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 // static
 177 IPAddressV6 IPAddressV6::fromInverseArpaName(const std::string& arpaname) {
 178   auto piece = StringPiece(arpaname);
 179   if (!piece.removeSuffix(".ip6.arpa")) {
 180     throw IPAddressFormatException(sformat(
 181         "Invalid input. Should end with 'ip6.arpa'. Got '{}'", arpaname));
 182   }
 183   std::vector<StringPiece> pieces;
 184   split(".", piece, pieces);
 185   if (pieces.size() != 32) {
 186     throw IPAddressFormatException(sformat("Invalid input. Got '{}'", piece));
 187   }
 188   std::array<char, IPAddressV6::kToFullyQualifiedSize> ip;
 189   size_t pos = 0;
 190   int count = 0;
 191   for (size_t i = 1; i <= pieces.size(); i++) {
 192     ip[pos] = pieces[pieces.size() - i][0];
 193     pos++;
 194     count++;
 195     // add ':' every 4 chars
 196     if (count == 4 && pos < ip.size()) {
 197       ip[pos++] = ':';
 198       count = 0;
 199     }
 200   }
 201   return IPAddressV6(folly::range(ip));
 202 }
 203
 204 // public
 205 IPAddressV4 IPAddressV6::createIPv4() const {
 206   if (!isIPv4Mapped()) {
 207     throw IPAddressFormatException("addr is not v4-to-v6-mapped");
 208   }
 209   const unsigned char* by = bytes();
 210   return IPAddressV4(detail::Bytes::mkAddress4(&by[12]));
 211 }
 212
 213 // convert two uint8_t bytes into a uint16_t as hibyte.lobyte
 214 static inline uint16_t unpack(uint8_t lobyte, uint8_t hibyte) {
 215   return uint16_t((uint16_t(hibyte) << 8) | lobyte);
 216 }
 217
 218 // given a src string, unpack count*2 bytes into dest
 219 // dest must have as much storage as count
 220 static inline void unpackInto(const unsigned char* src,
 221                               uint16_t* dest,
 222                               size_t count) {
 223   for (size_t i = 0, hi = 1, lo = 0; i < count; i++) {
 224     dest[i] = unpack(src[hi], src[lo]);
 225     hi += 2;
 226     lo += 2;
 227   }
 228 }
 229
 230 // public
 231 IPAddressV4 IPAddressV6::getIPv4For6To4() const {
 232   if (!is6To4()) {
 233     throw IPAddressV6::TypeError(format(
 234             "Invalid IP '{}': not a 6to4 address", str()).str());
 235   }
 236   // convert 16x8 bytes into first 4x16 bytes
 237   uint16_t ints[4] = {0,0,0,0};
 238   unpackInto(bytes(), ints, 4);
 239   // repack into 4x8
 240   union {
 241     unsigned char bytes[4];
 242     in_addr addr;
 243   } ipv4;
 244   ipv4.bytes[0] = (uint8_t)((ints[1] & 0xFF00) >> 8);
 245   ipv4.bytes[1] = (uint8_t)(ints[1] & 0x00FF);
 246   ipv4.bytes[2] = (uint8_t)((ints[2] & 0xFF00) >> 8);
 247   ipv4.bytes[3] = (uint8_t)(ints[2] & 0x00FF);
 248   return IPAddressV4(ipv4.addr);
 249 }
 250
 251 // public
 252 bool IPAddressV6::isIPv4Mapped() const {
 253   // v4 mapped addresses have their first 10 bytes set to 0, the next 2 bytes
 254   // set to 255 (0xff);
 255   const unsigned char* by = bytes();
 256
 257   // check if first 10 bytes are 0
 258   for (int i = 0; i < 10; i++) {
 259     if (by[i] != 0x00) {
 260       return false;
 261     }
 262   }
 263   // check if bytes 11 and 12 are 255
 264   if (by[10] == 0xff && by[11] == 0xff) {
 265     return true;
 266   }
 267   return false;
 268 }
 269
 270 // public
 271 IPAddressV6::Type IPAddressV6::type() const {
 272   // convert 16x8 bytes into first 2x16 bytes
 273   uint16_t ints[2] = {0,0};
 274   unpackInto(bytes(), ints, 2);
 275
 276   if ((((uint32_t)ints[0] << 16) | ints[1]) == IPAddressV6::PREFIX_TEREDO) {
 277     return Type::TEREDO;
 278   }
 279
 280   if ((uint32_t)ints[0] == IPAddressV6::PREFIX_6TO4) {
 281     return Type::T6TO4;
 282   }
 283
 284   return Type::NORMAL;
 285 }
 286
 287 // public
 288 string IPAddressV6::toJson() const {
 289   return format(
 290       "{{family:'AF_INET6', addr:'{}', hash:{}}}", str(), hash()).str();
 291 }
 292
 293 // public
 294 size_t IPAddressV6::hash() const {
 295   if (isIPv4Mapped()) {
 296     /* An IPAddress containing this object would be equal (i.e. operator==)
 297        to an IPAddress containing the corresponding IPv4.
