include/llvm/Support/MathExtras.h

   1 //===-- llvm/Support/MathExtras.h - Useful math functions -------*- C++ -*-===//
   2 //
   3 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
   4 // See https://llvm.org/LICENSE.txt for license information.
   5 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
   6 //
   7 //===----------------------------------------------------------------------===//
   8 //
   9 // This file contains some functions that are useful for math stuff.
  10 //
  11 //===----------------------------------------------------------------------===//
  12
  13 #ifndef LLVM_SUPPORT_MATHEXTRAS_H
  14 #define LLVM_SUPPORT_MATHEXTRAS_H
  15
  16 #include "llvm/Support/Compiler.h"
  17 #include "llvm/Support/SwapByteOrder.h"
  18 #include <algorithm>
  19 #include <cassert>
  20 #include <climits>
  21 #include <cstring>
  22 #include <limits>
  23 #include <type_traits>
  24
  25 #ifdef __ANDROID_NDK__
  26 #include <android/api-level.h>
  27 #endif
  28
  29 #ifdef _MSC_VER
  30 // Declare these intrinsics manually rather including intrin.h. It's very
  31 // expensive, and MathExtras.h is popular.
  32 // #include <intrin.h>
  33 extern "C" {
  34 unsigned char _BitScanForward(unsigned long *_Index, unsigned long _Mask);
  35 unsigned char _BitScanForward64(unsigned long *_Index, unsigned __int64 _Mask);
  36 unsigned char _BitScanReverse(unsigned long *_Index, unsigned long _Mask);
  37 unsigned char _BitScanReverse64(unsigned long *_Index, unsigned __int64 _Mask);
  38 }
  39 #endif
  40
  41 namespace llvm {
  42 /// The behavior an operation has on an input of 0.
  43 enum ZeroBehavior {
  44   /// The returned value is undefined.
  45   ZB_Undefined,
  46   /// The returned value is numeric_limits<T>::max()
  47   ZB_Max,
  48   /// The returned value is numeric_limits<T>::digits
  49   ZB_Width
  50 };
  51
  52 namespace detail {
  53 template <typename T, std::size_t SizeOfT> struct TrailingZerosCounter {
  54   static std::size_t count(T Val, ZeroBehavior) {
  55     if (!Val)
  56       return std::numeric_limits<T>::digits;
  57     if (Val & 0x1)
  58       return 0;
  59
  60     // Bisection method.
  61     std::size_t ZeroBits = 0;
  62     T Shift = std::numeric_limits<T>::digits >> 1;
  63     T Mask = std::numeric_limits<T>::max() >> Shift;
  64     while (Shift) {
  65       if ((Val & Mask) == 0) {
  66         Val >>= Shift;
  67         ZeroBits |= Shift;
  68       }
  69       Shift >>= 1;
  70       Mask >>= Shift;
  71     }
  72     return ZeroBits;
  73   }
  74 };
  75
  76 #if __GNUC__ >= 4 || defined(_MSC_VER)
  77 template <typename T> struct TrailingZerosCounter<T, 4> {
  78   static std::size_t count(T Val, ZeroBehavior ZB) {
  79     if (ZB != ZB_Undefined && Val == 0)
  80       return 32;
  81
  82 #if __has_builtin(__builtin_ctz) || LLVM_GNUC_PREREQ(4, 0, 0)
  83     return __builtin_ctz(Val);
  84 #elif defined(_MSC_VER)
  85     unsigned long Index;
  86     _BitScanForward(&Index, Val);
  87     return Index;
  88 #endif
  89   }
  90 };
  91
  92 #if !defined(_MSC_VER) || defined(_M_X64)
  93 template <typename T> struct TrailingZerosCounter<T, 8> {
  94   static std::size_t count(T Val, ZeroBehavior ZB) {
  95     if (ZB != ZB_Undefined && Val == 0)
  96       return 64;
  97
  98 #if __has_builtin(__builtin_ctzll) || LLVM_GNUC_PREREQ(4, 0, 0)
  99     return __builtin_ctzll(Val);
 100 #elif defined(_MSC_VER)
 101     unsigned long Index;
 102     _BitScanForward64(&Index, Val);
 103     return Index;
 104 #endif
 105   }
 106 };
 107 #endif
 108 #endif
 109 } // namespace detail
 110
 111 /// Count number of 0's from the least significant bit to the most
 112 ///   stopping at the first 1.
 113 ///
 114 /// Only unsigned integral types are allowed.
 115 ///
 116 /// \param ZB the behavior on an input of 0. Only ZB_Width and ZB_Undefined are
 117 ///   valid arguments.
