mfbt/MathAlgorithms.h

   1 /* -*- Mode: C++; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 2 -*- */
   2 /* vim: set ts=8 sts=2 et sw=2 tw=80: */
   3 /* This Source Code Form is subject to the terms of the Mozilla Public
   4  * License, v. 2.0. If a copy of the MPL was not distributed with this
   5  * file, You can obtain one at http://mozilla.org/MPL/2.0/. */
   6
   7 /* mfbt maths algorithms. */
   8
   9 #ifndef mozilla_MathAlgorithms_h
  10 #define mozilla_MathAlgorithms_h
  11
  12 #include "mozilla/Assertions.h"
  13 #include "mozilla/TypeTraits.h"
  14
  15 #include <cmath>
  16 #include <limits.h>
  17 #include <stdint.h>
  18
  19 namespace mozilla {
  20
  21 // Greatest Common Divisor
  22 template<typename IntegerType>
  23 MOZ_ALWAYS_INLINE IntegerType
  24 EuclidGCD(IntegerType a, IntegerType b)
  25 {
  26   // Euclid's algorithm; O(N) in the worst case.  (There are better
  27   // ways, but we don't need them for the current use of this algo.)
  28   MOZ_ASSERT(a > 0);
  29   MOZ_ASSERT(b > 0);
  30
  31   while (a != b) {
  32     if (a > b) {
  33       a = a - b;
  34     } else {
  35       b = b - a;
  36     }
  37   }
  38
  39   return a;
  40 }
  41
  42 // Least Common Multiple
  43 template<typename IntegerType>
  44 MOZ_ALWAYS_INLINE IntegerType
  45 EuclidLCM(IntegerType a, IntegerType b)
  46 {
  47   // Divide first to reduce overflow risk.
  48   return (a / EuclidGCD(a, b)) * b;
  49 }
  50
  51 namespace detail {
  52
  53 template<typename T>
  54 struct AllowDeprecatedAbsFixed : FalseType {};
  55
  56 template<> struct AllowDeprecatedAbsFixed<int32_t> : TrueType {};
  57 template<> struct AllowDeprecatedAbsFixed<int64_t> : TrueType {};
  58
  59 template<typename T>
  60 struct AllowDeprecatedAbs : AllowDeprecatedAbsFixed<T> {};
  61
  62 template<> struct AllowDeprecatedAbs<int> : TrueType {};
  63 template<> struct AllowDeprecatedAbs<long> : TrueType {};
  64
  65 } // namespace detail
  66
  67 // DO NOT USE DeprecatedAbs.  It exists only until its callers can be converted
  68 // to Abs below, and it will be removed when all callers have been changed.
  69 template<typename T>
  70 inline typename mozilla::EnableIf<detail::AllowDeprecatedAbs<T>::value, T>::Type
  71 DeprecatedAbs(const T t)
  72 {
  73   // The absolute value of the smallest possible value of a signed-integer type
  74   // won't fit in that type (on twos-complement systems -- and we're blithely
  75   // assuming we're on such systems, for the non-<stdint.h> types listed above),
  76   // so assert that the input isn't that value.
  77   //
  78   // This is the case if: the value is non-negative; or if adding one (giving a
  79   // value in the range [-maxvalue, 0]), then negating (giving a value in the
  80   // range [0, maxvalue]), doesn't produce maxvalue (because in twos-complement,
  81   // (minvalue + 1) == -maxvalue).
  82   MOZ_ASSERT(t >= 0 ||
  83              -(t + 1) != T((1ULL << (CHAR_BIT * sizeof(T) - 1)) - 1),
  84              "You can't negate the smallest possible negative integer!");
  85   return t >= 0 ? t : -t;
  86 }
  87
  88 namespace detail {
  89
  90 // For now mozilla::Abs only takes intN_T, the signed natural types, and
  91 // float/double/long double.  Feel free to add overloads for other standard,
  92 // signed types if you need them.
