Update LLVM to latest upstream. (#1080)

Also change header guards to WPI header guards.
Remove StringRef::c_str() customization, replacing the handful of uses with Twine or SmallString.
TCPStream: Include errno.h and make Windows includes lowercase for consistency.

Upstream LLVM version: eb4186cca7924fb1706357545311a2fa3de40c59

wpiutil/src/main/native/include/wpi/MathExtras.h

@@ -11,33 +11,108 @@
 //
 //===----------------------------------------------------------------------===//
 
-#ifndef LLVM_SUPPORT_MATHEXTRAS_H
-#define LLVM_SUPPORT_MATHEXTRAS_H
+#ifndef WPIUTIL_WPI_MATHEXTRAS_H
+#define WPIUTIL_WPI_MATHEXTRAS_H
 
 #include "wpi/Compiler.h"
 #include <cstdint>
 #include <algorithm>
 #include <cassert>
+#include <climits>
 #include <cmath>
 #include <cstring>
-#include <type_traits>
 #include <limits>
+#include <type_traits>
 
 #ifdef _MSC_VER
 #include <intrin.h>
 #endif
 
 namespace wpi {
-/// \brief The behavior an operation has on an input of 0.
+/// The behavior an operation has on an input of 0.
 enum ZeroBehavior {
-  /// \brief The returned value is undefined.
+  /// The returned value is undefined.
   ZB_Undefined,
-  /// \brief The returned value is numeric_limits<T>::max()
+  /// The returned value is numeric_limits<T>::max()
   ZB_Max,
-  /// \brief The returned value is numeric_limits<T>::digits
+  /// 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
+
+/// 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 wpi::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) {
@@ -92,7 +167,7 @@ template <typename T> struct LeadingZerosCounter<T, 8> {
 #endif
 } // namespace detail
 
-/// \brief Count number of 0's from the most significant bit to the least
+/// Count number of 0's from the most significant bit to the least
 ///   stopping at the first 1.
 ///
 /// Only unsigned integral types are allowed.
@@ -104,10 +179,51 @@ 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 detail::LeadingZerosCounter<T, sizeof(T)>::count(Val, ZB);
+  return wpi::detail::LeadingZerosCounter<T, sizeof(T)>::count(Val, ZB);
 }
 
-/// \brief Get the index of the last set bit starting from the least
+/// 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);
+}
+
+/// 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));
+}
+
+/// 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);
+}
+
+/// 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);
+}
+
+/// 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);
+}
+
+/// Get the index of the last set bit starting from the least
 ///   significant bit.
 ///
 /// Only unsigned integral types are allowed.
@@ -124,7 +240,7 @@ template <typename T> T findLastSet(T Val, ZeroBehavior ZB = ZB_Max) {
          (std::numeric_limits<T>::digits - 1);
 }
 
-/// \brief Macro compressed bit reversal table for 256 bits.
+/// Macro compressed bit reversal table for 256 bits.
 ///
 /// http://graphics.stanford.edu/~seander/bithacks.html#BitReverseTable
 static const unsigned char BitReverseTable256[256] = {
@@ -137,7 +253,7 @@ static const unsigned char BitReverseTable256[256] = {
 #undef R6
 };
 
-/// \brief Reverse the bits in \p Val.
+/// Reverse the bits in \p Val.
 template <typename T>
 T reverseBits(T Val) {
   unsigned char in[sizeof(Val)];
@@ -153,150 +269,165 @@ T reverseBits(T Val) {
 // type overloading so that signed and unsigned integers can be used without
 // ambiguity.
 
-/// Hi_32 - This function returns the high 32 bits of a 64 bit value.
-inline uint32_t Hi_32(uint64_t Value) {
+/// 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);
 }
 
-/// Lo_32 - This function returns the low 32 bits of a 64 bit value.
-inline uint32_t Lo_32(uint64_t Value) {
+/// 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_64 - This functions makes a 64-bit integer from a high / low pair of
-///           32-bit integers.
-inline uint64_t Make_64(uint32_t High, uint32_t Low) {
+/// 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;
 }
 
-/// isInt - Checks if an integer fits into the given bit width.
-template<unsigned N>
-inline bool isInt(int64_t x) {
+/// 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<>
-inline bool isInt<8>(int64_t x) {
+template <> constexpr inline bool isInt<8>(int64_t x) {
   return static_cast<int8_t>(x) == x;
 }
-template<>
-inline bool isInt<16>(int64_t x) {
+template <> constexpr inline bool isInt<16>(int64_t x) {
   return static_cast<int16_t>(x) == x;
 }
-template<>
-inline bool isInt<32>(int64_t x) {
+template <> constexpr inline bool isInt<32>(int64_t x) {
   return static_cast<int32_t>(x) == x;
 }
 
-/// isShiftedInt<N,S> - Checks if a signed integer is an N bit number shifted
-///                     left by S.
-template<unsigned N, unsigned S>
-inline bool isShiftedInt(int64_t x) {
-  return isInt<N+S>(x) && (x % (1<<S) == 0);
+/// 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);
 }
 
