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我需要在这个精彩的网站中使用这个设置计算一个 CRC-64：http: //www.sunshine2k.de/coding/javascript/crc/crc_js.html

如您所见，我需要“输入反射”，这意味着我需要反转任何字节的位顺序（有点烦人）。目前，我使用查找表（例如 0x55 -> 0xAA）实现了这一点，但我想知道 CRC 是否有任何属性可以用来提高效率。

这是我的代码（在 C 中）：

static const unsigned long long CRC64_TABLE[256] = {
    0x0000000000000000, 0x42F0E1EBA9EA3693, 0x85E1C3D753D46D26, 0xC711223CFA3E5BB5, 0x493366450E42ECDF, 0x0BC387AEA7A8DA4C, 0xCCD2A5925D9681F9, 0x8E224479F47CB76A,
    0x9266CC8A1C85D9BE, 0xD0962D61B56FEF2D, 0x17870F5D4F51B498, 0x5577EEB6E6BB820B, 0xDB55AACF12C73561, 0x99A54B24BB2D03F2, 0x5EB4691841135847, 0x1C4488F3E8F96ED4,
    0x663D78FF90E185EF, 0x24CD9914390BB37C, 0xE3DCBB28C335E8C9, 0xA12C5AC36ADFDE5A, 0x2F0E1EBA9EA36930, 0x6DFEFF5137495FA3, 0xAAEFDD6DCD770416, 0xE81F3C86649D3285,
    0xF45BB4758C645C51, 0xB6AB559E258E6AC2, 0x71BA77A2DFB03177, 0x334A9649765A07E4, 0xBD68D2308226B08E, 0xFF9833DB2BCC861D, 0x388911E7D1F2DDA8, 0x7A79F00C7818EB3B,
    0xCC7AF1FF21C30BDE, 0x8E8A101488293D4D, 0x499B3228721766F8, 0x0B6BD3C3DBFD506B, 0x854997BA2F81E701, 0xC7B97651866BD192, 0x00A8546D7C558A27, 0x4258B586D5BFBCB4,
    0x5E1C3D753D46D260, 0x1CECDC9E94ACE4F3, 0xDBFDFEA26E92BF46, 0x990D1F49C77889D5, 0x172F5B3033043EBF, 0x55DFBADB9AEE082C, 0x92CE98E760D05399, 0xD03E790CC93A650A,
    0xAA478900B1228E31, 0xE8B768EB18C8B8A2, 0x2FA64AD7E2F6E317, 0x6D56AB3C4B1CD584, 0xE374EF45BF6062EE, 0xA1840EAE168A547D, 0x66952C92ECB40FC8, 0x2465CD79455E395B,
    0x3821458AADA7578F, 0x7AD1A461044D611C, 0xBDC0865DFE733AA9, 0xFF3067B657990C3A, 0x711223CFA3E5BB50, 0x33E2C2240A0F8DC3, 0xF4F3E018F031D676, 0xB60301F359DBE0E5,
    0xDA050215EA6C212F, 0x98F5E3FE438617BC, 0x5FE4C1C2B9B84C09, 0x1D14202910527A9A, 0x93366450E42ECDF0, 0xD1C685BB4DC4FB63, 0x16D7A787B7FAA0D6, 0x5427466C1E109645,
    0x4863CE9FF6E9F891, 0x0A932F745F03CE02, 0xCD820D48A53D95B7, 0x8F72ECA30CD7A324, 0x0150A8DAF8AB144E, 0x43A04931514122DD, 0x84B16B0DAB7F7968, 0xC6418AE602954FFB,
    0xBC387AEA7A8DA4C0, 0xFEC89B01D3679253, 0x39D9B93D2959C9E6, 0x7B2958D680B3FF75, 0xF50B1CAF74CF481F, 0xB7FBFD44DD257E8C, 0x70EADF78271B2539, 0x321A3E938EF113AA,
    0x2E5EB66066087D7E, 0x6CAE578BCFE24BED, 0xABBF75B735DC1058, 0xE94F945C9C3626CB, 0x676DD025684A91A1, 0x259D31CEC1A0A732, 0xE28C13F23B9EFC87, 0xA07CF2199274CA14,
    0x167FF3EACBAF2AF1, 0x548F120162451C62, 0x939E303D987B47D7, 0xD16ED1D631917144, 0x5F4C95AFC5EDC62E, 0x1DBC74446C07F0BD, 0xDAAD56789639AB08, 0x985DB7933FD39D9B,
    0x84193F60D72AF34F, 0xC6E9DE8B7EC0C5DC, 0x01F8FCB784FE9E69, 0x43081D5C2D14A8FA, 0xCD2A5925D9681F90, 0x8FDAB8CE70822903, 0x48CB9AF28ABC72B6, 0x0A3B7B1923564425,
    0x70428B155B4EAF1E, 0x32B26AFEF2A4998D, 0xF5A348C2089AC238, 0xB753A929A170F4AB, 0x3971ED50550C43C1, 0x7B810CBBFCE67552, 0xBC902E8706D82EE7, 0xFE60CF6CAF321874,
