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math.h
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// 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>
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
}
// 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
}
#if defined(_MSC_VER) && !defined(_M_X64)
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
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));
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
// 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(_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(_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 {
#ifdef _M_X64
return static_cast<int>(__popcnt64(static_cast<uint64_t>(v)));
#elif 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
}
} // namespace ROCKSDB_NAMESPACE