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+// Copyright 2022 The Abseil Authors.
+//
+// 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
+//
+// https://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.
+
+// Implementation of CRCs (aka Rabin Fingerprints).
+// Treats the input as a polynomial with coefficients in Z(2),
+// and finds the remainder when divided by an irreducible polynomial
+// of the appropriate length.
+// It handles all CRC sizes from 8 to 128 bits.
+// It's somewhat complicated by having separate implementations optimized for
+// CRC's <=32 bits, <= 64 bits, and <= 128 bits.
+// The input string is prefixed with a "1" bit, and has "degree" "0" bits
+// appended to it before the remainder is found. This ensures that
+// short strings are scrambled somewhat and that strings consisting
+// of all nulls have a non-zero CRC.
+//
+// Uses the "interleaved word-by-word" method from
+// "Everything we know about CRC but afraid to forget" by Andrew Kadatch
+// and Bob Jenkins,
+// http://crcutil.googlecode.com/files/crc-doc.1.0.pdf
+//
+// The idea is to compute kStride CRCs simultaneously, allowing the
+// processor to more effectively use multiple execution units. Each of
+// the CRCs is calculated on one word of data followed by kStride - 1
+// words of zeroes; the CRC starting points are staggered by one word.
+// Assuming a stride of 4 with data words "ABCDABCDABCD", the first
+// CRC is over A000A000A, the second over 0B000B000B, and so on.
+// The CRC of the whole data is then calculated by properly aligning the
+// CRCs by appending zeroes until the data lengths agree then XORing
+// the CRCs.
+
+#include "absl/crc/internal/crc.h"
+
+#include <cstdint>
+
+#include "absl/base/internal/endian.h"
+#include "absl/base/internal/prefetch.h"
+#include "absl/base/internal/raw_logging.h"
+#include "absl/crc/internal/crc_internal.h"
+
+namespace absl {
+ABSL_NAMESPACE_BEGIN
+namespace crc_internal {
+
+namespace {
+
+// Constants
+#if defined(__i386__) || defined(__x86_64__)
+constexpr bool kNeedAlignedLoads = false;
+#else
+constexpr bool kNeedAlignedLoads = true;
+#endif
+
+// We express the number of zeroes as a number in base ZEROES_BASE. By
+// pre-computing the zero extensions for all possible components of such an
+// expression (numbers in a form a*ZEROES_BASE**b), we can calculate the
+// resulting extension by multiplying the extensions for individual components
+// using log_{ZEROES_BASE}(num_zeroes) polynomial multiplications. The tables of
+// zero extensions contain (ZEROES_BASE - 1) * (log_{ZEROES_BASE}(64)) entries.
+constexpr int ZEROES_BASE_LG = 4; // log_2(ZEROES_BASE)
+constexpr int ZEROES_BASE = (1 << ZEROES_BASE_LG); // must be a power of 2
+
+constexpr uint32_t kCrc32cPoly = 0x82f63b78;
+
+uint32_t ReverseBits(uint32_t bits) {
+ bits = (bits & 0xaaaaaaaau) >> 1 | (bits & 0x55555555u) << 1;
+ bits = (bits & 0xccccccccu) >> 2 | (bits & 0x33333333u) << 2;
+ bits = (bits & 0xf0f0f0f0u) >> 4 | (bits & 0x0f0f0f0fu) << 4;
+ return absl::gbswap_32(bits);
+}
+
+// Polynomial long multiplication mod the polynomial of degree 32.
+void PolyMultiply(uint32_t* val, uint32_t m, uint32_t poly) {
+ uint32_t l = *val;
+ uint32_t result = 0;
+ auto onebit = uint32_t{0x80000000u};
+ for (uint32_t one = onebit; one != 0; one >>= 1) {
+ if ((l & one) != 0) {
+ result ^= m;
+ }
+ if (m & 1) {
+ m = (m >> 1) ^ poly;
+ } else {
+ m >>= 1;
+ }
+ }
+ *val = result;
+}
+} // namespace
+
+void CRCImpl::FillWordTable(uint32_t poly, uint32_t last, int word_size,
+ Uint32By256* t) {
+ for (int j = 0; j != word_size; j++) { // for each byte of extension....
