MathExtras.h - platform/external/capstone - Gitiles

 //===-- 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.
 //
 //===----------------------------------------------------------------------===//

 /* Capstone Disassembly Engine */
 /* By Nguyen Anh Quynh <aquynh@gmail.com>, 2013-2014 */

 #ifndef CS_LLVM_SUPPORT_MATHEXTRAS_H
 #define CS_LLVM_SUPPORT_MATHEXTRAS_H

 #include <stdint.h>

 #ifdef _MSC_VER
 # include <intrin.h>
 #endif

 #ifndef __cplusplus
 #if defined (WIN32) || defined (WIN64) || defined (_WIN32) || defined (_WIN64)
 #define inline /* inline */
 #endif
 #endif

 // 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.

 /// Hi_32 - This function returns the high 32 bits of a 64 bit value.
 static inline uint32_t Hi_32(uint64_t Value) {
 	return (uint32_t)(Value >> 32);
 }

 /// Lo_32 - This function returns the low 32 bits of a 64 bit value.
 static inline uint32_t Lo_32(uint64_t Value) {
 	return (uint32_t)(Value);
 }

 /// isUIntN - Checks if an unsigned integer fits into the given (dynamic)
 /// bit width.
 static inline bool isUIntN(unsigned N, uint64_t x) {
 	return x == (x & (~0ULL >> (64 - N)));
 }

 /// isIntN - Checks if an signed integer fits into the given (dynamic)
 /// bit width.
 //static inline bool isIntN(unsigned N, int64_t x) {
 //  return N >= 64 || (-(INT64_C(1)<<(N-1)) <= x && x < (INT64_C(1)<<(N-1)));
 //}

 /// isMask_32 - This function returns true if the argument is a sequence of ones
 /// starting at the least significant bit with the remainder zero (32 bit
 /// version).   Ex. isMask_32(0x0000FFFFU) == true.
 static inline bool isMask_32(uint32_t Value) {
 	return Value && ((Value + 1) & Value) == 0;
 }

 /// isMask_64 - This function returns true if the argument is a sequence of ones
 /// starting at the least significant bit with the remainder zero (64 bit
 /// version).
 static inline bool isMask_64(uint64_t Value) {
 	return Value && ((Value + 1) & Value) == 0;
 }

 /// isShiftedMask_32 - This function returns true if the argument contains a
 /// sequence of ones with the remainder zero (32 bit version.)
 /// Ex. isShiftedMask_32(0x0000FF00U) == true.
 static inline bool isShiftedMask_32(uint32_t Value) {
 	return isMask_32((Value - 1) | Value);
 }

 /// isShiftedMask_64 - This function returns true if the argument contains a
 /// sequence of ones with the remainder zero (64 bit version.)
 static inline bool isShiftedMask_64(uint64_t Value) {
 	return 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.)
 static inline bool isPowerOf2_32(uint32_t Value) {
 	return Value && !(Value & (Value - 1));
 }

 /// CountLeadingZeros_32 - this function performs the platform optimal form of
 /// counting the number of zeros from the most significant bit to the first one
 /// bit.  Ex. CountLeadingZeros_32(0x00F000FF) == 8.
 /// Returns 32 if the word is zero.
 static inline unsigned CountLeadingZeros_32(uint32_t Value) {
 	unsigned Count; // result
 #if __GNUC__ >= 4
 	// PowerPC is defined for __builtin_clz(0)
 #if !defined(__ppc__) && !defined(__ppc64__)
 	if (!Value) return 32;
 #endif
 	Count = __builtin_clz(Value);
 #else
 	unsigned Shift;
 	if (!Value) return 32;
 	Count = 0;
 	// bisection method for count leading zeros
 	for (Shift = 32 >> 1; Shift; Shift >>= 1) {
 		uint32_t Tmp = Value >> Shift;
 		if (Tmp) {
 			Value = Tmp;
 		} else {
 			Count |= Shift;
 		}
 	}
 #endif
 	return Count;
 }

 /// CountLeadingOnes_32 - this function performs the operation of
 /// counting the number of ones from the most significant bit to the first zero
 /// bit.  Ex. CountLeadingOnes_32(0xFF0FFF00) == 8.
 /// Returns 32 if the word is all ones.
 static inline unsigned CountLeadingOnes_32(uint32_t Value) {
 	return CountLeadingZeros_32(~Value);
 }

