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I typically implement this CRC (CRC-16-CCITT) like this:

uint16_t update_crc(uint16_t crc, uint8_t b)
{
  crc ^= b;
  crc = (crc >> 4) ^ (0x1081 * (crc & 0xf));
  crc = (crc >> 4) ^ (0x1081 * (crc & 0xf));
  return crc;
}

The difference: this CRC is reflected, i.e. the bit order is reversed. This is the way it's used in protocols like HDLC, Bluetooth, PPP and a lot more. In serial communications the CRC is sent out most significant bit first, and because UARTs send out bytes least significant bit first you have to calculate a reflected CRC.
The reason this is done is to improve burst error detection.

On a processor that does not have fast multiplication instructions you're better off with the classical lookup table. This should produce the same results:

const uint16_t lut[] = {
    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,
};

uint16_t update_crc(uint16_t crc, uint8_t b)
{
  crc ^= b;
  return (crc >> 8) ^ lut[(crc & 0xff)];
}

(note that entry 128 in this table (0x8408) is you polynomial 0x1021 bit-reversed. This is not a coincidence)



On Thu, Oct 24, 2019 at 11:21 AM Phil Leblanc <philanc@gmail.com> wrote:
On Thu, Oct 24, 2019 at 4:03 AM Russell Haley <russ.haley@gmail.com> wrote:
>
> I have a working C hash function that I turned into a Lua module:
>
> int16_t crc_1021_c(int16_t old_crc, int8_t data)
> {
>     int16_t crc;
>     int16_t x;
>
>     x = ((old_crc>>8) ^ data) & 0xff;
>     x ^= x>>4;
[. . . ]
>
> Any ideas why I get a different number? All input greatly appreciated.

I _think_ (but didn't check or test)  there is an issue in your
original C code. The function crc_1021_c() and parameter old_crc
should be declared as _unsigned_ and not _signed_ short integers (ie.
uint16_t instead of int16_t.  -- parameter 'data' should also be
unsigned, but it should not make a difference.

The key issue here is that in C, I _think_ that right shift is
undefined behavior for signed integers. It is often implemented by
compilers as an _arithmetic shift_ (ie. a shift "with sign extension"
-- google arithmetic shift vs. logical shift)

Lua right shift is always a logical shift, without sign extension. So
the C line " x ^= x>>4;" and the Lua line "x = x ~ (x >> 4)" do not
compute the same result when 'x' happens to be negative.

This may explain that you get different results. As I said before, I
didn't checked.

HTH

Phil



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