28
// The constants here are for the CRC-32 generator
29
// polynomial, as defined in the Microsoft
30
// Systems Journal, March 1995, pp. 107-108
32
const unsigned int CRCTable [256] =
34
0x00000000, 0x77073096, 0xEE0E612C, 0x990951BA,
35
0x076DC419, 0x706AF48F, 0xE963A535, 0x9E6495A3,
36
0x0EDB8832, 0x79DCB8A4, 0xE0D5E91E, 0x97D2D988,
37
0x09B64C2B, 0x7EB17CBD, 0xE7B82D07, 0x90BF1D91,
38
0x1DB71064, 0x6AB020F2, 0xF3B97148, 0x84BE41DE,
39
0x1ADAD47D, 0x6DDDE4EB, 0xF4D4B551, 0x83D385C7,
40
0x136C9856, 0x646BA8C0, 0xFD62F97A, 0x8A65C9EC,
41
0x14015C4F, 0x63066CD9, 0xFA0F3D63, 0x8D080DF5,
42
0x3B6E20C8, 0x4C69105E, 0xD56041E4, 0xA2677172,
43
0x3C03E4D1, 0x4B04D447, 0xD20D85FD, 0xA50AB56B,
44
0x35B5A8FA, 0x42B2986C, 0xDBBBC9D6, 0xACBCF940,
45
0x32D86CE3, 0x45DF5C75, 0xDCD60DCF, 0xABD13D59,
46
0x26D930AC, 0x51DE003A, 0xC8D75180, 0xBFD06116,
47
0x21B4F4B5, 0x56B3C423, 0xCFBA9599, 0xB8BDA50F,
48
0x2802B89E, 0x5F058808, 0xC60CD9B2, 0xB10BE924,
49
0x2F6F7C87, 0x58684C11, 0xC1611DAB, 0xB6662D3D,
51
0x76DC4190, 0x01DB7106, 0x98D220BC, 0xEFD5102A,
52
0x71B18589, 0x06B6B51F, 0x9FBFE4A5, 0xE8B8D433,
53
0x7807C9A2, 0x0F00F934, 0x9609A88E, 0xE10E9818,
54
0x7F6A0DBB, 0x086D3D2D, 0x91646C97, 0xE6635C01,
55
0x6B6B51F4, 0x1C6C6162, 0x856530D8, 0xF262004E,
56
0x6C0695ED, 0x1B01A57B, 0x8208F4C1, 0xF50FC457,
57
0x65B0D9C6, 0x12B7E950, 0x8BBEB8EA, 0xFCB9887C,
58
0x62DD1DDF, 0x15DA2D49, 0x8CD37CF3, 0xFBD44C65,
59
0x4DB26158, 0x3AB551CE, 0xA3BC0074, 0xD4BB30E2,
60
0x4ADFA541, 0x3DD895D7, 0xA4D1C46D, 0xD3D6F4FB,
61
0x4369E96A, 0x346ED9FC, 0xAD678846, 0xDA60B8D0,
62
0x44042D73, 0x33031DE5, 0xAA0A4C5F, 0xDD0D7CC9,
63
0x5005713C, 0x270241AA, 0xBE0B1010, 0xC90C2086,
64
0x5768B525, 0x206F85B3, 0xB966D409, 0xCE61E49F,
65
0x5EDEF90E, 0x29D9C998, 0xB0D09822, 0xC7D7A8B4,
66
0x59B33D17, 0x2EB40D81, 0xB7BD5C3B, 0xC0BA6CAD,
68
0xEDB88320, 0x9ABFB3B6, 0x03B6E20C, 0x74B1D29A,
69
0xEAD54739, 0x9DD277AF, 0x04DB2615, 0x73DC1683,
70
0xE3630B12, 0x94643B84, 0x0D6D6A3E, 0x7A6A5AA8,
71
0xE40ECF0B, 0x9309FF9D, 0x0A00AE27, 0x7D079EB1,
72
0xF00F9344, 0x8708A3D2, 0x1E01F268, 0x6906C2FE,
73
0xF762575D, 0x806567CB, 0x196C3671, 0x6E6B06E7,
74
0xFED41B76, 0x89D32BE0, 0x10DA7A5A, 0x67DD4ACC,
75
0xF9B9DF6F, 0x8EBEEFF9, 0x17B7BE43, 0x60B08ED5,
76
0xD6D6A3E8, 0xA1D1937E, 0x38D8C2C4, 0x4FDFF252,
77
0xD1BB67F1, 0xA6BC5767, 0x3FB506DD, 0x48B2364B,
78
0xD80D2BDA, 0xAF0A1B4C, 0x36034AF6, 0x41047A60,
79
0xDF60EFC3, 0xA867DF55, 0x316E8EEF, 0x4669BE79,
80
0xCB61B38C, 0xBC66831A, 0x256FD2A0, 0x5268E236,
81
0xCC0C7795, 0xBB0B4703, 0x220216B9, 0x5505262F,
