Working with Packed Decimal and Zoned Decimal Data

Definitions

Packed decimal

specifies a method of encoding decimal numbers by using each byte to represent two decimal digits. Packed decimal representation stores decimal data with exact precision. The fractional part of the number is determined by the informat or format because there is no separate mantissa and exponent.

An advantage of using packed decimal data is that exact precision can be maintained. However, computations involving decimal data might become inexact due to the lack of native instructions.

Zoned decimal

specifies a method of encoding decimal numbers in which each digit requires one byte of storage. The last byte contains the number's sign as well as the last digit. Zoned decimal data produces a printable representation.

Nibble

specifies 1/2 of a byte.

Types of Data

Packed Decimal Data

A packed decimal representation stores decimal digits in each “nibble” of a byte. Each byte has two nibbles, and each nibble is indicated by a hexadecimal character. For example, the value 15 is stored in two nibbles, using the hexadecimal characters 1 and 5.

The sign indication is dependent on your operating environment. On IBM mainframes, the sign is indicated by the last nibble. With formats, C indicates a positive value, and D indicates a negative value. With informats, A, C, E, and F indicate positive values, and B and D indicate negative values. Any other nibble is invalid for signed packed decimal data. In all other operating environments, the sign is indicated in its own byte. If the high-order bit is 1, then the number is negative. Otherwise, it is positive.

The following applies to packed decimal data representation:

You can use the S370FPD format on all platforms to obtain the IBM mainframe configuration.
You can have unsigned packed data with no sign indicator. The packed decimal format and informat handles the representation. It is consistent between ASCII and EBCDIC platforms.
Note that the S370FPDU format and informat expects to have an F in the last nibble, while packed decimal expects no sign nibble.

Zoned Decimal Data

The following applies to zoned decimal data representation:

A zoned decimal representation stores a decimal digit in the low order nibble of each byte. For all but the byte containing the sign, the high-order nibble is the numeric zone nibble (F on EBCDIC and 3 on ASCII).
The sign can be merged into a byte with a digit, or it can be separate, depending on the representation. But the standard zoned decimal format and informat expects the sign to be merged into the last byte.
The EBCDIC and ASCII zoned decimal formats produce the same printable representation of numbers. There are two nibbles per byte, each indicated by a hexadecimal character. For example, the value 15 is stored in two bytes. The first byte contains the hexadecimal value F1 and the second byte contains the hexadecimal value C5.

Packed Julian Dates

The following applies to packed Julian dates:

The two formats and informats that handle Julian dates in packed decimal representation are PDJULI and PDJULG. PDJULI uses the IBM mainframe year computation, while PDJULG uses the Gregorian computation.
The IBM mainframe computation considers 1900 to be the base year, and the year values in the data indicate the offset from 1900. For example, 98 means 1998, 100 means 2000, and 102 means 2002. 1998 would mean 3898.
The Gregorian computation allows for 2–digit or 4–digit years. If you use 2–digit years, SAS uses the setting of the YEARCUTOFF= system option to determine the true year.

Platforms Supporting Packed Decimal and Zoned Decimal Data

Some platforms have native instructions to support packed and zoned decimal data, while others must use software to emulate the computations. For example, the IBM mainframe has an Add Pack instruction to add packed decimal data, but the Intel-based platforms have no such instruction and must convert the decimal data into some other format.

Languages Supporting Packed Decimal and Zoned Decimal Data

Several languages support packed decimal and zoned decimal data. The following table shows how COBOL picture clauses correspond to SAS formats and informats.

IBM VS COBOL II Clauses	Corresponding S370Fxxx Formats and Informats
PIC S9(X) PACKED-DECIMAL	S370FPDw.
PIC 9(X) PACKED-DECIMAL	S370FPDUw.
PIC S9(W) DISPLAY	S370FZDw.
PIC 9(W) DISPLAY	S370FZDUw.
PIC S9(W) DISPLAY SIGN LEADING	S370FZDLw.
PIC S9(W) DISPLAY SIGN LEADING SEPARATE	S370FZDSw.
PIC S9(W) DISPLAY SIGN TRAILING SEPARATE	S370FZDTw.

