/usr/include/crcutil/gf_util.h is in libcrcutil-dev 1.0-4.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 | // Copyright 2010 Google Inc. All rights reserved.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
// Defines GfUtil template class which implements
// 1. some useful operations in GF(2^n),
// 2. CRC helper function (e.g. concatenation of CRCs) which are
// not affected by specific implemenation of CRC computation per se.
//
// Please read crc.pdf to understand how it all works.
#ifndef CRCUTIL_GF_UTIL_H_
#define CRCUTIL_GF_UTIL_H_
#include "base_types.h" // uint8, uint64
#include "crc_casts.h" // TO_BYTE()
#include "platform.h" // GCC_ALIGN_ATTRIBUTE(16), SHIFT_*_SAFE
namespace crcutil {
#pragma pack(push, 16)
// "Crc" is the type used internally and to return values of N-bit CRC.
template<typename Crc> class GfUtil {
public:
// Initializes the tables given generating polynomial of degree (degree).
// If "canonical" is true, starting CRC value and computed CRC value will be
// XOR-ed with 111...111.
GfUtil() {}
GfUtil(const Crc &generating_polynomial, size_t degree, bool canonical) {
Init(generating_polynomial, degree, canonical);
}
void Init(const Crc &generating_polynomial, size_t degree, bool canonical) {
Crc one = 1;
one <<= degree - 1;
this->generating_polynomial_ = generating_polynomial;
this->crc_bytes_ = (degree + 7) >> 3;
this->degree_ = degree;
this->one_ = one;
if (canonical) {
this->canonize_ = one | (one - 1);
} else {
this->canonize_ = 0;
}
this->normalize_[0] = 0;
this->normalize_[1] = generating_polynomial;
Crc k = one >> 1;
for (size_t i = 0; i < sizeof(uint64) * 8; ++i) {
this->x_pow_2n_[i] = k;
k = Multiply(k, k);
}
this->crc_of_crc_ = Multiply(this->canonize_,
this->one_ ^ Xpow8N((degree + 7) >> 3));
FindLCD(Xpow8N(this->crc_bytes_), &this->x_pow_minus_W_);
}
// Returns generating polynomial.
Crc GeneratingPolynomial() const {
return this->generating_polynomial_;
}
// Returns number of bits in CRC (degree of generating polynomial).
size_t Degree() const {
return this->degree_;
}
// Returns start/finish adjustment constant.
Crc Canonize() const {
return this->canonize_;
}
// Returns normalized value of 1.
Crc One() const {
return this->one_;
}
// Returns value of CRC(A, |A|, start_new) given known
// crc=CRC(A, |A|, start_old) -- without touching the data.
Crc ChangeStartValue(const Crc &crc, uint64 bytes,
const Crc &start_old,
const Crc &start_new) const {
return (crc ^ Multiply(start_new ^ start_old, Xpow8N(bytes)));
}
// Returns CRC of concatenation of blocks A and B when CRCs
// of blocks A and B are known -- without touching the data.
//
// To be precise, given CRC(A, |A|, startA) and CRC(B, |B|, 0),
// returns CRC(AB, |AB|, startA).
Crc Concatenate(const Crc &crc_A, const Crc &crc_B, uint64 bytes_B) const {
return ChangeStartValue(crc_B, bytes_B, 0 /* start_B */, crc_A);
}
// Returns CRC of sequence of zeroes -- without touching the data.
Crc CrcOfZeroes(uint64 bytes, const Crc &start) const {
Crc tmp = Multiply(start ^ this->canonize_, Xpow8N(bytes));
return (tmp ^ this->canonize_);
}
// Given CRC of a message, stores extra (degree + 7)/8 bytes after
// the message so that CRC(message+extra, start) = result.
// Does not change CRC start value (use ChangeStartValue for that).
// Returns number of stored bytes.
size_t StoreComplementaryCrc(void *dst,
const Crc &message_crc,
const Crc &result) const {
Crc crc0 = Multiply(result ^ this->canonize_, this->x_pow_minus_W_);
crc0 ^= message_crc ^ this->canonize_;
uint8 *d = reinterpret_cast<uint8 *>(dst);
for (size_t i = 0; i < this->crc_bytes_; ++i) {
d[i] = TO_BYTE(crc0);
crc0 >>= 8;
}
return this->crc_bytes_;
}
// Stores given CRC of a message as (degree + 7)/8 bytes filled
// with 0s to the right. Returns number of stored bytes.
