folly/IPAddressV6.cpp

   1 /*
   2  * Copyright 2015 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
  27 using std::ostream;
  28 using std::string;
  29
  30 namespace folly {
  31
  32 // public static const
  33 const uint32_t IPAddressV6::PREFIX_TEREDO = 0x20010000;
  34 const uint32_t IPAddressV6::PREFIX_6TO4 = 0x2002;
  35
  36 // free functions
  37 size_t hash_value(const IPAddressV6& addr) {
  38   return addr.hash();
  39 }
  40 ostream& operator<<(ostream& os, const IPAddressV6& addr) {
  41   os << addr.str();
  42   return os;
  43 }
  44 void toAppend(IPAddressV6 addr, string* result) {
  45   result->append(addr.str());
  46 }
  47 void toAppend(IPAddressV6 addr, fbstring* result) {
  48   result->append(addr.str());
  49 }
  50
  51 // public default constructor
  52 IPAddressV6::IPAddressV6() {
  53 }
  54
  55 // public string constructor
  56 IPAddressV6::IPAddressV6(StringPiece addr) {
  57   auto ip = addr.str();
  58
  59   // Allow addresses surrounded in brackets
  60   if (ip.size() < 2) {
  61     throw IPAddressFormatException("Invalid IPv6 address '", ip,
  62                                    "': address too short");
  63   }
  64   if (ip.front() == '[' && ip.back() == ']') {
  65     ip = ip.substr(1, ip.size() - 2);
  66   }
  67
  68   struct addrinfo* result;
  69   struct addrinfo hints;
  70   memset(&hints, 0, sizeof(hints));
  71   hints.ai_family = AF_INET6;
  72   hints.ai_socktype = SOCK_STREAM;
  73   hints.ai_flags = AI_NUMERICHOST;
  74   if (!getaddrinfo(ip.c_str(), nullptr, &hints, &result)) {
  75     struct sockaddr_in6* ipAddr = (struct sockaddr_in6*)result->ai_addr;
  76     addr_.in6Addr_ = ipAddr->sin6_addr;
  77     scope_ = ipAddr->sin6_scope_id;
  78     freeaddrinfo(result);
  79   } else {
  80     throw IPAddressFormatException("Invalid IPv6 address '", ip, "'");
  81   }
  82 }
  83
  84 // in6_addr constructor
  85 IPAddressV6::IPAddressV6(const in6_addr& src)
  86   : addr_(src)
  87 {
  88 }
  89
  90 // sockaddr_in6 constructor
  91 IPAddressV6::IPAddressV6(const sockaddr_in6& src)
  92   : addr_(src.sin6_addr)
  93   , scope_(src.sin6_scope_id)
  94 {
  95 }
  96
  97 // ByteArray16 constructor
  98 IPAddressV6::IPAddressV6(const ByteArray16& src)
  99   : addr_(src)
 100 {
 101 }
 102
 103 // link-local constructor
 104 IPAddressV6::IPAddressV6(LinkLocalTag, MacAddress mac)
 105   : addr_(mac) {
 106 }
 107
 108 IPAddressV6::AddressStorage::AddressStorage(MacAddress mac) {
 109   // The link-local address uses modified EUI-64 format,
 110   // See RFC 4291 sections 2.5.1, 2.5.6, and Appendix A
 111   const auto* macBytes = mac.bytes();
 112   memcpy(&bytes_.front(), "\xfe\x80\x00\x00\x00\x00\x00\x00", 8);
 113   bytes_[8] = macBytes[0] ^ 0x02;
 114   bytes_[9] = macBytes[1];
 115   bytes_[10] = macBytes[2];
 116   bytes_[11] = 0xff;
 117   bytes_[12] = 0xfe;
 118   bytes_[13] = macBytes[3];
 119   bytes_[14] = macBytes[4];
 120   bytes_[15] = macBytes[5];
 121 }
 122
 123 void IPAddressV6::setFromBinary(ByteRange bytes) {
 124   if (bytes.size() != 16) {
 125     throw IPAddressFormatException("Invalid IPv6 binary data: length must "
 126                                    "be 16 bytes, got ", bytes.size());
 127   }
 128   memcpy(&addr_.in6Addr_.s6_addr, bytes.data(), sizeof(in6_addr));
 129   scope_ = 0;
 130 }
 131
 132 // public
 133 IPAddressV4 IPAddressV6::createIPv4() const {
 134   if (!isIPv4Mapped()) {
 135     throw IPAddressFormatException("addr is not v4-to-v6-mapped");
 136   }
 137   const unsigned char* by = bytes();
 138   return IPAddressV4(detail::Bytes::mkAddress4(&by[12]));
 139 }
 140
 141 // convert two uint8_t bytes into a uint16_t as hibyte.lobyte
 142 static inline uint16_t unpack(uint8_t lobyte, uint8_t hibyte) {
 143   return ((uint16_t)hibyte << 8) | (uint16_t)lobyte;
 144 }
 145
 146 // given a src string, unpack count*2 bytes into dest
 147 // dest must have as much storage as count
 148 static inline void unpackInto(const unsigned char* src,
 149                               uint16_t* dest,