 /// CountLeadingZeros_64 - This function performs the platform optimal form
 /// of counting the number of zeros from the most significant bit to the first
 /// one bit (64 bit edition.)
 /// Returns 64 if the word is zero.
 static inline unsigned CountLeadingZeros_64(uint64_t Value) {
 	unsigned Count; // result
 #if __GNUC__ >= 4
 	// PowerPC is defined for __builtin_clzll(0)
 #if !defined(__ppc__) && !defined(__ppc64__)
 	if (!Value) return 64;
 #endif
 	Count = __builtin_clzll(Value);
 #else
 #ifndef _MSC_VER
 	unsigned Shift;
 	if (sizeof(long) == sizeof(int64_t))
 	{
 		if (!Value) return 64;
 		Count = 0;
 		// bisection method for count leading zeros
 		for (Shift = 64 >> 1; Shift; Shift >>= 1) {
 			uint64_t Tmp = Value >> Shift;
 			if (Tmp) {
 				Value = Tmp;
 			} else {
 				Count |= Shift;
 			}
 		}
 	}
 	else
 #endif
 	{
 		// get hi portion
 		uint32_t Hi = Hi_32(Value);

 		// if some bits in hi portion
 		if (Hi) {
 			// leading zeros in hi portion plus all bits in lo portion
 			Count = CountLeadingZeros_32(Hi);
 		} else {
 			// get lo portion
 			uint32_t Lo = Lo_32(Value);
 			// same as 32 bit value
 			Count = CountLeadingZeros_32(Lo)+32;
 		}
 	}
 #endif
 	return Count;
 }

 /// CountLeadingOnes_64 - This function performs the operation
 /// of counting the number of ones from the most significant bit to the first
 /// zero bit (64 bit edition.)
 /// Returns 64 if the word is all ones.
 static inline unsigned CountLeadingOnes_64(uint64_t Value) {
 	return CountLeadingZeros_64(~Value);
 }

 /// CountTrailingZeros_32 - this function performs the platform optimal form of
 /// counting the number of zeros from the least significant bit to the first one
 /// bit.  Ex. CountTrailingZeros_32(0xFF00FF00) == 8.
 /// Returns 32 if the word is zero.
 static inline unsigned CountTrailingZeros_32(uint32_t Value) {
 #if __GNUC__ >= 4
 	return Value ? __builtin_ctz(Value) : 32;
 #else
 	static const unsigned Mod37BitPosition[] = {
 		32, 0, 1, 26, 2, 23, 27, 0, 3, 16, 24, 30, 28, 11, 0, 13,
 		4, 7, 17, 0, 25, 22, 31, 15, 29, 10, 12, 6, 0, 21, 14, 9,
 		5, 20, 8, 19, 18
 	};
 	// Replace "-Value" by "1+~Value" in the following commented code to avoid
 	// MSVC warning C4146
 	//    return Mod37BitPosition[(-Value & Value) % 37];
 	return Mod37BitPosition[((1 + ~Value) & Value) % 37];
 #endif
 }

 /// CountTrailingOnes_32 - this function performs the operation of
 /// counting the number of ones from the least significant bit to the first zero
 /// bit.  Ex. CountTrailingOnes_32(0x00FF00FF) == 8.
 /// Returns 32 if the word is all ones.
 static inline unsigned CountTrailingOnes_32(uint32_t Value) {
 	return CountTrailingZeros_32(~Value);
 }

