OSX/authd/crc.c

   1 /* Copyright (c) 2012 Apple Inc. All Rights Reserved. */
   2
   3 #include "crc.h"
   4
   5 // G(x): x^64 + x^62 + x^57 + x^55 + x^54 + x^53 + x^52 + x^47 + x^46 + x^45 + x^40 + x^39 +
   6 //       x^38 + x^37 + x^35 + x^33 + x^32 + x^31 + x^29 + x^27 + x^24 + x^23 + x^22 + x^21 +
   7 //       x^19 + x^17 + x^13 + x^12 + x^10 + x^9  + x^7  + x^4  + x^1  + 1
   8
   9 //    Mathematically, the CRC value corresponding to the given data is defined by the following proce-
  10 //    dure:
  11 //
  12 //    The n bits to be evaluated are considered to be the coefficients of a mod 2 polynomial
  13 //    M(x) of degree n-1.  These n bits are the bits from the data, with the most significant
  14 //    bit being the most significant bit of the first octet of the data and the last bit being
  15 //    the least significant bit of the last octet, padded with zero bits (if necessary) to
  16 //    achieve an integral number of octets, followed by one or more octets representing the
  17 //    length of the data as a binary value, least significant octet first.  The smallest num-
  18 //    ber of octets capable of representing this integer are used.
  19 //
  20 //    M(x) is multiplied by x^64 (i.e., shifted left 56 bits) and divided by G(x) using mod 2
  21 //    division, producing a remainder R(x) of degree <= 63.
  22 //
  23 //    The coefficients of R(x) are considered to be a 64-bit sequence.
  24 //
  25 //    The bit sequence is complemented and the result is the CRC.
  26
  27 const uint64_t xorout = 0xffffffffffffffffULL;
  28
  29 // polynomial = 0x42F0E1EBA9EA3693ULL using ECMA-182
  30
  31 const uint64_t _crc_table64[256] = {
  32     0x0000000000000000ULL, 0x42f0e1eba9ea3693ULL, 0x85e1c3d753d46d26ULL, 0xc711223cfa3e5bb5ULL,
  33     0x493366450e42ecdfULL, 0x0bc387aea7a8da4cULL, 0xccd2a5925d9681f9ULL, 0x8e224479f47cb76aULL,
  34     0x9266cc8a1c85d9beULL, 0xd0962d61b56fef2dULL, 0x17870f5d4f51b498ULL, 0x5577eeb6e6bb820bULL,
  35     0xdb55aacf12c73561ULL, 0x99a54b24bb2d03f2ULL, 0x5eb4691841135847ULL, 0x1c4488f3e8f96ed4ULL,
  36     0x663d78ff90e185efULL, 0x24cd9914390bb37cULL, 0xe3dcbb28c335e8c9ULL, 0xa12c5ac36adfde5aULL,
  37     0x2f0e1eba9ea36930ULL, 0x6dfeff5137495fa3ULL, 0xaaefdd6dcd770416ULL, 0xe81f3c86649d3285ULL,
  38     0xf45bb4758c645c51ULL, 0xb6ab559e258e6ac2ULL, 0x71ba77a2dfb03177ULL, 0x334a9649765a07e4ULL,
  39     0xbd68d2308226b08eULL, 0xff9833db2bcc861dULL, 0x388911e7d1f2dda8ULL, 0x7a79f00c7818eb3bULL,
  40     0xcc7af1ff21c30bdeULL, 0x8e8a101488293d4dULL, 0x499b3228721766f8ULL, 0x0b6bd3c3dbfd506bULL,
  41     0x854997ba2f81e701ULL, 0xc7b97651866bd192ULL, 0x00a8546d7c558a27ULL, 0x4258b586d5bfbcb4ULL,
  42     0x5e1c3d753d46d260ULL, 0x1cecdc9e94ace4f3ULL, 0xdbfdfea26e92bf46ULL, 0x990d1f49c77889d5ULL,
  43     0x172f5b3033043ebfULL, 0x55dfbadb9aee082cULL, 0x92ce98e760d05399ULL, 0xd03e790cc93a650aULL,
  44     0xaa478900b1228e31ULL, 0xe8b768eb18c8b8a2ULL, 0x2fa64ad7e2f6e317ULL, 0x6d56ab3c4b1cd584ULL,