 118 template <typename T>
 119 std::size_t countTrailingZeros(T Val, ZeroBehavior ZB = ZB_Width) {
 120   static_assert(std::numeric_limits<T>::is_integer &&
 121                     !std::numeric_limits<T>::is_signed,
 122                 "Only unsigned integral types are allowed.");
 123   return llvm::detail::TrailingZerosCounter<T, sizeof(T)>::count(Val, ZB);
 124 }
 125
 126 namespace detail {
 127 template <typename T, std::size_t SizeOfT> struct LeadingZerosCounter {
 128   static std::size_t count(T Val, ZeroBehavior) {
 129     if (!Val)
 130       return std::numeric_limits<T>::digits;
 131
 132     // Bisection method.
 133     std::size_t ZeroBits = 0;
 134     for (T Shift = std::numeric_limits<T>::digits >> 1; Shift; Shift >>= 1) {
 135       T Tmp = Val >> Shift;
 136       if (Tmp)
 137         Val = Tmp;
 138       else
 139         ZeroBits |= Shift;
 140     }
 141     return ZeroBits;
 142   }
 143 };
 144
 145 #if __GNUC__ >= 4 || defined(_MSC_VER)
 146 template <typename T> struct LeadingZerosCounter<T, 4> {
 147   static std::size_t count(T Val, ZeroBehavior ZB) {
 148     if (ZB != ZB_Undefined && Val == 0)
 149       return 32;
 150
 151 #if __has_builtin(__builtin_clz) || LLVM_GNUC_PREREQ(4, 0, 0)
 152     return __builtin_clz(Val);
 153 #elif defined(_MSC_VER)
 154     unsigned long Index;
 155     _BitScanReverse(&Index, Val);
 156     return Index ^ 31;
 157 #endif
 158   }
 159 };
 160
 161 #if !defined(_MSC_VER) || defined(_M_X64)
 162 template <typename T> struct LeadingZerosCounter<T, 8> {
 163   static std::size_t count(T Val, ZeroBehavior ZB) {
 164     if (ZB != ZB_Undefined && Val == 0)
 165       return 64;
 166
 167 #if __has_builtin(__builtin_clzll) || LLVM_GNUC_PREREQ(4, 0, 0)
 168     return __builtin_clzll(Val);
 169 #elif defined(_MSC_VER)
 170     unsigned long Index;
 171     _BitScanReverse64(&Index, Val);
 172     return Index ^ 63;
 173 #endif
 174   }
 175 };
 176 #endif
 177 #endif
 178 } // namespace detail
 179
 180 /// Count number of 0's from the most significant bit to the least
 181 ///   stopping at the first 1.
 182 ///
 183 /// Only unsigned integral types are allowed.
 184 ///
 185 /// \param ZB the behavior on an input of 0. Only ZB_Width and ZB_Undefined are
 186 ///   valid arguments.
 187 template <typename T>
 188 std::size_t countLeadingZeros(T Val, ZeroBehavior ZB = ZB_Width) {
 189   static_assert(std::numeric_limits<T>::is_integer &&
 190                     !std::numeric_limits<T>::is_signed,
 191                 "Only unsigned integral types are allowed.");
 192   return llvm::detail::LeadingZerosCounter<T, sizeof(T)>::count(Val, ZB);
 193 }
 194
 195 /// Get the index of the first set bit starting from the least
 196 ///   significant bit.
 197 ///
 198 /// Only unsigned integral types are allowed.
 199 ///
 200 /// \param ZB the behavior on an input of 0. Only ZB_Max and ZB_Undefined are
 201 ///   valid arguments.
 202 template <typename T> T findFirstSet(T Val, ZeroBehavior ZB = ZB_Max) {
 203   if (ZB == ZB_Max && Val == 0)
 204     return std::numeric_limits<T>::max();
 205
 206   return countTrailingZeros(Val, ZB_Undefined);
 207 }
 208
 209 /// Create a bitmask with the N right-most bits set to 1, and all other
 210 /// bits set to 0.  Only unsigned types are allowed.
 211 template <typename T> T maskTrailingOnes(unsigned N) {
 212   static_assert(std::is_unsigned<T>::value, "Invalid type!");
 213   const unsigned Bits = CHAR_BIT * sizeof(T);
 214   assert(N <= Bits && "Invalid bit index");
 215   return N == 0 ? 0 : (T(-1) >> (Bits - N));
 216 }
 217
 218 /// Create a bitmask with the N left-most bits set to 1, and all other
 219 /// bits set to 0.  Only unsigned types are allowed.
 220 template <typename T> T maskLeadingOnes(unsigned N) {
 221   return ~maskTrailingOnes<T>(CHAR_BIT * sizeof(T) - N);
 222 }
 223
 224 /// Create a bitmask with the N right-most bits set to 0, and all other
 225 /// bits set to 1.  Only unsigned types are allowed.
 226 template <typename T> T maskTrailingZeros(unsigned N) {
 227   return maskLeadingOnes<T>(CHAR_BIT * sizeof(T) - N);
 228 }
 229
 230 /// Create a bitmask with the N left-most bits set to 0, and all other
 231 /// bits set to 1.  Only unsigned types are allowed.