 298        So we must make sure that the hash values are the same as well */
 299     return IPAddress::createIPv4(*this).hash();
 300   }
 301
 302   static const uint64_t seed = AF_INET6;
 303   uint64_t hash1 = 0, hash2 = 0;
 304   hash::SpookyHashV2::Hash128(&addr_, 16, &hash1, &hash2);
 305   return hash::hash_combine(seed, hash1, hash2);
 306 }
 307
 308 // public
 309 bool IPAddressV6::inSubnet(StringPiece cidrNetwork) const {
 310   auto subnetInfo = IPAddress::createNetwork(cidrNetwork);
 311   auto addr = subnetInfo.first;
 312   if (!addr.isV6()) {
 313     throw IPAddressFormatException(to<std::string>(
 314         "Address '", addr.toJson(), "' ", "is not a V6 address"));
 315   }
 316   return inSubnetWithMask(addr.asV6(), fetchMask(subnetInfo.second));
 317 }
 318
 319 // public
 320 bool IPAddressV6::inSubnetWithMask(const IPAddressV6& subnet,
 321                                    const ByteArray16& cidrMask) const {
 322   const ByteArray16 mask = detail::Bytes::mask(toByteArray(), cidrMask);
 323   const ByteArray16 subMask = detail::Bytes::mask(subnet.toByteArray(),
 324                                                   cidrMask);
 325   return (mask == subMask);
 326 }
 327
 328 // public
 329 bool IPAddressV6::isLoopback() const {
 330   // Check if v4 mapped is loopback
 331   if (isIPv4Mapped() && createIPv4().isLoopback()) {
 332     return true;
 333   }
 334   auto socka = toSockAddr();
 335   return IN6_IS_ADDR_LOOPBACK(&socka.sin6_addr);
 336 }
 337
 338 bool IPAddressV6::isRoutable() const {
 339   return
 340     // 2000::/3 is the only assigned global unicast block
 341     inBinarySubnet({{0x20, 0x00}}, 3) ||
 342     // ffxe::/16 are global scope multicast addresses,
 343     // which are eligible to be routed over the internet
 344     (isMulticast() && getMulticastScope() == 0xe);
 345 }
 346
 347 bool IPAddressV6::isLinkLocalBroadcast() const {
 348   static const IPAddressV6 kLinkLocalBroadcast("ff02::1");
 349   return *this == kLinkLocalBroadcast;
 350 }
 351
 352 // public
 353 bool IPAddressV6::isPrivate() const {
 354   // Check if mapped is private
 355   if (isIPv4Mapped() && createIPv4().isPrivate()) {
 356     return true;
 357   }
 358   return isLoopback() || inBinarySubnet({{0xfc, 0x00}}, 7);
 359 }
 360
 361 // public
 362 bool IPAddressV6::isLinkLocal() const {
 363   return inBinarySubnet({{0xfe, 0x80}}, 10);
 364 }
 365
 366 bool IPAddressV6::isMulticast() const {
 367   return addr_.bytes_[0] == 0xff;
 368 }
 369
 370 uint8_t IPAddressV6::getMulticastFlags() const {
 371   DCHECK(isMulticast());
 372   return uint8_t((addr_.bytes_[1] >> 4) & 0xf);
 373 }
 374
 375 uint8_t IPAddressV6::getMulticastScope() const {
 376   DCHECK(isMulticast());
 377   return uint8_t(addr_.bytes_[1] & 0xf);
 378 }
 379
 380 IPAddressV6 IPAddressV6::getSolicitedNodeAddress() const {
 381   // Solicted node addresses must be constructed from unicast (or anycast)
 382   // addresses
 383   DCHECK(!isMulticast());
 384
 385   uint8_t bytes[16] = { 0xff, 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
 386                         0x00, 0x00, 0x00, 0x01, 0xff, 0x00, 0x00, 0x00 };
 387   bytes[13] = addr_.bytes_[13];
 388   bytes[14] = addr_.bytes_[14];
 389   bytes[15] = addr_.bytes_[15];
 390   return IPAddressV6::fromBinary(ByteRange(bytes, 16));
 391 }
 392
 393 // public
 394 IPAddressV6 IPAddressV6::mask(size_t numBits) const {
 395   static const auto bits = bitCount();
 396   if (numBits > bits) {
 397     throw IPAddressFormatException(
 398         to<std::string>("numBits(", numBits, ") > bitCount(", bits, ")"));
 399   }
 400   ByteArray16 ba = detail::Bytes::mask(fetchMask(numBits), addr_.bytes_);
 401   return IPAddressV6(ba);
 402 }
 403
 404 // public
 405 string IPAddressV6::str() const {
 406   char buffer[INET6_ADDRSTRLEN] = {0};
 407   sockaddr_in6 sock = toSockAddr();