    0xE224479F47CB76A0, 0xA0D4A674EE214033, 0x67C58448141F1B86, 0x253565A3BDF52D15, 0xAB1721DA49899A7F, 0xE9E7C031E063ACEC, 0x2EF6E20D1A5DF759, 0x6C0603E6B3B7C1CA,
    0xF6FAE5C07D3274CD, 0xB40A042BD4D8425E, 0x731B26172EE619EB, 0x31EBC7FC870C2F78, 0xBFC9838573709812, 0xFD39626EDA9AAE81, 0x3A28405220A4F534, 0x78D8A1B9894EC3A7,
    0x649C294A61B7AD73, 0x266CC8A1C85D9BE0, 0xE17DEA9D3263C055, 0xA38D0B769B89F6C6, 0x2DAF4F0F6FF541AC, 0x6F5FAEE4C61F773F, 0xA84E8CD83C212C8A, 0xEABE6D3395CB1A19,
    0x90C79D3FEDD3F122, 0xD2377CD44439C7B1, 0x15265EE8BE079C04, 0x57D6BF0317EDAA97, 0xD9F4FB7AE3911DFD, 0x9B041A914A7B2B6E, 0x5C1538ADB04570DB, 0x1EE5D94619AF4648,
    0x02A151B5F156289C, 0x4051B05E58BC1E0F, 0x87409262A28245BA, 0xC5B073890B687329, 0x4B9237F0FF14C443, 0x0962D61B56FEF2D0, 0xCE73F427ACC0A965, 0x8C8315CC052A9FF6,
    0x3A80143F5CF17F13, 0x7870F5D4F51B4980, 0xBF61D7E80F251235, 0xFD913603A6CF24A6, 0x73B3727A52B393CC, 0x31439391FB59A55F, 0xF652B1AD0167FEEA, 0xB4A25046A88DC879,
    0xA8E6D8B54074A6AD, 0xEA16395EE99E903E, 0x2D071B6213A0CB8B, 0x6FF7FA89BA4AFD18, 0xE1D5BEF04E364A72, 0xA3255F1BE7DC7CE1, 0x64347D271DE22754, 0x26C49CCCB40811C7,
    0x5CBD6CC0CC10FAFC, 0x1E4D8D2B65FACC6F, 0xD95CAF179FC497DA, 0x9BAC4EFC362EA149, 0x158E0A85C2521623, 0x577EEB6E6BB820B0, 0x906FC95291867B05, 0xD29F28B9386C4D96,
    0xCEDBA04AD0952342, 0x8C2B41A1797F15D1, 0x4B3A639D83414E64, 0x09CA82762AAB78F7, 0x87E8C60FDED7CF9D, 0xC51827E4773DF90E, 0x020905D88D03A2BB, 0x40F9E43324E99428,
    0x2CFFE7D5975E55E2, 0x6E0F063E3EB46371, 0xA91E2402C48A38C4, 0xEBEEC5E96D600E57, 0x65CC8190991CB93D, 0x273C607B30F68FAE, 0xE02D4247CAC8D41B, 0xA2DDA3AC6322E288,
    0xBE992B5F8BDB8C5C, 0xFC69CAB42231BACF, 0x3B78E888D80FE17A, 0x7988096371E5D7E9, 0xF7AA4D1A85996083, 0xB55AACF12C735610, 0x724B8ECDD64D0DA5, 0x30BB6F267FA73B36,
    0x4AC29F2A07BFD00D, 0x08327EC1AE55E69E, 0xCF235CFD546BBD2B, 0x8DD3BD16FD818BB8, 0x03F1F96F09FD3CD2, 0x41011884A0170A41, 0x86103AB85A2951F4, 0xC4E0DB53F3C36767,
    0xD8A453A01B3A09B3, 0x9A54B24BB2D03F20, 0x5D45907748EE6495, 0x1FB5719CE1045206, 0x919735E51578E56C, 0xD367D40EBC92D3FF, 0x1476F63246AC884A, 0x568617D9EF46BED9,
    0xE085162AB69D5E3C, 0xA275F7C11F7768AF, 0x6564D5FDE549331A, 0x279434164CA30589, 0xA9B6706FB8DFB2E3, 0xEB46918411358470, 0x2C57B3B8EB0BDFC5, 0x6EA7525342E1E956,
    0x72E3DAA0AA188782, 0x30133B4B03F2B111, 0xF7021977F9CCEAA4, 0xB5F2F89C5026DC37, 0x3BD0BCE5A45A6B5D, 0x79205D0E0DB05DCE, 0xBE317F32F78E067B, 0xFCC19ED95E6430E8,
    0x86B86ED5267CDBD3, 0xC4488F3E8F96ED40, 0x0359AD0275A8B6F5, 0x41A94CE9DC428066, 0xCF8B0890283E370C, 0x8D7BE97B81D4019F, 0x4A6ACB477BEA5A2A, 0x089A2AACD2006CB9,
    0x14DEA25F3AF9026D, 0x562E43B4931334FE, 0x913F6188692D6F4B, 0xD3CF8063C0C759D8, 0x5DEDC41A34BBEEB2, 0x1F1D25F19D51D821, 0xD80C07CD676F8394, 0x9AFCE626CE85B507
};

