LCOV - code coverage report
Current view: top level - include/llvm/Support - MathExtras.h (source / functions) Hit Total Coverage
Test: llvm-toolchain.info Lines: 120 123 97.6 %
Date: 2018-07-13 00:08:38 Functions: 9 10 90.0 %
Legend: Lines: hit not hit

          Line data    Source code
       1             : //===-- llvm/Support/MathExtras.h - Useful math functions -------*- C++ -*-===//
       2             : //
       3             : //                     The LLVM Compiler Infrastructure
       4             : //
       5             : // This file is distributed under the University of Illinois Open Source
       6             : // License. See LICENSE.TXT for details.
       7             : //
       8             : //===----------------------------------------------------------------------===//
       9             : //
      10             : // This file contains some functions that are useful for math stuff.
      11             : //
      12             : //===----------------------------------------------------------------------===//
      13             : 
      14             : #ifndef LLVM_SUPPORT_MATHEXTRAS_H
      15             : #define LLVM_SUPPORT_MATHEXTRAS_H
      16             : 
      17             : #include "llvm/Support/Compiler.h"
      18             : #include "llvm/Support/SwapByteOrder.h"
      19             : #include <algorithm>
      20             : #include <cassert>
      21             : #include <climits>
      22             : #include <cstring>
      23             : #include <limits>
      24             : #include <type_traits>
      25             : 
      26             : #ifdef __ANDROID_NDK__
      27             : #include <android/api-level.h>
      28             : #endif
      29             : 
      30             : #ifdef _MSC_VER
      31             : // Declare these intrinsics manually rather including intrin.h. It's very
      32             : // expensive, and MathExtras.h is popular.
      33             : // #include <intrin.h>
      34             : extern "C" {
      35             : unsigned char _BitScanForward(unsigned long *_Index, unsigned long _Mask);
      36             : unsigned char _BitScanForward64(unsigned long *_Index, unsigned __int64 _Mask);
      37             : unsigned char _BitScanReverse(unsigned long *_Index, unsigned long _Mask);
      38             : unsigned char _BitScanReverse64(unsigned long *_Index, unsigned __int64 _Mask);
      39             : }
      40             : #endif
      41             : 
      42             : namespace llvm {
      43             : /// The behavior an operation has on an input of 0.
      44             : enum ZeroBehavior {
      45             :   /// The returned value is undefined.
      46             :   ZB_Undefined,
      47             :   /// The returned value is numeric_limits<T>::max()
      48             :   ZB_Max,
      49             :   /// The returned value is numeric_limits<T>::digits
      50             :   ZB_Width
      51             : };
      52             : 
      53             : namespace detail {
      54             : template <typename T, std::size_t SizeOfT> struct TrailingZerosCounter {
      55             :   static std::size_t count(T Val, ZeroBehavior) {
      56         139 :     if (!Val)
      57             :       return std::numeric_limits<T>::digits;
      58         169 :     if (Val & 0x1)
      59             :       return 0;
      60             : 
      61             :     // Bisection method.
      62             :     std::size_t ZeroBits = 0;
      63             :     T Shift = std::numeric_limits<T>::digits >> 1;
      64             :     T Mask = std::numeric_limits<T>::max() >> Shift;
      65         554 :     while (Shift) {
      66         416 :       if ((Val & Mask) == 0) {
      67         216 :         Val >>= Shift;
      68         216 :         ZeroBits |= Shift;
      69             :       }
      70         416 :       Shift >>= 1;
      71         416 :       Mask >>= Shift;
      72             :     }
      73             :     return ZeroBits;
      74             :   }
      75             : };
      76             : 
      77             : #if __GNUC__ >= 4 || defined(_MSC_VER)
      78             : template <typename T> struct TrailingZerosCounter<T, 4> {
      79             :   static std::size_t count(T Val, ZeroBehavior ZB) {
      80      668938 :     if (ZB != ZB_Undefined && Val == 0)
      81             :       return 32;
      82             : 
      83             : #if __has_builtin(__builtin_ctz) || LLVM_GNUC_PREREQ(4, 0, 0)
      84    52271247 :     return __builtin_ctz(Val);
      85             : #elif defined(_MSC_VER)
      86             :     unsigned long Index;
      87             :     _BitScanForward(&Index, Val);
      88             :     return Index;
      89             : #endif
      90             :   }
      91             : };
      92             : 
      93             : #if !defined(_MSC_VER) || defined(_M_X64)
      94             : template <typename T> struct TrailingZerosCounter<T, 8> {
      95             :   static std::size_t count(T Val, ZeroBehavior ZB) {
      96    59996880 :     if (ZB != ZB_Undefined && Val == 0)
      97             :       return 64;
      98             : 
      99             : #if __has_builtin(__builtin_ctzll) || LLVM_GNUC_PREREQ(4, 0, 0)
     100   200154286 :     return __builtin_ctzll(Val);
     101             : #elif defined(_MSC_VER)
     102             :     unsigned long Index;
     103             :     _BitScanForward64(&Index, Val);
     104             :     return Index;
     105             : #endif
     106             :   }
     107             : };
     108             : #endif
     109             : #endif
     110             : } // namespace detail
     111             : 
     112             : /// Count number of 0's from the least significant bit to the most
     113             : ///   stopping at the first 1.
     114             : ///
     115             : /// Only unsigned integral types are allowed.
     116             : ///
     117             : /// \param ZB the behavior on an input of 0. Only ZB_Width and ZB_Undefined are
     118             : ///   valid arguments.