 150                               size_t count) {
 151   for (size_t i = 0, hi = 1, lo = 0; i < count; i++) {
 152     dest[i] = unpack(src[hi], src[lo]);
 153     hi += 2;
 154     lo += 2;
 155   }
 156 }
 157
 158 // public
 159 IPAddressV4 IPAddressV6::getIPv4For6To4() const {
 160   if (!is6To4()) {
 161     throw IPAddressV6::TypeError(format(
 162             "Invalid IP '{}': not a 6to4 address", str()).str());
 163   }
 164   // convert 16x8 bytes into first 4x16 bytes
 165   uint16_t ints[4] = {0,0,0,0};
 166   unpackInto(bytes(), ints, 4);
 167   // repack into 4x8
 168   union {
 169     unsigned char bytes[4];
 170     in_addr addr;
 171   } ipv4;
 172   ipv4.bytes[0] = (uint8_t)((ints[1] & 0xFF00) >> 8);
 173   ipv4.bytes[1] = (uint8_t)(ints[1] & 0x00FF);
 174   ipv4.bytes[2] = (uint8_t)((ints[2] & 0xFF00) >> 8);
 175   ipv4.bytes[3] = (uint8_t)(ints[2] & 0x00FF);
 176   return IPAddressV4(ipv4.addr);
 177 }
 178
 179 // public
 180 bool IPAddressV6::isIPv4Mapped() const {
 181   // v4 mapped addresses have their first 10 bytes set to 0, the next 2 bytes
 182   // set to 255 (0xff);
 183   const unsigned char* by = bytes();
 184
 185   // check if first 10 bytes are 0
 186   for (int i = 0; i < 10; i++) {
 187     if (by[i] != 0x00) {
 188       return false;
 189     }
 190   }
 191   // check if bytes 11 and 12 are 255
 192   if (by[10] == 0xff && by[11] == 0xff) {
 193     return true;
 194   }
 195   return false;
 196 }
 197
 198 // public
 199 IPAddressV6::Type IPAddressV6::type() const {
 200   // convert 16x8 bytes into first 2x16 bytes
 201   uint16_t ints[2] = {0,0};
 202   unpackInto(bytes(), ints, 2);
 203
 204   if ((((uint32_t)ints[0] << 16) | ints[1]) == IPAddressV6::PREFIX_TEREDO) {
 205     return Type::TEREDO;
 206   }
 207
 208   if ((uint32_t)ints[0] == IPAddressV6::PREFIX_6TO4) {
 209     return Type::T6TO4;
 210   }
 211
 212   return Type::NORMAL;
 213 }
 214
 215 // public
 216 string IPAddressV6::toJson() const {
 217   return format(
 218       "{{family:'AF_INET6', addr:'{}', hash:{}}}", str(), hash()).str();
 219 }
 220
 221 // public
 222 size_t IPAddressV6::hash() const {
 223   if (isIPv4Mapped()) {
 224     /* An IPAddress containing this object would be equal (i.e. operator==)
 225        to an IPAddress containing the corresponding IPv4.
 226        So we must make sure that the hash values are the same as well */
 227     return IPAddress::createIPv4(*this).hash();
 228   }
 229
 230   static const uint64_t seed = AF_INET6;
 231   uint64_t hash1 = 0, hash2 = 0;
 232   hash::SpookyHashV2::Hash128(&addr_, 16, &hash1, &hash2);
 233   return hash::hash_combine(seed, hash1, hash2);
 234 }
 235
 236 // public
 237 bool IPAddressV6::inSubnet(StringPiece cidrNetwork) const {
 238   auto subnetInfo = IPAddress::createNetwork(cidrNetwork);
 239   auto addr = subnetInfo.first;
 240   if (!addr.isV6()) {
 241     throw IPAddressFormatException("Address '", addr.toJson(), "' ",
 242                                    "is not a V6 address");
 243   }
 244   return inSubnetWithMask(addr.asV6(), fetchMask(subnetInfo.second));
 245 }
 246
 247 // public
 248 bool IPAddressV6::inSubnetWithMask(const IPAddressV6& subnet,
 249                                    const ByteArray16& cidrMask) const {
 250   const ByteArray16 mask = detail::Bytes::mask(toByteArray(), cidrMask);
 251   const ByteArray16 subMask = detail::Bytes::mask(subnet.toByteArray(),
 252                                                   cidrMask);
 253   return (mask == subMask);
 254 }
 255
 256 // public
 257 bool IPAddressV6::isLoopback() const {
 258   // Check if v4 mapped is loopback
 259   if (isIPv4Mapped() && createIPv4().isLoopback()) {
 260     return true;
 261   }
 262   auto socka = toSockAddr();
 263   return IN6_IS_ADDR_LOOPBACK(&socka.sin6_addr);
 264 }
 265
 266 bool IPAddressV6::isRoutable() const {
 267   return
 268     // 2000::/3 is the only assigned global unicast block
 269     inBinarySubnet({{0x20, 0x00}}, 3) ||
 270     // ffxe::/16 are global scope multicast addresses,
