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+//===-- llvm/Support/MathExtras.h - Useful math functions -------*- C++ -*-===//
+//
+// The LLVM Compiler Infrastructure
+//
+// This file is distributed under the University of Illinois Open Source
+// License. See LICENSE.TXT for details.
+//
+//===----------------------------------------------------------------------===//
+//
+// This file contains some functions that are useful for math stuff.
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_SUPPORT_MATHEXTRAS_H
+#define LLVM_SUPPORT_MATHEXTRAS_H
+
+#include "llvm/Support/Compiler.h"
+#include "llvm/Support/SwapByteOrder.h"
+#include <algorithm>
+#include <cassert>
+#include <climits>
+#include <cstring>
+#include <limits>
+#include <type_traits>
+
+#ifdef _MSC_VER
+#include <intrin.h>
+#endif
+
+#ifdef __ANDROID_NDK__
+#include <android/api-level.h>
+#endif
+
+namespace llvm {
+/// \brief The behavior an operation has on an input of 0.
+enum ZeroBehavior {
+ /// \brief The returned value is undefined.
+ ZB_Undefined,
+ /// \brief The returned value is numeric_limits<T>::max()
+ ZB_Max,
+ /// \brief The returned value is numeric_limits<T>::digits
+ ZB_Width
+};
+
+namespace detail {
+template <typename T, std::size_t SizeOfT> struct TrailingZerosCounter {
+ static std::size_t count(T Val, ZeroBehavior) {
+ if (!Val)
+ return std::numeric_limits<T>::digits;
+ if (Val & 0x1)
+ return 0;
+
+ // Bisection method.
+ std::size_t ZeroBits = 0;
+ T Shift = std::numeric_limits<T>::digits >> 1;
+ T Mask = std::numeric_limits<T>::max() >> Shift;
+ while (Shift) {
+ if ((Val & Mask) == 0) {
+ Val >>= Shift;
+ ZeroBits |= Shift;
+ }
+ Shift >>= 1;
+ Mask >>= Shift;
+ }
+ return ZeroBits;
+ }
+};
+
+#if __GNUC__ >= 4 || defined(_MSC_VER)
+template <typename T> struct TrailingZerosCounter<T, 4> {
+ static std::size_t count(T Val, ZeroBehavior ZB) {
+ if (ZB != ZB_Undefined && Val == 0)
+ return 32;
+
+#if __has_builtin(__builtin_ctz) || LLVM_GNUC_PREREQ(4, 0, 0)
+ return __builtin_ctz(Val);
+#elif defined(_MSC_VER)
+ unsigned long Index;
+ _BitScanForward(&Index, Val);
+ return Index;
+#endif
+ }
+};
+
+#if !defined(_MSC_VER) || defined(_M_X64)
+template <typename T> struct TrailingZerosCounter<T, 8> {
+ static std::size_t count(T Val, ZeroBehavior ZB) {
+ if (ZB != ZB_Undefined && Val == 0)
+ return 64;
+
+#if __has_builtin(__builtin_ctzll) || LLVM_GNUC_PREREQ(4, 0, 0)
+ return __builtin_ctzll(Val);
+#elif defined(_MSC_VER)
+ unsigned long Index;
+ _BitScanForward64(&Index, Val);
+ return Index;
+#endif
+ }
+};
+#endif
+#endif
+} // namespace detail
+
+/// \brief Count number of 0's from the least significant bit to the most
+/// stopping at the first 1.
+///
+/// Only unsigned integral types are allowed.
+///
+/// \param ZB the behavior on an input of 0. Only ZB_Width and ZB_Undefined are
+/// valid arguments.
+template <typename T>
+std::size_t countTrailingZeros(T Val, ZeroBehavior ZB = ZB_Width) {
+ static_assert(std::numeric_limits<T>::is_integer &&
+ !std::numeric_limits<T>::is_signed,
+ "Only unsigned integral types are allowed.");
+ return llvm::detail::TrailingZerosCounter<T, sizeof(T)>::count(Val, ZB);
+}
+
+namespace detail {
+template <typename T, std::size_t SizeOfT> struct LeadingZerosCounter {
+ static std::size_t count(T Val, ZeroBehavior) {
+ if (!Val)
+ return std::numeric_limits<T>::digits;
+
+ // Bisection method.