  93
  94 template<typename T>
  95 struct AbsReturnTypeFixed;
  96
  97 template<> struct AbsReturnTypeFixed<int8_t> { typedef uint8_t Type; };
  98 template<> struct AbsReturnTypeFixed<int16_t> { typedef uint16_t Type; };
  99 template<> struct AbsReturnTypeFixed<int32_t> { typedef uint32_t Type; };
 100 template<> struct AbsReturnTypeFixed<int64_t> { typedef uint64_t Type; };
 101
 102 template<typename T>
 103 struct AbsReturnType : AbsReturnTypeFixed<T> {};
 104
 105 template<> struct AbsReturnType<char> : EnableIf<char(-1) < char(0), unsigned char> {};
 106 template<> struct AbsReturnType<signed char> { typedef unsigned char Type; };
 107 template<> struct AbsReturnType<short> { typedef unsigned short Type; };
 108 template<> struct AbsReturnType<int> { typedef unsigned int Type; };
 109 template<> struct AbsReturnType<long> { typedef unsigned long Type; };
 110 template<> struct AbsReturnType<long long> { typedef unsigned long long Type; };
 111 template<> struct AbsReturnType<float> { typedef float Type; };
 112 template<> struct AbsReturnType<double> { typedef double Type; };
 113 template<> struct AbsReturnType<long double> { typedef long double Type; };
 114
 115 } // namespace detail
 116
 117 template<typename T>
 118 inline typename detail::AbsReturnType<T>::Type
 119 Abs(const T t)
 120 {
 121   typedef typename detail::AbsReturnType<T>::Type ReturnType;
 122   return t >= 0 ? ReturnType(t) : ~ReturnType(t) + 1;
 123 }
 124
 125 template<>
 126 inline float
 127 Abs<float>(const float f)
 128 {
 129   return std::fabs(f);
 130 }
 131
 132 template<>
 133 inline double
 134 Abs<double>(const double d)
 135 {
 136   return std::fabs(d);
 137 }
 138
 139 template<>
 140 inline long double
 141 Abs<long double>(const long double d)
 142 {
 143   return std::fabs(d);
 144 }
 145
 146 } // namespace mozilla
 147
 148 #if defined(_WIN32) && (_MSC_VER >= 1300) && (defined(_M_IX86) || defined(_M_AMD64) || defined(_M_X64))
 149 #  define MOZ_BITSCAN_WINDOWS
 150
 151   extern "C" {
 152     unsigned char _BitScanForward(unsigned long* Index, unsigned long mask);
 153     unsigned char _BitScanReverse(unsigned long* Index, unsigned long mask);
 154 #  pragma intrinsic(_BitScanForward, _BitScanReverse)
 155
 156 #  if defined(_M_AMD64) || defined(_M_X64)
 157 #    define MOZ_BITSCAN_WINDOWS64
 158     unsigned char _BitScanForward64(unsigned long* index, unsigned __int64 mask);
 159     unsigned char _BitScanReverse64(unsigned long* index, unsigned __int64 mask);
 160 #   pragma intrinsic(_BitScanForward64, _BitScanReverse64)
 161 #  endif
 162   } // extern "C"
 163
 164 #endif
 165
 166 namespace mozilla {
 167
 168 namespace detail {
 169
 170 #if defined(MOZ_BITSCAN_WINDOWS)
 171
 172   inline uint_fast8_t
 173   CountLeadingZeroes32(uint32_t u)
 174   {
 175     unsigned long index;
 176     _BitScanReverse(&index, static_cast<unsigned long>(u));
 177     return uint_fast8_t(31 - index);
 178   }
 179
 180
 181   inline uint_fast8_t
 182   CountTrailingZeroes32(uint32_t u)
 183   {
 184     unsigned long index;
 185     _BitScanForward(&index, static_cast<unsigned long>(u));
 186     return uint_fast8_t(index);
 187   }
 188
 189   inline uint_fast8_t
 190   CountPopulation32(uint32_t u)
 191   {
 192      uint32_t sum2  = (u     & 0x55555555) + ((u     & 0xaaaaaaaa) >> 1);
 193      uint32_t sum4  = (sum2  & 0x33333333) + ((sum2  & 0xcccccccc) >> 2);
 194      uint32_t sum8  = (sum4  & 0x0f0f0f0f) + ((sum4  & 0xf0f0f0f0) >> 4);
 195      uint32_t sum16 = (sum8  & 0x00ff00ff) + ((sum8  & 0xff00ff00) >> 8);
 196      return sum16;
 197   }
 198
 199   inline uint_fast8_t
 200   CountLeadingZeroes64(uint64_t u)
 201   {
 202 #  if defined(MOZ_BITSCAN_WINDOWS64)
 203     unsigned long index;
 204     _BitScanReverse64(&index, static_cast<unsigned __int64>(u));
 205     return uint_fast8_t(63 - index);
 206 #  else
 207     uint32_t hi = uint32_t(u >> 32);
 208     if (hi != 0)
 209       return CountLeadingZeroes32(hi);
 210     return 32 + CountLeadingZeroes32(uint32_t(u));
 211 #  endif
 212   }
 213
 214   inline uint_fast8_t
 215   CountTrailingZeroes64(uint64_t u)
 216   {
 217 #  if defined(MOZ_BITSCAN_WINDOWS64)
 218     unsigned long index;
 219     _BitScanForward64(&index, static_cast<unsigned __int64>(u));
 220     return uint_fast8_t(index);
 221 #  else
 222     uint32_t lo = uint32_t(u);
 223     if (lo != 0)
 224       return CountTrailingZeroes32(lo);
 225     return 32 + CountTrailingZeroes32(uint32_t(u >> 32));
 226 #  endif
 227   }
 228
 229 #  ifdef MOZ_HAVE_BITSCAN64
 230 #    undef MOZ_HAVE_BITSCAN64
 231 #  endif
 232
 233 #elif defined(__clang__) || defined(__GNUC__)
 234
 235 #  if defined(__clang__)
 236 #    if !__has_builtin(__builtin_ctz) || !__has_builtin(__builtin_clz)
 237 #      error "A clang providing __builtin_c[lt]z is required to build"
 238 #    endif
 239 #  else
 240      // gcc has had __builtin_clz and friends since 3.4: no need to check.
