+inline int
+shift_left (int value, int shiftamount)
+{
+ if (shiftamount < 0) return (value >> -shiftamount);
+ else return (value << shiftamount);
+}
+
+inline Real
+linear_interpolate (Real x, Real x1, Real x2, Real y1, Real y2)
+{
+ return (x2 - x) / (x2 - x1) * y1
+ + (x - x1) / (x2 - x1) * y2;
+}
+
+inline Real
+normalize (Real x, Real x1, Real x2)
+{
+ return (x - x1) / (x2 - x1);
+}
+
+Real directed_round (Real f, Direction d);
+
+Real peak_around (Real epsilon, Real threshold, Real x);
+Real convex_amplifier (Real standard_x, Real increase_factor, Real x);
+string camel_case_to_lisp_identifier (const string &in);