+ std::size_t ZeroBits = 0;
+ for (T Shift = std::numeric_limits<T>::digits >> 1; Shift; Shift >>= 1) {
+ T Tmp = Val >> Shift;
+ if (Tmp)
+ Val = Tmp;
+ else
+ ZeroBits |= Shift;
+ }
+ return ZeroBits;
+ }
+};
+
+#if __GNUC__ >= 4 || defined(_MSC_VER)
+template <typename T> struct LeadingZerosCounter<T, 4> {
+ static std::size_t count(T Val, ZeroBehavior ZB) {
+ if (ZB != ZB_Undefined && Val == 0)
+ return 32;
+
+#if __has_builtin(__builtin_clz) || LLVM_GNUC_PREREQ(4, 0, 0)
+ return __builtin_clz(Val);
+#elif defined(_MSC_VER)
+ unsigned long Index;
+ _BitScanReverse(&Index, Val);
+ return Index ^ 31;
+#endif
+ }
+};
+
+#if !defined(_MSC_VER) || defined(_M_X64)
+template <typename T> struct LeadingZerosCounter<T, 8> {
+ static std::size_t count(T Val, ZeroBehavior ZB) {
+ if (ZB != ZB_Undefined && Val == 0)
+ return 64;
+
+#if __has_builtin(__builtin_clzll) || LLVM_GNUC_PREREQ(4, 0, 0)
+ return __builtin_clzll(Val);
+#elif defined(_MSC_VER)
+ unsigned long Index;
+ _BitScanReverse64(&Index, Val);
+ return Index ^ 63;
+#endif
+ }
+};
+#endif
+#endif
+} // namespace detail
+
+/// \brief Count number of 0's from the most significant bit to the least
+/// stopping at the first 1.
+///
+/// Only unsigned integral types are allowed.
+///
+/// \param ZB the behavior on an input of 0. Only ZB_Width and ZB_Undefined are
+/// valid arguments.
+template <typename T>
+std::size_t countLeadingZeros(T Val, ZeroBehavior ZB = ZB_Width) {
+ static_assert(std::numeric_limits<T>::is_integer &&
+ !std::numeric_limits<T>::is_signed,
+ "Only unsigned integral types are allowed.");
+ return llvm::detail::LeadingZerosCounter<T, sizeof(T)>::count(Val, ZB);
+}
+
+/// \brief Get the index of the first set bit starting from the least
+/// significant bit.
+///
+/// Only unsigned integral types are allowed.
+///
+/// \param ZB the behavior on an input of 0. Only ZB_Max and ZB_Undefined are
+/// valid arguments.
+template <typename T> T findFirstSet(T Val, ZeroBehavior ZB = ZB_Max) {
+ if (ZB == ZB_Max && Val == 0)
+ return std::numeric_limits<T>::max();
+
+ return countTrailingZeros(Val, ZB_Undefined);
+}
+
+/// \brief Create a bitmask with the N right-most bits set to 1, and all other
+/// bits set to 0. Only unsigned types are allowed.
+template <typename T> T maskTrailingOnes(unsigned N) {
+ static_assert(std::is_unsigned<T>::value, "Invalid type!");
+ const unsigned Bits = CHAR_BIT * sizeof(T);
+ assert(N <= Bits && "Invalid bit index");
+ return N == 0 ? 0 : (T(-1) >> (Bits - N));
+}
+
+/// \brief Create a bitmask with the N left-most bits set to 1, and all other
+/// bits set to 0. Only unsigned types are allowed.
+template <typename T> T maskLeadingOnes(unsigned N) {
+ return ~maskTrailingOnes<T>(CHAR_BIT * sizeof(T) - N);
+}
+
+/// \brief Create a bitmask with the N right-most bits set to 0, and all other
+/// bits set to 1. Only unsigned types are allowed.
+template <typename T> T maskTrailingZeros(unsigned N) {
+ return maskLeadingOnes<T>(CHAR_BIT * sizeof(T) - N);
+}
+
+/// \brief Create a bitmask with the N left-most bits set to 0, and all other
+/// bits set to 1. Only unsigned types are allowed.
+template <typename T> T maskLeadingZeros(unsigned N) {
+ return maskTrailingOnes<T>(CHAR_BIT * sizeof(T) - N);
+}
+
+/// \brief Get the index of the last set bit starting from the least
+/// significant bit.
+///
+/// Only unsigned integral types are allowed.
+///
+/// \param ZB the behavior on an input of 0. Only ZB_Max and ZB_Undefined are
+/// valid arguments.
