rocksdb/util/math.h

295 lines
10 KiB
C++

// Copyright (c) Facebook, Inc. and its affiliates. All Rights Reserved.
// This source code is licensed under both the GPLv2 (found in the
// COPYING file in the root directory) and Apache 2.0 License
// (found in the LICENSE.Apache file in the root directory).
#pragma once
#include <assert.h>
#ifdef _MSC_VER
#include <intrin.h>
#endif
#include <cstdint>
#include <type_traits>
#include "rocksdb/rocksdb_namespace.h"
namespace ROCKSDB_NAMESPACE {
// Fast implementation of floor(log2(v)). Undefined for 0 or negative
// numbers (in case of signed type).
template <typename T>
inline int FloorLog2(T v) {
static_assert(std::is_integral<T>::value, "non-integral type");
assert(v > 0);
#ifdef _MSC_VER
static_assert(sizeof(T) <= sizeof(uint64_t), "type too big");
unsigned long idx = 0;
if (sizeof(T) <= sizeof(uint32_t)) {
_BitScanReverse(&idx, static_cast<uint32_t>(v));
} else {
#if defined(_M_X64) || defined(_M_ARM64)
_BitScanReverse64(&idx, static_cast<uint64_t>(v));
#else
const auto vh = static_cast<uint32_t>(static_cast<uint64_t>(v) >> 32);
if (vh != 0) {
_BitScanReverse(&idx, static_cast<uint32_t>(vh));
idx += 32;
} else {
_BitScanReverse(&idx, static_cast<uint32_t>(v));
}
#endif
}
return idx;
#else
static_assert(sizeof(T) <= sizeof(unsigned long long), "type too big");
if (sizeof(T) <= sizeof(unsigned int)) {
int lz = __builtin_clz(static_cast<unsigned int>(v));
return int{sizeof(unsigned int)} * 8 - 1 - lz;
} else if (sizeof(T) <= sizeof(unsigned long)) {
int lz = __builtin_clzl(static_cast<unsigned long>(v));
return int{sizeof(unsigned long)} * 8 - 1 - lz;
} else {
int lz = __builtin_clzll(static_cast<unsigned long long>(v));
return int{sizeof(unsigned long long)} * 8 - 1 - lz;
}
#endif
}
// Constexpr version of FloorLog2
template <typename T>
constexpr int ConstexprFloorLog2(T v) {
int rv = 0;
while (v > T{1}) {
++rv;
v >>= 1;
}
return rv;
}
// Number of low-order zero bits before the first 1 bit. Undefined for 0.
template <typename T>
inline int CountTrailingZeroBits(T v) {
static_assert(std::is_integral<T>::value, "non-integral type");
assert(v != 0);
#ifdef _MSC_VER
static_assert(sizeof(T) <= sizeof(uint64_t), "type too big");
unsigned long tz = 0;
if (sizeof(T) <= sizeof(uint32_t)) {
_BitScanForward(&tz, static_cast<uint32_t>(v));
} else {
#if defined(_M_X64) || defined(_M_ARM64)
_BitScanForward64(&tz, static_cast<uint64_t>(v));
#else
_BitScanForward(&tz, static_cast<uint32_t>(v));
if (tz == 0) {
_BitScanForward(&tz,
static_cast<uint32_t>(static_cast<uint64_t>(v) >> 32));
tz += 32;
}
#endif
}
return static_cast<int>(tz);
#else
static_assert(sizeof(T) <= sizeof(unsigned long long), "type too big");
if (sizeof(T) <= sizeof(unsigned int)) {
return __builtin_ctz(static_cast<unsigned int>(v));
} else if (sizeof(T) <= sizeof(unsigned long)) {
return __builtin_ctzl(static_cast<unsigned long>(v));
} else {
return __builtin_ctzll(static_cast<unsigned long long>(v));
}
#endif
}
// Not all MSVC compile settings will use `BitsSetToOneFallback()`. We include
// the following code at coarse granularity for simpler macros. It's important
// to exclude at least so our non-MSVC unit test coverage tool doesn't see it.
