Release calc version 2.11.0t10.5.1

lib/solve.cal

@@ -0,0 +1,43 @@
+/*
+ * Copyright (c) 1995 David I. Bell
+ * Permission is granted to use, distribute, or modify this source,
+ * provided that this copyright notice remains intact.
+ *
+ * Solve the equation f(x) = 0 to within the desired error value for x.
+ * The function 'f' must be defined outside of this routine, and the low
+ * and high values are guesses which must produce values with opposite signs.
+ */
+
+define solve(low, high, epsilon)
+{
+	local flow, fhigh, fmid, mid, places;
+
+	if (isnull(epsilon))
+		epsilon = epsilon();
+	if (epsilon <= 0)
+		quit "Non-positive epsilon value";
+	places = highbit(1 + int(1/epsilon)) + 1;
+	flow = f(low);
+	if (abs(flow) < epsilon)
+		return low;
+	fhigh = f(high);
+	if (abs(flow) < epsilon)
+		return high;
+	if (sgn(flow) == sgn(fhigh))
+		quit "Non-opposite signs";
+	while (1) {
+		mid = bround(high - fhigh * (high - low) / (fhigh - flow), places);
+		if ((mid == low) || (mid == high))
+			places++;
+		fmid = f(mid);
+		if (abs(fmid) < epsilon)
+			return mid;
+		if (sgn(fmid) == sgn(flow)) {
+			low = mid;
+			flow = fmid;
+		} else {
+			high = mid;
+			fhigh = fmid;
+		}
+	}
+}