LCOV - code coverage report
Current view: top level - include/llvm/Support - MathExtras.h (source / functions) Hit Total Coverage
Test: llvm-toolchain.info Lines: 130 132 98.5 %
Date: 2017-09-14 15:23:50 Functions: 8 9 88.9 %
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 _MSC_VER
      27             : #include <intrin.h>
      28             : #endif
      29             : 
      30             : #ifdef __ANDROID_NDK__
      31             : #include <android/api-level.h>
      32             : #endif
      33             : 
      34             : namespace llvm {
      35             : /// \brief The behavior an operation has on an input of 0.
      36             : enum ZeroBehavior {
      37             :   /// \brief The returned value is undefined.
      38             :   ZB_Undefined,
      39             :   /// \brief The returned value is numeric_limits<T>::max()
      40             :   ZB_Max,
      41             :   /// \brief The returned value is numeric_limits<T>::digits
      42             :   ZB_Width
      43             : };
      44             : 
      45             : namespace detail {
      46             : template <typename T, std::size_t SizeOfT> struct TrailingZerosCounter {
      47             :   static std::size_t count(T Val, ZeroBehavior) {
      48         126 :     if (!Val)
      49             :       return std::numeric_limits<T>::digits;
      50         156 :     if (Val & 0x1)
      51             :       return 0;
      52             : 
      53             :     // Bisection method.
      54             :     std::size_t ZeroBits = 0;
      55             :     T Shift = std::numeric_limits<T>::digits >> 1;
      56             :     T Mask = std::numeric_limits<T>::max() >> Shift;
      57         526 :     while (Shift) {
      58         395 :       if ((Val & Mask) == 0) {
      59         208 :         Val >>= Shift;
      60         208 :         ZeroBits |= Shift;
      61             :       }
      62         395 :       Shift >>= 1;
      63         395 :       Mask >>= Shift;
      64             :     }
      65             :     return ZeroBits;
      66             :   }
      67             : };
      68             : 
      69             : #if __GNUC__ >= 4 || defined(_MSC_VER)
      70             : template <typename T> struct TrailingZerosCounter<T, 4> {
      71             :   static std::size_t count(T Val, ZeroBehavior ZB) {
      72     5600303 :     if (ZB != ZB_Undefined && Val == 0)
      73             :       return 32;
      74             : 
      75             : #if __has_builtin(__builtin_ctz) || LLVM_GNUC_PREREQ(4, 0, 0)
      76    31523094 :     return __builtin_ctz(Val);
      77             : #elif defined(_MSC_VER)
      78             :     unsigned long Index;
      79             :     _BitScanForward(&Index, Val);
      80             :     return Index;
      81             : #endif
      82             :   }
      83             : };
      84             : 
      85             : #if !defined(_MSC_VER) || defined(_M_X64)
      86             : template <typename T> struct TrailingZerosCounter<T, 8> {
      87             :   static std::size_t count(T Val, ZeroBehavior ZB) {
      88    58474449 :     if (ZB != ZB_Undefined && Val == 0)
      89             :       return 64;
      90             : 
      91             : #if __has_builtin(__builtin_ctzll) || LLVM_GNUC_PREREQ(4, 0, 0)
      92    96063042 :     return __builtin_ctzll(Val);
      93             : #elif defined(_MSC_VER)
      94             :     unsigned long Index;
      95             :     _BitScanForward64(&Index, Val);
      96             :     return Index;
      97             : #endif
      98             :   }
      99             : };
     100             : #endif
     101             : #endif
     102             : } // namespace detail
     103             : 
     104             : /// \brief Count number of 0's from the least significant bit to the most
     105             : ///   stopping at the first 1.
     106             : ///
     107             : /// Only unsigned integral types are allowed.
     108             : ///
     109             : /// \param ZB the behavior on an input of 0. Only ZB_Width and ZB_Undefined are
     110             : ///   valid arguments.
     111             : template <typename T>
     112             : std::size_t countTrailingZeros(T Val, ZeroBehavior ZB = ZB_Width) {
     113             :   static_assert(std::numeric_limits<T>::is_integer &&
     114             :                     !std::numeric_limits<T>::is_signed,
     115             :                 "Only unsigned integral types are allowed.");
     116   132706379 :   return llvm::detail::TrailingZerosCounter<T, sizeof(T)>::count(Val, ZB);
     117             : }
     118             : 
     119             : namespace detail {
     120             : template <typename T, std::size_t SizeOfT> struct LeadingZerosCounter {
     121             :   static std::size_t count(T Val, ZeroBehavior) {
     122             :     if (!Val)
     123             :       return std::numeric_limits<T>::digits;
     124             : 
     125             :     // Bisection method.
