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llvm-mirror/include/llvm/Support/MathExtras.h

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19 KiB
C++

//===-- 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 "llvm/Support/type_traits.h"
#include <cstring>
#ifdef _MSC_VER
#include <intrin.h>
#include <limits>
#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
};
/// \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>
typename enable_if_c<std::numeric_limits<T>::is_integer &&
!std::numeric_limits<T>::is_signed, std::size_t>::type
countTrailingZeros(T Val, ZeroBehavior ZB = ZB_Width) {
(void)ZB;
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;
}
// Disable signed.
template <typename T>
typename enable_if_c<std::numeric_limits<T>::is_integer &&
std::numeric_limits<T>::is_signed, std::size_t>::type
countTrailingZeros(T Val, ZeroBehavior ZB = ZB_Width) LLVM_DELETED_FUNCTION;
#if __GNUC__ >= 4 || _MSC_VER
template <>
inline std::size_t countTrailingZeros<uint32_t>(uint32_t Val, ZeroBehavior ZB) {
if (ZB != ZB_Undefined && Val == 0)
return 32;
#if __has_builtin(__builtin_ctz) || __GNUC_PREREQ(4, 0)
return __builtin_ctz(Val);
#elif _MSC_VER
unsigned long Index;
_BitScanForward(&Index, Val);
return Index;
#endif
}
#if !defined(_MSC_VER) || defined(_M_X64)
template <>
inline std::size_t countTrailingZeros<uint64_t>(uint64_t Val, ZeroBehavior ZB) {
if (ZB != ZB_Undefined && Val == 0)
return 64;
#if __has_builtin(__builtin_ctzll) || __GNUC_PREREQ(4, 0)
return __builtin_ctzll(Val);
#elif _MSC_VER
unsigned long Index;
_BitScanForward64(&Index, Val);
return Index;
#endif
}
#endif
#endif
/// \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>
typename enable_if_c<std::numeric_limits<T>::is_integer &&
!std::numeric_limits<T>::is_signed, std::size_t>::type
countLeadingZeros(T Val, ZeroBehavior ZB = ZB_Width) {
(void)ZB;
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;
}
// Disable signed.
template <typename T>
typename enable_if_c<std::numeric_limits<T>::is_integer &&
std::numeric_limits<T>::is_signed, std::size_t>::type
countLeadingZeros(T Val, ZeroBehavior ZB = ZB_Width) LLVM_DELETED_FUNCTION;
#if __GNUC__ >= 4 || _MSC_VER
template <>
inline std::size_t countLeadingZeros<uint32_t>(uint32_t Val, ZeroBehavior ZB) {
if (ZB != ZB_Undefined && Val == 0)
return 32;
#if __has_builtin(__builtin_clz) || __GNUC_PREREQ(4, 0)
return __builtin_clz(Val);
#elif _MSC_VER
unsigned long Index;
_BitScanReverse(&Index, Val);
return Index ^ 31;
#endif
}
#if !defined(_MSC_VER) || defined(_M_X64)
template <>
inline std::size_t countLeadingZeros<uint64_t>(uint64_t Val, ZeroBehavior ZB) {
if (ZB != ZB_Undefined && Val == 0)
return 64;
#if __has_builtin(__builtin_clzll) || __GNUC_PREREQ(4, 0)
return __builtin_clzll(Val);
#elif _MSC_VER
unsigned long Index;
_BitScanReverse64(&Index, Val);
return Index ^ 63;
#endif
}
#endif
#endif
/// \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>
typename enable_if_c<std::numeric_limits<T>::is_integer &&
!std::numeric_limits<T>::is_signed, T>::type
findFirstSet(T Val, ZeroBehavior ZB = ZB_Max) {
if (ZB == ZB_Max && Val == 0)
return std::numeric_limits<T>::max();
return countTrailingZeros(Val, ZB_Undefined);
}
// Disable signed.
template <typename T>
typename enable_if_c<std::numeric_limits<T>::is_integer &&
std::numeric_limits<T>::is_signed, T>::type
findFirstSet(T Val, ZeroBehavior ZB = ZB_Max) LLVM_DELETED_FUNCTION;
/// \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>
typename enable_if_c<std::numeric_limits<T>::is_integer &&
!std::numeric_limits<T>::is_signed, T>::type
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);
}
// Disable signed.
template <typename T>
typename enable_if_c<std::numeric_limits<T>::is_integer &&
std::numeric_limits<T>::is_signed, T>::type
findLastSet(T Val, ZeroBehavior ZB = ZB_Max) LLVM_DELETED_FUNCTION;
/// \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)
};
/// \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.
/// 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;
}
/// 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);
}
/// 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;
}
/// 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);
}
/// isUIntN - Checks if an unsigned integer fits into the given (dynamic)
/// bit width.
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.
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.
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) {
return sys::SwapByteOrder_16(Value);
}
/// ByteSwap_32 - This function returns a byte-swapped representation of the
/// 32-bit argument, Value.
inline uint32_t ByteSwap_32(uint32_t Value) {
return sys::SwapByteOrder_32(Value);
}
/// ByteSwap_64 - This function returns a byte-swapped representation of the
/// 64-bit argument, Value.
inline uint64_t ByteSwap_64(uint64_t Value) {
return sys::SwapByteOrder_64(Value);
}
/// 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(~Value);
}
/// 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(~Value);
}
/// 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(~Value);
}
/// 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(~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(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(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(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(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.
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.
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
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.
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);
}
/// \brief Sign extend number in the bottom B bits of X to a 32-bit int.
/// Requires 0 < B <= 32.
inline int32_t SignExtend32(uint32_t X, unsigned B) {
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);
}
/// \brief Sign extend number in the bottom B bits of X to a 64-bit int.
/// Requires 0 < B <= 64.
inline int64_t SignExtend64(uint64_t X, unsigned B) {
return int64_t(X << (64 - B)) >> (64 - B);
}
#if defined(_MSC_VER)
// Visual Studio defines the HUGE_VAL class of macros using purposeful
// constant arithmetic overflow, which it then warns on when encountered.
const float huge_valf = std::numeric_limits<float>::infinity();
#else
const float huge_valf = HUGE_VALF;
#endif
} // End llvm namespace
#endif