added prime field based Cauchy Reed Solomon erasure coding

cauchy_reed_solomon_erasure_coding2.hh

@@ -0,0 +1,90 @@
+/*
+Cauchy Reed Solomon Erasure Coding
+
+Copyright 2024 Ahmet Inan <inan@aicodix.de>
+*/
+
+#pragma once
+
+namespace CODE {
+
+template <typename PF>
+struct CauchyReedSolomonErasureCoding2
+{
+	PF row_num, row_den;
+	// $a_{ij} = \frac{1}{x_i + y_j}$
+	__attribute__((flatten))
+	PF cauchy_matrix(int i, int j)
+	{
+		PF row(i), col(j);
+		return rcp(row + col);
+	}
+	// $b_{ij} = \frac{\prod_{k=1}^{n}{(x_j + y_k)(x_k + y_i)}}{(x_j + y_i)\prod_{k \ne j}^{n}{(x_j - x_k)}\prod_{k \ne i}^{n}{(y_i - y_k)}}$
+	__attribute__((flatten))
+	PF inverse_cauchy_matrix(const PF *rows, int i, int j, int n)
+	{
+#if 1
+		PF col_i(i);
+		PF prod_xy(1), prod_x(1), prod_y(1);
+		for (int k = 0; k < n; k++) {
+			PF col_k(k);
+			prod_xy *= (rows[j] + col_k) * (rows[k] + col_i);
+			if (k != j)
+				prod_x *= (rows[j] - rows[k]);
+			if (k != i)
+				prod_y *= (col_i - col_k);
+		}
+		return prod_xy / ((rows[j] + col_i) * prod_x * prod_y);
+#else
+		PF col_i(i);
+		if (j == 0) {
+			PF num(1), den(1);
+			for (int k = 0; k < n; k++) {
+				PF col_k(k);
+				num *= (rows[k] + col_i);
+				if (k != i)
+					den *= (col_i - col_k);
+			}
+			row_num = num;
+			row_den = den;
+		}
+		PF num(row_num), den(row_den);
+		for (int k = 0; k < n; k++) {
+			PF col_k(k);
+			num *= (rows[j] + col_k);
+			if (k != j)
+				den *= (rows[j] - rows[k]);
+		}
+		return num / ((rows[j] + col_i) * den);
+#endif
+	}
+	__attribute__((flatten))
+	static inline void multiply_accumulate(PF *c, const PF *a, PF 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 PF *data, PF *block, int block_id, int block_len, int block_cnt)
+	{
+		assert(block_id >= block_cnt && block_id < int(PF::P) / 2);
+		for (int k = 0; k < block_cnt; k++) {
+			PF a_ik = cauchy_matrix(block_id, k);
+			multiply_accumulate(block, data + block_len * k, a_ik, block_len, !k);
+		}
+	}
+	void decode(PF *data, const PF *blocks, const PF *block_ids, int block_idx, int block_len, int block_cnt)
+	{
+		for (int k = 0; k < block_cnt; k++) {
+			PF b_ik = inverse_cauchy_matrix(block_ids, block_idx, k, block_cnt);
+			multiply_accumulate(data, blocks + block_len * k, b_ik, block_len, !k);
+		}
+	}
+};
+
+}
+

tests/crs2_regression_test.cc

@@ -0,0 +1,81 @@
+/*
+Regression Test for the second Cauchy Reed Solomon Encoder and Decoder
+
+Copyright 2024 Ahmet Inan <inan@aicodix.de>
+*/
+
+#include <cstdlib>
+#include <cassert>
+#include <chrono>
+#include <random>
+#include <iostream>
+#include <functional>
+#include "prime_field.hh"
+#include "cauchy_reed_solomon_erasure_coding2.hh"
+
+template <typename TYPE, TYPE PRIME>
+void crs_test(int trials)
+{
+	int value_bits = log2(PRIME);
+	int value_bytes = value_bits / 8;
+	typedef CODE::PrimeField<TYPE, PRIME> PF;
+	CODE::CauchyReedSolomonErasureCoding2<PF> crs;
+	std::random_device rd;
+	std::default_random_engine generator(rd());
+	typedef std::uniform_int_distribution<int> distribution;
+	auto rnd_cnt = std::bind(distribution(1, std::min<int>(PF::P / 4, 256)), generator);
+	auto rnd_len = std::bind(distribution(1, 1 << 10), generator);
+	auto rnd_dat = std::bind(distribution(0, (1 << value_bits) - 1), generator);
+	while (--trials) {
+		int block_count = rnd_cnt();
+		int identifiers_total = PF::P / 2 - block_count;
+		int block_values = rnd_len();
+		int block_bytes = block_values * value_bytes;
+		int data_values = block_count * block_values;
+		int data_bytes = data_values * value_bytes;
+		PF *orig = new PF[data_values];
+		PF *data = new PF[data_values];
+		PF *blocks = new PF[data_values];
+		for (int i = 0; i < data_values; ++i)
+			orig[i] = PF(rnd_dat());
+		auto identifiers = new PF[identifiers_total];
+		for (int i = 0; i < identifiers_total; ++i)
+			identifiers[i] = PF(block_count + i);
+		for (int i = 0; i < block_count; i++) {
+			std::uniform_int_distribution<int> hat(i, identifiers_total - 1);
+			std::swap(identifiers[i], identifiers[hat(generator)]);
+		}
+		auto enc_start = std::chrono::system_clock::now();
+		for (int i = 0; i < block_count; ++i)
+			crs.encode(orig, blocks + block_values * i, identifiers[i](), block_values, block_count);
+		auto enc_end = std::chrono::system_clock::now();
+		auto enc_usec = std::chrono::duration_cast<std::chrono::microseconds>(enc_end - enc_start);
+		double enc_mbs = double(data_bytes) / enc_usec.count();
+		auto dec_start = std::chrono::system_clock::now();
+		for (int i = 0; i < block_count; ++i)
+			crs.decode(data + block_values * i, blocks, identifiers, i, block_values, block_count);
+		auto dec_end = std::chrono::system_clock::now();
+		auto dec_usec = std::chrono::duration_cast<std::chrono::microseconds>(dec_end - dec_start);
+		double dec_mbs = double(data_bytes) / dec_usec.count();
+		std::cout << "block count = " << block_count << ", block size = " << block_bytes << " bytes, encoding speed = " << enc_mbs << " megabyte per second, decoding speed = " << dec_mbs << " megabyte per second" << std::endl;
+		for (int i = 0; i < data_values; ++i)
+			assert(data[i] == orig[i]);
+		delete[] identifiers;
+		delete[] blocks;
+		delete[] orig;
+		delete[] data;
+	}
+}
+
+int main()
+{
+	if (1) {
+		crs_test<uint32_t, 257>(200);
+	}
+	if (1) {
+		crs_test<uint64_t, 65537>(100);
+	}
+	std::cerr << "Cauchy Reed Solomon Two regression test passed!" << std::endl;
+	return 0;
+}
+