Real life data tends to get corrupted because machines (and humans) are never as reliable as we wish for.
One efficient way is make sure your data wasn't unintendedly modifiied is to generate some kind of hash.
That hash shall be unique, compact and efficient:
unique: any kind of modification to the data shall generate a different hash
compact: as few bits or bytes as possible to keep the overhead low
efficient: use little computing resources, i.e. fast and low memory usage
Many protocols, like Ethernet and GZIP archives, append a so-called CRC hash to their data streams
which has a few weaknesses regarding uniqueness (sometimes data modifications remain undetected)
but is absolutely great when it comes to compactness (CRC32: 32 bits) and efficiency.
You find a CRC32 right below every Download button on my blog, too.
There is one very useful property of CRC32: it can be implemented as a rolling algorithm.
That means, if you already have some chunk of data and its CRC, then you can append new data and compute
the updated CRC but using your original CRC as a seed and just scanning through the appended data.
I don't want to go into mathematical details of Cyclic Redundancy Checking because there are tons
of information on the internet,
e.g. Wikipedia and the
Painless Guide To CRC Error Detection Algorithms.
This article only discusses how to write a fast CRC32 algorithm in C/C++.
If you aren't too keen on technical details and just want to have the fastest implementation for not-too-small datasets,
I strongly recommend using the crc32_fast function.
Note: The concepts behind the various CRC32 algorithm are not my original work - I only gathered them in one place.
I assume a little-endian architecture (Intel's x86 and x64 CPU default byte ordering) and ints
to be 32 bits wide (replace unsigned int by uint32_t if you use GCC64/Unix).
Update November 13, 2011: The code is more portable now, e.g. uint32_t is used.
I got it running on an Arduino board, see here
for more details.
Update May 4, 2013: Now the code is endian-aware.
Read my posting for instructions on how run a big endian virtual machine on Linux or Windows.
Update February 6, 2014: If you are interested in MD5, SHA1 and/or SHA256 hashes then take a look at my
portable C++ hashing library
which of course includes CRC32, too.
Update August 12, 2014: added a Javascript version of the simple bitwise algorithm
Update February 4, 2015: added Slicing-by-16 algorithm based on suggestions by Bulat Ziganshin
Update August 14, 2015: compiler-dependent #includes and #ifdefs were improved for Cygwin, MinGW and Clang. CRC32 code remained unchanged
Update October 21, 2016: changed code structure into a library format, added tableless byte algorithms
based on Slicing-by-8, improved by Bulat Ziganshin
512
16384 bytes
0.35 or 0.5 seconds*
3200 or 2000 MByte/s*
approx. 1 or 1.5*
Note: GCC 4.7 produces faster code than Visual C++ 2010 for Slicing-by-4, Slicing-by-8 and Slicing-by-16.
For the other algorithms, throughput is almost identical.
This software is provided 'as-is', without any express or implied
warranty. In no event will the authors be held liable for any damages
arising from the use of this software.
Permission is granted to anyone to use this software for any purpose,
including commercial applications, and to alter it and redistribute it
freely, subject to the following restrictions:
1. The origin of this software must not be misrepresented; you must not
claim that you wrote the original software. If you use this software
in a product, an acknowledgment in the product documentation would be
appreciated but is not required.
2. Altered source versions must be plainly marked as such, and must not be
misrepresented as being the original software.
3. This notice may not be removed or altered from any source distribution.zlib License
Changelog
version 8
May 27, 2019
fixed misspelt preprocessor symbol
Git tag crc32_v8
version 7
October 21, 2016
changed code structure into a library format
added tableless byte algorithms
Git tag crc32_v7
version 6
August 14, 2015
improved #ifdefs for Cygwin, MinGW and Clang
Git tag crc32_v6
version 5
February 4, 2015
added Slicing-by-16
Git tag crc32_v5
version 4
August 12, 2014
added Javascript port
Git tag crc32_v4
version 3
May 4, 2013
endian aware
slightly faster Slicing-by-8
Git tag crc32_v3
License
April 24, 2013
zlib-style license, applies to all past and future versions
version 2
November 13, 2011
improved portability
Git tag crc32_v2
version 1
November 10, 2011
initial release
Bitwise CRC32
Every CRC needs a predefined polynomial which hugely influences the uniqueness of the resulting
hashes (it doesn't affect compactness or efficiency).
There are many bad and few quite good polynomials.
The most common is (more on Wikipedia):
hide
Polynomial of zlib, Ethernet, ...constuint32_t Polynomial = 0xEDB88320;
The basic algorithm processes the input data bit-by-bit:
When full optimization is enabled, Visual C++ 2010 automatically unrolls the for-loop
eight times and processes about 35 MByte/s on my Intel Core i7 860 (2.8 GHz, Turbo Boost 3.2 GHz).
Still, the performance is limited by the branching if where the CPU's branch prediction
fails 50% (random data). Replacing the if by branch-free code almost doubles the speed:
The term (crc & 1)*Polynomial evaluates to Polynomial iff
(crc & 1) == 1 (first part of the if-clause) and 0 else.
Even though a multiplication was added and the XOR operation is always performed now
(previously only half of the time), the branch-free code better suits modern CPUs' architecture
and processes 61 MByte/s. This bit twiddling trick almost doubled the throughput !
A little less obvious is the further improved branch-free code:
The term -(int)(crc & 1) becomes either -1 (lowest bit of crc set)
or 0 (not set).
The integer representation of -1 is 0xFFFFFFFF and therefore ANDing it with
Polynomial gives the identical result as the first branch-free algorithm.
We added one more arithmetic operation (negation) and replaced the multiplication by AND.
The lower latency of these two binary operations is the reason why the improved branch-free algorithm
is the fastest (about 70 MByte/s) for bit-wise CRC calculation.
Note: Some very simple embedded CPUs without a deep pipeline might run faster with the
original algorithm.
Update November 13, 2011: See below for some performance figures on the Arduino platform
(Atmel AVR AtMega328P, 8 bit CPU/SoC).
Multiple Bits At Once
When using a pre-computed look-up table, multiple bits can be processed at once
leading to a further speed-up of up to 20x (Slicing-by-8 algorithm).
The most widespread implementation of CRC32 is based on a look-up table with 256 entries of
32-bit values (total: 1024 bytes)
and was published by Dilip V. Sarwate in 1988.
The look-up table contains the CRC of the 256 different byte values we might observe in the
input stream.
In order to compute the look-up table we need to run the bit-wise algorithm 256 times
(without the leading and trailing XOR 0xFFFFFFFF):
You will find that probably more than 90% of all CRC generators are written that way, e.g.
the CRC code in zlib, PHP, etc.
It's reasonably fast (375 MByte/s on my computer) and comes with only a small memory overhead.
Often the look-up table isn't pre-computed at runtime but rather stored as
a large table in the C code.
Slicing-By-4 and Slicing-By-8 Algorithm
In 2006, Intel engineers came up with the idea of enlarging the look-up table in order to process 4 or 8
bytes at once.
Their code is available on SourceForge, too.
Instead of a single table with 256 entries they precompute 4 or 8 tables.
The first one is identical to Sarwate's algorithm and the remaining 3 or 7 are derived from it:
Slicing-by-4 fetches one 32-bit integer from the input stream and updates the CRC accordingly.
If the number of input bytes is not divisible by 4, the remaining 1 to 3 bytes are
processed by the Sarwate algorithm:
Performance is more than doubled in comparison to the popular Sarwate algorithm
(840 or 1050 MByte/s instead of 375 MByte/s) at the cost of a 4k instead of 1k large pre-computed tables.
Update May 4, 2013: The code works for Little Endian CPUs only.
Scroll down to my update which explains modifications for Big Endian computers.
The downloads (incl. Git) were updated accordingly, too.
Slicing-by-8's inner loop has twice the size and comes with same tail-processing problem:
This nifty code crunches 1400 MByte/s (Visual C++ 2010) or even 1800 MByte/s (GCC 4.7) !
If the memory address used for fetching 4 data bytes at once (crc ^= *current++)
happens to be not aligned (depends on your CPU), performance might suffer.
By default, GCC and Visual C++ properly align pointers but the chunked computation (see next chapter)
might easily lead to such a mis-aligned situation.
Adjust DefaultChunkSize in the test program (Download)
to some odd number and see for yourself whether your throughputs drops.
On my Core i7 there is no major difference, though.
Slicing-By-16 Algorithm
Bulat Ziganshin contacted me by email and suggested the Slicing-By-16 algorithm.
Similar to the way Slicing-by-8 improves on Slicing-by-4,
his code processes twice as many bits by working on a twice as large lookup table.
Furthermore, his code's inner loop was unrolled manually which bloated the code.
I prefer keeping code short and simple and therefore rely on smart compilers:
if I wrap my inner loop in a for-loop with a known number of iterations,
then GCC's optimization level -O2 (and up) unrolls it automatically –
just play with the Unroll constant and see for yourself.
A small performance gain can be achieved if we instruct the CPU to load upcoming data a few moments before we actually need it.
This trick works best on pretty fast but not-too-new CPUs.
My Core i7 (manufactured in 2010) becomes a little less than 10% faster.
I you look at the code, you will notice PREFETCH which is a macro:
hide
Prefetch when using GCC or VIsual C++#ifdef _MSC_VER#include<xmmintrin.h>#define PREFETCH(location) _mm_prefetch(location, _MM_HINT_T0)#else#ifdef __GNUC__#definePREFETCH(location) __builtin_prefetch(location)#else#definePREFETCH(location) ;#endif#endif
And here's my version of the Slicing-by-16 algorithm:
If your data isn't available as single continuous block in memory, then you can split the
CRC computations into chunks:
hide
Chunked CRCuint32_t crc = 0; // also default parameter of crc32_xx functionswhile (haveMoreData())crc = crc32_8bytes(getData(), chunkSize, crc);
Of course, chunkSize, haveMoreData() and getData()
are specific to your problem/program.
You can replace crc32_8bytes by any other CRC algorithm presented here, too.
Half-Byte Algorithm
For certain embedded CPUs the bitwise algorithm might be too slow but there is not enough memory
available for the look-up tables of the faster algorithms either (between 1k and 8k).
The half-byte/nibble algorithm is a sweet compromise: its look-up table contains only 16 entries
for a total of 64 bytes and runs about three times faster than the best bitwise algorithm.
The look-up table contains every 16th entry of the standard look-up table:
lut[i] = Crc32Lookup[16*i]
For the default polynomial 0xEDB88320 we get:
Unless you need to change the polynomial at runtime you'll often get smaller binaries by
including the pre-computed look-up table in your C/C++ code because then you can skip the table generator.
It is possible to compute the CRC32 of a full byte without any lookup-tables.
However, the code is a little bit slower than the half-byte algorithm.
Due to the larger code size, there is no true benefit in real-life applications.
hide
Tableless Full-Byte Algorithm (sent to me by Hagai Gold)/// compute CRC32 (byte algorithm) without lookup tablesuint32_t crc32_1byte_tableless(constvoid* data, size_t length, uint32_t previousCrc32){uint32_t crc = ~previousCrc32; // same as previousCrc32 ^ 0xFFFFFFFFconstuint8_t* current = (constuint8_t*) data;while (length-- != 0) {uint8_t s = uint8_t(crc) ^ *current++;// Hagai Gold made me aware of this table-less algorithm and send me code// polynomial 0xEDB88320 can be written in binary as 11101101101110001000001100100000b// reverse the bits (or just assume bit 0 is the first one)// and we have bits set at position 0, 1, 2, 4, 5, 7, 8, 10, 11, 12, 16, 22, 23, 26// => those are the shift offsets://crc = (crc >> 8) ^// t ^// (t >> 1) ^ (t >> 2) ^ (t >> 4) ^ (t >> 5) ^ // == y// (t >> 7) ^ (t >> 8) ^ (t >> 10) ^ (t >> 11) ^ // == y >> 6// (t >> 12) ^ (t >> 16) ^ // == z// (t >> 22) ^ (t >> 26) ^ // == z >> 10// (t >> 23);// the fastest I can come up with:uint32_t low = (s ^ (s << 6)) & 0xFF;uint32_t a = (low * ((1 << 23) + (1 << 14) + (1 << 2)));crc = (crc >> 8) ^ (low * ((1 << 24) + (1 << 16) + (1 << 8))) ^ a ^ (a >> 1) ^ (low * ((1 << 20) + (1 << 12) )) ^ (low << 19) ^ (low << 17) ^ (low >> 2);// Hagai's code:/*uint32_t t = (s ^ (s << 6)) << 24; // some temporaries to optimize XOR uint32_t x = (t >> 1) ^ (t >> 2); uint32_t y = x ^ (x >> 3); uint32_t z = (t >> 12) ^ (t >> 16); crc = (crc >> 8) ^ t ^ (t >> 23) ^ y ^ (y >> 6) ^ z ^ (z >> 10);*/ }return ~crc; // same as crc ^ 0xFFFFFFFF}
A much more generic algorithm is about as fast on GCC but much slower on CLang++:
hide
Tableless Full-Byte Algorithm (based on book "Hacker's Delight" by Henry S. Warren)/// compute CRC32 (byte algorithm) without lookup tablesuint32_t crc32_1byte_tableless2(constvoid* data, size_t length, uint32_t previousCrc32){int32_t crc = ~previousCrc32; // note: signed integer, right shift distributes sign bit into lower bitsconstuint8_t* current = (constuint8_t*) data;while (length-- != 0) {crc = crc ^ *current++;uint32_t c = (((crc << 31) >> 31) & ((Polynomial >> 7) ^ (Polynomial >> 1))) ^ (((crc << 30) >> 31) & ((Polynomial >> 6) ^ Polynomial)) ^ (((crc << 29) >> 31) & (Polynomial >> 5)) ^ (((crc << 28) >> 31) & (Polynomial >> 4)) ^ (((crc << 27) >> 31) & (Polynomial >> 3)) ^ (((crc << 26) >> 31) & (Polynomial >> 2)) ^ (((crc << 25) >> 31) & (Polynomial >> 1)) ^ (((crc << 24) >> 31) & Polynomial);crc = ((uint32_t)crc >> 8) ^ c; // convert to unsigned integer before right shift }return ~crc; // same as crc ^ 0xFFFFFFFF}
Avoiding Precomputation At Runtime
If you know you only need the default polynomial 0xEDB88320 then it might make
sense to store the look-up tables directly in your executable (as seen with the half-byte algorithm)
and remove the table generator's code.
