folly/IPAddressV6.cpp

   1 /*
   2  * Copyright 2017 Facebook, Inc.
   3  *
   4  * Licensed under the Apache License, Version 2.0 (the "License");
   5  * you may not use this file except in compliance with the License.
   6  * You may obtain a copy of the License at
   7  *
   8  *   http://www.apache.org/licenses/LICENSE-2.0
   9  *
  10  * Unless required by applicable law or agreed to in writing, software
  11  * distributed under the License is distributed on an "AS IS" BASIS,
  12  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  13  * See the License for the specific language governing permissions and
  14  * limitations under the License.
  15  */
  16
  17 #include <folly/IPAddressV6.h>
  18
  19 #include <ostream>
  20 #include <string>
  21
  22 #include <folly/Format.h>
  23 #include <folly/IPAddress.h>
  24 #include <folly/IPAddressV4.h>
  25 #include <folly/MacAddress.h>
  26 #include <folly/detail/IPAddressSource.h>
  27
  28 using std::ostream;
  29 using std::string;
  30
  31 namespace folly {
  32
  33 // public static const
  34 const uint32_t IPAddressV6::PREFIX_TEREDO = 0x20010000;
  35 const uint32_t IPAddressV6::PREFIX_6TO4 = 0x2002;
  36
  37 // free functions
  38 size_t hash_value(const IPAddressV6& addr) {
  39   return addr.hash();
  40 }
  41 ostream& operator<<(ostream& os, const IPAddressV6& addr) {
  42   os << addr.str();
  43   return os;
  44 }
  45 void toAppend(IPAddressV6 addr, string* result) {
  46   result->append(addr.str());
  47 }
  48 void toAppend(IPAddressV6 addr, fbstring* result) {
  49   result->append(addr.str());
  50 }
  51
  52 bool IPAddressV6::validate(StringPiece ip) {
  53   if (ip.size() > 0 && ip.front() == '[' && ip.back() == ']') {
  54     ip = ip.subpiece(1, ip.size() - 2);
  55   }
  56
  57   constexpr size_t kStrMaxLen = INET6_ADDRSTRLEN;
  58   std::array<char, kStrMaxLen + 1> ip_cstr;
  59   const size_t len = std::min(ip.size(), kStrMaxLen);
  60   std::memcpy(ip_cstr.data(), ip.data(), len);
  61   ip_cstr[len] = 0;
  62   struct in6_addr addr;
  63   return 1 == inet_pton(AF_INET6, ip_cstr.data(), &addr);
  64 }
  65
  66 // public default constructor
  67 IPAddressV6::IPAddressV6() {
  68 }
  69
  70 // public string constructor
  71 IPAddressV6::IPAddressV6(StringPiece addr) {
  72   auto ip = addr.str();
  73
  74   // Allow addresses surrounded in brackets
  75   if (ip.size() < 2) {
  76     throw IPAddressFormatException(
  77         to<std::string>("Invalid IPv6 address '", ip, "': address too short"));
  78   }
  79   if (ip.front() == '[' && ip.back() == ']') {
  80     ip = ip.substr(1, ip.size() - 2);
  81   }
  82
  83   struct addrinfo* result;
  84   struct addrinfo hints;
  85   memset(&hints, 0, sizeof(hints));
  86   hints.ai_family = AF_INET6;
  87   hints.ai_socktype = SOCK_STREAM;
  88   hints.ai_flags = AI_NUMERICHOST;
  89   if (!getaddrinfo(ip.c_str(), nullptr, &hints, &result)) {
  90     struct sockaddr_in6* ipAddr = (struct sockaddr_in6*)result->ai_addr;
  91     addr_.in6Addr_ = ipAddr->sin6_addr;
  92     scope_ = uint16_t(ipAddr->sin6_scope_id);
  93     freeaddrinfo(result);
  94   } else {
  95     throw IPAddressFormatException(
  96         to<std::string>("Invalid IPv6 address '", ip, "'"));
  97   }
  98 }
  99
 100 // in6_addr constructor
 101 IPAddressV6::IPAddressV6(const in6_addr& src)
 102   : addr_(src)
 103 {
 104 }
 105
 106 // sockaddr_in6 constructor
 107 IPAddressV6::IPAddressV6(const sockaddr_in6& src)
 108   : addr_(src.sin6_addr)
 109   , scope_(uint16_t(src.sin6_scope_id))
 110 {
 111 }
 112
 113 // ByteArray16 constructor
 114 IPAddressV6::IPAddressV6(const ByteArray16& src)
 115   : addr_(src)
 116 {
 117 }
 118
 119 // link-local constructor
 120 IPAddressV6::IPAddressV6(LinkLocalTag, MacAddress mac)
 121   : addr_(mac) {
 122 }
 123
 124 IPAddressV6::AddressStorage::AddressStorage(MacAddress mac) {
 125   // The link-local address uses modified EUI-64 format,
 126   // See RFC 4291 sections 2.5.1, 2.5.6, and Appendix A
 127   const auto* macBytes = mac.bytes();
 128   memcpy(&bytes_.front(), "\xfe\x80\x00\x00\x00\x00\x00\x00", 8);
 129   bytes_[8] = uint8_t(macBytes[0] ^ 0x02);
 130   bytes_[9] = macBytes[1];
 131   bytes_[10] = macBytes[2];
 132   bytes_[11] = 0xff;
 133   bytes_[12] = 0xfe;
 134   bytes_[13] = macBytes[3];
 135   bytes_[14] = macBytes[4];
 136   bytes_[15] = macBytes[5];
 137 }
 138
 139 Optional<MacAddress> IPAddressV6::getMacAddressFromLinkLocal() const {
 140   // Returned MacAddress must be constructed from a link-local IPv6 address.
