CRC (Cyclic Redundancy Check) Cyclic Redundancy Check is a common method of data validation, many articles speaking CRC algorithm, the reason why he wrote this, is to change a method described CRC algorithm, we want to make it easier to understand CRC algorithm.
Let us talk about what is data validation. During data transmission (such as a file transfer between two computers through a network cable), and due to the transmission channel, there may be bit errors (for example, digital transmission and the recipient received 5 is 6), how to find error code it? By sending additional data recipient to verify correct, this is data validation. Calibrating method is most likely to think and checking, data is to be transmitted (in bytes manner) the calculated sum of data together, and the sum to the receiver side, after receiving the data the receiving side calculates a sum, and comparing the sum received is the same. If a transmission error occurs, then the sum is generally not the same, so as to know the error generated, so that the sender can resend data again.
CRC check also add additional data as a checksum, which is the CRC, the CRC is then how to get it?
Very simple, CRC checksum data is divided by a fixed number (for example, ANSI-CRC16, this number is 0x18005), the resulting remainder is CRC.
That there is a problem here, we send a string of bytes of data, rather than a data, how the data into a string of numbers it? It is also very simple, for example, 2 bytes B1, B2, then the corresponding number is (B1 << 8) + B2; if 3 bytes B1, B2, B3, then the corresponding number is ((B1 < <16) + (B2 << 8 ) + B3), such as a digital 0x01,0x02,0x03, then the corresponding number is 0x10203; and so on. If the number of bytes a lot, then the corresponding number of very, very large, but fortunately just need to get CRC remainder, without the need to get business.
From the principle described above, we can roughly know the exact rate of CRC, appears in the CRC8 the probability of error, but did not find that 1/256, the probability is 1/65536 of CRC16, CRC32 and the probability is 1/2 ^ 32, it is already very small, it is generally the case in the case of small data checksum CRC16 can be used, and in the entire file checksum CRC32 checksum for general use.
There is also a problem, if the dividend is less than the divisor, the remainder is the dividend itself, for example, just pass a byte, its CRC is its own, in order to avoid this, it first before doing the division shift, it is greater than the divisor, then shift how many do? This is related to the selected fixed divisor, and a left shift count less than the number of bits of the divisor, the following standard divisor is used:
the CRC8: polynomial X8 + X5 + X4 + 1, the corresponding number is 0x131, left shift 8
CRC12: polynomial X12 + X11 + X3 + X2 + 1, the corresponding number is 0x180D, left 12
CCITT CRC16: polynomial X16 + X12 + X5 + 1, the corresponding number is 0x11021, left 16
ANSI CRC16: polynomial X16 + X15 + X2 + 1, the corresponding number is 0x18005, left 16-bit
CRC32: polynomial X32 + X26 + X23 + X22 + X16 + X12 + X11 + X10 + X8 + X7 + X5 + X4 + X2 + X1 + 1, the corresponding figures are 0x104C11DB7, left 32
Thus, after obtaining the byte sequence number corresponding to the left and then the M-bit digital (such as ANSI-CRC16 is 16 bits left), the dividend is obtained .
Well, now we have a dividend and the divisor, then they would start doing a division of CRC demand. CRC calculation division with our written calculation division Similarly, the first is the high dividend and the divisor is aligned dividend divisor is subtracted, has been poor, then the divisor is aligned with the most significant difference, subtraction, and then align the further reduction until worse than divisor small, this difference is the remainder. However, ordinary subtraction difference is, the CRC addition (subtraction) process is not into the flag (C), such as 10 minus 01, the outcome is 11, instead of the subtracter 01 obtained by bit, so in practice CRC the obtained results of addition and subtraction are the same, such as the results of 10 plus 11, 10, 01 is the result of subtraction 01 is also 11, which is actually an XOR operation. Having said that though not necessarily make it clear that we still see some CRC division remainder program it:
unsigned short crc16_div()
{
unsigned long data = 0x880000;
unsigned long ccitt16 = 0x11021;
unsigned long cmp_value = 0x10000;
int i;
ccitt16 <<= 7;
cmp_value <<= 7;
the while (cmp_value> = 0x10000)
{
IF ((Data & cmp_value) = 0!)
