2 * CRC32 implementation.
4 * The basic concept of a CRC is that you treat your bit-string
5 * abcdefg... as a ludicrously long polynomial M=a+bx+cx^2+dx^3+...
6 * over Z[2]. You then take a modulus polynomial P, and compute the
7 * remainder of M on division by P. Thus, an erroneous message N
8 * will only have the same CRC if the difference E = M-N is an
9 * exact multiple of P. (Note that as we are working over Z[2], M-N
10 * = N-M = M+N; but that's not very important.)
12 * What makes the CRC good is choosing P to have good properties:
14 * - If its first and last terms are both nonzero then it cannot
15 * be a factor of any single term x^i. Therefore if M and N
16 * differ by exactly one bit their CRCs will guaranteeably
19 * - If it has a prime (irreducible) factor with three terms then
20 * it cannot divide a polynomial of the form x^i(1+x^j).
21 * Therefore if M and N differ by exactly _two_ bits they will
22 * have different CRCs.
24 * - If it has a factor (x+1) then it cannot divide a polynomial
25 * with an odd number of terms. Therefore if M and N differ by
26 * _any odd_ number of bits they will have different CRCs.
28 * - If the error term E is of the form x^i*B(x) where B(x) has
29 * order less than P (i.e. a short _burst_ of errors) then P
30 * cannot divide E (since no polynomial can divide a shorter
31 * one), so any such error burst will be spotted.
33 * The CRC32 standard polynomial is
34 * x^32+x^26+x^23+x^22+x^16+x^12+x^11+x^10+x^8+x^7+x^5+x^4+x^2+x^1+x^0
36 * In fact, we don't compute M mod P; we compute M*x^32 mod P.
38 * The concrete implementation of the CRC is this: we maintain at
39 * all times a 32-bit word which is the current remainder of the
40 * polynomial mod P. Whenever we receive an extra bit, we multiply
41 * the existing remainder by x, add (XOR) the x^32 term thus
42 * generated to the new x^32 term caused by the incoming bit, and
43 * remove the resulting combined x^32 term if present by replacing
46 * Bit 0 of the word is the x^31 term and bit 31 is the x^0 term.
47 * Thus, multiplying by x means shifting right. So the actual
48 * algorithm goes like this:
50 * x32term = (crcword & 1) ^ newbit;
51 * crcword = (crcword >> 1) ^ (x32term * 0xEDB88320);
53 * In practice, we pre-compute what will happen to crcword on any
54 * given sequence of eight incoming bits, and store that in a table
55 * which we then use at run-time to do the job:
57 * outgoingplusnew = (crcword & 0xFF) ^ newbyte;
58 * crcword = (crcword >> 8) ^ table[outgoingplusnew];
60 * where table[outgoingplusnew] is computed by setting crcword=0
61 * and then iterating the first code fragment eight times (taking
62 * the incoming byte low bit first).
64 * Note that all shifts are rightward and thus no assumption is
65 * made about exact word length! (Although word length must be at
66 * _least_ 32 bits, but ANSI C guarantees this for `unsigned long'
72 /* ----------------------------------------------------------------------
73 * Multi-function module. Can be compiled three ways.
75 * - Compile with no special #defines. Will generate a table
76 * that's already initialised at compile time, and one function
77 * crc32(buf,len) that uses it. Normal usage.
79 * - Compile with INITFUNC defined. Will generate an uninitialised
80 * array as the table, and as well as crc32(buf,len) it will
81 * also generate void crc32_init(void) which sets up the table
82 * at run time. Useful if binary size is important.
84 * - Compile with GENPROGRAM defined. Will create a standalone
85 * program that does the initialisation and outputs the table as
89 #define POLY (0xEDB88320L)
92 #define INITFUNC /* the gen program needs the init func :-) */
98 * This variant of the code generates the table at run-time from an
101 static unsigned long crc32_table
[256];
103 void crc32_init(void)
105 unsigned long crcword
;
108 for (i
= 0; i
< 256; i
++) {
109 unsigned long newbyte
, x32term
;
113 for (j
= 0; j
< 8; j
++) {
114 x32term
= (crcword
^ newbyte
) & 1;
115 crcword
= (crcword
>> 1) ^ (x32term
* POLY
);
118 crc32_table
[i
] = crcword
;
125 * This variant of the code has the data already prepared.