+template <typename T> T findLastSet(T Val, ZeroBehavior ZB = ZB_Max) {
+ if (ZB == ZB_Max && Val == 0)
+ return std::numeric_limits<T>::max();
+
+ // Use ^ instead of - because both gcc and llvm can remove the associated ^
+ // in the __builtin_clz intrinsic on x86.
+ return countLeadingZeros(Val, ZB_Undefined) ^
+ (std::numeric_limits<T>::digits - 1);
+}
+
+/// \brief Macro compressed bit reversal table for 256 bits.
+///
+/// http://graphics.stanford.edu/~seander/bithacks.html#BitReverseTable
+static const unsigned char BitReverseTable256[256] = {
+#define R2(n) n, n + 2 * 64, n + 1 * 64, n + 3 * 64
+#define R4(n) R2(n), R2(n + 2 * 16), R2(n + 1 * 16), R2(n + 3 * 16)
+#define R6(n) R4(n), R4(n + 2 * 4), R4(n + 1 * 4), R4(n + 3 * 4)
+ R6(0), R6(2), R6(1), R6(3)
+#undef R2
+#undef R4
+#undef R6
+};
+
+/// \brief Reverse the bits in \p Val.
+template <typename T>
+T reverseBits(T Val) {
+ unsigned char in[sizeof(Val)];
+ unsigned char out[sizeof(Val)];
+ std::memcpy(in, &Val, sizeof(Val));
+ for (unsigned i = 0; i < sizeof(Val); ++i)
+ out[(sizeof(Val) - i) - 1] = BitReverseTable256[in[i]];
+ std::memcpy(&Val, out, sizeof(Val));
+ return Val;
+}
+
+// NOTE: The following support functions use the _32/_64 extensions instead of
+// type overloading so that signed and unsigned integers can be used without
+// ambiguity.
+
+/// Return the high 32 bits of a 64 bit value.
+constexpr inline uint32_t Hi_32(uint64_t Value) {
+ return static_cast<uint32_t>(Value >> 32);
+}
+
+/// Return the low 32 bits of a 64 bit value.
+constexpr inline uint32_t Lo_32(uint64_t Value) {
+ return static_cast<uint32_t>(Value);
+}
+
+/// Make a 64-bit integer from a high / low pair of 32-bit integers.
+constexpr inline uint64_t Make_64(uint32_t High, uint32_t Low) {
+ return ((uint64_t)High << 32) | (uint64_t)Low;
+}
+
+/// Checks if an integer fits into the given bit width.
+template <unsigned N> constexpr inline bool isInt(int64_t x) {
+ return N >= 64 || (-(INT64_C(1)<<(N-1)) <= x && x < (INT64_C(1)<<(N-1)));
+}
+// Template specializations to get better code for common cases.
+template <> constexpr inline bool isInt<8>(int64_t x) {
+ return static_cast<int8_t>(x) == x;
+}
+template <> constexpr inline bool isInt<16>(int64_t x) {
+ return static_cast<int16_t>(x) == x;
+}
+template <> constexpr inline bool isInt<32>(int64_t x) {
+ return static_cast<int32_t>(x) == x;
+}
+
+/// Checks if a signed integer is an N bit number shifted left by S.
+template <unsigned N, unsigned S>
+constexpr inline bool isShiftedInt(int64_t x) {
+ static_assert(
+ N > 0, "isShiftedInt<0> doesn't make sense (refers to a 0-bit number.");
+ static_assert(N + S <= 64, "isShiftedInt<N, S> with N + S > 64 is too wide.");
+ return isInt<N + S>(x) && (x % (UINT64_C(1) << S) == 0);
+}
+
+/// Checks if an unsigned integer fits into the given bit width.
+///
+/// This is written as two functions rather than as simply
+///
+/// return N >= 64 || X < (UINT64_C(1) << N);
+///
+/// to keep MSVC from (incorrectly) warning on isUInt<64> that we're shifting
+/// left too many places.
+template <unsigned N>
+constexpr inline typename std::enable_if<(N < 64), bool>::type
+isUInt(uint64_t X) {
+ static_assert(N > 0, "isUInt<0> doesn't make sense");
+ return X < (UINT64_C(1) << (N));
+}
+template <unsigned N>
+constexpr inline typename std::enable_if<N >= 64, bool>::type
+isUInt(uint64_t X) {
+ return true;
+}
+
+// Template specializations to get better code for common cases.
