Messages in this thread | | | Subject | Re: CCITT-CRC16 in kernel | Date | Thu, 11 Aug 2005 11:19:59 -0400 | From | "linux-os \(Dick Johnson\)" <> |
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On Thu, 11 Aug 2005 linux@horizon.com 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 "roll-your-own".
> 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. >
Cheers, 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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