  45     0xe374ef45bf6062eeULL, 0xa1840eae168a547dULL, 0x66952c92ecb40fc8ULL, 0x2465cd79455e395bULL,
  46     0x3821458aada7578fULL, 0x7ad1a461044d611cULL, 0xbdc0865dfe733aa9ULL, 0xff3067b657990c3aULL,
  47     0x711223cfa3e5bb50ULL, 0x33e2c2240a0f8dc3ULL, 0xf4f3e018f031d676ULL, 0xb60301f359dbe0e5ULL,
  48     0xda050215ea6c212fULL, 0x98f5e3fe438617bcULL, 0x5fe4c1c2b9b84c09ULL, 0x1d14202910527a9aULL,
  49     0x93366450e42ecdf0ULL, 0xd1c685bb4dc4fb63ULL, 0x16d7a787b7faa0d6ULL, 0x5427466c1e109645ULL,
  50     0x4863ce9ff6e9f891ULL, 0x0a932f745f03ce02ULL, 0xcd820d48a53d95b7ULL, 0x8f72eca30cd7a324ULL,
  51     0x0150a8daf8ab144eULL, 0x43a04931514122ddULL, 0x84b16b0dab7f7968ULL, 0xc6418ae602954ffbULL,
  52     0xbc387aea7a8da4c0ULL, 0xfec89b01d3679253ULL, 0x39d9b93d2959c9e6ULL, 0x7b2958d680b3ff75ULL,
  53     0xf50b1caf74cf481fULL, 0xb7fbfd44dd257e8cULL, 0x70eadf78271b2539ULL, 0x321a3e938ef113aaULL,
  54     0x2e5eb66066087d7eULL, 0x6cae578bcfe24bedULL, 0xabbf75b735dc1058ULL, 0xe94f945c9c3626cbULL,
  55     0x676dd025684a91a1ULL, 0x259d31cec1a0a732ULL, 0xe28c13f23b9efc87ULL, 0xa07cf2199274ca14ULL,
  56     0x167ff3eacbaf2af1ULL, 0x548f120162451c62ULL, 0x939e303d987b47d7ULL, 0xd16ed1d631917144ULL,
  57     0x5f4c95afc5edc62eULL, 0x1dbc74446c07f0bdULL, 0xdaad56789639ab08ULL, 0x985db7933fd39d9bULL,
  58     0x84193f60d72af34fULL, 0xc6e9de8b7ec0c5dcULL, 0x01f8fcb784fe9e69ULL, 0x43081d5c2d14a8faULL,
  59     0xcd2a5925d9681f90ULL, 0x8fdab8ce70822903ULL, 0x48cb9af28abc72b6ULL, 0x0a3b7b1923564425ULL,
  60     0x70428b155b4eaf1eULL, 0x32b26afef2a4998dULL, 0xf5a348c2089ac238ULL, 0xb753a929a170f4abULL,
  61     0x3971ed50550c43c1ULL, 0x7b810cbbfce67552ULL, 0xbc902e8706d82ee7ULL, 0xfe60cf6caf321874ULL,
  62     0xe224479f47cb76a0ULL, 0xa0d4a674ee214033ULL, 0x67c58448141f1b86ULL, 0x253565a3bdf52d15ULL,
  63     0xab1721da49899a7fULL, 0xe9e7c031e063acecULL, 0x2ef6e20d1a5df759ULL, 0x6c0603e6b3b7c1caULL,
  64     0xf6fae5c07d3274cdULL, 0xb40a042bd4d8425eULL, 0x731b26172ee619ebULL, 0x31ebc7fc870c2f78ULL,
  65     0xbfc9838573709812ULL, 0xfd39626eda9aae81ULL, 0x3a28405220a4f534ULL, 0x78d8a1b9894ec3a7ULL,
  66     0x649c294a61b7ad73ULL, 0x266cc8a1c85d9be0ULL, 0xe17dea9d3263c055ULL, 0xa38d0b769b89f6c6ULL,
  67     0x2daf4f0f6ff541acULL, 0x6f5faee4c61f773fULL, 0xa84e8cd83c212c8aULL, 0xeabe6d3395cb1a19ULL,
  68     0x90c79d3fedd3f122ULL, 0xd2377cd44439c7b1ULL, 0x15265ee8be079c04ULL, 0x57d6bf0317edaa97ULL,
  69     0xd9f4fb7ae3911dfdULL, 0x9b041a914a7b2b6eULL, 0x5c1538adb04570dbULL, 0x1ee5d94619af4648ULL,
  70     0x02a151b5f156289cULL, 0x4051b05e58bc1e0fULL, 0x87409262a28245baULL, 0xc5b073890b687329ULL,
  71     0x4b9237f0ff14c443ULL, 0x0962d61b56fef2d0ULL, 0xce73f427acc0a965ULL, 0x8c8315cc052a9ff6ULL,
  72     0x3a80143f5cf17f13ULL, 0x7870f5d4f51b4980ULL, 0xbf61d7e80f251235ULL, 0xfd913603a6cf24a6ULL,
  73     0x73b3727a52b393ccULL, 0x31439391fb59a55fULL, 0xf652b1ad0167feeaULL, 0xb4a25046a88dc879ULL,
  74     0xa8e6d8b54074a6adULL, 0xea16395ee99e903eULL, 0x2d071b6213a0cb8bULL, 0x6ff7fa89ba4afd18ULL,
