In order to enable to quickly and efficiently execute, by one system, various modulation/demodulation/synchronous processes in a plurality of radio communication methods, a co-processor (22) for complex arithmetic processing, which forms a processor system (100), includes a complex arithmetic circuit (22) that executes for complex data a complex arithmetic operation required for radio communication in accordance with an instruction from a primary processor (10), and a memory controller (20, 21) that operates in parallel with the complex arithmetic circuit and accesses a memory. A trace circuit provided in the complex arithmetic circuit (22) monitors arithmetic result data for first complex data series sequentially read from the memory, and detects a normalization coefficient for normalizing the arithmetic result data.