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48 lines
978 B
48 lines
978 B
/*
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Copyright (c) 2020 tevador <tevador@gmail.com>
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All rights reserved.
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*/
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#pragma once
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#include <cstdint>
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#include <cassert>
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typedef uint_least16_t gf_storage;
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typedef uint_fast16_t gf_item;
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template<unsigned bits, gf_item primitive>
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class galois_field {
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public:
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galois_field();
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gf_item inverse(gf_item i) const {
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assert(i != 0);
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return i > 1 ? inv_table[i] : 1;
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}
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gf_item mult(gf_item a, gf_item b) const {
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if (b == 0 || a == 0)
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return 0;
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if (b == 1)
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return a;
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if (a == 1)
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return b;
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return exp_table[log_table[a] + log_table[b]];
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}
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gf_item exp(gf_item i) const {
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return exp_table[i];
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}
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static constexpr unsigned size() {
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return bits;
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}
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static constexpr unsigned elements() {
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return size_;
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}
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private:
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static_assert(bits <= 14, "field is too large");
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static constexpr gf_item size_ = 1u << bits;
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gf_storage log_table[size_];
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gf_storage exp_table[2 * size_];
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gf_storage inv_table[size_];
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};
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using gf_2048 = galois_field<11, 2053>;
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