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Added lfs_crc32c

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crc32c, with a polynomial of 0x11edc6f41, is generally numerically superior
to the more common crc32 standard. Catching more bit errors across
a wider range of message messages (except 2-bit errors) without any changes
to the underlying algorithm.

Philip Koopman has a large body of work exploring optimal polynomials here:
http://users.ece.cmu.edu/~koopman/crc/crc32.html

And from his experiments we know the maximum message size where we can
still detect a given number of bit errors for each polynomial:

                       1          2          3    4    5   6   7  8  9 10 11 12 13 14 15 16 17
  crc32  0x104c11db7 = ∞ 4294967263      91607 2974  268 171  91 57 34 21 12 10 10 10  -  -  -
  crc32c 0x11edc6f41 = ∞ 2147483615 2147483615 5243 5243 177 177 47 47 20 20  8  8  6  6  1  1

So really crc32c should be prefered where possible. Koopman also has
alternative polynomials with slightly different properties, but crc32c
is already popular enough to have a decent amount of hardware support.

---

Another nice feature of crc32c is that its polynomial has even parity.
It turns out that even-parity polynomials give us the nifty property
parity(crc(m)) == parity(m).

A quick proof:

  crc(m) = m(x) x^|P|-1 mod P(x)

  parity(m) = m(x) x mod x+1

  though note: x mod x+1 = 1, by hand
  so:

  parity(m) = m(x)*1 mod x+1
            = m(x) mod x+1

  solving for parity(crc(m)):

  parity(crc(m)) = (m(x) x^|P|-1 mod P(x)) mod x+1

  note: (a mod b) mod c = a mod c, if c divides b,
    aka (a mod b) mod c = a mod c, if b mod c = 0

  so if P(x) mod x+1 = 0,
    aka if parity(P) = 0:

  parity(crc(m)) = m(x) x^|P|-1 mod x+1

  but, like before: x^|P|-1 mod x+1 = 1, by hand
  so:

  parity(crc(m)) = m(x)*1 mod x+1
                 = m(x) mod x+1
                 = parity(m)

  so if parity(P) = 0:

  parity(crc(m)) = parity(m)