  75     0xe1d5bef04e364a72ULL, 0xa3255f1be7dc7ce1ULL, 0x64347d271de22754ULL, 0x26c49cccb40811c7ULL,
  76     0x5cbd6cc0cc10fafcULL, 0x1e4d8d2b65facc6fULL, 0xd95caf179fc497daULL, 0x9bac4efc362ea149ULL,
  77     0x158e0a85c2521623ULL, 0x577eeb6e6bb820b0ULL, 0x906fc95291867b05ULL, 0xd29f28b9386c4d96ULL,
  78     0xcedba04ad0952342ULL, 0x8c2b41a1797f15d1ULL, 0x4b3a639d83414e64ULL, 0x09ca82762aab78f7ULL,
  79     0x87e8c60fded7cf9dULL, 0xc51827e4773df90eULL, 0x020905d88d03a2bbULL, 0x40f9e43324e99428ULL,
  80     0x2cffe7d5975e55e2ULL, 0x6e0f063e3eb46371ULL, 0xa91e2402c48a38c4ULL, 0xebeec5e96d600e57ULL,
  81     0x65cc8190991cb93dULL, 0x273c607b30f68faeULL, 0xe02d4247cac8d41bULL, 0xa2dda3ac6322e288ULL,
  82     0xbe992b5f8bdb8c5cULL, 0xfc69cab42231bacfULL, 0x3b78e888d80fe17aULL, 0x7988096371e5d7e9ULL,
  83     0xf7aa4d1a85996083ULL, 0xb55aacf12c735610ULL, 0x724b8ecdd64d0da5ULL, 0x30bb6f267fa73b36ULL,
  84     0x4ac29f2a07bfd00dULL, 0x08327ec1ae55e69eULL, 0xcf235cfd546bbd2bULL, 0x8dd3bd16fd818bb8ULL,
  85     0x03f1f96f09fd3cd2ULL, 0x41011884a0170a41ULL, 0x86103ab85a2951f4ULL, 0xc4e0db53f3c36767ULL,
  86     0xd8a453a01b3a09b3ULL, 0x9a54b24bb2d03f20ULL, 0x5d45907748ee6495ULL, 0x1fb5719ce1045206ULL,
  87     0x919735e51578e56cULL, 0xd367d40ebc92d3ffULL, 0x1476f63246ac884aULL, 0x568617d9ef46bed9ULL,
  88     0xe085162ab69d5e3cULL, 0xa275f7c11f7768afULL, 0x6564d5fde549331aULL, 0x279434164ca30589ULL,
  89     0xa9b6706fb8dfb2e3ULL, 0xeb46918411358470ULL, 0x2c57b3b8eb0bdfc5ULL, 0x6ea7525342e1e956ULL,
  90     0x72e3daa0aa188782ULL, 0x30133b4b03f2b111ULL, 0xf7021977f9cceaa4ULL, 0xb5f2f89c5026dc37ULL,
  91     0x3bd0bce5a45a6b5dULL, 0x79205d0e0db05dceULL, 0xbe317f32f78e067bULL, 0xfcc19ed95e6430e8ULL,
  92     0x86b86ed5267cdbd3ULL, 0xc4488f3e8f96ed40ULL, 0x0359ad0275a8b6f5ULL, 0x41a94ce9dc428066ULL,
  93     0xcf8b0890283e370cULL, 0x8d7be97b81d4019fULL, 0x4a6acb477bea5a2aULL, 0x089a2aacd2006cb9ULL,
  94     0x14dea25f3af9026dULL, 0x562e43b4931334feULL, 0x913f6188692d6f4bULL, 0xd3cf8063c0c759d8ULL,
  95     0x5dedc41a34bbeeb2ULL, 0x1f1d25f19d51d821ULL, 0xd80c07cd676f8394ULL, 0x9afce626ce85b507ULL
  96 };
  97
  98 ////uint64_t poly = 0xA17870F5D4F51B49ULL; // reverse of reciprocal
  99 ////uint64_t poly = 0xC96C5795D7870F42ULL; // reverse
 100 //uint64_t poly = 0x42F0E1EBA9EA3693ULL; // normal
 101
 102 //uint64_t table[256];
 103
 104 //void generate_table()
 105 //{
 106 //    printf("static const uint64_t _crc_table64[256] = {\n");
 107 //
 108 //    for(uint64_t i=0; i<256; ++i)
 109 //    {
 110 //      uint64_t crc = i << 56;
 111 //
 112 //        int bits = 8 + 1;
 113 //        while (--bits) {
 114 //            crc = (crc & 0x8000000000000000ULL) ? (crc << 1) ^ poly : (crc << 1);
 115 //      }
 116 //
 117 //        //table[i] = crc;
 118 //        printf(" ");
 119 //        printf("0x%016llxULL", crc);
 120 //        if (i != 255) printf(",");
 121 //        if ((i+1) % 4 == 0) printf("\n");
 122 //    }
 123 //
 124 //    printf("};\n");
 125 //}