     119             : template <typename T>
     120             : std::size_t countTrailingZeros(T Val, ZeroBehavior ZB = ZB_Width) {
     121             :   static_assert(std::numeric_limits<T>::is_integer &&
     122             :                     !std::numeric_limits<T>::is_signed,
     123             :                 "Only unsigned integral types are allowed.");
     124             :   return llvm::detail::TrailingZerosCounter<T, sizeof(T)>::count(Val, ZB);
     125             : }
     126             : 
     127             : namespace detail {
     128             : template <typename T, std::size_t SizeOfT> struct LeadingZerosCounter {
     129             :   static std::size_t count(T Val, ZeroBehavior) {
     130           0 :     if (!Val)
     131             :       return std::numeric_limits<T>::digits;
     132             : 
     133             :     // Bisection method.
     134             :     std::size_t ZeroBits = 0;
     135          32 :     for (T Shift = std::numeric_limits<T>::digits >> 1; Shift; Shift >>= 1) {
     136          14 :       T Tmp = Val >> Shift;
     137          14 :       if (Tmp)
     138             :         Val = Tmp;
     139             :       else
     140           6 :         ZeroBits |= Shift;
     141             :     }
     142             :     return ZeroBits;
     143             :   }
     144             : };
     145             : 
     146             : #if __GNUC__ >= 4 || defined(_MSC_VER)
     147             : template <typename T> struct LeadingZerosCounter<T, 4> {
     148             :   static std::size_t count(T Val, ZeroBehavior ZB) {
     149    15894005 :     if (ZB != ZB_Undefined && Val == 0)
     150             :       return 32;
     151             : 
     152             : #if __has_builtin(__builtin_clz) || LLVM_GNUC_PREREQ(4, 0, 0)
     153    11092883 :     return __builtin_clz(Val);
     154             : #elif defined(_MSC_VER)
     155             :     unsigned long Index;
     156             :     _BitScanReverse(&Index, Val);
     157             :     return Index ^ 31;
     158             : #endif
     159             :   }
     160             : };
     161             : 
     162             : #if !defined(_MSC_VER) || defined(_M_X64)
     163             : template <typename T> struct LeadingZerosCounter<T, 8> {
     164             :   static std::size_t count(T Val, ZeroBehavior ZB) {
     165    98498309 :     if (ZB != ZB_Undefined && Val == 0)
     166             :       return 64;
     167             : 
     168             : #if __has_builtin(__builtin_clzll) || LLVM_GNUC_PREREQ(4, 0, 0)
     169   103617379 :     return __builtin_clzll(Val);
     170             : #elif defined(_MSC_VER)
     171             :     unsigned long Index;
     172             :     _BitScanReverse64(&Index, Val);
     173             :     return Index ^ 63;
     174             : #endif
     175             :   }
     176             : };
     177             : #endif
     178             : #endif
     179             : } // namespace detail
     180             : 
     181             : /// Count number of 0's from the most significant bit to the least
     182             : ///   stopping at the first 1.
     183             : ///
     184             : /// Only unsigned integral types are allowed.
     185             : ///
     186             : /// \param ZB the behavior on an input of 0. Only ZB_Width and ZB_Undefined are
     187             : ///   valid arguments.
     188             : template <typename T>
     189             : std::size_t countLeadingZeros(T Val, ZeroBehavior ZB = ZB_Width) {
     190             :   static_assert(std::numeric_limits<T>::is_integer &&
     191             :                     !std::numeric_limits<T>::is_signed,
     192             :                 "Only unsigned integral types are allowed.");
     193             :   return llvm::detail::LeadingZerosCounter<T, sizeof(T)>::count(Val, ZB);
     194             : }
     195             : 
     196             : /// Get the index of the first set bit starting from the least
     197             : ///   significant bit.
     198             : ///
     199             : /// Only unsigned integral types are allowed.
     200             : ///
     201             : /// \param ZB the behavior on an input of 0. Only ZB_Max and ZB_Undefined are
     202             : ///   valid arguments.
     203             : template <typename T> T findFirstSet(T Val, ZeroBehavior ZB = ZB_Max) {
     204        5073 :   if (ZB == ZB_Max && Val == 0)
     205             :     return std::numeric_limits<T>::max();
     206             : 
     207           2 :   return countTrailingZeros(Val, ZB_Undefined);
     208             : }
     209             : 
     210             : /// Create a bitmask with the N right-most bits set to 1, and all other
     211             : /// bits set to 0.  Only unsigned types are allowed.
     212             : template <typename T> T maskTrailingOnes(unsigned N) {
     213             :   static_assert(std::is_unsigned<T>::value, "Invalid type!");
     214             :   const unsigned Bits = CHAR_BIT * sizeof(T);
     215             :   assert(N <= Bits && "Invalid bit index");
     216   156333689 :   return N == 0 ? 0 : (T(-1) >> (Bits - N));
     217             : }
     218             : 
     219             : /// Create a bitmask with the N left-most bits set to 1, and all other
     220             : /// bits set to 0.  Only unsigned types are allowed.
     221             : template <typename T> T maskLeadingOnes(unsigned N) {
     222   145127415 :   return ~maskTrailingOnes<T>(CHAR_BIT * sizeof(T) - N);
     223             : }
     224             : 
     225             : /// Create a bitmask with the N right-most bits set to 0, and all other
     226             : /// bits set to 1.  Only unsigned types are allowed.