 /// CountTrailingZeros_64 - This function performs the platform optimal form
 /// of counting the number of zeros from the least significant bit to the first
 /// one bit (64 bit edition.)
 /// Returns 64 if the word is zero.
 static inline unsigned CountTrailingZeros_64(uint64_t Value) {
 #if __GNUC__ >= 4
 	return Value ? __builtin_ctzll(Value) : 64;
 #else
 	static const unsigned Mod67Position[] = {
 		64, 0, 1, 39, 2, 15, 40, 23, 3, 12, 16, 59, 41, 19, 24, 54,
 		4, 64, 13, 10, 17, 62, 60, 28, 42, 30, 20, 51, 25, 44, 55,
 		47, 5, 32, 65, 38, 14, 22, 11, 58, 18, 53, 63, 9, 61, 27,
 		29, 50, 43, 46, 31, 37, 21, 57, 52, 8, 26, 49, 45, 36, 56,
 		7, 48, 35, 6, 34, 33, 0
 	};
 	// Replace "-Value" by "1+~Value" in the following commented code to avoid
 	// MSVC warning C4146
 	//    return Mod67Position[(-Value & Value) % 67];
 	return Mod67Position[((1 + ~Value) & Value) % 67];
 #endif
 }

 /// CountTrailingOnes_64 - This function performs the operation
 /// of counting the number of ones from the least significant bit to the first
 /// zero bit (64 bit edition.)
 /// Returns 64 if the word is all ones.
 static inline unsigned CountTrailingOnes_64(uint64_t Value) {
 	return CountTrailingZeros_64(~Value);
 }

 /// CountPopulation_32 - this function counts the number of set bits in a value.
 /// Ex. CountPopulation(0xF000F000) = 8
 /// Returns 0 if the word is zero.
 static inline unsigned CountPopulation_32(uint32_t Value) {
 #if __GNUC__ >= 4
 	return __builtin_popcount(Value);
 #else
 	uint32_t v = Value - ((Value >> 1) & 0x55555555);
 	v = (v & 0x33333333) + ((v >> 2) & 0x33333333);
 	return (((v + (v >> 4)) & 0xF0F0F0F) * 0x1010101) >> 24;
 #endif
 }

 /// CountPopulation_64 - this function counts the number of set bits in a value,
 /// (64 bit edition.)
 static inline unsigned CountPopulation_64(uint64_t Value) {
 #if __GNUC__ >= 4
 	return __builtin_popcountll(Value);
 #else
 	uint64_t v = Value - ((Value >> 1) & 0x5555555555555555ULL);
 	v = (v & 0x3333333333333333ULL) + ((v >> 2) & 0x3333333333333333ULL);
 	v = (v + (v >> 4)) & 0x0F0F0F0F0F0F0F0FULL;
 	return (uint64_t)((v * 0x0101010101010101ULL) >> 56);
 #endif
 }

 /// Log2_32 - This function returns 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
 static inline unsigned Log2_32(uint32_t Value) {
 	return 31 - CountLeadingZeros_32(Value);
 }

 /// Log2_64 - This function returns the floor log base 2 of the specified value,
 /// -1 if the value is zero. (64 bit edition.)
 static inline unsigned Log2_64(uint64_t Value) {
 	return 63 - CountLeadingZeros_64(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).
 /// Ex. Log2_32_Ceil(32) == 5, Log2_32_Ceil(1) == 0, Log2_32_Ceil(6) == 3
 static inline unsigned Log2_32_Ceil(uint32_t Value) {
 	return 32-CountLeadingZeros_32(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.)
 static inline unsigned Log2_64_Ceil(uint64_t Value) {
 	return 64-CountLeadingZeros_64(Value-1);
 }

 /// GreatestCommonDivisor64 - Return the greatest common divisor of the two
 /// values using Euclid's algorithm.
 static inline uint64_t GreatestCommonDivisor64(uint64_t A, uint64_t B) {
 	while (B) {
 		uint64_t T = B;
 		B = A % B;
 		A = T;
 	}
 	return A;
 }

 /// BitsToDouble - This function takes a 64-bit integer and returns the bit
 /// equivalent double.
 static inline double BitsToDouble(uint64_t Bits) {
 	union {
 		uint64_t L;
 		double D;
 	} T;
 	T.L = Bits;
 	return T.D;
 }

 /// BitsToFloat - This function takes a 32-bit integer and returns the bit
 /// equivalent float.
 static inline float BitsToFloat(uint32_t Bits) {
 	union {
 		uint32_t I;
 		float F;
 	} T;
 	T.I = Bits;
 	return T.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.
 static inline uint64_t DoubleToBits(double Double) {
 	union {
 		uint64_t L;
 		double D;
 	} T;
 	T.D = Double;
 	return T.L;
 }

