Fast CRC32

posted by Stephan Brumme, updated

Error Checking

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: 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

CRC32 of 1 GByte published by bits per iteration table size time throughput CPU cycles/byte
Original (unknown) 1 - 29.2 seconds 35 MByte/s approx. 100
Branch-free (unknown) 1 - 16.7 seconds 61 MByte/s approx. 50
Improved Branch-free (unknown) 1 - 14.5 seconds 70 MByte/s approx. 40
Half-Byte (unknown) 4 64 bytes 4.8 seconds 210 MByte/s approx. 14
Tableless Full-Byte (sent to me by Hagai Gold) 8 - 6.2 seconds 160 MByte/s approx. 18
Tableless Full-Byte found in "Hacker's Delight"
by Henry S. Warren
8 - 6.3 seconds 155 MByte/s approx. 19
Standard Implementation Dilip V. Sarwate 8 1024 bytes 2.8 seconds 375 MByte/s approx. 8
Slicing-by-4 Intel Corp. 32 4096 bytes 0.95 or 1.2 seconds* 1050 or 840 MByte/s* approx. 3 or 4*
Slicing-by-8 Intel Corp. 64 8192 bytes 0.55 or 0.7 seconds* 1800 or 1400 MByte/s* approx. 1.75 or 2.25*
Slicing-by-16 based on Slicing-by-8,
improved by Bulat Ziganshin
128 16384 bytes 0.4 or 0.5 seconds* 3000 or 2000 MByte/s* approx. 1.1 or 1.5*
Slicing-by-16
4x unrolled with prefetch
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. Git users: scroll down to the repository link
Download  Crc32.h
Latest release: October 21, 2016, size: 3030 bytes, 66 lines

CRC32: 19983351
MD5: 3da627c55761c1a65dc6b4bc71750306
SHA1: 6fc6adb8b6cdf23e008d1785c2d66e13a68f824e
SHA256:fb93dff7c16c608dc73f7c4a6fb9c25eb38bff4a05e5552e017563972be4e70b

Download  Crc32.cpp
Latest release: October 21, 2016, size: 65.8 kBytes, 1120 lines

CRC32: 9d1ceee9
MD5: 4f963a6437c81618f194ffc83b70c41e
SHA1: cd75d5ec34eff3cf63e5fee8a69d2ff5085bc9dc
SHA256:cbc160f8f5746ae96a7fe555552b05b784944336ea6ced1fdd9a5359396292ce

Download  Crc32Test.cpp
Latest release: October 21, 2016, size: 4988 bytes, 161 lines

CRC32: 98c440c8
MD5: a17ceacb13ea73a72e152c4e8cbcbf44
SHA1: 087762dc528392aeb295390aa16f9ea1ca9c01aa
SHA256:baab8417594f3497a4a69e27016cbe13fdf91cb4cb6d0d7f6e815898da63b4c0

Stay up-to-date:git clone http://create.stephan-brumme.com/crc32/.git

Changelog

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, ... const uint32_t Polynomial = 0xEDB88320;
The basic algorithm processes the input data bit-by-bit:
hide Bitwise CRC32 uint32_t crc32_bitwise(const void* data, size_t length, uint32_t previousCrc32 = 0) { uint32_t crc = ~previousCrc32; // same as previousCrc32 ^ 0xFFFFFFFF unsigned char* current = (unsigned char*) data; while (length--) { crc ^= *current++; for (unsigned int j = 0; j < 8; j++) if (crc & 1) crc = (crc >> 1) ^ Polynomial; else crc = crc >> 1; } return ~crc; // same as crc ^ 0xFFFFFFFF }
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:
hide Branch-free for (unsigned int j = 0; j < 8; j++) crc = (crc >> 1) ^ (crc & 1)*Polynomial;
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:
hide Improved Branch-free for (unsigned int j = 0; j < 8; j++) crc = (crc >> 1) ^ (-int(crc & 1) & Polynomial);
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.