 232 template <typename T> T maskLeadingZeros(unsigned N) {
 233   return maskTrailingOnes<T>(CHAR_BIT * sizeof(T) - N);
 234 }
 235
 236 /// Get the index of the last set bit starting from the least
 237 ///   significant bit.
 238 ///
 239 /// Only unsigned integral types are allowed.
 240 ///
 241 /// \param ZB the behavior on an input of 0. Only ZB_Max and ZB_Undefined are
 242 ///   valid arguments.
 243 template <typename T> T findLastSet(T Val, ZeroBehavior ZB = ZB_Max) {
 244   if (ZB == ZB_Max && Val == 0)
 245     return std::numeric_limits<T>::max();
 246
 247   // Use ^ instead of - because both gcc and llvm can remove the associated ^
 248   // in the __builtin_clz intrinsic on x86.
 249   return countLeadingZeros(Val, ZB_Undefined) ^
 250          (std::numeric_limits<T>::digits - 1);
 251 }
 252
 253 /// Macro compressed bit reversal table for 256 bits.
 254 ///
 255 /// http://graphics.stanford.edu/~seander/bithacks.html#BitReverseTable
 256 static const unsigned char BitReverseTable256[256] = {
 257 #define R2(n) n, n + 2 * 64, n + 1 * 64, n + 3 * 64
 258 #define R4(n) R2(n), R2(n + 2 * 16), R2(n + 1 * 16), R2(n + 3 * 16)
 259 #define R6(n) R4(n), R4(n + 2 * 4), R4(n + 1 * 4), R4(n + 3 * 4)
 260   R6(0), R6(2), R6(1), R6(3)
 261 #undef R2
 262 #undef R4
 263 #undef R6
 264 };
 265
 266 /// Reverse the bits in \p Val.
 267 template <typename T>
 268 T reverseBits(T Val) {
 269   unsigned char in[sizeof(Val)];
 270   unsigned char out[sizeof(Val)];
 271   std::memcpy(in, &Val, sizeof(Val));
 272   for (unsigned i = 0; i < sizeof(Val); ++i)
 273     out[(sizeof(Val) - i) - 1] = BitReverseTable256[in[i]];
 274   std::memcpy(&Val, out, sizeof(Val));
 275   return Val;
 276 }
 277
 278 // NOTE: The following support functions use the _32/_64 extensions instead of
 279 // type overloading so that signed and unsigned integers can be used without
 280 // ambiguity.
 281
 282 /// Return the high 32 bits of a 64 bit value.
 283 constexpr inline uint32_t Hi_32(uint64_t Value) {
 284   return static_cast<uint32_t>(Value >> 32);
 285 }
 286
 287 /// Return the low 32 bits of a 64 bit value.
 288 constexpr inline uint32_t Lo_32(uint64_t Value) {
 289   return static_cast<uint32_t>(Value);
 290 }
 291
 292 /// Make a 64-bit integer from a high / low pair of 32-bit integers.
 293 constexpr inline uint64_t Make_64(uint32_t High, uint32_t Low) {
 294   return ((uint64_t)High << 32) | (uint64_t)Low;
 295 }
 296
 297 /// Checks if an integer fits into the given bit width.
 298 template <unsigned N> constexpr inline bool isInt(int64_t x) {
 299   return N >= 64 || (-(INT64_C(1)<<(N-1)) <= x && x < (INT64_C(1)<<(N-1)));
 300 }
 301 // Template specializations to get better code for common cases.
 302 template <> constexpr inline bool isInt<8>(int64_t x) {
 303   return static_cast<int8_t>(x) == x;
 304 }
 305 template <> constexpr inline bool isInt<16>(int64_t x) {
 306   return static_cast<int16_t>(x) == x;
 307 }
 308 template <> constexpr inline bool isInt<32>(int64_t x) {
 309   return static_cast<int32_t>(x) == x;
 310 }
 311
 312 /// Checks if a signed integer is an N bit number shifted left by S.
 313 template <unsigned N, unsigned S>
 314 constexpr inline bool isShiftedInt(int64_t x) {
 315   static_assert(
 316       N > 0, "isShiftedInt<0> doesn't make sense (refers to a 0-bit number.");
 317   static_assert(N + S <= 64, "isShiftedInt<N, S> with N + S > 64 is too wide.");
 318   return isInt<N + S>(x) && (x % (UINT64_C(1) << S) == 0);
 319 }
 320
 321 /// Checks if an unsigned integer fits into the given bit width.
 322 ///
 323 /// This is written as two functions rather than as simply
 324 ///
 325 ///   return N >= 64 || X < (UINT64_C(1) << N);
 326 ///
 327 /// to keep MSVC from (incorrectly) warning on isUInt<64> that we're shifting
 328 /// left too many places.
