Calculate a 32-bit CRC lookup table in C/C++
I want to calculate a 32-bit CRC lookup table. One way I tried is by using the following code from this website:
#include <iostream>
#include <stdint.h>
void make_crc_table()
{
unsigned long POLYNOMIAL = 0x04c11db7;
unsigned long WIDTH = 8 * sizeof(unsigned long);
unsigned long TOPBIT = 1 << (WIDTH - 1);
unsigned long crcTable[256];
unsigned long remainder;
// Compute the remainder of each possible dividend
for (int dividend = 0; dividend < 256; ++dividend)
{
// Start with the dividend followed by zeros
remainder = dividend << (WIDTH - 8);
// Perform modulo-2 division, a bit at a time
for (unsigned long bit = 8; bit > 0; --bit)
{
// Try to divide the current data bit
if (remainder & TOPBIT)
{
remainder = (remainder << 1) ^ POLYNOMIAL;
}
else
{
remainder = (remainder << 1);
}
}
crcTable[dividend] = remainder;
}
// Print the CRC table
for (int i = 0; i < 256; i++)
{
if (i % 4 == 0)
{
std::cout <<"\n";
}
std::cout << std::hex << crcTable[i];
std::cout << ", ";
}
}
int main()
{
make_crc_table();
return 0;
}
Another way I tried is by using the following code that I found from this StackOverflow question, and the code can be downloaded from here in a file called CRC Calculator.zip
#include <iostream>
#include <stdint.h>
#define POLYNOMIAL 0x04C11DB7
uint32_t A_crcLookupTable[256] = {0};
#define WIDTH (8 * sizeof(uint32_t))
#define TOPBIT (((uint32_t)1) << (WIDTH - 1))
#define FP_reflect_DATA(_DATO) (_DATO)
#define FP_reflect_CRCTableValue(_CRCTableValue) (_CRCTableValue)
uint32_t F_CRC_ObtenValorDeTabla(uint8_t VP_Pos_Tabla)
{
uint32_t VP_CRCTableValue = 0;
uint8_t VP_Pos_bit = 0;
VP_CRCTableValue = ((uint32_t) FP_reflect_DATA(VP_Pos_Tabla)) << (WIDTH - 8);
for (VP_Pos_bit = 0; VP_Pos_bit < 8; VP_Pos_bit++)
{
if (VP_CRCTableValue & TOPBIT)
{
VP_CRCTableValue = (VP_CRCTableValue << 1) ^ POLYNOMIAL;
}
else
{
VP_CRCTableValue = (VP_CRCTableValue << 1);
}
}
return (FP_reflect_CRCTableValue(VP_CRCTableValue));
}
void F_CRC_InicializaTabla(void)
{
uint16_t VP_Pos_Array = 0;
for (VP_Pos_Array = 0; VP_Pos_Array < 256; VP_Pos_Array++)
{
A_crcLookupTable[VP_Pos_Array] = F_CRC_ObtenValorDeTabla((uint8_t)(VP_Pos_Array &0xFF));
}
}
void make_crc_table()
{
F_CRC_InicializaTabla();
// Print the CRC table
for (int i = 0; i < 256; i++)
{
if (i % 4 == 0)
{
std::cout <<"\n";
}
std::cout << std::hex << A_crcLookupTable[i];
std::cout << ", ";
}
}
int main()
{
make_crc_table();
return 0;
}
Here is what the correct final table should be, based on this link:
// The constants here are for the CRC-32 generator
// polynomial, as defined in the Microsoft
// Systems Journal, March 1995, pp. 107-108
CONST
table: ARRAY[0..255] OF DWORD =
($00000000, $77073096, $EE0E612C, $990951BA,
$076DC419, $706AF48F, $E963A535, $9E6495A3,
$0EDB8832, $79DCB8A4, $E0D5E91E, $97D2D988,
$09B64C2B, $7EB17CBD, $E7B82D07, $90BF1D91,
$1DB71064, $6AB020F2, $F3B97148, $84BE41DE,
$1ADAD47D, $6DDDE4EB, $F4D4B551, $83D385C7,
$136C9856, $646BA8C0, $FD62F97A, $8A65C9EC,
$14015C4F, $63066CD9, $FA0F3D63, $8D080DF5,
$3B6E20C8, $4C69105E, $D56041E4, $A2677172,