static const unsigned char REVERSE_BITS_TABLE[256] = {
    // 0     1     2     3     4     5     6     7     8     9     A     B     C     D     E     F
    0x00, 0x80, 0x40, 0xC0, 0x20, 0xA0, 0x60, 0xE0, 0x10, 0x90, 0x50, 0xD0, 0x30, 0xB0, 0x70, 0xF0,
    0x08, 0x88, 0x48, 0xC8, 0x28, 0xA8, 0x68, 0xE8, 0x18, 0x98, 0x58, 0xD8, 0x38, 0xB8, 0x78, 0xF8,
    0x04, 0x84, 0x44, 0xC4, 0x24, 0xA4, 0x64, 0xE4, 0x14, 0x94, 0x54, 0xD4, 0x34, 0xB4, 0x74, 0xF4,
    0x0C, 0x8C, 0x4C, 0xCC, 0x2C, 0xAC, 0x6C, 0xEC, 0x1C, 0x9C, 0x5C, 0xDC, 0x3C, 0xBC, 0x7C, 0xFC,
    0x02, 0x82, 0x42, 0xC2, 0x22, 0xA2, 0x62, 0xE2, 0x12, 0x92, 0x52, 0xD2, 0x32, 0xB2, 0x72, 0xF2,
    0x0A, 0x8A, 0x4A, 0xCA, 0x2A, 0xAA, 0x6A, 0xEA, 0x1A, 0x9A, 0x5A, 0xDA, 0x3A, 0xBA, 0x7A, 0xFA,
    0x06, 0x86, 0x46, 0xC6, 0x26, 0xA6, 0x66, 0xE6, 0x16, 0x96, 0x56, 0xD6, 0x36, 0xB6, 0x76, 0xF6,
    0x0E, 0x8E, 0x4E, 0xCE, 0x2E, 0xAE, 0x6E, 0xEE, 0x1E, 0x9E, 0x5E, 0xDE, 0x3E, 0xBE, 0x7E, 0xFE,
    0x01, 0x81, 0x41, 0xC1, 0x21, 0xA1, 0x61, 0xE1, 0x11, 0x91, 0x51, 0xD1, 0x31, 0xB1, 0x71, 0xF1,
    0x09, 0x89, 0x49, 0xC9, 0x29, 0xA9, 0x69, 0xE9, 0x19, 0x99, 0x59, 0xD9, 0x39, 0xB9, 0x79, 0xF9,
    0x05, 0x85, 0x45, 0xC5, 0x25, 0xA5, 0x65, 0xE5, 0x15, 0x95, 0x55, 0xD5, 0x35, 0xB5, 0x75, 0xF5,
    0x0D, 0x8D, 0x4D, 0xCD, 0x2D, 0xAD, 0x6D, 0xED, 0x1D, 0x9D, 0x5D, 0xDD, 0x3D, 0xBD, 0x7D, 0xFD,
    0x03, 0x83, 0x43, 0xC3, 0x23, 0xA3, 0x63, 0xE3, 0x13, 0x93, 0x53, 0xD3, 0x33, 0xB3, 0x73, 0xF3,
    0x0B, 0x8B, 0x4B, 0xCB, 0x2B, 0xAB, 0x6B, 0xEB, 0x1B, 0x9B, 0x5B, 0xDB, 0x3B, 0xBB, 0x7B, 0xFB,
    0x07, 0x87, 0x47, 0xC7, 0x27, 0xA7, 0x67, 0xE7, 0x17, 0x97, 0x57, 0xD7, 0x37, 0xB7, 0x77, 0xF7,
    0x0F, 0x8F, 0x4F, 0xCF, 0x2F, 0xAF, 0x6F, 0xEF, 0x1F, 0x9F, 0x5F, 0xDF, 0x3F, 0xBF, 0x7F, 0xFF
};