+template <> constexpr inline bool isUInt<8>(uint64_t x) {
+ return static_cast<uint8_t>(x) == x;
+}
+template <> constexpr inline bool isUInt<16>(uint64_t x) {
+ return static_cast<uint16_t>(x) == x;
+}
+template <> constexpr inline bool isUInt<32>(uint64_t x) {
+ return static_cast<uint32_t>(x) == x;
+}
+
+/// Checks if a unsigned integer is an N bit number shifted left by S.
+template <unsigned N, unsigned S>
+constexpr inline bool isShiftedUInt(uint64_t x) {
+ static_assert(
+ N > 0, "isShiftedUInt<0> doesn't make sense (refers to a 0-bit number)");
+ static_assert(N + S <= 64,
+ "isShiftedUInt<N, S> with N + S > 64 is too wide.");
+ // Per the two static_asserts above, S must be strictly less than 64. So
+ // 1 << S is not undefined behavior.
+ return isUInt<N + S>(x) && (x % (UINT64_C(1) << S) == 0);
+}
+
+/// Gets the maximum value for a N-bit unsigned integer.
+inline uint64_t maxUIntN(uint64_t N) {
+ assert(N > 0 && N <= 64 && "integer width out of range");
+
+ // uint64_t(1) << 64 is undefined behavior, so we can't do
+ // (uint64_t(1) << N) - 1
+ // without checking first that N != 64. But this works and doesn't have a
+ // branch.
+ return UINT64_MAX >> (64 - N);
+}
+
+/// Gets the minimum value for a N-bit signed integer.
+inline int64_t minIntN(int64_t N) {
+ assert(N > 0 && N <= 64 && "integer width out of range");
+
+ return -(UINT64_C(1)<<(N-1));
+}
+
+/// Gets the maximum value for a N-bit signed integer.
+inline int64_t maxIntN(int64_t N) {
+ assert(N > 0 && N <= 64 && "integer width out of range");
+
+ // This relies on two's complement wraparound when N == 64, so we convert to
+ // int64_t only at the very end to avoid UB.
+ return (UINT64_C(1) << (N - 1)) - 1;
+}
+
+/// Checks if an unsigned integer fits into the given (dynamic) bit width.
+inline bool isUIntN(unsigned N, uint64_t x) {
+ return N >= 64 || x <= maxUIntN(N);
+}
+
+/// Checks if an signed integer fits into the given (dynamic) bit width.
+inline bool isIntN(unsigned N, int64_t x) {
+ return N >= 64 || (minIntN(N) <= x && x <= maxIntN(N));
+}
+
+/// Return true if the argument is a non-empty sequence of ones starting at the
+/// least significant bit with the remainder zero (32 bit version).
+/// Ex. isMask_32(0x0000FFFFU) == true.
+constexpr inline bool isMask_32(uint32_t Value) {
+ return Value && ((Value + 1) & Value) == 0;
+}
+
+/// Return true if the argument is a non-empty sequence of ones starting at the
+/// least significant bit with the remainder zero (64 bit version).
+constexpr inline bool isMask_64(uint64_t Value) {
+ return Value && ((Value + 1) & Value) == 0;
+}
+
+/// Return true if the argument contains a non-empty sequence of ones with the
+/// remainder zero (32 bit version.) Ex. isShiftedMask_32(0x0000FF00U) == true.
+constexpr inline bool isShiftedMask_32(uint32_t Value) {
+ return Value && isMask_32((Value - 1) | Value);
+}
+
+/// Return true if the argument contains a non-empty sequence of ones with the
+/// remainder zero (64 bit version.)
+constexpr inline bool isShiftedMask_64(uint64_t Value) {
+ return Value && isMask_64((Value - 1) | Value);
+}
+
+/// Return true if the argument is a power of two > 0.
+/// Ex. isPowerOf2_32(0x00100000U) == true (32 bit edition.)
+constexpr inline bool isPowerOf2_32(uint32_t Value) {
+ return Value && !(Value & (Value - 1));
+}
+
+/// Return true if the argument is a power of two > 0 (64 bit edition.)
+constexpr inline bool isPowerOf2_64(uint64_t Value) {
+ return Value && !(Value & (Value - 1));
+}
+
+/// Return a byte-swapped representation of the 16-bit argument.
+inline uint16_t ByteSwap_16(uint16_t Value) {
+ return sys::SwapByteOrder_16(Value);
+}
+
+/// Return a byte-swapped representation of the 32-bit argument.
