sys-file-reader: Avoid hanging forever if a system file has no variables.

[pspp] / doc / dev / system-file-format.texi

@node System File Format
@appendix System File Format

A system file encapsulates a set of cases and dictionary information
that describes how they may be interpreted.  This chapter describes
the format of a system file.

System files use four data types: 8-bit characters, 32-bit integers,
64-bit integers, 
and 64-bit floating points, called here @code{char}, @code{int32},
@code{int64}, and
@code{flt64}, respectively.  Data is not necessarily aligned on a word
or double-word boundary: the long variable name record (@pxref{Long
Variable Names Record}) and very long string records (@pxref{Very Long
String Record}) have arbitrary byte length and can therefore cause all
data coming after them in the file to be misaligned.

Integer data in system files may be big-endian or little-endian.  A
reader may detect the endianness of a system file by examining
@code{layout_code} in the file header record
(@pxref{layout_code,,@code{layout_code}}).

Floating-point data in system files may nominally be in IEEE 754, IBM,
or VAX formats.  A reader may detect the floating-point format in use
by examining @code{bias} in the file header record
(@pxref{bias,,@code{bias}}).

PSPP detects big-endian and little-endian integer formats in system
files and translates as necessary.  PSPP also detects the
floating-point format in use, as well as the endianness of IEEE 754
floating-point numbers, and translates as needed.  However, only IEEE
754 numbers with the same endianness as integer data in the same file
has actually been observed in system files, and it is likely that
other formats are obsolete or were never used.

System files use a few floating point values for special purposes:

@table @asis
@item SYSMIS
The system-missing value is represented by the largest possible
negative number in the floating point format (@code{-DBL_MAX}).

@item HIGHEST
HIGHEST is used as the high end of a missing value range with an
unbounded maximum.  It is represented by the largest possible positive
number (@code{DBL_MAX}).

@item LOWEST
LOWEST is used as the low end of a missing value range with an
unbounded minimum.  It was originally represented by the
second-largest negative number (in IEEE 754 format,
@code{0xffeffffffffffffe}).  System files written by SPSS 21 and later
instead use the largest negative number (@code{-DBL_MAX}), the same
value as SYSMIS.  This does not lead to ambiguity because LOWEST
appears in system files only in missing value ranges, which never
contain SYSMIS.
@end table

System files may use most character encodings based on an 8-bit unit.
UTF-16 and UTF-32, based on wider units, appear to be unacceptable.
@code{rec_type} in the file header record is sufficient to distinguish
between ASCII and EBCDIC based encodings.  The best way to determine
the specific encoding in use is to consult the character encoding
record (@pxref{Character Encoding Record}), if present, and failing
that the @code{character_code} in the machine integer info record
(@pxref{Machine Integer Info Record}).  The same encoding should be
used for the dictionary and the data in the file, although it is
possible to artificially synthesize files that use different encodings
(@pxref{Character Encoding Record}).

System files are divided into records, each of which begins with a
4-byte record type, usually regarded as an @code{int32}.

The records must appear in the following order:

@itemize @bullet
@item
File header record.

@item
Variable records.

@item
All pairs of value labels records and value label variables records,
if present.

@item
Document record, if present.

@item
Extension (type 7) records, in ascending numerical order of their
subtypes.

@item
Dictionary termination record.

@item
Data record.
@end itemize

Each type of record is described separately below.

