When diode selection circuits are fed with signals that vary linearly with an input variable, they produce as output a convex or concave function consisting of one linear section per diode. In the present circuits, by combining each diode with a suitable series ``interpolating'' resistor, and feeding the output connection with constant current, it is possible to produce 2n-1 linear sections with n diodes. The use of voltage dependent interpolating resistors replaces the linear sections by nonlinear curves making possible the generation of smooth nonlinear functions. The function generator is stable as compared with similar nonlinear circuits because its transfer characteristic is independent of the nonlinearity of the resistors in a first approximation. Accuracies of the order 0.5 per cent of full scale output are readily obtainable even in the simplest circuit configurations. 1° phase shift occurs at frequencies of the order of 10 kc for nonlinear interpolation and up to several hundred kc for linear interpolation. The representative example of a squarer is described in detail; an error analysis is given and it is shown how the circuit can be compensated for a constant linear load.