+inline uint32_t ByteSwap_32(uint32_t Value) {
+ return sys::SwapByteOrder_32(Value);
+}
+
+/// Return a byte-swapped representation of the 64-bit argument.
+inline uint64_t ByteSwap_64(uint64_t Value) {
+ return sys::SwapByteOrder_64(Value);
+}
+
+/// \brief Count the number of ones from the most significant bit to the first
+/// zero bit.
+///
+/// Ex. countLeadingOnes(0xFF0FFF00) == 8.
+/// Only unsigned integral types are allowed.
+///
+/// \param ZB the behavior on an input of all ones. Only ZB_Width and
+/// ZB_Undefined are valid arguments.
+template <typename T>
+std::size_t countLeadingOnes(T Value, ZeroBehavior ZB = ZB_Width) {
+ static_assert(std::numeric_limits<T>::is_integer &&
+ !std::numeric_limits<T>::is_signed,
+ "Only unsigned integral types are allowed.");
+ return countLeadingZeros(~Value, ZB);
+}
+
+/// \brief Count the number of ones from the least significant bit to the first
+/// zero bit.
+///
+/// Ex. countTrailingOnes(0x00FF00FF) == 8.
+/// Only unsigned integral types are allowed.
+///
+/// \param ZB the behavior on an input of all ones. Only ZB_Width and
+/// ZB_Undefined are valid arguments.
+template <typename T>
+std::size_t countTrailingOnes(T Value, ZeroBehavior ZB = ZB_Width) {
+ static_assert(std::numeric_limits<T>::is_integer &&
+ !std::numeric_limits<T>::is_signed,
+ "Only unsigned integral types are allowed.");
+ return countTrailingZeros(~Value, ZB);
+}
+
+namespace detail {
+template <typename T, std::size_t SizeOfT> struct PopulationCounter {
+ static unsigned count(T Value) {
+ // Generic version, forward to 32 bits.
+ static_assert(SizeOfT <= 4, "Not implemented!");
+#if __GNUC__ >= 4
+ return __builtin_popcount(Value);
+#else
+ uint32_t v = Value;
+ v = v - ((v >> 1) & 0x55555555);
+ v = (v & 0x33333333) + ((v >> 2) & 0x33333333);
+ return ((v + (v >> 4) & 0xF0F0F0F) * 0x1010101) >> 24;
+#endif
+ }
+};
+
+template <typename T> struct PopulationCounter<T, 8> {
+ static unsigned count(T Value) {
+#if __GNUC__ >= 4
+ return __builtin_popcountll(Value);
+#else
+ uint64_t v = Value;
+ v = v - ((v >> 1) & 0x5555555555555555ULL);
+ v = (v & 0x3333333333333333ULL) + ((v >> 2) & 0x3333333333333333ULL);
+ v = (v + (v >> 4)) & 0x0F0F0F0F0F0F0F0FULL;
+ return unsigned((uint64_t)(v * 0x0101010101010101ULL) >> 56);
+#endif
+ }
+};
+} // namespace detail
+
+/// \brief Count the number of set bits in a value.
+/// Ex. countPopulation(0xF000F000) = 8
+/// Returns 0 if the word is zero.
+template <typename T>
+inline unsigned countPopulation(T Value) {
+ static_assert(std::numeric_limits<T>::is_integer &&
+ !std::numeric_limits<T>::is_signed,
+ "Only unsigned integral types are allowed.");
+ return detail::PopulationCounter<T, sizeof(T)>::count(Value);
+}
+
+/// Return the log base 2 of the specified value.
+inline double Log2(double Value) {
+#if defined(__ANDROID_API__) && __ANDROID_API__ < 18
+ return __builtin_log(Value) / __builtin_log(2.0);
+#else
+ return log2(Value);
+#endif
+}
+
+/// Return the floor log base 2 of the specified value, -1 if the value is zero.
+/// (32 bit edition.)
+/// Ex. Log2_32(32) == 5, Log2_32(1) == 0, Log2_32(0) == -1, Log2_32(6) == 2
+inline unsigned Log2_32(uint32_t Value) {
+ return 31 - countLeadingZeros(Value);
+}
+
+/// Return the floor log base 2 of the specified value, -1 if the value is zero.
+/// (64 bit edition.)