 /// 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.
 static inline uint32_t FloatToBits(float Float) {
 	union {
 		uint32_t I;
 		float F;
 	} T;
 	T.F = Float;
 	return T.I;
 }

 /// MinAlign - A and B are either alignments or offsets.  Return the minimum
 /// alignment that may be assumed after adding the two together.
 static 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));
 }

 /// NextPowerOf2 - Returns the next power of two (in 64-bits)
 /// that is strictly greater than A.  Returns zero on overflow.
 static 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 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.
 ///
 /// Examples:
 /// \code
 ///   RoundUpToAlignment(5, 8) = 8
 ///   RoundUpToAlignment(17, 8) = 24
 ///   RoundUpToAlignment(~0LL, 8) = 0
 /// \endcode
 static inline uint64_t RoundUpToAlignment(uint64_t Value, uint64_t Align) {
 	return ((Value + Align - 1) / Align) * Align;
 }

 /// 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.
 static inline uint64_t OffsetToAlignment(uint64_t Value, uint64_t Align) {
 	return RoundUpToAlignment(Value, Align) - Value;
 }

 /// abs64 - absolute value of a 64-bit int.  Not all environments support
 /// "abs" on whatever their name for the 64-bit int type is.  The absolute
 /// value of the largest negative number is undefined, as with "abs".
 static inline int64_t abs64(int64_t x) {
 	return (x < 0) ? -x : x;
 }

 /// \brief Sign extend number in the bottom B bits of X to a 32-bit int.
 /// Requires 0 < B <= 32.
 static inline int32_t SignExtend32(uint32_t X, unsigned B) {
 	return (int32_t)(X << (32 - B)) >> (32 - B);
 }

 /// \brief Sign extend number in the bottom B bits of X to a 64-bit int.
 /// Requires 0 < B <= 64.
 static inline int64_t SignExtend64(uint64_t X, unsigned B) {
 	return (int64_t)(X << (64 - B)) >> (64 - B);
 }

 /// \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.
 static inline unsigned int countLeadingZeros(int x)
 {
 	unsigned count = 0;
 	int i;
 	const unsigned bits = sizeof(x) * 8;

 	for (i = bits; --i; ) {
 		if (x < 0) break;
 		count++;
 		x <<= 1;
 	}

 	return count;
 }

 #endif
	//===-- 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.
	//
	//===----------------------------------------------------------------------===//

	/* Capstone Disassembly Engine */
	/* By Nguyen Anh Quynh <aquynh@gmail.com>, 2013-2014 */

	#ifndef CS_LLVM_SUPPORT_MATHEXTRAS_H
	#define CS_LLVM_SUPPORT_MATHEXTRAS_H

	#include <stdint.h>

	#ifdef _MSC_VER
	# include <intrin.h>
	#endif

	#ifndef __cplusplus
	#if defined (WIN32) \|\| defined (WIN64) \|\| defined (_WIN32) \|\| defined (_WIN64)
	#define inline /* inline */
	#endif
	#endif

	// 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.

	/// Hi_32 - This function returns the high 32 bits of a 64 bit value.
	static inline uint32_t Hi_32(uint64_t Value) {
	return (uint32_t)(Value >> 32);
	}

	/// Lo_32 - This function returns the low 32 bits of a 64 bit value.
	static inline uint32_t Lo_32(uint64_t Value) {
	return (uint32_t)(Value);
	}

	/// isUIntN - Checks if an unsigned integer fits into the given (dynamic)
	/// bit width.
	static inline bool isUIntN(unsigned N, uint64_t x) {
	return x == (x & (~0ULL >> (64 - N)));
	}

	/// isIntN - Checks if an signed integer fits into the given (dynamic)
	/// bit width.
	//static inline bool isIntN(unsigned N, int64_t x) {
	// return N >= 64 \|\| (-(INT64_C(1)<<(N-1)) <= x && x < (INT64_C(1)<<(N-1)));
	//}

	/// isMask_32 - This function returns true if the argument is a sequence of ones
	/// starting at the least significant bit with the remainder zero (32 bit
	/// version). Ex. isMask_32(0x0000FFFFU) == true.
	static inline bool isMask_32(uint32_t Value) {
	return Value && ((Value + 1) & Value) == 0;
	}