 141   if (!(addr_.bytes_[0] == 0xfe && addr_.bytes_[1] == 0x80 &&
 142         addr_.bytes_[2] == 0x00 && addr_.bytes_[3] == 0x00 &&
 143         addr_.bytes_[4] == 0x00 && addr_.bytes_[5] == 0x00 &&
 144         addr_.bytes_[6] == 0x00 && addr_.bytes_[7] == 0x00 &&
 145         addr_.bytes_[11] == 0xff && addr_.bytes_[12] == 0xfe)) {
 146     return folly::none;
 147   }
 148   // The link-local address uses modified EUI-64 format,
 149   // See RFC 4291 sections 2.5.1, 2.5.6, and Appendix A
 150   std::array<uint8_t, MacAddress::SIZE> bytes;
 151   // Step 1: first 8 bytes are fe:80:00:00:00:00:00:00, and can be stripped
 152   // Step 2: invert the universal/local (U/L) flag (bit 7)
 153   bytes[0] = addr_.bytes_[8] ^ 0x02;
 154   // Step 3: copy thhese bytes are they are
 155   bytes[1] = addr_.bytes_[9];
 156   bytes[2] = addr_.bytes_[10];
 157   // Step 4: strip bytes (0xfffe), which are bytes_[11] and bytes_[12]
 158   // Step 5: copy the rest.
 159   bytes[3] = addr_.bytes_[13];
 160   bytes[4] = addr_.bytes_[14];
 161   bytes[5] = addr_.bytes_[15];
 162   return Optional<MacAddress>(MacAddress::fromBinary(range(bytes)));
 163 }
 164
 165 void IPAddressV6::setFromBinary(ByteRange bytes) {
 166   if (bytes.size() != 16) {
 167     throw IPAddressFormatException(to<std::string>(
 168         "Invalid IPv6 binary data: length must ",
 169         "be 16 bytes, got ",
 170         bytes.size()));
 171   }
 172   memcpy(&addr_.in6Addr_.s6_addr, bytes.data(), sizeof(in6_addr));
 173   scope_ = 0;
 174 }
 175
 176 // public
 177 IPAddressV4 IPAddressV6::createIPv4() const {
 178   if (!isIPv4Mapped()) {
 179     throw IPAddressFormatException("addr is not v4-to-v6-mapped");
 180   }
 181   const unsigned char* by = bytes();
 182   return IPAddressV4(detail::Bytes::mkAddress4(&by[12]));
 183 }
 184
 185 // convert two uint8_t bytes into a uint16_t as hibyte.lobyte
 186 static inline uint16_t unpack(uint8_t lobyte, uint8_t hibyte) {
 187   return uint16_t((uint16_t(hibyte) << 8) | lobyte);
 188 }
 189
 190 // given a src string, unpack count*2 bytes into dest
 191 // dest must have as much storage as count
 192 static inline void unpackInto(const unsigned char* src,
 193                               uint16_t* dest,
 194                               size_t count) {
 195   for (size_t i = 0, hi = 1, lo = 0; i < count; i++) {
 196     dest[i] = unpack(src[hi], src[lo]);
 197     hi += 2;
 198     lo += 2;
 199   }
 200 }
 201
 202 // public
 203 IPAddressV4 IPAddressV6::getIPv4For6To4() const {
 204   if (!is6To4()) {
 205     throw IPAddressV6::TypeError(format(
 206             "Invalid IP '{}': not a 6to4 address", str()).str());
 207   }
 208   // convert 16x8 bytes into first 4x16 bytes
 209   uint16_t ints[4] = {0,0,0,0};
 210   unpackInto(bytes(), ints, 4);
 211   // repack into 4x8
 212   union {
 213     unsigned char bytes[4];
 214     in_addr addr;
 215   } ipv4;
 216   ipv4.bytes[0] = (uint8_t)((ints[1] & 0xFF00) >> 8);
 217   ipv4.bytes[1] = (uint8_t)(ints[1] & 0x00FF);
 218   ipv4.bytes[2] = (uint8_t)((ints[2] & 0xFF00) >> 8);
 219   ipv4.bytes[3] = (uint8_t)(ints[2] & 0x00FF);
 220   return IPAddressV4(ipv4.addr);
 221 }
 222
 223 // public
 224 bool IPAddressV6::isIPv4Mapped() const {
 225   // v4 mapped addresses have their first 10 bytes set to 0, the next 2 bytes
 226   // set to 255 (0xff);
 227   const unsigned char* by = bytes();
 228
 229   // check if first 10 bytes are 0
 230   for (int i = 0; i < 10; i++) {
 231     if (by[i] != 0x00) {
 232       return false;
 233     }
 234   }
 235   // check if bytes 11 and 12 are 255
 236   if (by[10] == 0xff && by[11] == 0xff) {
 237     return true;
 238   }
 239   return false;
 240 }
 241
 242 // public
 243 IPAddressV6::Type IPAddressV6::type() const {
 244   // convert 16x8 bytes into first 2x16 bytes
 245   uint16_t ints[2] = {0,0};
 246   unpackInto(bytes(), ints, 2);
 247
 248   if ((((uint32_t)ints[0] << 16) | ints[1]) == IPAddressV6::PREFIX_TEREDO) {
 249     return Type::TEREDO;
 250   }
 251
 252   if ((uint32_t)ints[0] == IPAddressV6::PREFIX_6TO4) {
 253     return Type::T6TO4;
 254   }
 255
 256   return Type::NORMAL;
 257 }
 258
 259 // public
 260 string IPAddressV6::toJson() const {
 261   return format(
 262       "{{family:'AF_INET6', addr:'{}', hash:{}}}", str(), hash()).str();
 263 }
 264
 265 // public
 266 size_t IPAddressV6::hash() const {
 267   if (isIPv4Mapped()) {
 268     /* An IPAddress containing this object would be equal (i.e. operator==)
 269        to an IPAddress containing the corresponding IPv4.
