Re: [PATCH 2/4] lib: add crc64 calculation routines

Coly Li
2018-07-17T07:34:38Z

On 2018/7/17 3:13 PM, Eric Biggers wrote:
> On Tue, Jul 17, 2018 at 02:25:24PM +0800, Coly Li wrote:
>> On 2018/7/17 11:34 AM, Eric Biggers wrote:
>>> Hi Coly,
>>>
>>> On Tue, Jul 17, 2018 at 12:55:05AM +0800, Coly Li wrote:
>>>> This patch adds the re-write crc64 calculation routines for Linux kernel.
>>>> The CRC64 polynomical arithmetic follows ECMA-182 specification, inspired
>>>> by CRC paper of Dr. Ross N. Williams
>>>> (see http://www.ross.net/crc/download/crc_v3.txt) and other public domain
>>>> implementations.
>>>>
>>>> All the changes work in this way,
>>>> - When Linux kernel is built, host program lib/gen_crc64table.c will be
>>>> compiled to lib/gen_crc64table and executed.
>>>> - The output of gen_crc64table execution is an array called as lookup
>>>> table (a.k.a POLY 0x42f0e1eba9ea369) which contain 256 64bits-long
>>>> numbers, this talbe is dumped into header file lib/crc64table.h.
>>>> - Then the header file is included by lib/crc64.c for normal 64bit crc
>>>> calculation.
>>>> - Function declaration of the crc64 calculation routines is placed in
>>>> include/linux/crc64.h
>>>>
>>> [...]
>>>> diff --git a/lib/crc64.c b/lib/crc64.c
>>>> new file mode 100644
>>>> index 000000000000..03f078303bd3
>>>> --- /dev/null
>>>> +++ b/lib/crc64.c
>>>> @@ -0,0 +1,71 @@
>>>> +// SPDX-License-Identifier: GPL-2.0
>>>> +/*
>>>> + * Normal 64bit CRC calculation.
>>>> + *
>>>> + * This is a basic crc64 implementation following ECMA-182 specification,
>>>> + * which can be found from,
>>>> + * http://www.ecma-international.org/publications/standards/Ecma-182.htm
>>>> + *
>>>> + * Dr. Ross N. Williams has a great document to introduce the idea of CRC
>>>> + * algorithm, here the CRC64 code is also inspired by the table-driven
>>>> + * algorithm and detail example from this paper. This paper can be found
>>>> + * from,
>>>> + * http://www.ross.net/crc/download/crc_v3.txt
>>>> + *
>>>> + * crc64table_le[256] is the lookup table of a table-driver 64bit CRC
>>>> + * calculation, which is generated by gen_crc64table.c in kernel build
>>>> + * time. The polynomial of crc64 arithmetic is from ECMA-182 specification
>>>> + * as well, which is defined as,
>>>> + *
>>>> + * x^64 + x^62 + x^57 + x^55 + x^54 + x^53 + x^52 + x^47 + x^46 + x^45 +
>>>> + * x^40 + x^39 + x^38 + x^37 + x^35 + x^33 + x^32 + x^31 + x^29 + x^27 +
>>>> + * x^24 + x^23 + x^22 + x^21 + x^19 + x^17 + x^13 + x^12 + x^10 + x^9 +
>>>> + * x^7 + x^4 + x + 1
>>>> + *
>>>> + * Copyright 2018 SUSE Linux.
>>>> + * Author: Coly Li <colyli@suse.de>
>>>> + *
>>>> + */
>>>> +
>>>> +#include <linux/module.h>
>>>> +#include <uapi/linux/types.h>
>>>> +#include "crc64table.h"
>>>> +
>>>> +MODULE_DESCRIPTION("CRC64 calculations");
>>>> +MODULE_LICENSE("GPL");
>>>> +
>>>> +__le64 crc64_le_update(__le64 crc, const void *_p, size_t len)
>>>> +{
>>>> + size_t i, t;
>>>> +
>>>> + const unsigned char *p = _p;
>>>> +
>>>> + for (i = 0; i < len; i++) {
>>>> + t = ((crc >> 56) ^ (__le64)(*p++)) & 0xFF;
>>>> + crc = crc64table_le[t] ^ (crc << 8);
>>>> + }
>>>> +
>>>> + return crc;
>>>> +}
>>>> +EXPORT_SYMBOL_GPL(crc64_le_update);
>>>> +
>>>> +__le64 crc64_le(const void *p, size_t len)
>>>> +{
>>>> + __le64 crc = 0x0000000000000000ULL;
>>>> +
>>>> + crc = crc64_le_update(crc, p, len);
>>>> +
>>>> + return crc;
>>>> +}
>>>> +EXPORT_SYMBOL_GPL(crc64_le);
>>>> +
>>>> +/* For checksum calculation in drivers/md/bcache/ */
>>>> +__le64 crc64_le_bch(const void *p, size_t len)
>>>> +{
>>>> + __le64 crc = 0xFFFFFFFFFFFFFFFFULL;
>>>> +
>>>> + crc = crc64_le_update(crc, p, len);
>>>> +
>>>> + return (crc ^ 0xFFFFFFFFFFFFFFFFULL);
>>>> +}
>>>> +EXPORT_SYMBOL_GPL(crc64_le_bch);
>>>
>>
>> Hi Eric,
>>
>>> Using __le64 here makes no sense, because that type indicates the endianness of
>>> the *bytes*, whereas with CRC's "little endian" and "big endian" refer to the
>>> order in which the *bits* are mapped to the polynomial coefficients.
>>>
>>> Also as you can see for lib/crc32.c you really only need to provide a function
>>>
>>> u64 __pure crc64_le(u64 crc, unsigned char const *p, size_t len);
>>>
>>> and the callers can invert at the beginning and/or end if needed.
>>
>> Let me explain why I explicit use __le64 here. When crc64 is used as
>> on-disk checksum, the input of crc64 calculation should be in a explicit
>> specific byte order. Currently check sum in bcache code assumes the CPU
>> is in little endian and just feeds in-memory data into crc64
>> calculation, then the code does not work on big endian machine like s390x.
>>
>> To solve such problem, before calculating CRC the in-memory data should
>> be swapped into a specific byte order (in bcache case it should be
>> little endian). For data storage or transfer, CRC calculation without
>> explicit endian is more easy to introduce bugs.
>
> No, the implementation never loads multi-byte values, so CPU endianness doesn't
> matter for the input. CPU endianness *does* matter when serializing the final