$3C03E4D1, $4B04D447, $D20D85FD, $A50AB56B,
$35B5A8FA, $42B2986C, $DBBBC9D6, $ACBCF940,
$32D86CE3, $45DF5C75, $DCD60DCF, $ABD13D59,
$26D930AC, $51DE003A, $C8D75180, $BFD06116,
$21B4F4B5, $56B3C423, $CFBA9599, $B8BDA50F,
$2802B89E, $5F058808, $C60CD9B2, $B10BE924,
$2F6F7C87, $58684C11, $C1611DAB, $B6662D3D,
$76DC4190, $01DB7106, $98D220BC, $EFD5102A,
$71B18589, $06B6B51F, $9FBFE4A5, $E8B8D433,
$7807C9A2, $0F00F934, $9609A88E, $E10E9818,
$7F6A0DBB, $086D3D2D, $91646C97, $E6635C01,
$6B6B51F4, $1C6C6162, $856530D8, $F262004E,
$6C0695ED, $1B01A57B, $8208F4C1, $F50FC457,
$65B0D9C6, $12B7E950, $8BBEB8EA, $FCB9887C,
$62DD1DDF, $15DA2D49, $8CD37CF3, $FBD44C65,
$4DB26158, $3AB551CE, $A3BC0074, $D4BB30E2,
$4ADFA541, $3DD895D7, $A4D1C46D, $D3D6F4FB,
$4369E96A, $346ED9FC, $AD678846, $DA60B8D0,
$44042D73, $33031DE5, $AA0A4C5F, $DD0D7CC9,
$5005713C, $270241AA, $BE0B1010, $C90C2086,
$5768B525, $206F85B3, $B966D409, $CE61E49F,
$5EDEF90E, $29D9C998, $B0D09822, $C7D7A8B4,
$59B33D17, $2EB40D81, $B7BD5C3B, $C0BA6CAD,
$EDB88320, $9ABFB3B6, $03B6E20C, $74B1D29A,
$EAD54739, $9DD277AF, $04DB2615, $73DC1683,
$E3630B12, $94643B84, $0D6D6A3E, $7A6A5AA8,
$E40ECF0B, $9309FF9D, $0A00AE27, $7D079EB1,
$F00F9344, $8708A3D2, $1E01F268, $6906C2FE,
$F762575D, $806567CB, $196C3671, $6E6B06E7,
$FED41B76, $89D32BE0, $10DA7A5A, $67DD4ACC,
$F9B9DF6F, $8EBEEFF9, $17B7BE43, $60B08ED5,
$D6D6A3E8, $A1D1937E, $38D8C2C4, $4FDFF252,
$D1BB67F1, $A6BC5767, $3FB506DD, $48B2364B,
$D80D2BDA, $AF0A1B4C, $36034AF6, $41047A60,
$DF60EFC3, $A867DF55, $316E8EEF, $4669BE79,
$CB61B38C, $BC66831A, $256FD2A0, $5268E236,
$CC0C7795, $BB0B4703, $220216B9, $5505262F,
$C5BA3BBE, $B2BD0B28, $2BB45A92, $5CB36A04,
$C2D7FFA7, $B5D0CF31, $2CD99E8B, $5BDEAE1D,
$9B64C2B0, $EC63F226, $756AA39C, $026D930A,
$9C0906A9, $EB0E363F, $72076785, $05005713,
$95BF4A82, $E2B87A14, $7BB12BAE, $0CB61B38,
$92D28E9B, $E5D5BE0D, $7CDCEFB7, $0BDBDF21,
$86D3D2D4, $F1D4E242, $68DDB3F8, $1FDA836E,
$81BE16CD, $F6B9265B, $6FB077E1, $18B74777,
$88085AE6, $FF0F6A70, $66063BCA, $11010B5C,
$8F659EFF, $F862AE69, $616BFFD3, $166CCF45,
$A00AE278, $D70DD2EE, $4E048354, $3903B3C2,
$A7672661, $D06016F7, $4969474D, $3E6E77DB,
$AED16A4A, $D9D65ADC, $40DF0B66, $37D83BF0,
$A9BCAE53, $DEBB9EC5, $47B2CF7F, $30B5FFE9,
$BDBDF21C, $CABAC28A, $53B39330, $24B4A3A6,
$BAD03605, $CDD70693, $54DE5729, $23D967BF,
$B3667A2E, $C4614AB8, $5D681B02, $2A6F2B94,
$B40BBE37, $C30C8EA1, $5A05DF1B, $2D02EF8D);
However, this is what my output is from both programs (I diffed the output, and it's the same for both of them), and it's incorrect:
0, 4c11db7, 9823b6e, d4326d9,
130476dc, 17c56b6b, 1a864db2, 1e475005,
2608edb8, 22c9f00f, 2f8ad6d6, 2b4bcb61,
350c9b64, 31cd86d3, 3c8ea00a, 384fbdbd,
4c11db70, 48d0c6c7, 4593e01e, 4152fda9,
5f15adac, 5bd4b01b, 569796c2, 52568b75,
6a1936c8, 6ed82b7f, 639b0da6, 675a1011,
791d4014, 7ddc5da3, 709f7b7a, 745e66cd,
9823b6e0, 9ce2ab57, 91a18d8e, 95609039,
8b27c03c, 8fe6dd8b, 82a5fb52, 8664e6e5,
be2b5b58, baea46ef, b7a96036, b3687d81,
ad2f2d84, a9ee3033, a4ad16ea, a06c0b5d,
d4326d90, d0f37027, ddb056fe, d9714b49,