+ t[j][0] = 0; // a zero has no effect
+ for (int i = 128; i != 0; i >>= 1) { // fill in entries for powers of 2
+ if (j == 0 && i == 128) {
+ t[j][i] = last; // top bit in last byte is given
+ } else {
+ // each successive power of two is derived from the previous
+ // one, either in this table, or the last table
+ uint32_t pred;
+ if (i == 128) {
+ pred = t[j - 1][1];
+ } else {
+ pred = t[j][i << 1];
+ }
+ // Advance the CRC by one bit (multiply by X, and take remainder
+ // through one step of polynomial long division)
+ if (pred & 1) {
+ t[j][i] = (pred >> 1) ^ poly;
+ } else {
+ t[j][i] = pred >> 1;
+ }
+ }
+ }
+ // CRCs have the property that CRC(a xor b) == CRC(a) xor CRC(b)
+ // so we can make all the tables for non-powers of two by
+ // xoring previously created entries.
+ for (int i = 2; i != 256; i <<= 1) {
+ for (int k = i + 1; k != (i << 1); k++) {
+ t[j][k] = t[j][i] ^ t[j][k - i];
+ }
+ }
+ }
+}
+
+int CRCImpl::FillZeroesTable(uint32_t poly, Uint32By256* t) {
+ uint32_t inc = 1;
+ inc <<= 31;
+
+ // Extend by one zero bit. We know degree > 1 so (inc & 1) == 0.
+ inc >>= 1;
+
+ // Now extend by 2, 4, and 8 bits, so now `inc` is extended by one zero byte.
+ for (int i = 0; i < 3; ++i) {
+ PolyMultiply(&inc, inc, poly);
+ }
+
+ int j = 0;
+ for (uint64_t inc_len = 1; inc_len != 0; inc_len <<= ZEROES_BASE_LG) {
+ // Every entry in the table adds an additional inc_len zeroes.
+ uint32_t v = inc;
+ for (int a = 1; a != ZEROES_BASE; a++) {
+ t[0][j] = v;
+ PolyMultiply(&v, inc, poly);
+ j++;
+ }
+ inc = v;
+ }
+ ABSL_RAW_CHECK(j <= 256, "");
+ return j;
+}
+
+// Internal version of the "constructor".
+CRCImpl* CRCImpl::NewInternal() {
+ // Find an accelearated implementation first.
+ CRCImpl* result = TryNewCRC32AcceleratedX86ARMCombined();
+
+ // Fall back to generic implementions if no acceleration is available.
+ if (result == nullptr) {
+ result = new CRC32();
+ }
+
+ result->InitTables();
+
+ return result;
+}
+
+// The CRC of the empty string is always the CRC polynomial itself.
+void CRCImpl::Empty(uint32_t* crc) const { *crc = kCrc32cPoly; }
+
+// The 32-bit implementation
+
+void CRC32::InitTables() {
+ // Compute the table for extending a CRC by one byte.
+ Uint32By256* t = new Uint32By256[4];
+ FillWordTable(kCrc32cPoly, kCrc32cPoly, 1, t);
+ for (int i = 0; i != 256; i++) {
+ this->table0_[i] = t[0][i];
+ }
+
+ // Construct a table for updating the CRC by 4 bytes data followed by
+ // 12 bytes of zeroes.
+ //
+ // Note: the data word size could be larger than the CRC size; it might
+ // be slightly faster to use a 64-bit data word, but doing so doubles the
+ // table size.
