added Reed Solomon error correction

lifted from my FEC project:
https://github.com/xdsopl/FEC

reed_solomon_encoder.hh

@@ -0,0 +1,78 @@
+/*
+Reed Solomon Encoder
+
+Copyright 2018 Ahmet Inan <inan@aicodix.de>
+*/
+
+#ifndef REED_SOLOMON_ENCODER_HH
+#define REED_SOLOMON_ENCODER_HH
+
+namespace CODE {
+
+template <int NR, int FCR, typename GF>
+class ReedSolomonEncoder
+{
+public:
+	typedef typename GF::value_type value_type;
+	typedef typename GF::ValueType ValueType;
+	typedef typename GF::IndexType IndexType;
+	static const int N = GF::N, K = N - NR;
+	IndexType generator[NR+1];
+	ReedSolomonEncoder()
+	{
+		// $generator = \prod_{i=0}^{NR}(x-pe^{FCR+i})$
+		ValueType tmp[NR+1];
+		IndexType root(FCR), pe(1);
+		for (int i = 0; i < NR; ++i) {
+			tmp[i] = ValueType(1);
+			for (int j = i; j > 0; --j)
+				tmp[j] = fma(root, tmp[j], tmp[j-1]);
+			tmp[0] *= root;
+			root *= pe;
+		}
+		tmp[NR] = ValueType(1);
+		if (0) {
+			std::cout << "generator = ";
+			for (int i = NR; i > 0; --i) {
+				if (!tmp[i])
+					continue;
+				if (tmp[i] != ValueType(1))
+					std::cout << (int)tmp[i] << "*";
+				std::cout << "x";
+				if (i != 1)
+					std::cout << "^" << i;
+				std::cout << " + ";
+			}
+			std::cout << (int)tmp[0] << std::endl;
+		}
+		for (int i = 0; i <= NR; ++i)
+			generator[i] = index(tmp[i]);
+	}
+	void operator()(ValueType *code)
+	{
+		// $code = data * x^{NR} + (data * x^{NR}) \mod{generator}$
+		for (int i = 0; i < NR; ++i)
+			code[K+i] = ValueType(0);
+		for (int i = 0; i < K; ++i) {
+			ValueType feedback = code[i] + code[K];
+			if (feedback) {
+				IndexType fb = index(feedback);
+				for (int j = 1; j < NR; ++j)
+					code[K+j-1] = fma(fb, generator[NR-j], code[K+j]);
+				code[N-1] = value(generator[0] * fb);
+			} else {
+				for (int j = 1; j < NR; ++j)
+					code[K+j-1] = code[K+j];
+				code[N-1] = ValueType(0);
+			}
+		}
+	}
+	void operator()(value_type *code)
+	{
+		(*this)(reinterpret_cast<ValueType *>(code));
+	}
+};
+
+}
+
+#endif