 329 template <unsigned N>
 330 constexpr inline typename std::enable_if<(N < 64), bool>::type
 331 isUInt(uint64_t X) {
 332   static_assert(N > 0, "isUInt<0> doesn't make sense");
 333   return X < (UINT64_C(1) << (N));
 334 }
 335 template <unsigned N>
 336 constexpr inline typename std::enable_if<N >= 64, bool>::type
 337 isUInt(uint64_t X) {
 338   return true;
 339 }
 340
 341 // Template specializations to get better code for common cases.
 342 template <> constexpr inline bool isUInt<8>(uint64_t x) {
 343   return static_cast<uint8_t>(x) == x;
 344 }
 345 template <> constexpr inline bool isUInt<16>(uint64_t x) {
 346   return static_cast<uint16_t>(x) == x;
 347 }
 348 template <> constexpr inline bool isUInt<32>(uint64_t x) {
 349   return static_cast<uint32_t>(x) == x;
 350 }
 351
 352 /// Checks if a unsigned integer is an N bit number shifted left by S.
 353 template <unsigned N, unsigned S>
 354 constexpr inline bool isShiftedUInt(uint64_t x) {
 355   static_assert(
 356       N > 0, "isShiftedUInt<0> doesn't make sense (refers to a 0-bit number)");
 357   static_assert(N + S <= 64,
 358                 "isShiftedUInt<N, S> with N + S > 64 is too wide.");
 359   // Per the two static_asserts above, S must be strictly less than 64.  So
 360   // 1 << S is not undefined behavior.
 361   return isUInt<N + S>(x) && (x % (UINT64_C(1) << S) == 0);
 362 }
 363
 364 /// Gets the maximum value for a N-bit unsigned integer.
 365 inline uint64_t maxUIntN(uint64_t N) {
 366   assert(N > 0 && N <= 64 && "integer width out of range");
 367
 368   // uint64_t(1) << 64 is undefined behavior, so we can't do
 369   //   (uint64_t(1) << N) - 1
 370   // without checking first that N != 64.  But this works and doesn't have a
 371   // branch.
 372   return UINT64_MAX >> (64 - N);
 373 }
 374
 375 /// Gets the minimum value for a N-bit signed integer.
 376 inline int64_t minIntN(int64_t N) {
 377   assert(N > 0 && N <= 64 && "integer width out of range");
 378
 379   return -(UINT64_C(1)<<(N-1));
 380 }
 381
 382 /// Gets the maximum value for a N-bit signed integer.
 383 inline int64_t maxIntN(int64_t N) {
 384   assert(N > 0 && N <= 64 && "integer width out of range");
 385
 386   // This relies on two's complement wraparound when N == 64, so we convert to
 387   // int64_t only at the very end to avoid UB.
 388   return (UINT64_C(1) << (N - 1)) - 1;
 389 }
 390
 391 /// Checks if an unsigned integer fits into the given (dynamic) bit width.
 392 inline bool isUIntN(unsigned N, uint64_t x) {
 393   return N >= 64 || x <= maxUIntN(N);
 394 }
 395
 396 /// Checks if an signed integer fits into the given (dynamic) bit width.
 397 inline bool isIntN(unsigned N, int64_t x) {
 398   return N >= 64 || (minIntN(N) <= x && x <= maxIntN(N));
 399 }
 400
 401 /// Return true if the argument is a non-empty sequence of ones starting at the
 402 /// least significant bit with the remainder zero (32 bit version).
 403 /// Ex. isMask_32(0x0000FFFFU) == true.
 404 constexpr inline bool isMask_32(uint32_t Value) {
 405   return Value && ((Value + 1) & Value) == 0;
 406 }
 407
 408 /// Return true if the argument is a non-empty sequence of ones starting at the
 409 /// least significant bit with the remainder zero (64 bit version).
 410 constexpr inline bool isMask_64(uint64_t Value) {
 411   return Value && ((Value + 1) & Value) == 0;
 412 }
 413
 414 /// Return true if the argument contains a non-empty sequence of ones with the
 415 /// remainder zero (32 bit version.) Ex. isShiftedMask_32(0x0000FF00U) == true.
 416 constexpr inline bool isShiftedMask_32(uint32_t Value) {
 417   return Value && isMask_32((Value - 1) | Value);
 418 }
 419
 420 /// Return true if the argument contains a non-empty sequence of ones with the
 421 /// remainder zero (64 bit version.)
 422 constexpr inline bool isShiftedMask_64(uint64_t Value) {
 423   return Value && isMask_64((Value - 1) | Value);
 424 }
 425
 426 /// Return true if the argument is a power of two > 0.
 427 /// Ex. isPowerOf2_32(0x00100000U) == true (32 bit edition.)
 428 constexpr inline bool isPowerOf2_32(uint32_t Value) {
 429   return Value && !(Value & (Value - 1));
 430 }
 431
 432 /// Return true if the argument is a power of two > 0 (64 bit edition.)