unsigned long long calculateCRC64(unsigned char* data, unsigned long size)
{
    unsigned long long myCRC64 = 0;

    for(unsigned long i = 0; i < size; i++)
        myCRC64 = CRC64_TABLE[((myCRC64 >> 56) ^ REVERSE_BITS_TABLE[data[i]]) & 0xFF] ^ (myCRC64 << 8);

    return myCRC64;
}

提前感谢您的帮助！

更新：实际上我想知道 CRC 的某些属性是否允许我使用反射表、反向移位、倒数/反向多项式......等获得相同的结果。这将让我们跳过反转位的步骤。

解决方案：使用反射表，改变移位方向并反转最后一个结果的位：

static const unsigned long long CRC64_TABLE_REF[256] = {
    0x0000000000000000, 0xB32E4CBE03A75F6F, 0xF4843657A840A05B, 0x47AA7AE9ABE7FF34, 0x7BD0C384FF8F5E33, 0xC8FE8F3AFC28015C, 0x8F54F5D357CFFE68, 0x3C7AB96D5468A107,
    0xF7A18709FF1EBC66, 0x448FCBB7FCB9E309, 0x0325B15E575E1C3D, 0xB00BFDE054F94352, 0x8C71448D0091E255, 0x3F5F08330336BD3A, 0x78F572DAA8D1420E, 0xCBDB3E64AB761D61,
    0x7D9BA13851336649, 0xCEB5ED8652943926, 0x891F976FF973C612, 0x3A31DBD1FAD4997D, 0x064B62BCAEBC387A, 0xB5652E02AD1B6715, 0xF2CF54EB06FC9821, 0x41E11855055BC74E,
    0x8A3A2631AE2DDA2F, 0x39146A8FAD8A8540, 0x7EBE1066066D7A74, 0xCD905CD805CA251B, 0xF1EAE5B551A2841C, 0x42C4A90B5205DB73, 0x056ED3E2F9E22447, 0xB6409F5CFA457B28,
    0xFB374270A266CC92, 0x48190ECEA1C193FD, 0x0FB374270A266CC9, 0xBC9D3899098133A6, 0x80E781F45DE992A1, 0x33C9CD4A5E4ECDCE, 0x7463B7A3F5A932FA, 0xC74DFB1DF60E6D95,
    0x0C96C5795D7870F4, 0xBFB889C75EDF2F9B, 0xF812F32EF538D0AF, 0x4B3CBF90F69F8FC0, 0x774606FDA2F72EC7, 0xC4684A43A15071A8, 0x83C230AA0AB78E9C, 0x30EC7C140910D1F3,
    0x86ACE348F355AADB, 0x3582AFF6F0F2F5B4, 0x7228D51F5B150A80, 0xC10699A158B255EF, 0xFD7C20CC0CDAF4E8, 0x4E526C720F7DAB87, 0x09F8169BA49A54B3, 0xBAD65A25A73D0BDC,
    0x710D64410C4B16BD, 0xC22328FF0FEC49D2, 0x85895216A40BB6E6, 0x36A71EA8A7ACE989, 0x0ADDA7C5F3C4488E, 0xB9F3EB7BF06317E1, 0xFE5991925B84E8D5, 0x4D77DD2C5823B7BA,
    0x64B62BCAEBC387A1, 0xD7986774E864D8CE, 0x90321D9D438327FA, 0x231C512340247895, 0x1F66E84E144CD992, 0xAC48A4F017EB86FD, 0xEBE2DE19BC0C79C9, 0x58CC92A7BFAB26A6,
