Calculate CRC with words (16-bit) as a base variable

Question

Is there a simple CRC algorithm based on a lookup table, but with words entering the algorithm instead of bytes.

For example, this algorithm works with bytes:

#include <stdint.h>

const uint16_t wTable_CRC16_Modbus[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
};

uint16_t Modbus_Calculate_CRC16(uint8_t *frame, uint8_t size) {
    // Initialize CRC16 word
    uint16_t crc16 = 0xFFFF;

    // Calculate CRC16 word
    uint16_t ind;
    while(size--) {
        ind = ( crc16 ^ *frame++ ) & 0x00FF;
        crc16 >>= 8;
        crc16 ^= wTable_CRC16_Modbus[ind];
    }

    // Swap low and high bytes
    crc16 = (crc16<<8) | (crc16>>8);

    // Return the CRC16 word with
    // swapped low and high bytes
    return crc16;
}

Since I'm always going to send words, using the above algorithm I would need to break each WORD in LSB and MSB and repeat the code in the loop body twice, first for LSB and then for MSB. Instead of doing that, I would like to update CRC in one step, with WORD as the algorithm (loop body) input.

Answer 1

If and only if you read words from memory in little-endian order (least significant byte first), then you can read a 16-bit word at a time. You would still need to use the table twice to process the word. The loop would be:

    size >>= 1;                     // better have been even!
    uint16_t const *words = frame;  // better be little-endian!
    while (size--) {
        crc16 ^= *words++;
        crc16 = (crc16 >> 8) ^ wTable_CRC16_Modbus[crc16 & 0xff];
        crc16 = (crc16 >> 8) ^ wTable_CRC16_Modbus[crc16 & 0xff];
    }

Depending on your processor, you may also need to make sure that frame points to an even address. Note that if size is odd, this won't process the last byte. If size can be and is odd, you can just add the processing of the last byte after the loop.

If you would like a single table lookup per word, then you'll need a much bigger table. The existing table is simply the CRC of the single-byte values 0..255 (where the initial CRC is zero, not 0xffff). The bigger table would be the same thing, but for the two-byte values 0..65536, with the least significant byte processed first. You can make that table using the existing table:

void modbus_bigtable(uint16_t *table) {
    for (uint16_t lo = 0; lo < 256; lo++) {
        uint16_t crclo = wTable_CRC16_Modbus[lo];
        uint16_t crchi = crclo >> 8;
        crclo &= 0xff;
        uint16_t *nxt = table;
        for (uint16_t hi = 0; hi < 256; hi++) {
            *nxt = crchi ^ wTable_CRC16_Modbus[hi ^ crclo];
            nxt += 256;
        }
        table++;
    }
}

Then the loop becomes:

    size >>= 1;                     // better have been even!
    uint16_t const *words = frame;  // better be little-endian!
    while (size--)
        crc16 = table[crc16 ^ *words++];