 271     // which are eligible to be routed over the internet
 272     (isMulticast() && getMulticastScope() == 0xe);
 273 }
 274
 275 bool IPAddressV6::isLinkLocalBroadcast() const {
 276   static const IPAddressV6 kLinkLocalBroadcast("ff02::1");
 277   return *this == kLinkLocalBroadcast;
 278 }
 279
 280 // public
 281 bool IPAddressV6::isPrivate() const {
 282   // Check if mapped is private
 283   if (isIPv4Mapped() && createIPv4().isPrivate()) {
 284     return true;
 285   }
 286   return isLoopback() || inBinarySubnet({{0xfc, 0x00}}, 7);
 287 }
 288
 289 // public
 290 bool IPAddressV6::isLinkLocal() const {
 291   return inBinarySubnet({{0xfe, 0x80}}, 10);
 292 }
 293
 294 bool IPAddressV6::isMulticast() const {
 295   return addr_.bytes_[0] == 0xff;
 296 }
 297
 298 uint8_t IPAddressV6::getMulticastFlags() const {
 299   DCHECK(isMulticast());
 300   return ((addr_.bytes_[1] >> 4) & 0xf);
 301 }
 302
 303 uint8_t IPAddressV6::getMulticastScope() const {
 304   DCHECK(isMulticast());
 305   return (addr_.bytes_[1] & 0xf);
 306 }
 307
 308 IPAddressV6 IPAddressV6::getSolicitedNodeAddress() const {
 309   // Solicted node addresses must be constructed from unicast (or anycast)
 310   // addresses
 311   DCHECK(!isMulticast());
 312
 313   uint8_t bytes[16] = { 0xff, 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
 314                         0x00, 0x00, 0x00, 0x01, 0xff, 0x00, 0x00, 0x00 };
 315   bytes[13] = addr_.bytes_[13];
 316   bytes[14] = addr_.bytes_[14];
 317   bytes[15] = addr_.bytes_[15];
 318   return IPAddressV6::fromBinary(ByteRange(bytes, 16));
 319 }
 320
 321 // public
 322 IPAddressV6 IPAddressV6::mask(size_t numBits) const {
 323   static const auto bits = bitCount();
 324   if (numBits > bits) {
 325     throw IPAddressFormatException("numBits(", numBits, ") > bitCount(",
 326                                    bits, ")");
 327   }
 328   ByteArray16 ba = detail::Bytes::mask(fetchMask(numBits), addr_.bytes_);
 329   return IPAddressV6(ba);
 330 }
 331
 332 // public
 333 string IPAddressV6::str() const {
 334   char buffer[INET6_ADDRSTRLEN] = {0};
 335   sockaddr_in6 sock = toSockAddr();
 336   if (!getnameinfo(
 337         (sockaddr*)&sock, sizeof(sock),
 338         buffer, INET6_ADDRSTRLEN,
 339         nullptr, 0, NI_NUMERICHOST)) {
 340     string ip(buffer);
 341     return ip;
 342   } else {
 343     throw IPAddressFormatException("Invalid address with hex ",
 344                                    "'", detail::Bytes::toHex(bytes(), 16), "'");
 345   }
 346 }
 347
 348 // public
 349 string IPAddressV6::toFullyQualified() const {
 350   return detail::fastIpv6ToString(addr_.in6Addr_);
 351 }
 352
 353 // public
 354 uint8_t IPAddressV6::getNthMSByte(size_t byteIndex) const {
 355   const auto highestIndex = byteCount() - 1;
 356   if (byteIndex > highestIndex) {
 357     throw std::invalid_argument(to<string>("Byte index must be <= ",
 358         to<string>(highestIndex), " for addresses of type :",
 359         detail::familyNameStr(AF_INET6)));
 360   }
 361   return bytes()[byteIndex];
 362 }
 363
 364 // protected
 365 const ByteArray16 IPAddressV6::fetchMask(size_t numBits) {
 366   static const uint8_t bits = bitCount();
 367   if (numBits > bits) {
 368     throw IPAddressFormatException("IPv6 addresses are 128 bits.");
 369   }
 370   // masks_ is backed by an array so is zero indexed
 371   return masks_[numBits];
 372 }
 373
 374 // protected
 375 bool IPAddressV6::inBinarySubnet(const std::array<uint8_t, 2> addr,
 376                                  size_t numBits) const {
 377   const unsigned char* subbytes = mask(numBits).bytes();
 378   return (std::memcmp(addr.data(), subbytes, 2) == 0);
 379 }
 380
 381 // static private
 382 const std::array<ByteArray16, 129> IPAddressV6::masks_ = {{
 383 /* /0   */ {{ 0x00,0x00,0x00,0x00,
 384              0x00,0x00,0x00,0x00,
 385              0x00,0x00,0x00,0x00,
 386              0x00,0x00,0x00,0x00 }},
 387 /* /1   */ {{ 0x80,0x00,0x00,0x00,
 388              0x00,0x00,0x00,0x00,
 389              0x00,0x00,0x00,0x00,