 270        So we must make sure that the hash values are the same as well */
 271     return IPAddress::createIPv4(*this).hash();
 272   }
 273
 274   static const uint64_t seed = AF_INET6;
 275   uint64_t hash1 = 0, hash2 = 0;
 276   hash::SpookyHashV2::Hash128(&addr_, 16, &hash1, &hash2);
 277   return hash::hash_combine(seed, hash1, hash2);
 278 }
 279
 280 // public
 281 bool IPAddressV6::inSubnet(StringPiece cidrNetwork) const {
 282   auto subnetInfo = IPAddress::createNetwork(cidrNetwork);
 283   auto addr = subnetInfo.first;
 284   if (!addr.isV6()) {
 285     throw IPAddressFormatException(to<std::string>(
 286         "Address '", addr.toJson(), "' ", "is not a V6 address"));
 287   }
 288   return inSubnetWithMask(addr.asV6(), fetchMask(subnetInfo.second));
 289 }
 290
 291 // public
 292 bool IPAddressV6::inSubnetWithMask(const IPAddressV6& subnet,
 293                                    const ByteArray16& cidrMask) const {
 294   const ByteArray16 mask = detail::Bytes::mask(toByteArray(), cidrMask);
 295   const ByteArray16 subMask = detail::Bytes::mask(subnet.toByteArray(),
 296                                                   cidrMask);
 297   return (mask == subMask);
 298 }
 299
 300 // public
 301 bool IPAddressV6::isLoopback() const {
 302   // Check if v4 mapped is loopback
 303   if (isIPv4Mapped() && createIPv4().isLoopback()) {
 304     return true;
 305   }
 306   auto socka = toSockAddr();
 307   return IN6_IS_ADDR_LOOPBACK(&socka.sin6_addr);
 308 }
 309
 310 bool IPAddressV6::isRoutable() const {
 311   return
 312     // 2000::/3 is the only assigned global unicast block
 313     inBinarySubnet({{0x20, 0x00}}, 3) ||
 314     // ffxe::/16 are global scope multicast addresses,
 315     // which are eligible to be routed over the internet
 316     (isMulticast() && getMulticastScope() == 0xe);
 317 }
 318
 319 bool IPAddressV6::isLinkLocalBroadcast() const {
 320   static const IPAddressV6 kLinkLocalBroadcast("ff02::1");
 321   return *this == kLinkLocalBroadcast;
 322 }
 323
 324 // public
 325 bool IPAddressV6::isPrivate() const {
 326   // Check if mapped is private
 327   if (isIPv4Mapped() && createIPv4().isPrivate()) {
 328     return true;
 329   }
 330   return isLoopback() || inBinarySubnet({{0xfc, 0x00}}, 7);
 331 }
 332
 333 // public
 334 bool IPAddressV6::isLinkLocal() const {
 335   return inBinarySubnet({{0xfe, 0x80}}, 10);
 336 }
 337
 338 bool IPAddressV6::isMulticast() const {
 339   return addr_.bytes_[0] == 0xff;
 340 }
 341
 342 uint8_t IPAddressV6::getMulticastFlags() const {
 343   DCHECK(isMulticast());
 344   return uint8_t((addr_.bytes_[1] >> 4) & 0xf);
 345 }
 346
 347 uint8_t IPAddressV6::getMulticastScope() const {
 348   DCHECK(isMulticast());
 349   return uint8_t(addr_.bytes_[1] & 0xf);
 350 }
 351
 352 IPAddressV6 IPAddressV6::getSolicitedNodeAddress() const {
 353   // Solicted node addresses must be constructed from unicast (or anycast)
 354   // addresses
 355   DCHECK(!isMulticast());
 356
 357   uint8_t bytes[16] = { 0xff, 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
 358                         0x00, 0x00, 0x00, 0x01, 0xff, 0x00, 0x00, 0x00 };
 359   bytes[13] = addr_.bytes_[13];
 360   bytes[14] = addr_.bytes_[14];
 361   bytes[15] = addr_.bytes_[15];
 362   return IPAddressV6::fromBinary(ByteRange(bytes, 16));
 363 }
 364
 365 // public
 366 IPAddressV6 IPAddressV6::mask(size_t numBits) const {
 367   static const auto bits = bitCount();
 368   if (numBits > bits) {
 369     throw IPAddressFormatException(
 370         to<std::string>("numBits(", numBits, ") > bitCount(", bits, ")"));
 371   }
 372   ByteArray16 ba = detail::Bytes::mask(fetchMask(numBits), addr_.bytes_);
 373   return IPAddressV6(ba);
 374 }
 375
 376 // public
 377 string IPAddressV6::str() const {
 378   char buffer[INET6_ADDRSTRLEN] = {0};
 379   sockaddr_in6 sock = toSockAddr();
 380   if (!getnameinfo(
 381         (sockaddr*)&sock, sizeof(sock),
 382         buffer, INET6_ADDRSTRLEN,
 383         nullptr, 0, NI_NUMERICHOST)) {
 384     string ip(buffer);
 385     return ip;
 386   } else {
 387     throw IPAddressFormatException(to<std::string>(
 388         "Invalid address with hex ",
 389         "'",
 390         detail::Bytes::toHex(bytes(), 16),
 391         "'"));
 392   }
 393 }
 394
 395 // public
 396 string IPAddressV6::toFullyQualified() const {
 397   return detail::fastIpv6ToString(addr_.in6Addr_);