+ uint32_t last = kCrc32cPoly;
+ const size_t size = 12;
+ for (size_t i = 0; i < size; ++i) {
+ last = (last >> 8) ^ this->table0_[last & 0xff];
+ }
+ FillWordTable(kCrc32cPoly, last, 4, t);
+ for (size_t b = 0; b < 4; ++b) {
+ for (int i = 0; i < 256; ++i) {
+ this->table_[b][i] = t[b][i];
+ }
+ }
+
+ int j = FillZeroesTable(kCrc32cPoly, t);
+ ABSL_RAW_CHECK(j <= static_cast<int>(ABSL_ARRAYSIZE(this->zeroes_)), "");
+ for (int i = 0; i < j; i++) {
+ this->zeroes_[i] = t[0][i];
+ }
+
+ delete[] t;
+
+ // Build up tables for _reversing_ the operation of doing CRC operations on
+ // zero bytes.
+
+ // In C++, extending `crc` by a single zero bit is done by the following:
+ // (A) bool low_bit_set = (crc & 1);
+ // crc >>= 1;
+ // if (low_bit_set) crc ^= kCrc32cPoly;
+ //
+ // In particular note that the high bit of `crc` after this operation will be
+ // set if and only if the low bit of `crc` was set before it. This means that
+ // no information is lost, and the operation can be reversed, as follows:
+ // (B) bool high_bit_set = (crc & 0x80000000u);
+ // if (high_bit_set) crc ^= kCrc32cPoly;
+ // crc <<= 1;
+ // if (high_bit_set) crc ^= 1;
+ //
+ // Or, equivalently:
+ // (C) bool high_bit_set = (crc & 0x80000000u);
+ // crc <<= 1;
+ // if (high_bit_set) crc ^= ((kCrc32cPoly << 1) ^ 1);
+ //
+ // The last observation is, if we store our checksums in variable `rcrc`,
+ // with order of the bits reversed, the inverse operation becomes:
+ // (D) bool low_bit_set = (rcrc & 1);
+ // rcrc >>= 1;
+ // if (low_bit_set) rcrc ^= ReverseBits((kCrc32cPoly << 1) ^ 1)
+ //
+ // This is the same algorithm (A) that we started with, only with a different
+ // polynomial bit pattern. This means that by building up our tables with
+ // this alternate polynomial, we can apply the CRC algorithms to a
+ // bit-reversed CRC checksum to perform inverse zero-extension.
+
+ const uint32_t kCrc32cUnextendPoly =
+ ReverseBits(static_cast<uint32_t>((kCrc32cPoly << 1) ^ 1));
+ FillWordTable(kCrc32cUnextendPoly, kCrc32cUnextendPoly, 1, &reverse_table0_);
+
+ j = FillZeroesTable(kCrc32cUnextendPoly, &reverse_zeroes_);
+ ABSL_RAW_CHECK(j <= static_cast<int>(ABSL_ARRAYSIZE(this->reverse_zeroes_)),
+ "");
+}
+
+void CRC32::Extend(uint32_t* crc, const void* bytes, size_t length) const {
+ const uint8_t* p = static_cast<const uint8_t*>(bytes);
+ const uint8_t* e = p + length;
+ uint32_t l = *crc;
+
+ auto step_one_byte = [this, &p, &l] () {
+ int c = (l & 0xff) ^ *p++;
+ l = this->table0_[c] ^ (l >> 8);
+ };
+
+ if (kNeedAlignedLoads) {
+ // point x at first 4-byte aligned byte in string. this might be past the
+ // end of the string.
+ const uint8_t* x = RoundUp<4>(p);
+ if (x <= e) {
+ // Process bytes until finished or p is 4-byte aligned
+ while (p != x) {
+ step_one_byte();
+ }
+ }
+ }
+
+ const size_t kSwathSize = 16;
+ if (static_cast<size_t>(e - p) >= kSwathSize) {
+ // Load one swath of data into the operating buffers.