-/// isUInt - Checks if an unsigned integer fits into the given bit width.
-template<unsigned N>
-inline bool isUInt(uint64_t x) {
-  return N >= 64 || x < (UINT64_C(1)<<(N));
+/// 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<>
-inline bool isUInt<8>(uint64_t x) {
+template <> constexpr inline bool isUInt<8>(uint64_t x) {
   return static_cast<uint8_t>(x) == x;
 }
-template<>
-inline bool isUInt<16>(uint64_t x) {
+template <> constexpr inline bool isUInt<16>(uint64_t x) {
   return static_cast<uint16_t>(x) == x;
 }
-template<>
-inline bool isUInt<32>(uint64_t x) {
+template <> constexpr inline bool isUInt<32>(uint64_t x) {
   return static_cast<uint32_t>(x) == x;
 }
 
-/// isShiftedUInt<N,S> - Checks if a unsigned integer is an N bit number shifted
-///                     left by S.
-template<unsigned N, unsigned S>
-inline bool isShiftedUInt(uint64_t x) {
-  return isUInt<N+S>(x) && (x % (1<<S) == 0);
+/// 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");
 
-  return (UINT64_C(1) << N) - 1;
+  // 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 -(INT64_C(1)<<(N-1));
+  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");
 
-  return (INT64_C(1)<<(N-1)) - 1;
+  // 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;
 }
 
-/// isUIntN - Checks if an unsigned integer fits into the given (dynamic)
-/// bit width.
+/// 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);
 }
 
-/// isIntN - Checks if an signed integer fits into the given (dynamic)
-/// bit width.
+/// 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));
 }
 
-/// isMask_32 - This function returns 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.
-inline bool isMask_32(uint32_t Value) {
+/// 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;
 }
 
-/// isMask_64 - This function returns true if the argument is a non-empty
-/// sequence of ones starting at the least significant bit with the remainder
-/// zero (64 bit version).
-inline bool isMask_64(uint64_t Value) {
+/// 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;
 }
 
-/// isShiftedMask_32 - This function returns true if the argument contains a
-/// non-empty sequence of ones with the remainder zero (32 bit version.)
-/// Ex. isShiftedMask_32(0x0000FF00U) == true.
-inline bool isShiftedMask_32(uint32_t Value) {
+/// 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);
 }
 
-/// isShiftedMask_64 - This function returns true if the argument contains a
-/// non-empty sequence of ones with the remainder zero (64 bit version.)
-inline bool isShiftedMask_64(uint64_t 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);
 }
 
-/// isPowerOf2_32 - This function returns true if the argument is a power of
-/// two > 0. Ex. isPowerOf2_32(0x00100000U) == true (32 bit edition.)
-inline bool isPowerOf2_32(uint32_t 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));
 }
 
-/// isPowerOf2_64 - This function returns true if the argument is a power of two
-/// > 0 (64 bit edition.)
-inline bool isPowerOf2_64(uint64_t Value) {
-  return Value && !(Value & (Value - int64_t(1L)));
+/// 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));
 }
 
-/// \brief Count the number of ones from the most significant bit to the first
+/// Count the number of ones from the most significant bit to the first
 /// zero bit.
 ///
-/// Ex. CountLeadingOnes(0xFF0FFF00) == 8.
+/// Ex. countLeadingOnes(0xFF0FFF00) == 8.
 /// Only unsigned integral types are allowed.
 ///
 /// \param ZB the behavior on an input of all ones. Only ZB_Width and
@@ -306,7 +437,23 @@ 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);
+  return countLeadingZeros<T>(~Value, ZB);
+}
+
+/// 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<T>(~Value, ZB);
 }
 
 namespace detail {
@@ -340,7 +487,7 @@ template <typename T> struct PopulationCounter<T, 8> {
 };
 } // namespace detail
 
-/// \brief Count the number of set bits in a value.
+/// Count the number of set bits in a value.
 /// Ex. countPopulation(0xF000F000) = 8
 /// Returns 0 if the word is zero.
 template <typename T>
@@ -351,7 +498,7 @@ inline unsigned countPopulation(T Value) {
   return detail::PopulationCounter<T, sizeof(T)>::count(Value);
 }
 
-/// Log2 - This function returns the log base 2 of the specified 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);
@@ -360,34 +507,33 @@ inline double Log2(double Value) {
 #endif
 }
 
-/// Log2_32 - This function returns the floor log base 2 of the specified value,
-/// -1 if the value is zero. (32 bit edition.)
+/// 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);
 }
 
-/// Log2_64 - This function returns the floor log base 2 of the specified value,
-/// -1 if the value is zero. (64 bit edition.)
+/// 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);
 }
 
-/// Log2_32_Ceil - This function returns the ceil log base 2 of the specified
-/// value, 32 if the value is zero. (32 bit edition).
+/// 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);
 }
 
-/// Log2_64_Ceil - This function returns the ceil log base 2 of the specified
-/// value, 64 if the value is zero. (64 bit edition.)
+/// 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);
 }
 