+inline unsigned Log2_64(uint64_t Value) {
+ return 63 - countLeadingZeros(Value);
+}
+
+/// Return the ceil log base 2 of the specified value, 32 if the value is zero.
+/// (32 bit edition).
+/// Ex. Log2_32_Ceil(32) == 5, Log2_32_Ceil(1) == 0, Log2_32_Ceil(6) == 3
+inline unsigned Log2_32_Ceil(uint32_t Value) {
+ return 32 - countLeadingZeros(Value - 1);
+}
+
+/// Return the ceil log base 2 of the specified value, 64 if the value is zero.
+/// (64 bit edition.)
+inline unsigned Log2_64_Ceil(uint64_t Value) {
+ return 64 - countLeadingZeros(Value - 1);
+}
+
+/// Return the greatest common divisor of the values using Euclid's algorithm.
+inline uint64_t GreatestCommonDivisor64(uint64_t A, uint64_t B) {
+ while (B) {
+ uint64_t T = B;
+ B = A % B;
+ A = T;
+ }
+ return A;
+}
+
+/// This function takes a 64-bit integer and returns the bit equivalent double.
+inline double BitsToDouble(uint64_t Bits) {
+ double D;
+ static_assert(sizeof(uint64_t) == sizeof(double), "Unexpected type sizes");
+ memcpy(&D, &Bits, sizeof(Bits));
+ return D;
+}
+
+/// This function takes a 32-bit integer and returns the bit equivalent float.
+inline float BitsToFloat(uint32_t Bits) {
+ float F;
+ static_assert(sizeof(uint32_t) == sizeof(float), "Unexpected type sizes");
+ memcpy(&F, &Bits, sizeof(Bits));
+ return F;
+}
+
+/// This function takes a double and returns the bit equivalent 64-bit integer.
+/// Note that copying doubles around changes the bits of NaNs on some hosts,
+/// notably x86, so this routine cannot be used if these bits are needed.
+inline uint64_t DoubleToBits(double Double) {
+ uint64_t Bits;
+ static_assert(sizeof(uint64_t) == sizeof(double), "Unexpected type sizes");
+ memcpy(&Bits, &Double, sizeof(Double));
+ return Bits;
+}
+
+/// This function takes a float and returns the bit equivalent 32-bit integer.
+/// Note that copying floats around changes the bits of NaNs on some hosts,
+/// notably x86, so this routine cannot be used if these bits are needed.
+inline uint32_t FloatToBits(float Float) {
+ uint32_t Bits;
+ static_assert(sizeof(uint32_t) == sizeof(float), "Unexpected type sizes");
+ memcpy(&Bits, &Float, sizeof(Float));
+ return Bits;
+}
+
+/// A and B are either alignments or offsets. Return the minimum alignment that
+/// may be assumed after adding the two together.
+constexpr inline uint64_t MinAlign(uint64_t A, uint64_t B) {
+ // The largest power of 2 that divides both A and B.
+ //
+ // Replace "-Value" by "1+~Value" in the following commented code to avoid
+ // MSVC warning C4146
+ // return (A | B) & -(A | B);
+ return (A | B) & (1 + ~(A | B));
+}
+
+/// \brief Aligns \c Addr to \c Alignment bytes, rounding up.
+///
+/// Alignment should be a power of two. This method rounds up, so
+/// alignAddr(7, 4) == 8 and alignAddr(8, 4) == 8.
+inline uintptr_t alignAddr(const void *Addr, size_t Alignment) {
+ assert(Alignment && isPowerOf2_64((uint64_t)Alignment) &&
+ "Alignment is not a power of two!");
+
+ assert((uintptr_t)Addr + Alignment - 1 >= (uintptr_t)Addr);
+
+ return (((uintptr_t)Addr + Alignment - 1) & ~(uintptr_t)(Alignment - 1));
+}
+
+/// \brief Returns the necessary adjustment for aligning \c Ptr to \c Alignment
+/// bytes, rounding up.
+inline size_t alignmentAdjustment(const void *Ptr, size_t Alignment) {
+ return alignAddr(Ptr, Alignment) - (uintptr_t)Ptr;
+}
+
+/// Returns the next power of two (in 64-bits) that is strictly greater than A.
+/// Returns zero on overflow.
+inline uint64_t NextPowerOf2(uint64_t A) {
+ A |= (A >> 1);
+ A |= (A >> 2);
+ A |= (A >> 4);
+ A |= (A >> 8);
+ A |= (A >> 16);
+ A |= (A >> 32);
+ return A + 1;
+}
+
+/// Returns the power of two which is less than or equal to the given value.