+ uint32_t buf0 = absl::little_endian::Load32(p) ^ l;
+ uint32_t buf1 = absl::little_endian::Load32(p + 4);
+ uint32_t buf2 = absl::little_endian::Load32(p + 8);
+ uint32_t buf3 = absl::little_endian::Load32(p + 12);
+ p += kSwathSize;
+
+ // Increment a CRC value by a "swath"; this combines the four bytes
+ // starting at `ptr` and twelve zero bytes, so that four CRCs can be
+ // built incrementally and combined at the end.
+ const auto step_swath = [this](uint32_t crc_in, const std::uint8_t* ptr) {
+ return absl::little_endian::Load32(ptr) ^
+ this->table_[3][crc_in & 0xff] ^
+ this->table_[2][(crc_in >> 8) & 0xff] ^
+ this->table_[1][(crc_in >> 16) & 0xff] ^
+ this->table_[0][crc_in >> 24];
+ };
+
+ // Run one CRC calculation step over all swaths in one 16-byte stride
+ const auto step_stride = [&]() {
+ buf0 = step_swath(buf0, p);
+ buf1 = step_swath(buf1, p + 4);
+ buf2 = step_swath(buf2, p + 8);
+ buf3 = step_swath(buf3, p + 12);
+ p += 16;
+ };
+
+ // Process kStride interleaved swaths through the data in parallel.
+ while ((e - p) > kPrefetchHorizon) {
+ base_internal::PrefetchNta(
+ reinterpret_cast<const void*>(p + kPrefetchHorizon));
+ // Process 64 bytes at a time
+ step_stride();
+ step_stride();
+ step_stride();
+ step_stride();
+ }
+ while (static_cast<size_t>(e - p) >= kSwathSize) {
+ step_stride();
+ }
+
+ // Now advance one word at a time as far as possible. This isn't worth
+ // doing if we have word-advance tables.
+ while (static_cast<size_t>(e - p) >= 4) {
+ buf0 = step_swath(buf0, p);
+ uint32_t tmp = buf0;
+ buf0 = buf1;
+ buf1 = buf2;
+ buf2 = buf3;
+ buf3 = tmp;
+ p += 4;
+ }
+
+ // Combine the results from the different swaths. This is just a CRC
+ // on the data values in the bufX words.
+ auto combine_one_word = [this](uint32_t crc_in, uint32_t w) {
+ w ^= crc_in;
+ for (size_t i = 0; i < 4; ++i) {
+ w = (w >> 8) ^ this->table0_[w & 0xff];
+ }
+ return w;
+ };
+
+ l = combine_one_word(0, buf0);
+ l = combine_one_word(l, buf1);
+ l = combine_one_word(l, buf2);
+ l = combine_one_word(l, buf3);
+ }
+
+ // Process the last few bytes
+ while (p != e) {
+ step_one_byte();
+ }
+
+ *crc = l;
+}
+
+void CRC32::ExtendByZeroesImpl(uint32_t* crc, size_t length,
+ const uint32_t zeroes_table[256],
+ const uint32_t poly_table[256]) const {
+ if (length != 0) {
+ uint32_t l = *crc;
+ // For each ZEROES_BASE_LG bits in length
+ // (after the low-order bits have been removed)
+ // we lookup the appropriate polynomial in the zeroes_ array
+ // and do a polynomial long multiplication (mod the CRC polynomial)
+ // to extend the CRC by the appropriate number of bits.
+ for (int i = 0; length != 0;
+ i += ZEROES_BASE - 1, length >>= ZEROES_BASE_LG) {
+ int c = length & (ZEROES_BASE - 1); // pick next ZEROES_BASE_LG bits
+ if (c != 0) { // if they are not zero,
+ // multiply by entry in table
+ // Build a table to aid in multiplying 2 bits at a time.
+ // It takes too long to build tables for more bits.
+ uint64_t m = zeroes_table[c + i - 1];
+ m <<= 1;
+ uint64_t m2 = m << 1;
+ uint64_t mtab[4] = {0, m, m2, m2 ^ m};
+
+ // Do the multiply one byte at a time.
+ uint64_t result = 0;
+ for (int x = 0; x < 32; x += 8) {
+ // The carry-less multiply.