{
Data = ccitt16 ^;
}
the else
{
}
ccitt16 >> =. 1;
cmp_value >> =. 1;
}
return (Data & 0xFFFF);
}
well, now we will have to calculate a CRC checksum of 0x88, 0x880000 do it just for division remainder number only, but this is only seeking single-byte CRC checksum, and that if there are more than a dozen bytes how do ? Our computer also save any number of big Yeah, it seems we have some improvements to program, so that it can seek the division of large numbers.
Short crc16_div_2 unsigned ()
{
unsigned short data = 0x88;
unsigned short ccitt16 = 0x1021;
int i;
data <<= 8;
for (i=0; i<8; i++)
{
if (data & 0x8000)
{
data <<= 1;
data ^= ccitt16;
}
else
{
data <<= 1;
}
}
the Data return;
}
Now 0x88 CRC16 demand for single-byte, we only need two-byte integer type short on the line, without the need to have a long-type 0x880000, in fact, no matter how many bytes, only the short type can be calculated as before it CRC16. Here to talk about how demand multi-byte check code like:
When we find a byte (such as 0x88) of the CRC, then if there is another byte (such as 0x23) to join, request check code ,what can we do about it? It obtained previously is 0x880000 remainder divided by 0x11021, but now need to get is 0x88230000 remainder divided by 0x11021, previously calculated checksum is not in vain? No, because when we get the number (remainder here is 0x1080) divided by 0x11021 of more than 0x880000, on request 0x88230000 remainder divided by 0x11021, as long as the original remainder 0x1080 left eight divided by 0x11021 get a 0x98000000 divided by 0x11021 the remainder (think about why), plus the remainder of the division 0x11021 of 0x230000. This is actually seeking 0x108000 + 0x230000 remainder of dividing 0x11021 .. Therefore, according to this method, we can seek to write more bytes of CRC algorithms:
unsigned short crc16_ccitt(unsigned char data, unsigned short crc)
{
unsigned short ccitt16 = 0x1021;
int i;
crc ^= (data<<8);
for (i=0; i<8; i++)
{
if (crc & 0x8000)
{
crc <<= 1;
crc ^= ccitt16;
}
else
{
crc <<= 1;
}
}
return crc;
}
void main()
{
int i;
unsigned short crc;
char data[5] = { 0x71, 0x88, 0x93, 0xa5, 0x13 };
crc = 0;
for (i=0; i<5; i++)
{
crc = crc16_ccitt(data[i], crc);
}
printf ( "% crc the X-IS", crc);
}
Well, talking about this CRC algorithms have been introduced all over. What, finished? Not right, how I remember CRC programs have an array called CRC table or something, how do not you here?
Oh, actually using the CRC calculation table in order to save some time, advance quite good CRC stored in the array, and then calculate temporary save, save it from 0 to 0xff CRC code, let's generate a CRC own table:
unsigned CRC16_CCITT_TABLE Short [256];
void init_crc16_ccitt_table ()
{
int I;
for (I = 0; I <256; I ++)
{
CRC16_CCITT_TABLE [I] = crc16_ccitt (I, 0);
}
}
The above table is just one byte CRC, that CRC bytes plurality of how to calculate it? CRC method previously seeking similar to multi-byte, its code is as follows:
Short crc16_ccitt_2 unsigned (Data unsigned char, unsigned Short CRC)
{
unsigned char C;
C = >> CRC. 8;
CRC = <<. 8;
CRC CRC16_CCITT_TABLE ^ = [C ^ Data];
return CRC;
}
Finally the CRC the positive and reverse problems, such as positive sequence in front ccitt-crc16 is 0x1021, if it is the reverse is 0x8408 (0x1021 upside down is to become low high) Why reverse? This is because the data transmission may be transmitted to the low re-transmission of high (such as serial port is the least significant bit first). CRC algorithm and reverse the positive sequence similar, but need to pay attention to the direction of displacement of the opposite.