-/// GreatestCommonDivisor64 - Return the greatest common divisor of the two
-/// values using Euclid's algorithm.
+/// 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;
@@ -397,57 +543,45 @@ inline uint64_t GreatestCommonDivisor64(uint64_t A, uint64_t B) {
   return A;
 }
 
-/// BitsToDouble - This function takes a 64-bit integer and returns the bit
-/// equivalent double.
+/// This function takes a 64-bit integer and returns the bit equivalent double.
 inline double BitsToDouble(uint64_t Bits) {
-  union {
-    uint64_t L;
-    double D;
-  } T;
-  T.L = Bits;
-  return T.D;
+  double D;
+  static_assert(sizeof(uint64_t) == sizeof(double), "Unexpected type sizes");
+  memcpy(&D, &Bits, sizeof(Bits));
+  return D;
 }
 
-/// BitsToFloat - This function takes a 32-bit integer and returns the bit
-/// equivalent float.
+/// This function takes a 32-bit integer and returns the bit equivalent float.
 inline float BitsToFloat(uint32_t Bits) {
-  union {
-    uint32_t I;
-    float F;
-  } T;
-  T.I = Bits;
-  return T.F;
+  float F;
+  static_assert(sizeof(uint32_t) == sizeof(float), "Unexpected type sizes");
+  memcpy(&F, &Bits, sizeof(Bits));
+  return F;
 }
 
-/// DoubleToBits - 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.
+/// 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) {
-  union {
-    uint64_t L;
-    double D;
-  } T;
-  T.D = Double;
-  return T.L;
+  uint64_t Bits;
+  static_assert(sizeof(uint64_t) == sizeof(double), "Unexpected type sizes");
+  memcpy(&Bits, &Double, sizeof(Double));
+  return Bits;
 }
 
-/// FloatToBits - 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.
+/// 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) {
-  union {
-    uint32_t I;
-    float F;
-  } T;
-  T.F = Float;
-  return T.I;
+  uint32_t Bits;
+  static_assert(sizeof(uint32_t) == sizeof(float), "Unexpected type sizes");
+  memcpy(&Bits, &Float, sizeof(Float));
+  return Bits;
 }
 
-/// MinAlign - A and B are either alignments or offsets.  Return the minimum
-/// alignment that may be assumed after adding the two together.
-inline uint64_t MinAlign(uint64_t A, uint64_t B) {
+/// 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
@@ -456,7 +590,7 @@ inline uint64_t MinAlign(uint64_t A, uint64_t B) {
   return (A | B) & (1 + ~(A | B));
 }
 
-/// \brief Aligns \c Addr to \c Alignment bytes, rounding up.
+/// 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.
@@ -469,14 +603,14 @@ inline uintptr_t alignAddr(const void *Addr, size_t Alignment) {
   return (((uintptr_t)Addr + Alignment - 1) & ~(uintptr_t)(Alignment - 1));
 }
 
-/// \brief Returns the necessary adjustment for aligning \c Ptr to \c Alignment
+/// 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;
 }
 
-/// NextPowerOf2 - Returns the next power of two (in 64-bits)
-/// that is strictly greater than A.  Returns zero on overflow.
+/// 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);
@@ -494,6 +628,14 @@ inline uint64_t PowerOf2Floor(uint64_t A) {
   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.
 ///
@@ -515,13 +657,40 @@ inline uint64_t PowerOf2Floor(uint64_t A) {
 ///   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;
 }
@@ -533,42 +702,49 @@ inline uint64_t OffsetToAlignment(uint64_t Value, uint64_t Align) {
   return alignTo(Value, Align) - Value;
 }
 
-/// SignExtend32 - Sign extend B-bit number x to 32-bit int.
-/// Usage int32_t r = SignExtend32<5>(x);
-template <unsigned B> inline int32_t SignExtend32(uint32_t x) {
-  return int32_t(x << (32 - B)) >> (32 - B);
-}
-
-/// \brief Sign extend number in the bottom B bits of X to a 32-bit int.
+/// 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) {
+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);
 }
 
-/// SignExtend64 - Sign extend B-bit number x to 64-bit int.
-/// Usage int64_t r = SignExtend64<5>(x);
-template <unsigned B> inline int64_t SignExtend64(uint64_t x) {
+/// 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);
 }
 
-/// \brief Sign extend number in the bottom B bits of X to a 64-bit int.
-/// Requires 0 < B <= 64.
+/// 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);
 }
 
-/// \brief Subtract two unsigned integers, X and Y, of type T and return their
-/// absolute value.
+/// 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);
 }
 
-/// \brief 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.
+/// 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) {
@@ -583,10 +759,9 @@ SaturatingAdd(T X, T Y, bool *ResultOverflowed = nullptr) {
     return Z;
 }
 
-/// \brief 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.
+/// 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) {
@@ -629,12 +804,10 @@ SaturatingMultiply(T X, T Y, bool *ResultOverflowed = nullptr) {
   return Z;
 }
 
-/// \brief 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.
-/// Note that this is purely a convenience function as there is no distinction
-/// where overflow occurred in a 'fused' multiply-add for unsigned numbers.
+/// 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) {