 408   if (!getnameinfo(
 409         (sockaddr*)&sock, sizeof(sock),
 410         buffer, INET6_ADDRSTRLEN,
 411         nullptr, 0, NI_NUMERICHOST)) {
 412     string ip(buffer);
 413     return ip;
 414   } else {
 415     throw IPAddressFormatException(to<std::string>(
 416         "Invalid address with hex ",
 417         "'",
 418         detail::Bytes::toHex(bytes(), 16),
 419         "'"));
 420   }
 421 }
 422
 423 // public
 424 string IPAddressV6::toFullyQualified() const {
 425   return detail::fastIpv6ToString(addr_.in6Addr_);
 426 }
 427
 428 // public
 429 void IPAddressV6::toFullyQualifiedAppend(std::string& out) const {
 430   detail::fastIpv6AppendToString(addr_.in6Addr_, out);
 431 }
 432
 433 // public
 434 string IPAddressV6::toInverseArpaName() const {
 435   constexpr folly::StringPiece lut = "0123456789abcdef";
 436   std::array<char, 32> a;
 437   int j = 0;
 438   for (int i = 15; i >= 0; i--) {
 439     a[j] = (lut[bytes()[i] & 0xf]);
 440     a[j + 1] = (lut[bytes()[i] >> 4]);
 441     j += 2;
 442   }
 443   return sformat("{}.ip6.arpa", join(".", a));
 444 }
 445
 446 // public
 447 uint8_t IPAddressV6::getNthMSByte(size_t byteIndex) const {
 448   const auto highestIndex = byteCount() - 1;
 449   if (byteIndex > highestIndex) {
 450     throw std::invalid_argument(to<string>("Byte index must be <= ",
 451         to<string>(highestIndex), " for addresses of type :",
 452         detail::familyNameStr(AF_INET6)));
 453   }
 454   return bytes()[byteIndex];
 455 }
 456
 457 // protected
 458 const ByteArray16 IPAddressV6::fetchMask(size_t numBits) {
 459   static const size_t bits = bitCount();
 460   if (numBits > bits) {
 461     throw IPAddressFormatException("IPv6 addresses are 128 bits.");
 462   }
 463   // masks_ is backed by an array so is zero indexed
 464   return masks_[numBits];
 465 }
 466
 467 // public static
 468 CIDRNetworkV6 IPAddressV6::longestCommonPrefix(
 469     const CIDRNetworkV6& one,
 470     const CIDRNetworkV6& two) {
 471   auto prefix = detail::Bytes::longestCommonPrefix(
 472       one.first.addr_.bytes_, one.second, two.first.addr_.bytes_, two.second);
 473   return {IPAddressV6(prefix.first), prefix.second};
 474 }
 475
 476 // protected
 477 bool IPAddressV6::inBinarySubnet(const std::array<uint8_t, 2> addr,
 478                                  size_t numBits) const {
 479   auto masked = mask(numBits);
 480   return (std::memcmp(addr.data(), masked.bytes(), 2) == 0);
 481 }
 482
 483 // static private
 484 const std::array<ByteArray16, 129> IPAddressV6::masks_ = {{
 485 /* /0   */ {{ 0x00,0x00,0x00,0x00,
 486              0x00,0x00,0x00,0x00,
 487              0x00,0x00,0x00,0x00,
 488              0x00,0x00,0x00,0x00 }},
 489 /* /1   */ {{ 0x80,0x00,0x00,0x00,
 490              0x00,0x00,0x00,0x00,
 491              0x00,0x00,0x00,0x00,
 492              0x00,0x00,0x00,0x00 }},
 493 /* /2   */ {{ 0xc0,0x00,0x00,0x00,
 494              0x00,0x00,0x00,0x00,
 495              0x00,0x00,0x00,0x00,
 496              0x00,0x00,0x00,0x00 }},
 497 /* /3   */ {{ 0xe0,0x00,0x00,0x00,
 498              0x00,0x00,0x00,0x00,
 499              0x00,0x00,0x00,0x00,
 500              0x00,0x00,0x00,0x00 }},
 501 /* /4   */ {{ 0xf0,0x00,0x00,0x00,
 502              0x00,0x00,0x00,0x00,
 503              0x00,0x00,0x00,0x00,
 504              0x00,0x00,0x00,0x00 }},
 505 /* /5   */ {{ 0xf8,0x00,0x00,0x00,
 506              0x00,0x00,0x00,0x00,
 507              0x00,0x00,0x00,0x00,
 508              0x00,0x00,0x00,0x00 }},
 509 /* /6   */ {{ 0xfc,0x00,0x00,0x00,
 510              0x00,0x00,0x00,0x00,
 511              0x00,0x00,0x00,0x00,
 512              0x00,0x00,0x00,0x00 }},
 513 /* /7   */ {{ 0xfe,0x00,0x00,0x00,
 514              0x00,0x00,0x00,0x00,
 515              0x00,0x00,0x00,0x00,
 516              0x00,0x00,0x00,0x00 }},