unsigned short crc16_ccitt_r(unsigned char data, unsigned short crc)
{
unsigned short ccitt16 = 0x8408;
int i;
crc ^= data;
for (i=0; i<8; i++)
{
if (crc & 1)
{
crc >>= 1;
crc ^= ccitt16;
}
else
{
crc >>= 1;
}
}
return crc;
}
unsigned short crc16_ccitt_r2(unsigned char data, unsigned short crc)
{
unsigned char c;
CRC & 0xFF = C;
CRC = >>. 8;
CRC CRC16_CCITT_R_TABLE ^ = [C ^ Data];
return CRC;
}
article to end here, with the blog with two C program, a source of the article is all examples of the program, a look-up table is crc16 program, but do not know how to add attachments, and put CRC16 routines written in the following table:
unsigned short CRC16_TABLE[256] = {
0x0000, 0x8005, 0x800F, 0x000A, 0x801B, 0x001E, 0x0014, 0x8011,
0x8033, 0x0036, 0x003C, 0x8039, 0x0028, 0x802D, 0x8027, 0x0022,
0x8063, 0x0066, 0x006C, 0x8069, 0x0078, 0x807D, 0x8077, 0x0072,
0x0050, 0x8055, 0x805F, 0x005A, 0x804B, 0x004E, 0x0044, 0x8041,
0x80C3, 0x00C6, 0x00CC, 0x80C9, 0x00D8, 0x80DD, 0x80D7, 0x00D2,
0x00F0, 0x80F5, 0x80FF, 0x00FA, 0x80EB, 0x00EE, 0x00E4, 0x80E1,
0x00A0, 0x80A5, 0x80AF, 0x00AA, 0x80BB, 0x00BE, 0x00B4, 0x80B1,
0x8093, 0x0096, 0x009C, 0x8099, 0x0088, 0x808D, 0x8087, 0x0082,
0x8183, 0x0186, 0x018C, 0x8189, 0x0198, 0x819D, 0x8197, 0x0192,
0x01B0, 0x81B5, 0x81BF, 0x01BA, 0x81AB, 0x01AE, 0x01A4, 0x81A1,
0x01E0, 0x81E5, 0x81EF, 0x01EA, 0x81FB, 0x01FE, 0x01F4, 0x81F1,
0x81D3, 0x01D6, 0x01DC, 0x81D9, 0x01C8, 0x81CD, 0x81C7, 0x01C2,
0x0140, 0x8145, 0x814F, 0x014A, 0x815B, 0x015E, 0x0154, 0x8151,
0x8173, 0x0176, 0x017C, 0x8179, 0x0168, 0x816D, 0x8167, 0x0162,
0x8123, 0x0126, 0x012C, 0x8129, 0x0138, 0x813D, 0x8137, 0x0132,
0x0110, 0x8115, 0x811F, 0x011A, 0x810B, 0x010E, 0x0104, 0x8101,
0x8303, 0x0306, 0x030C, 0x8309, 0x0318, 0x831D, 0x8317, 0x0312,
0x0330, 0x8335, 0x833F, 0x033A, 0x832B, 0x032E, 0x0324, 0x8321,
0x0360, 0x8365, 0x836F, 0x036A, 0x837B, 0x037E, 0x0374, 0x8371,
0x8353, 0x0356, 0x035C, 0x8359, 0x0348, 0x834D, 0x8347, 0x0342,