+/// Essentially, it is a floor operation across the domain of powers of two.
+inline uint64_t PowerOf2Floor(uint64_t A) {
+ if (!A) return 0;
+ return 1ull << (63 - countLeadingZeros(A, ZB_Undefined));
+}
+
+/// Returns the power of two which is greater than or equal to the given value.
+/// Essentially, it is a ceil operation across the domain of powers of two.
+inline uint64_t PowerOf2Ceil(uint64_t A) {
+ if (!A)
+ return 0;
+ return NextPowerOf2(A - 1);
+}
+
+/// Returns the next integer (mod 2**64) that is greater than or equal to
+/// \p Value and is a multiple of \p Align. \p Align must be non-zero.
+///
+/// If non-zero \p Skew is specified, the return value will be a minimal
+/// integer that is greater than or equal to \p Value and equal to
+/// \p Align * N + \p Skew for some integer N. If \p Skew is larger than
+/// \p Align, its value is adjusted to '\p Skew mod \p Align'.
+///
+/// Examples:
+/// \code
+/// alignTo(5, 8) = 8
+/// alignTo(17, 8) = 24
+/// alignTo(~0LL, 8) = 0
+/// alignTo(321, 255) = 510
+///
+/// alignTo(5, 8, 7) = 7
+/// alignTo(17, 8, 1) = 17
+/// alignTo(~0LL, 8, 3) = 3
+/// alignTo(321, 255, 42) = 552
+/// \endcode
+inline uint64_t alignTo(uint64_t Value, uint64_t Align, uint64_t Skew = 0) {
+ assert(Align != 0u && "Align can't be 0.");
+ Skew %= Align;
+ return (Value + Align - 1 - Skew) / Align * Align + Skew;
+}
+
+/// Returns the next integer (mod 2**64) that is greater than or equal to
+/// \p Value and is a multiple of \c Align. \c Align must be non-zero.
+template <uint64_t Align> constexpr inline uint64_t alignTo(uint64_t Value) {
+ static_assert(Align != 0u, "Align must be non-zero");
+ return (Value + Align - 1) / Align * Align;
+}
+
+/// Returns the integer ceil(Numerator / Denominator).
+inline uint64_t divideCeil(uint64_t Numerator, uint64_t Denominator) {
+ return alignTo(Numerator, Denominator) / Denominator;
+}
+
+/// \c alignTo for contexts where a constant expression is required.
+/// \sa alignTo
+///
+/// \todo FIXME: remove when \c constexpr becomes really \c constexpr
+template <uint64_t Align>
+struct AlignTo {
+ static_assert(Align != 0u, "Align must be non-zero");
+ template <uint64_t Value>
+ struct from_value {
+ static const uint64_t value = (Value + Align - 1) / Align * Align;
+ };
+};
+
+/// Returns the largest uint64_t less than or equal to \p Value and is
+/// \p Skew mod \p Align. \p Align must be non-zero
+inline uint64_t alignDown(uint64_t Value, uint64_t Align, uint64_t Skew = 0) {
+ assert(Align != 0u && "Align can't be 0.");
+ Skew %= Align;
+ return (Value - Skew) / Align * Align + Skew;
+}
+
+/// Returns the offset to the next integer (mod 2**64) that is greater than
+/// or equal to \p Value and is a multiple of \p Align. \p Align must be
+/// non-zero.
+inline uint64_t OffsetToAlignment(uint64_t Value, uint64_t Align) {
+ return alignTo(Value, Align) - Value;
+}
+
+/// Sign-extend the number in the bottom B bits of X to a 32-bit integer.
+/// Requires 0 < B <= 32.
+template <unsigned B> constexpr inline int32_t SignExtend32(uint32_t X) {
+ static_assert(B > 0, "Bit width can't be 0.");
+ static_assert(B <= 32, "Bit width out of range.");
+ return int32_t(X << (32 - B)) >> (32 - B);
+}
+
+/// Sign-extend the number in the bottom B bits of X to a 32-bit integer.
+/// Requires 0 < B < 32.
+inline int32_t SignExtend32(uint32_t X, unsigned B) {
+ assert(B > 0 && "Bit width can't be 0.");
+ assert(B <= 32 && "Bit width out of range.");
+ return int32_t(X << (32 - B)) >> (32 - B);
+}
+
+/// Sign-extend the number in the bottom B bits of X to a 64-bit integer.