     126             :     std::size_t ZeroBits = 0;
     127          32 :     for (T Shift = std::numeric_limits<T>::digits >> 1; Shift; Shift >>= 1) {
     128          14 :       T Tmp = Val >> Shift;
     129          14 :       if (Tmp)
     130             :         Val = Tmp;
     131             :       else
     132           6 :         ZeroBits |= Shift;
     133             :     }
     134             :     return ZeroBits;
     135             :   }
     136             : };
     137             : 
     138             : #if __GNUC__ >= 4 || defined(_MSC_VER)
     139             : template <typename T> struct LeadingZerosCounter<T, 4> {
     140             :   static std::size_t count(T Val, ZeroBehavior ZB) {
     141    12479305 :     if (ZB != ZB_Undefined && Val == 0)
     142             :       return 32;
     143             : 
     144             : #if __has_builtin(__builtin_clz) || LLVM_GNUC_PREREQ(4, 0, 0)
     145     8940044 :     return __builtin_clz(Val);
     146             : #elif defined(_MSC_VER)
     147             :     unsigned long Index;
     148             :     _BitScanReverse(&Index, Val);
     149             :     return Index ^ 31;
     150             : #endif
     151             :   }
     152             : };
     153             : 
     154             : #if !defined(_MSC_VER) || defined(_M_X64)
     155             : template <typename T> struct LeadingZerosCounter<T, 8> {
     156             :   static std::size_t count(T Val, ZeroBehavior ZB) {
     157    88687568 :     if (ZB != ZB_Undefined && Val == 0)
     158             :       return 64;
     159             : 
     160             : #if __has_builtin(__builtin_clzll) || LLVM_GNUC_PREREQ(4, 0, 0)
     161    88488350 :     return __builtin_clzll(Val);
     162             : #elif defined(_MSC_VER)
     163             :     unsigned long Index;
     164             :     _BitScanReverse64(&Index, Val);
     165             :     return Index ^ 63;
     166             : #endif
     167             :   }
     168             : };
     169             : #endif
     170             : #endif
     171             : } // namespace detail
     172             : 
     173             : /// \brief Count number of 0's from the most significant bit to the least
     174             : ///   stopping at the first 1.
     175             : ///
     176             : /// Only unsigned integral types are allowed.
     177             : ///
     178             : /// \param ZB the behavior on an input of 0. Only ZB_Width and ZB_Undefined are
     179             : ///   valid arguments.
     180             : template <typename T>
     181             : std::size_t countLeadingZeros(T Val, ZeroBehavior ZB = ZB_Width) {
     182             :   static_assert(std::numeric_limits<T>::is_integer &&
     183             :                     !std::numeric_limits<T>::is_signed,
     184             :                 "Only unsigned integral types are allowed.");
     185   122165636 :   return llvm::detail::LeadingZerosCounter<T, sizeof(T)>::count(Val, ZB);
     186             : }
     187             : 
     188             : /// \brief Get the index of the first set bit starting from the least
     189             : ///   significant bit.
     190             : ///
     191             : /// Only unsigned integral types are allowed.
     192             : ///
     193             : /// \param ZB the behavior on an input of 0. Only ZB_Max and ZB_Undefined are
     194             : ///   valid arguments.
     195             : template <typename T> T findFirstSet(T Val, ZeroBehavior ZB = ZB_Max) {
     196        3584 :   if (ZB == ZB_Max && Val == 0)
     197             :     return std::numeric_limits<T>::max();
     198             : 
     199      285378 :   return countTrailingZeros(Val, ZB_Undefined);
     200             : }
     201             : 
     202             : /// \brief Create a bitmask with the N right-most bits set to 1, and all other
     203             : /// bits set to 0.  Only unsigned types are allowed.
     204             : template <typename T> T maskTrailingOnes(unsigned N) {
     205             :   static_assert(std::is_unsigned<T>::value, "Invalid type!");
     206    55764803 :   const unsigned Bits = CHAR_BIT * sizeof(T);
     207             :   assert(N <= Bits && "Invalid bit index");
     208    55764390 :   return N == 0 ? 0 : (T(-1) >> (Bits - N));
     209             : }
     210             : 
     211             : /// \brief Create a bitmask with the N left-most bits set to 1, and all other
     212             : /// bits set to 0.  Only unsigned types are allowed.
     213             : template <typename T> T maskLeadingOnes(unsigned N) {
     214    87954440 :   return ~maskTrailingOnes<T>(CHAR_BIT * sizeof(T) - N);
     215             : }
     216             : 
     217             : /// \brief Create a bitmask with the N right-most bits set to 0, and all other
     218             : /// bits set to 1.  Only unsigned types are allowed.
     219             : template <typename T> T maskTrailingZeros(unsigned N) {
     220    87954408 :   return maskLeadingOnes<T>(CHAR_BIT * sizeof(T) - N);
     221             : }
     222             : 
     223             : /// \brief Create a bitmask with the N left-most bits set to 0, and all other
     224             : /// bits set to 1.  Only unsigned types are allowed.
     225             : template <typename T> T maskLeadingZeros(unsigned N) {
     226             :   return maskTrailingOnes<T>(CHAR_BIT * sizeof(T) - N);
     227             : }
     228             : 
     229             : /// \brief Get the index of the last set bit starting from the least
     230             : ///   significant bit.
     231             : ///
     232             : /// Only unsigned integral types are allowed.
     233             : ///
     234             : /// \param ZB the behavior on an input of 0. Only ZB_Max and ZB_Undefined are
     235             : ///   valid arguments.
     236             : template <typename T> T findLastSet(T Val, ZeroBehavior ZB = ZB_Max) {
     237       12696 :   if (ZB == ZB_Max && Val == 0)
     238             :     return std::numeric_limits<T>::max();
     239             : 
     240             :   // Use ^ instead of - because both gcc and llvm can remove the associated ^
     241             :   // in the __builtin_clz intrinsic on x86.