 390              0x00,0x00,0x00,0x00 }},
 391 /* /2   */ {{ 0xc0,0x00,0x00,0x00,
 392              0x00,0x00,0x00,0x00,
 393              0x00,0x00,0x00,0x00,
 394              0x00,0x00,0x00,0x00 }},
 395 /* /3   */ {{ 0xe0,0x00,0x00,0x00,
 396              0x00,0x00,0x00,0x00,
 397              0x00,0x00,0x00,0x00,
 398              0x00,0x00,0x00,0x00 }},
 399 /* /4   */ {{ 0xf0,0x00,0x00,0x00,
 400              0x00,0x00,0x00,0x00,
 401              0x00,0x00,0x00,0x00,
 402              0x00,0x00,0x00,0x00 }},
 403 /* /5   */ {{ 0xf8,0x00,0x00,0x00,
 404              0x00,0x00,0x00,0x00,
 405              0x00,0x00,0x00,0x00,
 406              0x00,0x00,0x00,0x00 }},
 407 /* /6   */ {{ 0xfc,0x00,0x00,0x00,
 408              0x00,0x00,0x00,0x00,
 409              0x00,0x00,0x00,0x00,
 410              0x00,0x00,0x00,0x00 }},
 411 /* /7   */ {{ 0xfe,0x00,0x00,0x00,
 412              0x00,0x00,0x00,0x00,
 413              0x00,0x00,0x00,0x00,
 414              0x00,0x00,0x00,0x00 }},
 415 /* /8   */ {{ 0xff,0x00,0x00,0x00,
 416              0x00,0x00,0x00,0x00,
 417              0x00,0x00,0x00,0x00,
 418              0x00,0x00,0x00,0x00 }},
 419 /* /9   */ {{ 0xff,0x80,0x00,0x00,
 420              0x00,0x00,0x00,0x00,
 421              0x00,0x00,0x00,0x00,
 422              0x00,0x00,0x00,0x00 }},
 423 /* /10  */ {{ 0xff,0xc0,0x00,0x00,
 424              0x00,0x00,0x00,0x00,
 425              0x00,0x00,0x00,0x00,
 426              0x00,0x00,0x00,0x00 }},
 427 /* /11  */ {{ 0xff,0xe0,0x00,0x00,
 428              0x00,0x00,0x00,0x00,
 429              0x00,0x00,0x00,0x00,
 430              0x00,0x00,0x00,0x00 }},
 431 /* /12  */ {{ 0xff,0xf0,0x00,0x00,
 432              0x00,0x00,0x00,0x00,
 433              0x00,0x00,0x00,0x00,
 434              0x00,0x00,0x00,0x00 }},
 435 /* /13  */ {{ 0xff,0xf8,0x00,0x00,
 436              0x00,0x00,0x00,0x00,
 437              0x00,0x00,0x00,0x00,
 438              0x00,0x00,0x00,0x00 }},
 439 /* /14  */ {{ 0xff,0xfc,0x00,0x00,
 440              0x00,0x00,0x00,0x00,
 441              0x00,0x00,0x00,0x00,
 442              0x00,0x00,0x00,0x00 }},
 443 /* /15  */ {{ 0xff,0xfe,0x00,0x00,
 444              0x00,0x00,0x00,0x00,
 445              0x00,0x00,0x00,0x00,
 446              0x00,0x00,0x00,0x00 }},
 447 /* /16  */ {{ 0xff,0xff,0x00,0x00,
 448              0x00,0x00,0x00,0x00,
 449              0x00,0x00,0x00,0x00,
 450              0x00,0x00,0x00,0x00 }},
 451 /* /17  */ {{ 0xff,0xff,0x80,0x00,
 452              0x00,0x00,0x00,0x00,
 453              0x00,0x00,0x00,0x00,
 454              0x00,0x00,0x00,0x00 }},
 455 /* /18  */ {{ 0xff,0xff,0xc0,0x00,
 456              0x00,0x00,0x00,0x00,
 457              0x00,0x00,0x00,0x00,
 458              0x00,0x00,0x00,0x00 }},
 459 /* /19  */ {{ 0xff,0xff,0xe0,0x00,
 460              0x00,0x00,0x00,0x00,
 461              0x00,0x00,0x00,0x00,
 462              0x00,0x00,0x00,0x00 }},
 463 /* /20  */ {{ 0xff,0xff,0xf0,0x00,
 464              0x00,0x00,0x00,0x00,
 465              0x00,0x00,0x00,0x00,
 466              0x00,0x00,0x00,0x00 }},
 467 /* /21  */ {{ 0xff,0xff,0xf8,0x00,
 468              0x00,0x00,0x00,0x00,
 469              0x00,0x00,0x00,0x00,
 470              0x00,0x00,0x00,0x00 }},
 471 /* /22  */ {{ 0xff,0xff,0xfc,0x00,
 472              0x00,0x00,0x00,0x00,
 473              0x00,0x00,0x00,0x00,
 474              0x00,0x00,0x00,0x00 }},
 475 /* /23  */ {{ 0xff,0xff,0xfe,0x00,
 476              0x00,0x00,0x00,0x00,
 477              0x00,0x00,0x00,0x00,
 478              0x00,0x00,0x00,0x00 }},
 479 /* /24  */ {{ 0xff,0xff,0xff,0x00,
 480              0x00,0x00,0x00,0x00,
 481              0x00,0x00,0x00,0x00,
 482              0x00,0x00,0x00,0x00 }},
 483 /* /25  */ {{ 0xff,0xff,0xff,0x80,
 484              0x00,0x00,0x00,0x00,
 485              0x00,0x00,0x00,0x00,
 486              0x00,0x00,0x00,0x00 }},
 487 /* /26  */ {{ 0xff,0xff,0xff,0xc0,
 488              0x00,0x00,0x00,0x00,
 489              0x00,0x00,0x00,0x00,
 490              0x00,0x00,0x00,0x00 }},
 491 /* /27  */ {{ 0xff,0xff,0xff,0xe0,