     227             : template <typename T> T maskTrailingZeros(unsigned N) {
     228    73334675 :   return maskLeadingOnes<T>(CHAR_BIT * sizeof(T) - N);
     229             : }
     230             : 
     231             : /// Create a bitmask with the N left-most bits set to 0, and all other
     232             : /// bits set to 1.  Only unsigned types are allowed.
     233             : template <typename T> T maskLeadingZeros(unsigned N) {
     234             :   return maskTrailingOnes<T>(CHAR_BIT * sizeof(T) - N);
     235             : }
     236             : 
     237             : /// Get the index of the last set bit starting from the least
     238             : ///   significant bit.
     239             : ///
     240             : /// Only unsigned integral types are allowed.
     241             : ///
     242             : /// \param ZB the behavior on an input of 0. Only ZB_Max and ZB_Undefined are
     243             : ///   valid arguments.
     244             : template <typename T> T findLastSet(T Val, ZeroBehavior ZB = ZB_Max) {
     245       13514 :   if (ZB == ZB_Max && Val == 0)
     246             :     return std::numeric_limits<T>::max();
     247             : 
     248             :   // Use ^ instead of - because both gcc and llvm can remove the associated ^
     249             :   // in the __builtin_clz intrinsic on x86.
     250           2 :   return countLeadingZeros(Val, ZB_Undefined) ^
     251     1010399 :          (std::numeric_limits<T>::digits - 1);
     252             : }
     253             : 
     254             : /// Macro compressed bit reversal table for 256 bits.
     255             : ///
     256             : /// http://graphics.stanford.edu/~seander/bithacks.html#BitReverseTable
     257             : static const unsigned char BitReverseTable256[256] = {
     258             : #define R2(n) n, n + 2 * 64, n + 1 * 64, n + 3 * 64
     259             : #define R4(n) R2(n), R2(n + 2 * 16), R2(n + 1 * 16), R2(n + 3 * 16)
     260             : #define R6(n) R4(n), R4(n + 2 * 4), R4(n + 1 * 4), R4(n + 3 * 4)
     261             :   R6(0), R6(2), R6(1), R6(3)
     262             : #undef R2
     263             : #undef R4
     264             : #undef R6
     265             : };
     266             : 
     267             : /// Reverse the bits in \p Val.
     268             : template <typename T>
     269             : T reverseBits(T Val) {
     270             :   unsigned char in[sizeof(Val)];
     271             :   unsigned char out[sizeof(Val)];
     272       14605 :   std::memcpy(in, &Val, sizeof(Val));
     273      133017 :   for (unsigned i = 0; i < sizeof(Val); ++i)
     274       59410 :     out[(sizeof(Val) - i) - 1] = BitReverseTable256[in[i]];
     275       14605 :   std::memcpy(&Val, out, sizeof(Val));
     276             :   return Val;
     277             : }
     278             : 
     279             : // NOTE: The following support functions use the _32/_64 extensions instead of
     280             : // type overloading so that signed and unsigned integers can be used without
     281             : // ambiguity.
     282             : 
     283             : /// Return the high 32 bits of a 64 bit value.
     284             : constexpr inline uint32_t Hi_32(uint64_t Value) {
     285      305167 :   return static_cast<uint32_t>(Value >> 32);
     286             : }
     287             : 
     288             : /// Return the low 32 bits of a 64 bit value.
     289             : constexpr inline uint32_t Lo_32(uint64_t Value) {
     290      674279 :   return static_cast<uint32_t>(Value);
     291             : }
     292             : 
     293             : /// Make a 64-bit integer from a high / low pair of 32-bit integers.
     294             : constexpr inline uint64_t Make_64(uint32_t High, uint32_t Low) {
     295      353817 :   return ((uint64_t)High << 32) | (uint64_t)Low;
     296             : }
     297             : 
     298             : /// Checks if an integer fits into the given bit width.
     299             : template <unsigned N> constexpr inline bool isInt(int64_t x) {
     300      221422 :   return N >= 64 || (-(INT64_C(1)<<(N-1)) <= x && x < (INT64_C(1)<<(N-1)));
     301             : }
     302             : // Template specializations to get better code for common cases.
     303             : template <> constexpr inline bool isInt<8>(int64_t x) {
     304      382477 :   return static_cast<int8_t>(x) == x;
     305             : }
     306             : template <> constexpr inline bool isInt<16>(int64_t x) {
     307      363535 :   return static_cast<int16_t>(x) == x;
     308             : }
     309             : template <> constexpr inline bool isInt<32>(int64_t x) {
     310     3254576 :   return static_cast<int32_t>(x) == x;
     311             : }
     312             : 
     313             : /// Checks if a signed integer is an N bit number shifted left by S.
     314             : template <unsigned N, unsigned S>
     315             : constexpr inline bool isShiftedInt(int64_t x) {
     316             :   static_assert(
     317             :       N > 0, "isShiftedInt<0> doesn't make sense (refers to a 0-bit number.");
     318             :   static_assert(N + S <= 64, "isShiftedInt<N, S> with N + S > 64 is too wide.");
     319        5624 :   return isInt<N + S>(x) && (x % (UINT64_C(1) << S) == 0);
     320             : }
     321             : 
     322             : /// Checks if an unsigned integer fits into the given bit width.
     323             : ///
     324             : /// This is written as two functions rather than as simply
     325             : ///
     326             : ///   return N >= 64 || X < (UINT64_C(1) << N);
     327             : ///
     328             : /// to keep MSVC from (incorrectly) warning on isUInt<64> that we're shifting
     329             : /// left too many places.
