CRC16 calculation

Question

is there a fast way to calculate CRC16 on a String, starting from this table

NSArray* table16 = [NSArray arrayWithObjects:@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,nil];

Thanks.

Answer 1

That is a table to compute a 16-bit CRC a byte at a time, using polynomial 0x8005 reflected. There are two more pieces of information that you need to complete the picture, which is what is the initial CRC register contents, and what is the final CRC exclusive-ored with.

In this list of 16-bit CRCs, there are four CRC definitions that could use that table:

width=16 poly=0x8005 init=0x0000 refin=true refout=true xorout=0x0000 check=0xbb3d name="ARC"
width=16 poly=0x8005 init=0x0000 refin=true refout=true xorout=0xffff check=0x44c2 name="CRC-16/MAXIM"
width=16 poly=0x8005 init=0xffff refin=true refout=true xorout=0xffff check=0xb4c8 name="CRC-16/USB"
width=16 poly=0x8005 init=0xffff refin=true refout=true xorout=0x0000 check=0x4b37 name="MODBUS"

You will note that all have the same poly and all are refin and refout true (reflected), but they have different init and xorout values. The CRC you are looking for might be one of those, or it might be a different CRC not in the table.

To compute the CRC with that table, you would use code like this (in C):

crc = init;
while (len--)
    crc = (crc >> 8) ^ table[(crc ^ *data++) & 0xff];
crc ^= xorout;