If the checksum is generated on big endian machine and checked on little
endian machine, non-specific endianness will be problematic.

> calculated CRC into a byte array for storing on-disk, so maybe bcache gets that
> part wrong, I don't know. Either way, that has nothing to do with how the
> polynomial coefficients (bits) are ordered *within bytes*, which is what the
> "_be" and "_le" refer to in the CRC-32 implementation. Yes, the naming is
> unfortunate as it can easily be confused with the usual "bytewise" endianness,
> but you need to understand it.
>

I see, it seems I misunderstand _le and _be in CRC-32 implementation.
OK, I will find a way to fix the naming and data type issues in v3 series.

> Again, using __le64 makes absolutely no sense. You're even doing operations
> like shifts directly on a "__le64" which sparse will (correctly) complain about.
>

Sure, you are correct here :-)

>>
>> When I declare the type of input and output value as __le64, on big
>> endian machine, I expect a type mismatch warning if the input memory
>> buffer is not swapped into little endian. For u64, there is no such type
>> checking warning.
>>
>> This is the initial version of lib/crc64.c, people may add their crc64
>> calculation routines when necessary, e.g. crc64_be() or crc64(). I only
>> add crc64_le_update() and crc64_le_bch() because bcache code needs them.
>>
>> Indeed there is no user of crc64_le() for now, but the file is name as
>> lib/crc64.c, I think there should be a crc64 calculation at least, so I
>> add crc64_le().
>>
>>>
>>> Also your function names make it sound like inverting the bits is the exception
>>> or not recommended, since you called the function which does the inversions
>>> "crc32_le_bch()" so it sounds like a bcache-specific hack, while the one that
>>> doesn't do the inversions is simply called "crc32_le()". But actually it's
>>> normally recommended to do CRC's with the inversions, so that leading and
>>> trailing zeroes affect the resulting CRC.
>>>
>>
>> I notice this, normally there are two crc routines provided, with and
>> without inversion. The reason that there is no inversion version is
>> no-user in Linux kernel. Indeed there is no user of crc64_le() in Linnux
>> kernel so far. For performance reason, I doubt whether there will be
>> more user to do 64bit crc in kernel.
>>
>> I prefer two crc32 calculation for a 64bit value, but meta data checksum
>> by crc64 calculation is used in bcache for years, the consistency has to
>> be kept.
>
> Well, your response didn't actually address my points. But it raises the
> question: if there won't be any other users, then why move CRC-64 to lib/ at
> all?
>

The only motivation I can see is becachefs, which share part of the code
base with bcache, including crc64 calculation.