127 static const unsigned long crc32_table
[256] = {
128 0x00000000L
, 0x77073096L
, 0xEE0E612CL
, 0x990951BAL
,
129 0x076DC419L
, 0x706AF48FL
, 0xE963A535L
, 0x9E6495A3L
,
130 0x0EDB8832L
, 0x79DCB8A4L
, 0xE0D5E91EL
, 0x97D2D988L
,
131 0x09B64C2BL
, 0x7EB17CBDL
, 0xE7B82D07L
, 0x90BF1D91L
,
132 0x1DB71064L
, 0x6AB020F2L
, 0xF3B97148L
, 0x84BE41DEL
,
133 0x1ADAD47DL
, 0x6DDDE4EBL
, 0xF4D4B551L
, 0x83D385C7L
,
134 0x136C9856L
, 0x646BA8C0L
, 0xFD62F97AL
, 0x8A65C9ECL
,
135 0x14015C4FL
, 0x63066CD9L
, 0xFA0F3D63L
, 0x8D080DF5L
,
136 0x3B6E20C8L
, 0x4C69105EL
, 0xD56041E4L
, 0xA2677172L
,
137 0x3C03E4D1L
, 0x4B04D447L
, 0xD20D85FDL
, 0xA50AB56BL
,
138 0x35B5A8FAL
, 0x42B2986CL
, 0xDBBBC9D6L
, 0xACBCF940L
,
139 0x32D86CE3L
, 0x45DF5C75L
, 0xDCD60DCFL
, 0xABD13D59L
,
140 0x26D930ACL
, 0x51DE003AL
, 0xC8D75180L
, 0xBFD06116L
,
141 0x21B4F4B5L
, 0x56B3C423L
, 0xCFBA9599L
, 0xB8BDA50FL
,
142 0x2802B89EL
, 0x5F058808L
, 0xC60CD9B2L
, 0xB10BE924L
,
143 0x2F6F7C87L
, 0x58684C11L
, 0xC1611DABL
, 0xB6662D3DL
,
144 0x76DC4190L
, 0x01DB7106L
, 0x98D220BCL
, 0xEFD5102AL
,
145 0x71B18589L
, 0x06B6B51FL
, 0x9FBFE4A5L
, 0xE8B8D433L
,
146 0x7807C9A2L
, 0x0F00F934L
, 0x9609A88EL
, 0xE10E9818L
,
147 0x7F6A0DBBL
, 0x086D3D2DL
, 0x91646C97L
, 0xE6635C01L
,
148 0x6B6B51F4L
, 0x1C6C6162L
, 0x856530D8L
, 0xF262004EL
,
149 0x6C0695EDL
, 0x1B01A57BL
, 0x8208F4C1L
, 0xF50FC457L
,
150 0x65B0D9C6L
, 0x12B7E950L
, 0x8BBEB8EAL
, 0xFCB9887CL
,
151 0x62DD1DDFL
, 0x15DA2D49L
, 0x8CD37CF3L
, 0xFBD44C65L
,
152 0x4DB26158L
, 0x3AB551CEL
, 0xA3BC0074L
, 0xD4BB30E2L
,
153 0x4ADFA541L
, 0x3DD895D7L
, 0xA4D1C46DL
, 0xD3D6F4FBL
,
154 0x4369E96AL
, 0x346ED9FCL
, 0xAD678846L
, 0xDA60B8D0L
,
155 0x44042D73L
, 0x33031DE5L
, 0xAA0A4C5FL
, 0xDD0D7CC9L
,
156 0x5005713CL
, 0x270241AAL
, 0xBE0B1010L
, 0xC90C2086L
,
157 0x5768B525L
, 0x206F85B3L
, 0xB966D409L
, 0xCE61E49FL
,
158 0x5EDEF90EL
, 0x29D9C998L
, 0xB0D09822L
, 0xC7D7A8B4L
,
159 0x59B33D17L
, 0x2EB40D81L
, 0xB7BD5C3BL
, 0xC0BA6CADL
,
160 0xEDB88320L
, 0x9ABFB3B6L
, 0x03B6E20CL
, 0x74B1D29AL
,
161 0xEAD54739L
, 0x9DD277AFL
, 0x04DB2615L
, 0x73DC1683L
,
162 0xE3630B12L
, 0x94643B84L
, 0x0D6D6A3EL
, 0x7A6A5AA8L
,
163 0xE40ECF0BL