82
0xC5BA3BBE, 0xB2BD0B28, 0x2BB45A92, 0x5CB36A04,
83
0xC2D7FFA7, 0xB5D0CF31, 0x2CD99E8B, 0x5BDEAE1D,
85
0x9B64C2B0, 0xEC63F226, 0x756AA39C, 0x026D930A,
86
0x9C0906A9, 0xEB0E363F, 0x72076785, 0x05005713,
87
0x95BF4A82, 0xE2B87A14, 0x7BB12BAE, 0x0CB61B38,
88
0x92D28E9B, 0xE5D5BE0D, 0x7CDCEFB7, 0x0BDBDF21,
89
0x86D3D2D4, 0xF1D4E242, 0x68DDB3F8, 0x1FDA836E,
90
0x81BE16CD, 0xF6B9265B, 0x6FB077E1, 0x18B74777,
91
0x88085AE6, 0xFF0F6A70, 0x66063BCA, 0x11010B5C,
92
0x8F659EFF, 0xF862AE69, 0x616BFFD3, 0x166CCF45,
93
0xA00AE278, 0xD70DD2EE, 0x4E048354, 0x3903B3C2,
94
0xA7672661, 0xD06016F7, 0x4969474D, 0x3E6E77DB,
95
0xAED16A4A, 0xD9D65ADC, 0x40DF0B66, 0x37D83BF0,
96
0xA9BCAE53, 0xDEBB9EC5, 0x47B2CF7F, 0x30B5FFE9,
97
0xBDBDF21C, 0xCABAC28A, 0x53B39330, 0x24B4A3A6,
98
0xBAD03605, 0xCDD70693, 0x54DE5729, 0x23D967BF,
99
0xB3667A2E, 0xC4614AB8, 0x5D681B02, 0x2A6F2B94,
100
0xB40BBE37, 0xC30C8EA1, 0x5A05DF1B, 0x2D02EF8D
108
void NCRC32::Initialize(void)
110
Memset(&CRCTable, 0, sizeof(CRCTable));
111
// 256 values representing ASCII character codes.
112
for(int iCodes = 0; iCodes <= 0xFF; iCodes++)
114
CRCTable[iCodes] = Reflect(iCodes, 8) << 24;
115
for(int iPos = 0; iPos < 8; iPos++)
117
CRCTable[iCodes] = (CRCTable[iCodes] << 1) ^ (CRCTable[iCodes] & (1 << 31) ? CRC32_POLYNOMIAL : 0);
119
CRCTable[iCodes] = Reflect(CRCTable[iCodes], 32);
123
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
124
// Reflection is a requirement for the official CRC-32 standard.
125
// You can create CRCs without it, but they won't conform to the standard.
126
t_u32 NCRC32::Reflect(t_u32 ulReflect, char cChar)
130
// Swap bit 0 for bit 7 bit 1 For bit 6, etc....
131
for(int iPos = 1; iPos < (cChar + 1); iPos++)
134
ulValue |= 1 << (cChar - iPos);
141
t_u32 NCRC32::FileCRC(const char *sFileName)
143
t_u32 ulCRC = 0xffffffff;
145
FILE *fSource = NULL;
146
char sBuf[CRC32BUFSZ];
147
t_u32 iBytesRead = 0;
150
if(FOPEN_S(&fSource, sFileName, "rb") != 0)
152
if(FOPEN_S(fSource, sFileName, "rb") != 0)
160
iBytesRead = (t_u32)fread(sBuf, sizeof(char), CRC32BUFSZ, fSource);
161
PartialCRC(&ulCRC, sBuf, iBytesRead);
162
}while(iBytesRead == CRC32BUFSZ);
166
return(ulCRC ^ 0xffffffff);
169
// This function uses the CRCTable lookup table to generate a CRC for sData
170
t_u32 NCRC32::FullCRC(const char *sData, t_u32 ulLength)
172
t_u32 ulCRC = 0xffffffff;
173
PartialCRC(&ulCRC, sData, ulLength);
174
return ulCRC ^ 0xffffffff;
177
// Perform the algorithm on each character
178
// in the string, using the lookup table values.
