Provided are a method, system, and program for generating parity data when updating old data stored in an array of storage devices in a data organization type which utilizes parity data. In one embodiment, a logic engine has plural registers or store queues in which new data obtained in a read operation is stored. A logic function such as an Exclusive-OR function is performed on the new data in each of the plural registers using old data obtained in another read operation. A logic function such as an Exclusive-OR function is performed on the intermediate data in one of the plural registers using old parity data of a first type obtained in another read operation, to generate new parity data of the first type. A logic function such as an Exclusive-OR function is performed on the intermediate data in another of the plural registers using old parity data of a second type obtained in another read operation, to generate new parity data of the second type.