Introduce a template for numeric coding.

Numeric/NumericCoder.hpp

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+//
+//  NumericCoder.hpp
+//  Clock Signal
+//
+//  Created by Thomas Harte on 17/01/2023.
+//  Copyright © 2023 Thomas Harte. All rights reserved.
+//
+
+#ifndef NumericCoder_hpp
+#define NumericCoder_hpp
+
+namespace Numeric {
+
+/// Stores and retrieves an arbitrary number of fields into an int with arbitrary modulos.
+///
+/// E.g. NumericEncoder<8, 3, 14> establishes an encoder and decoder for three fields,
+/// the first is modulo 8, the second is modulo 3, the third is modulo 14.
+///
+/// NumericEncoder<8, 3, 14>::encode<2>(v, 9) will mutate v so that the third field
+/// (i.e. field 2) has value 9.
+template <int... Sizes> class NumericCoder {
+	public:
+		/// Modifies @c target to hold @c value at @c index.
+		template <int index> static void encode(int &target, int value) {
+			static_assert(index < sizeof...(Sizes), "Index must be within range");
+			NumericEncoderImp<Sizes...>::template encode<index, 0, 1>(target, value);
+		}
+		/// @returns The value from @c source at @c index.
+		template <int index> static int decode(int source) {
+			static_assert(index < sizeof...(Sizes), "Index must be within range");
+			return NumericEncoderImp<Sizes...>::template decode<index, 0, 1>(source);
+		}
+
+	private:
+
+		template <int size, int... Tail>
+		struct NumericEncoderImp {
+			template <int index, int i, int divider> static void encode(int &target, int value) {
+				if constexpr (i == index) {
+					const int suffix = target % divider;
+					target /= divider;
+					target -= target % size;
+					target += value % size;
+					target *= divider;
+					target += suffix;
+				} else {
+					NumericEncoderImp<Tail...>::template encode<index, i+1, divider*size>(target, value);
+				}
+			}
+
+			template <int index, int i, int divider> static int decode(int source) {
+				if constexpr (i == index) {
+					return (source / divider) % size;
+				} else {
+					return NumericEncoderImp<Tail...>::template decode<index, i+1, divider*size>(source);
+				}
+			}
+
+		};
+};
+
+}
+
+#endif /* NumericCoder_hpp */