 433 constexpr inline bool isPowerOf2_64(uint64_t Value) {
 434   return Value && !(Value & (Value - 1));
 435 }
 436
 437 /// Return a byte-swapped representation of the 16-bit argument.
 438 inline uint16_t ByteSwap_16(uint16_t Value) {
 439   return sys::SwapByteOrder_16(Value);
 440 }
 441
 442 /// Return a byte-swapped representation of the 32-bit argument.
 443 inline uint32_t ByteSwap_32(uint32_t Value) {
 444   return sys::SwapByteOrder_32(Value);
 445 }
 446
 447 /// Return a byte-swapped representation of the 64-bit argument.
 448 inline uint64_t ByteSwap_64(uint64_t Value) {
 449   return sys::SwapByteOrder_64(Value);
 450 }
 451
 452 /// Count the number of ones from the most significant bit to the first
 453 /// zero bit.
 454 ///
 455 /// Ex. countLeadingOnes(0xFF0FFF00) == 8.
 456 /// Only unsigned integral types are allowed.
 457 ///
 458 /// \param ZB the behavior on an input of all ones. Only ZB_Width and
 459 /// ZB_Undefined are valid arguments.
 460 template <typename T>
 461 std::size_t countLeadingOnes(T Value, ZeroBehavior ZB = ZB_Width) {
 462   static_assert(std::numeric_limits<T>::is_integer &&
 463                     !std::numeric_limits<T>::is_signed,
 464                 "Only unsigned integral types are allowed.");
 465   return countLeadingZeros<T>(~Value, ZB);
 466 }
 467
 468 /// Count the number of ones from the least significant bit to the first
 469 /// zero bit.
 470 ///
 471 /// Ex. countTrailingOnes(0x00FF00FF) == 8.
 472 /// Only unsigned integral types are allowed.
 473 ///
 474 /// \param ZB the behavior on an input of all ones. Only ZB_Width and
 475 /// ZB_Undefined are valid arguments.
 476 template <typename T>
 477 std::size_t countTrailingOnes(T Value, ZeroBehavior ZB = ZB_Width) {
 478   static_assert(std::numeric_limits<T>::is_integer &&
 479                     !std::numeric_limits<T>::is_signed,
 480                 "Only unsigned integral types are allowed.");
 481   return countTrailingZeros<T>(~Value, ZB);
 482 }
 483
 484 namespace detail {
 485 template <typename T, std::size_t SizeOfT> struct PopulationCounter {
 486   static unsigned count(T Value) {
 487     // Generic version, forward to 32 bits.
 488     static_assert(SizeOfT <= 4, "Not implemented!");
 489 #if __GNUC__ >= 4
 490     return __builtin_popcount(Value);
 491 #else
 492     uint32_t v = Value;
 493     v = v - ((v >> 1) & 0x55555555);
 494     v = (v & 0x33333333) + ((v >> 2) & 0x33333333);
 495     return ((v + (v >> 4) & 0xF0F0F0F) * 0x1010101) >> 24;
 496 #endif
 497   }
 498 };
 499
 500 template <typename T> struct PopulationCounter<T, 8> {
 501   static unsigned count(T Value) {
 502 #if __GNUC__ >= 4
 503     return __builtin_popcountll(Value);
 504 #else
 505     uint64_t v = Value;
 506     v = v - ((v >> 1) & 0x5555555555555555ULL);
 507     v = (v & 0x3333333333333333ULL) + ((v >> 2) & 0x3333333333333333ULL);
 508     v = (v + (v >> 4)) & 0x0F0F0F0F0F0F0F0FULL;
 509     return unsigned((uint64_t)(v * 0x0101010101010101ULL) >> 56);
 510 #endif
 511   }
 512 };
 513 } // namespace detail
 514
 515 /// Count the number of set bits in a value.
 516 /// Ex. countPopulation(0xF000F000) = 8
 517 /// Returns 0 if the word is zero.
 518 template <typename T>
 519 inline unsigned countPopulation(T Value) {
 520   static_assert(std::numeric_limits<T>::is_integer &&
 521                     !std::numeric_limits<T>::is_signed,
 522                 "Only unsigned integral types are allowed.");
 523   return detail::PopulationCounter<T, sizeof(T)>::count(Value);
 524 }
 525
 526 /// Return the log base 2 of the specified value.
 527 inline double Log2(double Value) {
 528 #if defined(__ANDROID_API__) && __ANDROID_API__ < 18
 529   return __builtin_log(Value) / __builtin_log(2.0);
 530 #else
 531   return log2(Value);
 532 #endif
 533 }
 534
 535 /// Return the floor log base 2 of the specified value, -1 if the value is zero.
 536 /// (32 bit edition.)
 537 /// Ex. Log2_32(32) == 5, Log2_32(1) == 0, Log2_32(0) == -1, Log2_32(6) == 2
 538 inline unsigned Log2_32(uint32_t Value) {
 539   return 31 - countLeadingZeros(Value);
 540 }
 541
 542 /// Return the floor log base 2 of the specified value, -1 if the value is zero.