 492              0x00,0x00,0x00,0x00,
 493              0x00,0x00,0x00,0x00,
 494              0x00,0x00,0x00,0x00 }},
 495 /* /28  */ {{ 0xff,0xff,0xff,0xf0,
 496              0x00,0x00,0x00,0x00,
 497              0x00,0x00,0x00,0x00,
 498              0x00,0x00,0x00,0x00 }},
 499 /* /29  */ {{ 0xff,0xff,0xff,0xf8,
 500              0x00,0x00,0x00,0x00,
 501              0x00,0x00,0x00,0x00,
 502              0x00,0x00,0x00,0x00 }},
 503 /* /30  */ {{ 0xff,0xff,0xff,0xfc,
 504              0x00,0x00,0x00,0x00,
 505              0x00,0x00,0x00,0x00,
 506              0x00,0x00,0x00,0x00 }},
 507 /* /31  */ {{ 0xff,0xff,0xff,0xfe,
 508              0x00,0x00,0x00,0x00,
 509              0x00,0x00,0x00,0x00,
 510              0x00,0x00,0x00,0x00 }},
 511 /* /32  */ {{ 0xff,0xff,0xff,0xff,
 512              0x00,0x00,0x00,0x00,
 513              0x00,0x00,0x00,0x00,
 514              0x00,0x00,0x00,0x00 }},
 515 /* /33  */ {{ 0xff,0xff,0xff,0xff,
 516              0x80,0x00,0x00,0x00,
 517              0x00,0x00,0x00,0x00,
 518              0x00,0x00,0x00,0x00 }},
 519 /* /34  */ {{ 0xff,0xff,0xff,0xff,
 520              0xc0,0x00,0x00,0x00,
 521              0x00,0x00,0x00,0x00,
 522              0x00,0x00,0x00,0x00 }},
 523 /* /35  */ {{ 0xff,0xff,0xff,0xff,
 524              0xe0,0x00,0x00,0x00,
 525              0x00,0x00,0x00,0x00,
 526              0x00,0x00,0x00,0x00 }},
 527 /* /36  */ {{ 0xff,0xff,0xff,0xff,
 528              0xf0,0x00,0x00,0x00,
 529              0x00,0x00,0x00,0x00,
 530              0x00,0x00,0x00,0x00 }},
 531 /* /37  */ {{ 0xff,0xff,0xff,0xff,
 532              0xf8,0x00,0x00,0x00,
 533              0x00,0x00,0x00,0x00,
 534              0x00,0x00,0x00,0x00 }},
 535 /* /38  */ {{ 0xff,0xff,0xff,0xff,
 536              0xfc,0x00,0x00,0x00,
 537              0x00,0x00,0x00,0x00,
 538              0x00,0x00,0x00,0x00 }},
 539 /* /39  */ {{ 0xff,0xff,0xff,0xff,
 540              0xfe,0x00,0x00,0x00,
 541              0x00,0x00,0x00,0x00,
 542              0x00,0x00,0x00,0x00 }},
 543 /* /40  */ {{ 0xff,0xff,0xff,0xff,
 544              0xff,0x00,0x00,0x00,
 545              0x00,0x00,0x00,0x00,
 546              0x00,0x00,0x00,0x00 }},
 547 /* /41  */ {{ 0xff,0xff,0xff,0xff,
 548              0xff,0x80,0x00,0x00,
 549              0x00,0x00,0x00,0x00,
 550              0x00,0x00,0x00,0x00 }},
 551 /* /42  */ {{ 0xff,0xff,0xff,0xff,
 552              0xff,0xc0,0x00,0x00,
 553              0x00,0x00,0x00,0x00,
 554              0x00,0x00,0x00,0x00 }},
 555 /* /43  */ {{ 0xff,0xff,0xff,0xff,
 556              0xff,0xe0,0x00,0x00,
 557              0x00,0x00,0x00,0x00,
 558              0x00,0x00,0x00,0x00 }},
 559 /* /44  */ {{ 0xff,0xff,0xff,0xff,
 560              0xff,0xf0,0x00,0x00,
 561              0x00,0x00,0x00,0x00,
 562              0x00,0x00,0x00,0x00 }},
 563 /* /45  */ {{ 0xff,0xff,0xff,0xff,
 564              0xff,0xf8,0x00,0x00,
 565              0x00,0x00,0x00,0x00,
 566              0x00,0x00,0x00,0x00 }},
 567 /* /46  */ {{ 0xff,0xff,0xff,0xff,
 568              0xff,0xfc,0x00,0x00,
 569              0x00,0x00,0x00,0x00,
 570              0x00,0x00,0x00,0x00 }},
 571 /* /47  */ {{ 0xff,0xff,0xff,0xff,
 572              0xff,0xfe,0x00,0x00,
 573              0x00,0x00,0x00,0x00,
 574              0x00,0x00,0x00,0x00 }},
 575 /* /48  */ {{ 0xff,0xff,0xff,0xff,
 576              0xff,0xff,0x00,0x00,
 577              0x00,0x00,0x00,0x00,
 578              0x00,0x00,0x00,0x00 }},
 579 /* /49  */ {{ 0xff,0xff,0xff,0xff,
 580              0xff,0xff,0x80,0x00,
 581              0x00,0x00,0x00,0x00,
 582              0x00,0x00,0x00,0x00 }},
 583 /* /50  */ {{ 0xff,0xff,0xff,0xff,
 584              0xff,0xff,0xc0,0x00,
 585              0x00,0x00,0x00,0x00,
 586              0x00,0x00,0x00,0x00 }},
 587 /* /51  */ {{ 0xff,0xff,0xff,0xff,
 588              0xff,0xff,0xe0,0x00,
 589              0x00,0x00,0x00,0x00,
 590              0x00,0x00,0x00,0x00 }},
 591 /* /52  */ {{ 0xff,0xff,0xff,0xff,
 592              0xff,0xff,0xf0,0x00,
 593              0x00,0x00,0x00,0x00,