, 0x9309FF9DL
, 0x0A00AE27L
, 0x7D079EB1L
,
164 0xF00F9344L
, 0x8708A3D2L
, 0x1E01F268L
, 0x6906C2FEL
,
165 0xF762575DL
, 0x806567CBL
, 0x196C3671L
, 0x6E6B06E7L
,
166 0xFED41B76L
, 0x89D32BE0L
, 0x10DA7A5AL
, 0x67DD4ACCL
,
167 0xF9B9DF6FL
, 0x8EBEEFF9L
, 0x17B7BE43L
, 0x60B08ED5L
,
168 0xD6D6A3E8L
, 0xA1D1937EL
, 0x38D8C2C4L
, 0x4FDFF252L
,
169 0xD1BB67F1L
, 0xA6BC5767L
, 0x3FB506DDL
, 0x48B2364BL
,
170 0xD80D2BDAL
, 0xAF0A1B4CL
, 0x36034AF6L
, 0x41047A60L
,
171 0xDF60EFC3L
, 0xA867DF55L
, 0x316E8EEFL
, 0x4669BE79L
,
172 0xCB61B38CL
, 0xBC66831AL
, 0x256FD2A0L
, 0x5268E236L
,
173 0xCC0C7795L
, 0xBB0B4703L
, 0x220216B9L
, 0x5505262FL
,
174 0xC5BA3BBEL
, 0xB2BD0B28L
, 0x2BB45A92L
, 0x5CB36A04L
,
175 0xC2D7FFA7L
, 0xB5D0CF31L
, 0x2CD99E8BL
, 0x5BDEAE1DL
,
176 0x9B64C2B0L
, 0xEC63F226L
, 0x756AA39CL
, 0x026D930AL
,
177 0x9C0906A9L
, 0xEB0E363FL
, 0x72076785L
, 0x05005713L
,
178 0x95BF4A82L
, 0xE2B87A14L
, 0x7BB12BAEL
, 0x0CB61B38L
,
179 0x92D28E9BL
, 0xE5D5BE0DL
, 0x7CDCEFB7L
, 0x0BDBDF21L
,
180 0x86D3D2D4L
, 0xF1D4E242L
, 0x68DDB3F8L
, 0x1FDA836EL
,
181 0x81BE16CDL
, 0xF6B9265BL
, 0x6FB077E1L
, 0x18B74777L
,
182 0x88085AE6L
, 0xFF0F6A70L
, 0x66063BCAL
, 0x11010B5CL
,
183 0x8F659EFFL
, 0xF862AE69L
, 0x616BFFD3L
, 0x166CCF45L
,
184 0xA00AE278L
, 0xD70DD2EEL
, 0x4E048354L
, 0x3903B3C2L
,
185 0xA7672661L
, 0xD06016F7L
, 0x4969474DL
, 0x3E6E77DBL
,
186 0xAED16A4AL
, 0xD9D65ADCL
, 0x40DF0B66L
, 0x37D83BF0L
,
187 0xA9BCAE53L
, 0xDEBB9EC5L
, 0x47B2CF7FL
, 0x30B5FFE9L
,
188 0xBDBDF21CL
, 0xCABAC28AL
, 0x53B39330L
, 0x24B4A3A6L
,
189 0xBAD03605L
, 0xCDD70693L
, 0x54DE5729L
, 0x23D967BFL
,
190 0xB3667A2EL
, 0xC4614AB8L
, 0x5D681B02L
, 0x2A6F2B94L
,
191 0xB40BBE37L
, 0xC30C8EA1L
, 0x5A05DF1BL
, 0x2D02EF8DL
199 unsigned long crcword
;
203 for (i
= 0; i
< 256; i
++) {
204 printf("%s0x%08XL%s",
205 (i
% 4 == 0 ?
" " : " "),
207 (i
% 4 == 3 ?
(i
== 255 ?
"\n" : ",\n") : ","));
214 unsigned long crc32(const void *buf
, size_t len
)
216 unsigned long crcword
= 0L;
217 const unsigned char *p
= (const unsigned char *) buf
;
219 unsigned long newbyte
= *p
++;
220 newbyte
^= crcword
& 0xFFL
;
221 crcword
= (crcword
>> 8) ^ crc32_table
[newbyte
];