Efficient implementations of arithmetic functions in programmable ICs include carry chain multiplexers driven by dual-output programmable function generators. A function generator having two output signals is programmed to generate both an exclusive OR (XOR) function of first and second input signals and a second function. In some embodiments, the second function is simply the second input signal to the XOR function. In other embodiments, the second function is a different function optionally independent of the first and second input signals. The XOR function output drives the select terminal of a carry multiplexer, which selects between a carry in signal and one of the second input signal and the second function output signal to provide the carry out output signal. The sum or multiplier output value is provided by an XOR gate driven by the XOR function output and by the carry in signal, and can be optionally registered.