     242      700144 :   return countLeadingZeros(Val, ZB_Undefined) ^
     243      700142 :          (std::numeric_limits<T>::digits - 1);
     244             : }
     245             : 
     246             : /// \brief Macro compressed bit reversal table for 256 bits.
     247             : ///
     248             : /// http://graphics.stanford.edu/~seander/bithacks.html#BitReverseTable
     249             : static const unsigned char BitReverseTable256[256] = {
     250             : #define R2(n) n, n + 2 * 64, n + 1 * 64, n + 3 * 64
     251             : #define R4(n) R2(n), R2(n + 2 * 16), R2(n + 1 * 16), R2(n + 3 * 16)
     252             : #define R6(n) R4(n), R4(n + 2 * 4), R4(n + 1 * 4), R4(n + 3 * 4)
     253             :   R6(0), R6(2), R6(1), R6(3)
     254             : #undef R2
     255             : #undef R4
     256             : #undef R6
     257             : };
     258             : 
     259             : /// \brief Reverse the bits in \p Val.
     260             : template <typename T>
     261             : T reverseBits(T Val) {
     262             :   unsigned char in[sizeof(Val)];
     263             :   unsigned char out[sizeof(Val)];
     264       14199 :   std::memcpy(in, &Val, sizeof(Val));
     265       71273 :   for (unsigned i = 0; i < sizeof(Val); ++i)
     266       57074 :     out[(sizeof(Val) - i) - 1] = BitReverseTable256[in[i]];
     267       14199 :   std::memcpy(&Val, out, sizeof(Val));
     268             :   return Val;
     269             : }
     270             : 
     271             : // NOTE: The following support functions use the _32/_64 extensions instead of
     272             : // type overloading so that signed and unsigned integers can be used without
     273             : // ambiguity.
     274             : 
     275             : /// Return the high 32 bits of a 64 bit value.
     276             : constexpr inline uint32_t Hi_32(uint64_t Value) {
     277      384793 :   return static_cast<uint32_t>(Value >> 32);
     278             : }
     279             : 
     280             : /// Return the low 32 bits of a 64 bit value.
     281             : constexpr inline uint32_t Lo_32(uint64_t Value) {
     282      580206 :   return static_cast<uint32_t>(Value);
     283             : }
     284             : 
     285             : /// Make a 64-bit integer from a high / low pair of 32-bit integers.
     286             : constexpr inline uint64_t Make_64(uint32_t High, uint32_t Low) {
     287      297139 :   return ((uint64_t)High << 32) | (uint64_t)Low;
     288             : }
     289             : 
     290             : /// Checks if an integer fits into the given bit width.
     291             : template <unsigned N> constexpr inline bool isInt(int64_t x) {
     292      152700 :   return N >= 64 || (-(INT64_C(1)<<(N-1)) <= x && x < (INT64_C(1)<<(N-1)));
     293             : }
     294             : // Template specializations to get better code for common cases.
     295             : template <> constexpr inline bool isInt<8>(int64_t x) {
     296      538260 :   return static_cast<int8_t>(x) == x;
     297             : }
     298             : template <> constexpr inline bool isInt<16>(int64_t x) {
     299      290179 :   return static_cast<int16_t>(x) == x;
     300             : }
     301             : template <> constexpr inline bool isInt<32>(int64_t x) {
     302     3231572 :   return static_cast<int32_t>(x) == x;
     303             : }
     304             : 
     305             : /// Checks if a signed integer is an N bit number shifted left by S.
     306             : template <unsigned N, unsigned S>
     307             : constexpr inline bool isShiftedInt(int64_t x) {
     308             :   static_assert(
     309             :       N > 0, "isShiftedInt<0> doesn't make sense (refers to a 0-bit number.");
     310             :   static_assert(N + S <= 64, "isShiftedInt<N, S> with N + S > 64 is too wide.");
     311       12575 :   return isInt<N + S>(x) && (x % (UINT64_C(1) << S) == 0);
     312             : }
     313             : 
     314             : /// Checks if an unsigned integer fits into the given bit width.
     315             : ///
     316             : /// This is written as two functions rather than as simply
     317             : ///
     318             : ///   return N >= 64 || X < (UINT64_C(1) << N);
     319             : ///
     320             : /// to keep MSVC from (incorrectly) warning on isUInt<64> that we're shifting
     321             : /// left too many places.
     322             : template <unsigned N>
     323             : constexpr inline typename std::enable_if<(N < 64), bool>::type
     324             : isUInt(uint64_t X) {
     325             :   static_assert(N > 0, "isUInt<0> doesn't make sense");
     326       25897 :   return X < (UINT64_C(1) << (N));
     327             : }
     328             : template <unsigned N>
     329             : constexpr inline typename std::enable_if<N >= 64, bool>::type
     330             : isUInt(uint64_t X) {
     331             :   return true;
     332             : }
     333             : 
     334             : // Template specializations to get better code for common cases.
