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89 lines
2.1 KiB
C++
89 lines
2.1 KiB
C++
/*
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Cauchy Mersenne 2^31-1 Prime Field Erasure Coding
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Copyright 2026 Ahmet Inan <inan@aicodix.de>
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*/
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#pragma once
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#include "mersenne_31.hh"
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namespace CODE {
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struct CauchyMersenneErasureCoding
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{
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typedef Mersenne31 M31;
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M31 row_num, row_den;
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// $a_{ij} = \frac{1}{x_i + y_j}$
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M31 cauchy_matrix(int i, int j)
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{
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M31 row(i), col(j);
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return rcp(row + col);
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}
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// $b_{ij} = \frac{\prod_{k=1}^{n}{(x_j + y_k)(x_k + y_i)}}{(x_j + y_i)\prod_{k \ne j}^{n}{(x_j - x_k)}\prod_{k \ne i}^{n}{(y_i - y_k)}}$
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M31 inverse_cauchy_matrix(const int *rows, int i, int j, int n)
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{
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#if 0
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M31 row_j(rows[j]), col_i(i);
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M31 prod_xy(1), prod_x(1), prod_y(1);
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for (int k = 0; k < n; k++) {
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M31 row_k(rows[k]), col_k(k);
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prod_xy *= (row_j + col_k) * (row_k + col_i);
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if (k != j)
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prod_x *= (row_j - row_k);
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if (k != i)
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prod_y *= (col_i - col_k);
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}
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return prod_xy / ((row_j + col_i) * prod_x * prod_y);
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#else
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M31 row_j(rows[j]), col_i(i);
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if (j == 0) {
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M31 num(1), den(1);
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for (int k = 0; k < n; k++) {
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M31 row_k(rows[k]), col_k(k);
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num *= row_k + col_i;
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if (k != i)
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den *= col_i - col_k;
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}
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row_num = num;
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row_den = den;
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}
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M31 num(row_num), den(row_den);
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for (int k = 0; k < n; k++) {
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M31 row_k(rows[k]), col_k(k);
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num *= row_j + col_k;
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if (k != j)
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den *= row_j - row_k;
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}
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return num / ((row_j + col_i) * den);
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#endif
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}
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void mac(M31 *c, const M31 *a, M31 b, int len, bool init)
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{
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if (init) {
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for (int i = 0; i < len; i++)
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c[i] = b * a[i];
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} else {
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for (int i = 0; i < len; i++)
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c[i] += b * a[i];
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}
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}
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void encode(const M31 *data, M31 *block, int block_id, int block_len, int block_cnt)
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{
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assert(block_id >= block_cnt && block_id < int(M31::P) / 2);
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for (int k = 0; k < block_cnt; k++) {
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M31 a_ik = cauchy_matrix(block_id, k);
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mac(block, data + block_len * k, a_ik, block_len, !k);
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}
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}
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void decode(M31 *data, const M31 *blocks, const int *block_ids, int block_idx, int block_len, int block_cnt)
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{
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for (int k = 0; k < block_cnt; k++) {
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M31 b_ik = inverse_cauchy_matrix(block_ids, block_idx, k, block_cnt);
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mac(data, blocks + block_len * k, b_ik, block_len, !k);
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}
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}
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};
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}
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