#ifdef _MSC_VER
namespace detail {
template <typename T>
int BitsSetToOneFallback(T v) {
const int kBits = static_cast<int>(sizeof(T)) * 8;
static_assert((kBits & (kBits - 1)) == 0, "must be power of two bits");
// we static_cast these bit patterns in order to truncate them to the correct
// size. Warning C4309 dislikes this technique, so disable it here.
#pragma warning(disable : 4309)
v = static_cast<T>(v - ((v >> 1) & static_cast<T>(0x5555555555555555ull)));
v = static_cast<T>((v & static_cast<T>(0x3333333333333333ull)) +
((v >> 2) & static_cast<T>(0x3333333333333333ull)));
v = static_cast<T>((v + (v >> 4)) & static_cast<T>(0x0F0F0F0F0F0F0F0Full));
#pragma warning(default : 4309)
for (int shift_bits = 8; shift_bits < kBits; shift_bits <<= 1) {
v += static_cast<T>(v >> shift_bits);
}
// we want the bottom "slot" that's big enough to represent a value up to
// (and including) kBits.
return static_cast<int>(v & static_cast<T>(kBits | (kBits - 1)));
}
} // namespace detail
#endif // _MSC_VER
// Number of bits set to 1. Also known as "population count".
template <typename T>
inline int BitsSetToOne(T v) {
static_assert(std::is_integral<T>::value, "non-integral type");
#ifdef _MSC_VER
static_assert(sizeof(T) <= sizeof(uint64_t), "type too big");
if (sizeof(T) < sizeof(uint32_t)) {
// This bit mask is to avoid a compiler warning on unused path
constexpr auto mm = 8 * sizeof(uint32_t) - 1;
// The bit mask is to neutralize sign extension on small signed types
constexpr uint32_t m = (uint32_t{1} << ((8 * sizeof(T)) & mm)) - 1;
#if defined(HAVE_SSE42) && (defined(_M_X64) || defined(_M_IX86))
return static_cast<int>(__popcnt(static_cast<uint32_t>(v) & m));
#else
return static_cast<int>(detail::BitsSetToOneFallback(v) & m);
#endif
} else if (sizeof(T) == sizeof(uint32_t)) {
#if defined(HAVE_SSE42) && (defined(_M_X64) || defined(_M_IX86))
return static_cast<int>(__popcnt(static_cast<uint32_t>(v)));
#else
return detail::BitsSetToOneFallback(static_cast<uint32_t>(v));
#endif
} else {
#if defined(HAVE_SSE42) && defined(_M_X64)
return static_cast<int>(__popcnt64(static_cast<uint64_t>(v)));
#elif defined(HAVE_SSE42) && defined(_M_IX86)
return static_cast<int>(
__popcnt(static_cast<uint32_t>(static_cast<uint64_t>(v) >> 32) +
__popcnt(static_cast<uint32_t>(v))));
#else
return detail::BitsSetToOneFallback(static_cast<uint64_t>(v));
#endif
}
#else
static_assert(sizeof(T) <= sizeof(unsigned long long), "type too big");
if (sizeof(T) < sizeof(unsigned int)) {
// This bit mask is to avoid a compiler warning on unused path
constexpr auto mm = 8 * sizeof(unsigned int) - 1;
// This bit mask is to neutralize sign extension on small signed types
constexpr unsigned int m = (1U << ((8 * sizeof(T)) & mm)) - 1;
return __builtin_popcount(static_cast<unsigned int>(v) & m);
} else if (sizeof(T) == sizeof(unsigned int)) {
return __builtin_popcount(static_cast<unsigned int>(v));
} else if (sizeof(T) <= sizeof(unsigned long)) {
return __builtin_popcountl(static_cast<unsigned long>(v));
} else {
return __builtin_popcountll(static_cast<unsigned long long>(v));
}
#endif
}
template <typename T>
inline int BitParity(T v) {
static_assert(std::is_integral<T>::value, "non-integral type");
#ifdef _MSC_VER
// bit parity == oddness of popcount
return BitsSetToOne(v) & 1;
#else
static_assert(sizeof(T) <= sizeof(unsigned long long), "type too big");
if (sizeof(T) <= sizeof(unsigned int)) {
// On any sane systen, potential sign extension here won't change parity
return __builtin_parity(static_cast<unsigned int>(v));
} else if (sizeof(T) <= sizeof(unsigned long)) {
return __builtin_parityl(static_cast<unsigned long>(v));
} else {
return __builtin_parityll(static_cast<unsigned long long>(v));
}
#endif
}
// Swaps between big and little endian. Can be used in combination with the
// little-endian encoding/decoding functions in coding_lean.h and coding.h to
// encode/decode big endian.