You save a few cycles every time during program start but enlarge your binary file by up to 16k.
Moreover, you avoid potential bugs due to accidently missing table initialization.
And now let's waste precious internet bandwidth ... (click show to display the look-up table)
show
Look-up tables for Polynomial = 0xEDB88320staticconstuint32_t Crc32Lookup[16][256] ={// note: the first number of every second row corresponds to the half-byte look-up table ! {0x00000000,0x77073096,0xEE0E612C,0x990951BA,0x076DC419,0x706AF48F,0xE963A535,0x9E6495A3,0x0EDB8832,0x79DCB8A4,0xE0D5E91E,0x97D2D988,0x09B64C2B,0x7EB17CBD,0xE7B82D07,0x90BF1D91,0x1DB71064,0x6AB020F2,0xF3B97148,0x84BE41DE,0x1ADAD47D,0x6DDDE4EB,0xF4D4B551,0x83D385C7,0x136C9856,0x646BA8C0,0xFD62F97A,0x8A65C9EC,0x14015C4F,0x63066CD9,0xFA0F3D63,0x8D080DF5,0x3B6E20C8,0x4C69105E,0xD56041E4,0xA2677172,0x3C03E4D1,0x4B04D447,0xD20D85FD,0xA50AB56B,0x35B5A8FA,0x42B2986C,0xDBBBC9D6,0xACBCF940,0x32D86CE3,0x45DF5C75,0xDCD60DCF,0xABD13D59,0x26D930AC,0x51DE003A,0xC8D75180,0xBFD06116,0x21B4F4B5,0x56B3C423,0xCFBA9599,0xB8BDA50F,0x2802B89E,0x5F058808,0xC60CD9B2,0xB10BE924,0x2F6F7C87,0x58684C11,0xC1611DAB,0xB6662D3D,0x76DC4190,0x01DB7106,0x98D220BC,0xEFD5102A,0x71B18589,0x06B6B51F,0x9FBFE4A5,0xE8B8D433,0x7807C9A2,0x0F00F934,0x9609A88E,0xE10E9818,0x7F6A0DBB,0x086D3D2D,0x91646C97,0xE6635C01,0x6B6B51F4,0x1C6C6162,0x856530D8,0xF262004E,0x6C0695ED,0x1B01A57B,0x8208F4C1,0xF50FC457,0x65B0D9C6,0x12B7E950,0x8BBEB8EA,0xFCB9887C,0x62DD1DDF,0x15DA2D49,0x8CD37CF3,0xFBD44C65,0x4DB26158,0x3AB551CE,0xA3BC0074,0xD4BB30E2,0x4ADFA541,0x3DD895D7,0xA4D1C46D,0xD3D6F4FB,0x4369E96A,0x346ED9FC,0xAD678846,0xDA60B8D0,0x44042D73,0x33031DE5,0xAA0A4C5F,0xDD0D7CC9,0x5005713C,0x270241AA,0xBE0B1010,0xC90C2086,0x5768B525,0x206F85B3,0xB966D409,0xCE61E49F,0x5EDEF90E,0x29D9C998,0xB0D09822,0xC7D7A8B4,0x59B33D17,0x2EB40D81,0xB7BD5C3B,0xC0BA6CAD,0xEDB88320,0x9ABFB3B6,0x03B6E20C,0x74B1D29A,0xEAD54739,0x9DD277AF,0x04DB2615,0x73DC1683,0xE3630B12,0x94643B84,0x0D6D6A3E,0x7A6A5AA8,0xE40ECF0B,0x9309FF9D,0x0A00AE27,0x7D079EB1,0xF00F9344,0x8708A3D2,0x1E01F268,0x6906C2FE,0xF762575D,0x806567CB,0x196C3671,0x6E6B06E7,0xFED41B76,0x89D32BE0,0x10DA7A5A,0x67DD4ACC,0xF9B9DF6F,0x8EBEEFF9,0x17B7BE43,0x60B08ED5,0xD6D6A3E8,0xA1D1937E,0x38D8C2C4,0x4FDFF252,0xD1BB67F1,0xA6BC5767,0x3FB506DD,0x48B2364B,0xD80D2BDA,0xAF0A1B4C,0x36034AF6,0x41047A60,0xDF60EFC3,0xA867DF55,0x316E8EEF,0x4669BE79,0xCB61B38C,0xBC66831A,0x256FD2A0,0x5268E236,0xCC0C7795,0xBB0B4703,0x220216B9,0x5505262F,0xC5BA3BBE,0xB2BD0B28,0x2BB45A92,0x5CB36A04,0xC2D7FFA7,0xB5D0CF31,0x2CD99E8B,0x5BDEAE1D,0x9B64C2B0,0xEC63F226,0x756AA39C,0x026D930A,0x9C0906A9,0xEB0E363F,0x72076785,0x05005713,0x95BF4A82,0xE2B87A14,0x7BB12BAE,0x0CB61B38,0x92D28E9B,0xE5D5BE0D,0x7CDCEFB7,0x0BDBDF21,0x86D3D2D4,0xF1D4E242,0x68DDB3F8,0x1FDA836E,0x81BE16CD,0xF6B9265B,0x6FB077E1,0x18B74777,0x88085AE6,0xFF0F6A70,0x66063BCA,0x11010B5C,0x8F659EFF,0xF862AE69,0x616BFFD3,0x166CCF45,0xA00AE278,0xD70DD2EE,0x4E048354,0x3903B3C2,0xA7672661,0xD06016F7,0x4969474D,0x3E6E77DB,0xAED16A4A,0xD9D65ADC,0x40DF0B66,0x37D83BF0,0xA9BCAE53,0xDEBB9EC5,0x47B2CF7F,0x30B5FFE9,0xBDBDF21C,0xCABAC28A,0x53B39330,0x24B4A3A6,0xBAD03605,0xCDD70693,0x54DE5729,0x23D967BF,0xB3667A2E,0xC4614AB8,0x5D681B02,0x2A6F2B94,0xB40BBE37,0xC30C8EA1,0x5A05DF1B,0x2D02EF8D, }#if defined(CRC32_USE_LOOKUP_TABLE_SLICING_BY_4) || defined(CRC32_USE_LOOKUP_TABLE_SLICING_BY_8) || defined(CRC32_USE_LOOKUP_TABLE_SLICING_BY_16)// beyond this point only relevant for Slicing-by-4, Slicing-by-8 and Slicing-by-16 ,{0x00000000,0x191B3141,0x32366282,0x2B2D53C3,0x646CC504,0x7D77F445,0x565AA786,0x4F4196C7,0xC8D98A08,0xD1C2BB49,0xFAEFE88A,0xE3F4D9CB,0xACB54F0C,0xB5AE7E4D,0x9E832D8E,0x87981CCF,0x4AC21251,0x53D92310,0x78F470D3,0x61EF4192,0x2EAED755,0x37B5E614,0x1C98B5D7,0x05838496,0x821B9859,0x9B00A918,0xB02DFADB,0xA936CB9A,0xE6775D5D,0xFF6C6C1C,0xD4413FDF,0xCD5A0E9E,0x958424A2,0x8C9F15E3,0xA7B24620,0xBEA97761,0xF1E8E1A6,0xE8F3D0E7,0xC3DE8324,0xDAC5B265,0x5D5DAEAA,0x44469FEB,0x6F6BCC28,0x7670FD69,0x39316BAE,0x202A5AEF,0x0B07092C,0x121C386D,0xDF4636F3,0xC65D07B2,0xED705471,0xF46B6530,0xBB2AF3F7,0xA231C2B6,0x891C9175,0x9007A034,0x179FBCFB,0x0E848DBA,0x25A9DE79,0x3CB2EF38,0x73F379FF,0x6AE848BE,0x41C51B7D,0x58DE2A3C,0xF0794F05,0xE9627E44,0xC24F2D87,0xDB541CC6,0x94158A01,0x8D0EBB40,0xA623E883,0xBF38D9C2,0x38A0C50D,0x21BBF44C,0x0A96A78F,0x138D96CE,0x5CCC0009,0x45D73148,0x6EFA628B,0x77E153CA,0xBABB5D54,0xA3A06C15,0x888D3FD6,0x91960E97,0xDED79850,0xC7CCA911,0xECE1FAD2,0xF5FACB93,0x7262D75C,0x6B79E61D,0x4054B5DE,0x594F849F,0x160E1258,0x0F152319,0x243870DA,0x3D23419B,0x65FD6BA7,0x7CE65AE6,0x57CB0925,0x4ED03864,0x0191AEA3,0x188A9FE2,0x33A7CC21,0x2ABCFD60,0xAD24E1AF,0xB43FD0EE,0x9F12832D,0x8609B26C,0xC94824AB,0xD05315EA,0xFB7E4629,0xE2657768,0x2F3F79F6,0x362448B7,0x1D091B74,0x04122A35,0x4B53BCF2,0x52488DB3,0x7965DE70,0x607EEF31,0xE7E6F3FE,0xFEFDC2BF,0xD5D0917C,0xCCCBA03D,0x838A36FA,0x9A9107BB,0xB1BC5478,0xA8A76539,0x3B83984B,0x2298A90A,0x09B5FAC9,0x10AECB88,0x5FEF5D4F,0x46F46C0E,0x6DD93FCD,0x74C20E8C,0xF35A1243,0xEA412302,0xC16C70C1,0xD8774180,0x9736D747,0x8E2DE606,0xA500B5C5,0xBC1B8484,0x71418A1A,0x685ABB5B,0x4377E898,0x5A6CD9D9,0x152D4F1E,0x0C367E5F,0x271B2D9C,0x3E001CDD,0xB9980012,0xA0833153,0x8BAE6290,0x92B553D1,0xDDF4C516,0xC4EFF457,0xEFC2A794,0xF6D996D5,0xAE07BCE9,0xB71C8DA8,0x9C31DE6B,0x852AEF2A,0xCA6B79ED,0xD37048AC,0xF85D1B6F,0xE1462A2E,0x66DE36E1,0x7FC507A0,0x54E85463,0x4DF36522,0x02B2F3E5,0x1BA9C2A4,0x30849167,0x299FA026,0xE4C5AEB8,0xFDDE9FF9,0xD6F3CC3A,0xCFE8FD7B,0x80A96BBC,0x99B25AFD,0xB29F093E,0xAB84387F,0x2C1C24B0,0x350715F1,0x1E2A4632,0x07317773,0x4870E1B4,0x516BD0F5,0x7A468336,0x635DB277,0xCBFAD74E,0xD2E1E60F,0xF9CCB5CC,0xE0D7848D,0xAF96124A,0xB68D230B,0x9DA070C8,0x84BB4189,0x03235D46,0x1A386C07,0x31153FC4,0x280E0E85,0x674F9842,0x7E54A903,0x5579FAC0,0x4C62CB81,0x8138C51F,0x9823F45E,0xB30EA79D,0xAA1596DC,0xE554001B,0xFC4F315A,0xD7626299,0xCE7953D8,0x49E14F17,0x50FA7E56,0x7BD72D95,0x62CC1CD4,0x2D8D8A13,0x3496BB52,0x1FBBE891,0x06A0D9D0,0x5E7EF3EC,0x4765C2AD,0x6C48916E,0x7553A02F,0x3A1236E8,0x230907A9,0x0824546A,0x113F652B,0x96A779E4,0x8FBC48A5,0xA4911B66,0xBD8A2A27,0xF2CBBCE0,0xEBD08DA1,0xC0FDDE62,0xD9E6EF23,0x14BCE1BD,0x0DA7D0FC,0x268A833F,0x3F91B27E,0x70D024B9,0x69CB15F8,0x42E6463B,0x5BFD777A,0xDC656BB5,0xC57E5AF4,0xEE530937,0xF7483876,0xB809AEB1,0xA1129FF0,0x8A3FCC33,0x9324FD72, }, {0x00000000,0x01C26A37,0x0384D46E,0x0246BE59,0x0709A8DC,0x06CBC2EB,0x048D7CB2,0x054F1685,0x0E1351B8,0x0FD13B8F,0x0D9785D6,0x0C55EFE1,0x091AF964,0x08D89353,0x0A9E2D0A,0x0B5C473D,0x1C26A370,0x1DE4C947,0x1FA2771E,0x1E601D29,0x1B2F0BAC,0x1AED619B,0x18ABDFC2,0x1969B5F5,0x1235F2C8,0x13F798FF,0x11B126A6,0x10734C91,0x153C5A14,0x14FE3023,0x16B88E7A,0x177AE44D,0x384D46E0,0x398F2CD7,0x3BC9928E,0x3A0BF8B9,0x3F44EE3C,0x3E86840B,0x3CC03A52,0x3D025065,0x365E1758,0x379C7D6F,0x35DAC336,0x3418A901,0x3157BF84,0x3095D5B3,0x32D36BEA,0x331101DD,0x246BE590,0x25A98FA7,0x27EF31FE,0x262D5BC9,0x23624D4C,0x22A0277B,0x20E69922,0x2124F315,0x2A78B428,0x2BBADE1F,0x29FC6046,0x283E0A71,0x2D711CF4,0x2CB376C3,0x2EF5C89A,0x2F37A2AD,0x709A8DC0,0x7158E7F7,0x731E59AE,0x72DC3399,0x7793251C,0x76514F2B,0x7417F172,0x75D59B45,0x7E89DC78,0x7F4BB64F,0x7D0D0816,0x7CCF6221,0x798074A4,0x78421E93,0x7A04A0CA,0x7BC6CAFD,0x6CBC2EB0,0x6D7E4487,0x6F38FADE,0x6EFA90E9,0x6BB5866C,0x6A77EC5B,0x68315202,0x69F33835,0x62AF7F08,0x636D153F,0x612BAB66,0x60E9C151,0x65A6D7D4,0x6464BDE3,0x662203BA,0x67E0698D,0x48D7CB20,0x4915A117,0x4B531F4E,0x4A917579,0x4FDE63FC,0x4E1C09CB,0x4C5AB792,0x4D98DDA5,0x46C49A98,0x4706F0AF,0x45404EF6,0x448224C1,0x41CD3244,0x400F5873,0x4249E62A,0x438B8C1D,0x54F16850,0x55330267,0x5775BC3E,0x56B7D609,0x53F8C08C,0x523AAABB,0x507C14E2,0x51BE7ED5,0x5AE239E8,0x5B2053DF,0x5966ED86,0x58A487B1,0x5DEB9134,0x5C29FB03,0x5E6F455A,0x5FAD2F6D,0xE1351B80,0xE0F771B7,0xE2B1CFEE,0xE373A5D9,0xE63CB35C,0xE7FED96B,0xE5B86732,0xE47A0D05,0xEF264A38,0xEEE4200F,0xECA29E56,0xED60F461,0xE82