    0x9317ACC314DD3BC7, 0x2039E07D177A64A8, 0x67939A94BC9D9B9C, 0xD4BDD62ABF3AC4F3, 0xE8C76F47EB5265F4, 0x5BE923F9E8F53A9B, 0x1C4359104312C5AF, 0xAF6D15AE40B59AC0,
    0x192D8AF2BAF0E1E8, 0xAA03C64CB957BE87, 0xEDA9BCA512B041B3, 0x5E87F01B11171EDC, 0x62FD4976457FBFDB, 0xD1D305C846D8E0B4, 0x96797F21ED3F1F80, 0x2557339FEE9840EF,
    0xEE8C0DFB45EE5D8E, 0x5DA24145464902E1, 0x1A083BACEDAEFDD5, 0xA9267712EE09A2BA, 0x955CCE7FBA6103BD, 0x267282C1B9C65CD2, 0x61D8F8281221A3E6, 0xD2F6B4961186FC89,
    0x9F8169BA49A54B33, 0x2CAF25044A02145C, 0x6B055FEDE1E5EB68, 0xD82B1353E242B407, 0xE451AA3EB62A1500, 0x577FE680B58D4A6F, 0x10D59C691E6AB55B, 0xA3FBD0D71DCDEA34,
    0x6820EEB3B6BBF755, 0xDB0EA20DB51CA83A, 0x9CA4D8E41EFB570E, 0x2F8A945A1D5C0861, 0x13F02D374934A966, 0xA0DE61894A93F609, 0xE7741B60E174093D, 0x545A57DEE2D35652,
    0xE21AC88218962D7A, 0x5134843C1B317215, 0x169EFED5B0D68D21, 0xA5B0B26BB371D24E, 0x99CA0B06E7197349, 0x2AE447B8E4BE2C26, 0x6D4E3D514F59D312, 0xDE6071EF4CFE8C7D,
    0x15BB4F8BE788911C, 0xA6950335E42FCE73, 0xE13F79DC4FC83147, 0x521135624C6F6E28, 0x6E6B8C0F1807CF2F, 0xDD45C0B11BA09040, 0x9AEFBA58B0476F74, 0x29C1F6E6B3E0301B,
    0xC96C5795D7870F42, 0x7A421B2BD420502D, 0x3DE861C27FC7AF19, 0x8EC62D7C7C60F076, 0xB2BC941128085171, 0x0192D8AF2BAF0E1E, 0x4638A2468048F12A, 0xF516EEF883EFAE45,
    0x3ECDD09C2899B324, 0x8DE39C222B3EEC4B, 0xCA49E6CB80D9137F, 0x7967AA75837E4C10, 0x451D1318D716ED17, 0xF6335FA6D4B1B278, 0xB199254F7F564D4C, 0x02B769F17CF11223,
    0xB4F7F6AD86B4690B, 0x07D9BA1385133664, 0x4073C0FA2EF4C950, 0xF35D8C442D53963F, 0xCF273529793B3738, 0x7C0979977A9C6857, 0x3BA3037ED17B9763, 0x888D4FC0D2DCC80C,
    0x435671A479AAD56D, 0xF0783D1A7A0D8A02, 0xB7D247F3D1EA7536, 0x04FC0B4DD24D2A59, 0x3886B22086258B5E, 0x8BA8FE9E8582D431, 0xCC0284772E652B05, 0x7F2CC8C92DC2746A,