+/// Requires 0 < B < 64.
+template <unsigned B> constexpr inline int64_t SignExtend64(uint64_t x) {
+ static_assert(B > 0, "Bit width can't be 0.");
+ static_assert(B <= 64, "Bit width out of range.");
+ return int64_t(x << (64 - B)) >> (64 - B);
+}
+
+/// Sign-extend the number in the bottom B bits of X to a 64-bit integer.
+/// Requires 0 < B < 64.
+inline int64_t SignExtend64(uint64_t X, unsigned B) {
+ assert(B > 0 && "Bit width can't be 0.");
+ assert(B <= 64 && "Bit width out of range.");
+ return int64_t(X << (64 - B)) >> (64 - B);
+}
+
+/// Subtract two unsigned integers, X and Y, of type T and return the absolute
+/// value of the result.
+template <typename T>
+typename std::enable_if<std::is_unsigned<T>::value, T>::type
+AbsoluteDifference(T X, T Y) {
+ return std::max(X, Y) - std::min(X, Y);
+}
+
+/// Add two unsigned integers, X and Y, of type T. Clamp the result to the
+/// maximum representable value of T on overflow. ResultOverflowed indicates if
+/// the result is larger than the maximum representable value of type T.
+template <typename T>
+typename std::enable_if<std::is_unsigned<T>::value, T>::type
+SaturatingAdd(T X, T Y, bool *ResultOverflowed = nullptr) {
+ bool Dummy;
+ bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
+ // Hacker's Delight, p. 29
+ T Z = X + Y;
+ Overflowed = (Z < X || Z < Y);
+ if (Overflowed)
+ return std::numeric_limits<T>::max();
+ else
+ return Z;
+}
+
+/// Multiply two unsigned integers, X and Y, of type T. Clamp the result to the
+/// maximum representable value of T on overflow. ResultOverflowed indicates if
+/// the result is larger than the maximum representable value of type T.
+template <typename T>
+typename std::enable_if<std::is_unsigned<T>::value, T>::type
+SaturatingMultiply(T X, T Y, bool *ResultOverflowed = nullptr) {
+ bool Dummy;
+ bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
+
+ // Hacker's Delight, p. 30 has a different algorithm, but we don't use that
+ // because it fails for uint16_t (where multiplication can have undefined
+ // behavior due to promotion to int), and requires a division in addition
+ // to the multiplication.
+
+ Overflowed = false;
+
+ // Log2(Z) would be either Log2Z or Log2Z + 1.
+ // Special case: if X or Y is 0, Log2_64 gives -1, and Log2Z
+ // will necessarily be less than Log2Max as desired.
+ int Log2Z = Log2_64(X) + Log2_64(Y);
+ const T Max = std::numeric_limits<T>::max();
+ int Log2Max = Log2_64(Max);
+ if (Log2Z < Log2Max) {
+ return X * Y;
+ }
+ if (Log2Z > Log2Max) {
+ Overflowed = true;
+ return Max;
+ }
+
+ // We're going to use the top bit, and maybe overflow one
+ // bit past it. Multiply all but the bottom bit then add
+ // that on at the end.
+ T Z = (X >> 1) * Y;
+ if (Z & ~(Max >> 1)) {
+ Overflowed = true;
+ return Max;
+ }
+ Z <<= 1;
+ if (X & 1)
+ return SaturatingAdd(Z, Y, ResultOverflowed);
+
+ return Z;
+}
+
+/// Multiply two unsigned integers, X and Y, and add the unsigned integer, A to
+/// the product. Clamp the result to the maximum representable value of T on
+/// overflow. ResultOverflowed indicates if the result is larger than the
+/// maximum representable value of type T.
+template <typename T>
+typename std::enable_if<std::is_unsigned<T>::value, T>::type
+SaturatingMultiplyAdd(T X, T Y, T A, bool *ResultOverflowed = nullptr) {
+ bool Dummy;
+ bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
+
+ T Product = SaturatingMultiply(X, Y, &Overflowed);
+ if (Overflowed)
+ return Product;
+
+ return SaturatingAdd(A, Product, &Overflowed);
+}
+
+/// Use this rather than HUGE_VALF; the latter causes warnings on MSVC.
+extern const float huge_valf;
+} // End llvm namespace
+
+#endif