FE2E4,0xE9ED88D3,0xEBAB368A,0xEA695CBD,0xFD13B8F0,0xFCD1D2C7,0xFE976C9E,0xFF5506A9,0xFA1A102C,0xFBD87A1B,0xF99EC442,0xF85CAE75,0xF300E948,0xF2C2837F,0xF0843D26,0xF1465711,0xF4094194,0xF5CB2BA3,0xF78D95FA,0xF64FFFCD,0xD9785D60,0xD8BA3757,0xDAFC890E,0xDB3EE339,0xDE71F5BC,0xDFB39F8B,0xDDF521D2,0xDC374BE5,0xD76B0CD8,0xD6A966EF,0xD4EFD8B6,0xD52DB281,0xD062A404,0xD1A0CE33,0xD3E6706A,0xD2241A5D,0xC55EFE10,0xC49C9427,0xC6DA2A7E,0xC7184049,0xC25756CC,0xC3953CFB,0xC1D382A2,0xC011E895,0xCB4DAFA8,0xCA8FC59F,0xC8C97BC6,0xC90B11F1,0xCC440774,0xCD866D43,0xCFC0D31A,0xCE02B92D,0x91AF9640,0x906DFC77,0x922B422E,0x93E92819,0x96A63E9C,0x976454AB,0x9522EAF2,0x94E080C5,0x9FBCC7F8,0x9E7EADCF,0x9C381396,0x9DFA79A1,0x98B56F24,0x99770513,0x9B31BB4A,0x9AF3D17D,0x8D893530,0x8C4B5F07,0x8E0DE15E,0x8FCF8B69,0x8A809DEC,0x8B42F7DB,0x89044982,0x88C623B5,0x839A6488,0x82580EBF,0x801EB0E6,0x81DCDAD1,0x8493CC54,0x8551A663,0x8717183A,0x86D5720D,0xA9E2D0A0,0xA820BA97,0xAA6604CE,0xABA46EF9,0xAEEB787C,0xAF29124B,0xAD6FAC12,0xACADC625,0xA7F18118,0xA633EB2F,0xA4755576,0xA5B73F41,0xA0F829C4,0xA13A43F3,0xA37CFDAA,0xA2BE979D,0xB5C473D0,0xB40619E7,0xB640A7BE,0xB782CD89,0xB2CDDB0C,0xB30FB13B,0xB1490F62,0xB08B6555,0xBBD72268,0xBA15485F,0xB853F606,0xB9919C31,0xBCDE8AB4,0xBD1CE083,0xBF5A5EDA,0xBE9834ED, }, {0x00000000,0xB8BC6765,0xAA09C88B,0x12B5AFEE,0x8F629757,0x37DEF032,0x256B5FDC,0x9DD738B9,0xC5B428EF,0x7D084F8A,0x6FBDE064,0xD7018701,0x4AD6BFB8,0xF26AD8DD,0xE0DF7733,0x58631056,0x5019579F,0xE8A530FA,0xFA109F14,0x42ACF871,0xDF7BC0C8,0x67C7A7AD,0x75720843,0xCDCE6F26,0x95AD7F70,0x2D111815,0x3FA4B7FB,0x8718D09E,0x1ACFE827,0xA2738F42,0xB0C620AC,0x087A47C9,0xA032AF3E,0x188EC85B,0x0A3B67B5,0xB28700D0,0x2F503869,0x97EC5F0C,0x8559F0E2,0x3DE59787,0x658687D1,0xDD3AE0B4,0xCF8F4F5A,0x7733283F,0xEAE41086,0x525877E3,0x40EDD80D,0xF851BF68,0xF02BF8A1,0x48979FC4,0x5A22302A,0xE29E574F,0x7F496FF6,0xC7F50893,0xD540A77D,0x6DFCC018,0x359FD04E,0x8D23B72B,0x9F9618C5,0x272A7FA0,0xBAFD4719,0x0241207C,0x10F48F92,0xA848E8F7,0x9B14583D,0x23A83F58,0x311D90B6,0x89A1F7D3,0x1476CF6A,0xACCAA80F,0xBE7F07E1,0x06C36084,0x5EA070D2,0xE61C17B7,0xF4A9B859,0x4C15DF3C,0xD1C2E785,0x697E80E0,0x7BCB2F0E,0xC377486B,0xCB0D0FA2,0x73B168C7,0x6104C729,0xD9B8A04C,0x446F98F5,0xFCD3FF90,0xEE66507E,0x56DA371B,0x0EB9274D,0xB6054028,0xA4B0EFC6,0x1C0C88A3,0x81DBB01A,0x3967D77F,0x2BD27891,0x936E1FF4,0x3B26F703,0x839A9066,0x912F3F88,0x299358ED,0xB4446054,0x0CF80731,0x1E4DA8DF,0xA6F1CFBA,0xFE92DFEC,0x462EB889,0x549B1767,0xEC277002,0x71F048BB,0xC94C2FDE,0xDBF98030,0x6345E755,0x6B3FA09C,0xD383C7F9,0xC1366817,0x798A0F72,0xE45D37CB,0x5CE150AE,0x4E54FF40,0xF6E89825,0xAE8B8873,0x1637EF16,0x048240F8,0xBC3E279D,0x21E91F24,0x99557841,0x8BE0D7AF,0x335CB0CA,0xED59B63B,0x55E5D15E,0x47507EB0,0xFFEC19D5,0x623B216C,0xDA874609,0xC832E9E7,0x708E8E82,0x28ED9ED4,0x9051F9B1,0x82E4565F,0x3A58313A,0xA78F0983,0x1F336EE6,0x0D86C108,0xB53AA66D,0xBD40E1A4,0x05FC86C1,0x1749292F,0xAFF54E4A,0x322276F3,0x8A9E1196,0x982BBE78,0x2097D91D,0x78F4C94B,0xC048AE2E,0xD2FD01C0,0x6A4166A5,0xF7965E1C,0x4F2A3979,0x5D9F9697,0xE523F1F2,0x4D6B1905,0xF5D77E60,0xE762D18E,0x5FDEB6EB,0xC2098E52,0x7AB5E937,0x680046D9,0xD0BC21BC,0x88DF31EA,0x3063568F,0x22D6F961,0x9A6A9E04,0x07BDA6BD,0xBF01C1D8,0xADB46E36,0x15080953,0x1D724E9A,0xA5CE29FF,0xB77B8611,0x0FC7E174,0x9210D9CD,0x2AACBEA8,0x38191146,0x80A57623,0xD8C66675,0x607A0110,0x72CFAEFE,0xCA73C99B,0x57A4F122,0xEF189647,0xFDAD39A9,0x45115ECC,0x764DEE06,0xCEF18963,0xDC44268D,0x64F841E8,0xF92F7951,0x41931E34,0x5326B1DA,0xEB9AD6BF,0xB3F9C6E9,0x0B45A18C,0x19F00E62,0xA14C6907,0x3C9B51BE,0x842736DB,0x96929935,0x2E2EFE50,0x2654B999,0x9EE8DEFC,0x8C5D7112,0x34E11677,0xA9362ECE,0x118A49AB,0x033FE645,0xBB838120,0xE3E09176,0x5B5CF613,0x49E959FD,0xF1553E98,0x6C820621,0xD43E6144,0xC68BCEAA,0x7E37A9CF,0xD67F4138,0x6EC3265D,0x7C7689B3,0xC4CAEED6,0x591DD66F,0xE1A1B10A,0xF3141EE4,0x4BA87981,0x13CB69D7,0xAB770EB2,0xB9C2A15C,0x017EC639,0x9CA9FE80,0x241599E5,0x36A0360B,0x8E1C516E,0x866616A7,0x3EDA71C2,0x2C6FDE2C,0x94D3B949,0x090481F0,0xB1B8E695,0xA30D497B,0x1BB12E1E,0x43D23E48,0xFB6E592D,0xE9DBF6C3,0x516791A6,0xCCB0A91F,0x740CCE7A,0x66B96194,0xDE0506F1, }#endif// defined(CRC32_USE_LOOKUP_TABLE_SLICING_BY_4) || defined(CRC32_USE_LOOKUP_TABLE_SLICING_BY_8) || defined(CRC32_USE_LOOKUP_TABLE_SLICING_BY_16)#ifdefined (CRC32_USE_LOOKUP_TABLE_SLICING_BY_8) || defined(CRC32_USE_LOOKUP_TABLE_SLICING_BY_16)// beyond this point only relevant for Slicing-by-8 and Slicing-by-16 ,{0x00000000,0x3D6029B0,0x7AC05360,0x47A07AD0,0xF580A6C0,0xC8E08F70,0x8F40F5A0,0xB220DC10,0x30704BC1,0x0D106271,0x4AB018A1,0x77D03111,0xC5F0ED01,0xF890C4B1,0xBF30BE61,0x825097D1,0x60E09782,0x5D80BE32,0x1A20C4E2,0x2740ED52,0x95603142,0xA80018F2,0xEFA06222,0xD2C04B92,0x5090DC43,0x6DF0F5F3,0x2A508F23,0x1730A693,0xA5107A83,0x98705333,0xDFD029E3,0xE2B00053,0xC1C12F04,0xFCA106B4,0xBB017C64,0x866155D4,0x344189C4,0x0921A074,0x4E81DAA4,0x73E1F314,0xF1B164C5,0xCCD14D75,0x8B7137A5,0xB6111E15,0x0431C205,0x3951EBB5,0x7EF19165,0x4391B8D5,0xA121B886,0x9C419136,0xDBE1EBE6,0xE681C256,0x54A11E46,0x69C137F6,0x2E614D26,0x13016496,0x9151F347,0xAC31DAF7,0xEB91A027,0xD6F18997,0x64D15587,0x59B17C37,0x1E1106E7,0x23712F57,0x58F35849,0x659371F9,0x22330B29,0x1F532299,0xAD73FE89,0x9013D739,0xD7B3ADE9,0xEAD38459,0x68831388,0x55E33A38,0x124340E8,0x2F236958,0x9D03B548,0xA0639CF8,0xE7C3E628,0xDAA3CF98,0x3813CFCB,0x0573E67B,0x42D39CAB,0x7FB3B51B,0xCD93690B,0xF0F340BB,0xB7533A6B,0x8A3313DB,0x0863840A,0x3503ADBA,0x72A3D76A,0x4FC3FEDA,0xFDE322CA,0xC0830B7A,0x872371AA,0xBA43581A,0x9932774D,0xA4525EFD,0xE3F2242D,0xDE920D9D,0x6CB2D18D,0x51D2F83D,0x167282ED,0x2B12AB5D,0xA9423C8C,0x9422153C,0xD3826FEC,0xEEE2465C,0x5CC29A4C,0x61A2B3FC,0x2602C92C,0x1B62E09C,0xF9D2E0CF,0xC4B2C97F,0x8312B3AF,0xBE729A1F,0x0C52460F,0x31326FBF,0x7692156F,0x4BF23CDF,0xC9A2AB0E,0xF4C282BE,0xB362F86E,0x8E02D1DE,0x3C220DCE,0x0142247E,0x46E25EAE,0x7B82771E,0xB1E6B092,0x8C869922,0xCB26E3F2,0xF646CA42,0x44661652,0x79063FE2,0x3EA64532,0x03C66C82,0x8196FB53,0xBCF6D2E3,0xFB56A833,0xC6368183,0x74165D93,0x49767423,0x0ED60EF3,0x33B62743,0xD1062710,0xEC660EA0,0xABC67470,0x96A65DC0,0x248681D0,0x19E6A860,0x5E46D2B0,0x6326FB00,0xE1766CD1,0xDC164561,0x9BB63FB1,0xA6D61601,0x14F6CA11,0x2996E3A1,0x6E369971,0x5356B0C1,0x70279F96,0x4D47B626,0x0AE7CCF6,0x3787E546,0x85A73956,0xB8C710E6,0xFF676A36,0xC2074386,0x4057D457,0x7D37FDE7,0x3A978737,0x07F7AE87,0xB5D77297,0x88B75B27,0xCF1721F7,0xF2770847,0x10C70814,0x2DA721A4,0x6A075B74,0x576772C4,0xE547AED4,0xD8278764,0x9F87FDB4,0xA2E7D404,0x20B743D5,0x1DD76A65,0x5A7710B5,0x67173905,0xD537E515,0xE857CCA5,0xAFF7B675,0x92979FC5,0xE915E8DB,0xD475C16B,0x93D5BBBB,0xAEB5920B,0x1C954E1B,0x21F567AB,0x66551D7B,0x5B3534CB,0xD965A31A,0xE4058AAA,0xA3A5F07A,0x9EC5D9CA,0x2CE505DA,0x11852C6A,0x562556BA,0x6B457F0A,0x89F57F59,0xB49556E9,0xF3352C39,0xCE550589,0x7C75D999,0x4115F029,0x06B58AF9,0x3BD5A349,0xB9853498,0x84E51D28,0xC34567F8,0xFE254E48,0x4C059258,0x7165BBE8,0x36C5C138,0x0BA5E888,0x28D4C7DF,0x15B4EE6F,0x521494BF,0x6F74BD0F,0xDD54611F,0xE03448AF,0xA794327F,0x9AF41BCF,0x18A48C1E,0x25C4A5AE,0x6264DF7E,0x5F04F6CE,0xED242ADE,0xD044036E,0x97E479BE,0xAA84500E,0x4834505D,0x755479ED,0x32F4033D,0x0F942A8D,0xBDB4F69D,0x80D4DF2D,0xC774A5FD,0xFA148C4D,0x78441B9C,0x4524322C,0x028448FC,0x3FE4614C,0x8DC4BD5C,0xB0A494EC,0xF704EE3C,0xCA64C78C, }, {0x00000000,0xCB5CD3A5,0x4DC8A10B,0x869472AE,0x9B914216,0x50CD91B3,0xD659E31D,0x1D0530B8,0xEC53826D,0x270F51C8,0xA19B2366,0x6AC7F0C3,0x77C2C07B,0xBC9E13DE,0x3A0A6170,0xF156B2D5,0x03D6029B,0xC88AD13E,0x4E1EA390,0x85427035,0x9847408D,0x531B9328,0xD58FE186,0x1ED33223,0xEF8580F6,0x24D95353,0xA24D21FD,0x6911F258,0x7414C2E0,0xBF481145,0x39DC63EB,0xF280B04E,0x07AC0536,0xCCF0D693,0x4A64A43D,0x81387798,0x9C3D4720,0x57619485,0xD1F5E62B,0x1AA9358E,0xEBFF875B,0x20A354FE,0xA6372650,0x6D6BF5F5,0x706EC54D,0xBB3216E8,0x3DA66446,0xF6FAB7E3,0x047A07AD,0xCF26D408,0x49B2A6A6,0x82EE7503,0x9FEB45BB,0x54B7961E,0xD223E4B0,0x197F3715,0xE82985C0,0x23755