179
void NCRC32::PartialCRC(t_u32 *ulInCRC, const char *sData, t_u32 ulLength)
183
*ulInCRC = (*ulInCRC >> 8) ^ CRCTable[(*ulInCRC & 0xFF) ^ *sData++];
190
* A brief CRC tutorial.
192
* A CRC is a long-division remainder. You add the CRC to the message,
193
* and the whole thing (message+CRC) is a multiple of the given
194
* CRC polynomial. To check the CRC, you can either check that the
195
* CRC matches the recomputed value, *or* you can check that the
196
* remainder computed on the message+CRC is 0. This latter approach
197
* is used by a lot of hardware implementations, and is why so many
198
* protocols put the end-of-frame flag after the CRC.
200
* It's actually the same long division you learned in school, except that
201
* - We're working in binary, so the digits are only 0 and 1, and
202
* - When dividing polynomials, there are no carries. Rather than add and
203
* subtract, we just xor. Thus, we tend to get a bit sloppy about
204
* the difference between adding and subtracting.
206
* A 32-bit CRC polynomial is actually 33 bits long. But since it's
207
* 33 bits long, bit 32 is always going to be set, so usually the CRC
208
* is written in hex with the most significant bit omitted. (If you're
209
* familiar with the IEEE 754 floating-point format, it's the same idea.)
211
* Note that a CRC is computed over a string of *bits*, so you have
212
* to decide on the endianness of the bits within each byte. To get
213
* the best error-detecting properties, this should correspond to the
214
* order they're actually sent. For example, standard RS-232 serial is
215
* little-endian; the most significant bit (sometimes used for parity)
216
* is sent last. And when appending a CRC word to a message, you should
217
* do it in the right order, matching the endianness.
219
* Just like with ordinary division, the remainder is always smaller than
220
* the divisor (the CRC polynomial) you're dividing by. Each step of the
221
* division, you take one more digit (bit) of the dividend and append it
222
* to the current remainder. Then you figure out the appropriate multiple
223
* of the divisor to subtract to being the remainder back into range.
224
* In binary, it's easy - it has to be either 0 or 1, and to make the
225
* XOR cancel, it's just a copy of bit 32 of the remainder.
227
* When computing a CRC, we don't care about the quotient, so we can
228
* throw the quotient bit away, but subtract the appropriate multiple of
229
* the polynomial from the remainder and we're back to where we started,
230
* ready to process the next bit.
232
* A big-endian CRC written this way would be coded like:
233
* for (i = 0; i < input_bits; i++) {
234
* multiple = remainder & 0x80000000 ? CRCPOLY : 0;
235
* remainder = (remainder << 1 | next_input_bit()) ^ multiple;
237
* Notice how, to get at bit 32 of the shifted remainder, we look
238
* at bit 31 of the remainder *before* shifting it.
240
* But also notice how the next_input_bit() bits we're shifting into
241
* the remainder don't actually affect any decision-making until
242
* 32 bits later. Thus, the first 32 cycles of this are pretty boring.
243
* Also, to add the CRC to a message, we need a 32-bit-long hole for it at
244
* the end, so we have to add 32 extra cycles shifting in zeros at the
245
* end of every message,
247
* So the standard trick is to rearrage merging in the next_input_bit()
248
* until the moment it's needed. Then the first 32 cycles can be precomputed,
249
* and merging in the final 32 zero bits to make room for the CRC can be
251
* This changes the code to:
252
* for (i = 0; i < input_bits; i++) {
253
* remainder ^= next_input_bit() << 31;
254
* multiple = (remainder & 0x80000000) ? CRCPOLY : 0;
255
* remainder = (remainder << 1) ^ multiple;
257
* With this optimization, the little-endian code is simpler:
258
* for (i = 0; i < input_bits; i++) {
259
* remainder ^= next_input_bit();
260
* multiple = (remainder & 1) ? CRCPOLY : 0;
261
* remainder = (remainder >> 1) ^ multiple;
264
* Note that the other details of endianness have been hidden in CRCPOLY
265
* (which must be bit-reversed) and next_input_bit().