     330             : template <unsigned N>
     331             : constexpr inline typename std::enable_if<(N < 64), bool>::type
     332             : isUInt(uint64_t X) {
     333             :   static_assert(N > 0, "isUInt<0> doesn't make sense");
     334       23901 :   return X < (UINT64_C(1) << (N));
     335             : }
     336             : template <unsigned N>
     337             : constexpr inline typename std::enable_if<N >= 64, bool>::type
     338             : isUInt(uint64_t X) {
     339             :   return true;
     340             : }
     341             : 
     342             : // Template specializations to get better code for common cases.
     343             : template <> constexpr inline bool isUInt<8>(uint64_t x) {
     344       10490 :   return static_cast<uint8_t>(x) == x;
     345             : }
     346             : template <> constexpr inline bool isUInt<16>(uint64_t x) {
     347         749 :   return static_cast<uint16_t>(x) == x;
     348             : }
     349             : template <> constexpr inline bool isUInt<32>(uint64_t x) {
     350        7137 :   return static_cast<uint32_t>(x) == x;
     351             : }
     352             : 
     353             : /// Checks if a unsigned integer is an N bit number shifted left by S.
     354             : template <unsigned N, unsigned S>
     355             : constexpr inline bool isShiftedUInt(uint64_t x) {
     356             :   static_assert(
     357             :       N > 0, "isShiftedUInt<0> doesn't make sense (refers to a 0-bit number)");
     358             :   static_assert(N + S <= 64,
     359             :                 "isShiftedUInt<N, S> with N + S > 64 is too wide.");
     360             :   // Per the two static_asserts above, S must be strictly less than 64.  So
     361             :   // 1 << S is not undefined behavior.
     362       13128 :   return isUInt<N + S>(x) && (x % (UINT64_C(1) << S) == 0);
     363             : }
     364             : 
     365             : /// Gets the maximum value for a N-bit unsigned integer.
     366             : inline uint64_t maxUIntN(uint64_t N) {
     367             :   assert(N > 0 && N <= 64 && "integer width out of range");
     368             : 
     369             :   // uint64_t(1) << 64 is undefined behavior, so we can't do
     370             :   //   (uint64_t(1) << N) - 1
     371             :   // without checking first that N != 64.  But this works and doesn't have a
     372             :   // branch.
     373       24896 :   return UINT64_MAX >> (64 - N);
     374             : }
     375             : 
     376             : /// Gets the minimum value for a N-bit signed integer.
     377             : inline int64_t minIntN(int64_t N) {
     378             :   assert(N > 0 && N <= 64 && "integer width out of range");
     379             : 
     380       31833 :   return -(UINT64_C(1)<<(N-1));
     381             : }
     382             : 
     383             : /// Gets the maximum value for a N-bit signed integer.
     384             : inline int64_t maxIntN(int64_t N) {
     385             :   assert(N > 0 && N <= 64 && "integer width out of range");
     386             : 
     387             :   // This relies on two's complement wraparound when N == 64, so we convert to
     388             :   // int64_t only at the very end to avoid UB.
     389       31695 :   return (UINT64_C(1) << (N - 1)) - 1;
     390             : }
     391             : 
     392             : /// Checks if an unsigned integer fits into the given (dynamic) bit width.
     393             : inline bool isUIntN(unsigned N, uint64_t x) {
     394      610785 :   return N >= 64 || x <= maxUIntN(N);
     395             : }
     396             : 
     397             : /// Checks if an signed integer fits into the given (dynamic) bit width.
     398             : inline bool isIntN(unsigned N, int64_t x) {
     399       93843 :   return N >= 64 || (minIntN(N) <= x && x <= maxIntN(N));
     400             : }
     401             : 
     402             : /// Return true if the argument is a non-empty sequence of ones starting at the
     403             : /// least significant bit with the remainder zero (32 bit version).
     404             : /// Ex. isMask_32(0x0000FFFFU) == true.
     405             : constexpr inline bool isMask_32(uint32_t Value) {
     406        6681 :   return Value && ((Value + 1) & Value) == 0;
     407             : }
     408             : 
     409             : /// Return true if the argument is a non-empty sequence of ones starting at the
     410             : /// least significant bit with the remainder zero (64 bit version).
     411             : constexpr inline bool isMask_64(uint64_t Value) {
     412      199438 :   return Value && ((Value + 1) & Value) == 0;
     413             : }
     414             : 
     415             : /// Return true if the argument contains a non-empty sequence of ones with the
     416             : /// remainder zero (32 bit version.) Ex. isShiftedMask_32(0x0000FF00U) == true.
     417             : constexpr inline bool isShiftedMask_32(uint32_t Value) {
     418        1516 :   return Value && isMask_32((Value - 1) | Value);
     419             : }
     420             : 
     421             : /// Return true if the argument contains a non-empty sequence of ones with the
     422             : /// remainder zero (64 bit version.)
     423             : constexpr inline bool isShiftedMask_64(uint64_t Value) {
     424       12658 :   return Value && isMask_64((Value - 1) | Value);
     425             : }
     426             : 
     427             : /// Return true if the argument is a power of two > 0.
     428             : /// Ex. isPowerOf2_32(0x00100000U) == true (32 bit edition.)
     429             : constexpr inline bool isPowerOf2_32(uint32_t Value) {
     430     8895053 :   return Value && !(Value & (Value - 1));
     431             : }
     432             : 
     433             : /// Return true if the argument is a power of two > 0 (64 bit edition.)
