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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/System/DataTypes.h"
namespace llvm {
// 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.
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 static_cast<uint32_t>(Value);
}
/// isInt - Checks if an integer fits into the given bit width.
template<unsigned N>
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) {
return static_cast<int8_t>(x) == x;
}
template<>
inline bool isInt<16>(int64_t x) {
return static_cast<int16_t>(x) == x;
}
template<>
inline bool isInt<32>(int64_t x) {
return static_cast<int32_t>(x) == x;
}
/// 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);
}
// Template specializations to get better code for common cases.
template<>
inline bool isUInt<8>(uint64_t x) {
return static_cast<uint8_t>(x) == x;
}
template<>
inline bool isUInt<16>(uint64_t x) {
return static_cast<uint16_t>(x) == x;
}
template<>
inline bool isUInt<32>(uint64_t x) {
return static_cast<uint32_t>(x) == x;
}
/// 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.
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).
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.
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.)
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.)
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)));
}
/// ByteSwap_16 - This function returns a byte-swapped representation of the
/// 16-bit argument, Value.
inline uint16_t ByteSwap_16(uint16_t Value) {
#if defined(_MSC_VER) && !defined(_DEBUG)
// The DLL version of the runtime lacks these functions (bug!?), but in a
// release build they're replaced with BSWAP instructions anyway.
return _byteswap_ushort(Value);
#else
uint16_t Hi = Value << 8;
uint16_t Lo = Value >> 8;
return Hi | Lo;
#endif
}
/// ByteSwap_32 - This function returns a byte-swapped representation of the
/// 32-bit argument, Value.
inline uint32_t ByteSwap_32(uint32_t Value) {
#if (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 3)) && !defined(__ICC)
return __builtin_bswap32(Value);
#elif defined(_MSC_VER) && !defined(_DEBUG)
return _byteswap_ulong(Value);
#else
uint32_t Byte0 = Value & 0x000000FF;
uint32_t Byte1 = Value & 0x0000FF00;
uint32_t Byte2 = Value & 0x00FF0000;
uint32_t Byte3 = Value & 0xFF000000;
return (Byte0 << 24) | (Byte1 << 8) | (Byte2 >> 8) | (Byte3 >> 24);
#endif
}
/// ByteSwap_64 - This function returns a byte-swapped representation of the
/// 64-bit argument, Value.
inline uint64_t ByteSwap_64(uint64_t Value) {
#if (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 3)) && !defined(__ICC)
return __builtin_bswap64(Value);
#elif defined(_MSC_VER) && !defined(_DEBUG)
return _byteswap_uint64(Value);
#else
uint64_t Hi = ByteSwap_32(uint32_t(Value));
uint32_t Lo = ByteSwap_32(uint32_t(Value >> 32));
return (Hi << 32) | Lo;
#endif
}
/// 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.
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
if (!Value) return 32;
Count = 0;
// bisection method for count leading zeros
for (unsigned 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.
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.
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
if (sizeof(long) == sizeof(int64_t)) {
if (!Value) return 64;
Count = 0;
// bisection method for count leading zeros
for (unsigned Shift = 64 >> 1; Shift; Shift >>= 1) {
uint64_t Tmp = Value >> Shift;
if (Tmp) {
Value = Tmp;
} else {
Count |= Shift;
}
}
} else {
// 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.
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.
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
};
return Mod37BitPosition[(-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.
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.
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
};
return Mod67Position[(-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.
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.
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.)
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 unsigned((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
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.)
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
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.)
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.
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.
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.
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.
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.
inline uint32_t FloatToBits(float Float) {
union {
uint32_t I;
float F;
} T;
T.F = Float;
return T.I;
}
/// Platform-independent wrappers for the C99 isnan() function.
int IsNAN(float f);
int IsNAN(double d);
/// Platform-independent wrappers for the C99 isinf() function.
int IsInf(float f);
int IsInf(double d);
/// 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.
return (A | B) & -(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;
}
/// RoundUpToAlignment - Returns the next integer (mod 2**64) that is
/// greater than or equal to \arg Value and is a multiple of \arg
/// Align. Align must be non-zero.
///
/// Examples:
/// RoundUpToAlignment(5, 8) = 8
/// RoundUpToAlignment(17, 8) = 24
/// RoundUpToAlignment(~0LL, 8) = 0
inline uint64_t RoundUpToAlignment(uint64_t Value, uint64_t Align) {
return ((Value + Align - 1) / Align) * Align;
}
/// OffsetToAlignment - Return the offset to the next integer (mod 2**64) that
/// is greater than or equal to \arg Value and is a multiple of \arg
/// Align. Align must be non-zero.
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".
inline int64_t abs64(int64_t x) {
return (x < 0) ? -x : x;
}
/// 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);
}
/// 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) {
return int64_t(x << (64 - B)) >> (64 - B);
}
} // End llvm namespace
#endif
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