300 | template<typename T> constexpr bool hasTwoOrMoreBitsSet(T value) |
| 301 | { |
| 302 | return !hasZeroOrOneBitsSet(value); |
| 303 | } |
| 304 | |
| 305 | template<typename T> inline T divideRoundedUp(T a, T b) |
| 306 | { |
| 307 | return (a + b - 1) / b; |
| 308 | } |
| 309 | |
| 310 | template<typename T> inline T timesThreePlusOneDividedByTwo(T value) |
| 311 | { |
| 312 | // Mathematically equivalent to: |
| 313 | // (value * 3 + 1) / 2; |
| 314 | // or: |
| 315 | // (unsigned)ceil(value * 1.5)); |
| 316 | // This form is not prone to internal overflow. |
| 317 | return value + (value >> 1) + (value & 1); |
| 318 | } |
| 319 | |
| 320 | template<typename T> inline bool isNotZeroAndOrdered(T value) |
| 321 | { |
| 322 | return value > 0.0 || value < 0.0; |
| 323 | } |
| 324 | |
| 325 | template<typename T> inline bool isZeroOrUnordered(T value) |
| 326 | { |
| 327 | return !isNotZeroAndOrdered(value); |
| 328 | } |
| 329 | |
| 330 | template<typename T> inline bool isGreaterThanNonZeroPowerOfTwo(T value, unsigned power) |
| 331 | { |
| 332 | // The crazy way of testing of index >= 2 ** power |
| 333 | // (where I use ** to denote pow()). |
| 334 | return !!((value >> 1) >> (power - 1)); |
| 335 | } |
| 336 | |
| 337 | template<typename T> constexpr bool isLessThan(const T& a, const T& b) { return a < b; } |
| 338 | template<typename T> constexpr bool isLessThanEqual(const T& a, const T& b) { return a <= b; } |
| 339 | template<typename T> constexpr bool isGreaterThan(const T& a, const T& b) { return a > b; } |
| 340 | template<typename T> constexpr bool isGreaterThanEqual(const T& a, const T& b) { return a >= b; } |
| 341 | |
| 342 | #ifndef UINT64_C |
| 343 | #if COMPILER(MSVC) |
| 344 | #define UINT64_C(c) c ## ui64 |
| 345 | #else |
| 346 | #define UINT64_C(c) c ## ull |
| 347 | #endif |
| 348 | #endif |
| 349 | |
| 350 | #if COMPILER(MINGW64) && (!defined(__MINGW64_VERSION_RC) || __MINGW64_VERSION_RC < 1) |
| 351 | inline double wtf_pow(double x, double y) |
| 352 | { |
| 353 | // MinGW-w64 has a custom implementation for pow. |
| 354 | // This handles certain special cases that are different. |
| 355 | if ((x == 0.0 || std::isinf(x)) && std::isfinite(y)) { |
| 356 | double f; |
| 357 | if (modf(y, &f) != 0.0) |
| 358 | return ((x == 0.0) ^ (y > 0.0)) ? std::numeric_limits<double>::infinity() : 0.0; |
| 359 | } |
| 360 | |
| 361 | if (x == 2.0) { |
| 362 | int yInt = static_cast<int>(y); |
| 363 | if (y == yInt) |
| 364 | return ldexp(1.0, yInt); |
| 365 | } |
| 366 | |
| 367 | return pow(x, y); |
| 368 | } |
| 369 | #define pow(x, y) wtf_pow(x, y) |
| 370 | #endif // COMPILER(MINGW64) && (!defined(__MINGW64_VERSION_RC) || __MINGW64_VERSION_RC < 1) |
| 371 | |
| 372 | |
| 373 | // decompose 'number' to its sign, exponent, and mantissa components. |
| 374 | // The result is interpreted as: |
| 375 | // (sign ? -1 : 1) * pow(2, exponent) * (mantissa / (1 << 52)) |
| 376 | inline void decomposeDouble(double number, bool& sign, int32_t& exponent, uint64_t& mantissa) |
| 377 | { |
| 378 | ASSERT(std::isfinite(number)); |
| 379 | |
| 380 | sign = std::signbit(number); |
| 381 | |
