Template out the usual repetitive stuff of segment finding.

Numeric/UpperBound.hpp

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+//
+//  UpperBound.hpp
+//  Clock Signal
+//
+//  Created by Thomas Harte on 11/12/2024.
+//  Copyright © 2024 Thomas Harte. All rights reserved.
+//
+
+#pragma once
+
+namespace Numeric {
+
+/// @returns The element that is `index - offset` into the list given by the rest of the
+/// variadic arguments or the final element if `offset` is out of bounds.
+///
+/// E.g. @c at_index<0, 3, 5, 6, 7, 8, 9>() returns the `3 - 0` = 4th element from the
+/// list 5, 6, 7, 8, 9, i.e. 8.
+template<int origin, int index, int T, int... Args>
+int at_index() {
+	if constexpr (origin == index || sizeof...(Args) == 0) {
+		return T;
+	} else {
+		return at_index<origin + 1, index, Args...>();
+	}
+}
+
+/// @returns The result of binary searching for the first thing in the range `[left, right)` within
+/// the other template arguments that is strictly greater than @c location.
+template <int left, int right, int... Args>
+int upper_bound_bounded(int location) {
+	if constexpr (left + 1 == right) {
+		return at_index<0, left+1, Args...>();
+	}
+
+	constexpr auto midpoint = (left + right) >> 1;
+	if(location >= at_index<0, midpoint, Args...>()) {
+		return upper_bound_bounded<midpoint, right, Args...>(location);
+	} else {
+		return upper_bound_bounded<left, midpoint, Args...>(location);
+	}
+}
+
+/// @returns The result of binary searching for the first thing in the template arguments
+/// is strictly greater than @c location.
+template <int... Args>
+int upper_bound(int location) {
+	return upper_bound_bounded<0, sizeof...(Args), Args...>(location);
+}
+
+}