 517 /* /8   */ {{ 0xff,0x00,0x00,0x00,
 518              0x00,0x00,0x00,0x00,
 519              0x00,0x00,0x00,0x00,
 520              0x00,0x00,0x00,0x00 }},
 521 /* /9   */ {{ 0xff,0x80,0x00,0x00,
 522              0x00,0x00,0x00,0x00,
 523              0x00,0x00,0x00,0x00,
 524              0x00,0x00,0x00,0x00 }},
 525 /* /10  */ {{ 0xff,0xc0,0x00,0x00,
 526              0x00,0x00,0x00,0x00,
 527              0x00,0x00,0x00,0x00,
 528              0x00,0x00,0x00,0x00 }},
 529 /* /11  */ {{ 0xff,0xe0,0x00,0x00,
 530              0x00,0x00,0x00,0x00,
 531              0x00,0x00,0x00,0x00,
 532              0x00,0x00,0x00,0x00 }},
 533 /* /12  */ {{ 0xff,0xf0,0x00,0x00,
 534              0x00,0x00,0x00,0x00,
 535              0x00,0x00,0x00,0x00,
 536              0x00,0x00,0x00,0x00 }},
 537 /* /13  */ {{ 0xff,0xf8,0x00,0x00,
 538              0x00,0x00,0x00,0x00,
 539              0x00,0x00,0x00,0x00,
 540              0x00,0x00,0x00,0x00 }},
 541 /* /14  */ {{ 0xff,0xfc,0x00,0x00,
 542              0x00,0x00,0x00,0x00,
 543              0x00,0x00,0x00,0x00,
 544              0x00,0x00,0x00,0x00 }},
 545 /* /15  */ {{ 0xff,0xfe,0x00,0x00,
 546              0x00,0x00,0x00,0x00,
 547              0x00,0x00,0x00,0x00,
 548              0x00,0x00,0x00,0x00 }},
 549 /* /16  */ {{ 0xff,0xff,0x00,0x00,
 550              0x00,0x00,0x00,0x00,
 551              0x00,0x00,0x00,0x00,
 552              0x00,0x00,0x00,0x00 }},
 553 /* /17  */ {{ 0xff,0xff,0x80,0x00,
 554              0x00,0x00,0x00,0x00,
 555              0x00,0x00,0x00,0x00,
 556              0x00,0x00,0x00,0x00 }},
 557 /* /18  */ {{ 0xff,0xff,0xc0,0x00,
 558              0x00,0x00,0x00,0x00,
 559              0x00,0x00,0x00,0x00,
 560              0x00,0x00,0x00,0x00 }},
 561 /* /19  */ {{ 0xff,0xff,0xe0,0x00,
 562              0x00,0x00,0x00,0x00,
 563              0x00,0x00,0x00,0x00,
 564              0x00,0x00,0x00,0x00 }},
 565 /* /20  */ {{ 0xff,0xff,0xf0,0x00,
 566              0x00,0x00,0x00,0x00,
 567              0x00,0x00,0x00,0x00,
 568              0x00,0x00,0x00,0x00 }},
 569 /* /21  */ {{ 0xff,0xff,0xf8,0x00,
 570              0x00,0x00,0x00,0x00,
 571              0x00,0x00,0x00,0x00,
 572              0x00,0x00,0x00,0x00 }},
 573 /* /22  */ {{ 0xff,0xff,0xfc,0x00,
 574              0x00,0x00,0x00,0x00,
 575              0x00,0x00,0x00,0x00,
 576              0x00,0x00,0x00,0x00 }},
 577 /* /23  */ {{ 0xff,0xff,0xfe,0x00,
 578              0x00,0x00,0x00,0x00,
 579              0x00,0x00,0x00,0x00,
 580              0x00,0x00,0x00,0x00 }},
 581 /* /24  */ {{ 0xff,0xff,0xff,0x00,
 582              0x00,0x00,0x00,0x00,
 583              0x00,0x00,0x00,0x00,
 584              0x00,0x00,0x00,0x00 }},
 585 /* /25  */ {{ 0xff,0xff,0xff,0x80,
 586              0x00,0x00,0x00,0x00,
 587              0x00,0x00,0x00,0x00,
 588              0x00,0x00,0x00,0x00 }},
 589 /* /26  */ {{ 0xff,0xff,0xff,0xc0,
 590              0x00,0x00,0x00,0x00,
 591              0x00,0x00,0x00,0x00,
 592              0x00,0x00,0x00,0x00 }},
 593 /* /27  */ {{ 0xff,0xff,0xff,0xe0,
 594              0x00,0x00,0x00,0x00,
 595              0x00,0x00,0x00,0x00,
 596              0x00,0x00,0x00,0x00 }},
 597 /* /28  */ {{ 0xff,0xff,0xff,0xf0,
 598              0x00,0x00,0x00,0x00,
 599              0x00,0x00,0x00,0x00,
 600              0x00,0x00,0x00,0x00 }},
 601 /* /29  */ {{ 0xff,0xff,0xff,0xf8,
 602              0x00,0x00,0x00,0x00,
 603              0x00,0x00,0x00,0x00,
 604              0x00,0x00,0x00,0x00 }},
 605 /* /30  */ {{ 0xff,0xff,0xff,0xfc,
 606              0x00,0x00,0x00,0x00,
 607              0x00,0x00,0x00,0x00,
 608              0x00,0x00,0x00,0x00 }},
 609 /* /31  */ {{ 0xff,0xff,0xff,0xfe,
 610              0x00,0x00,0x00,0x00,
 611              0x00,0x00,0x00,0x00,
 612              0x00,0x00,0x00,0x00 }},
 613 /* /32  */ {{ 0xff,0xff,0xff,0xff,
