the new value including the program identifier embedded by the function f the function f is a function inputting two values and outputting one value on the other hand the inverse function g is a function inputting one value and outputting two values if z is the output of f x y g z outputs x and y a conceivably simplest example of the function f is a function to concatenate a program identifier with a specific value on the high order side of the specific value as high order bits of a resulting new value a conceivably simplest example of the inverse function g is a function to extract the high order bits from the resulting new value to give the program identifier and the original specific value the function f and the inverse function g can be applied to a case in which the real storage capacity of a logical volume is small so that high order bits of the address are not used since types of the function f and the inverse function g have nothing to do with the embodiments described below the following description does not specifically describe the types of the function f and the inverse function g fig1 is a diagram showing a program 101 using the function f examples of the program 101 are an application program and middleware using a storage apparatus examples of such middleware are a database management system and a web server the program 101 comprises a processing main module 102 and an io processing module 103 for inputting and outputting data from and to a storage apparatus in the implementation.