1 /* crc32.c -- output crc32 tables
2 * Copyright (C) 1995-2006, 2010, 2011, 2012, 2016, 2018 Mark Adler
3 * For conditions of distribution and use, see copyright notice in zlib.h
4 */
5
6 #include <stdio.h>
7 #include <inttypes.h>
8 #include "zbuild.h"
9 #include "deflate.h"
10 #include "crc32_p.h"
11
12 static uint32_t crc_table[8][256];
13 static uint32_t crc_comb[GF2_DIM][GF2_DIM];
14
15 static void gf2_matrix_square(uint32_t *square, const uint32_t *mat);
16 static void make_crc_table(void);
17 static void print_crc32_tables();
18 static void write_table(const uint32_t *, int);
19
20
21 /* ========================================================================= */
gf2_matrix_square(uint32_t * square,const uint32_t * mat)22 static void gf2_matrix_square(uint32_t *square, const uint32_t *mat) {
23 int n;
24
25 for (n = 0; n < GF2_DIM; n++)
26 square[n] = gf2_matrix_times(mat, mat[n]);
27 }
28
29 /* =========================================================================
30 Generate tables for a byte-wise 32-bit CRC calculation on the polynomial:
31 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.
32
33 Polynomials over GF(2) are represented in binary, one bit per coefficient,
34 with the lowest powers in the most significant bit. Then adding polynomials
35 is just exclusive-or, and multiplying a polynomial by x is a right shift by
36 one. If we call the above polynomial p, and represent a byte as the
37 polynomial q, also with the lowest power in the most significant bit (so the
38 byte 0xb1 is the polynomial x^7+x^3+x+1), then the CRC is (q*x^32) mod p,
39 where a mod b means the remainder after dividing a by b.
40
41 This calculation is done using the shift-register method of multiplying and
42 taking the remainder. The register is initialized to zero, and for each
43 incoming bit, x^32 is added mod p to the register if the bit is a one (where
44 x^32 mod p is p+x^32 = x^26+...+1), and the register is multiplied mod p by
45 x (which is shifting right by one and adding x^32 mod p if the bit shifted
46 out is a one). We start with the highest power (least significant bit) of
47 q and repeat for all eight bits of q.
48
49 The first table is simply the CRC of all possible eight bit values. This is
50 all the information needed to generate CRCs on data a byte at a time for all
51 combinations of CRC register values and incoming bytes. The remaining tables
52 allow for word-at-a-time CRC calculation for both big-endian and little-
53 endian machines, where a word is four bytes.
54 */
make_crc_table()55 static void make_crc_table() {
56 int n, k;
57 uint32_t c;
58 uint32_t poly; /* polynomial exclusive-or pattern */
59 /* terms of polynomial defining this crc (except x^32): */
60 static const unsigned char p[] = {0, 1, 2, 4, 5, 7, 8, 10, 11, 12, 16, 22, 23, 26};
61
62 /* make exclusive-or pattern from polynomial (0xedb88320) */
63 poly = 0;
64 for (n = 0; n < (int)(sizeof(p)/sizeof(unsigned char)); n++)
65 poly |= (uint32_t)1 << (31 - p[n]);
66
67 /* generate a crc for every 8-bit value */
68 for (n = 0; n < 256; n++) {
69 c = (uint32_t)n;
70 for (k = 0; k < 8; k++)
71 c = c & 1 ? poly ^ (c >> 1) : c >> 1;
72 crc_table[0][n] = c;
73 }
74
75 /* generate crc for each value followed by one, two, and three zeros,
76 and then the byte reversal of those as well as the first table */
77 for (n = 0; n < 256; n++) {
78 c = crc_table[0][n];
79 crc_table[4][n] = ZSWAP32(c);
80 for (k = 1; k < 4; k++) {
81 c = crc_table[0][c & 0xff] ^ (c >> 8);
82 crc_table[k][n] = c;
83 crc_table[k + 4][n] = ZSWAP32(c);
84 }
85 }
86
87 /* generate zero operators table for crc32_combine() */
88
89 /* generate the operator to apply a single zero bit to a CRC -- the
90 first row adds the polynomial if the low bit is a 1, and the
91 remaining rows shift the CRC right one bit */
92 k = GF2_DIM - 3;
93 crc_comb[k][0] = 0xedb88320UL; /* CRC-32 polynomial */
94 uint32_t row = 1;
95 for (n = 1; n < GF2_DIM; n++) {
96 crc_comb[k][n] = row;
97 row <<= 1;
98 }
99 /* generate operators that apply 2, 4, and 8 zeros to a CRC, putting
100 the last one, the operator for one zero byte, at the 0 position */
101 gf2_matrix_square(crc_comb[k + 1], crc_comb[k]);
102 gf2_matrix_square(crc_comb[k + 2], crc_comb[k + 1]);
103 gf2_matrix_square(crc_comb[0], crc_comb[k + 2]);
104
105 /* generate operators for applying 2^n zero bytes to a CRC, filling out
106 the remainder of the table -- the operators repeat after GF2_DIM
107 values of n, so the table only needs GF2_DIM entries, regardless of
108 the size of the length being processed */
109 for (n = 1; n < k; n++)
110 gf2_matrix_square(crc_comb[n], crc_comb[n - 1]);
111 }
112
print_crc32_tables()113 static void print_crc32_tables() {
114 int k;
115 printf("#ifndef CRC32_TBL_H_\n");
116 printf("#define CRC32_TBL_H_\n\n");
117 printf("/* crc32_tbl.h -- tables for rapid CRC calculation\n");
118 printf(" * Generated automatically by makecrct.c\n */\n\n");
119
120 /* print CRC table */
121 printf("static const uint32_t ");
122 printf("crc_table[8][256] =\n{\n {\n");
123 write_table(crc_table[0], 256);
124 for (k = 1; k < 8; k++) {
125 printf(" },\n {\n");
126 write_table(crc_table[k], 256);
127 }
128 printf(" }\n};\n");
129
130 /* print zero operator table */
131 printf("\nstatic const uint32_t ");
132 printf("crc_comb[%d][%d] =\n{\n {\n", GF2_DIM, GF2_DIM);
133 write_table(crc_comb[0], GF2_DIM);
134 for (k = 1; k < GF2_DIM; k++) {
135 printf(" },\n {\n");
136 write_table(crc_comb[k], GF2_DIM);
137 }
138 printf(" }\n};\n");
139 printf("#endif /* CRC32_TBL_H_ */\n");
140 }
141
write_table(const uint32_t * table,int k)142 static void write_table(const uint32_t *table, int k) {
143 int n;
144
145 for (n = 0; n < k; n++)
146 printf("%s0x%08" PRIx32 "%s", n % 5 ? "" : " ",
147 (uint32_t)(table[n]),
148 n == k - 1 ? "\n" : (n % 5 == 4 ? ",\n" : ", "));
149 }
150
151 // The output of this application can be piped out to recreate crc32.h
main()152 int main() {
153 make_crc_table();
154 print_crc32_tables();
155 return 0;
156 }
157