c7361b4c, c3f706fb, ceb42022, ca753d95,
f23a8028, f6fb9d9f, fbb8bb46, ff79a6f1,
e13ef6f4, e5ffeb43, e8bccd9a, ec7dd02d,
34867077, 30476dc0, 3d044b19, 39c556ae,
278206ab, 23431b1c, 2e003dc5, 2ac12072,
128e9dcf, 164f8078, 1b0ca6a1, 1fcdbb16,
18aeb13, 54bf6a4, 808d07d, cc9cdca,
7897ab07, 7c56b6b0, 71159069, 75d48dde,
6b93dddb, 6f52c06c, 6211e6b5, 66d0fb02,
5e9f46bf, 5a5e5b08, 571d7dd1, 53dc6066,
4d9b3063, 495a2dd4, 44190b0d, 40d816ba,
aca5c697, a864db20, a527fdf9, a1e6e04e,
bfa1b04b, bb60adfc, b6238b25, b2e29692,
8aad2b2f, 8e6c3698, 832f1041, 87ee0df6,
99a95df3, 9d684044, 902b669d, 94ea7b2a,
e0b41de7, e4750050, e9362689, edf73b3e,
f3b06b3b, f771768c, fa325055, fef34de2,
c6bcf05f, c27dede8, cf3ecb31, cbffd686,
d5b88683, d1799b34, dc3abded, d8fba05a,
690ce0ee, 6dcdfd59, 608edb80, 644fc637,
7a089632, 7ec98b85, 738aad5c, 774bb0eb,
4f040d56, 4bc510e1, 46863638, 42472b8f,
5c007b8a, 58c1663d, 558240e4, 51435d53,
251d3b9e, 21dc2629, 2c9f00f0, 285e1d47,
36194d42, 32d850f5, 3f9b762c, 3b5a6b9b,
315d626, 7d4cb91, a97ed48, e56f0ff,
1011a0fa, 14d0bd4d, 19939b94, 1d528623,
f12f560e, f5ee4bb9, f8ad6d60, fc6c70d7,
e22b20d2, e6ea3d65, eba91bbc, ef68060b,
d727bbb6, d3e6a601, dea580d8, da649d6f,
c423cd6a, c0e2d0dd, cda1f604, c960ebb3,
bd3e8d7e, b9ff90c9, b4bcb610, b07daba7,
ae3afba2, aafbe615, a7b8c0cc, a379dd7b,
9b3660c6, 9ff77d71, 92b45ba8, 9675461f,
8832161a, 8cf30bad, 81b02d74, 857130c3,
5d8a9099, 594b8d2e, 5408abf7, 50c9b640,
4e8ee645, 4a4ffbf2, 470cdd2b, 43cdc09c,
7b827d21, 7f436096, 7200464f, 76c15bf8,
68860bfd, 6c47164a, 61043093, 65c52d24,
119b4be9, 155a565e, 18197087, 1cd86d30,
29f3d35, 65e2082, b1d065b, fdc1bec,
3793a651, 3352bbe6, 3e119d3f, 3ad08088,
2497d08d, 2056cd3a, 2d15ebe3, 29d4f654,
c5a92679, c1683bce, cc2b1d17, c8ea00a0,
d6ad50a5, d26c4d12, df2f6bcb, dbee767c,
e3a1cbc1, e760d676, ea23f0af, eee2ed18,
f0a5bd1d, f464a0aa, f9278673, fde69bc4,
89b8fd09, 8d79e0be, 803ac667, 84fbdbd0,
9abc8bd5, 9e7d9662, 933eb0bb, 97ffad0c,
afb010b1, ab710d06, a6322bdf, a2f33668,
bcb4666d, b8757bda, b5365d03, b1f740b4,
Answer
The bits are reversed. Note that the table entry for array[0x80] (0x80 is 0x01 reversed) = 0xEDB88320, which is 0x04C11DB7 reversed.
Example code:
#include <iostream>
#include <iomanip>
void make_crc_table(unsigned long crcTable[]) {
unsigned long POLYNOMIAL = 0xEDB88320;
unsigned long remainder;
unsigned char b = 0;
do {
// Start with the data byte
remainder = b;
for (unsigned long bit = 8; bit > 0; --bit) {
if (remainder & 1)
remainder = (remainder >> 1) ^ POLYNOMIAL;
else
remainder = (remainder >> 1);
}
crcTable[(size_t)b] = remainder;
} while(0 != ++b);
}
unsigned long gen_crc(unsigned char *p, size_t n, unsigned long crcTable[]) {
unsigned long crc = 0xfffffffful;
size_t i;
for(i = 0; i < n; i++)
crc = crcTable[*p++ ^ (crc&0xff)] ^ (crc>>8);
return(~crc);
}
int main() {
unsigned long crcTable[256];
make_crc_table(crcTable);
// Print the CRC table
for (size_t i = 0; i < 256; i++) {
std::cout << std::setfill('0') << std::setw(8) << std::hex << crcTable[i];
if (i % 4 == 3)
std::cout << std::endl;
else
std::cout << ", ";
}
return 0;
}