665,0xA5E124CB,0x6EBDF76E,0x73B8C7D6,0xB8E41473,0x3E7066DD,0xF52CB578,0x0F580A6C,0xC404D9C9,0x4290AB67,0x89CC78C2,0x94C9487A,0x5F959BDF,0xD901E971,0x125D3AD4,0xE30B8801,0x28575BA4,0xAEC3290A,0x659FFAAF,0x789ACA17,0xB3C619B2,0x35526B1C,0xFE0EB8B9,0x0C8E08F7,0xC7D2DB52,0x4146A9FC,0x8A1A7A59,0x971F4AE1,0x5C439944,0xDAD7EBEA,0x118B384F,0xE0DD8A9A,0x2B81593F,0xAD152B91,0x6649F834,0x7B4CC88C,0xB0101B29,0x36846987,0xFDD8BA22,0x08F40F5A,0xC3A8DCFF,0x453CAE51,0x8E607DF4,0x93654D4C,0x58399EE9,0xDEADEC47,0x15F13FE2,0xE4A78D37,0x2FFB5E92,0xA96F2C3C,0x6233FF99,0x7F36CF21,0xB46A1C84,0x32FE6E2A,0xF9A2BD8F,0x0B220DC1,0xC07EDE64,0x46EAACCA,0x8DB67F6F,0x90B34FD7,0x5BEF9C72,0xDD7BEEDC,0x16273D79,0xE7718FAC,0x2C2D5C09,0xAAB92EA7,0x61E5FD02,0x7CE0CDBA,0xB7BC1E1F,0x31286CB1,0xFA74BF14,0x1EB014D8,0xD5ECC77D,0x5378B5D3,0x98246676,0x852156CE,0x4E7D856B,0xC8E9F7C5,0x03B52460,0xF2E396B5,0x39BF4510,0xBF2B37BE,0x7477E41B,0x6972D4A3,0xA22E0706,0x24BA75A8,0xEFE6A60D,0x1D661643,0xD63AC5E6,0x50AEB748,0x9BF264ED,0x86F75455,0x4DAB87F0,0xCB3FF55E,0x006326FB,0xF135942E,0x3A69478B,0xBCFD3525,0x77A1E680,0x6AA4D638,0xA1F8059D,0x276C7733,0xEC30A496,0x191C11EE,0xD240C24B,0x54D4B0E5,0x9F886340,0x828D53F8,0x49D1805D,0xCF45F2F3,0x04192156,0xF54F9383,0x3E134026,0xB8873288,0x73DBE12D,0x6EDED195,0xA5820230,0x2316709E,0xE84AA33B,0x1ACA1375,0xD196C0D0,0x5702B27E,0x9C5E61DB,0x815B5163,0x4A0782C6,0xCC93F068,0x07CF23CD,0xF6999118,0x3DC542BD,0xBB513013,0x700DE3B6,0x6D08D30E,0xA65400AB,0x20C07205,0xEB9CA1A0,0x11E81EB4,0xDAB4CD11,0x5C20BFBF,0x977C6C1A,0x8A795CA2,0x41258F07,0xC7B1FDA9,0x0CED2E0C,0xFDBB9CD9,0x36E74F7C,0xB0733DD2,0x7B2FEE77,0x662ADECF,0xAD760D6A,0x2BE27FC4,0xE0BEAC61,0x123E1C2F,0xD962CF8A,0x5FF6BD24,0x94AA6E81,0x89AF5E39,0x42F38D9C,0xC467FF32,0x0F3B2C97,0xFE6D9E42,0x35314DE7,0xB3A53F49,0x78F9ECEC,0x65FCDC54,0xAEA00FF1,0x28347D5F,0xE368AEFA,0x16441B82,0xDD18C827,0x5B8CBA89,0x90D0692C,0x8DD55994,0x46898A31,0xC01DF89F,0x0B412B3A,0xFA1799EF,0x314B4A4A,0xB7DF38E4,0x7C83EB41,0x6186DBF9,0xAADA085C,0x2C4E7AF2,0xE712A957,0x15921919,0xDECECABC,0x585AB812,0x93066BB7,0x8E035B0F,0x455F88AA,0xC3CBFA04,0x089729A1,0xF9C19B74,0x329D48D1,0xB4093A7F,0x7F55E9DA,0x6250D962,0xA90C0AC7,0x2F987869,0xE4C4ABCC, }, {0x00000000,0xA6770BB4,0x979F1129,0x31E81A9D,0xF44F2413,0x52382FA7,0x63D0353A,0xC5A73E8E,0x33EF4E67,0x959845D3,0xA4705F4E,0x020754FA,0xC7A06A74,0x61D761C0,0x503F7B5D,0xF64870E9,0x67DE9CCE,0xC1A9977A,0xF0418DE7,0x56368653,0x9391B8DD,0x35E6B369,0x040EA9F4,0xA279A240,0x5431D2A9,0xF246D91D,0xC3AEC380,0x65D9C834,0xA07EF6BA,0x0609FD0E,0x37E1E793,0x9196EC27,0xCFBD399C,0x69CA3228,0x582228B5,0xFE552301,0x3BF21D8F,0x9D85163B,0xAC6D0CA6,0x0A1A0712,0xFC5277FB,0x5A257C4F,0x6BCD66D2,0xCDBA6D66,0x081D53E8,0xAE6A585C,0x9F8242C1,0x39F54975,0xA863A552,0x0E14AEE6,0x3FFCB47B,0x998BBFCF,0x5C2C8141,0xFA5B8AF5,0xCBB39068,0x6DC49BDC,0x9B8CEB35,0x3DFBE081,0x0C13FA1C,0xAA64F1A8,0x6FC3CF26,0xC9B4C492,0xF85CDE0F,0x5E2BD5BB,0x440B7579,0xE27C7ECD,0xD3946450,0x75E36FE4,0xB044516A,0x16335ADE,0x27DB4043,0x81AC4BF7,0x77E43B1E,0xD19330AA,0xE07B2A37,0x460C2183,0x83AB1F0D,0x25DC14B9,0x14340E24,0xB2430590,0x23D5E9B7,0x85A2E203,0xB44AF89E,0x123DF32A,0xD79ACDA4,0x71EDC610,0x4005DC8D,0xE672D739,0x103AA7D0,0xB64DAC64,0x87A5B6F9,0x21D2BD4D,0xE47583C3,0x42028877,0x73EA92EA,0xD59D995E,0x8BB64CE5,0x2DC14751,0x1C295DCC,0xBA5E5678,0x7FF968F6,0xD98E6342,0xE86679DF,0x4E11726B,0xB8590282,0x1E2E0936,0x2FC613AB,0x89B1181F,0x4C162691,0xEA612D25,0xDB8937B8,0x7DFE3C0C,0xEC68D02B,0x4A1FDB9F,0x7BF7C102,0xDD80CAB6,0x1827F438,0xBE50FF8C,0x8FB8E511,0x29CFEEA5,0xDF879E4C,0x79F095F8,0x48188F65,0xEE6F84D1,0x2BC8BA5F,0x8DBFB1EB,0xBC57AB76,0x1A20A0C2,0x8816EAF2,0x2E61E146,0x1F89FBDB,0xB9FEF06F,0x7C59CEE1,0xDA2EC555,0xEBC6DFC8,0x4DB1D47C,0xBBF9A495,0x1D8EAF21,0x2C66B5BC,0x8A11BE08,0x4FB68086,0xE9C18B32,0xD82991AF,0x7E5E9A1B,0xEFC8763C,0x49BF7D88,0x78576715,0xDE206CA1,0x1B87522F,0xBDF0599B,0x8C184306,0x2A6F48B2,0xDC27385B,0x7A5033EF,0x4BB82972,0xEDCF22C6,0x28681C48,0x8E1F17FC,0xBFF70D61,0x198006D5,0x47ABD36E,0xE1DCD8DA,0xD034C247,0x7643C9F3,0xB3E4F77D,0x1593FCC9,0x247BE654,0x820CEDE0,0x74449D09,0xD23396BD,0xE3DB8C20,0x45AC8794,0x800BB91A,0x267CB2AE,0x1794A833,0xB1E3A387,0x20754FA0,0x86024414,0xB7EA5E89,0x119D553D,0xD43A6BB3,0x724D6007,0x43A57A9A,0xE5D2712E,0x139A01C7,0xB5ED0A73,0x840510EE,0x22721B5A,0xE7D525D4,0x41A22E60,0x704A34FD,0xD63D3F49,0xCC1D9F8B,0x6A6A943F,0x5B828EA2,0xFDF58516,0x3852BB98,0x9E25B02C,0xAFCDAAB1,0x09BAA105,0xFFF2D1EC,0x5985DA58,0x686DC0C5,0xCE1ACB71,0x0BBDF5FF,0xADCAFE4B,0x9C22E4D6,0x3A55EF62,0xABC30345,0x0DB408F1,0x3C5C126C,0x9A2B19D8,0x5F8C2756,0xF9FB2CE2,0xC813367F,0x6E643DCB,0x982C4D22,0x3E5B4696,0x0FB35C0B,0xA9C457BF,0x6C636931,0xCA146285,0xFBFC7818,0x5D8B73AC,0x03A0A617,0xA5D7ADA3,0x943FB73E,0x3248BC8A,0xF7EF8204,0x519889B0,0x6070932D,0xC6079899,0x304FE870,0x9638E3C4,0xA7D0F959,0x01A7F2ED,0xC400CC63,0x6277C7D7,0x539FDD4A,0xF5E8D6FE,0x647E3AD9,0xC209316D,0xF3E12BF0,0x55962044,0x90311ECA,0x3646157E,0x07AE0FE3,0xA1D90457,0x579174BE,0xF1E67F0A,0xC00E6597,0x66796E23,0xA3DE50AD,0x05A95B19,0x34414184,0x92364A30, }, {0x00000000,0xCCAA009E,0x4225077D,0x8E8F07E3,0x844A0EFA,0x48E00E64,0xC66F0987,0x0AC50919,0xD3E51BB5,0x1F4F1B2B,0x91C01CC8,0x5D6A1C56,0x57AF154F,0x9B0515D1,0x158A1232,0xD92012AC,0x7CBB312B,0xB01131B5,0x3E9E3656,0xF23436C8,0xF8F13FD1,0x345B3F4F,0xBAD438AC,0x767E3832,0xAF5E2A9E,0x63F42A00,0xED7B2DE3,0x21D12D7D,0x2B142464,0xE7BE24FA,0x69312319,0xA59B2387,0xF9766256,0x35DC62C8,0xBB53652B,0x77F965B5,0x7D3C6CAC,0xB1966C32,0x3F196BD1,0xF3B36B4F,0x2A9379E3,0xE639797D,0x68B67E9E,0xA41C7E00,0xAED97719,0x62737787,0xECFC7064,0x205670FA,0x85CD537D,0x496753E3,0xC7E85400,0x0B42549E,0x01875D87,0xCD2D5D19,0x43A25AFA,0x8F085A64,0x562848C8,0x9A824856,0x140D4FB5,0xD8A74F2B,0xD2624632,0x1EC846AC,0x9047414F,0x5CED41D1,0x299DC2ED,0xE537C273,0x6BB8C590,0xA712C50E,0xADD7CC17,0x617DCC89,0xEFF2CB6A,0x2358CBF4,0xFA78D958,0x36D2D9C6,0xB85DDE25,0x74F7DEBB,0x7E32D7A2,0xB298D73C,0x3C17D0DF,0xF0BDD041,0x5526F3C6,0x998CF358,0x1703F4BB,0xDBA9F425,0xD16CFD3C,0x1DC6FDA2,0x9349FA41,0x5FE3FADF,0x86C3E873,0x4A69E8ED,0xC4E6EF0E,0x084CEF90,0x0289E689,0xCE23E617,0x40ACE1F4,0x8C06E16A,0xD0EBA0BB,0x1C41A025,0x92CEA7C6,0x5E64A758,0x54A1AE41,0x980BAEDF,0x1684A93C,0xDA2EA9A2,0x030EBB0E,0xCFA4BB90,0x412BBC73,0x8D81BCED,0x8744B5F4,0x4BEEB56A,0xC561B289,0x09CBB217,0xAC509190,0x60FA910E,0xEE7596ED,0x22DF9673,0x281A9F6A,0xE4B09FF4,0x6A3F9817,0xA6959889,0x7FB58A25,0xB31F8ABB,0x3D908D58,0xF13A8DC6,0xFBFF84DF,0x37558441,0xB9DA83A2,0x7570833C,0x533B85DA,0x9F918544,0x111E82A7,0xDDB48239,0xD7718B20,0x1BDB8BBE,0x95548C5D,0x59FE8CC3,0x80DE9E6F,0x4C749EF1,0xC2FB9912,0x0E51998C,0x04949095,0xC83E900B,0x46B197E8,0x8A1B9776,0x2F80B4F1,0xE32AB46F,0x6DA5B38C,0xA10FB312,0xABCABA0B,0x6760BA95,0xE9EFBD76,0x2545BDE8,0xFC65AF44,0x30CFAFDA,0xBE40A839,0x72EAA8A7,0x782FA1BE,0xB485A120,0x3A0AA6C3,0xF6A0A65D,0xAA4DE78C,0x66E7E712,0xE868E0F1,0x24C2E06F,0x2E07E976,0xE2ADE9E8,0x6C22EE0B,0xA088EE95,0x79A8FC39,0xB502FCA7,0x3B8DFB44,0xF727FBDA,0xFDE2F2C3,0x3148F25D,0xBFC7F5BE,0x736DF520,0xD6F6D6A7,0x1A5CD639,0x94D3D1DA,0x5879D144,0x52BCD85D,0x9E16D8C3,0x1099DF20,0xDC33DFBE,0x0513CD12,0xC9B9CD8C,0x4736CA6F,0x8B9CCAF1,0x8159C3E8,0x4DF3C376,0xC37CC495,0x0FD6C40B,0x7AA64737,0xB60C47A9,0x3883404A,0xF42940D4,0xFEEC49CD,0x32464953,0xBCC94EB0,0x70634E2E,0xA9435C82,0x65E95C1C,0xEB665BFF,0x27CC5B61,0x2D095278,0xE1A352E6,0x6F2C5505,0xA386559B,0x061D761C,0xCAB77682,0x44387161,0x889271FF,0x825778E6,0x4EFD7878,0xC0727F9B,0x0CD87F05,0xD5F86DA9,0x19526D37,0x97DD6AD4,0x5B776A4A,0x51B26353,0x9D1863CD,0x1397642E,0xDF3D64B0,0x83D02561,0x4F7A25FF,0xC1F5221C,0x0D5F2282,0x079A2B9B,0xCB302B05,0x45BF2CE6,0x89152C78,0x50353ED4,0x9C9F3E4A,0x121039A9,0xDEBA3937,0xD47F302E,0x18D530B0,0x965A3753,0x5AF037CD,0xFF6B144A,0x33C114D4,0xBD4E1337,0x71E413A9,0x7B211AB0,0xB78B1A2E,0x39041DCD,0xF5AE1D53,0x2C8E0FFF,0xE0240F61,0x6EAB0882,0xA201081C,0xA8C40105,0x646E019B,0xEAE10678,0x264B06E6, }#endif// CRC32_USE_LOOKUP_TABLE_SLICING_BY_8 || CRC32_USE_LOOKUP_TABLE_SLICING_BY_16#ifdefCRC32_USE_LOOKUP_TABLE_SLICING_BY_16// beyond this point only relevant for Slicing-by-16 ,{0x00000000,0x177B1443,0x2EF62886,0x398D3CC5,0x5DEC510C,0x4A97454F,0x731A798A,0x64616DC9,0xBBD8A218,0xACA3B65B,0x952E8A9E,0x82559EDD,0xE634F314,0xF14FE757,0xC8C2DB92,0xDFB9CFD1,0xACC04271,0xBBBB5632,0x82366AF7,0x954D7EB4,0xF12C137D,0xE657073E,0xDFDA3BFB,0xC8A12FB8,0x1718E069,0x0063F42A,0x39EEC8EF,0x2E95DCAC,0x4AF4B165,0x5D8FA526,0x640299E3,0x73798DA0,0x82F182A3,0x958A96E0,0xAC07AA25,0xBB7CBE66,0xDF1DD3AF,0xC866C7EC,0xF1EBFB29,0xE690EF6A,0x392920BB,0x2E5234F8,0x17DF083D,0x00A41C7E,0x64C571B7,0x73BE65F4,0x4A335931,0x5D484D72,0x2E31C0D2,0x394AD491,0x00C7E854,0x17BCFC17,0x73DD91DE,0x64A6859D,0x5D2BB958,0x4A50AD1B,0x95E962CA,0x82927689,0xBB1F4A4C,0xAC645E0F,0xC80533C6,0xDF7E2785,0xE6F31B40,0xF1880F03,0xDE920307,0xC9E91744,0xF0642B81,0xE71F3FC2,0x837E520B,0x94054648,0xAD887A8D,0xBAF36ECE,0x654AA11F,0x7231B55C,0x4BBC8999,0x5CC79DDA,0x38A6F013,0x2FDDE450,0x1650D895,0x012BCCD6,0x72524176,0x65295535,0x5CA469F0,0x4BDF7DB3,0x2FBE107A,0x38C50439,0x014838FC,0x16332CBF,0xC98AE36E,0xDEF1F72D,0xE77CCBE8,0xF007DFAB,0x9466B262,0x831DA621,0xBA909AE4,0xADEB8EA7,0x5C6381A4,0x4B1895E7,0x7295A922,0x65EEBD61,0x018FD0A8,0x16F4C4EB,0x2F79F82E,0x3802EC6D,0xE7BB23BC,0xF0C037FF,0xC94D0B3A,0xDE361F79,0xBA5772B0,0xAD2C66F3,0x94A15A36,0x83DA4E75,0xF0A3C3D5,0xE7D8D796,0xDE55EB53,0xC92EFF10,0xAD4F92D9,0xBA34869A,0x83B9BA5F,0x94C2AE1C,0x4B7B61CD,0x5C00758E,0x658D494B,0x72F65D08,0x169730C1,0x01EC2482,0x38611847,0x2F1A0C04,0x6655004F,0x712E140C,0x48A328C9,0x5FD83C8A,0x3BB95143,0x2CC24500,0x154F79C5,0x02346D86,0xDD8DA257,0xCAF6B614,0xF37B8AD1,0xE4009E92,0x8061F35B,0x971AE718,0xAE97DBDD,0xB9ECCF9E,0xCA95423E,0xDDEE567D,0xE4636AB8,0xF3187EFB,0x97791332,0x80020771,0xB98F3BB4,0xAEF42FF7,0x714DE026,0x6636F465,0x5FBBC8A0,0x48C0DCE3,0x2CA1B12A,0x3BDAA569,0x025799AC,0x152C8DEF,0xE4A482EC,0xF3DF96AF,0xCA52AA6A,0xDD29BE29,0xB948D3E0,0xAE33C7A3,0x97BEFB66,0x80C5EF25,0x5F7C20F4,0x480734B7,0x718A0872,0x66F11C31,0x029071F8,0x15EB65BB,0x2C66597E,0x3B1D4D3D,0x4864C09D,0x5F1FD4DE,0x6692E81B,0x71E9FC58,0x15889191,0x02F385D2,0x3B7EB917,0x2C05AD54,0xF3BC6285,0xE4C776C6,0xDD4A4A03,0xCA315E40,0xAE503389,0xB92B27CA,0x80A61B0F,0x97DD0F4C,0xB8C70348,0xAFBC170B,0x96312BCE,0x814A3F8D,0xE52B5244,0xF2504607,0xCBDD7AC2,0xDCA66E81,0x031FA150,0x1464B513,0x2DE989D6,0x3A929D95,0x5EF3F05C,0x4988E41F,0x7005D8DA,0x677ECC99,0x14074139,0x037C557A,0x3AF169BF,0x2D8A7DFC,0x49EB1035,0x5E900476,0x671D38B3,0x70662CF0,0xAFDFE321,0xB8A4F762,0x8129CBA7,0x9652DFE4,0xF233B22D,0xE548A66E,0xDCC59AAB,0xCBBE8EE8,0x3A3681EB,0x2D4D95A8,0x14C0A96D,0x03BBBD2E,0x67DAD0E7,0x70A1C4A4,0x492CF861,0x5E57EC22,0x81EE23F3,0x969537B0,0xAF180B75,0xB8631F36,0xDC0272FF,0xCB7966BC,0xF2F45A79,0xE58F4E3A,0x96F6C39A,0x818DD7D9,0xB800EB1C,0xAF7BFF5F,0xCB1A9296,0xDC6186D5,0xE5ECBA10,0xF297AE53,0x2D2E6182,0x3A5575C1,0x03D84904,0x14A35D47,0x70C2308E,0x67B924CD,0x5E341808,0x494F0C4B, }, {0x00000000,0xEFC26B3E,0x04F5D03D,0xEB37BB03,0x09EBA07A,0xE629CB44,0x0D1E7047,0xE2DC1B79,0x13D740F4,0xFC152BCA,0x172290C9,0xF8E0FBF7,0x1A3CE08E,0xF5FE8BB0,0x1EC930B3,0xF10B5B8D,0x27AE81E8,0xC86CEAD6,0x235B51D5,0xCC993AEB,0x2E452192,0xC1874AAC,0x2AB0F1AF,0xC5729A91,0x3479C11C,0xDBBBAA22,0x308C1121,0xDF4E7A1F,0x3D926166,0xD2500A58,0x3967B15B,0xD6A5DA65,0x4F5D03D0,0xA09F68EE,0x4BA8D3ED,0xA46AB8D3,0x46B6A3AA,0xA974C894,0x42437397,0xAD8118A9,0x5C8A4324,0xB348281A,0x587F9319,0xB7BDF827,0x5561E35E,0xBAA38860,0x51943363,0xBE56585D,0x68F38238,0x8731E906,0x6C065205,0x83C4393B,0x61182242,0x8EDA497C,0x65EDF27F,0x8A2F9941,0x7B24C2CC,0x94E6A9F2,0x7FD112F1,0x901379CF,0x72CF62B6,0x9D0D0988,0x763AB28B,0x99F8D9B5,0x9EBA07A0,0x71786C9E,0x9A4FD79D,0x758DBCA3,0x9751A7DA,0x7893CCE4,0x93A477E7,0x7C661CD9,0x8D6D4754,0x62AF2C6A,0x89989769,0x665AFC57,0x8486E72E,0x6B448C10,0x80733713,0x6FB15C2D,0xB9148648,0x56D6ED76,0xBDE15675,0x52233D4B,0xB0FF2632,0x5F3D4D0C,0xB40AF60F,0x5BC89D31,0xAAC3C6BC,0x4501AD82,0xAE361681,0x41F47DBF,0xA32866C6,0x4CEA0DF8,0xA7DDB6FB,0x481FDDC5,0xD1E70470,0x3E256F4E,0xD512D44D,0x3AD0BF73,0xD80CA40A,0x37CECF34,0xDCF97437,0x333B1F09,0xC2304484,0x2DF22FBA,0xC6C594B9,0x2907FF87,0xCBDBE4FE,0x24198FC0,0xCF2E34C3,0x20EC5FFD,0xF6498598,0x198BEEA6,0xF2BC55A5,0x1D7E3E9B,0xFFA225E2,0x10604EDC,0xFB57F5DF,0x14959EE1,0xE59EC56C,0x0A5CAE52,0xE16B1551,0x0EA97E6F,0xEC756516,0x03B70E28,0xE880B52B,0x0742DE15,0xE6050901,0x09C7623F,0xE2F0D93C,0x0D32B202,0xEFEEA97B,0x002CC245,0xEB1B7946,0x04D91278,0xF5D249F5,0x1A1022CB,0xF12799C8,0x1EE5F2F6,0xFC39E98F,0x13FB82B1,0xF8CC39B2,0x170E528C,0xC1AB88E9,0x2E69E3D7,0xC55E58D4,0x2A9C33EA,0xC8402893,0x278243AD,0xCCB5F8AE,0x23779390,0xD27CC81D,0x3DBEA323,0xD6891820,0x394B731E,0xDB976867,0x34550359,0xDF62B85A,0x30A0D364,0xA9580AD1,0x469A61EF,0xADADDAEC,0x426FB1D2,0xA0B3AAAB,0x4F71C195,0xA4467A96,0x4B8411A8,0xBA8F4A25,0x554D211B,0xBE7A9A18,0x51B8F126,0xB364EA5F,0x5CA68161,0xB7913A62,0x5853515C,0x8EF68B39,0x6134E007,0x8A035B04,0x65C1303A,0x871D2B43,0x68DF407D,0x83E8FB7E,0x6C2A9040,0x9D21CBCD,0x72E3A0F3,0x99D41BF0,0x761670CE,0x94CA6BB7,0x7B080089,0x903FBB8A,0x7FFDD0B4,0x78BF0EA1,0x977D659F,0x7C4ADE9C,0x9388B5A2,0x7154AEDB,0x9E96C5E5,0x75A17EE6,0x9A6315D8,0x6B684E55,0x84AA256B,0x6F9D9E68,0x805FF556,0x6283EE2F,0x8D418511,0x66763E12,0x89B4552C,0x5F118F49,0xB0D3E477,0x5BE45F74,0xB426344A,0x56FA2F33,0xB938440D,0x520FFF0E,0xBDCD9430,0x4CC6CFBD,0xA304A483,0x48331F80,0xA7F174BE,0x452D6FC7,0xAAEF04F9,0x41D8BFFA,0xAE1AD4C4,0x37E20D71,0xD820664F,0x3317DD4C,0xDCD5B672,0x3E09AD0B,0xD1CBC635,0x3AFC7D36,0xD53E1608,0x24354D85,0xCBF726BB,0x20C09DB8,0xCF02F686,0x2DDEEDFF,0xC21C86C1,0x292B3DC2,0xC6E956FC,0x104C8C99,0xFF8EE7A7,0x14B95CA4,0xFB7B379A,0x19A72CE3,0xF66547DD,0x1D52FCDE,0xF29097E0,0x039BCC6D,0xEC59A753,0x076E1C50,0xE8AC776E,0x0A706C17,0xE5B20729,0x0E85BC2A,0xE147D714, }, {0x00000000,0xC18EDFC0,0x586CB9C1,0x99E26601,0xB0D97382,0x7157AC42,0xE8B5CA43,0x293B1583,0xBAC3E145,0x7B4D3E85,0xE2AF5884,0x23218744,0x0A1A92C7,0xCB944D07,0x52762B06,0x93F8F4C6,0xAEF6C4CB,0x6F781B0B,0xF69A7D0A,0x3714A2CA,0x1E2FB749,0xDFA16889,0x46430E88,0x87CDD148,0x1435258E,0xD5BBFA4E,0x4C599C4F,0x8DD7438F,0xA4EC560C,0x656289CC,0xFC80EFCD,0x3D0E300D,0x869C8FD7,0x47125017,0xDEF03616,0x1F7EE9D6,0x3645FC55,0xF7CB2395,0x6E294594,0xAFA79A54,0x3C5F6E92,0xFDD1B152,0x6433D753,0xA5BD0893,0x8C861D10,0x4D08C2D0,0xD4EAA4D1,0x15647B11,0x286A4B1C,0xE9E494DC,0x7006F2DD,0xB1882D1D,0x98B3389E,0x593DE75E,0xC0DF815F,0x01515E9F,0x92A9AA59,0x53277599,0xCAC51398,0x0B4BCC58,0x2270D9DB,0xE3FE061B,0x7A1C601A,0xBB92BFDA,0xD64819EF,0x17C6C62F,0x8E24A02E,0x4FAA7FEE,0x66916A6D,0xA71FB5AD,0x3EFDD3AC,0xFF730C6C,0x6C8BF8AA,0xAD05276A,0x34E7416B,0xF5699EAB,0xDC528B28,0x1DDC54E8,0x843E32E9,0x45B0ED29,0x78BEDD24,0xB93002E4,0x20D264E5,0xE15CBB25,0xC867AEA6,0x09E97166,0x900B1767,0x5185C8A7,0xC27D3C61,0x03F3E3A1,0x9A1185A0,0x5B9F5A60,0x72A44FE3,0xB32A9023,0x2AC8F622,0xEB4629E2,0x50D49638,0x915A49F8,0x08B82FF9,0xC936F039,0xE00DE5BA,0x21833A7A,0xB8615C7B,0x79EF83BB,0xEA17777D,0x2B99A8BD,0xB27BCEBC,0x73F5117C,0x5ACE04FF,0x9B40DB3F,0x02A2BD3E,0xC32C62FE,0xFE2252F3,0x3FAC8D33,0xA64EEB32,0x67C034F2,0x4EFB2171,0x8F75FEB1,0x169798B0,0xD7194770,0x44E1B3B6,0x856F6C76,0x1C8D0A77,0xDD03D5B7,0xF438C034,0x35B61FF4,0xAC5479F5,0x6DDAA635,0x77E1359F,0xB66FEA5F,0x2F8D8C5E,0xEE03539E,0xC738461D,0x06B699DD,0x9F54FFDC,0x5EDA201C,0xCD22D4DA,0x0CAC0B1A,0x954E6D1B,0x54C0B2DB,0x7DFBA758,0xBC757898,0x25971E99,0xE419C159,0xD917F154,0x18992E94,0x817B4895,0x40F59755,0x69CE82D6,0xA8405D16,0x31A23B17,0xF02CE4D7,0x63D41011,0xA25ACFD1,0x3BB8A9D0,0xFA367610,0xD30D6393,0x1283BC53,0x8B61DA52,0x4AEF0592,0xF17DBA48,0x30F36588,0xA9110389,0x689FDC49,0x41A4C9CA,0x802A160A,0x19C8700B,0xD846AFCB,0x4BBE5B0D,0x8A3084CD,0x13D2E2CC,0xD25C3D0C,0xFB67288F,0x3AE9F74F,0xA30B914E,0x62854E8E,0x5F8B7E83,0x9E05A143,0x07E7C742,0xC6691882,0xEF520D01,0x2EDCD2C1,0xB73EB4C0,0x76B06B00,0xE5489FC6,0x24C64006,0xBD242607,0x7CAAF9C7,0x5591EC44,0x941F3384,0