     434             : constexpr inline bool isPowerOf2_64(uint64_t Value) {
     435     4496565 :   return Value && !(Value & (Value - 1));
     436             : }
     437             : 
     438             : /// Return a byte-swapped representation of the 16-bit argument.
     439             : inline uint16_t ByteSwap_16(uint16_t Value) {
     440             :   return sys::SwapByteOrder_16(Value);
     441             : }
     442             : 
     443             : /// Return a byte-swapped representation of the 32-bit argument.
     444             : inline uint32_t ByteSwap_32(uint32_t Value) {
     445             :   return sys::SwapByteOrder_32(Value);
     446             : }
     447             : 
     448             : /// Return a byte-swapped representation of the 64-bit argument.
     449             : inline uint64_t ByteSwap_64(uint64_t Value) {
     450             :   return sys::SwapByteOrder_64(Value);
     451             : }
     452             : 
     453             : /// Count the number of ones from the most significant bit to the first
     454             : /// zero bit.
     455             : ///
     456             : /// Ex. countLeadingOnes(0xFF0FFF00) == 8.
     457             : /// Only unsigned integral types are allowed.
     458             : ///
     459             : /// \param ZB the behavior on an input of all ones. Only ZB_Width and
     460             : /// ZB_Undefined are valid arguments.
     461             : template <typename T>
     462             : std::size_t countLeadingOnes(T Value, ZeroBehavior ZB = ZB_Width) {
     463             :   static_assert(std::numeric_limits<T>::is_integer &&
     464             :                     !std::numeric_limits<T>::is_signed,
     465             :                 "Only unsigned integral types are allowed.");
     466     6894207 :   return countLeadingZeros<T>(~Value, ZB);
     467             : }
     468             : 
     469             : /// Count the number of ones from the least significant bit to the first
     470             : /// zero bit.
     471             : ///
     472             : /// Ex. countTrailingOnes(0x00FF00FF) == 8.
     473             : /// Only unsigned integral types are allowed.
     474             : ///
     475             : /// \param ZB the behavior on an input of all ones. Only ZB_Width and
     476             : /// ZB_Undefined are valid arguments.
     477             : template <typename T>
     478             : std::size_t countTrailingOnes(T Value, ZeroBehavior ZB = ZB_Width) {
     479             :   static_assert(std::numeric_limits<T>::is_integer &&
     480             :                     !std::numeric_limits<T>::is_signed,
     481             :                 "Only unsigned integral types are allowed.");
     482    40388513 :   return countTrailingZeros<T>(~Value, ZB);
     483             : }
     484             : 
     485             : namespace detail {
     486             : template <typename T, std::size_t SizeOfT> struct PopulationCounter {
     487             :   static unsigned count(T Value) {
     488             :     // Generic version, forward to 32 bits.
     489             :     static_assert(SizeOfT <= 4, "Not implemented!");
     490             : #if __GNUC__ >= 4
     491     1410680 :     return __builtin_popcount(Value);
     492             : #else
     493             :     uint32_t v = Value;
     494             :     v = v - ((v >> 1) & 0x55555555);
     495             :     v = (v & 0x33333333) + ((v >> 2) & 0x33333333);
     496             :     return ((v + (v >> 4) & 0xF0F0F0F) * 0x1010101) >> 24;
     497             : #endif
     498             :   }
     499             : };
     500             : 
     501             : template <typename T> struct PopulationCounter<T, 8> {
     502             :   static unsigned count(T Value) {
     503             : #if __GNUC__ >= 4
     504    21943533 :     return __builtin_popcountll(Value);
     505             : #else
     506             :     uint64_t v = Value;
     507             :     v = v - ((v >> 1) & 0x5555555555555555ULL);
     508             :     v = (v & 0x3333333333333333ULL) + ((v >> 2) & 0x3333333333333333ULL);
     509             :     v = (v + (v >> 4)) & 0x0F0F0F0F0F0F0F0FULL;
     510             :     return unsigned((uint64_t)(v * 0x0101010101010101ULL) >> 56);
     511             : #endif
     512             :   }
     513             : };
     514             : } // namespace detail
     515             : 
     516             : /// Count the number of set bits in a value.
     517             : /// Ex. countPopulation(0xF000F000) = 8
     518             : /// Returns 0 if the word is zero.
     519             : template <typename T>
     520      442572 : inline unsigned countPopulation(T Value) {
     521             :   static_assert(std::numeric_limits<T>::is_integer &&
     522             :                     !std::numeric_limits<T>::is_signed,
     523             :                 "Only unsigned integral types are allowed.");
     524      442572 :   return detail::PopulationCounter<T, sizeof(T)>::count(Value);
     525             : }
     526             : 
     527             : /// Return the log base 2 of the specified value.
     528           0 : inline double Log2(double Value) {
     529             : #if defined(__ANDROID_API__) && __ANDROID_API__ < 18
     530             :   return __builtin_log(Value) / __builtin_log(2.0);
     531             : #else
     532           0 :   return log2(Value);
     533             : #endif
     534             : }
     535             : 
     536             : /// Return the floor log base 2 of the specified value, -1 if the value is zero.
     537             : /// (32 bit edition.)