0x03C0, 0x83C5, 0x83CF, 0x03CA, 0x83DB, 0x03DE, 0x03D4, 0x83D1,
0x83F3, 0x03F6, 0x03FC, 0x83F9, 0x03E8, 0x83ED, 0x83E7, 0x03E2,
0x83A3, 0x03A6, 0x03AC, 0x83A9, 0x03B8, 0x83BD, 0x83B7, 0x03B2,
0x0390, 0x8395, 0x839F, 0x039A, 0x838B, 0x038E, 0x0384, 0x8381,
0x0280, 0x8285, 0x828F, 0x028A, 0x829B, 0x029E, 0x0294, 0x8291,
0x82B3, 0x02B6, 0x02BC, 0x82B9, 0x02A8, 0x82AD, 0x82A7, 0x02A2,
0x82E3, 0x02E6, 0x02EC, 0x82E9, 0x02F8, 0x82FD, 0x82F7, 0x02F2,
0x02D0, 0x82D5, 0x82DF, 0x02DA, 0x82CB, 0x02CE, 0x02C4, 0x82C1,
0x8243, 0x0246, 0x024C, 0x8249, 0x0258, 0x825D, 0x8257, 0x0252,
0x0270, 0x8275, 0x827F, 0x027A, 0x826B, 0x026E, 0x0264, 0x8261,
0x0220, 0x8225, 0x822F, 0x022A, 0x823B, 0x023E, 0x0234, 0x8231,
0x8213, 0x0216, 0x021C, 0x8219, 0x0208, 0x820D, 0x8207, 0x0202,
};
unsigned short CRC16R_TABLE[256] = {
0x0000, 0xC0C1, 0xC181, 0x0140, 0xC301, 0x03C0, 0x0280, 0xC241,
0xC601, 0x06C0, 0x0780, 0xC741, 0x0500, 0xC5C1, 0xC481, 0x0440,
0xCC01, 0x0CC0, 0x0D80, 0xCD41, 0x0F00, 0xCFC1, 0xCE81, 0x0E40,
0x0A00, 0xCAC1, 0xCB81, 0x0B40, 0xC901, 0x09C0, 0x0880, 0xC841,
0xD801, 0x18C0, 0x1980, 0xD941, 0x1B00, 0xDBC1, 0xDA81, 0x1A40,
0x1E00, 0xDEC1, 0xDF81, 0x1F40, 0xDD01, 0x1DC0, 0x1C80, 0xDC41,
0x1400, 0xD4C1, 0xD581, 0x1540, 0xD701, 0x17C0, 0x1680, 0xD641,
0xD201, 0x12C0, 0x1380, 0xD341, 0x1100, 0xD1C1, 0xD081, 0x1040,
0xF001, 0x30C0, 0x3180, 0xF141, 0x3300, 0xF3C1, 0xF281, 0x3240,
0x3600, 0xF6C1, 0xF781, 0x3740, 0xF501, 0x35C0, 0x3480, 0xF441,
0x3C00, 0xFCC1, 0xFD81, 0x3D40, 0xFF01, 0x3FC0, 0x3E80, 0xFE41,
0xFA01, 0x3AC0, 0x3B80, 0xFB41, 0x3900, 0xF9C1, 0xF881, 0x3840,
0x2800, 0xE8C1, 0xE981, 0x2940, 0xEB01, 0x2BC0, 0x2A80, 0xEA41,
0xEE01, 0x2EC0, 0x2F80, 0xEF41, 0x2D00, 0xEDC1, 0xEC81, 0x2C40,
0xE401, 0x24C0, 0x2580, 0xE541, 0x2700, 0xE7C1, 0xE681, 0x2640,
0x2200, 0xE2C1, 0xE381, 0x2340, 0xE101, 0x21C0, 0x2080, 0xE041,
0xA001, 0x60C0, 0x6180, 0xA141, 0x6300, 0xA3C1, 0xA281, 0x6240,