x0DFD5585,0xCC738A45,0xA1A92C70,0x6027F3B0,0xF9C595B1,0x384B4A71,0x11705FF2,0xD0FE8032,0x491CE633,0x889239F3,0x1B6ACD35,0xDAE412F5,0x430674F4,0x8288AB34,0xABB3BEB7,0x6A3D6177,0xF3DF0776,0x3251D8B6,0x0F5FE8BB,0xCED1377B,0x5733517A,0x96BD8EBA,0xBF869B39,0x7E0844F9,0xE7EA22F8,0x2664FD38,0xB59C09FE,0x7412D63E,0xEDF0B03F,0x2C7E6FFF,0x05457A7C,0xC4CBA5BC,0x5D29C3BD,0x9CA71C7D,0x2735A3A7,0xE6BB7C67,0x7F591A66,0xBED7C5A6,0x97ECD025,0x56620FE5,0xCF8069E4,0x0E0EB624,0x9DF642E2,0x5C789D22,0xC59AFB23,0x041424E3,0x2D2F3160,0xECA1EEA0,0x754388A1,0xB4CD5761,0x89C3676C,0x484DB8AC,0xD1AFDEAD,0x1021016D,0x391A14EE,0xF894CB2E,0x6176AD2F,0xA0F872EF,0x33008629,0xF28E59E9,0x6B6C3FE8,0xAAE2E028,0x83D9F5AB,0x42572A6B,0xDBB54C6A,0x1A3B93AA, }, {0x00000000,0x9BA54C6F,0xEC3B9E9F,0x779ED2F0,0x03063B7F,0x98A37710,0xEF3DA5E0,0x7498E98F,0x060C76FE,0x9DA93A91,0xEA37E861,0x7192A40E,0x050A4D81,0x9EAF01EE,0xE931D31E,0x72949F71,0x0C18EDFC,0x97BDA193,0xE0237363,0x7B863F0C,0x0F1ED683,0x94BB9AEC,0xE325481C,0x78800473,0x0A149B02,0x91B1D76D,0xE62F059D,0x7D8A49F2,0x0912A07D,0x92B7EC12,0xE5293EE2,0x7E8C728D,0x1831DBF8,0x83949797,0xF40A4567,0x6FAF0908,0x1B37E087,0x8092ACE8,0xF70C7E18,0x6CA93277,0x1E3DAD06,0x8598E169,0xF2063399,0x69A37FF6,0x1D3B9679,0x869EDA16,0xF10008E6,0x6AA54489,0x14293604,0x8F8C7A6B,0xF812A89B,0x63B7E4F4,0x172F0D7B,0x8C8A4114,0xFB1493E4,0x60B1DF8B,0x122540FA,0x89800C95,0xFE1EDE65,0x65BB920A,0x11237B85,0x8A8637EA,0xFD18E51A,0x66BDA975,0x3063B7F0,0xABC6FB9F,0xDC58296F,0x47FD6500,0x33658C8F,0xA8C0C0E0,0xDF5E1210,0x44FB5E7F,0x366FC10E,0xADCA8D61,0xDA545F91,0x41F113FE,0x3569FA71,0xAECCB61E,0xD95264EE,0x42F72881,0x3C7B5A0C,0xA7DE1663,0xD040C493,0x4BE588FC,0x3F7D6173,0xA4D82D1C,0xD346FFEC,0x48E3B383,0x3A772CF2,0xA1D2609D,0xD64CB26D,0x4DE9FE02,0x3971178D,0xA2D45BE2,0xD54A8912,0x4EEFC57D,0x28526C08,0xB3F72067,0xC469F297,0x5FCCBEF8,0x2B545777,0xB0F11B18,0xC76FC9E8,0x5CCA8587,0x2E5E1AF6,0xB5FB5699,0xC2658469,0x59C0C806,0x2D582189,0xB6FD6DE6,0xC163BF16,0x5AC6F379,0x244A81F4,0xBFEFCD9B,0xC8711F6B,0x53D45304,0x274CBA8B,0xBCE9F6E4,0xCB772414,0x50D2687B,0x2246F70A,0xB9E3BB65,0xCE7D6995,0x55D825FA,0x2140CC75,0xBAE5801A,0xCD7B52EA,0x56DE1E85,0x60C76FE0,0xFB62238F,0x8CFCF17F,0x1759BD10,0x63C1549F,0xF86418F0,0x8FFACA00,0x145F866F,0x66CB191E,0xFD6E5571,0x8AF08781,0x1155CBEE,0x65CD2261,0xFE686E0E,0x89F6BCFE,0x1253F091,0x6CDF821C,0xF77ACE73,0x80E41C83,0x1B4150EC,0x6FD9B963,0xF47CF50C,0x83E227FC,0x18476B93,0x6AD3F4E2,0xF176B88D,0x86E86A7D,0x1D4D2612,0x69D5CF9D,0xF27083F2,0x85EE5102,0x1E4B1D6D,0x78F6B418,0xE353F877,0x94CD2A87,0x0F6866E8,0x7BF08F67,0xE055C308,0x97CB11F8,0x0C6E5D97,0x7EFAC2E6,0xE55F8E89,0x92C15C79,0x09641016,0x7DFCF999,0xE659B5F6,0x91C76706,0x0A622B69,0x74EE59E4,0xEF4B158B,0x98D5C77B,0x03708B14,0x77E8629B,0xEC4D2EF4,0x9BD3FC04,0x0076B06B,0x72E22F1A,0xE9476375,0x9ED9B185,0x057CFDEA,0x71E41465,0xEA41580A,0x9DDF8AFA,0x067AC695,0x50A4D810,0xCB01947F,0xBC9F468F,0x273A0AE0,0x53A2E36F,0xC807AF00,0xBF997DF0,0x243C319F,0x56A8AEEE,0xCD0DE281,0xBA933071,0x21367C1E,0x55AE9591,0xCE0BD9FE,0xB9950B0E,0x22304761,0x5CBC35EC,0xC7197983,0xB087AB73,0x2B22E71C,0x5FBA0E93,0xC41F42FC,0xB381900C,0x2824DC63,0x5AB04312,0xC1150F7D,0xB68BDD8D,0x2D2E91E2,0x59B6786D,0xC2133402,0xB58DE6F2,0x2E28AA9D,0x489503E8,0xD3304F87,0xA4AE9D77,0x3F0BD118,0x4B933897,0xD03674F8,0xA7A8A608,0x3C0DEA67,0x4E997516,0xD53C3979,0xA2A2EB89,0x3907A7E6,0x4D9F4E69,0xD63A0206,0xA1A4D0F6,0x3A019C99,0x448DEE14,0xDF28A27B,0xA8B6708B,0x33133CE4,0x478BD56B,0xDC2E9904,0xABB04BF4,0x3015079B,0x428198EA,0xD924D485,0xAEBA0675,0x351F4A1A,0x4187A395,0xDA22EFFA,0xADBC3D0A,0x36197165, }, {0x00000000,0xDD96D985,0x605CB54B,0xBDCA6CCE,0xC0B96A96,0x1D2FB313,0xA0E5DFDD,0x7D730658,0x5A03D36D,0x87950AE8,0x3A5F6626,0xE7C9BFA3,0x9ABAB9FB,0x472C607E,0xFAE60CB0,0x2770D535,0xB407A6DA,0x69917F5F,0xD45B1391,0x09CDCA14,0x74BECC4C,0xA92815C9,0x14E27907,0xC974A082,0xEE0475B7,0x3392AC32,0x8E58C0FC,0x53CE1979,0x2EBD1F21,0xF32BC6A4,0x4EE1AA6A,0x937773EF,0xB37E4BF5,0x6EE89270,0xD322FEBE,0x0EB4273B,0x73C72163,0xAE51F8E6,0x139B9428,0xCE0D4DAD,0xE97D9898,0x34EB411D,0x89212DD3,0x54B7F456,0x29C4F20E,0xF4522B8B,0x49984745,0x940E9EC0,0x0779ED2F,0xDAEF34AA,0x67255864,0xBAB381E1,0xC7C087B9,0x1A565E3C,0xA79C32F2,0x7A0AEB77,0x5D7A3E42,0x80ECE7C7,0x3D268B09,0xE0B0528C,0x9DC354D4,0x40558D51,0xFD9FE19F,0x2009381A,0xBD8D91AB,0x601B482E,0xDDD124E0,0x0047FD65,0x7D34FB3D,0xA0A222B8,0x1D684E76,0xC0FE97F3,0xE78E42C6,0x3A189B43,0x87D2F78D,0x5A442E08,0x27372850,0xFAA1F1D5,0x476B9D1B,0x9AFD449E,0x098A3771,0xD41CEEF4,0x69D6823A,0xB4405BBF,0xC9335DE7,0x14A58462,0xA96FE8AC,0x74F93129,0x5389E41C,0x8E1F3D99,0x33D55157,0xEE4388D2,0x93308E8A,0x4EA6570F,0xF36C3BC1,0x2EFAE244,0x0EF3DA5E,0xD36503DB,0x6EAF6F15,0xB339B690,0xCE4AB0C8,0x13DC694D,0xAE160583,0x7380DC06,0x54F00933,0x8966D0B6,0x34ACBC78,0xE93A65FD,0x944963A5,0x49DFBA20,0xF415D6EE,0x29830F6B,0xBAF47C84,0x6762A501,0xDAA8C9CF,0x073E104A,0x7A4D1612,0xA7DBCF97,0x1A11A359,0xC7877ADC,0xE0F7AFE9,0x3D61766C,0x80AB1AA2,0x5D3DC327,0x204EC57F,0xFDD81CFA,0x40127034,0x9D84A9B1,0xA06A2517,0x7DFCFC92,0xC036905C,0x1DA049D9,0x60D34F81,0xBD459604,0x008FFACA,0xDD19234F,0xFA69F67A,0x27FF2FFF,0x9A354331,0x47A39AB4,0x3AD09CEC,0xE7464569,0x5A8C29A7,0x871AF022,0x146D83CD,0xC9FB5A48,0x74313686,0xA9A7EF03,0xD4D4E95B,0x094230DE,0xB4885C10,0x691E8595,0x4E6E50A0,0x93F88925,0x2E32E5EB,0xF3A43C6E,0x8ED73A36,0x5341E3B3,0xEE8B8F7D,0x331D56F8,0x13146EE2,0xCE82B767,0x7348DBA9,0xAEDE022C,0xD3AD0474,0x0E3BDDF1,0xB3F1B13F,0x6E6768BA,0x4917BD8F,0x9481640A,0x294B08C4,0xF4DDD141,0x89AED719,0x54380E9C,0xE9F26252,0x3464BBD7,0xA713C838,0x7A8511BD,0xC74F7D73,0x1AD9A4F6,0x67AAA2AE,0xBA3C7B2B,0x07F617E5,0xDA60CE60,0xFD101B55,0x2086C2D0,0x9D4CAE1E,0x40DA779B,0x3DA971C3,0xE03FA846,0x5DF5C488,0x80631D0D,0x1DE7B4BC,0xC0716D39,0x7DBB01F7,0xA02DD872,0xDD5EDE2A,0x00C807AF,0xBD026B61,0x6094B2E4,0x47E467D1,0x9A72BE54,0x27B8D29A,0xFA2E0B1F,0x875D0D47,0x5ACBD4C2,0xE701B80C,0x3A976189,0xA9E01266,0x7476CBE3,0xC9BCA72D,0x142A7EA8,0x695978F0,0xB4CFA175,0x0905CDBB,0xD493143E,0xF3E3C10B,0x2E75188E,0x93BF7440,0x4E29ADC5,0x335AAB9D,0xEECC7218,0x53061ED6,0x8E90C753,0xAE99FF49,0x730F26CC,0xCEC54A02,0x13539387,0x6E2095DF,0xB3B64C5A,0x0E7C2094,0xD3EAF911,0xF49A2C24,0x290CF5A1,0x94C6996F,0x495040EA,0x342346B2,0xE9B59F37,0x547FF3F9,0x89E92A7C,0x1A9E5993,0xC7088016,0x7AC2ECD8,0xA754355D,0xDA273305,0x07B1EA80,0xBA7B864E,0x67ED5FCB,0x409D8AFE,0x9D0B537B,0x20C13FB5,0xFD57E630,0x8024E068,0x5DB239ED,0xE0785523,0x3DEE8CA6, }, {0x00000000,0x9D0FE176,0xE16EC4AD,0x7C6125DB,0x19AC8F1B,0x84A36E6D,0xF8C24BB6,0x65CDAAC0,0x33591E36,0xAE56FF40,0xD237DA9B,0x4F383BED,0x2AF5912D,0xB7FA705B,0xCB9B5580,0x5694B4F6,0x66B23C6C,0xFBBDDD1A,0x87DCF8C1,0x1AD319B7,0x7F1EB377,0xE2115201,0x9E7077DA,0x037F96AC,0x55EB225A,0xC8E4C32C,0xB485E6F7,0x298A0781,0x4C47AD41,0xD1484C37,0xAD2969EC,0x3026889A,0xCD6478D8,0x506B99AE,0x2C0ABC75,0xB1055D03,0xD4C8F7C3,0x49C716B5,0x35A6336E,0xA8A9D218,0xFE3D66EE,0x63328798,0x1F53A243,0x825C4335,0xE791E9F5,0x7A9E0883,0x06FF2D58,0x9BF0CC2E,0xABD644B4,0x36D9A5C2,0x4AB88019,0xD7B7616F,0xB27ACBAF,0x2F752AD9,0x53140F02,0xCE1BEE74,0x988F5A82,0x0580BBF4,0x79E19E2F,0xE4EE7F59,0x8123D599,0x1C2C34EF,0x604D1134,0xFD42F042,0x41B9F7F1,0xDCB61687,0xA0D7335C,0x3DD8D22A,0x581578EA,0xC51A999C,0xB97BBC47,0x24745D31,0x72E0E9C7,0xEFEF08B1,0x938E2D6A,0x0E81CC1C,0x6B4C66DC,0xF64387AA,0x8A22A271,0x172D4307,0x270BCB9D,0xBA042AEB,0xC6650F30,0x5B6AEE46,0x3EA74486,0xA3A8A5F0,0xDFC9802B,0x42C6615D,0x1452D5AB,0x895D34DD,0xF53C1106,0x6833F070,0x0DFE5AB0,0x90F1BBC6,0xEC909E1D,0x719F7F6B,0x8CDD8F29,0x11D26E5F,0x6DB34B84,0xF0BCAAF2,0x95710032,0x087EE144,0x741FC49F,0xE91025E9,0xBF84911F,0x228B7069,0x5EEA55B2,0xC3E5B4C4,0xA6281E04,0x3B27FF72,0x4746DAA9,0xDA493BDF,0xEA6FB345,0x77605233,0x0B0177E8,0x960E969E,0xF3C33C5E,0x6ECCDD28,0x12ADF8F3,0x8FA21985,0xD936AD73,0x44394C05,0x385869DE,0xA55788A8,0xC09A2268,0x5D95C31E,0x21F4E6C5,0xBCFB07B3,0x8373EFE2,0x1E7C0E94,0x621D2B4F,0xFF12CA39,0x9ADF60F9,0x07D0818F,0x7BB1A454,0xE6BE4522,0xB02AF1D4,0x2D2510A2,0x51443579,0xCC4BD40F,0xA9867ECF,0x34899FB9,0x48E8BA62,0xD5E75B14,0xE5C1D38E,0x78CE32F8,0x04AF1723,0x99A0F655,0xFC6D5C95,0x6162BDE3,0x1D039838,0x800C794E,0xD698CDB8,0x4B972CCE,0x37F60915,0xAAF9E863,0xCF3442A3,0x523BA3D5,0x2E5A860E,0xB3556778,0x4E17973A,0xD318764C,0xAF795397,0x3276B2E1,0x57BB1821,0xCAB4F957,0xB6D5DC8C,0x2BDA3DFA,0x7D4E890C,0xE041687A,0x9C204DA1,0x012FACD7,0x64E20617,0xF9EDE761,0x858CC2BA,0x188323CC,0x28A5AB56,0xB5AA4A20,0xC9CB6FFB,0x54C48E8D,0x3109244D,0xAC06C53B,0xD067E0E0,0x4D680196,0x1BFCB560,0x86F35416,0xFA9271CD,0x679D90BB,0x02503A7B,0x9F5FDB0D,0xE33EFED6,0x7E311FA0,0xC2CA1813,0x5FC5F965,0x23A4DCBE,0xBEAB3DC8,0xDB669708,0x4669767E,0x3A0853A5,0xA707B2D3,0xF1930625,0x6C9CE753,0x10FDC288,0x8DF223FE,0xE83F893E,0x75306848,0x09514D93,0x945EACE5,0xA478247F,0x3977C509,0x4516E0D2,0xD81901A4,0xBDD4AB64,0x20DB4A12,0x5CBA6FC9,0xC1B58EBF,0x97213A49,0x0A2EDB3F,0x764FFEE4,0xEB401F92,0x8E8DB552,0x13825424,0x6FE371FF,0xF2EC9089,0x0FAE60CB,0x92A181BD,0xEEC0A466,0x73CF4510,0x1602EFD0,0x8B0D0EA6,0xF76C2B7D,0x6A63CA0B,0x3CF77EFD,0xA1F89F8B,0xDD99BA50,0x40965B26,0x255BF1E6,0xB8541090,0xC435354B,0x593AD43D,0x691C5CA7,0xF413BDD1,0x8872980A,0x157D797C,0x70B0D3BC,0xEDBF32CA,0x91DE1711,0x0CD1F667,0x5A454291,0xC74AA3E7,0xBB2B863C,0x2624674A,0x43E9CD8A,0xDEE62CFC,0xA2870927,0x3F88E851, }, {0x00000000,0xB9FBDBE8,0xA886B191,0x117D6A79,0x8A7C6563,0x3387BE8B,0x22FAD4F2,0x9B010F1A,0xCF89CC87,0x7672176F,0x670F7D16,0xDEF4A6FE,0x45F5A9E4,0xFC0E720C,0xED731875,0x5488C39D,0x44629F4F,0xFD9944A7,0xECE42EDE,0x551FF536,0xCE1EFA2C,0x77E521C4,0x66984BBD,0xDF639055,0x8BEB53C8,0x32108820,0x236DE259,0x9A9639B1,0x019736AB,0xB86CED43,0xA911873A,0x10EA5CD2,0x88C53E9E,0x313EE576,0x20438F0F,0x99B854E7,0x02B95BFD,0xBB428015,0xAA3FEA6C,0x13C43184,0x474CF219,0xFEB729F1,0xEFCA4388,0x56319860,0xCD30977A,0x74CB4C92,0x65B626EB,0xDC4DFD03,0xCCA7A1D1,0x755C7A39,0x64211040,0xDDDACBA8,0x46DBC4B2,0xFF201F5A,0xEE5D7523,0x57A6AECB,0x032E6D56,0xBAD5B6BE,0xABA8DCC7,0x1253072F,0x89520835,0x30A9D3DD,0x21D4B9A4,0x982F624C,0xCAFB7B7D,0x7300A095,0x627DCAEC,0xDB861104,0x40871E1E,0xF97CC5F6,0xE801AF8F,0x51FA7467,0x0572B7FA,0xBC896C12,0xADF4066B,0x140FDD83,0x8F0ED299,0x36F50971,0x27886308,0x9E73B8E0,0x8E99E432,0x37623FDA,0x261F55A3,0x9FE48E4B,0x04E58151,0xBD1E5AB9,0xAC6330C0,0x1598EB28,0x411028B5,0xF8EBF35D,0xE9969924,0x506D42CC,0xCB6C4DD6,0x7297963E,0x63EAFC47,0xDA1127AF,0x423E45E3,0xFBC59E0B,0xEAB8F472,0x53432F9A,0xC8422080,0x71B9FB68,0x60C49111,0xD93F4AF9,0x8DB78964,0x344C528C,0x253138F5,0x9CCAE31D,0x07CBEC07,0xBE3037EF,0xAF4D5D96,0x16B6867E,0x065CDAAC,0xBFA70144,0xAEDA6B3D,0x1721B0D5,0x8C20BFCF,0x35DB6427,0x24A60E5E,0x9D5DD5B6,0xC9D5162B,0x702ECDC3,0x6153A7BA,0xD8A87C52,0x43A97348,0xFA52A8A0,0xEB2FC2D9,0x52D41931,0x4E87F0BB,0xF77C2B53,0xE601412A,0x5FFA9AC2,0xC4FB95D8,0x7D004E30,0x6C7D2449,0xD586FFA1,0x810E3C3C,0x38F5E7D4,0x29888DAD,0x90735645,0x0B72595F,0xB28982B7,0xA3F4E8CE,0x1A0F3326,0x0AE56FF4,0xB31EB41C,0xA263DE65,0x1B98058D,0x80990A97,0x3962D17F,0x281FBB06,0x91E460EE,0xC56CA373,0x7C97789B,0x6DEA12E2,0xD411C90A,0x4F10C610,0xF6EB1DF8,0xE7967781,0x5E6DAC69,0xC642CE25,0x7FB915CD,0x6EC47FB4,0xD73FA45C,0x4C3EAB46,0xF5C570AE,0xE4B81AD7,0x5D43C13F,0x09CB02A2,0xB030D94A,0xA14DB333,0x18B668DB,0x83B767C1,0x3A4CBC29,0x2B31D650,0x92CA0DB8,0x8220516A,0x3BDB8A82,0x2AA6E0FB,0x935D3B13,0x085C3409,0xB1A7EFE1,0xA0DA8598,0x19215E70,0x4DA99DED,0xF4524605,0xE52F2C7C,0x5CD4F794,0xC7D5F88E,0x7E2E2366,0x6F53491F,0xD6A892F7,0x847C8BC6,0x3D87502E,0x2CFA3A57,0x9501E1BF,0x0E00EEA5,0xB7FB354D,0xA6865F34,0x1F7D84DC,0x4BF54741,0xF20E9CA9,0xE373F6D0,0x5A882D38,0xC1892222,0x7872F9CA,0x690F93B3,0xD0F4485B,0xC01E1489,0x79E5CF61,0x6898A518,0xD1637EF0,0x4A6271EA,0xF399AA02,0xE2E4C07B,0x5B1F1B93,0x0F97D80E,0xB66C03E6,0xA711699F,0x1EEAB277,0x85EBBD6D,0x3C106685,0x2D6D0CFC,0x9496D714,0x0CB9B558,0xB5426EB0,0xA43F04C9,0x1DC4DF21,0x86C5D03B,0x3F3E0BD3,0x2E4361AA,0x97B8BA42,0xC33079DF,0x7ACBA237,0x6BB6C84E,0xD24D13A6,0x494C1CBC,0xF0B7C754,0xE1CAAD2D,0x583176C5,0x48DB2A17,0xF120F1FF,0xE05D9B86,0x59A6406E,0xC2A74F74,0x7B5C949C,0x6A21FEE5,0xD3DA250D,0x8752E690,0x3EA93D78,0x2FD45701,0x962F8CE9,0x0D2E83F3,0xB4D5581B,0xA5A83262,0x1C53E98A, }, {0x00000000,0xAE689191,0x87A02563,0x29C8B4F2,0xD4314C87,0x7A59DD16,0x539169E4,0xFDF9F875,0x73139F4F,0xDD7B0EDE,0xF4B3BA2C,0x5ADB2BBD,0xA722D3C8,0x094A4259,0x2082F6AB,0x8EEA673A,0xE6273E9E,0x484FAF0F,0x61871BFD,0xCFEF8A6C,0x32167219,0x9C7EE388,0xB5B6577A,0x1BDEC6EB,0x9534A1D1,0x3B5C3040,0x129484B2,0xBCFC1523,0x4105ED56,0xEF6D7CC7,0xC6A5C835,0x68CD59A4,0x173F7B7D,0xB957EAEC,0x909F5E1E,0x3EF7CF8F,0xC30E37FA,0x6D66A66B,0x44AE1299,0xEAC68308,0x642CE432,0xCA4475A3,0xE38CC151,0x4DE450C0,0xB01DA8B5,0x1E753924,0x37BD8DD6,0x99D51C47,0xF11845E3,0x5F70D472,0x76B86080,0xD8D0F111,0x25290964,0x8B4198F5,0xA2892C07,0x0CE1BD96,0x820BDAAC,0x2C634B3D,0x05ABFFCF,0xABC36E5E,0x563A962B,0xF85207BA,0xD19AB348,0x7FF222D9,0x2E7EF6FA,0x8016676B,0xA9DED399,0x07B64208,0xFA4FBA7D,0x54272BEC,0x7DEF9F1E,0xD3870E8F,0x5D6D69B5,0xF305F824,0xDACD4CD6,0x74A5DD47,0x895C2532,0x2734B4A3,0x0EFC0051,0xA09491C0,0xC859C864,0x663159F5,0x4FF9ED07,0xE1917C96,0x1C6884E3,0xB2001572,0x9BC8A180,0x35A03011,0xBB4A572B,0x1522C6BA,0x3CEA7248,0x9282E3D9,0x6F7B1BAC,0xC1138A3D,0xE8DB3ECF,0x46B3AF5E,0x39418D87,0x97291C16,0xBEE1A8E4,0x10893975,0xED70C100,0x43185091,0x6AD0E463,0xC4B875F2,0x4A5212C8,0xE43A8359,0xCDF237AB,0x639AA63A,0x9E635E4F,0x300BCFDE,0x19C37B2C,0xB7ABEABD,0xDF66B319,0x710E2288,0x58C6967A,0xF6AE07EB,0x0B57FF9E,0xA53F6E0F,0x8CF7DAFD,0x229F4B6C,0xAC752C56,0x021DBDC7,0x2BD50935,0x85BD98A4,0x784460D1,0xD62CF140,0xFFE445B2,0x518CD423,0x5CFDEDF4,0xF2957C65,0xDB5DC897,0x75355906,0x88CCA173,0x26A430E2,0x0F6C8410,0xA1041581,0x2FEE72BB,0x8186E32A,0xA84E57D8,0x0626C649,0xFBDF3E3C,0x55B7AFAD,0x7C7F1B5F,0xD2178ACE,0xBADAD36A,0x14B242FB,0x3D7AF609,0x93126798,0x6EEB9FED,0xC0830E7C,0xE94BBA8E,0x47232B1F,0xC9C94C25,0x67A1DDB4,0x4E696946,0xE001F8D7,0x1DF800A2,0xB3909133,0x9A5825C1,0x3430B450,0x4BC29689,0xE5AA0718,0xCC62B3EA,0x620A227B,0x9FF3DA0E,0x319B4B9F,0x1853FF6D,0xB63B6EFC,0x38D109C6,0x96B99857,0xBF712CA5,0x1119BD34,0xECE04541,0x4288D4D0,0x6B406022,0xC528F1B3,0xADE5A817,0x038D3986,0x2A458D74,0x842D1CE5,0x79D4E490,0xD7BC7501,0xFE74C1F3,0x501C5062,0xDEF63758,0x709EA6C9,0x5956123B,0xF73E83AA,0x0AC77BDF,0xA4AFEA4E,0x8D675EBC,0x230FCF2D,0x72831B0E,0xDCEB8A9F,0xF5233E6D,0x5B4BAFFC,0xA6B25789,0x08DAC618,0x211272EA,0x8F7AE37B,0x01908441,0xAFF815D0,0x8630A122,0x285830B3,0xD5A1C8C6,0x7BC95957,0x5201EDA5,0xFC697C34,0x94A42590,0x3ACCB401,0x130400F3,0xBD6C9162,0x40956917,0xEEFDF886,0xC7354C74,0x695DDDE5,0xE7B7BADF,0x49DF2B4E,0x60179FBC,0xCE7F0E2D,0x3386F658,0x9DEE67C9,0xB426D33B,0x1A4E42AA,0x65BC6073,0xCBD4F1E2,0xE21C4510,0x4C74D481,0xB18D2CF4,0x1FE5BD65,0x362D0997,0x98459806,0x16AFFF3C,0xB8C76EAD,0x910FDA5F,0x3F674BCE,0xC29EB3BB,0x6CF6222A,0x453E96D8,0xEB560749,0x839B5EED,0x2DF3CF7C,0x043B7B8E,0xAA53EA1F,0x57AA126A,0xF9C283FB,0xD00A3709,0x7E62A698,0xF088C1A2,0x5EE05033,0x7728E4C1,0xD9407550,0x24B98D25,0x8AD11CB4,0xA319A846,0x0D7139D7, }#endif// CRC32_USE_LOOKUP_TABLE_SLICING_BY_16};
Note: I only included this rather large look-up table to study how search engines
will refer to my site. I'm a nerd, I know.
Faster Precomputation
Computing the first 256 values of the lookup table takes about 1.5 nanoseconds on my PC.
It's pretty much the same code you will find in every other CRC implementation on the internet. Old and trusted.
In February 2021, a user named "Wolf" sent me code for a faster precomputation. And indeed, it's much, much faster: about 7 times (≈0.22 nanoseconds) !
That got me interested again and I spent an hour or two on improving his ideas: in the end I was able to make a few modifications so that it can be done in ≈0.18 nanoseconds.
Without further ado, here are the three implementations with lots of comments explaining the algorithms:
hide