     538             : /// Ex. Log2_32(32) == 5, Log2_32(1) == 0, Log2_32(0) == -1, Log2_32(6) == 2
     539             : inline unsigned Log2_32(uint32_t Value) {
     540    11863168 :   return 31 - countLeadingZeros(Value);
     541             : }
     542             : 
     543             : /// Return the floor log base 2 of the specified value, -1 if the value is zero.
     544             : /// (64 bit edition.)
     545             : inline unsigned Log2_64(uint64_t Value) {
     546      119973 :   return 63 - countLeadingZeros(Value);
     547             : }
     548             : 
     549             : /// Return the ceil log base 2 of the specified value, 32 if the value is zero.
     550             : /// (32 bit edition).
     551             : /// Ex. Log2_32_Ceil(32) == 5, Log2_32_Ceil(1) == 0, Log2_32_Ceil(6) == 3
     552             : inline unsigned Log2_32_Ceil(uint32_t Value) {
     553     9885746 :   return 32 - countLeadingZeros(Value - 1);
     554             : }
     555             : 
     556             : /// Return the ceil log base 2 of the specified value, 64 if the value is zero.
     557             : /// (64 bit edition.)
     558             : inline unsigned Log2_64_Ceil(uint64_t Value) {
     559    75970321 :   return 64 - countLeadingZeros(Value - 1);
     560             : }
     561             : 
     562             : /// Return the greatest common divisor of the values using Euclid's algorithm.
     563             : inline uint64_t GreatestCommonDivisor64(uint64_t A, uint64_t B) {
     564        5619 :   while (B) {
     565             :     uint64_t T = B;
     566        3498 :     B = A % B;
     567             :     A = T;
     568             :   }
     569             :   return A;
     570             : }
     571             : 
     572             : /// This function takes a 64-bit integer and returns the bit equivalent double.
     573             : inline double BitsToDouble(uint64_t Bits) {
     574             :   double D;
     575             :   static_assert(sizeof(uint64_t) == sizeof(double), "Unexpected type sizes");
     576             :   memcpy(&D, &Bits, sizeof(Bits));
     577             :   return D;
     578             : }
     579             : 
     580             : /// This function takes a 32-bit integer and returns the bit equivalent float.
     581             : inline float BitsToFloat(uint32_t Bits) {
     582             :   float F;
     583             :   static_assert(sizeof(uint32_t) == sizeof(float), "Unexpected type sizes");
     584             :   memcpy(&F, &Bits, sizeof(Bits));
     585             :   return F;
     586             : }
     587             : 
     588             : /// This function takes a double and returns the bit equivalent 64-bit integer.
     589             : /// Note that copying doubles around changes the bits of NaNs on some hosts,
     590             : /// notably x86, so this routine cannot be used if these bits are needed.
     591             : inline uint64_t DoubleToBits(double Double) {
     592             :   uint64_t Bits;
     593             :   static_assert(sizeof(uint64_t) == sizeof(double), "Unexpected type sizes");
     594     4059191 :   memcpy(&Bits, &Double, sizeof(Double));
     595             :   return Bits;
     596             : }
     597             : 
     598             : /// This function takes a float and returns the bit equivalent 32-bit integer.
     599             : /// Note that copying floats around changes the bits of NaNs on some hosts,
     600             : /// notably x86, so this routine cannot be used if these bits are needed.
     601             : inline uint32_t FloatToBits(float Float) {
     602             :   uint32_t Bits;
     603             :   static_assert(sizeof(uint32_t) == sizeof(float), "Unexpected type sizes");
     604       24860 :   memcpy(&Bits, &Float, sizeof(Float));
     605             :   return Bits;
     606             : }
     607             : 
     608             : /// A and B are either alignments or offsets. Return the minimum alignment that
     609             : /// may be assumed after adding the two together.
     610             : constexpr inline uint64_t MinAlign(uint64_t A, uint64_t B) {
     611             :   // The largest power of 2 that divides both A and B.
     612             :   //
     613             :   // Replace "-Value" by "1+~Value" in the following commented code to avoid
     614             :   // MSVC warning C4146
     615             :   //    return (A | B) & -(A | B);
     616    17163137 :   return (A | B) & (1 + ~(A | B));
     617             : }
     618             : 
     619             : /// Aligns \c Addr to \c Alignment bytes, rounding up.
     620             : ///
     621             : /// Alignment should be a power of two.  This method rounds up, so
     622             : /// alignAddr(7, 4) == 8 and alignAddr(8, 4) == 8.
     623             : inline uintptr_t alignAddr(const void *Addr, size_t Alignment) {
     624             :   assert(Alignment && isPowerOf2_64((uint64_t)Alignment) &&
     625             :          "Alignment is not a power of two!");
     626             : 
     627             :   assert((uintptr_t)Addr + Alignment - 1 >= (uintptr_t)Addr);
     628             : 
     629   597323360 :   return (((uintptr_t)Addr + Alignment - 1) & ~(uintptr_t)(Alignment - 1));
     630             : }
     631             : 
     632             : /// Returns the necessary adjustment for aligning \c Ptr to \c Alignment
     633             : /// bytes, rounding up.
     634             : inline size_t alignmentAdjustment(const void *Ptr, size_t Alignment) {
     635   588628767 :   return alignAddr(Ptr, Alignment) - (uintptr_t)Ptr;
     636             : }
     637             : 
     638             : /// Returns the next power of two (in 64-bits) that is strictly greater than A.
     639             : /// Returns zero on overflow.