     335             : template <> constexpr inline bool isUInt<8>(uint64_t x) {
     336       14028 :   return static_cast<uint8_t>(x) == x;
     337             : }
     338             : template <> constexpr inline bool isUInt<16>(uint64_t x) {
     339         750 :   return static_cast<uint16_t>(x) == x;
     340             : }
     341             : template <> constexpr inline bool isUInt<32>(uint64_t x) {
     342        6934 :   return static_cast<uint32_t>(x) == x;
     343             : }
     344             : 
     345             : /// Checks if a unsigned integer is an N bit number shifted left by S.
     346             : template <unsigned N, unsigned S>
     347             : constexpr inline bool isShiftedUInt(uint64_t x) {
     348             :   static_assert(
     349             :       N > 0, "isShiftedUInt<0> doesn't make sense (refers to a 0-bit number)");
     350             :   static_assert(N + S <= 64,
     351             :                 "isShiftedUInt<N, S> with N + S > 64 is too wide.");
     352             :   // Per the two static_asserts above, S must be strictly less than 64.  So
     353             :   // 1 << S is not undefined behavior.
     354        5575 :   return isUInt<N + S>(x) && (x % (UINT64_C(1) << S) == 0);
     355             : }
     356             : 
     357             : /// Gets the maximum value for a N-bit unsigned integer.
     358             : inline uint64_t maxUIntN(uint64_t N) {
     359             :   assert(N > 0 && N <= 64 && "integer width out of range");
     360             : 
     361             :   // uint64_t(1) << 64 is undefined behavior, so we can't do
     362             :   //   (uint64_t(1) << N) - 1
     363             :   // without checking first that N != 64.  But this works and doesn't have a
     364             :   // branch.
     365       14043 :   return UINT64_MAX >> (64 - N);
     366             : }
     367             : 
     368             : /// Gets the minimum value for a N-bit signed integer.
     369             : inline int64_t minIntN(int64_t N) {
     370             :   assert(N > 0 && N <= 64 && "integer width out of range");
     371             : 
     372       15102 :   return -(UINT64_C(1)<<(N-1));
     373             : }
     374             : 
     375             : /// Gets the maximum value for a N-bit signed integer.
     376             : inline int64_t maxIntN(int64_t N) {
     377             :   assert(N > 0 && N <= 64 && "integer width out of range");
     378             : 
     379             :   // This relies on two's complement wraparound when N == 64, so we convert to
     380             :   // int64_t only at the very end to avoid UB.
     381       15005 :   return (UINT64_C(1) << (N - 1)) - 1;
     382             : }
     383             : 
     384             : /// Checks if an unsigned integer fits into the given (dynamic) bit width.
     385             : inline bool isUIntN(unsigned N, uint64_t x) {
     386      197639 :   return N >= 64 || x <= maxUIntN(N);
     387             : }
     388             : 
     389             : /// Checks if an signed integer fits into the given (dynamic) bit width.
     390             : inline bool isIntN(unsigned N, int64_t x) {
     391       54079 :   return N >= 64 || (minIntN(N) <= x && x <= maxIntN(N));
     392             : }
     393             : 
     394             : /// Return true if the argument is a non-empty sequence of ones starting at the
     395             : /// least significant bit with the remainder zero (32 bit version).
     396             : /// Ex. isMask_32(0x0000FFFFU) == true.
     397             : constexpr inline bool isMask_32(uint32_t Value) {
     398        7040 :   return Value && ((Value + 1) & Value) == 0;
     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 (64 bit version).
     403             : constexpr inline bool isMask_64(uint64_t Value) {
     404       42258 :   return Value && ((Value + 1) & Value) == 0;
     405             : }
     406             : 
     407             : /// Return true if the argument contains a non-empty sequence of ones with the
     408             : /// remainder zero (32 bit version.) Ex. isShiftedMask_32(0x0000FF00U) == true.
     409             : constexpr inline bool isShiftedMask_32(uint32_t Value) {
     410         883 :   return Value && isMask_32((Value - 1) | Value);
     411             : }
     412             : 
     413             : /// Return true if the argument contains a non-empty sequence of ones with the
     414             : /// remainder zero (64 bit version.)
     415             : constexpr inline bool isShiftedMask_64(uint64_t Value) {
     416        8911 :   return Value && isMask_64((Value - 1) | Value);
     417             : }
     418             : 
     419             : /// Return true if the argument is a power of two > 0.
     420             : /// Ex. isPowerOf2_32(0x00100000U) == true (32 bit edition.)
     421             : constexpr inline bool isPowerOf2_32(uint32_t Value) {
     422     7476277 :   return Value && !(Value & (Value - 1));
     423             : }
     424             : 
     425             : /// Return true if the argument is a power of two > 0 (64 bit edition.)
     426             : constexpr inline bool isPowerOf2_64(uint64_t Value) {
     427     3454574 :   return Value && !(Value & (Value - 1));
     428             : }
     429             : 
     430             : /// Return a byte-swapped representation of the 16-bit argument.
     431             : inline uint16_t ByteSwap_16(uint16_t Value) {
     432         959 :   return sys::SwapByteOrder_16(Value);
     433             : }
     434             : 
     435             : /// Return a byte-swapped representation of the 32-bit argument.