 594              0x00,0x00,0x00,0x00 }},
 595 /* /53  */ {{ 0xff,0xff,0xff,0xff,
 596              0xff,0xff,0xf8,0x00,
 597              0x00,0x00,0x00,0x00,
 598              0x00,0x00,0x00,0x00 }},
 599 /* /54  */ {{ 0xff,0xff,0xff,0xff,
 600              0xff,0xff,0xfc,0x00,
 601              0x00,0x00,0x00,0x00,
 602              0x00,0x00,0x00,0x00 }},
 603 /* /55  */ {{ 0xff,0xff,0xff,0xff,
 604              0xff,0xff,0xfe,0x00,
 605              0x00,0x00,0x00,0x00,
 606              0x00,0x00,0x00,0x00 }},
 607 /* /56  */ {{ 0xff,0xff,0xff,0xff,
 608              0xff,0xff,0xff,0x00,
 609              0x00,0x00,0x00,0x00,
 610              0x00,0x00,0x00,0x00 }},
 611 /* /57  */ {{ 0xff,0xff,0xff,0xff,
 612              0xff,0xff,0xff,0x80,
 613              0x00,0x00,0x00,0x00,
 614              0x00,0x00,0x00,0x00 }},
 615 /* /58  */ {{ 0xff,0xff,0xff,0xff,
 616              0xff,0xff,0xff,0xc0,
 617              0x00,0x00,0x00,0x00,
 618              0x00,0x00,0x00,0x00 }},
 619 /* /59  */ {{ 0xff,0xff,0xff,0xff,
 620              0xff,0xff,0xff,0xe0,
 621              0x00,0x00,0x00,0x00,
 622              0x00,0x00,0x00,0x00 }},
 623 /* /60  */ {{ 0xff,0xff,0xff,0xff,
 624              0xff,0xff,0xff,0xf0,
 625              0x00,0x00,0x00,0x00,
 626              0x00,0x00,0x00,0x00 }},
 627 /* /61  */ {{ 0xff,0xff,0xff,0xff,
 628              0xff,0xff,0xff,0xf8,
 629              0x00,0x00,0x00,0x00,
 630              0x00,0x00,0x00,0x00 }},
 631 /* /62  */ {{ 0xff,0xff,0xff,0xff,
 632              0xff,0xff,0xff,0xfc,
 633              0x00,0x00,0x00,0x00,
 634              0x00,0x00,0x00,0x00 }},
 635 /* /63  */ {{ 0xff,0xff,0xff,0xff,
 636              0xff,0xff,0xff,0xfe,
 637              0x00,0x00,0x00,0x00,
 638              0x00,0x00,0x00,0x00 }},
 639 /* /64  */ {{ 0xff,0xff,0xff,0xff,
 640              0xff,0xff,0xff,0xff,
 641              0x00,0x00,0x00,0x00,
 642              0x00,0x00,0x00,0x00 }},
 643 /* /65  */ {{ 0xff,0xff,0xff,0xff,
 644              0xff,0xff,0xff,0xff,
 645              0x80,0x00,0x00,0x00,
 646              0x00,0x00,0x00,0x00 }},
 647 /* /66  */ {{ 0xff,0xff,0xff,0xff,
 648              0xff,0xff,0xff,0xff,
 649              0xc0,0x00,0x00,0x00,
 650              0x00,0x00,0x00,0x00 }},
 651 /* /67  */ {{ 0xff,0xff,0xff,0xff,
 652              0xff,0xff,0xff,0xff,
 653              0xe0,0x00,0x00,0x00,
 654              0x00,0x00,0x00,0x00 }},
 655 /* /68  */ {{ 0xff,0xff,0xff,0xff,
 656              0xff,0xff,0xff,0xff,
 657              0xf0,0x00,0x00,0x00,
 658              0x00,0x00,0x00,0x00 }},
 659 /* /69  */ {{ 0xff,0xff,0xff,0xff,
 660              0xff,0xff,0xff,0xff,
 661              0xf8,0x00,0x00,0x00,
 662              0x00,0x00,0x00,0x00 }},
 663 /* /70  */ {{ 0xff,0xff,0xff,0xff,
 664              0xff,0xff,0xff,0xff,
 665              0xfc,0x00,0x00,0x00,
 666              0x00,0x00,0x00,0x00 }},
 667 /* /71  */ {{ 0xff,0xff,0xff,0xff,
 668              0xff,0xff,0xff,0xff,
 669              0xfe,0x00,0x00,0x00,
 670              0x00,0x00,0x00,0x00 }},
 671 /* /72  */ {{ 0xff,0xff,0xff,0xff,
 672              0xff,0xff,0xff,0xff,
 673              0xff,0x00,0x00,0x00,
 674              0x00,0x00,0x00,0x00 }},
 675 /* /73  */ {{ 0xff,0xff,0xff,0xff,
 676              0xff,0xff,0xff,0xff,
 677              0xff,0x80,0x00,0x00,
 678              0x00,0x00,0x00,0x00 }},
 679 /* /74  */ {{ 0xff,0xff,0xff,0xff,
 680              0xff,0xff,0xff,0xff,
 681              0xff,0xc0,0x00,0x00,
 682              0x00,0x00,0x00,0x00 }},
 683 /* /75  */ {{ 0xff,0xff,0xff,0xff,
 684              0xff,0xff,0xff,0xff,
 685              0xff,0xe0,0x00,0x00,
 686              0x00,0x00,0x00,0x00 }},
 687 /* /76  */ {{ 0xff,0xff,0xff,0xff,
 688              0xff,0xff,0xff,0xff,
 689              0xff,0xf0,0x00,0x00,
 690              0x00,0x00,0x00,0x00 }},
 691 /* /77  */ {{ 0xff,0xff,0xff,0xff,
 692              0xff,0xff,0xff,0xff,
 693              0xff,0xf8,0x00,0x00,
 694              0x00,0x00,0x00,0x00 }},
 695 /* /78  */ {{ 0xff,0xff,0xff,0xff,