@menu
* File Header Record::
* Variable Record::
* Value Labels Records::
* Document Record::
* Machine Integer Info Record::
* Machine Floating-Point Info Record::
* Multiple Response Sets Records::
* Extra Product Info Record::
* Variable Display Parameter Record::
* Long Variable Names Record::
* Very Long String Record::
* Character Encoding Record::
* Long String Value Labels Record::
* Long String Missing Values Record::
* Data File and Variable Attributes Records::
* Extended Number of Cases Record::
* Miscellaneous Informational Records::
* Dictionary Termination Record::
* Data Record::
* Encrypted System Files::
@end menu

@node File Header Record
@section File Header Record

The file header is always the first record in the file.  It has the
following format:

@example
char                rec_type[4];
char                prod_name[60];
int32               layout_code;
int32               nominal_case_size;
int32               compression;
int32               weight_index;
int32               ncases;
flt64               bias;
char                creation_date[9];
char                creation_time[8];
char                file_label[64];
char                padding[3];
@end example

@table @code
@item char rec_type[4];
Record type code, either @samp{$FL2} for system files with
uncompressed data or data compressed with simple bytecode compression,
or @samp{$FL3} for system files with ZLIB compressed data.

This is truly a character field that uses the character encoding as
other strings.  Thus, in a file with an ASCII-based character encoding
this field contains @code{24 46 4c 32} or @code{24 46 4c 33}, and in a
file with an EBCDIC-based encoding this field contains @code{5b c6 d3
f2}.  (No EBCDIC-based ZLIB-compressed files have been observed.)

@item char prod_name[60];
Product identification string.  This always begins with the characters
@samp{@@(#) SPSS DATA FILE}.  PSPP uses the remaining characters to
give its version and the operating system name; for example, @samp{GNU
pspp 0.1.4 - sparc-sun-solaris2.5.2}.  The string is truncated if it
would be longer than 60 characters; otherwise it is padded on the right
with spaces.

@anchor{layout_code}
@item int32 layout_code;
Normally set to 2, although a few system files have been spotted in
the wild with a value of 3 here.  PSPP use this value to determine the
file's integer endianness (@pxref{System File Format}).

@item int32 nominal_case_size;
Number of data elements per case.  This is the number of variables,
except that long string variables add extra data elements (one for every
8 characters after the first 8).  However, string variables do not
contribute to this value beyond the first 255 bytes.   Further, system
files written by some systems set this value to -1.  In general, it is
unsafe for systems reading system files to rely upon this value.

@item int32 compression;
Set to 0 if the data in the file is not compressed, 1 if the data is
compressed with simple bytecode compression, 2 if the data is ZLIB
compressed.  This field has value 2 if and only if @code{rec_type} is
@samp{$FL3}.

@item int32 weight_index;
If one of the variables in the data set is used as a weighting
variable, set to the dictionary index of that variable, plus 1
(@pxref{Dictionary Index}).  Otherwise, set to 0.

@item int32 ncases;
Set to the number of cases in the file if it is known, or -1 otherwise.

In the general case it is not possible to determine the number of cases
that will be output to a system file at the time that the header is
written.  The way that this is dealt with is by writing the entire
system file, including the header, then seeking back to the beginning of
the file and writing just the @code{ncases} field.  For files in which
this is not valid, the seek operation fails.  In this case,
@code{ncases} remains -1.

@anchor{bias}
@item flt64 bias;
Compression bias, ordinarily set to 100.  Only integers between
@code{1 - bias} and @code{251 - bias} can be compressed.

By assuming that its value is 100, PSPP uses @code{bias} to determine
the file's floating-point format and endianness (@pxref{System File
Format}).  If the compression bias is not 100, PSPP cannot auto-detect
the floating-point format and assumes that it is IEEE 754 format with
the same endianness as the system file's integers, which is correct
for all known system files.

@item char creation_date[9];
Date of creation of the system file, in @samp{dd mmm yy}
format, with the month as standard English abbreviations, using an
initial capital letter and following with lowercase.  If the date is not
available then this field is arbitrarily set to @samp{01 Jan 70}.

@item char creation_time[8];
Time of creation of the system file, in @samp{hh:mm:ss}
format and using 24-hour time.  If the time is not available then this
field is arbitrarily set to @samp{00:00:00}.

@item char file_label[64];
File label declared by the user, if any (@pxref{FILE LABEL,,,pspp,
PSPP Users Guide}).  Padded on the right with spaces.