The final code of crc32_bitwise becomes:
hide Fastest Bitwise CRC32 uint32_t crc32_bitwise(const void* data, size_t length, uint32_t previousCrc32 = 0) { uint32_t crc = ~previousCrc32; unsigned char* current = (unsigned char*) data; while (length--) { crc ^= *current++; for (unsigned int j = 0; j < 8; j++) crc = (crc >> 1) ^ (-int(crc & 1) & Polynomial); } return ~crc; // same as crc ^ 0xFFFFFFFF }
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):
hide Precomputation of Look-up Table for (unsigned int i = 0; i <= 0xFF; i++) { uint32_t crc = i; for (unsigned int j = 0; j < 8; j++) crc = (crc >> 1) ^ (-int(crc & 1) & Polynomial); Crc32Lookup[i] = crc; }
Then the main CRC computation becomes extremely short:
hide Standard Implementation uint32_t crc32_1byte(const void* data, size_t length, uint32_t previousCrc32 = 0) { uint32_t crc = ~previousCrc32; unsigned char* current = (unsigned char*) data; while (length--) crc = (crc >> 8) ^ Crc32Lookup[(crc & 0xFF) ^ *current++]; return ~crc; }
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:
hide Precomputation of Slicing-by-8 // same as before for (unsigned int i = 0; i <= 0xFF; i++) { uint32_t crc = i; for (unsigned int j = 0; j < 8; j++) crc = (crc >> 1) ^ ((crc & 1) * Polynomial); Crc32Lookup[0][i] = crc; } for (unsigned int i = 0; i <= 0xFF; i++) { // for Slicing-by-4 and Slicing-by-8 Crc32Lookup[1][i] = (Crc32Lookup[0][i] >> 8) ^ Crc32Lookup[0][Crc32Lookup[0][i] & 0xFF]; Crc32Lookup[2][i] = (Crc32Lookup[1][i] >> 8) ^ Crc32Lookup[0][Crc32Lookup[1][i] & 0xFF]; Crc32Lookup[3][i] = (Crc32Lookup[2][i] >> 8) ^ Crc32Lookup[0][Crc32Lookup[2][i] & 0xFF]; // only Slicing-by-8 Crc32Lookup[4][i] = (Crc32Lookup[3][i] >> 8) ^ Crc32Lookup[0][Crc32Lookup[3][i] & 0xFF]; Crc32Lookup[5][i] = (Crc32Lookup[4][i] >> 8) ^ Crc32Lookup[0][Crc32Lookup[4][i] & 0xFF]; Crc32Lookup[6][i] = (Crc32Lookup[5][i] >> 8) ^ Crc32Lookup[0][Crc32Lookup[5][i] & 0xFF]; Crc32Lookup[7][i] = (Crc32Lookup[6][i] >> 8) ^ Crc32Lookup[0][Crc32Lookup[6][i] & 0xFF]; }
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:
hide Slicing-by-4 / Little Endian uint32_t crc32_4bytes(const void* data, size_t length, uint32_t previousCrc32 = 0) { uint32_t* current = (uint32_t*) data; uint32_t crc = ~previousCrc32; // process four bytes at once while (length >= 4) { crc ^= *current++; crc = Crc32Lookup[3][ crc & 0xFF] ^ Crc32Lookup[2][(crc>>8 ) & 0xFF] ^ Crc32Lookup[1][(crc>>16) & 0xFF] ^ Crc32Lookup[0][ crc>>24 ]; length -= 4; } const unsigned char* currentChar = (unsigned char*) current; // remaining 1 to 3 bytes while (length--) crc = (crc >> 8) ^ crc32Lookup[0][(crc & 0xFF) ^ *currentChar++]; return ~crc; }
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:
hide Slicing-by-8 uint32_t crc32_8bytes(const void* data, size_t length, uint32_t previousCrc32 = 0) { uint32_t* current = (uint32_t*) data; uint32_t crc = ~previousCrc32; // process eight bytes at once while (length >= 8) { uint32_t one = *current++ ^ crc; uint32_t two = *current++; crc = Crc32Lookup[7][ one & 0xFF] ^ Crc32Lookup[6][(one>> 8) & 0xFF] ^ Crc32Lookup[5][(one>>16) & 0xFF] ^ Crc32Lookup[4][ one>>24 ] ^ Crc32Lookup[3][ two & 0xFF] ^ Crc32Lookup[2][(two>> 8) & 0xFF] ^ Crc32Lookup[1][(two>>16) & 0xFF] ^ Crc32Lookup[0][ two>>24 ]; length -= 8; } unsigned char* currentChar = (unsigned char*) current; // remaining 1 to 7 bytes while (length--) crc = (crc >> 8) ^ crc32Lookup[0][(crc & 0xFF) ^ *currentChar++]; return ~crc; }