     436             : inline uint32_t ByteSwap_32(uint32_t Value) {
     437        6880 :   return sys::SwapByteOrder_32(Value);
     438             : }
     439             : 
     440             : /// Return a byte-swapped representation of the 64-bit argument.
     441             : inline uint64_t ByteSwap_64(uint64_t Value) {
     442        2810 :   return sys::SwapByteOrder_64(Value);
     443             : }
     444             : 
     445             : /// \brief Count the number of ones from the most significant bit to the first
     446             : /// zero bit.
     447             : ///
     448             : /// Ex. countLeadingOnes(0xFF0FFF00) == 8.
     449             : /// Only unsigned integral types are allowed.
     450             : ///
     451             : /// \param ZB the behavior on an input of all ones. Only ZB_Width and
     452             : /// ZB_Undefined are valid arguments.
     453             : template <typename T>
     454             : std::size_t countLeadingOnes(T Value, ZeroBehavior ZB = ZB_Width) {
     455             :   static_assert(std::numeric_limits<T>::is_integer &&
     456             :                     !std::numeric_limits<T>::is_signed,
     457             :                 "Only unsigned integral types are allowed.");
     458    12516408 :   return countLeadingZeros(~Value, ZB);
     459             : }
     460             : 
     461             : /// \brief Count the number of ones from the least significant bit to the first
     462             : /// zero bit.
     463             : ///
     464             : /// Ex. countTrailingOnes(0x00FF00FF) == 8.
     465             : /// Only unsigned integral types are allowed.
     466             : ///
     467             : /// \param ZB the behavior on an input of all ones. Only ZB_Width and
     468             : /// ZB_Undefined are valid arguments.
     469             : template <typename T>
     470             : std::size_t countTrailingOnes(T Value, ZeroBehavior ZB = ZB_Width) {
     471             :   static_assert(std::numeric_limits<T>::is_integer &&
     472             :                     !std::numeric_limits<T>::is_signed,
     473             :                 "Only unsigned integral types are allowed.");
     474    73377588 :   return countTrailingZeros(~Value, ZB);
     475             : }
     476             : 
     477             : namespace detail {
     478             : template <typename T, std::size_t SizeOfT> struct PopulationCounter {
     479             :   static unsigned count(T Value) {
     480             :     // Generic version, forward to 32 bits.
     481             :     static_assert(SizeOfT <= 4, "Not implemented!");
     482             : #if __GNUC__ >= 4
     483      932904 :     return __builtin_popcount(Value);
     484             : #else
     485             :     uint32_t v = Value;
     486             :     v = v - ((v >> 1) & 0x55555555);
     487             :     v = (v & 0x33333333) + ((v >> 2) & 0x33333333);
     488             :     return ((v + (v >> 4) & 0xF0F0F0F) * 0x1010101) >> 24;
     489             : #endif
     490             :   }
     491             : };
     492             : 
     493             : template <typename T> struct PopulationCounter<T, 8> {
     494             :   static unsigned count(T Value) {
     495             : #if __GNUC__ >= 4
     496     9360219 :     return __builtin_popcountll(Value);
     497             : #else
     498             :     uint64_t v = Value;
     499             :     v = v - ((v >> 1) & 0x5555555555555555ULL);
     500             :     v = (v & 0x3333333333333333ULL) + ((v >> 2) & 0x3333333333333333ULL);
     501             :     v = (v + (v >> 4)) & 0x0F0F0F0F0F0F0F0FULL;
     502             :     return unsigned((uint64_t)(v * 0x0101010101010101ULL) >> 56);
     503             : #endif
     504             :   }
     505             : };
     506             : } // namespace detail
     507             : 
     508             : /// \brief Count the number of set bits in a value.
     509             : /// Ex. countPopulation(0xF000F000) = 8
     510             : /// Returns 0 if the word is zero.
     511             : template <typename T>
     512             : inline unsigned countPopulation(T Value) {
     513             :   static_assert(std::numeric_limits<T>::is_integer &&
     514             :                     !std::numeric_limits<T>::is_signed,
     515             :                 "Only unsigned integral types are allowed.");
     516    10293123 :   return detail::PopulationCounter<T, sizeof(T)>::count(Value);
     517             : }
     518             : 
     519             : /// Return the log base 2 of the specified value.
     520           0 : inline double Log2(double Value) {
     521             : #if defined(__ANDROID_API__) && __ANDROID_API__ < 18
     522             :   return __builtin_log(Value) / __builtin_log(2.0);
     523             : #else
     524           0 :   return log2(Value);
     525             : #endif
     526             : }
     527             : 
     528             : /// Return the floor log base 2 of the specified value, -1 if the value is zero.
     529             : /// (32 bit edition.)
     530             : /// Ex. Log2_32(32) == 5, Log2_32(1) == 0, Log2_32(0) == -1, Log2_32(6) == 2
     531             : inline unsigned Log2_32(uint32_t Value) {
     532     9091962 :   return 31 - countLeadingZeros(Value);
     533             : }
     534             : 
     535             : /// Return the floor log base 2 of the specified value, -1 if the value is zero.
     536             : /// (64 bit edition.)
     537             : inline unsigned Log2_64(uint64_t Value) {
     538       86023 :   return 63 - countLeadingZeros(Value);
     539             : }
     540             : 
     541             : /// Return the ceil log base 2 of the specified value, 32 if the value is zero.