A product that identifies itself as @code{VOXCO INTERVIEWER 4.3} uses
CR-only line ends in this field, rather than the more usual LF-only or
CR LF line ends.

@item char padding[3];
Ignored padding bytes to make the structure a multiple of 32 bits in
length.  Set to zeros.
@end table

@node Variable Record
@section Variable Record

There must be one variable record for each numeric variable and each
string variable with width 8 bytes or less.  String variables wider
than 8 bytes have one variable record for each 8 bytes, rounding up.
The first variable record for a long string specifies the variable's
correct dictionary information.  Subsequent variable records for a
long string are filled with dummy information: a type of -1, no
variable label or missing values, print and write formats that are
ignored, and an empty string as name.  A few system files have been
encountered that include a variable label on dummy variable records,
so readers should take care to parse dummy variable records in the
same way as other variable records.

@anchor{Dictionary Index}
The @dfn{dictionary index} of a variable is its offset in the set of
variable records, including dummy variable records for long string
variables.  The first variable record has a dictionary index of 0, the
second has a dictionary index of 1, and so on.

The system file format does not directly support string variables
wider than 255 bytes.  Such very long string variables are represented
by a number of narrower string variables.  @xref{Very Long String
Record}, for details.

A system file should contain at least one variable and thus at least
one variable record, but system files have been observed in the wild
without any variables (thus, no data either).

@example
int32               rec_type;
int32               type;
int32               has_var_label;
int32               n_missing_values;
int32               print;
int32               write;
char                name[8];

/* @r{Present only if @code{has_var_label} is 1.} */
int32               label_len;
char                label[];

/* @r{Present only if @code{n_missing_values} is nonzero}. */
flt64               missing_values[];
@end example

@table @code
@item int32 rec_type;
Record type code.  Always set to 2.

@item int32 type;
Variable type code.  Set to 0 for a numeric variable.  For a short
string variable or the first part of a long string variable, this is set
to the width of the string.  For the second and subsequent parts of a
long string variable, set to -1, and the remaining fields in the
structure are ignored.

@item int32 has_var_label;
If this variable has a variable label, set to 1; otherwise, set to 0.

@item int32 n_missing_values;
If the variable has no missing values, set to 0.  If the variable has
one, two, or three discrete missing values, set to 1, 2, or 3,
respectively.  If the variable has a range for missing variables, set to
-2; if the variable has a range for missing variables plus a single
discrete value, set to -3.

A long string variable always has the value 0 here.  A separate record
indicates missing values for long string variables (@pxref{Long String
Missing Values Record}).

@item int32 print;
Print format for this variable.  See below.

@item int32 write;
Write format for this variable.  See below.

@item char name[8];
Variable name.  The variable name must begin with a capital letter or
the at-sign (@samp{@@}).  Subsequent characters may also be digits, octothorpes
(@samp{#}), dollar signs (@samp{$}), underscores (@samp{_}), or full
stops (@samp{.}).  The variable name is padded on the right with spaces.

The @samp{name} fields should be unique within a system file.  System
files written by SPSS that contain very long string variables with
similar names sometimes contain duplicate names that are later
eliminated by resolving the very long string names (@pxref{Very Long
String Record}).  PSPP handles duplicates by assigning them new,
unique names.

@item int32 label_len;
This field is present only if @code{has_var_label} is set to 1.  It is
set to the length, in characters, of the variable label.  The
documented maximum length varies from 120 to 255 based on SPSS
version, but some files have been seen with longer labels.  PSPP
accepts labels of any length.

@item char label[];
This field is present only if @code{has_var_label} is set to 1.  It has
length @code{label_len}, rounded up to the nearest multiple of 32 bits.
The first @code{label_len} characters are the variable's variable label.