0x6600, 0xA6C1, 0xA781, 0x6740, 0xA501, 0x65C0, 0x6480, 0xA441,
0x6C00, 0xACC1, 0xAD81, 0x6D40, 0xAF01, 0x6FC0, 0x6E80, 0xAE41,
0xAA01, 0x6AC0, 0x6B80, 0xAB41, 0x6900, 0xA9C1, 0xA881, 0x6840,
0x7800, 0xB8C1, 0xB981, 0x7940, 0xBB01, 0x7BC0, 0x7A80, 0xBA41,
0xBE01, 0x7EC0, 0x7F80, 0xBF41, 0x7D00, 0xBDC1, 0xBC81, 0x7C40,
0xB401, 0x74C0, 0x7580, 0xB541, 0x7700, 0xB7C1, 0xB681, 0x7640,
0x7200, 0xB2C1, 0xB381, 0x7340, 0xB101, 0x71C0, 0x7080, 0xB041,
0x5000, 0x90C1, 0x9181, 0x5140, 0x9301, 0x53C0, 0x5280, 0x9241,
0x9601, 0x56C0, 0x5780, 0x9741, 0x5500, 0x95C1, 0x9481, 0x5440,
0x9C01, 0x5CC0, 0x5D80, 0x9D41, 0x5F00, 0x9FC1, 0x9E81, 0x5E40,
0x5A00, 0x9AC1, 0x9B81, 0x5B40, 0x9901, 0x59C0, 0x5880, 0x9841,
0x8801, 0x48C0, 0x4980, 0x8941, 0x4B00, 0x8BC1, 0x8A81, 0x4A40,
0x4E00, 0x8EC1, 0x8F81, 0x4F40, 0x8D01, 0x4DC0, 0x4C80, 0x8C41,
0x4400, 0x84C1, 0x8581, 0x4540, 0x8701, 0x47C0, 0x4680, 0x8641,
0x8201, 0x42C0, 0x4380, 0x8341, 0x4100, 0x81C1, 0x8081, 0x4040,
};
unsigned short CCITT_CRC16_TABLE[256] = {
0x0000, 0x1021, 0x2042, 0x3063, 0x4084, 0x50A5, 0x60C6, 0x70E7,
0x8108, 0x9129, 0xA14A, 0xB16B, 0xC18C, 0xD1AD, 0xE1CE, 0xF1EF,
0x1231, 0x0210, 0x3273, 0x2252, 0x52B5, 0x4294, 0x72F7, 0x62D6,
0x9339, 0x8318, 0xB37B, 0xA35A, 0xD3BD, 0xC39C, 0xF3FF, 0xE3DE,
0x2462, 0x3443, 0x0420, 0x1401, 0x64E6, 0x74C7, 0x44A4, 0x5485,
0xA56A, 0xB54B, 0x8528, 0x9509, 0xE5EE, 0xF5CF, 0xC5AC, 0xD58D,
0x3653, 0x2672, 0x1611, 0x0630, 0x76D7, 0x66F6, 0x5695, 0x46B4,
0xB75B, 0xA77A, 0x9719, 0x8738, 0xF7DF, 0xE7FE, 0xD79D, 0xC7BC,
0x48C4, 0x58E5, 0x6886, 0x78A7, 0x0840, 0x1861, 0x2802, 0x3823,
0xC9CC, 0xD9ED, 0xE98E, 0xF9AF, 0x8948, 0x9969, 0xA90A, 0xB92B,
0x5AF5, 0x4AD4, 0x7AB7, 0x6A96, 0x1A71, 0x0A50, 0x3A33, 0x2A12,
0xDBFD, 0xCBDC, 0xFBBF, 0xEB9E, 0x9B79, 0x8B58, 0xBB3B, 0xAB1A,
0x6CA6, 0x7C87, 0x4CE4, 0x5CC5, 0x2C22, 0x3C03, 0x0C60, 0x1C41,
0xEDAE, 0xFD8F, 0xCDEC, 0xDDCD, 0xAD2A, 0xBD0B, 0x8D68, 0x9D49,
0x7E97, 0x6EB6, 0x5ED5, 0x4EF4, 0x3E13, 0x2E32, 0x1E51, 0x0E70,