 696              0xff,0xff,0xff,0xff,
 697              0xff,0xfc,0x00,0x00,
 698              0x00,0x00,0x00,0x00 }},
 699 /* /79  */ {{ 0xff,0xff,0xff,0xff,
 700              0xff,0xff,0xff,0xff,
 701              0xff,0xfe,0x00,0x00,
 702              0x00,0x00,0x00,0x00 }},
 703 /* /80  */ {{ 0xff,0xff,0xff,0xff,
 704              0xff,0xff,0xff,0xff,
 705              0xff,0xff,0x00,0x00,
 706              0x00,0x00,0x00,0x00 }},
 707 /* /81  */ {{ 0xff,0xff,0xff,0xff,
 708              0xff,0xff,0xff,0xff,
 709              0xff,0xff,0x80,0x00,
 710              0x00,0x00,0x00,0x00 }},
 711 /* /82  */ {{ 0xff,0xff,0xff,0xff,
 712              0xff,0xff,0xff,0xff,
 713              0xff,0xff,0xc0,0x00,
 714              0x00,0x00,0x00,0x00 }},
 715 /* /83  */ {{ 0xff,0xff,0xff,0xff,
 716              0xff,0xff,0xff,0xff,
 717              0xff,0xff,0xe0,0x00,
 718              0x00,0x00,0x00,0x00 }},
 719 /* /84  */ {{ 0xff,0xff,0xff,0xff,
 720              0xff,0xff,0xff,0xff,
 721              0xff,0xff,0xf0,0x00,
 722              0x00,0x00,0x00,0x00 }},
 723 /* /85  */ {{ 0xff,0xff,0xff,0xff,
 724              0xff,0xff,0xff,0xff,
 725              0xff,0xff,0xf8,0x00,
 726              0x00,0x00,0x00,0x00 }},
 727 /* /86  */ {{ 0xff,0xff,0xff,0xff,
 728              0xff,0xff,0xff,0xff,
 729              0xff,0xff,0xfc,0x00,
 730              0x00,0x00,0x00,0x00 }},
 731 /* /87  */ {{ 0xff,0xff,0xff,0xff,
 732              0xff,0xff,0xff,0xff,
 733              0xff,0xff,0xfe,0x00,
 734              0x00,0x00,0x00,0x00 }},
 735 /* /88  */ {{ 0xff,0xff,0xff,0xff,
 736              0xff,0xff,0xff,0xff,
 737              0xff,0xff,0xff,0x00,
 738              0x00,0x00,0x00,0x00 }},
 739 /* /89  */ {{ 0xff,0xff,0xff,0xff,
 740              0xff,0xff,0xff,0xff,
 741              0xff,0xff,0xff,0x80,
 742              0x00,0x00,0x00,0x00 }},
 743 /* /90  */ {{ 0xff,0xff,0xff,0xff,
 744              0xff,0xff,0xff,0xff,
 745              0xff,0xff,0xff,0xc0,
 746              0x00,0x00,0x00,0x00 }},
 747 /* /91  */ {{ 0xff,0xff,0xff,0xff,
 748              0xff,0xff,0xff,0xff,
 749              0xff,0xff,0xff,0xe0,
 750              0x00,0x00,0x00,0x00 }},
 751 /* /92  */ {{ 0xff,0xff,0xff,0xff,
 752              0xff,0xff,0xff,0xff,
 753              0xff,0xff,0xff,0xf0,
 754              0x00,0x00,0x00,0x00 }},
 755 /* /93  */ {{ 0xff,0xff,0xff,0xff,
 756              0xff,0xff,0xff,0xff,
 757              0xff,0xff,0xff,0xf8,
 758              0x00,0x00,0x00,0x00 }},
 759 /* /94  */ {{ 0xff,0xff,0xff,0xff,
 760              0xff,0xff,0xff,0xff,
 761              0xff,0xff,0xff,0xfc,
 762              0x00,0x00,0x00,0x00 }},
 763 /* /95  */ {{ 0xff,0xff,0xff,0xff,
 764              0xff,0xff,0xff,0xff,
 765              0xff,0xff,0xff,0xfe,
 766              0x00,0x00,0x00,0x00 }},
 767 /* /96  */ {{ 0xff,0xff,0xff,0xff,
 768              0xff,0xff,0xff,0xff,
 769              0xff,0xff,0xff,0xff,
 770              0x00,0x00,0x00,0x00 }},
 771 /* /97  */ {{ 0xff,0xff,0xff,0xff,
 772              0xff,0xff,0xff,0xff,
 773              0xff,0xff,0xff,0xff,
 774              0x80,0x00,0x00,0x00 }},
 775 /* /98  */ {{ 0xff,0xff,0xff,0xff,
 776              0xff,0xff,0xff,0xff,
 777              0xff,0xff,0xff,0xff,
 778              0xc0,0x00,0x00,0x00 }},
 779 /* /99  */ {{ 0xff,0xff,0xff,0xff,
 780              0xff,0xff,0xff,0xff,
 781              0xff,0xff,0xff,0xff,
 782              0xe0,0x00,0x00,0x00 }},
 783 /* /100 */ {{ 0xff,0xff,0xff,0xff,
 784              0xff,0xff,0xff,0xff,
 785              0xff,0xff,0xff,0xff,
 786              0xf0,0x00,0x00,0x00 }},
 787 /* /101 */ {{ 0xff,0xff,0xff,0xff,
 788              0xff,0xff,0xff,0xff,
 789              0xff,0xff,0xff,0xff,
 790              0xf8,0x00,0x00,0x00 }},
 791 /* /102 */ {{ 0xff,0xff,0xff,0xff,
 792              0xff,0xff,0xff,0xff,
 793              0xff,0xff,0xff,0xff,
 794              0xfc,0x00,0x00,0x00 }},
 795 /* /103 */ {{ 0xff,0xff,0xff,0xff,
 796              0xff,0xff,0xff,0xff,
 797              0xff,0xff,0xff,0xff,