// CRC of the message and stored CRC is a constant value returned
// by CrcOfCrc() -- it does not depend on contents of the message.
size_t StoreCrc(void *dst, const Crc &crc) const {
uint8 *d = reinterpret_cast<uint8 *>(dst);
Crc crc0 = crc;
for (size_t i = 0; i < this->crc_bytes_; ++i) {
d[i] = TO_BYTE(crc0);
crc0 >>= 8;
}
return this->crc_bytes_;
}
// Returns expected CRC value of CRC(Message,CRC(Message))
// when CRC is stored after the message. This value is fixed
// and does not depend on the message or CRC start value.
Crc CrcOfCrc() const {
return this->crc_of_crc_;
}
// Returns ((a * b) mod P) where "a" and "b" are of degree <= (D-1).
Crc Multiply(const Crc &aa, const Crc &bb) const {
Crc a = aa;
Crc b = bb;
if ((a ^ (a - 1)) < (b ^ (b - 1))) {
Crc temp = a;
a = b;
b = temp;
}
if (a == 0) {
return a;
}
Crc product = 0;
Crc one = this->one_;
for (; a != 0; a <<= 1) {
if ((a & one) != 0) {
product ^= b;
a ^= one;
}
b = (b >> 1) ^ this->normalize_[Downcast<Crc, size_t>(b & 1)];
}
return product;
}
// Returns ((unnorm * m) mod P) where degree of m is <= (D-1)
// and degree of value "unnorm" is provided explicitly.
Crc MultiplyUnnormalized(const Crc &unnorm, size_t degree,
const Crc &m) const {
Crc v = unnorm;
Crc result = 0;
while (degree > this->degree_) {
degree -= this->degree_;
Crc value = v & (this->one_ | (this->one_ - 1));
result ^= Multiply(value, Multiply(m, XpowN(degree)));
v >>= this->degree_;
}
result ^= Multiply(v << (this->degree_ - degree), m);
return result;
}
// returns ((x ** n) mod P).
Crc XpowN(uint64 n) const {
Crc one = this->one_;
Crc result = one;
for (size_t i = 0; n != 0; ++i, n >>= 1) {
if (n & 1) {
result = Multiply(result, this->x_pow_2n_[i]);
}
}
return result;
}
// Returns (x ** (8 * n) mod P).
Crc Xpow8N(uint64 n) const {
return XpowN(n << 3);
}
// Returns remainder (A mod B) and sets *q = (A/B) of division
// of two polynomials:
// A = dividend + dividend_x_pow_D_coef * x**degree,
// B = divisor.
Crc Divide(const Crc ÷nd0, int dividend_x_pow_D_coef,
const Crc &divisor0, Crc *q) const {
Crc divisor = divisor0;
Crc dividend = dividend0;
Crc quotient = 0;
Crc coef = this->one_;
while ((divisor & 1) == 0) {
divisor >>= 1;
coef >>= 1;
}
if (dividend_x_pow_D_coef) {
quotient = coef >> 1;
dividend ^= divisor >> 1;
}
Crc x_pow_degree_b = 1;
for (;;) {
if ((dividend & x_pow_degree_b) != 0) {
dividend ^= divisor;
quotient ^= coef;
}
if (coef == this->one_) {
break;
}
coef <<= 1;
x_pow_degree_b <<= 1;
divisor <<= 1;
}
*q = quotient;
return dividend;
}
// Extended Euclid's algorith -- for given A finds LCD(A, P) and
// value B such that (A * B) mod P = LCD(A, P).
Crc FindLCD(const Crc &A, Crc *B) const {
if (A == 0 || A == this->one_) {
*B = A;
return A;
}
// Actually, generating polynomial is
// (generating_polynomial_ + x**degree).
int r0_x_pow_D_coef = 1;
Crc r0 = this->generating_polynomial_;
Crc b0 = 0;
Crc r1 = A;
Crc b1 = this->one_;
for (;;) {
Crc q;
Crc r = Divide(r0, r0_x_pow_D_coef, r1, &q);
if (r == 0) {
break;
}
r0_x_pow_D_coef = 0;
r0 = r1;
r1 = r;
Crc b = b0 ^ Multiply(q, b1);
b0 = b1;
b1 = b;
}
*B = b1;
return r1;
}
protected:
Crc canonize_;
Crc x_pow_2n_[sizeof(uint64) * 8];
Crc generating_polynomial_;
Crc one_;
Crc x_pow_minus_W_;
Crc crc_of_crc_;
Crc normalize_[2];
size_t crc_bytes_;
size_t degree_;
} GCC_ALIGN_ATTRIBUTE(16);
#pragma pack(pop)
} // namespace crcutil
#endif // CRCUTIL_GF_UTIL_H_
|