This has the potential to replace the 1-bit counter in the metadata tags
with a more general solution that doesn't require extra state.
This commit is contained in:
Christopher Haster
2022-12-17 22:42:07 -06:00
parent 2d272bb62a
commit 0f72d18b14
2 changed files with 129 additions and 0 deletions
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lfs_util.c
+120
View File
@@ -30,5 +30,125 @@ uint32_t lfs_crc(uint32_t crc, const void *buffer, size_t size) {
return crc;
}
// Calculate crc32c incrementally
uint32_t lfs_crc32c(uint32_t crc, const void *buffer, size_t size) {
// init with 0xffffffff so prefixed zeros affect the crc
const uint8_t *data = buffer;
crc ^= 0xffffffff;
// A couple crc32c implementations to choose from.
//
// The default, "small-table" implementation offers a decent performance
// without much additional code-size, reasonable for microcontrollers. For
// anything larger where you really don't care about an extra 1KiB of code
// the "big-table" implementation is probably better.
//
// Some quick measurements with GCC 11 using -Os -mcpu=cortex-m55, with
// instruction counts from QEMU and an input size of 4KiB. Note these are
// not cycle-accurate:
//
// code stack ins ld/st branch
// naive 48 12 221192 4099 36865
// small-table 316 12 49160 12291 4097
// big-table 1064 8 32776 8195 4097
//
#if defined(LFS_SMALLER_CRC32C)
for (size_t i = 0; i < size; i++) {
crc = crc ^ data[i];
for (size_t j = 0; j < 8; j++) {
crc = (crc >> 1) ^ ((crc & 1) ? 0x82f63b78 : 0);
}
}
#elif !defined(LFS_FASTER_CRC32C)
static const uint32_t lfs_crc32c_table[64] = {
0x00000000, 0x105ec76f, 0x20bd8ede, 0x30e349b1,
0x417b1dbc, 0x5125dad3, 0x61c69362, 0x7198540d,
0x82f63b78, 0x92a8fc17, 0xa24bb5a6, 0xb21572c9,
0xc38d26c4, 0xd3d3e1ab, 0xe330a81a, 0xf36e6f75,
};
for (size_t i = 0; i < size; i++) {
crc = (crc >> 4) ^ lfs_crc32c_table[0xf & (crc ^ (data[i] >> 0))];
crc = (crc >> 4) ^ lfs_crc32c_table[0xf & (crc ^ (data[i] >> 4))];
}
#else
static const uint32_t lfs_crc32c_table[256] = {
0x00000000, 0xf26b8303, 0xe13b70f7, 0x1350f3f4,
0xc79a971f, 0x35f1141c, 0x26a1e7e8, 0xd4ca64eb,
0x8ad958cf, 0x78b2dbcc, 0x6be22838, 0x9989ab3b,
0x4d43cfd0, 0xbf284cd3, 0xac78bf27, 0x5e133c24,
0x105ec76f, 0xe235446c, 0xf165b798, 0x030e349b,
0xd7c45070, 0x25afd373, 0x36ff2087, 0xc494a384,
0x9a879fa0, 0x68ec1ca3, 0x7bbcef57, 0x89d76c54,
0x5d1d08bf, 0xaf768bbc, 0xbc267848, 0x4e4dfb4b,
0x20bd8ede, 0xd2d60ddd, 0xc186fe29, 0x33ed7d2a,
0xe72719c1, 0x154c9ac2, 0x061c6936, 0xf477ea35,
0xaa64d611, 0x580f5512, 0x4b5fa6e6, 0xb93425e5,
0x6dfe410e, 0x9f95c20d, 0x8cc531f9, 0x7eaeb2fa,
0x30e349b1, 0xc288cab2, 0xd1d83946, 0x23b3ba45,
0xf779deae, 0x05125dad, 0x1642ae59, 0xe4292d5a,
0xba3a117e, 0x4851927d, 0x5b016189, 0xa96ae28a,
0x7da08661, 0x8fcb0562, 0x9c9bf696, 0x6ef07595,
0x417b1dbc, 0xb3109ebf, 0xa0406d4b, 0x522bee48,
0x86e18aa3, 0x748a09a0, 0x67dafa54, 0x95b17957,
0xcba24573, 0x39c9c670, 0x2a993584, 0xd8f2b687,