     640             : inline uint64_t NextPowerOf2(uint64_t A) {
     641    51821847 :   A |= (A >> 1);
     642    51821847 :   A |= (A >> 2);
     643    51821847 :   A |= (A >> 4);
     644    51821843 :   A |= (A >> 8);
     645    51821843 :   A |= (A >> 16);
     646     2854043 :   A |= (A >> 32);
     647    51821846 :   return A + 1;
     648             : }
     649             : 
     650             : /// Returns the power of two which is less than or equal to the given value.
     651             : /// Essentially, it is a floor operation across the domain of powers of two.
     652             : inline uint64_t PowerOf2Floor(uint64_t A) {
     653      148757 :   if (!A) return 0;
     654      158477 :   return 1ull << (63 - countLeadingZeros(A, ZB_Undefined));
     655             : }
     656             : 
     657             : /// Returns the power of two which is greater than or equal to the given value.
     658             : /// Essentially, it is a ceil operation across the domain of powers of two.
     659             : inline uint64_t PowerOf2Ceil(uint64_t A) {
     660      303955 :   if (!A)
     661             :     return 0;
     662      303767 :   return NextPowerOf2(A - 1);
     663             : }
     664             : 
     665             : /// Returns the next integer (mod 2**64) that is greater than or equal to
     666             : /// \p Value and is a multiple of \p Align. \p Align must be non-zero.
     667             : ///
     668             : /// If non-zero \p Skew is specified, the return value will be a minimal
     669             : /// integer that is greater than or equal to \p Value and equal to
     670             : /// \p Align * N + \p Skew for some integer N. If \p Skew is larger than
     671             : /// \p Align, its value is adjusted to '\p Skew mod \p Align'.
     672             : ///
     673             : /// Examples:
     674             : /// \code
     675             : ///   alignTo(5, 8) = 8
     676             : ///   alignTo(17, 8) = 24
     677             : ///   alignTo(~0LL, 8) = 0
     678             : ///   alignTo(321, 255) = 510
     679             : ///
     680             : ///   alignTo(5, 8, 7) = 7
     681             : ///   alignTo(17, 8, 1) = 17
     682             : ///   alignTo(~0LL, 8, 3) = 3
     683             : ///   alignTo(321, 255, 42) = 552
     684             : /// \endcode
     685             : inline uint64_t alignTo(uint64_t Value, uint64_t Align, uint64_t Skew = 0) {
     686             :   assert(Align != 0u && "Align can't be 0.");
     687      382997 :   Skew %= Align;
     688   230298433 :   return (Value + Align - 1 - Skew) / Align * Align + Skew;
     689             : }
     690             : 
     691             : /// Returns the next integer (mod 2**64) that is greater than or equal to
     692             : /// \p Value and is a multiple of \c Align. \c Align must be non-zero.
     693             : template <uint64_t Align> constexpr inline uint64_t alignTo(uint64_t Value) {
     694             :   static_assert(Align != 0u, "Align must be non-zero");
     695       18926 :   return (Value + Align - 1) / Align * Align;
     696             : }
     697             : 
     698             : /// Returns the integer ceil(Numerator / Denominator).
     699             : inline uint64_t divideCeil(uint64_t Numerator, uint64_t Denominator) {
     700        5914 :   return alignTo(Numerator, Denominator) / Denominator;
     701             : }
     702             : 
     703             : /// \c alignTo for contexts where a constant expression is required.
     704             : /// \sa alignTo
     705             : ///
     706             : /// \todo FIXME: remove when \c constexpr becomes really \c constexpr
     707             : template <uint64_t Align>
     708             : struct AlignTo {
     709             :   static_assert(Align != 0u, "Align must be non-zero");
     710             :   template <uint64_t Value>
     711             :   struct from_value {
     712             :     static const uint64_t value = (Value + Align - 1) / Align * Align;
     713             :   };
     714             : };
     715             : 
     716             : /// Returns the largest uint64_t less than or equal to \p Value and is
     717             : /// \p Skew mod \p Align. \p Align must be non-zero
     718             : inline uint64_t alignDown(uint64_t Value, uint64_t Align, uint64_t Skew = 0) {
     719             :   assert(Align != 0u && "Align can't be 0.");
     720             :   Skew %= Align;
     721      549168 :   return (Value - Skew) / Align * Align + Skew;
     722             : }
     723             : 
     724             : /// Returns the offset to the next integer (mod 2**64) that is greater than
     725             : /// or equal to \p Value and is a multiple of \p Align. \p Align must be
     726             : /// non-zero.
     727             : inline uint64_t OffsetToAlignment(uint64_t Value, uint64_t Align) {
     728      883605 :   return alignTo(Value, Align) - Value;
     729             : }
     730             : 
     731             : /// Sign-extend the number in the bottom B bits of X to a 32-bit integer.
     732             : /// Requires 0 < B <= 32.
     733             : template <unsigned B> constexpr inline int32_t SignExtend32(uint32_t X) {
     734             :   static_assert(B > 0, "Bit width can't be 0.");
     735             :   static_assert(B <= 32, "Bit width out of range.");
     736        7155 :   return int32_t(X << (32 - B)) >> (32 - B);
     737             : }
     738             : 
     739             : /// Sign-extend the number in the bottom B bits of X to a 32-bit integer.
     740             : /// Requires 0 < B < 32.
     741             : inline int32_t SignExtend32(uint32_t X, unsigned B) {
     742             :   assert(B > 0 && "Bit width can't be 0.");
     743             :   assert(B <= 32 && "Bit width out of range.");
     744        6033 :   return int32_t(X << (32 - B)) >> (32 - B);
     745             : }
     746             : 
     747             : /// Sign-extend the number in the bottom B bits of X to a 64-bit integer.