 398 }
 399
 400 // public
 401 uint8_t IPAddressV6::getNthMSByte(size_t byteIndex) const {
 402   const auto highestIndex = byteCount() - 1;
 403   if (byteIndex > highestIndex) {
 404     throw std::invalid_argument(to<string>("Byte index must be <= ",
 405         to<string>(highestIndex), " for addresses of type :",
 406         detail::familyNameStr(AF_INET6)));
 407   }
 408   return bytes()[byteIndex];
 409 }
 410
 411 // protected
 412 const ByteArray16 IPAddressV6::fetchMask(size_t numBits) {
 413   static const size_t bits = bitCount();
 414   if (numBits > bits) {
 415     throw IPAddressFormatException("IPv6 addresses are 128 bits.");
 416   }
 417   // masks_ is backed by an array so is zero indexed
 418   return masks_[numBits];
 419 }
 420
 421 // public static
 422 CIDRNetworkV6 IPAddressV6::longestCommonPrefix(
 423     const CIDRNetworkV6& one,
 424     const CIDRNetworkV6& two) {
 425   auto prefix = detail::Bytes::longestCommonPrefix(
 426       one.first.addr_.bytes_, one.second, two.first.addr_.bytes_, two.second);
 427   return {IPAddressV6(prefix.first), prefix.second};
 428 }
 429
 430 // protected
 431 bool IPAddressV6::inBinarySubnet(const std::array<uint8_t, 2> addr,
 432                                  size_t numBits) const {
 433   auto masked = mask(numBits);
 434   return (std::memcmp(addr.data(), masked.bytes(), 2) == 0);
 435 }
 436
 437 // static private
 438 const std::array<ByteArray16, 129> IPAddressV6::masks_ = {{
 439 /* /0   */ {{ 0x00,0x00,0x00,0x00,
 440              0x00,0x00,0x00,0x00,
 441              0x00,0x00,0x00,0x00,
 442              0x00,0x00,0x00,0x00 }},
 443 /* /1   */ {{ 0x80,0x00,0x00,0x00,
 444              0x00,0x00,0x00,0x00,
 445              0x00,0x00,0x00,0x00,
 446              0x00,0x00,0x00,0x00 }},
 447 /* /2   */ {{ 0xc0,0x00,0x00,0x00,
 448              0x00,0x00,0x00,0x00,
 449              0x00,0x00,0x00,0x00,
 450              0x00,0x00,0x00,0x00 }},
 451 /* /3   */ {{ 0xe0,0x00,0x00,0x00,
 452              0x00,0x00,0x00,0x00,
 453              0x00,0x00,0x00,0x00,
 454              0x00,0x00,0x00,0x00 }},
 455 /* /4   */ {{ 0xf0,0x00,0x00,0x00,
 456              0x00,0x00,0x00,0x00,
 457              0x00,0x00,0x00,0x00,
 458              0x00,0x00,0x00,0x00 }},
 459 /* /5   */ {{ 0xf8,0x00,0x00,0x00,
 460              0x00,0x00,0x00,0x00,
 461              0x00,0x00,0x00,0x00,
 462              0x00,0x00,0x00,0x00 }},
 463 /* /6   */ {{ 0xfc,0x00,0x00,0x00,
 464              0x00,0x00,0x00,0x00,
 465              0x00,0x00,0x00,0x00,
 466              0x00,0x00,0x00,0x00 }},
 467 /* /7   */ {{ 0xfe,0x00,0x00,0x00,
 468              0x00,0x00,0x00,0x00,
 469              0x00,0x00,0x00,0x00,
 470              0x00,0x00,0x00,0x00 }},
 471 /* /8   */ {{ 0xff,0x00,0x00,0x00,
 472              0x00,0x00,0x00,0x00,
 473              0x00,0x00,0x00,0x00,
 474              0x00,0x00,0x00,0x00 }},
 475 /* /9   */ {{ 0xff,0x80,0x00,0x00,
 476              0x00,0x00,0x00,0x00,
 477              0x00,0x00,0x00,0x00,
 478              0x00,0x00,0x00,0x00 }},
 479 /* /10  */ {{ 0xff,0xc0,0x00,0x00,
 480              0x00,0x00,0x00,0x00,
 481              0x00,0x00,0x00,0x00,
 482              0x00,0x00,0x00,0x00 }},
 483 /* /11  */ {{ 0xff,0xe0,0x00,0x00,
 484              0x00,0x00,0x00,0x00,
 485              0x00,0x00,0x00,0x00,
 486              0x00,0x00,0x00,0x00 }},
 487 /* /12  */ {{ 0xff,0xf0,0x00,0x00,
 488              0x00,0x00,0x00,0x00,
 489              0x00,0x00,0x00,0x00,
 490              0x00,0x00,0x00,0x00 }},
 491 /* /13  */ {{ 0xff,0xf8,0x00,0x00,
 492              0x00,0x00,0x00,0x00,
 493              0x00,0x00,0x00,0x00,
 494              0x00,0x00,0x00,0x00 }},
 495 /* /14  */ {{ 0xff,0xfc,0x00,0x00,
 496              0x00,0x00,0x00,0x00,
 497              0x00,0x00,0x00,0x00,
 498              0x00,0x00,0x00,0x00 }},
 499 /* /15  */ {{ 0xff,0xfe,0x00,0x00,
 500              0x00,0x00,0x00,0x00,
 501              0x00,0x00,0x00,0x00,
 502              0x00,0x00,0x00,0x00 }},
 503 /* /16  */ {{ 0xff,0xff,0x00,0x00,
 504              0x00,0x00,0x00,0x00,
 505              0x00,0x00,0x00,0x00,
 506              0x00,0x00,0x00,0x00 }},
 507 /* /17  */ {{ 0xff,0xff,0x80,0x00,
 508              0x00,0x00,0x00,0x00,
 509              0x00,0x00,0x00,0x00,
 510              0x00,0x00,0x00,0x00 }},
 511 /* /18  */ {{ 0xff,0xff,0xc0,0x00,
 512              0x00,0x00,0x00,0x00,