 614              0x00,0x00,0x00,0x00,
 615              0x00,0x00,0x00,0x00,
 616              0x00,0x00,0x00,0x00 }},
 617 /* /33  */ {{ 0xff,0xff,0xff,0xff,
 618              0x80,0x00,0x00,0x00,
 619              0x00,0x00,0x00,0x00,
 620              0x00,0x00,0x00,0x00 }},
 621 /* /34  */ {{ 0xff,0xff,0xff,0xff,
 622              0xc0,0x00,0x00,0x00,
 623              0x00,0x00,0x00,0x00,
 624              0x00,0x00,0x00,0x00 }},
 625 /* /35  */ {{ 0xff,0xff,0xff,0xff,
 626              0xe0,0x00,0x00,0x00,
 627              0x00,0x00,0x00,0x00,
 628              0x00,0x00,0x00,0x00 }},
 629 /* /36  */ {{ 0xff,0xff,0xff,0xff,
 630              0xf0,0x00,0x00,0x00,
 631              0x00,0x00,0x00,0x00,
 632              0x00,0x00,0x00,0x00 }},
 633 /* /37  */ {{ 0xff,0xff,0xff,0xff,
 634              0xf8,0x00,0x00,0x00,
 635              0x00,0x00,0x00,0x00,
 636              0x00,0x00,0x00,0x00 }},
 637 /* /38  */ {{ 0xff,0xff,0xff,0xff,
 638              0xfc,0x00,0x00,0x00,
 639              0x00,0x00,0x00,0x00,
 640              0x00,0x00,0x00,0x00 }},
 641 /* /39  */ {{ 0xff,0xff,0xff,0xff,
 642              0xfe,0x00,0x00,0x00,
 643              0x00,0x00,0x00,0x00,
 644              0x00,0x00,0x00,0x00 }},
 645 /* /40  */ {{ 0xff,0xff,0xff,0xff,
 646              0xff,0x00,0x00,0x00,
 647              0x00,0x00,0x00,0x00,
 648              0x00,0x00,0x00,0x00 }},
 649 /* /41  */ {{ 0xff,0xff,0xff,0xff,
 650              0xff,0x80,0x00,0x00,
 651              0x00,0x00,0x00,0x00,
 652              0x00,0x00,0x00,0x00 }},
 653 /* /42  */ {{ 0xff,0xff,0xff,0xff,
 654              0xff,0xc0,0x00,0x00,
 655              0x00,0x00,0x00,0x00,
 656              0x00,0x00,0x00,0x00 }},
 657 /* /43  */ {{ 0xff,0xff,0xff,0xff,
 658              0xff,0xe0,0x00,0x00,
 659              0x00,0x00,0x00,0x00,
 660              0x00,0x00,0x00,0x00 }},
 661 /* /44  */ {{ 0xff,0xff,0xff,0xff,
 662              0xff,0xf0,0x00,0x00,
 663              0x00,0x00,0x00,0x00,
 664              0x00,0x00,0x00,0x00 }},
 665 /* /45  */ {{ 0xff,0xff,0xff,0xff,
 666              0xff,0xf8,0x00,0x00,
 667              0x00,0x00,0x00,0x00,
 668              0x00,0x00,0x00,0x00 }},
 669 /* /46  */ {{ 0xff,0xff,0xff,0xff,
 670              0xff,0xfc,0x00,0x00,
 671              0x00,0x00,0x00,0x00,
 672              0x00,0x00,0x00,0x00 }},
 673 /* /47  */ {{ 0xff,0xff,0xff,0xff,
 674              0xff,0xfe,0x00,0x00,
 675              0x00,0x00,0x00,0x00,
 676              0x00,0x00,0x00,0x00 }},
 677 /* /48  */ {{ 0xff,0xff,0xff,0xff,
 678              0xff,0xff,0x00,0x00,
 679              0x00,0x00,0x00,0x00,
 680              0x00,0x00,0x00,0x00 }},
 681 /* /49  */ {{ 0xff,0xff,0xff,0xff,
 682              0xff,0xff,0x80,0x00,
 683              0x00,0x00,0x00,0x00,
 684              0x00,0x00,0x00,0x00 }},
 685 /* /50  */ {{ 0xff,0xff,0xff,0xff,
 686              0xff,0xff,0xc0,0x00,
 687              0x00,0x00,0x00,0x00,
 688              0x00,0x00,0x00,0x00 }},
 689 /* /51  */ {{ 0xff,0xff,0xff,0xff,
 690              0xff,0xff,0xe0,0x00,
 691              0x00,0x00,0x00,0x00,
 692              0x00,0x00,0x00,0x00 }},
 693 /* /52  */ {{ 0xff,0xff,0xff,0xff,
 694              0xff,0xff,0xf0,0x00,
 695              0x00,0x00,0x00,0x00,
 696              0x00,0x00,0x00,0x00 }},
 697 /* /53  */ {{ 0xff,0xff,0xff,0xff,
 698              0xff,0xff,0xf8,0x00,
 699              0x00,0x00,0x00,0x00,
 700              0x00,0x00,0x00,0x00 }},
 701 /* /54  */ {{ 0xff,0xff,0xff,0xff,
 702              0xff,0xff,0xfc,0x00,
 703              0x00,0x00,0x00,0x00,
 704              0x00,0x00,0x00,0x00 }},
 705 /* /55  */ {{ 0xff,0xff,0xff,0xff,
 706              0xff,0xff,0xfe,0x00,
 707              0x00,0x00,0x00,0x00,
 708              0x00,0x00,0x00,0x00 }},
 709 /* /56  */ {{ 0xff,0xff,0xff,0xff,
 710              0xff,0xff,0xff,0x00,
