136 lines
3.8 KiB
C++
136 lines
3.8 KiB
C++
/*
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* Copyright (c) Facebook, Inc. and its affiliates.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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#pragma once
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#include <stddef.h>
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#include <cstdint>
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namespace folly {
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namespace detail {
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/**
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* Representation of a polynomial of degree DEG over GF(2) (that is,
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* with binary coefficients).
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*
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* Probably of no use outside of Fingerprint code; used by
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* GenerateFingerprintTables and the unittest.
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*/
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template <int DEG>
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class FingerprintPolynomial {
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public:
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static constexpr int size() {
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return 1 + DEG / 64;
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}
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constexpr FingerprintPolynomial() {}
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constexpr explicit FingerprintPolynomial(const uint64_t (&vals)[size()]) {
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for (int i = 0; i < size(); i++) {
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val_[i] = vals[i];
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}
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}
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constexpr uint64_t get(size_t i) const {
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return val_[i];
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}
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constexpr void add(const FingerprintPolynomial<DEG>& other) {
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for (int i = 0; i < size(); i++) {
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val_[i] ^= other.val_[i];
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}
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}
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// Multiply by X. The actual degree must be < DEG.
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constexpr void mulX() {
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uint64_t b = 0;
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for (int i = size() - 1; i >= 0; i--) {
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uint64_t nb = val_[i] >> 63;
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val_[i] = (val_[i] << 1) | b;
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b = nb;
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}
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}
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// Compute (this * X) mod P(X), where P(X) is a monic polynomial of degree
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// DEG+1 (represented as a FingerprintPolynomial<DEG> object, with the
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// implicit coefficient of X^(DEG+1)==1)
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//
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// This is a bit tricky. If k=DEG+1:
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// Let P(X) = X^k + p_(k-1) * X^(k-1) + ... + p_1 * X + p_0
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// Let this = A(X) = a_(k-1) * X^(k-1) + ... + a_1 * X + a_0
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// Then:
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// A(X) * X
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// = a_(k-1) * X^k + (a_(k-2) * X^(k-1) + ... + a_1 * X^2 + a_0 * X)
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// = a_(k-1) * X^k + (the binary representation of A, left shift by 1)
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//
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// if a_(k-1) = 0, we can ignore the first term.
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// if a_(k-1) = 1, then:
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// X^k mod P(X)
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// = X^k - P(X)
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// = P(X) - X^k
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// = p_(k-1) * X^(k-1) + ... + p_1 * X + p_0
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// = exactly the binary representation passed in as an argument to this
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// function!
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//
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// So A(X) * X mod P(X) is:
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// the binary representation of A, left shift by 1,
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// XOR p if a_(k-1) == 1
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constexpr void mulXmod(const FingerprintPolynomial<DEG>& p) {
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bool needXOR = (val_[0] & (1ULL << 63));
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val_[0] &= ~(1ULL << 63);
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mulX();
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if (needXOR) {
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add(p);
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}
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}
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// Compute (this * X^k) mod P(X) by repeatedly multiplying by X (see above)
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constexpr void mulXkmod(int k, const FingerprintPolynomial<DEG>& p) {
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for (int i = 0; i < k; i++) {
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mulXmod(p);
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}
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}
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// add X^k, where k <= DEG
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constexpr void addXk(int k) {
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int word_offset = (DEG - k) / 64;
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int bit_offset = 63 - (DEG - k) % 64;
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val_[word_offset] ^= (1ULL << bit_offset);
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}
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// Set the highest 8 bits to val.
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// If val is interpreted as polynomial of degree 7, then this sets *this
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// to val * X^(DEG-7)
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constexpr void setHigh8Bits(uint8_t val) {
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val_[0] = ((uint64_t)val) << (64 - 8);
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for (int i = 1; i < size(); i++) {
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val_[i] = 0;
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}
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}
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private:
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// Internal representation: big endian
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// val_[0] contains the highest order coefficients, with bit 63 as the
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// highest order coefficient
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//
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// If DEG+1 is not a multiple of 64, val_[size()-1] only uses the highest
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// order (DEG+1)%64 bits (the others are always 0)
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uint64_t val_[size()] = {};
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};
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} // namespace detail
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} // namespace folly
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