0xFF9F, 0xEFBE, 0xDFDD, 0xCFFC, 0xBF1B, 0xAF3A, 0x9F59, 0x8F78,
0x9188, 0x81A9, 0xB1CA, 0xA1EB, 0xD10C, 0xC12D, 0xF14E, 0xE16F,
0x1080, 0x00A1, 0x30C2, 0x20E3, 0x5004, 0x4025, 0x7046, 0x6067,
0x83B9, 0x9398, 0xA3FB, 0xB3DA, 0xC33D, 0xD31C, 0xE37F, 0xF35E,
0x02B1, 0x1290, 0x22F3, 0x32D2, 0x4235, 0x5214, 0x6277, 0x7256,
0xB5EA, 0xA5CB, 0x95A8, 0x8589, 0xF56E, 0xE54F, 0xD52C, 0xC50D,
0x34E2, 0x24C3, 0x14A0, 0x0481, 0x7466, 0x6447, 0x5424, 0x4405,
0xA7DB, 0xB7FA, 0x8799, 0x97B8, 0xE75F, 0xF77E, 0xC71D, 0xD73C,
0x26D3, 0x36F2, 0x0691, 0x16B0, 0x6657, 0x7676, 0x4615, 0x5634,
0xD94C, 0xC96D, 0xF90E, 0xE92F, 0x99C8, 0x89E9, 0xB98A, 0xA9AB,
0x5844, 0x4865, 0x7806, 0x6827, 0x18C0, 0x08E1, 0x3882, 0x28A3,
0xCB7D, 0xDB5C, 0xEB3F, 0xFB1E, 0x8BF9, 0x9BD8, 0xABBB, 0xBB9A,
0x4A75, 0x5A54, 0x6A37, 0x7A16, 0x0AF1, 0x1AD0, 0x2AB3, 0x3A92,
0xFD2E, 0xED0F, 0xDD6C, 0xCD4D, 0xBDAA, 0xAD8B, 0x9DE8, 0x8DC9,
0x7C26, 0x6C07, 0x5C64, 0x4C45, 0x3CA2, 0x2C83, 0x1CE0, 0x0CC1,
0xEF1F, 0xFF3E, 0xCF5D, 0xDF7C, 0xAF9B, 0xBFBA, 0x8FD9, 0x9FF8,
0x6E17, 0x7E36, 0x4E55, 0x5E74, 0x2E93, 0x3EB2, 0x0ED1, 0x1EF0,
};
unsigned short CCITT_CRC16R_TABLE[256] = {
0x0000, 0x1189, 0x2312, 0x329B, 0x4624, 0x57AD, 0x6536, 0x74BF,
0x8C48, 0x9DC1, 0xAF5A, 0xBED3, 0xCA6C, 0xDBE5, 0xE97E, 0xF8F7,
0x1081, 0x0108, 0x3393, 0x221A, 0x56A5, 0x472C, 0x75B7, 0x643E,
0x9CC9, 0x8D40, 0xBFDB, 0xAE52, 0xDAED, 0xCB64, 0xF9FF, 0xE876,
0x2102, 0x308B, 0x0210, 0x1399, 0x6726, 0x76AF, 0x4434, 0x55BD,
0xAD4A, 0xBCC3, 0x8E58, 0x9FD1, 0xEB6E, 0xFAE7, 0xC87C, 0xD9F5,
0x3183, 0x200A, 0x1291, 0x0318, 0x77A7, 0x662E, 0x54B5, 0x453C,
0xBDCB, 0xAC42, 0x9ED9, 0x8F50, 0xFBEF, 0xEA66, 0xD8FD, 0xC974,
0x4204, 0x538D, 0x6116, 0x709F, 0x0420, 0x15A9, 0x2732, 0x36BB,
0xCE4C, 0xDFC5, 0xED5E, 0xFCD7, 0x8868, 0x99E1, 0xAB7A, 0xBAF3,
0x5285, 0x430C, 0x7197, 0x601E, 0x14A1, 0x0528, 0x37B3, 0x263A,
0xDECD, 0xCF44, 0xFDDF, 0xEC56, 0x98E9, 0x8960, 0xBBFB, 0xAA72,