+ result ^= mtab[l & 3] ^ (mtab[(l >> 2) & 3] << 2) ^
+ (mtab[(l >> 4) & 3] << 4) ^ (mtab[(l >> 6) & 3] << 6);
+ l >>= 8;
+
+ // Reduce modulo the polynomial
+ result = (result >> 8) ^ poly_table[result & 0xff];
+ }
+ l = static_cast<uint32_t>(result);
+ }
+ }
+ *crc = l;
+ }
+}
+
+void CRC32::ExtendByZeroes(uint32_t* crc, size_t length) const {
+ return CRC32::ExtendByZeroesImpl(crc, length, zeroes_, table0_);
+}
+
+void CRC32::UnextendByZeroes(uint32_t* crc, size_t length) const {
+ // See the comment in CRC32::InitTables() for an explanation of the algorithm
+ // below.
+ *crc = ReverseBits(*crc);
+ ExtendByZeroesImpl(crc, length, reverse_zeroes_, reverse_table0_);
+ *crc = ReverseBits(*crc);
+}
+
+void CRC32::Scramble(uint32_t* crc) const {
+ // Rotate by near half the word size plus 1. See the scramble comment in
+ // crc_internal.h for an explanation.
+ constexpr int scramble_rotate = (32 / 2) + 1;
+ *crc = RotateRight<uint32_t>(static_cast<unsigned int>(*crc + kScrambleLo),
+ 32, scramble_rotate) &
+ MaskOfLength<uint32_t>(32);
+}
+
+void CRC32::Unscramble(uint32_t* crc) const {
+ constexpr int scramble_rotate = (32 / 2) + 1;
+ uint64_t rotated = RotateRight<uint32_t>(static_cast<unsigned int>(*crc), 32,
+ 32 - scramble_rotate);
+ *crc = (rotated - kScrambleLo) & MaskOfLength<uint32_t>(32);
+}
+
+// Constructor and destructor for base class CRC.
+CRC::~CRC() {}
+CRC::CRC() {}
+
+// The "constructor" for a CRC32C with a standard polynomial.
+CRC* CRC::Crc32c() {
+ static CRC* singleton = CRCImpl::NewInternal();
+ return singleton;
+}
+
+// This Concat implementation works for arbitrary polynomials.
+void CRC::Concat(uint32_t* px, uint32_t y, size_t ylen) {
+ // https://en.wikipedia.org/wiki/Mathematics_of_cyclic_redundancy_checks
+ // The CRC of a message M is the remainder of polynomial divison modulo G,
+ // where the coefficient arithmetic is performed modulo 2 (so +/- are XOR):
+ // R(x) = M(x) x**n (mod G)
+ // (n is the degree of G)
+ // In practice, we use an initial value A and a bitmask B to get
+ // R = (A ^ B)x**|M| ^ Mx**n ^ B (mod G)
+ // If M is the concatenation of two strings S and T, and Z is the string of
+ // len(T) 0s, then the remainder CRC(ST) can be expressed as:
+ // R = (A ^ B)x**|ST| ^ STx**n ^ B
+ // = (A ^ B)x**|SZ| ^ SZx**n ^ B ^ Tx**n
+ // = CRC(SZ) ^ Tx**n
+ // CRC(Z) = (A ^ B)x**|T| ^ B
+ // CRC(T) = (A ^ B)x**|T| ^ Tx**n ^ B
+ // So R = CRC(SZ) ^ CRC(Z) ^ CRC(T)
+ //
+ // And further, since CRC(SZ) = Extend(CRC(S), Z),
+ // CRC(SZ) ^ CRC(Z) = Extend(CRC(S) ^ CRC(''), Z).
+ uint32_t z;
+ uint32_t t;
+ Empty(&z);
+ t = *px ^ z;
+ ExtendByZeroes(&t, ylen);
+ *px = t ^ y;
+}
+
+} // namespace crc_internal
+ABSL_NAMESPACE_END
+} // namespace absl
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