0x0c38d26c, 0xfe53516f, 0xed03a29b, 0x1f682198,
0x5125dad3, 0xa34e59d0, 0xb01eaa24, 0x42752927,
0x96bf4dcc, 0x64d4cecf, 0x77843d3b, 0x85efbe38,
0xdbfc821c, 0x2997011f, 0x3ac7f2eb, 0xc8ac71e8,
0x1c661503, 0xee0d9600, 0xfd5d65f4, 0x0f36e6f7,
0x61c69362, 0x93ad1061, 0x80fde395, 0x72966096,
0xa65c047d, 0x5437877e, 0x4767748a, 0xb50cf789,
0xeb1fcbad, 0x197448ae, 0x0a24bb5a, 0xf84f3859,
0x2c855cb2, 0xdeeedfb1, 0xcdbe2c45, 0x3fd5af46,
0x7198540d, 0x83f3d70e, 0x90a324fa, 0x62c8a7f9,
0xb602c312, 0x44694011, 0x5739b3e5, 0xa55230e6,
0xfb410cc2, 0x092a8fc1, 0x1a7a7c35, 0xe811ff36,
0x3cdb9bdd, 0xceb018de, 0xdde0eb2a, 0x2f8b6829,
0x82f63b78, 0x709db87b, 0x63cd4b8f, 0x91a6c88c,
0x456cac67, 0xb7072f64, 0xa457dc90, 0x563c5f93,
0x082f63b7, 0xfa44e0b4, 0xe9141340, 0x1b7f9043,
0xcfb5f4a8, 0x3dde77ab, 0x2e8e845f, 0xdce5075c,
0x92a8fc17, 0x60c37f14, 0x73938ce0, 0x81f80fe3,
0x55326b08, 0xa759e80b, 0xb4091bff, 0x466298fc,
0x1871a4d8, 0xea1a27db, 0xf94ad42f, 0x0b21572c,
0xdfeb33c7, 0x2d80b0c4, 0x3ed04330, 0xccbbc033,
0xa24bb5a6, 0x502036a5, 0x4370c551, 0xb11b4652,
0x65d122b9, 0x97baa1ba, 0x84ea524e, 0x7681d14d,
0x2892ed69, 0xdaf96e6a, 0xc9a99d9e, 0x3bc21e9d,
0xef087a76, 0x1d63f975, 0x0e330a81, 0xfc588982,
0xb21572c9, 0x407ef1ca, 0x532e023e, 0xa145813d,
0x758fe5d6, 0x87e466d5, 0x94b49521, 0x66df1622,
0x38cc2a06, 0xcaa7a905, 0xd9f75af1, 0x2b9cd9f2,
0xff56bd19, 0x0d3d3e1a, 0x1e6dcdee, 0xec064eed,
0xc38d26c4, 0x31e6a5c7, 0x22b65633, 0xd0ddd530,
0x0417b1db, 0xf67c32d8, 0xe52cc12c, 0x1747422f,
0x49547e0b, 0xbb3ffd08, 0xa86f0efc, 0x5a048dff,
0x8ecee914, 0x7ca56a17, 0x6ff599e3, 0x9d9e1ae0,
0xd3d3e1ab, 0x21b862a8, 0x32e8915c, 0xc083125f,
0x144976b4, 0xe622f5b7, 0xf5720643, 0x07198540,
0x590ab964, 0xab613a67, 0xb831c993, 0x4a5a4a90,
0x9e902e7b, 0x6cfbad78, 0x7fab5e8c, 0x8dc0dd8f,
0xe330a81a, 0x115b2b19, 0x020bd8ed, 0xf0605bee,
0x24aa3f05, 0xd6c1bc06, 0xc5914ff2, 0x37faccf1,
0x69e9f0d5, 0x9b8273d6, 0x88d28022, 0x7ab90321,
0xae7367ca, 0x5c18e4c9, 0x4f48173d, 0xbd23943e,
0xf36e6f75, 0x0105ec76, 0x12551f82, 0xe03e9c81,
0x34f4f86a, 0xc69f7b69, 0xd5cf889d, 0x27a40b9e,
0x79b737ba, 0x8bdcb4b9, 0x988c474d, 0x6ae7c44e,
0xbe2da0a5, 0x4c4623a6, 0x5f16d052, 0xad7d5351,
};
for (size_t i = 0; i < size; i++) {
crc = (crc >> 8) ^ lfs_crc32c_table[0xff & (crc ^ data[i])];
}
#endif
// fini with 0xffffffff to cancel out init when called incrementally
crc ^= 0xffffffff;
return crc;
}
#endif
lfs_util.h
+9
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@@ -215,6 +215,15 @@ static inline uint32_t lfs_tobe32(uint32_t a) {
// Calculate CRC-32 with polynomial = 0x04c11db7
uint32_t lfs_crc(uint32_t crc, const void *buffer, size_t size);
// Calculate crc32c incrementally
//
// polynomial = 0x11edc6f41
// init = 0xffffffff
// fini = 0xffffffff
//
uint32_t lfs_crc32c(uint32_t crc, const void *buffer, size_t size);
// Allocate memory, only used if buffers are not provided to littlefs
// Note, memory must be 64-bit aligned
static inline void *lfs_malloc(size_t size) {