Integrated circuits such as application specific circuits or programmable logic devices may include specialized blocks such as configurable storage blocks and configurable processing blocks. Such specialized blocks may be controlled by clock signals and operated at single data rate or at double data rate. For instance, configurable storage blocks may be configured to use a double data rate communications scheme or a single data rate communication scheme to communicate data with other blocks. Configurable processing blocks may be configured to process data at a double data rate or a single data rate. Furthermore, configurable processing blocks that include accumulator circuitry may be configured to perform one accumulation at a single data rate or at a double data rate. Such configurable processing blocks may also be configured to perform two accumulations at a single data rate.