     542             : /// (32 bit edition).
     543             : /// Ex. Log2_32_Ceil(32) == 5, Log2_32_Ceil(1) == 0, Log2_32_Ceil(6) == 3
     544             : inline unsigned Log2_32_Ceil(uint32_t Value) {
     545     8743208 :   return 32 - countLeadingZeros(Value - 1);
     546             : }
     547             : 
     548             : /// Return the ceil log base 2 of the specified value, 64 if the value is zero.
     549             : /// (64 bit edition.)
     550             : inline unsigned Log2_64_Ceil(uint64_t Value) {
     551    67055872 :   return 64 - countLeadingZeros(Value - 1);
     552             : }
     553             : 
     554             : /// Return the greatest common divisor of the values using Euclid's algorithm.
     555             : inline uint64_t GreatestCommonDivisor64(uint64_t A, uint64_t B) {
     556        5634 :   while (B) {
     557        3523 :     uint64_t T = B;
     558        3523 :     B = A % B;
     559        3523 :     A = T;
     560             :   }
     561             :   return A;
     562             : }
     563             : 
     564             : /// This function takes a 64-bit integer and returns the bit equivalent double.
     565             : inline double BitsToDouble(uint64_t Bits) {
     566             :   double D;
     567             :   static_assert(sizeof(uint64_t) == sizeof(double), "Unexpected type sizes");
     568             :   memcpy(&D, &Bits, sizeof(Bits));
     569             :   return D;
     570             : }
     571             : 
     572             : /// This function takes a 32-bit integer and returns the bit equivalent float.
     573             : inline float BitsToFloat(uint32_t Bits) {
     574             :   float F;
     575             :   static_assert(sizeof(uint32_t) == sizeof(float), "Unexpected type sizes");
     576             :   memcpy(&F, &Bits, sizeof(Bits));
     577             :   return F;
     578             : }
     579             : 
     580             : /// This function takes a double and returns the bit equivalent 64-bit integer.
     581             : /// Note that copying doubles around changes the bits of NaNs on some hosts,
     582             : /// notably x86, so this routine cannot be used if these bits are needed.
     583             : inline uint64_t DoubleToBits(double Double) {
     584             :   uint64_t Bits;
     585             :   static_assert(sizeof(uint64_t) == sizeof(double), "Unexpected type sizes");
     586     3193587 :   memcpy(&Bits, &Double, sizeof(Double));
     587             :   return Bits;
     588             : }
     589             : 
     590             : /// This function takes a float and returns the bit equivalent 32-bit integer.
     591             : /// Note that copying floats around changes the bits of NaNs on some hosts,
     592             : /// notably x86, so this routine cannot be used if these bits are needed.
     593             : inline uint32_t FloatToBits(float Float) {
     594             :   uint32_t Bits;
     595             :   static_assert(sizeof(uint32_t) == sizeof(float), "Unexpected type sizes");
     596     2737037 :   memcpy(&Bits, &Float, sizeof(Float));
     597             :   return Bits;
     598             : }
     599             : 
     600             : /// A and B are either alignments or offsets. Return the minimum alignment that
     601             : /// may be assumed after adding the two together.
     602             : constexpr inline uint64_t MinAlign(uint64_t A, uint64_t B) {
     603             :   // The largest power of 2 that divides both A and B.
     604             :   //
     605             :   // Replace "-Value" by "1+~Value" in the following commented code to avoid
     606             :   // MSVC warning C4146
     607             :   //    return (A | B) & -(A | B);
     608    14568878 :   return (A | B) & (1 + ~(A | B));
     609             : }
     610             : 
     611             : /// \brief Aligns \c Addr to \c Alignment bytes, rounding up.
     612             : ///
     613             : /// Alignment should be a power of two.  This method rounds up, so
     614             : /// alignAddr(7, 4) == 8 and alignAddr(8, 4) == 8.
     615             : inline uintptr_t alignAddr(const void *Addr, size_t Alignment) {
     616             :   assert(Alignment && isPowerOf2_64((uint64_t)Alignment) &&
     617             :          "Alignment is not a power of two!");
     618             : 
     619             :   assert((uintptr_t)Addr + Alignment - 1 >= (uintptr_t)Addr);
     620             : 
     621   373993378 :   return (((uintptr_t)Addr + Alignment - 1) & ~(uintptr_t)(Alignment - 1));
     622             : }
     623             : 
     624             : /// \brief Returns the necessary adjustment for aligning \c Ptr to \c Alignment
     625             : /// bytes, rounding up.
     626             : inline size_t alignmentAdjustment(const void *Ptr, size_t Alignment) {
     627   368280489 :   return alignAddr(Ptr, Alignment) - (uintptr_t)Ptr;
     628             : }
     629             : 
     630             : /// Returns the next power of two (in 64-bits) that is strictly greater than A.
     631             : /// Returns zero on overflow.
     632             : inline uint64_t NextPowerOf2(uint64_t A) {
     633    91391229 :   A |= (A >> 1);
     634    91391229 :   A |= (A >> 2);
     635    91391229 :   A |= (A >> 4);
     636    91391229 :   A |= (A >> 8);
     637    91391229 :   A |= (A >> 16);
     638    91391229 :   A |= (A >> 32);
     639    46617330 :   return A + 1;
     640             : }
     641             : 
     642             : /// Returns the power of two which is less than or equal to the given value.