267
* However, as long as next_input_bit is returning the bits in a sensible
268
* order, we can actually do the merging 8 or more bits at a time rather
269
* than one bit at a time:
270
* for (i = 0; i < input_bytes; i++) {
271
* remainder ^= next_input_byte() << 24;
272
* for (j = 0; j < 8; j++) {
273
* multiple = (remainder & 0x80000000) ? CRCPOLY : 0;
274
* remainder = (remainder << 1) ^ multiple;
277
* Or in little-endian:
278
* for (i = 0; i < input_bytes; i++) {
279
* remainder ^= next_input_byte();
280
* for (j = 0; j < 8; j++) {
281
* multiple = (remainder & 1) ? CRCPOLY : 0;
282
* remainder = (remainder << 1) ^ multiple;
285
* If the input is a multiple of 32 bits, you can even XOR in a 32-bit
286
* word at a time and increase the inner loop count to 32.
288
* You can also mix and match the two loop styles, for example doing the
289
* bulk of a message byte-at-a-time and adding bit-at-a-time processing
290
* for any fractional bytes at the end.
292
* The only remaining optimization is to the byte-at-a-time table method.
293
* Here, rather than just shifting one bit of the remainder to decide
294
* in the correct multiple to subtract, we can shift a byte at a time.
295
* This produces a 40-bit (rather than a 33-bit) intermediate remainder,
296
* but again the multiple of the polynomial to subtract depends only on
297
* the high bits, the high 8 bits in this case.
299
* The multile we need in that case is the low 32 bits of a 40-bit
300
* value whose high 8 bits are given, and which is a multiple of the
301
* generator polynomial. This is simply the CRC-32 of the given
304
* Two more details: normally, appending zero bits to a message which
305
* is already a multiple of a polynomial produces a larger multiple of that
306
* polynomial. To enable a CRC to detect this condition, it's common to
307
* invert the CRC before appending it. This makes the remainder of the
308
* message+crc come out not as zero, but some fixed non-zero value.
310
* The same problem applies to zero bits prepended to the message, and
311
* a similar solution is used. Instead of starting with a remainder of
312
* 0, an initial remainder of all ones is used. As long as you start
313
* the same way on decoding, it doesn't make a difference.
28
// The constants here are for the CRC-32 generator
29
// polynomial, as defined in the Microsoft
30
// Systems Journal, March 1995, pp. 107-108
32
const unsigned int CRCTable [256] =
34
0x00000000, 0x77073096, 0xEE0E612C, 0x990951BA,
35
0x076DC419, 0x706AF48F, 0xE963A535, 0x9E6495A3,
36
0x0EDB8832, 0x79DCB8A4, 0xE0D5E91E, 0x97D2D988,
37
0x09B64C2B, 0x7EB17CBD, 0xE7B82D07, 0x90BF1D91,
38
0x1DB71064, 0x6AB020F2, 0xF3B97148, 0x84BE41DE,
39
0x1ADAD47D, 0x6DDDE4EB, 0xF4D4B551, 0x83D385C7,
40
0x136C9856, 0x646BA8C0, 0xFD62F97A, 0x8A65C9EC,
41
0x14015C4F, 0x63066CD9, 0xFA0F3D63, 0x8D080DF5,
42
0x3B6E20C8, 0x4C69105E, 0xD56041E4, 0xA2677172,
43