@item flt64 missing_values[];
This field is present only if @code{n_missing_values} is nonzero.  It
has the same number of 8-byte elements as the absolute value of
@code{n_missing_values}.  Each element is interpreted as a number for
numeric variables (with HIGHEST and LOWEST indicated as described in
the chapter introduction).  For string variables of width less than 8
bytes, elements are right-padded with spaces; for string variables
wider than 8 bytes, only the first 8 bytes of each missing value are
specified, with the remainder implicitly all spaces.

For discrete missing values, each element represents one missing
value.  When a range is present, the first element denotes the minimum
value in the range, and the second element denotes the maximum value
in the range.  When a range plus a value are present, the third
element denotes the additional discrete missing value.
@end table

@anchor{System File Output Formats}
The @code{print} and @code{write} members of sysfile_variable are output
formats coded into @code{int32} types.  The least-significant byte
of the @code{int32} represents the number of decimal places, and the
next two bytes in order of increasing significance represent field width
and format type, respectively.  The most-significant byte is not
used and should be set to zero.

Format types are defined as follows:

@quotation
@multitable {Value} {@code{DATETIME}}
@headitem Value
@tab Meaning
@item 0
@tab Not used.
@item 1
@tab @code{A}
@item 2
@tab @code{AHEX}
@item 3
@tab @code{COMMA}
@item 4
@tab @code{DOLLAR}
@item 5
@tab @code{F}
@item 6
@tab @code{IB}
@item 7
@tab @code{PIBHEX}
@item 8
@tab @code{P}
@item 9
@tab @code{PIB}
@item 10
@tab @code{PK}
@item 11
@tab @code{RB}
@item 12
@tab @code{RBHEX}
@item 13
@tab Not used.
@item 14
@tab Not used.
@item 15
@tab @code{Z}
@item 16
@tab @code{N}
@item 17
@tab @code{E}
@item 18
@tab Not used.
@item 19
@tab Not used.
@item 20
@tab @code{DATE}
@item 21
@tab @code{TIME}
@item 22
@tab @code{DATETIME}
@item 23
@tab @code{ADATE}
@item 24
@tab @code{JDATE}
@item 25
@tab @code{DTIME}
@item 26
@tab @code{WKDAY}
@item 27
@tab @code{MONTH}
@item 28
@tab @code{MOYR}
@item 29
@tab @code{QYR}
@item 30
@tab @code{WKYR}
@item 31
@tab @code{PCT}
@item 32
@tab @code{DOT}
@item 33
@tab @code{CCA}
@item 34
@tab @code{CCB}
@item 35
@tab @code{CCC}
@item 36
@tab @code{CCD}
@item 37
@tab @code{CCE}
@item 38
@tab @code{EDATE}
@item 39
@tab @code{SDATE}
@end multitable
@end quotation

A few system files have been observed in the wild with invalid
@code{write} fields, in particular with value 0.  Readers should
probably treat invalid @code{print} or @code{write} fields as some
default format.

@node Value Labels Records
@section Value Labels Records

The value label records documented in this section are used for
numeric and short string variables only.  Long string variables may
have value labels, but their value labels are recorded using a
different record type (@pxref{Long String Value Labels Record}).

The value label record has the following format:

@example
int32               rec_type;
int32               label_count;

/* @r{Repeated @code{label_cnt} times}. */
char                value[8];
char                label_len;
char                label[];
@end example

@table @code
@item int32 rec_type;
Record type.  Always set to 3.

@item int32 label_count;
Number of value labels present in this record.
@end table

The remaining fields are repeated @code{count} times.  Each
repetition specifies one value label.

@table @code
@item char value[8];
A numeric value or a short string value padded as necessary to 8 bytes
in length.  Its type and width cannot be determined until the
following value label variables record (see below) is read.

@item char label_len;
The label's length, in bytes.  The documented maximum length varies
from 60 to 120 based on SPSS version.  PSPP supports value labels up
to 255 bytes long.