	/// isMask_64 - This function returns true if the argument is a sequence of ones
	/// starting at the least significant bit with the remainder zero (64 bit
	/// version).
	static inline bool isMask_64(uint64_t Value) {
	return Value && ((Value + 1) & Value) == 0;
	}

	/// isShiftedMask_32 - This function returns true if the argument contains a
	/// sequence of ones with the remainder zero (32 bit version.)
	/// Ex. isShiftedMask_32(0x0000FF00U) == true.
	static inline bool isShiftedMask_32(uint32_t Value) {
	return isMask_32((Value - 1) \| Value);
	}

	/// isShiftedMask_64 - This function returns true if the argument contains a
	/// sequence of ones with the remainder zero (64 bit version.)
	static inline bool isShiftedMask_64(uint64_t Value) {
	return 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.)
	static inline bool isPowerOf2_32(uint32_t Value) {
	return Value && !(Value & (Value - 1));
	}

	/// CountLeadingZeros_32 - this function performs the platform optimal form of
	/// counting the number of zeros from the most significant bit to the first one
	/// bit. Ex. CountLeadingZeros_32(0x00F000FF) == 8.
	/// Returns 32 if the word is zero.
	static inline unsigned CountLeadingZeros_32(uint32_t Value) {
	unsigned Count; // result
	#if __GNUC__ >= 4
	// PowerPC is defined for __builtin_clz(0)
	#if !defined(__ppc__) && !defined(__ppc64__)
	if (!Value) return 32;
	#endif
	Count = __builtin_clz(Value);
	#else
	unsigned Shift;
	if (!Value) return 32;
	Count = 0;
	// bisection method for count leading zeros
	for (Shift = 32 >> 1; Shift; Shift >>= 1) {
	uint32_t Tmp = Value >> Shift;
	if (Tmp) {
	Value = Tmp;
	} else {
	Count \|= Shift;
	}
	}
	#endif
	return Count;
	}

	/// CountLeadingOnes_32 - this function performs the operation of
	/// counting the number of ones from the most significant bit to the first zero
	/// bit. Ex. CountLeadingOnes_32(0xFF0FFF00) == 8.
	/// Returns 32 if the word is all ones.
	static inline unsigned CountLeadingOnes_32(uint32_t Value) {
	return CountLeadingZeros_32(~Value);
	}

	/// CountLeadingZeros_64 - This function performs the platform optimal form
	/// of counting the number of zeros from the most significant bit to the first
	/// one bit (64 bit edition.)
	/// Returns 64 if the word is zero.
	static inline unsigned CountLeadingZeros_64(uint64_t Value) {
	unsigned Count; // result
	#if __GNUC__ >= 4
	// PowerPC is defined for __builtin_clzll(0)
	#if !defined(__ppc__) && !defined(__ppc64__)
	if (!Value) return 64;
	#endif
	Count = __builtin_clzll(Value);
	#else
	#ifndef _MSC_VER
	unsigned Shift;
	if (sizeof(long) == sizeof(int64_t))
	{
	if (!Value) return 64;
	Count = 0;
	// bisection method for count leading zeros
	for (Shift = 64 >> 1; Shift; Shift >>= 1) {
	uint64_t Tmp = Value >> Shift;
	if (Tmp) {
	Value = Tmp;
	} else {
	Count \|= Shift;
	}
	}
	}
	else
	#endif
	{
	// get hi portion
	uint32_t Hi = Hi_32(Value);

	// if some bits in hi portion
	if (Hi) {
	// leading zeros in hi portion plus all bits in lo portion
	Count = CountLeadingZeros_32(Hi);
	} else {
	// get lo portion
	uint32_t Lo = Lo_32(Value);
	// same as 32 bit value
	Count = CountLeadingZeros_32(Lo)+32;
	}
	}
	#endif
	return Count;
	}

	/// CountLeadingOnes_64 - This function performs the operation
	/// of counting the number of ones from the most significant bit to the first
	/// zero bit (64 bit edition.)
	/// Returns 64 if the word is all ones.
	static inline unsigned CountLeadingOnes_64(uint64_t Value) {
	return CountLeadingZeros_64(~Value);
	}