 543 /// (64 bit edition.)
 544 inline unsigned Log2_64(uint64_t Value) {
 545   return 63 - countLeadingZeros(Value);
 546 }
 547
 548 /// Return the ceil log base 2 of the specified value, 32 if the value is zero.
 549 /// (32 bit edition).
 550 /// Ex. Log2_32_Ceil(32) == 5, Log2_32_Ceil(1) == 0, Log2_32_Ceil(6) == 3
 551 inline unsigned Log2_32_Ceil(uint32_t Value) {
 552   return 32 - countLeadingZeros(Value - 1);
 553 }
 554
 555 /// Return the ceil log base 2 of the specified value, 64 if the value is zero.
 556 /// (64 bit edition.)
 557 inline unsigned Log2_64_Ceil(uint64_t Value) {
 558   return 64 - countLeadingZeros(Value - 1);
 559 }
 560
 561 /// Return the greatest common divisor of the values using Euclid's algorithm.
 562 inline uint64_t GreatestCommonDivisor64(uint64_t A, uint64_t B) {
 563   while (B) {
 564     uint64_t T = B;
 565     B = A % B;
 566     A = T;
 567   }
 568   return A;
 569 }
 570
 571 /// This function takes a 64-bit integer and returns the bit equivalent double.
 572 inline double BitsToDouble(uint64_t Bits) {
 573   double D;
 574   static_assert(sizeof(uint64_t) == sizeof(double), "Unexpected type sizes");
 575   memcpy(&D, &Bits, sizeof(Bits));
 576   return D;
 577 }
 578
 579 /// This function takes a 32-bit integer and returns the bit equivalent float.
 580 inline float BitsToFloat(uint32_t Bits) {
 581   float F;
 582   static_assert(sizeof(uint32_t) == sizeof(float), "Unexpected type sizes");
 583   memcpy(&F, &Bits, sizeof(Bits));
 584   return F;
 585 }
 586
 587 /// This function takes a double and returns the bit equivalent 64-bit integer.
 588 /// Note that copying doubles around changes the bits of NaNs on some hosts,
 589 /// notably x86, so this routine cannot be used if these bits are needed.
 590 inline uint64_t DoubleToBits(double Double) {
 591   uint64_t Bits;
 592   static_assert(sizeof(uint64_t) == sizeof(double), "Unexpected type sizes");
 593   memcpy(&Bits, &Double, sizeof(Double));
 594   return Bits;
 595 }
 596
 597 /// This function takes a float and returns the bit equivalent 32-bit integer.
 598 /// Note that copying floats around changes the bits of NaNs on some hosts,
 599 /// notably x86, so this routine cannot be used if these bits are needed.
 600 inline uint32_t FloatToBits(float Float) {
 601   uint32_t Bits;
 602   static_assert(sizeof(uint32_t) == sizeof(float), "Unexpected type sizes");
 603   memcpy(&Bits, &Float, sizeof(Float));
 604   return Bits;
 605 }
 606
 607 /// A and B are either alignments or offsets. Return the minimum alignment that
 608 /// may be assumed after adding the two together.
 609 constexpr inline uint64_t MinAlign(uint64_t A, uint64_t B) {
 610   // The largest power of 2 that divides both A and B.
 611   //
 612   // Replace "-Value" by "1+~Value" in the following commented code to avoid
 613   // MSVC warning C4146
 614   //    return (A | B) & -(A | B);
 615   return (A | B) & (1 + ~(A | B));
 616 }
 617
 618 /// Aligns \c Addr to \c Alignment bytes, rounding up.
 619 ///
 620 /// Alignment should be a power of two.  This method rounds up, so
 621 /// alignAddr(7, 4) == 8 and alignAddr(8, 4) == 8.
 622 inline uintptr_t alignAddr(const void *Addr, size_t Alignment) {
 623   assert(Alignment && isPowerOf2_64((uint64_t)Alignment) &&
 624          "Alignment is not a power of two!");
 625
 626   assert((uintptr_t)Addr + Alignment - 1 >= (uintptr_t)Addr);
 627
 628   return (((uintptr_t)Addr + Alignment - 1) & ~(uintptr_t)(Alignment - 1));
 629 }
 630
 631 /// Returns the necessary adjustment for aligning \c Ptr to \c Alignment
 632 /// bytes, rounding up.
 633 inline size_t alignmentAdjustment(const void *Ptr, size_t Alignment) {
 634   return alignAddr(Ptr, Alignment) - (uintptr_t)Ptr;
 635 }
 636
 637 /// Returns the next power of two (in 64-bits) that is strictly greater than A.
 638 /// Returns zero on overflow.