 241 #  endif
 242
 243   inline uint_fast8_t
 244   CountLeadingZeroes32(uint32_t u)
 245   {
 246     return __builtin_clz(u);
 247   }
 248
 249   inline uint_fast8_t
 250   CountTrailingZeroes32(uint32_t u)
 251   {
 252     return __builtin_ctz(u);
 253   }
 254
 255   inline uint_fast8_t
 256   CountPopulation32(uint32_t u)
 257   {
 258     return __builtin_popcount(u);
 259   }
 260
 261   inline uint_fast8_t
 262   CountLeadingZeroes64(uint64_t u)
 263   {
 264     return __builtin_clzll(u);
 265   }
 266
 267   inline uint_fast8_t
 268   CountTrailingZeroes64(uint64_t u)
 269   {
 270     return __builtin_ctzll(u);
 271   }
 272
 273 #else
 274 #  error "Implement these!"
 275   inline uint_fast8_t CountLeadingZeroes32(uint32_t u) MOZ_DELETE;
 276   inline uint_fast8_t CountTrailingZeroes32(uint32_t u) MOZ_DELETE;
 277   inline uint_fast8_t CountPopulation32(uint32_t u) MOZ_DELETE;
 278   inline uint_fast8_t CountLeadingZeroes64(uint64_t u) MOZ_DELETE;
 279   inline uint_fast8_t CountTrailingZeroes64(uint64_t u) MOZ_DELETE;
 280 #endif
 281
 282 } // namespace detail
 283
 284 /**
 285  * Compute the number of high-order zero bits in the NON-ZERO number |u|.  That
 286  * is, looking at the bitwise representation of the number, with the highest-
 287  * valued bits at the start, return the number of zeroes before the first one
 288  * is observed.
 289  *
 290  * CountLeadingZeroes32(0xF0FF1000) is 0;
 291  * CountLeadingZeroes32(0x7F8F0001) is 1;
 292  * CountLeadingZeroes32(0x3FFF0100) is 2;
 293  * CountLeadingZeroes32(0x1FF50010) is 3; and so on.
 294  */
 295 inline uint_fast8_t
 296 CountLeadingZeroes32(uint32_t u)
 297 {
 298   MOZ_ASSERT(u != 0);
 299   return detail::CountLeadingZeroes32(u);
 300 }
 301
 302 /**
 303  * Compute the number of low-order zero bits in the NON-ZERO number |u|.  That
 304  * is, looking at the bitwise representation of the number, with the lowest-
 305  * valued bits at the start, return the number of zeroes before the first one
 306  * is observed.
 307  *
 308  * CountTrailingZeroes32(0x0100FFFF) is 0;
 309  * CountTrailingZeroes32(0x7000FFFE) is 1;
 310  * CountTrailingZeroes32(0x0080FFFC) is 2;
 311  * CountTrailingZeroes32(0x0080FFF8) is 3; and so on.
