Circuitry for increasing the precision of multipliers by a desired factor while limiting the increase in arithmetic complexity of the multiplier to that factor can be provided in a fixed logic device, or can be configured into a programmable integrated circuit device such as a programmable logic device (PLD). The smaller increase in arithmetic complexity, so that the increase is proportional to the increase in precision, rather than to the square of the increase in precision, is achieved by using specialized processing block components differently on alternating clock cycles. For example, to implement double precision, the same multiplier components are used in each of two clock cycles, but some specialized processing block internal structures (e.g., shifters and adders) are used differently in the two cycles, so that over the two cycles, a larger multiplication may be calculated from smaller partial products.