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added Cauchy Mersenne 31 prime field erasure encoding

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Ahmet Inan 2026-04-27 13:37:24 +02:00
commit 686983cd32
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cauchy_mersenne_erasure_coding.hh Normal file
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/*
Cauchy Mersenne 2^31-1 Prime Field Erasure Coding
Copyright 2026 Ahmet Inan <inan@aicodix.de>
*/
#pragma once
#include "mersenne_31.hh"
namespace CODE {
struct CauchyMersenneErasureCoding
{
typedef Mersenne31 M31;
M31 row_num, row_den;
// $a_{ij} = \frac{1}{x_i + y_j}$
M31 cauchy_matrix(int i, int j)
{
M31 row(i), col(j);
return rcp(row + col);
}
// $b_{ij} = \frac{\prod_{k=1}^{n}{(x_j + y_k)(x_k + y_i)}}{(x_j + y_i)\prod_{k \ne j}^{n}{(x_j - x_k)}\prod_{k \ne i}^{n}{(y_i - y_k)}}$
M31 inverse_cauchy_matrix(const int *rows, int i, int j, int n)
{
#if 0
M31 row_j(rows[j]), col_i(i);
M31 prod_xy(1), prod_x(1), prod_y(1);
for (int k = 0; k < n; k++) {
M31 row_k(rows[k]), col_k(k);
prod_xy *= (row_j + col_k) * (row_k + col_i);
if (k != j)
prod_x *= (row_j - row_k);
if (k != i)
prod_y *= (col_i - col_k);
}
return prod_xy / ((row_j + col_i) * prod_x * prod_y);
#else
M31 row_j(rows[j]), col_i(i);
if (j == 0) {
M31 num(1), den(1);
for (int k = 0; k < n; k++) {
M31 row_k(rows[k]), col_k(k);
num *= row_k + col_i;
if (k != i)
den *= col_i - col_k;
}
row_num = num;
row_den = den;
}
M31 num(row_num), den(row_den);
for (int k = 0; k < n; k++) {
M31 row_k(rows[k]), col_k(k);
num *= row_j + col_k;
if (k != j)
den *= row_j - row_k;
}
return num / ((row_j + col_i) * den);
#endif
}
void mac(M31 *c, const M31 *a, M31 b, int len, bool init)
{
if (init) {
for (int i = 0; i < len; i++)
c[i] = b * a[i];
} else {
for (int i = 0; i < len; i++)
c[i] += b * a[i];
}
}
void encode(const M31 *data, M31 *block, int block_id, int block_len, int block_cnt)
{
assert(block_id >= block_cnt && block_id < int(M31::P) / 2);
for (int k = 0; k < block_cnt; k++) {
M31 a_ik = cauchy_matrix(block_id, k);
mac(block, data + block_len * k, a_ik, block_len, !k);
}
}
void decode(M31 *data, const M31 *blocks, const int *block_ids, int block_idx, int block_len, int block_cnt)
{
for (int k = 0; k < block_cnt; k++) {
M31 b_ik = inverse_cauchy_matrix(block_ids, block_idx, k, block_cnt);
mac(data, blocks + block_len * k, b_ik, block_len, !k);
}
}
};
}