    0x325B15E575E1C3D0, 0x8175595B76469CBF, 0xC6DF23B2DDA1638B, 0x75F16F0CDE063CE4, 0x498BD6618A6E9DE3, 0xFAA59ADF89C9C28C, 0xBD0FE036222E3DB8, 0x0E21AC88218962D7,
    0xC5FA92EC8AFF7FB6, 0x76D4DE52895820D9, 0x317EA4BB22BFDFED, 0x8250E80521188082, 0xBE2A516875702185, 0x0D041DD676D77EEA, 0x4AAE673FDD3081DE, 0xF9802B81DE97DEB1,
    0x4FC0B4DD24D2A599, 0xFCEEF8632775FAF6, 0xBB44828A8C9205C2, 0x086ACE348F355AAD, 0x34107759DB5DFBAA, 0x873E3BE7D8FAA4C5, 0xC094410E731D5BF1, 0x73BA0DB070BA049E,
    0xB86133D4DBCC19FF, 0x0B4F7F6AD86B4690, 0x4CE50583738CB9A4, 0xFFCB493D702BE6CB, 0xC3B1F050244347CC, 0x709FBCEE27E418A3, 0x3735C6078C03E797, 0x841B8AB98FA4B8F8,
    0xADDA7C5F3C4488E3, 0x1EF430E13FE3D78C, 0x595E4A08940428B8, 0xEA7006B697A377D7, 0xD60ABFDBC3CBD6D0, 0x6524F365C06C89BF, 0x228E898C6B8B768B, 0x91A0C532682C29E4,
    0x5A7BFB56C35A3485, 0xE955B7E8C0FD6BEA, 0xAEFFCD016B1A94DE, 0x1DD181BF68BDCBB1, 0x21AB38D23CD56AB6, 0x9285746C3F7235D9, 0xD52F0E859495CAED, 0x6601423B97329582,
    0xD041DD676D77EEAA, 0x636F91D96ED0B1C5, 0x24C5EB30C5374EF1, 0x97EBA78EC690119E, 0xAB911EE392F8B099, 0x18BF525D915FEFF6, 0x5F1528B43AB810C2, 0xEC3B640A391F4FAD,
    0x27E05A6E926952CC, 0x94CE16D091CE0DA3, 0xD3646C393A29F297, 0x604A2087398EADF8, 0x5C3099EA6DE60CFF, 0xEF1ED5546E415390, 0xA8B4AFBDC5A6ACA4, 0x1B9AE303C601F3CB,
    0x56ED3E2F9E224471, 0xE5C372919D851B1E, 0xA26908783662E42A, 0x114744C635C5BB45, 0x2D3DFDAB61AD1A42, 0x9E13B115620A452D, 0xD9B9CBFCC9EDBA19, 0x6A978742CA4AE576,
    0xA14CB926613CF817, 0x1262F598629BA778, 0x55C88F71C97C584C, 0xE6E6C3CFCADB0723, 0xDA9C7AA29EB3A624, 0x69B2361C9D14F94B, 0x2E184CF536F3067F, 0x9D36004B35545910,
    0x2B769F17CF112238, 0x9858D3A9CCB67D57, 0xDFF2A94067518263, 0x6CDCE5FE64F6DD0C, 0x50A65C93309E7C0B, 0xE388102D33392364, 0xA4226AC498DEDC50, 0x170C267A9B79833F,
    0xDCD7181E300F9E5E, 0x6FF954A033A8C131, 0x28532E49984F3E05, 0x9B7D62F79BE8616A, 0xA707DB9ACF80C06D, 0x14299724CC279F02, 0x5383EDCD67C06036, 0xE0ADA17364673F59
};

