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

Coly Li
2018-07-17T06:25:39Z

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.

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.

>> 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 ?

Thanks.

Coly Li