summaryrefslogtreecommitdiff
path: root/util/math.h
blob: 2254b4aab17f6b233501c3c45020f1f0e494579e (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
//  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
}

// 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;
}

}  // namespace ROCKSDB_NAMESPACE