 513              0x00,0x00,0x00,0x00,
 514              0x00,0x00,0x00,0x00 }},
 515 /* /19  */ {{ 0xff,0xff,0xe0,0x00,
 516              0x00,0x00,0x00,0x00,
 517              0x00,0x00,0x00,0x00,
 518              0x00,0x00,0x00,0x00 }},
 519 /* /20  */ {{ 0xff,0xff,0xf0,0x00,
 520              0x00,0x00,0x00,0x00,
 521              0x00,0x00,0x00,0x00,
 522              0x00,0x00,0x00,0x00 }},
 523 /* /21  */ {{ 0xff,0xff,0xf8,0x00,
 524              0x00,0x00,0x00,0x00,
 525              0x00,0x00,0x00,0x00,
 526              0x00,0x00,0x00,0x00 }},
 527 /* /22  */ {{ 0xff,0xff,0xfc,0x00,
 528              0x00,0x00,0x00,0x00,
 529              0x00,0x00,0x00,0x00,
 530              0x00,0x00,0x00,0x00 }},
 531 /* /23  */ {{ 0xff,0xff,0xfe,0x00,
 532              0x00,0x00,0x00,0x00,
 533              0x00,0x00,0x00,0x00,
 534              0x00,0x00,0x00,0x00 }},
 535 /* /24  */ {{ 0xff,0xff,0xff,0x00,
 536              0x00,0x00,0x00,0x00,
 537              0x00,0x00,0x00,0x00,
 538              0x00,0x00,0x00,0x00 }},
 539 /* /25  */ {{ 0xff,0xff,0xff,0x80,
 540              0x00,0x00,0x00,0x00,
 541              0x00,0x00,0x00,0x00,
 542              0x00,0x00,0x00,0x00 }},
 543 /* /26  */ {{ 0xff,0xff,0xff,0xc0,
 544              0x00,0x00,0x00,0x00,
 545              0x00,0x00,0x00,0x00,
 546              0x00,0x00,0x00,0x00 }},
 547 /* /27  */ {{ 0xff,0xff,0xff,0xe0,
 548              0x00,0x00,0x00,0x00,
 549              0x00,0x00,0x00,0x00,
 550              0x00,0x00,0x00,0x00 }},
 551 /* /28  */ {{ 0xff,0xff,0xff,0xf0,
 552              0x00,0x00,0x00,0x00,
 553              0x00,0x00,0x00,0x00,
 554              0x00,0x00,0x00,0x00 }},
 555 /* /29  */ {{ 0xff,0xff,0xff,0xf8,
 556              0x00,0x00,0x00,0x00,
 557              0x00,0x00,0x00,0x00,
 558              0x00,0x00,0x00,0x00 }},
 559 /* /30  */ {{ 0xff,0xff,0xff,0xfc,
 560              0x00,0x00,0x00,0x00,
 561              0x00,0x00,0x00,0x00,
 562              0x00,0x00,0x00,0x00 }},
 563 /* /31  */ {{ 0xff,0xff,0xff,0xfe,
 564              0x00,0x00,0x00,0x00,
 565              0x00,0x00,0x00,0x00,
 566              0x00,0x00,0x00,0x00 }},
 567 /* /32  */ {{ 0xff,0xff,0xff,0xff,
 568              0x00,0x00,0x00,0x00,
 569              0x00,0x00,0x00,0x00,
 570              0x00,0x00,0x00,0x00 }},
 571 /* /33  */ {{ 0xff,0xff,0xff,0xff,
 572              0x80,0x00,0x00,0x00,
 573              0x00,0x00,0x00,0x00,
 574              0x00,0x00,0x00,0x00 }},
 575 /* /34  */ {{ 0xff,0xff,0xff,0xff,
 576              0xc0,0x00,0x00,0x00,
 577              0x00,0x00,0x00,0x00,
 578              0x00,0x00,0x00,0x00 }},
 579 /* /35  */ {{ 0xff,0xff,0xff,0xff,
 580              0xe0,0x00,0x00,0x00,
 581              0x00,0x00,0x00,0x00,
 582              0x00,0x00,0x00,0x00 }},
 583 /* /36  */ {{ 0xff,0xff,0xff,0xff,
 584              0xf0,0x00,0x00,0x00,
 585              0x00,0x00,0x00,0x00,
 586              0x00,0x00,0x00,0x00 }},
 587 /* /37  */ {{ 0xff,0xff,0xff,0xff,
 588              0xf8,0x00,0x00,0x00,
 589              0x00,0x00,0x00,0x00,
 590              0x00,0x00,0x00,0x00 }},
 591 /* /38  */ {{ 0xff,0xff,0xff,0xff,
 592              0xfc,0x00,0x00,0x00,
 593              0x00,0x00,0x00,0x00,
 594              0x00,0x00,0x00,0x00 }},
 595 /* /39  */ {{ 0xff,0xff,0xff,0xff,
 596              0xfe,0x00,0x00,0x00,
 597              0x00,0x00,0x00,0x00,
 598              0x00,0x00,0x00,0x00 }},
 599 /* /40  */ {{ 0xff,0xff,0xff,0xff,
 600              0xff,0x00,0x00,0x00,
 601              0x00,0x00,0x00,0x00,
 602              0x00,0x00,0x00,0x00 }},
 603 /* /41  */ {{ 0xff,0xff,0xff,0xff,
 604              0xff,0x80,0x00,0x00,
 605              0x00,0x00,0x00,0x00,
 606              0x00,0x00,0x00,0x00 }},
 607 /* /42  */ {{ 0xff,0xff,0xff,0xff,
 608              0xff,0xc0,0x00,0x00,
 609              0x00,0x00,0x00,0x00,
 610              0x00,0x00,0x00,0x00 }},
 611 /* /43  */ {{ 0xff,0xff,0xff,0xff,
 612              0xff,0xe0,0x00,0x00,
 613              0x00,0x00,0x00,0x00,
 614              0x00,0x00,0x00,0x00 }},
 615 /* /44  */ {{ 0xff,0xff,0xff,0xff,
 616              0xff,0xf0,0x00,0x00,
 617              0x00,0x00,0x00,0x00,
 618              0x00,0x00,0x00,0x00 }},
 619 /* /45  */ {{ 0xff,0xff,0xff,0xff,
 620              0xff,0xf8,0x00,0x00,
 621              0x00,0x00,0x00,0x00,
 622              0x00,0x00,0x00,0x00 }},