@item char label[];
@code{label_len} bytes of the actual label, followed by up to 7 bytes
of padding to bring @code{label} and @code{label_len} together to a
multiple of 8 bytes in length.
@end table

The value label record is always immediately followed by a value label
variables record with the following format:

@example
int32               rec_type;
int32               var_count;
int32               vars[];
@end example

@table @code
@item int32 rec_type;
Record type.  Always set to 4.

@item int32 var_count;
Number of variables that the associated value labels from the value
label record are to be applied.

@item int32 vars[];
A list of dictionary indexes of variables to which to apply the value
labels (@pxref{Dictionary Index}).  There are @code{var_count}
elements.

String variables wider than 8 bytes may not be specified in this list.
@end table

@node Document Record
@section Document Record

The document record, if present, has the following format:

@example
int32               rec_type;
int32               n_lines;
char                lines[][80];
@end example

@table @code
@item int32 rec_type;
Record type.  Always set to 6.

@item int32 n_lines;
Number of lines of documents present.

@item char lines[][80];
Document lines.  The number of elements is defined by @code{n_lines}.
Lines shorter than 80 characters are padded on the right with spaces.
@end table

@node Machine Integer Info Record
@section Machine Integer Info Record

The integer info record, if present, has the following format:

@example
/* @r{Header.} */
int32               rec_type;
int32               subtype;
int32               size;
int32               count;

/* @r{Data.} */
int32               version_major;
int32               version_minor;
int32               version_revision;
int32               machine_code;
int32               floating_point_rep;
int32               compression_code;
int32               endianness;
int32               character_code;
@end example

@table @code
@item int32 rec_type;
Record type.  Always set to 7.

@item int32 subtype;
Record subtype.  Always set to 3.

@item int32 size;
Size of each piece of data in the data part, in bytes.  Always set to 4.

@item int32 count;
Number of pieces of data in the data part.  Always set to 8.

@item int32 version_major;
PSPP major version number.  In version @var{x}.@var{y}.@var{z}, this
is @var{x}.

@item int32 version_minor;
PSPP minor version number.  In version @var{x}.@var{y}.@var{z}, this
is @var{y}.

@item int32 version_revision;
PSPP version revision number.  In version @var{x}.@var{y}.@var{z},
this is @var{z}.

@item int32 machine_code;
Machine code.  PSPP always set this field to value to -1, but other
values may appear.

@item int32 floating_point_rep;
Floating point representation code.  For IEEE 754 systems this is 1.
IBM 370 sets this to 2, and DEC VAX E to 3.

@item int32 compression_code;
Compression code.  Always set to 1, regardless of whether or how the
file is compressed.

@item int32 endianness;
Machine endianness.  1 indicates big-endian, 2 indicates little-endian.

@item int32 character_code;
@anchor{character-code} Character code.  The following values have
been actually observed in system files:

@table @asis
@item 1
EBCDIC.

@item 2
7-bit ASCII.

@item 1250
The @code{windows-1250} code page for Central European and Eastern
European languages.

@item 1252
The @code{windows-1252} code page for Western European languages.

@item 28591
ISO 8859-1.

@item 65001
UTF-8.
@end table

The following additional values are known to be defined:

@table @asis
@item 3
8-bit ``ASCII''.

@item 4
DEC Kanji.
@end table

Other Windows code page numbers are known to be generally valid.

Old versions of SPSS for Unix and Windows always wrote value 2 in this
field, regardless of the encoding in use.  Newer versions also write
the character encoding as a string (see @ref{Character Encoding
Record}).
@end table

@node Machine Floating-Point Info Record
@section Machine Floating-Point Info Record

The floating-point info record, if present, has the following format:

@example
/* @r{Header.} */
int32               rec_type;
int32               subtype;
int32               size;
int32               count;

/* @r{Data.} */
flt64               sysmis;
flt64               highest;
flt64               lowest;
@end example

@table @code
@item int32 rec_type;
Record type.  Always set to 7.