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__ #define PREFETCH(location) __builtin_prefetch(location) #else #define PREFETCH(location) ; #endif #endif
And here's my version of the Slicing-by-16 algorithm:
hide Slicing-by-16 /// compute CRC32 (Slicing-by-16 algorithm, prefetch upcoming data blocks) uint32_t crc32_16bytes_prefetch(const void* data, size_t length, uint32_t previousCrc32 = 0, size_t prefetchAhead = 256) { // CRC code is identical to crc32_16bytes (including unrolling), only added prefetching // 256 bytes look-ahead seems to be the sweet spot on Core i7 CPUs uint32_t crc = ~previousCrc32; // same as previousCrc32 ^ 0xFFFFFFFF const uint32_t* current = (const uint32_t*) data; // enabling optimization (at least -O2) automatically unrolls the for-loop const size_t Unroll = 4; const size_t BytesAtOnce = 16 * Unroll; while (length >= BytesAtOnce + prefetchAhead) { PREFETCH(((const char*) current) + prefetchAhead); for (size_t unrolling = 0; unrolling < Unroll; unrolling++) { #if __BYTE_ORDER == __BIG_ENDIAN uint32_t one = *current++ ^ swap(crc); uint32_t two = *current++; uint32_t three = *current++; uint32_t four = *current++ crc = Crc32Lookup[ 0][ four & 0xFF] ^ Crc32Lookup[ 1][(four >> 8) & 0xFF] ^ Crc32Lookup[ 2][(four >> 16) & 0xFF] ^ Crc32Lookup[ 3][(four >> 24) & 0xFF] ^ Crc32Lookup[ 4][ three & 0xFF] ^ Crc32Lookup[ 5][(three >> 8) & 0xFF] ^ Crc32Lookup[ 6][(three >> 16) & 0xFF] ^ Crc32Lookup[ 7][(three >> 24) & 0xFF] ^ Crc32Lookup[ 8][ two & 0xFF] ^ Crc32Lookup[ 9][(two >> 8) & 0xFF] ^ Crc32Lookup[10][(two >> 16) & 0xFF] ^ Crc32Lookup[11][(two >> 24) & 0xFF] ^ Crc32Lookup[12][ one & 0xFF] ^ Crc32Lookup[13][(one >> 8) & 0xFF] ^ Crc32Lookup[14][(one >> 16) & 0xFF] ^ Crc32Lookup[15][(one >> 24) & 0xFF]; #else uint32_t one = *current++ ^ crc; uint32_t two = *current++; uint32_t three = *current++; uint32_t four = *current++ crc = Crc32Lookup[ 0][(four >> 24) & 0xFF] ^ Crc32Lookup[ 1][(four >> 16) & 0xFF] ^ Crc32Lookup[ 2][(four >> 8) & 0xFF] ^ Crc32Lookup[ 3][ four & 0xFF] ^ Crc32Lookup[ 4][(three >> 24) & 0xFF] ^ Crc32Lookup[ 5][(three >> 16) & 0xFF] ^ Crc32Lookup[ 6][(three >> 8) & 0xFF] ^ Crc32Lookup[ 7][ three & 0xFF] ^ Crc32Lookup[ 8][(two >> 24) & 0xFF] ^ Crc32Lookup[ 9][(two >> 16) & 0xFF] ^ Crc32Lookup[10][(two >> 8) & 0xFF] ^ Crc32Lookup[11][ two & 0xFF] ^ Crc32Lookup[12][(one >> 24) & 0xFF] ^ Crc32Lookup[13][(one >> 16) & 0xFF] ^ Crc32Lookup[14][(one >> 8) & 0xFF] ^ Crc32Lookup[15][ one & 0xFF]; #endif } length -= BytesAtOnce; } const uint8_t* currentChar = (const uint8_t*) current; // remaining 1 to 63 bytes (standard algorithm) while (length-- != 0) crc = (crc >> 8) ^ Crc32Lookup[0][(crc & 0xFF) ^ *currentChar++]; return ~crc; // same as crc ^ 0xFFFFFFFF }