0x3C03E4D1, 0x4B04D447, 0xD20D85FD, 0xA50AB56B,
44
0x35B5A8FA, 0x42B2986C, 0xDBBBC9D6, 0xACBCF940,
45
0x32D86CE3, 0x45DF5C75, 0xDCD60DCF, 0xABD13D59,
46
0x26D930AC, 0x51DE003A, 0xC8D75180, 0xBFD06116,
47
0x21B4F4B5, 0x56B3C423, 0xCFBA9599, 0xB8BDA50F,
48
0x2802B89E, 0x5F058808, 0xC60CD9B2, 0xB10BE924,
49
0x2F6F7C87, 0x58684C11, 0xC1611DAB, 0xB6662D3D,
51
0x76DC4190, 0x01DB7106, 0x98D220BC, 0xEFD5102A,
52
0x71B18589, 0x06B6B51F, 0x9FBFE4A5, 0xE8B8D433,
53
0x7807C9A2, 0x0F00F934, 0x9609A88E, 0xE10E9818,
54
0x7F6A0DBB, 0x086D3D2D, 0x91646C97, 0xE6635C01,
55
0x6B6B51F4, 0x1C6C6162, 0x856530D8, 0xF262004E,
56
0x6C0695ED, 0x1B01A57B, 0x8208F4C1, 0xF50FC457,
57
0x65B0D9C6, 0x12B7E950, 0x8BBEB8EA, 0xFCB9887C,
58
0x62DD1DDF, 0x15DA2D49, 0x8CD37CF3, 0xFBD44C65,
59
0x4DB26158, 0x3AB551CE, 0xA3BC0074, 0xD4BB30E2,
60
0x4ADFA541, 0x3DD895D7, 0xA4D1C46D, 0xD3D6F4FB,
61
0x4369E96A, 0x346ED9FC, 0xAD678846, 0xDA60B8D0,
62
0x44042D73, 0x33031DE5, 0xAA0A4C5F, 0xDD0D7CC9,
63
0x5005713C, 0x270241AA, 0xBE0B1010, 0xC90C2086,
64
0x5768B525, 0x206F85B3, 0xB966D409, 0xCE61E49F,
65
0x5EDEF90E, 0x29D9C998, 0xB0D09822, 0xC7D7A8B4,
66
0x59B33D17, 0x2EB40D81, 0xB7BD5C3B, 0xC0BA6CAD,
68
0xEDB88320, 0x9ABFB3B6, 0x03B6E20C, 0x74B1D29A,
69
0xEAD54739, 0x9DD277AF, 0x04DB2615, 0x73DC1683,
70
0xE3630B12, 0x94643B84, 0x0D6D6A3E, 0x7A6A5AA8,
71
0xE40ECF0B, 0x9309FF9D, 0x0A00AE27, 0x7D079EB1,
72
0xF00F9344, 0x8708A3D2, 0x1E01F268, 0x6906C2FE,
73
0xF762575D, 0x806567CB, 0x196C3671, 0x6E6B06E7,
74
0xFED41B76, 0x89D32BE0, 0x10DA7A5A, 0x67DD4ACC,
75
0xF9B9DF6F, 0x8EBEEFF9, 0x17B7BE43, 0x60B08ED5,
76
0xD6D6A3E8, 0xA1D1937E, 0x38D8C2C4, 0x4FDFF252,
77
0xD1BB67F1, 0xA6BC5767, 0x3FB506DD, 0x48B2364B,
78
0xD80D2BDA, 0xAF0A1B4C, 0x36034AF6, 0x41047A60,
79
0xDF60EFC3, 0xA867DF55, 0x316E8EEF, 0x4669BE79,
80
0xCB61B38C, 0xBC66831A, 0x256FD2A0, 0x5268E236,
81
0xCC0C7795, 0xBB0B4703, 0x220216B9, 0x5505262F,
82
0xC5BA3BBE, 0xB2BD0B28, 0x2BB45A92, 0x5CB36A04,
83
0xC2D7FFA7, 0xB5D0CF31, 0x2CD99E8B, 0x5BDEAE1D,
85
0x9B64C2B0, 0xEC63F226, 0x756AA39C, 0x026D930A,
86
0x9C0906A9, 0xEB0E363F, 0x72076785, 0x05005713,
87
0x95BF4A82, 0xE2B87A14, 0x7BB12BAE, 0x0CB61B38,
88
0x92D28E9B, 0xE5D5BE0D, 0x7CDCEFB7, 0x0BDBDF21,
89
0x86D3D2D4, 0xF1D4E242, 0x68DDB3F8, 0x1FDA836E,
90
0x81BE16CD, 0xF6B9265B, 0x6FB077E1, 0x18B74777,
91
0x88085AE6, 0xFF0F6A70, 0x66063BCA, 0x11010B5C,
92
0x8F659EFF, 0xF862AE69, 0x616BFFD3, 0x166CCF45,
93
0xA00AE278, 0xD70DD2EE, 0x4E048354, 0x3903B3C2,
94
0xA7672661, 0xD06016F7, 0x4969474D, 0x3E6E77DB,
95
0xAED16A4A, 0xD9D65ADC, 0x40DF0B66, 0x37D83BF0,
96
0xA9BCAE53, 0xDEBB9EC5, 0x47B2CF7F, 0x30B5FFE9,
97
0xBDBDF21C, 0xCABAC28A, 0x53B39330, 0x24B4A3A6,
98
0xBAD03605, 0xCDD70693, 0x54DE5729, 0x23D967BF,
99
0xB3667A2E, 0xC4614AB8, 0x5D681B02, 0x2A6F2B94,
100
0xB40BBE37, 0xC30C8EA1, 0x5A05DF1B, 0x2D02EF8D
108
void NCRC32::Initialize(void)
110
Memset(&CRCTable, 0, sizeof(CRCTable));
111
// 256 values representing ASCII character codes.