@item int32 subtype;
Record subtype.  Always set to 4.

@item int32 size;
Size of each piece of data in the data part, in bytes.  Always set to 8.

@item int32 count;
Number of pieces of data in the data part.  Always set to 3.

@item flt64 sysmis;
The system missing value.

@item flt64 highest;
The value used for HIGHEST in missing values.

@item flt64 lowest;
The value used for LOWEST in missing values.
@end table

@node Multiple Response Sets Records
@section Multiple Response Sets Records

The system file format has two different types of records that
represent multiple response sets (@pxref{MRSETS,,,pspp, PSPP Users
Guide}).  The first type of record describes multiple response sets
that can be understood by SPSS before version 14.  The second type of
record, with a closely related format, is used for multiple dichotomy
sets that use the CATEGORYLABELS=COUNTEDVALUES feature added in
version 14.

@example
/* @r{Header.} */
int32               rec_type;
int32               subtype;
int32               size;
int32               count;

/* @r{Exactly @code{count} bytes of data.} */
char                mrsets[];
@end example

@table @code
@item int32 rec_type;
Record type.  Always set to 7.

@item int32 subtype;
Record subtype.  Set to 7 for records that describe multiple response
sets understood by SPSS before version 14, or to 19 for records that
describe dichotomy sets that use the CATEGORYLABELS=COUNTEDVALUES
feature added in version 14.

@item int32 size;
The size of each element in the @code{mrsets} member. Always set to 1.

@item int32 count;
The total number of bytes in @code{mrsets}.

@item char mrsets[];
Zero or more line feeds (byte 0x0a), followed by a series of multiple
response sets, each of which consists of the following:

@itemize @bullet
@item
The set's name (an identifier that begins with @samp{$}), in mixed
upper and lower case.

@item
An equals sign (@samp{=}).

@item
@samp{C} for a multiple category set, @samp{D} for a multiple
dichotomy set with CATEGORYLABELS=VARLABELS, or @samp{E} for a
multiple dichotomy set with CATEGORYLABELS=COUNTEDVALUES.

@item
For a multiple dichotomy set with CATEGORYLABELS=COUNTEDVALUES, a
space, followed by a number expressed as decimal digits, followed by a
space.  If LABELSOURCE=VARLABEL was specified on MRSETS, then the
number is 11; otherwise it is 1.@footnote{This part of the format may
not be fully understood, because only a single example of each
possibility has been examined.}

@item
For either kind of multiple dichotomy set, the counted value, as a
positive integer count specified as decimal digits, followed by a
space, followed by as many string bytes as specified in the count.  If
the set contains numeric variables, the string consists of the counted
integer value expressed as decimal digits.  If the set contains string
variables, the string contains the counted string value.  Either way,
the string may be padded on the right with spaces (older versions of
SPSS seem to always pad to a width of 8 bytes; newer versions don't).

@item
A space.

@item
The multiple response set's label, using the same format as for the
counted value for multiple dichotomy sets.  A string of length 0 means
that the set does not have a label.  A string of length 0 is also
written if LABELSOURCE=VARLABEL was specified.

@item
A space.

@item
The short names of the variables in the set, converted to lowercase,
each separated from the previous by a single space.

Even though a multiple response set must have at least two variables,
some system files contain multiple response sets with no variables at
all.  The source and meaning of these multiple response sets is
unknown.  (Perhaps they arise from creating a multiple response set
then deleting all the variables that it contains?)