 623 /* /46  */ {{ 0xff,0xff,0xff,0xff,
 624              0xff,0xfc,0x00,0x00,
 625              0x00,0x00,0x00,0x00,
 626              0x00,0x00,0x00,0x00 }},
 627 /* /47  */ {{ 0xff,0xff,0xff,0xff,
 628              0xff,0xfe,0x00,0x00,
 629              0x00,0x00,0x00,0x00,
 630              0x00,0x00,0x00,0x00 }},
 631 /* /48  */ {{ 0xff,0xff,0xff,0xff,
 632              0xff,0xff,0x00,0x00,
 633              0x00,0x00,0x00,0x00,
 634              0x00,0x00,0x00,0x00 }},
 635 /* /49  */ {{ 0xff,0xff,0xff,0xff,
 636              0xff,0xff,0x80,0x00,
 637              0x00,0x00,0x00,0x00,
 638              0x00,0x00,0x00,0x00 }},
 639 /* /50  */ {{ 0xff,0xff,0xff,0xff,
 640              0xff,0xff,0xc0,0x00,
 641              0x00,0x00,0x00,0x00,
 642              0x00,0x00,0x00,0x00 }},
 643 /* /51  */ {{ 0xff,0xff,0xff,0xff,
 644              0xff,0xff,0xe0,0x00,
 645              0x00,0x00,0x00,0x00,
 646              0x00,0x00,0x00,0x00 }},
 647 /* /52  */ {{ 0xff,0xff,0xff,0xff,
 648              0xff,0xff,0xf0,0x00,
 649              0x00,0x00,0x00,0x00,
 650              0x00,0x00,0x00,0x00 }},
 651 /* /53  */ {{ 0xff,0xff,0xff,0xff,
 652              0xff,0xff,0xf8,0x00,
 653              0x00,0x00,0x00,0x00,
 654              0x00,0x00,0x00,0x00 }},
 655 /* /54  */ {{ 0xff,0xff,0xff,0xff,
 656              0xff,0xff,0xfc,0x00,
 657              0x00,0x00,0x00,0x00,
 658              0x00,0x00,0x00,0x00 }},
 659 /* /55  */ {{ 0xff,0xff,0xff,0xff,
 660              0xff,0xff,0xfe,0x00,
 661              0x00,0x00,0x00,0x00,
 662              0x00,0x00,0x00,0x00 }},
 663 /* /56  */ {{ 0xff,0xff,0xff,0xff,
 664              0xff,0xff,0xff,0x00,
 665              0x00,0x00,0x00,0x00,
 666              0x00,0x00,0x00,0x00 }},
 667 /* /57  */ {{ 0xff,0xff,0xff,0xff,
 668              0xff,0xff,0xff,0x80,
 669              0x00,0x00,0x00,0x00,
 670              0x00,0x00,0x00,0x00 }},
 671 /* /58  */ {{ 0xff,0xff,0xff,0xff,
 672              0xff,0xff,0xff,0xc0,
 673              0x00,0x00,0x00,0x00,
 674              0x00,0x00,0x00,0x00 }},
 675 /* /59  */ {{ 0xff,0xff,0xff,0xff,
 676              0xff,0xff,0xff,0xe0,
 677              0x00,0x00,0x00,0x00,
 678              0x00,0x00,0x00,0x00 }},
 679 /* /60  */ {{ 0xff,0xff,0xff,0xff,
 680              0xff,0xff,0xff,0xf0,
 681              0x00,0x00,0x00,0x00,
 682              0x00,0x00,0x00,0x00 }},
 683 /* /61  */ {{ 0xff,0xff,0xff,0xff,
 684              0xff,0xff,0xff,0xf8,
 685              0x00,0x00,0x00,0x00,
 686              0x00,0x00,0x00,0x00 }},
 687 /* /62  */ {{ 0xff,0xff,0xff,0xff,
 688              0xff,0xff,0xff,0xfc,
 689              0x00,0x00,0x00,0x00,
 690              0x00,0x00,0x00,0x00 }},
 691 /* /63  */ {{ 0xff,0xff,0xff,0xff,
 692              0xff,0xff,0xff,0xfe,
 693              0x00,0x00,0x00,0x00,
 694              0x00,0x00,0x00,0x00 }},
 695 /* /64  */ {{ 0xff,0xff,0xff,0xff,
 696              0xff,0xff,0xff,0xff,
 697              0x00,0x00,0x00,0x00,
 698              0x00,0x00,0x00,0x00 }},
 699 /* /65  */ {{ 0xff,0xff,0xff,0xff,
 700              0xff,0xff,0xff,0xff,
 701              0x80,0x00,0x00,0x00,
 702              0x00,0x00,0x00,0x00 }},
 703 /* /66  */ {{ 0xff,0xff,0xff,0xff,
 704              0xff,0xff,0xff,0xff,
 705              0xc0,0x00,0x00,0x00,
 706              0x00,0x00,0x00,0x00 }},
 707 /* /67  */ {{ 0xff,0xff,0xff,0xff,
 708              0xff,0xff,0xff,0xff,
 709              0xe0,0x00,0x00,0x00,
 710              0x00,0x00,0x00,0x00 }},
 711 /* /68  */ {{ 0xff,0xff,0xff,0xff,
 712              0xff,0xff,0xff,0xff,
 713              0xf0,0x00,0x00,0x00,
 714              0x00,0x00,0x00,0x00 }},
 715 /* /69  */ {{ 0xff,0xff,0xff,0xff,
 716              0xff,0xff,0xff,0xff,
 717              0xf8,0x00,0x00,0x00,
 718              0x00,0x00,0x00,0x00 }},
 719 /* /70  */ {{ 0xff,0xff,0xff,0xff,
 720              0xff,0xff,0xff,0xff,
 721              0xfc,0x00,0x00,0x00,
 722              0x00,0x00,0x00,0x00 }},
 723 /* /71  */ {{ 0xff,0xff,0xff,0xff,
 724              0xff,0xff,0xff,0xff,
 725              0xfe,0x00,0x00,0x00,
 726              0x00,0x00,0x00,0x00 }},
 727 /* /72  */ {{ 0xff,0xff,0xff,0xff,
 728              0xff,0xff,0xff,0xff,
 729              0xff,0x00,0x00,0x00,
 730              0x00,0x00,0x00,0x00 }},
 731 /* /73  */ {{ 0xff,0xff,0xff,0xff,
 732              0xff,0xff,0xff,0xff,
 733              0xff,0x80,0x00,0x00,