 639 inline uint64_t NextPowerOf2(uint64_t A) {
 640   A |= (A >> 1);
 641   A |= (A >> 2);
 642   A |= (A >> 4);
 643   A |= (A >> 8);
 644   A |= (A >> 16);
 645   A |= (A >> 32);
 646   return A + 1;
 647 }
 648
 649 /// Returns the power of two which is less than or equal to the given value.
 650 /// Essentially, it is a floor operation across the domain of powers of two.
 651 inline uint64_t PowerOf2Floor(uint64_t A) {
 652   if (!A) return 0;
 653   return 1ull << (63 - countLeadingZeros(A, ZB_Undefined));
 654 }
 655
 656 /// Returns the power of two which is greater than or equal to the given value.
 657 /// Essentially, it is a ceil operation across the domain of powers of two.
 658 inline uint64_t PowerOf2Ceil(uint64_t A) {
 659   if (!A)
 660     return 0;
 661   return NextPowerOf2(A - 1);
 662 }
 663
 664 /// Returns the next integer (mod 2**64) that is greater than or equal to
 665 /// \p Value and is a multiple of \p Align. \p Align must be non-zero.
 666 ///
 667 /// If non-zero \p Skew is specified, the return value will be a minimal
 668 /// integer that is greater than or equal to \p Value and equal to
 669 /// \p Align * N + \p Skew for some integer N. If \p Skew is larger than
 670 /// \p Align, its value is adjusted to '\p Skew mod \p Align'.
 671 ///
 672 /// Examples:
 673 /// \code
 674 ///   alignTo(5, 8) = 8
 675 ///   alignTo(17, 8) = 24
 676 ///   alignTo(~0LL, 8) = 0
 677 ///   alignTo(321, 255) = 510
 678 ///
 679 ///   alignTo(5, 8, 7) = 7
 680 ///   alignTo(17, 8, 1) = 17
 681 ///   alignTo(~0LL, 8, 3) = 3
 682 ///   alignTo(321, 255, 42) = 552
 683 /// \endcode
 684 inline uint64_t alignTo(uint64_t Value, uint64_t Align, uint64_t Skew = 0) {
 685   assert(Align != 0u && "Align can't be 0.");
 686   Skew %= Align;
 687   return (Value + Align - 1 - Skew) / Align * Align + Skew;
 688 }
 689
 690 /// Returns the next integer (mod 2**64) that is greater than or equal to
 691 /// \p Value and is a multiple of \c Align. \c Align must be non-zero.
 692 template <uint64_t Align> constexpr inline uint64_t alignTo(uint64_t Value) {
 693   static_assert(Align != 0u, "Align must be non-zero");
 694   return (Value + Align - 1) / Align * Align;
 695 }
 696
 697 /// Returns the integer ceil(Numerator / Denominator).
 698 inline uint64_t divideCeil(uint64_t Numerator, uint64_t Denominator) {
 699   return alignTo(Numerator, Denominator) / Denominator;
 700 }
 701
 702 /// \c alignTo for contexts where a constant expression is required.
 703 /// \sa alignTo
 704 ///
 705 /// \todo FIXME: remove when \c constexpr becomes really \c constexpr
 706 template <uint64_t Align>
 707 struct AlignTo {
 708   static_assert(Align != 0u, "Align must be non-zero");
 709   template <uint64_t Value>
 710   struct from_value {
 711     static const uint64_t value = (Value + Align - 1) / Align * Align;
 712   };
 713 };
 714
 715 /// Returns the largest uint64_t less than or equal to \p Value and is
 716 /// \p Skew mod \p Align. \p Align must be non-zero
 717 inline uint64_t alignDown(uint64_t Value, uint64_t Align, uint64_t Skew = 0) {
 718   assert(Align != 0u && "Align can't be 0.");
 719   Skew %= Align;
 720   return (Value - Skew) / Align * Align + Skew;
 721 }
 722
 723 /// Returns the offset to the next integer (mod 2**64) that is greater than
 724 /// or equal to \p Value and is a multiple of \p Align. \p Align must be
 725 /// non-zero.
 726 inline uint64_t OffsetToAlignment(uint64_t Value, uint64_t Align) {
 727   return alignTo(Value, Align) - Value;
 728 }
 729
 730 /// Sign-extend the number in the bottom B bits of X to a 32-bit integer.
 731 /// Requires 0 < B <= 32.
 732 template <unsigned B> constexpr inline int32_t SignExtend32(uint32_t X) {
 733   static_assert(B > 0, "Bit width can't be 0.");
 734   static_assert(B <= 32, "Bit width out of range.");
 735   return int32_t(X << (32 - B)) >> (32 - B);
 736 }
 737
 738 /// Sign-extend the number in the bottom B bits of X to a 32-bit integer.
 739 /// Requires 0 < B < 32.
