Disclosed is a parallel prefix adder structure with a carry bit generation circuit that generates primary carry bits for only some bit pairs and a sum circuit with ripple carry adders that use these primary carry bits to generate secondary carry bits and sum bits for a final sum. The carry bit generation circuit has different sections, which process different sequential sets of bit pairs and which have different sparsity configurations. As a result, generation of the primary carry bits is non-uniform. That is, in the different sections the primary carry bits are generated at different carry bit-to-bit pair ratios (e.g., the carry bit-to-bit pair ratios for the different sections can be 1:2, 1:4, and 1:2, respectively). For optimal performance, the specific bit pairs for which these primary carry bits are generated varies depending upon whether the maximum operand size is an odd number of bits or an even number.