Split Data Into Chunks

If your data isn't available as single continuous block in memory, then you can split the CRC computations into chunks:
hide Chunked CRC uint32_t crc = 0; // also default parameter of crc32_xx functions while (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:
hide Half-byte CRC uint32_t crc32_halfbyte(const void* data, size_t length, uint32_t previousCrc32 = 0) { uint32_t crc = ~previousCrc32; unsigned char* current = (unsigned char*) data; static uint32_t int lut[16] = { 0x00000000,0x1DB71064,0x3B6E20C8,0x26D930AC,0x76DC4190,0x6B6B51F4,0x4DB26158,0x5005713C, 0xEDB88320,0xF00F9344,0xD6D6A3E8,0xCB61B38C,0x9B64C2B0,0x86D3D2D4,0xA00AE278,0xBDBDF21C }; while (length--) { crc = lut[(crc ^ *current ) & 0x0F] ^ (crc >> 4); crc = lut[(crc ^ (*current >> 4)) & 0x0F] ^ (crc >> 4); current++; } return ~crc; }
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.
hide Half-byte Table Generator for (unsigned int i = 0; i < 16; i++) { unsigned int crc = i * 16; for (unsigned int j = 0; j < 8; j++) crc = (crc >> 1) ^ (-int(crc & 1) & Polynomial); lut[i] = crc; }

Tableless Full-Byte Algorithms

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 tables uint32_t crc32_1byte_tableless(const void* data, size_t length, uint32_t previousCrc32) { uint32_t crc = ~previousCrc32; // same as previousCrc32 ^ 0xFFFFFFFF const uint8_t* current = (const uint8_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 tables uint32_t crc32_1byte_tableless2(const void* data, size_t length, uint32_t previousCrc32) { int32_t crc = ~previousCrc32; // note: signed integer, right shift distributes sign bit into lower bits const uint8_t* current = (const uint8_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 = 0xEDB88320 static const uint32_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) #if defined (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 #ifdef CRC32_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, 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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.

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_VER typedef unsigned __int8 uint8_t; typedef unsigned __int32 uint32_t; typedef __int32 int32_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.
hide Swap Endianness of a 32 Bit Integer /// swap endianess static inline uint32_t swap(uint32_t x) { #if defined(__GNUC__) || defined(__clang__) return __builtin_bswap32(x); #else return (x >> 24) | ((x >> 8) & 0x0000FF00) | ((x << 8) & 0x00FF0000) | (x << 24); #endif }
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 endian uint32_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 before uint32_t one = *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:
hide Modificated crc32_8bytes #if __BYTE_ORDER == __BIG_ENDIAN uint32_t one = *current++ ^ swap(crc); uint32_t two = *current++; crc = Crc32Lookup[0][ two & 0xFF] ^ Crc32Lookup[1][(two>> 8) & 0xFF] ^ Crc32Lookup[2][(two>>16) & 0xFF] ^ Crc32Lookup[3][(two>>24) & 0xFF] ^ Crc32Lookup[4][ one & 0xFF] ^ Crc32Lookup[5][(one>> 8) & 0xFF] ^ Crc32Lookup[6][(one>>16) & 0xFF] ^ Crc32Lookup[7][(one>>24) & 0xFF]; #else uint32_t one = *current++ ^ crc; uint32_t two = *current++; crc = Crc32Lookup[0][(two>>24) & 0xFF] ^ Crc32Lookup[1][(two>>16) & 0xFF] ^ Crc32Lookup[2][(two>> 8) & 0xFF] ^ Crc32Lookup[3][ two & 0xFF] ^ Crc32Lookup[4][(one>>24) & 0xFF] ^ Crc32Lookup[5][(one>>16) & 0xFF] ^ Crc32Lookup[6][(one>> 8) & 0xFF] ^ Crc32Lookup[7][ one & 0xFF]; #endif