| 382 | uint64_t bits = WTF::bitwise_cast<uint64_t>(number); |
| 383 | exponent = (static_cast<int32_t>(bits >> 52) & 0x7ff) - 0x3ff; |
| 384 | mantissa = bits & 0xFFFFFFFFFFFFFull; |
| 385 | |
| 386 | // Check for zero/denormal values; if so, adjust the exponent, |
| 387 | // if not insert the implicit, omitted leading 1 bit. |
| 388 | if (exponent == -0x3ff) |
| 389 | exponent = mantissa ? -0x3fe : 0; |
| 390 | else |
| 391 | mantissa |= 0x10000000000000ull; |
| 392 | } |
| 393 | |
| 394 | // Calculate d % 2^{64}. |
| 395 | inline void doubleToInteger(double d, unsigned long long& value) |
| 396 | { |
| 397 | if (std::isnan(d) || std::isinf(d)) |
| 398 | value = 0; |
| 399 | else { |
| 400 | // -2^{64} < fmodValue < 2^{64}. |
| 401 | double fmodValue = fmod(trunc(d), std::numeric_limits<unsigned long long>::max() + 1.0); |
| 402 | if (fmodValue >= 0) { |
| 403 | // 0 <= fmodValue < 2^{64}. |
| 404 | // 0 <= value < 2^{64}. This cast causes no loss. |
| 405 | value = static_cast<unsigned long long>(fmodValue); |
| 406 | } else { |
| 407 | // -2^{64} < fmodValue < 0. |
| 408 | // 0 < fmodValueInUnsignedLongLong < 2^{64}. This cast causes no loss. |
| 409 | unsigned long long fmodValueInUnsignedLongLong = static_cast<unsigned long long>(-fmodValue); |
| 410 | // -1 < (std::numeric_limits<unsigned long long>::max() - fmodValueInUnsignedLongLong) < 2^{64} - 1. |
| 411 | // 0 < value < 2^{64}. |
| 412 | value = std::numeric_limits<unsigned long long>::max() - fmodValueInUnsignedLongLong + 1; |
| 413 | } |
| 414 | } |
| 415 | } |
| 416 | |
| 417 | namespace WTF { |
| 418 | |
| 419 | // From http://graphics.stanford.edu/~seander/bithacks.html#RoundUpPowerOf2 |
| 420 | constexpr uint32_t roundUpToPowerOfTwo(uint32_t v) |
| 421 | { |
| 422 | v--; |
| 423 | v |= v >> 1; |
| 424 | v |= v >> 2; |
| 425 | v |= v >> 4; |
| 426 | v |= v >> 8; |
| 427 | v |= v >> 16; |
| 428 | v++; |
| 429 | return v; |
| 430 | } |
| 431 | |
| 432 | constexpr unsigned maskForSize(unsigned size) |
| 433 | { |
| 434 | if (!size) |
| 435 | return 0; |
| 436 | return roundUpToPowerOfTwo(size) - 1; |
| 437 | } |
| 438 | |
| 439 | inline unsigned fastLog2(unsigned i) |
| 440 | { |
| 441 | unsigned log2 = 0; |
| 442 | if (i & (i - 1)) |
| 443 | log2 += 1; |
| 444 | if (i >> 16) { |
| 445 | log2 += 16; |
| 446 | i >>= 16; |
| 447 | } |
| 448 | if (i >> 8) { |
| 449 | log2 += 8; |
| 450 | i >>= 8; |
| 451 | } |
| 452 | if (i >> 4) { |
| 453 | log2 += 4; |
| 454 | i >>= 4; |
| 455 | } |
| 456 | if (i >> 2) { |
| 457 | log2 += 2; |
| 458 | i >>= 2; |
| 459 | } |
| 460 | if (i >> 1) |
| 461 | log2 += 1; |
| 462 | return log2; |
| 463 | } |
| 464 | |
| 465 | inline unsigned fastLog2(uint64_t value) |
| 466 | { |
| 467 | unsigned high = static_cast<unsigned>(value >> 32); |
| 468 | if (high) |
| 469 | return fastLog2(high) + 32; |
| 470 | return fastLog2(static_cast<unsigned>(value)); |
| 471 | } |
| 472 | |
| 473 | template <typename T> |
| 474 | inline typename std::enable_if<std::is_floating_point<T>::value, T>::type safeFPDivision(T u, T v) |
| 475 | { |
| 476 | // Protect against overflow / underflow. |
| 477 | if (v < 1 && u > v * std::numeric_limits<T>::max()) |