 798              0xfe,0x00,0x00,0x00 }},
 799 /* /104 */ {{ 0xff,0xff,0xff,0xff,
 800              0xff,0xff,0xff,0xff,
 801              0xff,0xff,0xff,0xff,
 802              0xff,0x00,0x00,0x00 }},
 803 /* /105 */ {{ 0xff,0xff,0xff,0xff,
 804              0xff,0xff,0xff,0xff,
 805              0xff,0xff,0xff,0xff,
 806              0xff,0x80,0x00,0x00 }},
 807 /* /106 */ {{ 0xff,0xff,0xff,0xff,
 808              0xff,0xff,0xff,0xff,
 809              0xff,0xff,0xff,0xff,
 810              0xff,0xc0,0x00,0x00 }},
 811 /* /107 */ {{ 0xff,0xff,0xff,0xff,
 812              0xff,0xff,0xff,0xff,
 813              0xff,0xff,0xff,0xff,
 814              0xff,0xe0,0x00,0x00 }},
 815 /* /108 */ {{ 0xff,0xff,0xff,0xff,
 816              0xff,0xff,0xff,0xff,
 817              0xff,0xff,0xff,0xff,
 818              0xff,0xf0,0x00,0x00 }},
 819 /* /109 */ {{ 0xff,0xff,0xff,0xff,
 820              0xff,0xff,0xff,0xff,
 821              0xff,0xff,0xff,0xff,
 822              0xff,0xf8,0x00,0x00 }},
 823 /* /110 */ {{ 0xff,0xff,0xff,0xff,
 824              0xff,0xff,0xff,0xff,
 825              0xff,0xff,0xff,0xff,
 826              0xff,0xfc,0x00,0x00 }},
 827 /* /111 */ {{ 0xff,0xff,0xff,0xff,
 828              0xff,0xff,0xff,0xff,
 829              0xff,0xff,0xff,0xff,
 830              0xff,0xfe,0x00,0x00 }},
 831 /* /112 */ {{ 0xff,0xff,0xff,0xff,
 832              0xff,0xff,0xff,0xff,
 833              0xff,0xff,0xff,0xff,
 834              0xff,0xff,0x00,0x00 }},
 835 /* /113 */ {{ 0xff,0xff,0xff,0xff,
 836              0xff,0xff,0xff,0xff,
 837              0xff,0xff,0xff,0xff,
 838              0xff,0xff,0x80,0x00 }},
 839 /* /114 */ {{ 0xff,0xff,0xff,0xff,
 840              0xff,0xff,0xff,0xff,
 841              0xff,0xff,0xff,0xff,
 842              0xff,0xff,0xc0,0x00 }},
 843 /* /115 */ {{ 0xff,0xff,0xff,0xff,
 844              0xff,0xff,0xff,0xff,
 845              0xff,0xff,0xff,0xff,
 846              0xff,0xff,0xe0,0x00 }},
 847 /* /116 */ {{ 0xff,0xff,0xff,0xff,
 848              0xff,0xff,0xff,0xff,
 849              0xff,0xff,0xff,0xff,
 850              0xff,0xff,0xf0,0x00 }},
 851 /* /117 */ {{ 0xff,0xff,0xff,0xff,
 852              0xff,0xff,0xff,0xff,
 853              0xff,0xff,0xff,0xff,
 854              0xff,0xff,0xf8,0x00 }},
 855 /* /118 */ {{ 0xff,0xff,0xff,0xff,
 856              0xff,0xff,0xff,0xff,
 857              0xff,0xff,0xff,0xff,
 858              0xff,0xff,0xfc,0x00 }},
 859 /* /119 */ {{ 0xff,0xff,0xff,0xff,
 860              0xff,0xff,0xff,0xff,
 861              0xff,0xff,0xff,0xff,
 862              0xff,0xff,0xfe,0x00 }},
 863 /* /120 */ {{ 0xff,0xff,0xff,0xff,
 864              0xff,0xff,0xff,0xff,
 865              0xff,0xff,0xff,0xff,
 866              0xff,0xff,0xff,0x00 }},
 867 /* /121 */ {{ 0xff,0xff,0xff,0xff,
 868              0xff,0xff,0xff,0xff,
 869              0xff,0xff,0xff,0xff,
 870              0xff,0xff,0xff,0x80 }},
 871 /* /122 */ {{ 0xff,0xff,0xff,0xff,
 872              0xff,0xff,0xff,0xff,
 873              0xff,0xff,0xff,0xff,
 874              0xff,0xff,0xff,0xc0 }},
 875 /* /123 */ {{ 0xff,0xff,0xff,0xff,
 876              0xff,0xff,0xff,0xff,
 877              0xff,0xff,0xff,0xff,
 878              0xff,0xff,0xff,0xe0 }},
 879 /* /124 */ {{ 0xff,0xff,0xff,0xff,
 880              0xff,0xff,0xff,0xff,
 881              0xff,0xff,0xff,0xff,
 882              0xff,0xff,0xff,0xf0 }},
 883 /* /125 */ {{ 0xff,0xff,0xff,0xff,
 884              0xff,0xff,0xff,0xff,
 885              0xff,0xff,0xff,0xff,
 886              0xff,0xff,0xff,0xf8 }},
 887 /* /126 */ {{ 0xff,0xff,0xff,0xff,
 888              0xff,0xff,0xff,0xff,
 889              0xff,0xff,0xff,0xff,
 890              0xff,0xff,0xff,0xfc }},
 891 /* /127 */ {{ 0xff,0xff,0xff,0xff,
 892              0xff,0xff,0xff,0xff,
 893              0xff,0xff,0xff,0xff,
 894              0xff,0xff,0xff,0xfe }},
 895 /* /128 */ {{ 0xff,0xff,0xff,0xff,
 896              0xff,0xff,0xff,0xff,
 897              0xff,0xff,0xff,0xff,
 898              0xff,0xff,0xff,0xff }},
 899 }};
 900
 901 } // folly