 734              0x00,0x00,0x00,0x00 }},
 735 /* /74  */ {{ 0xff,0xff,0xff,0xff,
 736              0xff,0xff,0xff,0xff,
 737              0xff,0xc0,0x00,0x00,
 738              0x00,0x00,0x00,0x00 }},
 739 /* /75  */ {{ 0xff,0xff,0xff,0xff,
 740              0xff,0xff,0xff,0xff,
 741              0xff,0xe0,0x00,0x00,
 742              0x00,0x00,0x00,0x00 }},
 743 /* /76  */ {{ 0xff,0xff,0xff,0xff,
 744              0xff,0xff,0xff,0xff,
 745              0xff,0xf0,0x00,0x00,
 746              0x00,0x00,0x00,0x00 }},
 747 /* /77  */ {{ 0xff,0xff,0xff,0xff,
 748              0xff,0xff,0xff,0xff,
 749              0xff,0xf8,0x00,0x00,
 750              0x00,0x00,0x00,0x00 }},
 751 /* /78  */ {{ 0xff,0xff,0xff,0xff,
 752              0xff,0xff,0xff,0xff,
 753              0xff,0xfc,0x00,0x00,
 754              0x00,0x00,0x00,0x00 }},
 755 /* /79  */ {{ 0xff,0xff,0xff,0xff,
 756              0xff,0xff,0xff,0xff,
 757              0xff,0xfe,0x00,0x00,
 758              0x00,0x00,0x00,0x00 }},
 759 /* /80  */ {{ 0xff,0xff,0xff,0xff,
 760              0xff,0xff,0xff,0xff,
 761              0xff,0xff,0x00,0x00,
 762              0x00,0x00,0x00,0x00 }},
 763 /* /81  */ {{ 0xff,0xff,0xff,0xff,
 764              0xff,0xff,0xff,0xff,
 765              0xff,0xff,0x80,0x00,
 766              0x00,0x00,0x00,0x00 }},
 767 /* /82  */ {{ 0xff,0xff,0xff,0xff,
 768              0xff,0xff,0xff,0xff,
 769              0xff,0xff,0xc0,0x00,
 770              0x00,0x00,0x00,0x00 }},
 771 /* /83  */ {{ 0xff,0xff,0xff,0xff,
 772              0xff,0xff,0xff,0xff,
 773              0xff,0xff,0xe0,0x00,
 774              0x00,0x00,0x00,0x00 }},
 775 /* /84  */ {{ 0xff,0xff,0xff,0xff,
 776              0xff,0xff,0xff,0xff,
 777              0xff,0xff,0xf0,0x00,
 778              0x00,0x00,0x00,0x00 }},
 779 /* /85  */ {{ 0xff,0xff,0xff,0xff,
 780              0xff,0xff,0xff,0xff,
 781              0xff,0xff,0xf8,0x00,
 782              0x00,0x00,0x00,0x00 }},
 783 /* /86  */ {{ 0xff,0xff,0xff,0xff,
 784              0xff,0xff,0xff,0xff,
 785              0xff,0xff,0xfc,0x00,
 786              0x00,0x00,0x00,0x00 }},
 787 /* /87  */ {{ 0xff,0xff,0xff,0xff,
 788              0xff,0xff,0xff,0xff,
 789              0xff,0xff,0xfe,0x00,
 790              0x00,0x00,0x00,0x00 }},
 791 /* /88  */ {{ 0xff,0xff,0xff,0xff,
 792              0xff,0xff,0xff,0xff,
 793              0xff,0xff,0xff,0x00,
 794              0x00,0x00,0x00,0x00 }},
 795 /* /89  */ {{ 0xff,0xff,0xff,0xff,
 796              0xff,0xff,0xff,0xff,
 797              0xff,0xff,0xff,0x80,
 798              0x00,0x00,0x00,0x00 }},
 799 /* /90  */ {{ 0xff,0xff,0xff,0xff,
 800              0xff,0xff,0xff,0xff,
 801              0xff,0xff,0xff,0xc0,
 802              0x00,0x00,0x00,0x00 }},
 803 /* /91  */ {{ 0xff,0xff,0xff,0xff,
 804              0xff,0xff,0xff,0xff,
 805              0xff,0xff,0xff,0xe0,
 806              0x00,0x00,0x00,0x00 }},
 807 /* /92  */ {{ 0xff,0xff,0xff,0xff,
 808              0xff,0xff,0xff,0xff,
 809              0xff,0xff,0xff,0xf0,
 810              0x00,0x00,0x00,0x00 }},
 811 /* /93  */ {{ 0xff,0xff,0xff,0xff,
 812              0xff,0xff,0xff,0xff,
 813              0xff,0xff,0xff,0xf8,
 814              0x00,0x00,0x00,0x00 }},
 815 /* /94  */ {{ 0xff,0xff,0xff,0xff,
 816              0xff,0xff,0xff,0xff,
 817              0xff,0xff,0xff,0xfc,
 818              0x00,0x00,0x00,0x00 }},
 819 /* /95  */ {{ 0xff,0xff,0xff,0xff,
 820              0xff,0xff,0xff,0xff,
 821              0xff,0xff,0xff,0xfe,
 822              0x00,0x00,0x00,0x00 }},
 823 /* /96  */ {{ 0xff,0xff,0xff,0xff,
 824              0xff,0xff,0xff,0xff,
 825              0xff,0xff,0xff,0xff,
 826              0x00,0x00,0x00,0x00 }},
 827 /* /97  */ {{ 0xff,0xff,0xff,0xff,
 828              0xff,0xff,0xff,0xff,
 829              0xff,0xff,0xff,0xff,
 830              0x80,0x00,0x00,0x00 }},
 831 /* /98  */ {{ 0xff,0xff,0xff,0xff,
 832              0xff,0xff,0xff,0xff,
 833              0xff,0xff,0xff,0xff,
 834              0xc0,0x00,0x00,0x00 }},
 835 /* /99  */ {{ 0xff,0xff,0xff,0xff,
 836              0xff,0xff,0xff,0xff,
 837              0xff,0xff,0xff,0xff,
 838              0xe0,0x00,0x00,0x00 }},
 839 /* /100 */ {{ 0xff,0xff,0xff,0xff,
 840              0xff,0xff,0xff,0xff,
 841              0xff,0xff,0xff,0xff,
 842              0xf0,0x00,0x00,0x00 }},
 843 /* /101 */ {{ 0xff,0xff,0xff,0xff,
 844              0xff,0xff,0xff,0xff,