 711              0x00,0x00,0x00,0x00,
 712              0x00,0x00,0x00,0x00 }},
 713 /* /57  */ {{ 0xff,0xff,0xff,0xff,
 714              0xff,0xff,0xff,0x80,
 715              0x00,0x00,0x00,0x00,
 716              0x00,0x00,0x00,0x00 }},
 717 /* /58  */ {{ 0xff,0xff,0xff,0xff,
 718              0xff,0xff,0xff,0xc0,
 719              0x00,0x00,0x00,0x00,
 720              0x00,0x00,0x00,0x00 }},
 721 /* /59  */ {{ 0xff,0xff,0xff,0xff,
 722              0xff,0xff,0xff,0xe0,
 723              0x00,0x00,0x00,0x00,
 724              0x00,0x00,0x00,0x00 }},
 725 /* /60  */ {{ 0xff,0xff,0xff,0xff,
 726              0xff,0xff,0xff,0xf0,
 727              0x00,0x00,0x00,0x00,
 728              0x00,0x00,0x00,0x00 }},
 729 /* /61  */ {{ 0xff,0xff,0xff,0xff,
 730              0xff,0xff,0xff,0xf8,
 731              0x00,0x00,0x00,0x00,
 732              0x00,0x00,0x00,0x00 }},
 733 /* /62  */ {{ 0xff,0xff,0xff,0xff,
 734              0xff,0xff,0xff,0xfc,
 735              0x00,0x00,0x00,0x00,
 736              0x00,0x00,0x00,0x00 }},
 737 /* /63  */ {{ 0xff,0xff,0xff,0xff,
 738              0xff,0xff,0xff,0xfe,
 739              0x00,0x00,0x00,0x00,
 740              0x00,0x00,0x00,0x00 }},
 741 /* /64  */ {{ 0xff,0xff,0xff,0xff,
 742              0xff,0xff,0xff,0xff,
 743              0x00,0x00,0x00,0x00,
 744              0x00,0x00,0x00,0x00 }},
 745 /* /65  */ {{ 0xff,0xff,0xff,0xff,
 746              0xff,0xff,0xff,0xff,
 747              0x80,0x00,0x00,0x00,
 748              0x00,0x00,0x00,0x00 }},
 749 /* /66  */ {{ 0xff,0xff,0xff,0xff,
 750              0xff,0xff,0xff,0xff,
 751              0xc0,0x00,0x00,0x00,
 752              0x00,0x00,0x00,0x00 }},
 753 /* /67  */ {{ 0xff,0xff,0xff,0xff,
 754              0xff,0xff,0xff,0xff,
 755              0xe0,0x00,0x00,0x00,
 756              0x00,0x00,0x00,0x00 }},
 757 /* /68  */ {{ 0xff,0xff,0xff,0xff,
 758              0xff,0xff,0xff,0xff,
 759              0xf0,0x00,0x00,0x00,
 760              0x00,0x00,0x00,0x00 }},
 761 /* /69  */ {{ 0xff,0xff,0xff,0xff,
 762              0xff,0xff,0xff,0xff,
 763              0xf8,0x00,0x00,0x00,
 764              0x00,0x00,0x00,0x00 }},
 765 /* /70  */ {{ 0xff,0xff,0xff,0xff,
 766              0xff,0xff,0xff,0xff,
 767              0xfc,0x00,0x00,0x00,
 768              0x00,0x00,0x00,0x00 }},
 769 /* /71  */ {{ 0xff,0xff,0xff,0xff,
 770              0xff,0xff,0xff,0xff,
 771              0xfe,0x00,0x00,0x00,
 772              0x00,0x00,0x00,0x00 }},
 773 /* /72  */ {{ 0xff,0xff,0xff,0xff,
 774              0xff,0xff,0xff,0xff,
 775              0xff,0x00,0x00,0x00,
 776              0x00,0x00,0x00,0x00 }},
 777 /* /73  */ {{ 0xff,0xff,0xff,0xff,
 778              0xff,0xff,0xff,0xff,
 779              0xff,0x80,0x00,0x00,
 780              0x00,0x00,0x00,0x00 }},
 781 /* /74  */ {{ 0xff,0xff,0xff,0xff,
 782              0xff,0xff,0xff,0xff,
 783              0xff,0xc0,0x00,0x00,
 784              0x00,0x00,0x00,0x00 }},
 785 /* /75  */ {{ 0xff,0xff,0xff,0xff,
 786              0xff,0xff,0xff,0xff,
 787              0xff,0xe0,0x00,0x00,
 788              0x00,0x00,0x00,0x00 }},
 789 /* /76  */ {{ 0xff,0xff,0xff,0xff,
 790              0xff,0xff,0xff,0xff,
 791              0xff,0xf0,0x00,0x00,
 792              0x00,0x00,0x00,0x00 }},
 793 /* /77  */ {{ 0xff,0xff,0xff,0xff,
 794              0xff,0xff,0xff,0xff,
 795              0xff,0xf8,0x00,0x00,
 796              0x00,0x00,0x00,0x00 }},
 797 /* /78  */ {{ 0xff,0xff,0xff,0xff,
 798              0xff,0xff,0xff,0xff,
 799              0xff,0xfc,0x00,0x00,
 800              0x00,0x00,0x00,0x00 }},
 801 /* /79  */ {{ 0xff,0xff,0xff,0xff,
 802              0xff,0xff,0xff,0xff,
 803              0xff,0xfe,0x00,0x00,
 804              0x00,0x00,0x00,0x00 }},
 805 /* /80  */ {{ 0xff,0xff,0xff,0xff,
 806              0xff,0xff,0xff,0xff,
 807              0xff,0xff,0x00,0x00,