template <typename T>
inline T EndianSwapValue(T v) {
static_assert(std::is_integral<T>::value, "non-integral type");
#ifdef _MSC_VER
if (sizeof(T) == 2) {
return static_cast<T>(_byteswap_ushort(static_cast<uint16_t>(v)));
} else if (sizeof(T) == 4) {
return static_cast<T>(_byteswap_ulong(static_cast<uint32_t>(v)));
} else if (sizeof(T) == 8) {
return static_cast<T>(_byteswap_uint64(static_cast<uint64_t>(v)));
}
#else
if (sizeof(T) == 2) {
return static_cast<T>(__builtin_bswap16(static_cast<uint16_t>(v)));
} else if (sizeof(T) == 4) {
return static_cast<T>(__builtin_bswap32(static_cast<uint32_t>(v)));
} else if (sizeof(T) == 8) {
return static_cast<T>(__builtin_bswap64(static_cast<uint64_t>(v)));
}
#endif
// Recognized by clang as bswap, but not by gcc :(
T ret_val = 0;
for (std::size_t i = 0; i < sizeof(T); ++i) {
ret_val |= ((v >> (8 * i)) & 0xff) << (8 * (sizeof(T) - 1 - i));
}
return ret_val;
}
// Reverses the order of bits in an integral value
template <typename T>
inline T ReverseBits(T v) {
T r = EndianSwapValue(v);
const T kHighestByte = T{1} << ((sizeof(T) - 1) * 8);
const T kEveryByte = kHighestByte | (kHighestByte / 255);
r = ((r & (kEveryByte * 0x0f)) << 4) | ((r >> 4) & (kEveryByte * 0x0f));
r = ((r & (kEveryByte * 0x33)) << 2) | ((r >> 2) & (kEveryByte * 0x33));
r = ((r & (kEveryByte * 0x55)) << 1) | ((r >> 1) & (kEveryByte * 0x55));
return r;
}
// Every output bit depends on many input bits in the same and higher
// positions, but not lower positions. Specifically, this function
// * Output highest bit set to 1 is same as input (same FloorLog2, or
// equivalently, same number of leading zeros)
// * Is its own inverse (an involution)
// * Guarantees that b bottom bits of v and c bottom bits of
// DownwardInvolution(v) uniquely identify b + c bottom bits of v
// (which is all of v if v < 2**(b + c)).
// ** A notable special case is that modifying c adjacent bits at
// some chosen position in the input is bijective with the bottom c
// output bits.
// * Distributes over xor, as in DI(a ^ b) == DI(a) ^ DI(b)
//
// This transformation is equivalent to a matrix*vector multiplication in
// GF(2) where the matrix is recursively defined by the pattern matrix
// P = | 1 1 |
// | 0 1 |
// and replacing 1's with P and 0's with 2x2 zero matices to some depth,
// e.g. depth of 6 for 64-bit T. An essential feature of this matrix
// is that all square sub-matrices that include the top row are invertible.
template <typename T>
inline T DownwardInvolution(T v) {
static_assert(std::is_integral<T>::value, "non-integral type");
static_assert(sizeof(T) <= 8, "only supported up to 64 bits");
uint64_t r = static_cast<uint64_t>(v);
if constexpr (sizeof(T) > 4) {
r ^= r >> 32;
}
if constexpr (sizeof(T) > 2) {
r ^= (r & 0xffff0000ffff0000U) >> 16;
}
if constexpr (sizeof(T) > 1) {
r ^= (r & 0xff00ff00ff00ff00U) >> 8;
}
r ^= (r & 0xf0f0f0f0f0f0f0f0U) >> 4;
r ^= (r & 0xccccccccccccccccU) >> 2;
r ^= (r & 0xaaaaaaaaaaaaaaaaU) >> 1;
return static_cast<T>(r);
}
} // namespace ROCKSDB_NAMESPACE