112
for(int iCodes = 0; iCodes <= 0xFF; iCodes++)
114
CRCTable[iCodes] = Reflect(iCodes, 8) << 24;
115
for(int iPos = 0; iPos < 8; iPos++)
117
CRCTable[iCodes] = (CRCTable[iCodes] << 1) ^ (CRCTable[iCodes] & (1 << 31) ? CRC32_POLYNOMIAL : 0);
119
CRCTable[iCodes] = Reflect(CRCTable[iCodes], 32);
123
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
124
// Reflection is a requirement for the official CRC-32 standard.
125
// You can create CRCs without it, but they won't conform to the standard.
126
t_u32 NCRC32::Reflect(t_u32 ulReflect, char cChar)
130
// Swap bit 0 for bit 7 bit 1 For bit 6, etc....
131
for(int iPos = 1; iPos < (cChar + 1); iPos++)
134
ulValue |= 1 << (cChar - iPos);
141
t_u32 NCRC32::FileCRC(const char *sFileName)
143
t_u32 ulCRC = 0xffffffff;
145
FILE *fSource = NULL;
146
char sBuf[CRC32BUFSZ];
147
t_u32 iBytesRead = 0;
150
if(FOPEN_S(&fSource, sFileName, "rb") != 0)
152
if(FOPEN_S(fSource, sFileName, "rb") != 0)
160
iBytesRead = (t_u32)fread(sBuf, sizeof(char), CRC32BUFSZ, fSource);
161
PartialCRC(&ulCRC, sBuf, iBytesRead);
162
}while(iBytesRead == CRC32BUFSZ);
166
return(ulCRC ^ 0xffffffff);
169
// This function uses the CRCTable lookup table to generate a CRC for sData
170
t_u32 NCRC32::FullCRC(const char *sData, t_u32 ulLength)
172
t_u32 ulCRC = 0xffffffff;
173
PartialCRC(&ulCRC, sData, ulLength);
174
return ulCRC ^ 0xffffffff;
177
// Perform the algorithm on each character
178
// in the string, using the lookup table values.
179
void NCRC32::PartialCRC(t_u32 *ulInCRC, const char *sData, t_u32 ulLength)
183
*ulInCRC = (*ulInCRC >> 8) ^ CRCTable[(*ulInCRC & 0xFF) ^ *sData++];
190
* A brief CRC tutorial.
192
* A CRC is a long-division remainder. You add the CRC to the message,
193
* and the whole thing (message+CRC) is a multiple of the given
194
* CRC polynomial. To check the CRC, you can either check that the
195
* CRC matches the recomputed value, *or* you can check that the
196
* remainder computed on the message+CRC is 0. This latter approach
197
* is used by a lot of hardware implementations, and is why so many
198
* protocols put the end-of-frame flag after the CRC.
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* It's actually the same long division you learned in school, except that
201
* - We're working in binary, so the digits are only 0 and 1, and
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* - When dividing polynomials, there are no carries. Rather than add and
203
* subtract, we just xor. Thus, we tend to get a bit sloppy about
204
* the difference between adding and subtracting.
206
* A 32-bit CRC polynomial is actually 33 bits long. But since it's
207
* 33 bits long, bit 32 is always going to be set, so usually the CRC
208
* is written in hex with the most significant bit omitted. (If you're
209
* familiar with the IEEE 754 floating-point format, it's the same idea.)
211
* Note that a CRC is computed over a string of *bits*, so you have
212
* to decide on the endianness of the bits within each byte. To get
213
* the best error-detecting properties, this should correspond to the
214
* order they're actually sent. For example, standard RS-232 serial is
215
* little-endian; the most significant bit (sometimes used for parity)
216
* is sent last. And when appending a CRC word to a message, you should
217
* do it in the right order, matching the endianness.
219
* Just like with ordinary division, the remainder is always smaller than
220
* the divisor (the CRC polynomial) you're dividing by. Each step of the
221
* division, you take one more digit (bit) of the dividend and append it
222
* to the current remainder. Then you figure out the appropriate multiple
223
* of the divisor to subtract to being the remainder back into range.