	/// CountTrailingZeros_32 - this function performs the platform optimal form of
	/// counting the number of zeros from the least significant bit to the first one
	/// bit. Ex. CountTrailingZeros_32(0xFF00FF00) == 8.
	/// Returns 32 if the word is zero.
	static inline unsigned CountTrailingZeros_32(uint32_t Value) {
	#if __GNUC__ >= 4
	return Value ? __builtin_ctz(Value) : 32;
	#else
	static const unsigned Mod37BitPosition[] = {
	32, 0, 1, 26, 2, 23, 27, 0, 3, 16, 24, 30, 28, 11, 0, 13,
	4, 7, 17, 0, 25, 22, 31, 15, 29, 10, 12, 6, 0, 21, 14, 9,
	5, 20, 8, 19, 18
	};
	// Replace "-Value" by "1+~Value" in the following commented code to avoid
	// MSVC warning C4146
	// return Mod37BitPosition[(-Value & Value) % 37];
	return Mod37BitPosition[((1 + ~Value) & Value) % 37];
	#endif
	}

	/// CountTrailingOnes_32 - this function performs the operation of
	/// counting the number of ones from the least significant bit to the first zero
	/// bit. Ex. CountTrailingOnes_32(0x00FF00FF) == 8.
	/// Returns 32 if the word is all ones.
	static inline unsigned CountTrailingOnes_32(uint32_t Value) {
	return CountTrailingZeros_32(~Value);
	}

	/// CountTrailingZeros_64 - This function performs the platform optimal form
	/// of counting the number of zeros from the least significant bit to the first
	/// one bit (64 bit edition.)
	/// Returns 64 if the word is zero.
	static inline unsigned CountTrailingZeros_64(uint64_t Value) {
	#if __GNUC__ >= 4
	return Value ? __builtin_ctzll(Value) : 64;
	#else
	static const unsigned Mod67Position[] = {
	64, 0, 1, 39, 2, 15, 40, 23, 3, 12, 16, 59, 41, 19, 24, 54,
	4, 64, 13, 10, 17, 62, 60, 28, 42, 30, 20, 51, 25, 44, 55,
	47, 5, 32, 65, 38, 14, 22, 11, 58, 18, 53, 63, 9, 61, 27,
	29, 50, 43, 46, 31, 37, 21, 57, 52, 8, 26, 49, 45, 36, 56,
	7, 48, 35, 6, 34, 33, 0
	};
	// Replace "-Value" by "1+~Value" in the following commented code to avoid
	// MSVC warning C4146
	// return Mod67Position[(-Value & Value) % 67];
	return Mod67Position[((1 + ~Value) & Value) % 67];
	#endif
	}

	/// CountTrailingOnes_64 - This function performs the operation
	/// of counting the number of ones from the least significant bit to the first
	/// zero bit (64 bit edition.)
	/// Returns 64 if the word is all ones.
	static inline unsigned CountTrailingOnes_64(uint64_t Value) {
	return CountTrailingZeros_64(~Value);
	}

	/// CountPopulation_32 - this function counts the number of set bits in a value.
	/// Ex. CountPopulation(0xF000F000) = 8
	/// Returns 0 if the word is zero.
	static inline unsigned CountPopulation_32(uint32_t Value) {
	#if __GNUC__ >= 4
	return __builtin_popcount(Value);
	#else
	uint32_t v = Value - ((Value >> 1) & 0x55555555);
	v = (v & 0x33333333) + ((v >> 2) & 0x33333333);
	return (((v + (v >> 4)) & 0xF0F0F0F) * 0x1010101) >> 24;
	#endif
	}

	/// CountPopulation_64 - this function counts the number of set bits in a value,
	/// (64 bit edition.)
	static inline unsigned CountPopulation_64(uint64_t Value) {
	#if __GNUC__ >= 4
	return __builtin_popcountll(Value);
	#else
	uint64_t v = Value - ((Value >> 1) & 0x5555555555555555ULL);
	v = (v & 0x3333333333333333ULL) + ((v >> 2) & 0x3333333333333333ULL);
	v = (v + (v >> 4)) & 0x0F0F0F0F0F0F0F0FULL;
	return (uint64_t)((v * 0x0101010101010101ULL) >> 56);
	#endif
	}