     643             : /// Essentially, it is a floor operation across the domain of powers of two.
     644             : inline uint64_t PowerOf2Floor(uint64_t A) {
     645       11388 :   if (!A) return 0;
     646       48349 :   return 1ull << (63 - countLeadingZeros(A, ZB_Undefined));
     647             : }
     648             : 
     649             : /// Returns the power of two which is greater than or equal to the given value.
     650             : /// Essentially, it is a ceil operation across the domain of powers of two.
     651             : inline uint64_t PowerOf2Ceil(uint64_t A) {
     652      142541 :   if (!A)
     653             :     return 0;
     654      284832 :   return NextPowerOf2(A - 1);
     655             : }
     656             : 
     657             : /// Returns the next integer (mod 2**64) that is greater than or equal to
     658             : /// \p Value and is a multiple of \p Align. \p Align must be non-zero.
     659             : ///
     660             : /// If non-zero \p Skew is specified, the return value will be a minimal
     661             : /// integer that is greater than or equal to \p Value and equal to
     662             : /// \p Align * N + \p Skew for some integer N. If \p Skew is larger than
     663             : /// \p Align, its value is adjusted to '\p Skew mod \p Align'.
     664             : ///
     665             : /// Examples:
     666             : /// \code
     667             : ///   alignTo(5, 8) = 8
     668             : ///   alignTo(17, 8) = 24
     669             : ///   alignTo(~0LL, 8) = 0
     670             : ///   alignTo(321, 255) = 510
     671             : ///
     672             : ///   alignTo(5, 8, 7) = 7
     673             : ///   alignTo(17, 8, 1) = 17
     674             : ///   alignTo(~0LL, 8, 3) = 3
     675             : ///   alignTo(321, 255, 42) = 552
     676             : /// \endcode
     677             : inline uint64_t alignTo(uint64_t Value, uint64_t Align, uint64_t Skew = 0) {
     678             :   assert(Align != 0u && "Align can't be 0.");
     679   186446816 :   Skew %= Align;
     680   149450654 :   return (Value + Align - 1 - Skew) / Align * Align + Skew;
     681             : }
     682             : 
     683             : /// Returns the next integer (mod 2**64) that is greater than or equal to
     684             : /// \p Value and is a multiple of \c Align. \c Align must be non-zero.
     685             : template <uint64_t Align> constexpr inline uint64_t alignTo(uint64_t Value) {
     686             :   static_assert(Align != 0u, "Align must be non-zero");
     687        7160 :   return (Value + Align - 1) / Align * Align;
     688             : }
     689             : 
     690             : /// Returns the integer ceil(Numerator / Denominator).
     691             : inline uint64_t divideCeil(uint64_t Numerator, uint64_t Denominator) {
     692        4699 :   return alignTo(Numerator, Denominator) / Denominator;
     693             : }
     694             : 
     695             : /// \c alignTo for contexts where a constant expression is required.
     696             : /// \sa alignTo
     697             : ///
     698             : /// \todo FIXME: remove when \c constexpr becomes really \c constexpr
     699             : template <uint64_t Align>
     700             : struct AlignTo {
     701             :   static_assert(Align != 0u, "Align must be non-zero");
     702             :   template <uint64_t Value>
     703             :   struct from_value {
     704             :     static const uint64_t value = (Value + Align - 1) / Align * Align;
     705             :   };
     706             : };
     707             : 
     708             : /// Returns the largest uint64_t less than or equal to \p Value and is
     709             : /// \p Skew mod \p Align. \p Align must be non-zero
     710             : inline uint64_t alignDown(uint64_t Value, uint64_t Align, uint64_t Skew = 0) {
     711             :   assert(Align != 0u && "Align can't be 0.");
     712      418501 :   Skew %= Align;
     713      418501 :   return (Value - Skew) / Align * Align + Skew;
     714             : }
     715             : 
     716             : /// Returns the offset to the next integer (mod 2**64) that is greater than
     717             : /// or equal to \p Value and is a multiple of \p Align. \p Align must be
     718             : /// non-zero.
     719             : inline uint64_t OffsetToAlignment(uint64_t Value, uint64_t Align) {
     720      909318 :   return alignTo(Value, Align) - Value;
     721             : }
     722             : 
     723             : /// Sign-extend the number in the bottom B bits of X to a 32-bit integer.
     724             : /// Requires 0 < B <= 32.
     725             : template <unsigned B> constexpr inline int32_t SignExtend32(uint32_t X) {
     726             :   static_assert(B > 0, "Bit width can't be 0.");
     727             :   static_assert(B <= 32, "Bit width out of range.");
     728        4842 :   return int32_t(X << (32 - B)) >> (32 - B);
     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             : inline int32_t SignExtend32(uint32_t X, unsigned B) {
     734             :   assert(B > 0 && "Bit width can't be 0.");
     735             :   assert(B <= 32 && "Bit width out of range.");
     736         136 :   return int32_t(X << (32 - B)) >> (32 - B);
     737             : }
     738             : 
     739             : /// Sign-extend the number in the bottom B bits of X to a 64-bit integer.