 312  */
 313 inline uint_fast8_t
 314 CountTrailingZeroes32(uint32_t u)
 315 {
 316   MOZ_ASSERT(u != 0);
 317   return detail::CountTrailingZeroes32(u);
 318 }
 319
 320 /**
 321  * Compute the number of one bits in the number |u|,
 322  */
 323 inline uint_fast8_t
 324 CountPopulation32(uint32_t u)
 325 {
 326   return detail::CountPopulation32(u);
 327 }
 328
 329 /** Analogous to CountLeadingZeroes32, but for 64-bit numbers. */
 330 inline uint_fast8_t
 331 CountLeadingZeroes64(uint64_t u)
 332 {
 333   MOZ_ASSERT(u != 0);
 334   return detail::CountLeadingZeroes64(u);
 335 }
 336
 337 /** Analogous to CountTrailingZeroes32, but for 64-bit numbers. */
 338 inline uint_fast8_t
 339 CountTrailingZeroes64(uint64_t u)
 340 {
 341   MOZ_ASSERT(u != 0);
 342   return detail::CountTrailingZeroes64(u);
 343 }
 344
 345 namespace detail {
 346
 347 template<typename T, size_t Size = sizeof(T)>
 348 class CeilingLog2;
 349
 350 template<typename T>
 351 class CeilingLog2<T, 4>
 352 {
 353   public:
 354     static uint_fast8_t compute(const T t) {
 355       // Check for <= 1 to avoid the == 0 undefined case.
 356       return t <= 1 ? 0 : 32 - CountLeadingZeroes32(t - 1);
 357     }
 358 };
 359
 360 template<typename T>
 361 class CeilingLog2<T, 8>
 362 {
 363   public:
 364     static uint_fast8_t compute(const T t) {
 365       // Check for <= 1 to avoid the == 0 undefined case.
 366       return t <= 1 ? 0 : 64 - CountLeadingZeroes64(t - 1);
 367     }
 368 };
 369
 370 } // namespace detail
 371
 372 /**
 373  * Compute the log of the least power of 2 greater than or equal to |t|.
 374  *
 375  * CeilingLog2(0..1) is 0;
 376  * CeilingLog2(2) is 1;
 377  * CeilingLog2(3..4) is 2;
 378  * CeilingLog2(5..8) is 3;
 379  * CeilingLog2(9..16) is 4; and so on.
 380  */
 381 template<typename T>
 382 inline uint_fast8_t
 383 CeilingLog2(const T t)
 384 {
 385   return detail::CeilingLog2<T>::compute(t);
 386 }
 387
 388 /** A CeilingLog2 variant that accepts only size_t. */
 389 inline uint_fast8_t
 390 CeilingLog2Size(size_t n)
 391 {
 392   return CeilingLog2(n);
 393 }
 394
 395 namespace detail {
 396
 397 template<typename T, size_t Size = sizeof(T)>
 398 class FloorLog2;
 399
 400 template<typename T>
 401 class FloorLog2<T, 4>
 402 {
 403   public:
 404     static uint_fast8_t compute(const T t) {
 405       return 31 - CountLeadingZeroes32(t | 1);
 406     }
 407 };
 408
 409 template<typename T>
 410 class FloorLog2<T, 8>
 411 {
 412   public:
 413     static uint_fast8_t compute(const T t) {
 414       return 63 - CountLeadingZeroes64(t | 1);
 415     }
 416 };
 417
 418 } // namespace detail
 419
 420 /**
 421  * Compute the log of the greatest power of 2 less than or equal to |t|.
 422  *
 423  * FloorLog2(0..1) is 0;
 424  * FloorLog2(2..3) is 1;
 425  * FloorLog2(4..7) is 2;
 426  * FloorLog2(8..15) is 3; and so on.
 427  */
 428 template<typename T>
 429 inline uint_fast8_t
 430 FloorLog2(const T t)
 431 {
 432   return detail::FloorLog2<T>::compute(t);
 433 }
 434
 435 /** A FloorLog2 variant that accepts only size_t. */
 436 inline uint_fast8_t
 437 FloorLog2Size(size_t n)
 438 {
 439   return FloorLog2(n);
 440 }
 441
 442 /*
 443  * Compute the smallest power of 2 greater than or equal to |x|.  |x| must not
 444  * be so great that the computed value would overflow |size_t|.
 445  */
 446 inline size_t
 447 RoundUpPow2(size_t x)
 448 {
 449   MOZ_ASSERT(x <= (size_t(1) << (sizeof(size_t) * CHAR_BIT - 1)),
 450              "can't round up -- will overflow!");
 451   return size_t(1) << CeilingLog2(x);
 452 }
 453
 454 } /* namespace mozilla */
 455
 456 #endif /* mozilla_MathAlgorithms_h */