| 478 | return std::numeric_limits<T>::max(); |
| 479 | if (v > 1 && u < v * std::numeric_limits<T>::min()) |
| 480 | return 0; |
| 481 | return u / v; |
| 482 | } |
| 483 | |
| 484 | // Floating point numbers comparison: |
| 485 | // u is "essentially equal" [1][2] to v if: | u - v | / |u| <= e and | u - v | / |v| <= e |
| 486 | // |
| 487 | // [1] Knuth, D. E. "Accuracy of Floating Point Arithmetic." The Art of Computer Programming. 3rd ed. Vol. 2. |
| 488 | // Boston: Addison-Wesley, 1998. 229-45. |
| 489 | // [2] http://www.boost.org/doc/libs/1_34_0/libs/test/doc/components/test_tools/floating_point_comparison.html |
| 490 | template <typename T> |
| 491 | 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()) |
| 492 | { |
| 493 | if (u == v) |
| 494 | return true; |
| 495 | |
| 496 | const T delta = std::abs(u - v); |
| 497 | return safeFPDivision(delta, std::abs(u)) <= epsilon && safeFPDivision(delta, std::abs(v)) <= epsilon; |
| 498 | } |
| 499 | |
| 500 | // Match behavior of Math.min, where NaN is returned if either argument is NaN. |
| 501 | template <typename T> |
| 502 | inline typename std::enable_if<std::is_floating_point<T>::value, T>::type nanPropagatingMin(T a, T b) |
| 503 | { |
| 504 | return std::isnan(a) || std::isnan(b) ? std::numeric_limits<T>::quiet_NaN() : std::min(a, b); |
| 505 | } |
| 506 | |
| 507 | // Match behavior of Math.max, where NaN is returned if either argument is NaN. |
| 508 | template <typename T> |
| 509 | inline typename std::enable_if<std::is_floating_point<T>::value, T>::type nanPropagatingMax(T a, T b) |
| 510 | { |
| 511 | return std::isnan(a) || std::isnan(b) ? std::numeric_limits<T>::quiet_NaN() : std::max(a, b); |
| 512 | } |
| 513 | |
| 514 | inline bool isIntegral(float value) |
| 515 | { |
| 516 | return static_cast<int>(value) == value; |
| 517 | } |
| 518 | |
| 519 | template<typename T> |
| 520 | inline void incrementWithSaturation(T& value) |
| 521 | { |
| 522 | if (value != std::numeric_limits<T>::max()) |
| 523 | value++; |
| 524 | } |
| 525 | |
| 526 | template<typename T> |
| 527 | inline T leftShiftWithSaturation(T value, unsigned shiftAmount, T max = std::numeric_limits<T>::max()) |
| 528 | { |
| 529 | T result = value << shiftAmount; |
| 530 | // We will have saturated if shifting right doesn't recover the original value. |
| 531 | if (result >> shiftAmount != value) |
| 532 | return max; |
| 533 | if (result > max) |
| 534 | return max; |
| 535 | return result; |
| 536 | } |
| 537 | |
| 538 | // Check if two ranges overlap assuming that neither range is empty. |
| 539 | template<typename T> |
| 540 | inline bool nonEmptyRangesOverlap(T leftMin, T leftMax, T rightMin, T rightMax) |
| 541 | { |
| 542 | ASSERT(leftMin < leftMax); |
| 543 | ASSERT(rightMin < rightMax); |
| 544 | |
| 545 | return leftMax > rightMin && rightMax > leftMin; |
| 546 | } |
| 547 | |
| 548 | // Pass ranges with the min being inclusive and the max being exclusive. For example, this should |
| 549 | // return false: |
| 550 | // |
| 551 | // rangesOverlap(0, 8, 8, 16) |
| 552 | template<typename T> |
| 553 | inline bool rangesOverlap(T leftMin, T leftMax, T rightMin, T rightMax) |
| 554 | { |