 845              0xff,0xff,0xff,0xff,
 846              0xf8,0x00,0x00,0x00 }},
 847 /* /102 */ {{ 0xff,0xff,0xff,0xff,
 848              0xff,0xff,0xff,0xff,
 849              0xff,0xff,0xff,0xff,
 850              0xfc,0x00,0x00,0x00 }},
 851 /* /103 */ {{ 0xff,0xff,0xff,0xff,
 852              0xff,0xff,0xff,0xff,
 853              0xff,0xff,0xff,0xff,
 854              0xfe,0x00,0x00,0x00 }},
 855 /* /104 */ {{ 0xff,0xff,0xff,0xff,
 856              0xff,0xff,0xff,0xff,
 857              0xff,0xff,0xff,0xff,
 858              0xff,0x00,0x00,0x00 }},
 859 /* /105 */ {{ 0xff,0xff,0xff,0xff,
 860              0xff,0xff,0xff,0xff,
 861              0xff,0xff,0xff,0xff,
 862              0xff,0x80,0x00,0x00 }},
 863 /* /106 */ {{ 0xff,0xff,0xff,0xff,
 864              0xff,0xff,0xff,0xff,
 865              0xff,0xff,0xff,0xff,
 866              0xff,0xc0,0x00,0x00 }},
 867 /* /107 */ {{ 0xff,0xff,0xff,0xff,
 868              0xff,0xff,0xff,0xff,
 869              0xff,0xff,0xff,0xff,
 870              0xff,0xe0,0x00,0x00 }},
 871 /* /108 */ {{ 0xff,0xff,0xff,0xff,
 872              0xff,0xff,0xff,0xff,
 873              0xff,0xff,0xff,0xff,
 874              0xff,0xf0,0x00,0x00 }},
 875 /* /109 */ {{ 0xff,0xff,0xff,0xff,
 876              0xff,0xff,0xff,0xff,
 877              0xff,0xff,0xff,0xff,
 878              0xff,0xf8,0x00,0x00 }},
 879 /* /110 */ {{ 0xff,0xff,0xff,0xff,
 880              0xff,0xff,0xff,0xff,
 881              0xff,0xff,0xff,0xff,
 882              0xff,0xfc,0x00,0x00 }},
 883 /* /111 */ {{ 0xff,0xff,0xff,0xff,
 884              0xff,0xff,0xff,0xff,
 885              0xff,0xff,0xff,0xff,
 886              0xff,0xfe,0x00,0x00 }},
 887 /* /112 */ {{ 0xff,0xff,0xff,0xff,
 888              0xff,0xff,0xff,0xff,
 889              0xff,0xff,0xff,0xff,
 890              0xff,0xff,0x00,0x00 }},
 891 /* /113 */ {{ 0xff,0xff,0xff,0xff,
 892              0xff,0xff,0xff,0xff,
 893              0xff,0xff,0xff,0xff,
 894              0xff,0xff,0x80,0x00 }},
 895 /* /114 */ {{ 0xff,0xff,0xff,0xff,
 896              0xff,0xff,0xff,0xff,
 897              0xff,0xff,0xff,0xff,
 898              0xff,0xff,0xc0,0x00 }},
 899 /* /115 */ {{ 0xff,0xff,0xff,0xff,
 900              0xff,0xff,0xff,0xff,
 901              0xff,0xff,0xff,0xff,
 902              0xff,0xff,0xe0,0x00 }},
 903 /* /116 */ {{ 0xff,0xff,0xff,0xff,
 904              0xff,0xff,0xff,0xff,
 905              0xff,0xff,0xff,0xff,
 906              0xff,0xff,0xf0,0x00 }},
 907 /* /117 */ {{ 0xff,0xff,0xff,0xff,
 908              0xff,0xff,0xff,0xff,
 909              0xff,0xff,0xff,0xff,
 910              0xff,0xff,0xf8,0x00 }},
 911 /* /118 */ {{ 0xff,0xff,0xff,0xff,
 912              0xff,0xff,0xff,0xff,
 913              0xff,0xff,0xff,0xff,
 914              0xff,0xff,0xfc,0x00 }},
 915 /* /119 */ {{ 0xff,0xff,0xff,0xff,
 916              0xff,0xff,0xff,0xff,
 917              0xff,0xff,0xff,0xff,
 918              0xff,0xff,0xfe,0x00 }},
 919 /* /120 */ {{ 0xff,0xff,0xff,0xff,
 920              0xff,0xff,0xff,0xff,
 921              0xff,0xff,0xff,0xff,
 922              0xff,0xff,0xff,0x00 }},
 923 /* /121 */ {{ 0xff,0xff,0xff,0xff,
 924              0xff,0xff,0xff,0xff,
 925              0xff,0xff,0xff,0xff,
 926              0xff,0xff,0xff,0x80 }},
 927 /* /122 */ {{ 0xff,0xff,0xff,0xff,
 928              0xff,0xff,0xff,0xff,
 929              0xff,0xff,0xff,0xff,
 930              0xff,0xff,0xff,0xc0 }},
 931 /* /123 */ {{ 0xff,0xff,0xff,0xff,
 932              0xff,0xff,0xff,0xff,
 933              0xff,0xff,0xff,0xff,
 934              0xff,0xff,0xff,0xe0 }},
 935 /* /124 */ {{ 0xff,0xff,0xff,0xff,
 936              0xff,0xff,0xff,0xff,
 937              0xff,0xff,0xff,0xff,
 938              0xff,0xff,0xff,0xf0 }},
 939 /* /125 */ {{ 0xff,0xff,0xff,0xff,
 940              0xff,0xff,0xff,0xff,
 941              0xff,0xff,0xff,0xff,
 942              0xff,0xff,0xff,0xf8 }},
 943 /* /126 */ {{ 0xff,0xff,0xff,0xff,
 944              0xff,0xff,0xff,0xff,
 945              0xff,0xff,0xff,0xff,
 946              0xff,0xff,0xff,0xfc }},
 947 /* /127 */ {{ 0xff,0xff,0xff,0xff,
 948              0xff,0xff,0xff,0xff,
 949              0xff,0xff,0xff,0xff,
 950              0xff,0xff,0xff,0xfe }},
 951 /* /128 */ {{ 0xff,0xff,0xff,0xff,
 952              0xff,0xff,0xff,0xff,
 953              0xff,0xff,0xff,0xff,
 954              0xff,0xff,0xff,0xff }},
 955 }};
 956
 957 } // folly