[lib/util] Added binary search functions in Ranges.v3 (#288)

lib/util/Ranges.v3

@@ -76,4 +76,40 @@ component Ranges {
 		}
 		return i;
 	}
+	// Performs binary search and returns the index.
+	def binarySearch<T>(range: Range<T>, val: T, lt: (T, T) -> bool) -> int {
+		var l = 0, r = range.length;
+		while (l < r) {
+			var mid = (l + r) >> 1;
+			var mid_val = range[mid];
+			if (lt(val, mid_val)) r = mid - 1;
+			else if (lt(mid_val, val)) l = mid + 1;
+			else return mid;
+		}
+		return -1;
+	}
+	// Returns the *first* element that is *not less* than `val` in a sorted range.
+	def lowerbound<T>(range: Range<T>, val: T, lt: (T, T) -> bool) -> int {
+		var start = 0;
+		var count = range.length;
+		while (count > 0) {
+			var step = count >> 1;
+			var mid = start + step;
+			if (lt(range[mid], val)) { start = mid + 1; count -= step + 1; }
+			else count = step;
+		}
+		return start;
+	} 
+	// Returns the *first* element that is *greater* than `val` in a sorted range.
+	def upperbound<T>(range: Range<T>, val: T, lt: (T, T) -> bool) -> int {
+		var start = 0;
+		var count = range.length;
+		while (count > 0) {
+			var step = count >> 1;
+			var mid = start + step;
+			if (!lt(val, range[mid])) { start = mid + 1; count -= step + 1; }
+			else count = step;
+		}
+		return start;
+	}
 }