And before CPU supports build-in instructors for CRC64, I don't see the
reason why people should use 64bit CRC other than 32bit ones.

>>
>>
>>>> diff --git a/lib/gen_crc64table.c b/lib/gen_crc64table.c
>>>> new file mode 100644
>>>> index 000000000000..5f292f287498
>>>> --- /dev/null
>>>> +++ b/lib/gen_crc64table.c
>>>> @@ -0,0 +1,77 @@
>>>> +// SPDX-License-Identifier: GPL-2.0
>>>> +/*
>>>> + * Generate lookup table for the talbe-driven CRC64 calculation.
>>>> + *
>>>> + * gen_crc64table is executed in kernel build time and generates
>>>> + * lib/crc64table.h. This header is included by lib/crc64.c for
>>>> + * the table-driver CRC64 calculation.
>>>> + *
>>>> + * See lib/crc64.c for more information about which specification
>>>> + * and polynomical arithmetic that gen_crc64table.c follows to
>>>> + * generate the lookup table.
>>>> + *
>>>> + * Copyright 2018 SUSE Linux.
>>>> + * Author: Coly Li <colyli@suse.de>
>>>> + *
>>>> + */
>>>> +
>>>> +#include <inttypes.h>
>>>> +#include <linux/swab.h>
>>>> +#include <stdio.h>
>>>> +#include "../usr/include/asm/byteorder.h"
>>>> +
>>>> +#define CRC64_ECMA182_POLY 0x42F0E1EBA9EA3693ULL
>>>
>>> Okay, that's actually the ECMA-182 polynomial in "big endian" form (highest
>>> order bit is the coefficient of x^63, lowest order bit is the coefficient of
>>> x^0), so you're actually doing a "big endian" CRC. So everything in your patch
>>> series that claims it's a little endian or "le" CRC is incorrect.
>>>
>>>> +
>>>> +#ifdef __LITTLE_ENDIAN
>>>> +# define cpu_to_le64(x) ((__le64)(x))
>>>> +#else
>>>> +# define cpu_to_le64(x) ((__le64)__swab64(x))
>>>> +#endif
>>>> +
>>>> +static int64_t crc64_table[256] = {0,};
>>>> +
>>>> +static void generate_crc64_table(void)
>>>> +{
>>>> + uint64_t i, j, c, crc;
>>>> +
>>>> + for (i = 0; i < 256; i++) {
>>>> + crc = 0;
>>>> + c = i << 56;
>>>> +
>>>> + for (j = 0; j < 8; j++) {
>>>> + if ((crc ^ c) & 0x8000000000000000ULL)
>>>> + crc = (crc << 1) ^ CRC64_ECMA182_POLY;
>>>> + else
>>>> + crc <<= 1;
>>>> + c <<= 1;
>>>
>>> See here, it's shifting out the most significant bit, which means it's the
>>> coefficient of the x^63 term ("big endian" or "normal" convention), not the x^0
>>> term ("little endian" or "reversed" convention).
>>
>> I see your point here. I am not expert in coding theory, the knowledge I
>> have is from wikipedia, ECMA-182 and the document from Dr. Ross
>> Williams. From ECMA-182 document, I don't see any word with 'big
>> endian', so I take it as a standard poly and regardless the byte order.
>>
>> And on wikepedia page
>> https://en.wikipedia.org/wiki/Cyclic_redundancy_check , CRC-64-ECMA
>> references the same poly and call "0x42F0E1EBA9EA3693" as normal poly,
>> which one links to polynomial
>> "x^64 + x^62 + x^57 + x^55 + x^54 + ....x^7 + x^4 + x + 1"
>> if I understand correctly. But from your information, it seems the
>> polynomial in generate_crc64_table() is x^64 + x^61 ..... Maybe I
>> misunderstand you, could you please give me more hint ?
>
> As I said, the "normal" convention is the same as "big endian", and the
> "reversed" convention is the same as "little endian" (again, meaning "bitwise"
> endianness, not the usual "bytewise" endianness). The polynomial is correct but
> you are claiming the polynomial coefficients are mapped to bits in a different
> order than they actually are.

Copied, thanks for the hint :-)

Coly Li