| 555 | ASSERT(leftMin <= leftMax); |
| 556 | ASSERT(rightMin <= rightMax); |
| 557 | |
| 558 | // Empty ranges interfere with nothing. |
| 559 | if (leftMin == leftMax) |
| 560 | return false; |
| 561 | if (rightMin == rightMax) |
| 562 | return false; |
| 563 | |
| 564 | return nonEmptyRangesOverlap(leftMin, leftMax, rightMin, rightMax); |
| 565 | } |
| 566 | |
| 567 | // This mask is not necessarily the minimal mask, specifically if size is |
| 568 | // a power of 2. It has the advantage that it's fast to compute, however. |
| 569 | inline uint32_t computeIndexingMask(uint32_t size) |
| 570 | { |
| 571 | return static_cast<uint64_t>(static_cast<uint32_t>(-1)) >> std::clz(size); |
| 572 | } |
| 573 | |
| 574 | constexpr unsigned preciseIndexMaskShiftForSize(unsigned size) |
| 575 | { |
| 576 | return size * 8 - 1; |
| 577 | } |
| 578 | |
| 579 | template<typename T> |
| 580 | constexpr unsigned preciseIndexMaskShift() |
| 581 | { |
| 582 | return preciseIndexMaskShiftForSize(sizeof(T)); |
| 583 | } |
| 584 | |
| 585 | template<typename T> |
| 586 | T opaque(T pointer) |
| 587 | { |
| 588 | #if !OS(WINDOWS) |
| 589 | asm("" : "+r" (pointer)); |
| 590 | #endif |
| 591 | return pointer; |
| 592 | } |
| 593 | |
| 594 | // This masks the given pointer with 0xffffffffffffffff (ptrwidth) if `index < |
| 595 | // length`. Otherwise, it masks the pointer with 0. Similar to Linux kernel's array_ptr. |
| 596 | template<typename T> |
| 597 | inline T* preciseIndexMaskPtr(uintptr_t index, uintptr_t length, T* value) |
| 598 | { |
| 599 | uintptr_t result = bitwise_cast<uintptr_t>(value) & static_cast<uintptr_t>( |
| 600 | static_cast<intptr_t>(index - opaque(length)) >> |
| 601 | static_cast<intptr_t>(preciseIndexMaskShift<T*>())); |
| 602 | return bitwise_cast<T*>(result); |
| 603 | } |
| 604 | |
| 605 | template<typename VectorType, typename RandomFunc> |
| 606 | void shuffleVector(VectorType& vector, size_t size, const RandomFunc& randomFunc) |
| 607 | { |
| 608 | for (size_t i = 0; i + 1 < size; ++i) |
| 609 | std::swap(vector[i], vector[i + randomFunc(size - i)]); |
| 610 | } |
| 611 | |
| 612 | template<typename VectorType, typename RandomFunc> |
| 613 | void shuffleVector(VectorType& vector, const RandomFunc& randomFunc) |
| 614 | { |
| 615 | shuffleVector(vector, vector.size(), randomFunc); |
| 616 | } |
| 617 | |
| 618 | template <typename T> |
| 619 | constexpr unsigned clzConstexpr(T value) |
| 620 | { |
| 621 | constexpr unsigned bitSize = sizeof(T) * CHAR_BIT; |
| 622 | |
| 623 | using UT = typename std::make_unsigned<T>::type; |
| 624 | UT uValue = value; |
| 625 | |
| 626 | unsigned zeroCount = 0; |
| 627 | for (int i = bitSize - 1; i >= 0; i--) { |
| 628 | if (uValue >> i) |
| 629 | break; |
| 630 | zeroCount++; |
| 631 | } |
| 632 | return zeroCount; |
| 633 | } |
| 634 | |
| 635 | template<typename T> |
| 636 | inline unsigned clz(T value) |
| 637 | { |
| 638 | constexpr unsigned bitSize = sizeof(T) * CHAR_BIT; |
| 639 | |
| 640 | using UT = typename std::make_unsigned<T>::type; |
| 641 | UT uValue = value; |
| 642 | |
| 643 | #if COMPILER(GCC_COMPATIBLE) |
| 644 | constexpr unsigned bitSize64 = sizeof(uint64_t) * CHAR_BIT; |
