Re: CCITT-CRC16 in kernel

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On Thu, 11 Aug 2005 [email protected] wrote:

>>> Using this bit-ordering, and omitting the x^16 term as is
>>> conventional (it's implicit in the implementation), the polynomials
>>> come out as:
>>> CRC-16: 0xa001
>>> CRC-CCITT: 0x8408
>> Huh? That's the problem.
>> X^16 + X^12 + X^5 + X^0 = 0x1021, not 0xa001
>> Also,
>> X^16 + X^15 + X^2 + X^0 = 0x8005, not 0x8408
> You're wrong in two ways:
> 1) You've got CRC-16 and CRC-CCITT mixed up, and
> 2) You've got the bit ordering backwards.  Remember, I said very clearly,
>   the lsbit is the first bit, and the first bit is the highest power
>   of x.  You can reverse the convention and still have a CRC, but that's
>   not the way it's usually done and it's more awkward in software.
> CRC-CCITT = X^16 + X^12 + X^5 + X^0 = 0x8408, and NOT 0x1021
> CRC-16 =  X^16 + X^15 + X^2 + X^0 = 0xa001, and NOT 0x8005

Thank you very much for your time, but what you say is completely
different than anything else I have found on the net.

Do the math:

 	2^ 16 = 65536
 	2^ 12 =  4096
 	2^  5 =    32
 	2^  0 =     1
                 69655 = 0x11021

That's by convention 0x1021 as the X^16 is thrown away. I have
no clue how you could possibly get 0x8408 out of this, nor
how the CRC of 1 could possibly lie at offset 128 in a table
of CRC polynomials. Now I read it in the header, but that
doesn't make it right.

The "RS-232C" order to which you refer simply means that the
string of "bits" needs to handled as a string of bytes, not
words or longwords, in other words, not interpreted as
words, just bytes. If this isn't correct then ZMODEM and
a few other protocols are wrong. You certainly don't
swap every BIT in a string do you? You are not claiming
that (0x01 == 0x80) and (0x02 == 0x40), etc, are you?

According to the stuff on the web, CCITT just refers
to a CRC-16 with all bits set to begin with, and the
polynominal cited above. The end result is not inverted
nor byte-swapped.

>> Attached is a program that will generate a table of polynomials
>> for the conventional CRC lookup-table code. If you look at
>> the table in the kernel code, offset 1, you will see that
>> the polynomial is 0x1189. This corresponds to the CRC of
>> the value 1. It does not correspond to either your polynomials
>> or the ones documented on numerous web pages.

Well the table provided worked for a couple of years. I was
just trying to use the stuff in the kernel rather than some

> No, it doesn't.  The table entry at offset *128* is the CRC polynomial,
> which is 0x8408, exactly as the comment just above the table says.
>> I think somebody just guessed and came up with "magic" because the
>> table being used isn't correct.
> The table being used is 100% correct.  There is no mistake.
> If you think you've found a mistake, there's something you're not
> understanding.
> Sorry to be so blunt, but it's true.
>>> The *other* think you have to do is append the checksum to the message
>>> correctly.  As mentioned earlier, the lsbit of a byte is considered
>>> first, so the lsbyte of the 16-bit accumulator is appended first.
>> Right, but the hardware did that. I have no control over that. I
>> have to figure out if:
>> (1) It started with 0xffff or something else.
>> (2) It was inverted after.
>> (3) The result was byte-swapped.
>> With the "usual" CRC-16 that I used before, using the lookup-
>> table that is for the 0x1021 polynomial, hardware was found
>> to have inverted and byte-swapped, but started with 0xefde
>> (0x1021 inverted). Trying to use the in-kernel CRC, I was
>> unable to find anything that made sense.
> You can get rid of the starting value and inversion by XORing together
> two messages (with valid CRCs) of equal length.  The result has a valid
> CRC with preset to 0 and no inversion.  You can figure that out later.
> Then, the only questions are the polynomial and bit ordering.
> (You can also have a screwed-up CRC byte ordering, but that's rare
> except in software written by people who don't know better.  Hardware
> invariably gets it right.)
> As I said, the commonest case is to consider the lsbit first.
> However, some implementations take the msbit of each byte first.
> Here's code to do it both ways.  This is the bit-at-a-time version,
> not using a table.  You can verify that the first implementation,
> fed an initial crc=0, poly=0x8408, and all possible 1-byte messages,
> produces the table in crc-ccitt.c.
> /*
> * Expects poly encoded so 0x8000 is x^0 and 0x0001 is x^15.
> * CRC should be appended lsbyte first.
> */
> uint16_t
> crc_lsb_first(uint16_t crc, uint16_t poly, unsigned char const *p, size_t len)
> {
> 	while (len--) {
> 		unsigned i;
> 		crc ^= (unsigned char)*p++;
> 		for (i = 0; i < 8; i++)
> 			crc = (crc >> 1) ^ ((crc & 1) ? poly : 0);
> 	}
> 	return crc;
> }
> /*
> * Expects poly encoded so 0x0001 is x^0 and 0x8000 is x^15.
> * CRC should be appended msbyte first.
> */
> uint16_t
> crc_msb_first(uint16_t crc, uint16_t poly, unsigned char const *p, size_t len)
> {
> 	while (len--) {
> 		unsigned i;
> 		crc ^= (uint16_t)(unsigned char)*p++ << 8;
> 		for (i = 0; i < 8; i++)
> 			crc = (crc << 1) ^ ((crc & 0x8000) ? poly : 0);
> 	}
> 	return crc;
> }
> If you're trying to reverse-engineer an unknown CRC, get two valid
> messages of the same length, form their XOR, and try a few different
> polynomials.  (There's a way to do it more efficiently using a GCD, but
> on a modern machine, it's faster to try all 32768 possible polynomials
> than to write and debug the GCD code.)
> After that, you can figure out the preset and final inversion, if any.
> For fixed-length messages, you can merge them into a single 16-bit
> constant that you can include at the beginning or the end, but if
> you have variable-length messages, it matters.

Dick Johnson
Penguin : Linux version 2.6.12 on an i686 machine (5537.79 BogoMips).
Warning : 98.36% of all statistics are fiction.
I apologize for the following. I tried to kill it with the above dot :

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