 740 inline int32_t SignExtend32(uint32_t X, unsigned B) {
 741   assert(B > 0 && "Bit width can't be 0.");
 742   assert(B <= 32 && "Bit width out of range.");
 743   return int32_t(X << (32 - B)) >> (32 - B);
 744 }
 745
 746 /// Sign-extend the number in the bottom B bits of X to a 64-bit integer.
 747 /// Requires 0 < B < 64.
 748 template <unsigned B> constexpr inline int64_t SignExtend64(uint64_t x) {
 749   static_assert(B > 0, "Bit width can't be 0.");
 750   static_assert(B <= 64, "Bit width out of range.");
 751   return int64_t(x << (64 - B)) >> (64 - B);
 752 }
 753
 754 /// Sign-extend the number in the bottom B bits of X to a 64-bit integer.
 755 /// Requires 0 < B < 64.
 756 inline int64_t SignExtend64(uint64_t X, unsigned B) {
 757   assert(B > 0 && "Bit width can't be 0.");
 758   assert(B <= 64 && "Bit width out of range.");
 759   return int64_t(X << (64 - B)) >> (64 - B);
 760 }
 761
 762 /// Subtract two unsigned integers, X and Y, of type T and return the absolute
 763 /// value of the result.
 764 template <typename T>
 765 typename std::enable_if<std::is_unsigned<T>::value, T>::type
 766 AbsoluteDifference(T X, T Y) {
 767   return std::max(X, Y) - std::min(X, Y);
 768 }
 769
 770 /// Add two unsigned integers, X and Y, of type T.  Clamp the result to the
 771 /// maximum representable value of T on overflow.  ResultOverflowed indicates if
 772 /// the result is larger than the maximum representable value of type T.
 773 template <typename T>
 774 typename std::enable_if<std::is_unsigned<T>::value, T>::type
 775 SaturatingAdd(T X, T Y, bool *ResultOverflowed = nullptr) {
 776   bool Dummy;
 777   bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
 778   // Hacker's Delight, p. 29
 779   T Z = X + Y;
 780   Overflowed = (Z < X || Z < Y);
 781   if (Overflowed)
 782     return std::numeric_limits<T>::max();
 783   else
 784     return Z;
 785 }
 786
 787 /// Multiply two unsigned integers, X and Y, of type T.  Clamp the result to the
 788 /// maximum representable value of T on overflow.  ResultOverflowed indicates if
 789 /// the result is larger than the maximum representable value of type T.
 790 template <typename T>
 791 typename std::enable_if<std::is_unsigned<T>::value, T>::type
 792 SaturatingMultiply(T X, T Y, bool *ResultOverflowed = nullptr) {
 793   bool Dummy;
 794   bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
 795
 796   // Hacker's Delight, p. 30 has a different algorithm, but we don't use that
 797   // because it fails for uint16_t (where multiplication can have undefined
 798   // behavior due to promotion to int), and requires a division in addition
 799   // to the multiplication.
 800
 801   Overflowed = false;
 802
 803   // Log2(Z) would be either Log2Z or Log2Z + 1.
 804   // Special case: if X or Y is 0, Log2_64 gives -1, and Log2Z
 805   // will necessarily be less than Log2Max as desired.
 806   int Log2Z = Log2_64(X) + Log2_64(Y);
 807   const T Max = std::numeric_limits<T>::max();
 808   int Log2Max = Log2_64(Max);
 809   if (Log2Z < Log2Max) {
 810     return X * Y;
 811   }
 812   if (Log2Z > Log2Max) {
 813     Overflowed = true;
 814     return Max;
 815   }
 816
 817   // We're going to use the top bit, and maybe overflow one
 818   // bit past it. Multiply all but the bottom bit then add
 819   // that on at the end.
 820   T Z = (X >> 1) * Y;
 821   if (Z & ~(Max >> 1)) {
 822     Overflowed = true;
 823     return Max;
 824   }
 825   Z <<= 1;
 826   if (X & 1)
 827     return SaturatingAdd(Z, Y, ResultOverflowed);
 828
 829   return Z;
 830 }
 831
 832 /// Multiply two unsigned integers, X and Y, and add the unsigned integer, A to
 833 /// the product. Clamp the result to the maximum representable value of T on
 834 /// overflow. ResultOverflowed indicates if the result is larger than the
 835 /// maximum representable value of type T.
 836 template <typename T>
 837 typename std::enable_if<std::is_unsigned<T>::value, T>::type
 838 SaturatingMultiplyAdd(T X, T Y, T A, bool *ResultOverflowed = nullptr) {
 839   bool Dummy;
 840   bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
 841
 842   T Product = SaturatingMultiply(X, Y, &Overflowed);
 843   if (Overflowed)
 844     return Product;
 845
 846   return SaturatingAdd(A, Product, &Overflowed);
 847 }
 848
 849 /// Use this rather than HUGE_VALF; the latter causes warnings on MSVC.
 850 extern const float huge_valf;
 851 } // End llvm namespace
 852
 853 #endif