	/// Log2_32 - This function returns 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
	static inline unsigned Log2_32(uint32_t Value) {
	return 31 - CountLeadingZeros_32(Value);
	}

	/// Log2_64 - This function returns the floor log base 2 of the specified value,
	/// -1 if the value is zero. (64 bit edition.)
	static inline unsigned Log2_64(uint64_t Value) {
	return 63 - CountLeadingZeros_64(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).
	/// Ex. Log2_32_Ceil(32) == 5, Log2_32_Ceil(1) == 0, Log2_32_Ceil(6) == 3
	static inline unsigned Log2_32_Ceil(uint32_t Value) {
	return 32-CountLeadingZeros_32(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.)
	static inline unsigned Log2_64_Ceil(uint64_t Value) {
	return 64-CountLeadingZeros_64(Value-1);
	}

	/// GreatestCommonDivisor64 - Return the greatest common divisor of the two
	/// values using Euclid's algorithm.
	static inline uint64_t GreatestCommonDivisor64(uint64_t A, uint64_t B) {
	while (B) {
	uint64_t T = B;
	B = A % B;
	A = T;
	}
	return A;
	}

	/// BitsToDouble - This function takes a 64-bit integer and returns the bit
	/// equivalent double.
	static inline double BitsToDouble(uint64_t Bits) {
	union {
	uint64_t L;
	double D;
	} T;
	T.L = Bits;
	return T.D;
	}

	/// BitsToFloat - This function takes a 32-bit integer and returns the bit
	/// equivalent float.
	static inline float BitsToFloat(uint32_t Bits) {
	union {
	uint32_t I;
	float F;
	} T;
	T.I = Bits;
	return T.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.
	static inline uint64_t DoubleToBits(double Double) {
	union {
	uint64_t L;
	double D;
	} T;
	T.D = Double;
	return T.L;
	}

	/// 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.
	static inline uint32_t FloatToBits(float Float) {
	union {
	uint32_t I;
	float F;
	} T;
	T.F = Float;
	return T.I;
	}

	/// MinAlign - A and B are either alignments or offsets. Return the minimum
	/// alignment that may be assumed after adding the two together.
	static 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));
	}

	/// NextPowerOf2 - Returns the next power of two (in 64-bits)
	/// that is strictly greater than A. Returns zero on overflow.
	static 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 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.
	///
	/// Examples:
	/// \code
	/// RoundUpToAlignment(5, 8) = 8
	/// RoundUpToAlignment(17, 8) = 24
	/// RoundUpToAlignment(~0LL, 8) = 0
	/// \endcode
	static inline uint64_t RoundUpToAlignment(uint64_t Value, uint64_t Align) {
	return ((Value + Align - 1) / Align) * Align;
	}

	/// 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.
	static inline uint64_t OffsetToAlignment(uint64_t Value, uint64_t Align) {
	return RoundUpToAlignment(Value, Align) - Value;
	}

	/// abs64 - absolute value of a 64-bit int. Not all environments support
	/// "abs" on whatever their name for the 64-bit int type is. The absolute
	/// value of the largest negative number is undefined, as with "abs".
	static inline int64_t abs64(int64_t x) {
	return (x < 0) ? -x : x;
	}

	/// \brief Sign extend number in the bottom B bits of X to a 32-bit int.
	/// Requires 0 < B <= 32.
	static inline int32_t SignExtend32(uint32_t X, unsigned B) {
	return (int32_t)(X << (32 - B)) >> (32 - B);
	}

	/// \brief Sign extend number in the bottom B bits of X to a 64-bit int.
	/// Requires 0 < B <= 64.
	static inline int64_t SignExtend64(uint64_t X, unsigned B) {
	return (int64_t)(X << (64 - B)) >> (64 - B);
	}

	/// \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.
	static inline unsigned int countLeadingZeros(int x)
	{
	unsigned count = 0;
	int i;
	const unsigned bits = sizeof(x) * 8;

	for (i = bits; --i; ) {
	if (x < 0) break;
	count++;
	x <<= 1;
	}

	return count;
	}

	#endif