 808              0x00,0x00,0x00,0x00 }},
 809 /* /81  */ {{ 0xff,0xff,0xff,0xff,
 810              0xff,0xff,0xff,0xff,
 811              0xff,0xff,0x80,0x00,
 812              0x00,0x00,0x00,0x00 }},
 813 /* /82  */ {{ 0xff,0xff,0xff,0xff,
 814              0xff,0xff,0xff,0xff,
 815              0xff,0xff,0xc0,0x00,
 816              0x00,0x00,0x00,0x00 }},
 817 /* /83  */ {{ 0xff,0xff,0xff,0xff,
 818              0xff,0xff,0xff,0xff,
 819              0xff,0xff,0xe0,0x00,
 820              0x00,0x00,0x00,0x00 }},
 821 /* /84  */ {{ 0xff,0xff,0xff,0xff,
 822              0xff,0xff,0xff,0xff,
 823              0xff,0xff,0xf0,0x00,
 824              0x00,0x00,0x00,0x00 }},
 825 /* /85  */ {{ 0xff,0xff,0xff,0xff,
 826              0xff,0xff,0xff,0xff,
 827              0xff,0xff,0xf8,0x00,
 828              0x00,0x00,0x00,0x00 }},
 829 /* /86  */ {{ 0xff,0xff,0xff,0xff,
 830              0xff,0xff,0xff,0xff,
 831              0xff,0xff,0xfc,0x00,
 832              0x00,0x00,0x00,0x00 }},
 833 /* /87  */ {{ 0xff,0xff,0xff,0xff,
 834              0xff,0xff,0xff,0xff,
 835              0xff,0xff,0xfe,0x00,
 836              0x00,0x00,0x00,0x00 }},
 837 /* /88  */ {{ 0xff,0xff,0xff,0xff,
 838              0xff,0xff,0xff,0xff,
 839              0xff,0xff,0xff,0x00,
 840              0x00,0x00,0x00,0x00 }},
 841 /* /89  */ {{ 0xff,0xff,0xff,0xff,
 842              0xff,0xff,0xff,0xff,
 843              0xff,0xff,0xff,0x80,
 844              0x00,0x00,0x00,0x00 }},
 845 /* /90  */ {{ 0xff,0xff,0xff,0xff,
 846              0xff,0xff,0xff,0xff,
 847              0xff,0xff,0xff,0xc0,
 848              0x00,0x00,0x00,0x00 }},
 849 /* /91  */ {{ 0xff,0xff,0xff,0xff,
 850              0xff,0xff,0xff,0xff,
 851              0xff,0xff,0xff,0xe0,
 852              0x00,0x00,0x00,0x00 }},
 853 /* /92  */ {{ 0xff,0xff,0xff,0xff,
 854              0xff,0xff,0xff,0xff,
 855              0xff,0xff,0xff,0xf0,
 856              0x00,0x00,0x00,0x00 }},
 857 /* /93  */ {{ 0xff,0xff,0xff,0xff,
 858              0xff,0xff,0xff,0xff,
 859              0xff,0xff,0xff,0xf8,
 860              0x00,0x00,0x00,0x00 }},
 861 /* /94  */ {{ 0xff,0xff,0xff,0xff,
 862              0xff,0xff,0xff,0xff,
 863              0xff,0xff,0xff,0xfc,
 864              0x00,0x00,0x00,0x00 }},
 865 /* /95  */ {{ 0xff,0xff,0xff,0xff,
 866              0xff,0xff,0xff,0xff,
 867              0xff,0xff,0xff,0xfe,
 868              0x00,0x00,0x00,0x00 }},
 869 /* /96  */ {{ 0xff,0xff,0xff,0xff,
 870              0xff,0xff,0xff,0xff,
 871              0xff,0xff,0xff,0xff,
 872              0x00,0x00,0x00,0x00 }},
 873 /* /97  */ {{ 0xff,0xff,0xff,0xff,
 874              0xff,0xff,0xff,0xff,
 875              0xff,0xff,0xff,0xff,
 876              0x80,0x00,0x00,0x00 }},
 877 /* /98  */ {{ 0xff,0xff,0xff,0xff,
 878              0xff,0xff,0xff,0xff,
 879              0xff,0xff,0xff,0xff,
 880              0xc0,0x00,0x00,0x00 }},
 881 /* /99  */ {{ 0xff,0xff,0xff,0xff,
 882              0xff,0xff,0xff,0xff,
 883              0xff,0xff,0xff,0xff,
 884              0xe0,0x00,0x00,0x00 }},
 885 /* /100 */ {{ 0xff,0xff,0xff,0xff,
 886              0xff,0xff,0xff,0xff,
 887              0xff,0xff,0xff,0xff,
 888              0xf0,0x00,0x00,0x00 }},
 889 /* /101 */ {{ 0xff,0xff,0xff,0xff,
 890              0xff,0xff,0xff,0xff,
 891              0xff,0xff,0xff,0xff,
 892              0xf8,0x00,0x00,0x00 }},
 893 /* /102 */ {{ 0xff,0xff,0xff,0xff,
 894              0xff,0xff,0xff,0xff,
 895              0xff,0xff,0xff,0xff,
 896              0xfc,0x00,0x00,0x00 }},
 897 /* /103 */ {{ 0xff,0xff,0xff,0xff,
 898              0xff,0xff,0xff,0xff,
 899              0xff,0xff,0xff,0xff,
 900              0xfe,0x00,0x00,0x00 }},
 901 /* /104 */ {{ 0xff,0xff,0xff,0xff,
 902              0xff,0xff,0xff,0xff,
 903              0xff,0xff,0xff,0xff,
 904              0xff,0x00,0x00,0x00 }},