@item
One line feed (byte 0x0a).  Sometimes multiple, even hundreds, of line
feeds are present.
@end itemize
@end table

Example: Given appropriate variable definitions, consider the
following MRSETS command:

@example
MRSETS /MCGROUP NAME=$a LABEL='my mcgroup' VARIABLES=a b c
       /MDGROUP NAME=$b VARIABLES=g e f d VALUE=55
       /MDGROUP NAME=$c LABEL='mdgroup #2' VARIABLES=h i j VALUE='Yes'
       /MDGROUP NAME=$d LABEL='third mdgroup' CATEGORYLABELS=COUNTEDVALUES
        VARIABLES=k l m VALUE=34
       /MDGROUP NAME=$e CATEGORYLABELS=COUNTEDVALUES LABELSOURCE=VARLABEL
        VARIABLES=n o p VALUE='choice'.
@end example

The above would generate the following multiple response set record of
subtype 7:

@example
$a=C 10 my mcgroup a b c
$b=D2 55 0  g e f d
$c=D3 Yes 10 mdgroup #2 h i j
@end example

It would also generate the following multiple response set record with
subtype 19:

@example
$d=E 1 2 34 13 third mdgroup k l m
$e=E 11 6 choice 0  n o p
@end example

@node Extra Product Info Record
@section Extra Product Info Record

This optional record appears to contain a text string that describes
the program that wrote the file and the source of the data.  (This is
redundant with the file label and product info found in the file
header record.)

@example
/* @r{Header.} */
int32               rec_type;
int32               subtype;
int32               size;
int32               count;

/* @r{Exactly @code{count} bytes of data.} */
char                info[];
@end example

@table @code
@item int32 rec_type;
Record type.  Always set to 7.

@item int32 subtype;
Record subtype.  Always set to 10.

@item int32 size;
The size of each element in the @code{info} member. Always set to 1.

@item int32 count;
The total number of bytes in @code{info}.

@item char info[];
A text string.  A product that identifies itself as @code{VOXCO
INTERVIEWER 4.3} uses CR-only line ends in this field, rather than the
more usual LF-only or CR LF line ends.
@end table

@node Variable Display Parameter Record
@section Variable Display Parameter Record

The variable display parameter record, if present, has the following
format:

@example
/* @r{Header.} */
int32               rec_type;
int32               subtype;
int32               size;
int32               count;

/* @r{Repeated @code{count} times}. */
int32               measure;
int32               width;           /* @r{Not always present.} */
int32               alignment;
@end example

@table @code
@item int32 rec_type;
Record type.  Always set to 7.

@item int32 subtype;
Record subtype.  Always set to 11.

@item int32 size;
The size of @code{int32}.  Always set to 4.

@item int32 count;
The number of sets of variable display parameters (ordinarily the
number of variables in the dictionary), times 2 or 3.
@end table

The remaining members are repeated @code{count} times, in the same
order as the variable records.  No element corresponds to variable
records that continue long string variables.  The meanings of these
members are as follows:

@table @code
@item int32 measure;
The measurement type of the variable:
@table @asis
@item 1
Nominal Scale
@item 2
Ordinal Scale
@item 3
Continuous Scale
@end table

SPSS sometimes writes a @code{measure} of 0.  PSPP interprets this as
nominal scale.

@item int32 width;
The width of the display column for the variable in characters.

This field is present if @var{count} is 3 times the number of
variables in the dictionary.  It is omitted if @var{count} is 2 times
the number of variables.

@item int32 alignment;
The alignment of the variable for display purposes:

@table @asis
@item 0
Left aligned
@item 1
Right aligned
@item 2
Centre aligned
@end table
@end table

@node Long Variable Names Record
@section Long Variable Names Record

If present, the long variable names record has the following format:

@example
/* @r{Header.} */
int32               rec_type;
int32               subtype;
int32               size;
int32               count;

/* @r{Exactly @code{count} bytes of data.} */
char                var_name_pairs[];
@end example

@table @code
@item int32 rec_type;
Record type.  Always set to 7.

@item int32 subtype;
Record subtype.  Always set to 13.

@item int32 size;
The size of each element in the @code{var_name_pairs} member. Always set to 1.

@item int32 count;
The total number of bytes in @code{var_name_pairs}.