     748             : /// Requires 0 < B < 64.
     749             : template <unsigned B> constexpr inline int64_t SignExtend64(uint64_t x) {
     750             :   static_assert(B > 0, "Bit width can't be 0.");
     751             :   static_assert(B <= 64, "Bit width out of range.");
     752       11885 :   return int64_t(x << (64 - B)) >> (64 - B);
     753             : }
     754             : 
     755             : /// Sign-extend the number in the bottom B bits of X to a 64-bit integer.
     756             : /// Requires 0 < B < 64.
     757             : inline int64_t SignExtend64(uint64_t X, unsigned B) {
     758             :   assert(B > 0 && "Bit width can't be 0.");
     759             :   assert(B <= 64 && "Bit width out of range.");
     760    96660056 :   return int64_t(X << (64 - B)) >> (64 - B);
     761             : }
     762             : 
     763             : /// Subtract two unsigned integers, X and Y, of type T and return the absolute
     764             : /// value of the result.
     765             : template <typename T>
     766             : typename std::enable_if<std::is_unsigned<T>::value, T>::type
     767             : AbsoluteDifference(T X, T Y) {
     768         526 :   return std::max(X, Y) - std::min(X, Y);
     769             : }
     770             : 
     771             : /// Add two unsigned integers, X and Y, of type T.  Clamp the result to the
     772             : /// maximum representable value of T on overflow.  ResultOverflowed indicates if
     773             : /// the result is larger than the maximum representable value of type T.
     774             : template <typename T>
     775             : typename std::enable_if<std::is_unsigned<T>::value, T>::type
     776             : SaturatingAdd(T X, T Y, bool *ResultOverflowed = nullptr) {
     777             :   bool Dummy;
     778         413 :   bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
     779             :   // Hacker's Delight, p. 29
     780     1339746 :   T Z = X + Y;
     781     1339746 :   Overflowed = (Z < X || Z < Y);
     782     1339746 :   if (Overflowed)
     783             :     return std::numeric_limits<T>::max();
     784             :   else
     785             :     return Z;
     786             : }
     787             : 
     788             : /// Multiply two unsigned integers, X and Y, of type T.  Clamp the result to the
     789             : /// maximum representable value of T on overflow.  ResultOverflowed indicates if
     790             : /// the result is larger than the maximum representable value of type T.
     791             : template <typename T>
     792             : typename std::enable_if<std::is_unsigned<T>::value, T>::type
     793        3235 : SaturatingMultiply(T X, T Y, bool *ResultOverflowed = nullptr) {
     794             :   bool Dummy;
     795        3235 :   bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
     796             : 
     797             :   // Hacker's Delight, p. 30 has a different algorithm, but we don't use that
     798             :   // because it fails for uint16_t (where multiplication can have undefined
     799             :   // behavior due to promotion to int), and requires a division in addition
     800             :   // to the multiplication.
     801             : 
     802        3263 :   Overflowed = false;
     803             : 
     804             :   // Log2(Z) would be either Log2Z or Log2Z + 1.
     805             :   // Special case: if X or Y is 0, Log2_64 gives -1, and Log2Z
     806             :   // will necessarily be less than Log2Max as desired.
     807        3943 :   int Log2Z = Log2_64(X) + Log2_64(Y);
     808             :   const T Max = std::numeric_limits<T>::max();
     809             :   int Log2Max = Log2_64(Max);
     810        3235 :   if (Log2Z < Log2Max) {
     811        2694 :     return X * Y;
     812             :   }
     813         541 :   if (Log2Z > Log2Max) {
     814          27 :     Overflowed = true;
     815          15 :     return Max;
     816             :   }
     817             : 
     818             :   // We're going to use the top bit, and maybe overflow one
     819             :   // bit past it. Multiply all but the bottom bit then add
     820             :   // that on at the end.
     821         526 :   T Z = (X >> 1) * Y;
     822         526 :   if (Z & ~(Max >> 1)) {
     823         112 :     Overflowed = true;
     824         112 :     return Max;
     825             :   }
     826         414 :   Z <<= 1;
     827         414 :   if (X & 1)
     828         413 :     return SaturatingAdd(Z, Y, ResultOverflowed);
     829             : 
     830             :   return Z;
     831             : }
     832             : 
     833             : /// Multiply two unsigned integers, X and Y, and add the unsigned integer, A to
     834             : /// the product. Clamp the result to the maximum representable value of T on
     835             : /// overflow. ResultOverflowed indicates if the result is larger than the
     836             : /// maximum representable value of type T.
     837             : template <typename T>
     838             : typename std::enable_if<std::is_unsigned<T>::value, T>::type
     839        2428 : SaturatingMultiplyAdd(T X, T Y, T A, bool *ResultOverflowed = nullptr) {
     840             :   bool Dummy;
     841        2428 :   bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
     842             : 
     843        2428 :   T Product = SaturatingMultiply(X, Y, &Overflowed);
     844        2428 :   if (Overflowed)
     845             :     return Product;
     846             : 
     847        2413 :   return SaturatingAdd(A, Product, &Overflowed);
     848             : }
     849             : 
     850             : /// Use this rather than HUGE_VALF; the latter causes warnings on MSVC.
     851             : extern const float huge_valf;
     852             : } // End llvm namespace
     853             : 
     854             : #endif

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