0x6306, 0x728F, 0x4014, 0x519D, 0x2522, 0x34AB, 0x0630, 0x17B9,
0xEF4E, 0xFEC7, 0xCC5C, 0xDDD5, 0xA96A, 0xB8E3, 0x8A78, 0x9BF1,
0x7387, 0x620E, 0x5095, 0x411C, 0x35A3, 0x242A, 0x16B1, 0x0738,
0xFFCF, 0xEE46, 0xDCDD, 0xCD54, 0xB9EB, 0xA862, 0x9AF9, 0x8B70,
0x8408, 0x9581, 0xA71A, 0xB693, 0xC22C, 0xD3A5, 0xE13E, 0xF0B7,
0x0840, 0x19C9, 0x2B52, 0x3ADB, 0x4E64, 0x5FED, 0x6D76, 0x7CFF,
0x9489, 0x8500, 0xB79B, 0xA612, 0xD2AD, 0xC324, 0xF1BF, 0xE036,
0x18C1, 0x0948, 0x3BD3, 0x2A5A, 0x5EE5, 0x4F6C, 0x7DF7, 0x6C7E,
0xA50A, 0xB483, 0x8618, 0x9791, 0xE32E, 0xF2A7, 0xC03C, 0xD1B5,
0x2942, 0x38CB, 0x0A50, 0x1BD9, 0x6F66, 0x7EEF, 0x4C74, 0x5DFD,
0xB58B, 0xA402, 0x9699, 0x8710, 0xF3AF, 0xE226, 0xD0BD, 0xC134,
0x39C3, 0x284A, 0x1AD1, 0x0B58, 0x7FE7, 0x6E6E, 0x5CF5, 0x4D7C,
0xC60C, 0xD785, 0xE51E, 0xF497, 0x8028, 0x91A1, 0xA33A, 0xB2B3,
0x4A44, 0x5BCD, 0x6956, 0x78DF, 0x0C60, 0x1DE9, 0x2F72, 0x3EFB,
0xD68D, 0xC704, 0xF59F, 0xE416, 0x90A9, 0x8120, 0xB3BB, 0xA232,
0x5AC5, 0x4B4C, 0x79D7, 0x685E, 0x1CE1, 0x0D68, 0x3FF3, 0x2E7A,
0xE70E, 0xF687, 0xC41C, 0xD595, 0xA12A, 0xB0A3, 0x8238, 0x93B1,
0x6B46, 0x7ACF, 0x4854, 0x59DD, 0x2D62, 0x3CEB, 0x0E70, 0x1FF9,
0xF78F, 0xE606, 0xD49D, 0xC514, 0xB1AB, 0xA022, 0x92B9, 0x8330,
0x7BC7, 0x6A4E, 0x58D5, 0x495C, 0x3DE3, 0x2C6A, 0x1EF1, 0x0F78,
};
unsigned short get_crc16(unsigned char data, unsigned short crc)
{
unsigned char c;
c = crc >> 8;
crc <<= 8;
crc ^= CRC16_TABLE[data ^ c];
return crc;
}
unsigned short get_crc16r(unsigned char data, unsigned short crc)
{
unsigned char c;
c = crc & 0xff;
crc >>= 8;
crc ^= CRC16R_TABLE[data ^ c];
return crc;
}
unsigned short get_ccitt_crc16(unsigned char data, unsigned short crc)
{
unsigned char c;
c = crc >> 8;
crc <<= 8;
crc ^= CCITT_CRC16_TABLE[data ^ c];
return crc;
}
unsigned short get_ccitt_crc16r(unsigned char data, unsigned short crc)
{
unsigned char c;
c = crc & 0xff;
crc >>= 8;
crc ^= CCITT_CRC16R_TABLE[data ^ c];
return crc;
}