LUN calculation

The DS6000™ series uses a volume capacity algorithm (calculation) to provide a logical unit number (LUN).

The following volume capacities are expressed in both binary (GB - 2³⁰) and decimal (GB - 10⁹) conventions, independent of the capacity algorithm that is used to create the volume.

GB (2³⁰) = Bytes / 2³⁰ = Bytes / 1 073 741 824

GB (10⁹) = Bytes / 10⁹= Bytes / 1 000 000 000

Computer memory capacity is typically described in powers of 2; for example, MB(2²⁰), GB (2³⁰), TB (2⁴⁰). Computer storage capacity is typically described in powers of 10; for example, MB(10⁶), GB(10⁹), TB(10¹²).

In the DS6000 family, physical storage capacities such as DDMs are generally expressed in powers of 10. Logical or effective storage capacities (logical volumes, ranks, extent pools) and processor memory capacities are expressed in powers of 2. Both of these conventions are used for logical volume effective storage capacities.

The logical volume capacity is accurate to 0.1 GB for either decimal or binary capacity convention. For logical volumes that are created with the decimal capacity algorithm, each decimal GB capacity value defines a unique volume size (the value that is used to create the volume). However, two decimal GB sizes might indicate the same binary GB size, because rounding to the nearest 0.1 GB is not sufficient to delineate all supported sizes. Similarly, two logical volumes with the same binary GB and decimal GB sizes are not necessarily the same size if they were created with a different capacity algorithm.

On open volumes with 512-byte blocks, you can determine the exact capacity of the volume in bytes by multiplying the number of blocks by 512. For open volumes with 520-byte blocks (such as iSeries™ volumes), you can determine the exact capacity of the volume in bytes by multiplying the number of blocks by 520. However, capacity of these volumes in bytes is expressed by multiplying the number of blocks by 512, because only 512 of the 520 bytes are used to store customer data.

On CKD volumes, the volume is created when a number of cylinders are specified. On DS6000, the basic allocation unit for CKD volumes is a CKD extent, which is exactly 1113 cylinders. The volume can be created with any number of integral cylinders in the range of 1 to 65 520 ('FFF0'X) cylinders, although volumes that are an exact multiple of 1113 cylinders do not waste any capacity in the last extent. The capacity of a CKD volume can be expressed in bytes, although the actual capacity of the volume varies depending on the format of every track on the volume. Every cylinder contains 15 tracks. A track with a 3390 track format is generally expressed as having a maximum capacity of 56 664 bytes. A track with a 3380 track format is generally expressed as having a maximum capacity of 47 476 bytes. The binary and decimal GB value that is displayed for CKD volumes is based on these capacities (for example: capacity of a volume with a 3390 track format in decimal GB = cylinders × 15 × 56782 / 10⁹).

The logical volumes are created using one of the following three algorithms.

Binary Capacity Algorithm (B):

This algorithm provides LUNs that fully use the capacity in every extent and also are supported across the DS6000 family. The input to the GUI is the exact size of the volume in integral GB (2³⁰). The supported sizes are limited to integral multiples of the supported extent size and are further limited on larger LUNs to allow larger extent sizes in the future. The following sizes are valid:

1 to 64 GB (in 1 GB increments)

64 to 256 GB (in 4 GB increments)

256 to 1024 GB (in 16 GB increments)

1024 to 2048 GB (in 64 GB increments)

Decimal Capacity Algorithm (D):

This algorithm provides LUNs that are supported across the DS6000 family. The last extent on the volume might not be fully used because these sizes are not an integral multiple of the extent size.

You can calculate exact volume sizes as follows:

bytes = blocks × 512 = INT( ( INT( xxx.X×10⁹/512 ) + 63 ) / 64 ) × 64 × 512, where xxx.X is the value that is input by the user to the configuration process that is specified in GB (10⁹). That is, this value is rounded down to a block or rounded up to a 32 KB track size.

The following sizes are valid:

0.1 to 982.2 GB (in 0.1 GB [10⁸] increments)

iSeries Capacity Algorithm (I):

This algorithm provides iSeries LUN sizes that are specified in decimal GBs (with the assumption that each logical block contains 512 bytes of data). The set that is allowed is the complete set that is supported by iSeries.

You can define storage unit LUNs as either protected or unprotected. You can create iSeries LUNs as either logically protected or unprotected. An unprotected LUN is available for OS/400^® to mirror that volume (either internal or external) to another of equal capacity. Protected logical volumes do not use OS/400, or host-based, mirroring. All IBM^® iSeries physical volumes are RAID 5 or RAID 10 volumes and are protected within the storage unit.

OS/400 only supports certain fixed volume sizes; for example, model sizes of 8.5 GB, 17.5 GB, and 35.1 GB. Because these volume sizes are not multiples of 1 GB, some space is left unused depending on the chosen model. iSeries LUNs make available a 520-byte block to the host. The operating system uses 8 of these bytes; therefore, the usable space is still 512 bytes like other SCSI LUNs. The capacities that are quoted for the iSeries LUNs are normally 512-byte block storage capacity and are expressed in decimal GB (10⁹). Convert these capacities to binary GB (2³⁰) to maximize the use of extents that are 1 GB (2³⁰).

Table 1 provides models of storage capacity and disk volumes of the IBM iSeries systems.