     740             : /// Requires 0 < B < 64.
     741             : template <unsigned B> constexpr inline int64_t SignExtend64(uint64_t x) {
     742             :   static_assert(B > 0, "Bit width can't be 0.");
     743             :   static_assert(B <= 64, "Bit width out of range.");
     744        9919 :   return int64_t(x << (64 - B)) >> (64 - 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             : inline int64_t SignExtend64(uint64_t X, unsigned B) {
     750             :   assert(B > 0 && "Bit width can't be 0.");
     751             :   assert(B <= 64 && "Bit width out of range.");
     752    79537840 :   return int64_t(X << (64 - B)) >> (64 - B);
     753             : }
     754             : 
     755             : /// Subtract two unsigned integers, X and Y, of type T and return the absolute
     756             : /// value of the result.
     757             : template <typename T>
     758             : typename std::enable_if<std::is_unsigned<T>::value, T>::type
     759             : AbsoluteDifference(T X, T Y) {
     760          66 :   return std::max(X, Y) - std::min(X, Y);
     761             : }
     762             : 
     763             : /// Add two unsigned integers, X and Y, of type T.  Clamp the result to the
     764             : /// maximum representable value of T on overflow.  ResultOverflowed indicates if
     765             : /// the result is larger than the maximum representable value of type T.
     766             : template <typename T>
     767             : typename std::enable_if<std::is_unsigned<T>::value, T>::type
     768             : SaturatingAdd(T X, T Y, bool *ResultOverflowed = nullptr) {
     769             :   bool Dummy;
     770     1320907 :   bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
     771             :   // Hacker's Delight, p. 29
     772     1320907 :   T Z = X + Y;
     773     1320907 :   Overflowed = (Z < X || Z < Y);
     774     1320867 :   if (Overflowed)
     775             :     return std::numeric_limits<T>::max();
     776             :   else
     777             :     return Z;
     778             : }
     779             : 
     780             : /// Multiply two unsigned integers, X and Y, of type T.  Clamp the result to the
     781             : /// maximum representable value of T on overflow.  ResultOverflowed indicates if
     782             : /// the result is larger than the maximum representable value of type T.
     783             : template <typename T>
     784             : typename std::enable_if<std::is_unsigned<T>::value, T>::type
     785        3034 : SaturatingMultiply(T X, T Y, bool *ResultOverflowed = nullptr) {
     786             :   bool Dummy;
     787        3114 :   bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
     788             : 
     789             :   // Hacker's Delight, p. 30 has a different algorithm, but we don't use that
     790             :   // because it fails for uint16_t (where multiplication can have undefined
     791             :   // behavior due to promotion to int), and requires a division in addition
     792             :   // to the multiplication.
     793             : 
     794        3105 :   Overflowed = false;
     795             : 
     796             :   // Log2(Z) would be either Log2Z or Log2Z + 1.
     797             :   // Special case: if X or Y is 0, Log2_64 gives -1, and Log2Z
     798             :   // will necessarily be less than Log2Max as desired.
     799        6642 :   int Log2Z = Log2_64(X) + Log2_64(Y);
     800        3114 :   const T Max = std::numeric_limits<T>::max();
     801        3114 :   int Log2Max = Log2_64(Max);
     802        3034 :   if (Log2Z < Log2Max) {
     803        2493 :     return X * Y;
     804             :   }
     805         541 :   if (Log2Z > Log2Max) {
     806          39 :     Overflowed = true;
     807          15 :     return Max;
     808             :   }
     809             : 
     810             :   // We're going to use the top bit, and maybe overflow one
     811             :   // bit past it. Multiply all but the bottom bit then add
     812             :   // that on at the end.
     813         526 :   T Z = (X >> 1) * Y;
     814         526 :   if (Z & ~(Max >> 1)) {
     815         112 :     Overflowed = true;
     816         112 :     return Max;
     817             :   }
     818         414 :   Z <<= 1;
     819         414 :   if (X & 1)
     820         413 :     return SaturatingAdd(Z, Y, ResultOverflowed);
     821             : 
     822             :   return Z;
     823             : }
     824             : 
     825             : /// Multiply two unsigned integers, X and Y, and add the unsigned integer, A to
     826             : /// the product. Clamp the result to the maximum representable value of T on
     827             : /// overflow. ResultOverflowed indicates if the result is larger than the
     828             : /// maximum representable value of type T.
     829             : template <typename T>
     830             : typename std::enable_if<std::is_unsigned<T>::value, T>::type
     831        2227 : SaturatingMultiplyAdd(T X, T Y, T A, bool *ResultOverflowed = nullptr) {
     832             :   bool Dummy;
     833        2227 :   bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
     834             : 
     835        2227 :   T Product = SaturatingMultiply(X, Y, &Overflowed);
     836        2227 :   if (Overflowed)
     837             :     return Product;
     838             : 
     839        2212 :   return SaturatingAdd(A, Product, &Overflowed);
     840             : }
     841             : 
     842             : /// Use this rather than HUGE_VALF; the latter causes warnings on MSVC.
     843             : extern const float huge_valf;
     844             : } // End llvm namespace
     845             : 
     846             : #endif

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