 905 /* /105 */ {{ 0xff,0xff,0xff,0xff,
 906              0xff,0xff,0xff,0xff,
 907              0xff,0xff,0xff,0xff,
 908              0xff,0x80,0x00,0x00 }},
 909 /* /106 */ {{ 0xff,0xff,0xff,0xff,
 910              0xff,0xff,0xff,0xff,
 911              0xff,0xff,0xff,0xff,
 912              0xff,0xc0,0x00,0x00 }},
 913 /* /107 */ {{ 0xff,0xff,0xff,0xff,
 914              0xff,0xff,0xff,0xff,
 915              0xff,0xff,0xff,0xff,
 916              0xff,0xe0,0x00,0x00 }},
 917 /* /108 */ {{ 0xff,0xff,0xff,0xff,
 918              0xff,0xff,0xff,0xff,
 919              0xff,0xff,0xff,0xff,
 920              0xff,0xf0,0x00,0x00 }},
 921 /* /109 */ {{ 0xff,0xff,0xff,0xff,
 922              0xff,0xff,0xff,0xff,
 923              0xff,0xff,0xff,0xff,
 924              0xff,0xf8,0x00,0x00 }},
 925 /* /110 */ {{ 0xff,0xff,0xff,0xff,
 926              0xff,0xff,0xff,0xff,
 927              0xff,0xff,0xff,0xff,
 928              0xff,0xfc,0x00,0x00 }},
 929 /* /111 */ {{ 0xff,0xff,0xff,0xff,
 930              0xff,0xff,0xff,0xff,
 931              0xff,0xff,0xff,0xff,
 932              0xff,0xfe,0x00,0x00 }},
 933 /* /112 */ {{ 0xff,0xff,0xff,0xff,
 934              0xff,0xff,0xff,0xff,
 935              0xff,0xff,0xff,0xff,
 936              0xff,0xff,0x00,0x00 }},
 937 /* /113 */ {{ 0xff,0xff,0xff,0xff,
 938              0xff,0xff,0xff,0xff,
 939              0xff,0xff,0xff,0xff,
 940              0xff,0xff,0x80,0x00 }},
 941 /* /114 */ {{ 0xff,0xff,0xff,0xff,
 942              0xff,0xff,0xff,0xff,
 943              0xff,0xff,0xff,0xff,
 944              0xff,0xff,0xc0,0x00 }},
 945 /* /115 */ {{ 0xff,0xff,0xff,0xff,
 946              0xff,0xff,0xff,0xff,
 947              0xff,0xff,0xff,0xff,
 948              0xff,0xff,0xe0,0x00 }},
 949 /* /116 */ {{ 0xff,0xff,0xff,0xff,
 950              0xff,0xff,0xff,0xff,
 951              0xff,0xff,0xff,0xff,
 952              0xff,0xff,0xf0,0x00 }},
 953 /* /117 */ {{ 0xff,0xff,0xff,0xff,
 954              0xff,0xff,0xff,0xff,
 955              0xff,0xff,0xff,0xff,
 956              0xff,0xff,0xf8,0x00 }},
 957 /* /118 */ {{ 0xff,0xff,0xff,0xff,
 958              0xff,0xff,0xff,0xff,
 959              0xff,0xff,0xff,0xff,
 960              0xff,0xff,0xfc,0x00 }},
 961 /* /119 */ {{ 0xff,0xff,0xff,0xff,
 962              0xff,0xff,0xff,0xff,
 963              0xff,0xff,0xff,0xff,
 964              0xff,0xff,0xfe,0x00 }},
 965 /* /120 */ {{ 0xff,0xff,0xff,0xff,
 966              0xff,0xff,0xff,0xff,
 967              0xff,0xff,0xff,0xff,
 968              0xff,0xff,0xff,0x00 }},
 969 /* /121 */ {{ 0xff,0xff,0xff,0xff,
 970              0xff,0xff,0xff,0xff,
 971              0xff,0xff,0xff,0xff,
 972              0xff,0xff,0xff,0x80 }},
 973 /* /122 */ {{ 0xff,0xff,0xff,0xff,
 974              0xff,0xff,0xff,0xff,
 975              0xff,0xff,0xff,0xff,
 976              0xff,0xff,0xff,0xc0 }},
 977 /* /123 */ {{ 0xff,0xff,0xff,0xff,
 978              0xff,0xff,0xff,0xff,
 979              0xff,0xff,0xff,0xff,
 980              0xff,0xff,0xff,0xe0 }},
 981 /* /124 */ {{ 0xff,0xff,0xff,0xff,
 982              0xff,0xff,0xff,0xff,
 983              0xff,0xff,0xff,0xff,
 984              0xff,0xff,0xff,0xf0 }},
 985 /* /125 */ {{ 0xff,0xff,0xff,0xff,
 986              0xff,0xff,0xff,0xff,
 987              0xff,0xff,0xff,0xff,
 988              0xff,0xff,0xff,0xf8 }},
 989 /* /126 */ {{ 0xff,0xff,0xff,0xff,
 990              0xff,0xff,0xff,0xff,
 991              0xff,0xff,0xff,0xff,
 992              0xff,0xff,0xff,0xfc }},
 993 /* /127 */ {{ 0xff,0xff,0xff,0xff,
 994              0xff,0xff,0xff,0xff,
 995              0xff,0xff,0xff,0xff,
 996              0xff,0xff,0xff,0xfe }},
 997 /* /128 */ {{ 0xff,0xff,0xff,0xff,
 998              0xff,0xff,0xff,0xff,
 999              0xff,0xff,0xff,0xff,
1000              0xff,0xff,0xff,0xff }},
1001 }};
1002
1003 } // folly