Most efficent way to calculate CRC64 with reflected input

I need to calculate a CRC-64 using this setup into this wonderful website: http://www.sunshine2k.de/coding/javascript/crc/crc_js.html

As you can see I require "input reflected" and that means that I need to reverse the bit order of any byte (a bit annoying). For the moment, I implemented this with a lookup table (for example 0x55 -> 0xAA), but I was wondering if there is any property of CRC which can be used to be more efficient.

This is my code (in C):

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;
}

Thanks in advance for any help!

Update: actually I'm wondering if some properties of CRC allow me to get the same result using reflected table, opposite shifting, reciprocal / reverse polynomial... etc. That would let skip the step of reversing bits.

Solution: using reflected table, changing shift direction and reversing bits just of the very last result:

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;
}

Thanks to everybody for the help!

Solution

actually I'm wondering if some properties of CRC allow me to get the same result using reflected table, opposite shifting, reciprocal / reverse polynomial... etc. That would let skip the step of reversing bits.

There is such a property, and you only need one reverse, in the end. The whole logic of the CRC can be bit-reversed*, so that the bits stream the opposite way and don't need to be reversed during the calculation itself:

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 is like CRC64_TABLE, but with the entries and indexes both bit-reversed. So they relate to each other like this: (naturally you would hard-code this table)

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

rbit is just some function that reverses bits, I used this really dumb one, use a better one if you want but it's only used once:

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;
}

*: really what this means is that the integer holding the bits during the calculation is viewed in reverse, with what would normally be its least significant bit instead held in its most significant bit etc. So depending on how you look at it, the calculation is not even different. The same bits are created, but we hold them in a variable differently.