unsigned long long calculateCRC64(unsigned char* data, unsigned long size)
{
    unsigned long long myCRC64 = 0;

    for(unsigned long i = 0; i < size; i++)
        myCRC64 = CRC64_TABLE_REF[(myCRC64 ^ data[i]) & 0xFF] ^ (myCRC64 >> 8);

    unsigned long long tmp = myCRC64;
    myCRC64 = 0;
    for (int i = 0; i < 64; i++) {
        myCRC64 = (myCRC64 << 1) | (tmp & 1);
        tmp >>= 1;
    }

    return myCRC64;
}

感谢大家的帮助！

4

2 回答 2

5

实际上，我想知道 CRC 的某些属性是否允许我使用反射表、反向移位、倒数/反向多项式......等获得相同的结果。这将让我们跳过反转位的步骤。

有这样一个属性，最后只需要一个反转。CRC 的整个逻辑可以位反转*，以便位以相反的方式流式传输，并且在计算过程中不需要反转：

unsigned long long CRC64(unsigned char* data, unsigned long size)
{
    unsigned long long crc = 0;

    for(unsigned long i = 0; i < size; i++)
        crc = CRC64_TABLE_R[(crc & 0xff) ^ data[i]] ^ (crc >> 8);

    return rbit(crc);
}

CRC64_TABLE_R就像CRC64_TABLE，但条目和索引都是位反转的。所以它们像这样相互关联：（当然你会硬编码这个表）

for (int i = 0; i < 256; i++) {
    CRC64_TABLE_R[REVERSE_BITS_TABLE[i]] = rbit(CRC64_TABLE[i]);
}

rbit只是一些反转位的功能，我使用了这个非常愚蠢的功能，如果您愿意，可以使用更好的功能，但它只使用一次：

unsigned long long rbit(unsigned long long n)
{
    unsigned long long x = 0;
    for (int i = 0; i < 64; i++) {
        x = (x << 1) | (n & 1);
        n >>= 1;
    }
    return x;
}

*：这实际上意味着在计算过程中保存位的整数被反向查看，通常是它的最低有效位而不是最高有效位等。所以取决于你如何看待它，计算甚至没有什么不同。创建了相同的位，但我们将它们保存在不同的变量中。

于 2020-02-17T21:33:37.400 回答
2

代码只需从左移 CRC 切换到右移 CRC，多项式位反转。“#if 0”用于在两个常用多项式之间进行选择，在这种情况下，“#if 0”将使用 CRC64 ecma，即问题的 CRC 表中显示的内容。（0x42F0E1EBA9EA3693 位反转 == 0xC96C5795D7870F42）。

uint64_t crctbl[256];

void gentbl(void)
{
uint64_t crc;
uint64_t b;
uint64_t c;
uint64_t i;
    for(c = 0; c < 0x100; c++){
        crc = c;
        for(i = 0; i < 8; i++){
            b = crc&1;
            crc >>= 1;
#if 0
            crc ^= (0 - b) & 0xd800000000000000ull; // crc64 iso
#else
            crc ^= (0 - b) & 0xc96c5795d7870f42ull; // crc64 ecma
#endif
        }
        crctbl[c] = crc;
    }
}

uint64_t crc64c(uint64_t crc64, uint8_t * bfr, size_t size)
{
uint64_t crc = crc64;
    while(size--)
        crc = (crc >> 8) ^ crctbl[(crc & 0xff)^*bfr++];
    return(crc);
}

“最有效的方式” - 如果在 X86 X64 上运行无进位乘法，一个非常快的 CRC，比上面显示的表方法快 20 倍以上（对于 256 MB 数据的 CRC，英特尔酷睿 i7-10510U .475 秒表, .015 秒 pclmulqdq, 31.5 倍的速度) , 可以使用 pclmulqdq 指令和 xmm 寄存器来执行。链接到 520+ 行汇编文件的 zip，用于 Visual Studio 的 MASM (ML64.EXE)，用于 64 位反射 CRC，使用与上述 gentbl() 函数相同的“if 0”在两个 CRC 多项式之间进行选择。

http://rcgldr.net/misc/crc64ra.zip

解释 32 位 CRC 算法的英特尔文档：

https://www.intel.com/content/dam/www/public/us/en/documents/white-papers/fast-crc-computation-generic-polynomials-pclmulqdq-paper.pdf

两个 64 位非反射操作数的无进位乘法在位 126 (msb) 到位 0 (lsb) 中产生 127 位乘积。对于反射操作数，无进位乘法有效地将乘积乘以 2，这与常数一起考虑。对于 64 位 CRC，poly 是 65 位，因此还需要进行一些调整来处理它。

于 2020-02-17T22:12:13.727 回答