Faster Precomputationconstuint32_t Polynomial = 0xEDB88320;// -----------------------------------------------// standard initialization// approx. 1.5 nanoseconds on my PC / GCC9-x64for (unsignedint i = 0; i <= 0xFF; i++){uint32_t crc = i;for (unsignedint j = 0; j < 8; j++)crc = (crc >> 1) ^ ((crc & 1) * Polynomial); Crc32Lookup[0][i] = crc;}// -----------------------------------------------// code by a user named "Wolf"// approx. 0.22 nanoseconds on my PC / GCC9-x64Crc32Lookup[0][0] = 0;// start with powers of twouint32_tcrc = Crc32Lookup[0][0x80] = Polynomial;for (unsignedint step = 0x40; step != 0; step >>= 1){// each power of two has only a single bit set// so we need just one iterationcrc = (crc >> 1) ^ ((crc & 1) * Polynomial);Crc32Lookup[0][step] = crc;// and compute all not-yet-processed multiplesfor (unsignedint i = step * 3; i <= 0xFF; i += step << 1)Crc32Lookup[0][i] = crc ^ Crc32Lookup[0][i - step];// note: step*2 was already filled, therefore start at step*3// and compute all odd multiples}// -----------------------------------------------// my improvement of Wolf's code// approx. 0.18 nanoseconds on my PC / GCC9-x64Crc32Lookup[0][0] = 0;// compute each power of two (all numbers with exactly one bit set)uint32_tcrc = Crc32Lookup[0][0x80] = Polynomial;for (unsignedint next = 0x40; next != 0; next >>= 1){crc = (crc >> 1) ^ ((crc & 1) * Polynomial);Crc32Lookup[0][next] = crc;}// the main idea is:// table[a ^ b] = table[a] ^ table[b];// therefore if we know all values up to a power of two called x// we can compute table[x + y] where x > y:// table[x + y] = table[x ^ y] = table[x] ^ table[y]// example:// the previous loop computed table[1] and table[2],// so that x = 2 (a power of two) and y = 1 (fulfilling x > y)// now x + y = x ^ y = 2 + 1 = 2 ^ 1// and table[x + y] = table[x ^ y] = table[x] ^ table[y]// which means table[3] = table[2] ^ table[1]// compute all values between two powers of two// i.e. 3, 5,6,7, 9,10,11,12,13,14,15, 17,...for (unsignedint powerOfTwo = 2; powerOfTwo <= 0x80; powerOfTwo <<= 1){uint32_t crcExtraBit = Crc32Lookup[0][powerOfTwo];for (unsignedint i = 1; i < powerOfTwo; i++)Crc32Lookup[0][i + powerOfTwo] = Crc32Lookup[0][i] ^ crcExtraBit;}
Endianness
Initially, my code for the Slicing-by-4/8/16 algorithms worked only on little endian computers, that means x86 and x64 (and similiar).
All other CRC algorithms on this page were okay with big endian machines,
but the way Slicing-by-4/8*16 accesses memory was strictly little endian focused.
Therefore I modified my Slicing-by-4/8/16 code in version 3 (download) and added a secondary path for those big endian computers.
The QEMU based PowerPC emulator I posted yesterday shows the correct results.
The Linux standard header endian.h defines __BYTE_ORDER which is either __LITTLE_ENDIAN or __BIG_ENDIAN.
There is no such thing for Visual C++ / Windows. If your system doesn't ship with endian.h you can use the constants on your own.
The platform dependent code becomes:
hide
// define endianess and some integer data types#ifdef _MSC_VERtypedefunsigned __int8 uint8_t;typedefunsigned __int32 uint32_t;typedef__int32int32_t;#define __LITTLE_ENDIAN 1234#define __BIG_ENDIAN 4321#define __BYTE_ORDER __LITTLE_ENDIAN#else// uint8_t, uint32_t, in32_t#include<stdint.h>// defines __BYTE_ORDER as __LITTLE_ENDIAN or __BIG_ENDIAN#include<endian.h>#endif
We need a method to swap the bytes of a 32 bit integer from one endianness to the other.
GCC and CLang offer __builtin_bswap32 which maps on most CPU architectures to a dedicated intrinsic assembler instruction
(Intel: bswap) and is super-fast.
The inner loop of crc32_4bytes needs to swap the CRC before XORing it and then reverses the shifts on big endian machines, too:
hide
Modificated crc32_4bytes#if __BYTE_ORDER == __BIG_ENDIAN// new path for big endianuint32_t one = *current++ ^ swap(crc);crc = Crc32Lookup[0][ one & 0xFF] ^Crc32Lookup[1][(one>> 8) & 0xFF] ^Crc32Lookup[2][(one>>16) & 0xFF] ^Crc32Lookup[3][(one>>24) & 0xFF];#else// pretty much the same as beforeuint32_tone = *current++ ^ crc;crc = Crc32Lookup[0][(one>>24) & 0xFF] ^Crc32Lookup[1][(one>>16) & 0xFF] ^Crc32Lookup[2][(one>> 8) & 0xFF] ^Crc32Lookup[3][ one & 0xFF];#endif
You might have noticed that I shuffled around the order of the Crc32Lookup in the little endian path as well
(in comparison to version 2 of my code). The algorithm becomes about 4% faster this way on my test computer.
The modifications to Slicing-by-8 are almost identical:
The Arduino is a cheap microcontroller including SRAM, Flash, USB and
lots of digital/analog I/O pins based on an Atmel AVR CPU (8 bit RISC architecture).
Frankly, I haven't used it in more than a year (even though it's a great toy)
but somehow I wanted to know how this little piece performs against a modern 64 bit desktop CPU (like my Core i7).
Arduino
Core i7 860
Arduinos can be easily programmed in C/C++ and, in fact, GCC is the most common compiler.
The most prominent change to the CRC code is that the look-up tables do not fit into the 2k SRAM.
Actually, crc32_1byte's table can be stored there (it's 1k) but reading memory access
to Flash is as fast as SRAM. Therefore the tables are declared a bit differently:
PROGMEM uint32_t crc32Lookup[8*256] = /* same table here */
And accessing an element is more work, too, instead of crc32Lookup[x][y] I have to write:
uint32_t z = pgm_read_dword_near(crc32Lookup + x*256 + y);
Arduino's CPU is clocked at 16 MHz, only 1/200th of my desktop CPU.
To compensate for the lower frequency, I reduced my dataset from 1 GByte to 1 MByte:
CRC32 of 1 MByte
table size
time
throughput
CPU cycles/byte
Original
-
10.4 seconds
100 kByte/s
approx. 160
Branch-free
-
40.6 seconds
25 kByte/s
approx. 650
Improved Branch-free
-
16.3 seconds
64 kByte/s
approx. 250
Half-Byte
64 bytes
9.5 seconds
110 kByte/s
approx. 150
Standard
1024 bytes
2.4 seconds
440 kByte/s
approx. 37
Slicing-By-4
4096 bytes
2.1 seconds
510 kByte/s
approx. 32
Slicing-By-8
8192 bytes
3.0 seconds
350 kByte/s
approx. 47
The Arduino doesn't come with fancy caches, multiple cores and other high-tech stuff.
Instead, most instructions need exactly one CPU cycle to execute. A very predictable chip.
All the branch-free tricks' arithmetic overhead severely decrease performance and in the end the
original algorithm remains the best among all table-less.
The slightly higher arithmetic complexity of Slicing-by-8 causes a lower throughput compared to
the overall winner Slicing-by-4, too. I didn't even try Slicing-by-16.
Considering the available Flash of the Arduino (only 32 kByte), I would prefer the Standard
implementation. It's still faster than most Ethernet add-ons or the serial/USB connection.
The Arduino doesn't only consist of hardware: it's an Open Source IDE with a sufficiently large C/C++ library.
Unfortunately it hides the compiler settings and I'm pretty sure they optimize for size, not speed.
However, the original CRC algorithm can be made faster:
Not only the binary shrinks by a few bytes, the throughput surpasses the half-byte algorithm and
achieves 120 kByte/s (8.7 seconds for 1 MByte).
Manually unrolling the loop of course increases the binary against but manages 150 kByte/s
(6.7 seconds).
Here is an overview of the algorithms I consider most appropriate for the Arduino
(size refers to the binary produces by Crc32Best.ino
and includes look-up tables if needed):
size (total)
size (delta)
throughput
CPU cycles/byte
(sketch overhead)
2296 bytes
-
-
-
Original
2454 bytes
+158 bytes
100 kByte/s
approx. 160
Shift Outside If-Clause
2384 bytes
+88 bytes
120 kByte/s
approx. 130
Unrolled
2616 bytes
+320 bytes
150 kByte/s
approx. 105
Standard
3406 bytes
+1110 bytes
440 kByte/s
approx. 37
Both downloadable sketches (see below) were created using a beta version of the upcoming Arduino 1.0 IDE
(GCC 4.3 backend).
If you still run an older version of the Arduino IDE just rename the file extension from
.ino to .pde.