For the packed decimal representation listed above, X indicates the number of digits represented, and W is the number of bytes. For PIC S9(X) PACKED-DECIMAL, W is ceil((x+1)/2). For PIC 9(X) PACKED-DECIMAL, W is ceil(x/2). For example, PIC S9(5) PACKED-DECIMAL represents five digits. If a sign is included, six nibbles are needed. ceil((5+1)/2) has a length of three bytes, and the value of W is 3.

Note that you can substitute COMP-3 for PACKED-DECIMAL.

In IBM assembly language, the P directive indicates packed decimal, and the Z directive indicates zoned decimal. The following shows an excerpt from an assembly language listing, showing the offset, the value, and the DC statement:

offset  value (in hex)      inst label     directive

+000000 00001C                2 PEX1       DC PL3'1' 
+000003 00001D                3 PEX2       DC PL3'-1'
+000006 F0F0C1                4 ZEX1       DC ZL3'1' 
+000009 F0F0D1                5 ZEX2       DC ZL3'1'

In PL/I, the FIXED DECIMAL attribute is used in conjunction with packed decimal data. You must use the PICTURE specification to represent zoned decimal data. There is no standardized representation of decimal data for the Fortran or the C languages.

Summary of Packed Decimal and Zoned Decimal Formats and Informats

SAS uses a group of formats and informats to handle packed and zoned decimal data. The following table lists the type of data representation for these formats and informats. Note that the formats and informats that begin with S370 refer to IBM mainframe representation.

Format	Data Type Representation	Corresponding Informat	Comments
PD	Packed decimal	PD	Local signed packed decimal
PK	Packed decimal	PK	Unsigned packed decimal; not specific to your operating environment
ZD	Zoned decimal	ZD	Local zoned decimal
none	Zoned decimal	ZDB	Translates EBCDIC blank (x'40') to EBCDIC zero (x'F0'), and then corresponds to the informat as zoned decimal
none	Zoned decimal	ZDV	Non-IBM zoned decimal representation
S370FPD	Packed decimal	S370FPD	Last nibble C (positive) or D (negative)
S370FPDU	Packed decimal	S370FPDU	Last nibble always F (positive)
S370FZD	Zoned decimal	S370FZD	Last byte contains sign in upper nibble: C (positive) or D (negative)
S370FZDU	Zoned decimal	S370FZDU	Unsigned; sign nibble always F
S370FZDL	Zoned decimal	S370FZDL	Sign nibble in first byte in informat; separate leading sign byte of x'C0' (positive) or x'D0' (negative) in format
S370FZDS	Zoned decimal	S370FZDS	Leading sign of - (x'60') or + (x'4E')
S370FZDT	Zoned decimal	S370FZDT	Trailing sign of - (x'60') or + (x'4E')
PDJULI	Packed decimal	PDJULI	Julian date in packed representation - IBM computation
PDJULG	Packed decimal	PDJULG	Julian date in packed representation - Gregorian computation
none	Packed decimal	RMFDUR	Input layout is: mmsstttF
none	Packed decimal	SHRSTAMP	Input layout is: yyyydddFhhmmssth, where yyyydddF is the packed Julian date; yyyy is a 0-based year from 1900
none	Packed decimal	SMFSTAMP	Input layout is: xxxxxxxxyyyydddF, where yyyydddF is the packed Julian date; yyyy is a 0-based year from 1900
none	Packed decimal	PDTIME	Input layout is: 0hhmmssF
none	Packed decimal	RMFSTAMP	Input layout is: 0hhmmssFyyyydddF, where yyyydddF is the packed Julian date; yyyy is a 0-based year from 1900