| 645 | if (uValue) |
| 646 | return __builtin_clzll(uValue) - (bitSize64 - bitSize); |
| 647 | return bitSize; |
| 648 | #elif COMPILER(MSVC) && !CPU(X86) |
| 649 | // Visual Studio 2008 or upper have __lzcnt, but we can't detect Intel AVX at compile time. |
| 650 | // So we use bit-scan-reverse operation to calculate clz. |
| 651 | // _BitScanReverse64 is defined in X86_64 and ARM in MSVC supported environments. |
| 652 | unsigned long ret = 0; |
| 653 | if (_BitScanReverse64(&ret, uValue)) |
| 654 | return bitSize - 1 - ret; |
| 655 | return bitSize; |
| 656 | #else |
| 657 | UNUSED_PARAM(bitSize); |
| 658 | UNUSED_PARAM(uValue); |
| 659 | return clzConstexpr(value); |
| 660 | #endif |
| 661 | } |
| 662 | |
| 663 | template <typename T> |
| 664 | constexpr unsigned ctzConstexpr(T value) |
| 665 | { |
| 666 | constexpr unsigned bitSize = sizeof(T) * CHAR_BIT; |
| 667 | |
| 668 | using UT = typename std::make_unsigned<T>::type; |
| 669 | UT uValue = value; |
| 670 | |
| 671 | unsigned zeroCount = 0; |
| 672 | for (unsigned i = 0; i < bitSize; i++) { |
| 673 | if (uValue & 1) |
| 674 | break; |
| 675 | |
| 676 | zeroCount++; |
| 677 | uValue >>= 1; |
| 678 | } |
| 679 | return zeroCount; |
| 680 | } |
| 681 | |
| 682 | template<typename T> |
| 683 | inline unsigned ctz(T value) |
| 684 | { |
| 685 | constexpr unsigned bitSize = sizeof(T) * CHAR_BIT; |
| 686 | |
| 687 | using UT = typename std::make_unsigned<T>::type; |
| 688 | UT uValue = value; |
| 689 | |
| 690 | #if COMPILER(GCC_COMPATIBLE) |
| 691 | if (uValue) |
| 692 | return __builtin_ctzll(uValue); |
| 693 | return bitSize; |
| 694 | #elif COMPILER(MSVC) && !CPU(X86) |
| 695 | unsigned long ret = 0; |
| 696 | if (_BitScanForward64(&ret, uValue)) |
| 697 | return ret; |
| 698 | return bitSize; |
| 699 | #else |
| 700 | UNUSED_PARAM(bitSize); |
| 701 | UNUSED_PARAM(uValue); |
| 702 | return ctzConstexpr(value); |
| 703 | #endif |
| 704 | } |
| 705 | |
| 706 | template<typename T> |
| 707 | inline unsigned getLSBSet(T t) |
| 708 | { |
| 709 | ASSERT(t); |
| 710 | return ctz(t); |
| 711 | } |
| 712 | |
| 713 | template<typename T> |
| 714 | constexpr unsigned getLSBSetConstexpr(T t) |
| 715 | { |
| 716 | ASSERT_UNDER_CONSTEXPR_CONTEXT(t); |
| 717 | return ctzConstexpr(t); |
| 718 | } |
| 719 | |
| 720 | template<typename T> |
| 721 | inline unsigned getMSBSet(T t) |
| 722 | { |
| 723 | constexpr unsigned bitSize = sizeof(T) * CHAR_BIT; |
| 724 | ASSERT(t); |
| 725 | return bitSize - 1 - clz(t); |
| 726 | } |
| 727 | |
| 728 | template<typename T> |
| 729 | constexpr unsigned getMSBSetConstexpr(T t) |
| 730 | { |
| 731 | constexpr unsigned bitSize = sizeof(T) * CHAR_BIT; |
| 732 | ASSERT_UNDER_CONSTEXPR_CONTEXT(t); |
| 733 | return bitSize - 1 - clzConstexpr(t); |
| 734 | } |
| 735 | |
| 736 | } // namespace WTF |
| 737 | |
| 738 | using WTF::opaque; |
| 739 | using WTF::preciseIndexMaskPtr; |
| 740 | using WTF::preciseIndexMaskShift; |
| 741 | using WTF::preciseIndexMaskShiftForSize; |
| 742 | using WTF::shuffleVector; |
| 743 | using WTF::clz; |
| 744 | using WTF::ctz; |
| 745 | using WTF::getLSBSet; |
| 746 | using WTF::getMSBSet; |
| 747 | |