A semiconductor memory in which arbitrary operation mode information is set in a plurality of CRs at test time and by which a test cost is reduced and a method for testing such a semiconductor memory. The plurality of CRs hold operation mode information. When a CR control circuit detects write commands to write to an address for register access or read commands to read from the address for register access in a predetermined order, the CR control circuit updates the operation mode information for each of the plurality of CRs on a time division basis. A command generation section generates the write commands, the read commands, or a test start command by which write operation or read operation does not occur, in response to a control signal from the outside. In addition, the command generation section regenerates the test start command each time the plurality of CRs are updated. A data pad compression circuit changes the operation mode information to be written to the plurality of CRs by using test data inputted to part of data pads, after inverting the test data or in its original condition according to a code, as data for a rest of the data pads, the code represented by part of an address inputted at the time of the test start command being sent.