224
* In binary, it's easy - it has to be either 0 or 1, and to make the
225
* XOR cancel, it's just a copy of bit 32 of the remainder.
227
* When computing a CRC, we don't care about the quotient, so we can
228
* throw the quotient bit away, but subtract the appropriate multiple of
229
* the polynomial from the remainder and we're back to where we started,
230
* ready to process the next bit.
232
* A big-endian CRC written this way would be coded like:
233
* for (i = 0; i < input_bits; i++) {
234
* multiple = remainder & 0x80000000 ? CRCPOLY : 0;
235
* remainder = (remainder << 1 | next_input_bit()) ^ multiple;
237
* Notice how, to get at bit 32 of the shifted remainder, we look
238
* at bit 31 of the remainder *before* shifting it.
240
* But also notice how the next_input_bit() bits we're shifting into
241
* the remainder don't actually affect any decision-making until
242
* 32 bits later. Thus, the first 32 cycles of this are pretty boring.
243
* Also, to add the CRC to a message, we need a 32-bit-long hole for it at
244
* the end, so we have to add 32 extra cycles shifting in zeros at the
245
* end of every message,
247
* So the standard trick is to rearrage merging in the next_input_bit()
248
* until the moment it's needed. Then the first 32 cycles can be precomputed,
249
* and merging in the final 32 zero bits to make room for the CRC can be
251
* This changes the code to:
252
* for (i = 0; i < input_bits; i++) {
253
* remainder ^= next_input_bit() << 31;
254
* multiple = (remainder & 0x80000000) ? CRCPOLY : 0;
255
* remainder = (remainder << 1) ^ multiple;
257
* With this optimization, the little-endian code is simpler:
258
* for (i = 0; i < input_bits; i++) {
259
* remainder ^= next_input_bit();
260
* multiple = (remainder & 1) ? CRCPOLY : 0;
261
* remainder = (remainder >> 1) ^ multiple;
264
* Note that the other details of endianness have been hidden in CRCPOLY
265
* (which must be bit-reversed) and next_input_bit().
267
* However, as long as next_input_bit is returning the bits in a sensible
268
* order, we can actually do the merging 8 or more bits at a time rather
269
* than one bit at a time:
270
* for (i = 0; i < input_bytes; i++) {
271
* remainder ^= next_input_byte() << 24;
272
* for (j = 0; j < 8; j++) {
273
* multiple = (remainder & 0x80000000) ? CRCPOLY : 0;
274
* remainder = (remainder << 1) ^ multiple;
277
* Or in little-endian:
278
* for (i = 0; i < input_bytes; i++) {
279
* remainder ^= next_input_byte();
280
* for (j = 0; j < 8; j++) {
281
* multiple = (remainder & 1) ? CRCPOLY : 0;
282
* remainder = (remainder << 1) ^ multiple;
285
* If the input is a multiple of 32 bits, you can even XOR in a 32-bit
286
* word at a time and increase the inner loop count to 32.
288
* You can also mix and match the two loop styles, for example doing the
289
* bulk of a message byte-at-a-time and adding bit-at-a-time processing
290
* for any fractional bytes at the end.
292
* The only remaining optimization is to the byte-at-a-time table method.
293
* Here, rather than just shifting one bit of the remainder to decide
294
* in the correct multiple to subtract, we can shift a byte at a time.
295
* This produces a 40-bit (rather than a 33-bit) intermediate remainder,
296
* but again the multiple of the polynomial to subtract depends only on
297
* the high bits, the high 8 bits in this case.
299
* The multile we need in that case is the low 32 bits of a 40-bit
300
* value whose high 8 bits are given, and which is a multiple of the
301
* generator polynomial. This is simply the CRC-32 of the given
304
* Two more details: normally, appending zero bits to a message which
305
* is already a multiple of a polynomial produces a larger multiple of that
306
* polynomial. To enable a CRC to detect this condition, it's common to
307
* invert the CRC before appending it. This makes the remainder of the
308
* message+crc come out not as zero, but some fixed non-zero value.
310
* The same problem applies to zero bits prepended to the message, and
311
* a similar solution is used. Instead of starting with a remainder of
312
* 0, an initial remainder of all ones is used. As long as you start
313
* the same way on decoding, it doesn't make a difference.
added
removed
NuxCore/NCRC32.cpp