Arduino

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
Arduino

Core i7 860
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:
hide crc32_bitwise / Tuned for Arduino uint32_t crc32_bitwise(const void* data, size_t length, uint32_t previousCrc32 = 0) { uint32_t crc = ~previousCrc32; uint8_t* current = (uint8_t*) data; while (length--) { crc ^= *current++; for (uint8_t j = 0; j < 8; j++) { //// instead of //if (crc & 1) // crc = (crc >> 1) ^ Polynomial; //else // crc = crc >> 1; uint8_t lowestBit = crc & 1; crc >>= 1; if (lowestBit) crc ^= Polynomial; } } return ~crc; }
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.
Download  Crc32Best.ino
Latest release: April 24, 2013, size: 5175 bytes, 142 lines

CRC32: 64734b18
MD5: cee9a8a180c1a1be5070d876a01c559f
SHA1: 87f7c96a0fa9f6ca074489da16fb558e167e6a9d
SHA256:fa9b3ac8dfd340b10edb77d3a08657e5cf02ba25af661a2082548cd30ba145cf

Stay up-to-date:git clone http://create.stephan-brumme.com/crc32/.git

Download  Crc32.ino
Latest release: April 24, 2013, size: 30.3 kBytes, 546 lines

CRC32: bfa47b26
MD5: bbd4479141875f990901128b5de48387
SHA1: 6a13eb56b257a2bdb5697a6d4a7df24d49792e8f
SHA256:a7b579d63e71a81489c307d64a7b6a25f98d65f9a9685d81c4f7f07c6a0c2535

Stay up-to-date:git clone http://create.stephan-brumme.com/crc32/.git


Javascript

Converting the bitwise algorithm to Javascript is pretty straightforward. The hardest part was dealing with hexadecimal output (function hex).

Live demo:     → CRC32: 00000000
hide // ////////////////////////////////////////////////////////// // crc32.js // Copyright (c) 2014 Stephan Brumme. All rights reserved. // see http://create.stephan-brumme.com/disclaimer.html // function hex(what) { // adjust negative numbers if (what < 0) what = 0xFFFFFFFF + what + 1; // convert to hexadecimal string var result = what.toString(16); // add leading zeros return ('0000000' + result).slice(-8); } function crc32_bitwise(text) { // CRC32b polynomial var Polynomial = 0xEDB88320; // start value var crc = 0xFFFFFFFF; for (var i = 0; i < text.length; i++) { // XOR next byte into state crc ^= text.charCodeAt(i); // process 8 bits for (var bit = 0; bit < 8; bit++) { // look at lowest bit if ((crc & 1) != 0) crc = (crc >>> 1) ^ Polynomial; else crc = crc >>> 1; } } // return hex string return hex(~crc); }
Download  crc32.js
Latest release: August 12, 2014, size: 917 bytes, 43 lines

CRC32: d383fd7f
MD5: 91e47c21aa10a4fdcbfc0f94f43f5268
SHA1: 4e3112c137300993b0722869e676977edd9ecac9
SHA256:ebd9ffc6e37008d57013b31392f1ad9bbd66d120b99cc26fe0e409c0fd5860ee

Stay up-to-date:git clone http://create.stephan-brumme.com/crc32/.git

Appendix

Cksum

The Unix tool cksum differs in a few details and generates a different CRC result. This is a very good explanation about it: http://developers.blog.box.com/2011/10/12/crc32-checksums-the-good-the-bad-and-the-ugly/
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