@item char var_name_pairs[];
A list of @var{key}--@var{value} tuples, where @var{key} is the name
of a variable, and @var{value} is its long variable name.
The @var{key} field is at most 8 bytes long and must match the
name of a variable which appears in the variable record (@pxref{Variable
Record}).
The @var{value} field is at most 64 bytes long.
The @var{key} and @var{value} fields are separated by a @samp{=} byte.
Each tuple is separated by a byte whose value is 09.  There is no
trailing separator following the last tuple.
The total length is @code{count} bytes.
@end table

@node Very Long String Record
@section Very Long String Record

Old versions of SPSS limited string variables to a width of 255 bytes.
For backward compatibility with these older versions, the system file
format represents a string longer than 255 bytes, called a @dfn{very
long string}, as a collection of strings no longer than 255 bytes
each.  The strings concatenated to make a very long string are called
its @dfn{segments}; for consistency, variables other than very long
strings are considered to have a single segment.

A very long string with a width of @var{w} has @var{n} =
(@var{w} + 251) / 252 segments, that is, one segment for every
252 bytes of width, rounding up.  It would be logical, then, for each
of the segments except the last to have a width of 252 and the last
segment to have the remainder, but this is not the case.  In fact,
each segment except the last has a width of 255 bytes.  The last
segment has width @var{w} - (@var{n} - 1) * 252; some versions
of SPSS make it slightly wider, but not wide enough to make the last
segment require another 8 bytes of data.

Data is packed tightly into segments of a very long string, 255 bytes
per segment.  Because 255 bytes of segment data are allocated for
every 252 bytes of the very long string's width (approximately), some
unused space is left over at the end of the allocated segments.  Data
in unused space is ignored.

Example: Consider a very long string of width 20,000.  Such a very
long string has 20,000 / 252 = 80 (rounding up) segments.  The first
79 segments have width 255; the last segment has width 20,000 - 79 *
252 = 92 or slightly wider (up to 96 bytes, the next multiple of 8).
The very long string's data is actually stored in the 19,890 bytes in
the first 78 segments, plus the first 110 bytes of the 79th segment
(19,890 + 110 = 20,000).  The remaining 145 bytes of the 79th segment
and all 92 bytes of the 80th segment are unused.

The very long string record explains how to stitch together segments
to obtain very long string data.  For each of the very long string
variables in the dictionary, it specifies the name of its first
segment's variable and the very long string variable's actual width.
The remaining segments immediately follow the named variable in the
system file's dictionary.

The very long string record, which is present only if the system file
contains very long string variables, has the following format:

@example
/* @r{Header.} */
int32               rec_type;
int32               subtype;
int32               size;
int32               count;

/* @r{Exactly @code{count} bytes of data.} */
char                string_lengths[];
@end example

@table @code
@item int32 rec_type;
Record type.  Always set to 7.

@item int32 subtype;
Record subtype.  Always set to 14.

@item int32 size;
The size of each element in the @code{string_lengths} member. Always set to 1.

@item int32 count;
The total number of bytes in @code{string_lengths}.

@item char string_lengths[];
A list of @var{key}--@var{value} tuples, where @var{key} is the name
of a variable, and @var{value} is its length.
The @var{key} field is at most 8 bytes long and must match the
name of a variable which appears in the variable record (@pxref{Variable
Record}).
The @var{value} field is exactly 5 bytes long. It is a zero-padded,
ASCII-encoded string that is the length of the variable.
The @var{key} and @var{value} fields are separated by a @samp{=} byte.
Tuples are delimited by a two-byte sequence @{00, 09@}.
After the last tuple, there may be a single byte 00, or @{00, 09@}.
The total length is @code{count} bytes.
@end table

@node Character Encoding Record
@section Character Encoding Record

This record, if present, indicates the character encoding for string data,
long variable names, variable labels, value labels and other strings in the
file.

@example
/* @r{Header.} */
int32               rec_type;
int32               subtype;
int32               size;
int32               count;

/* @r{Exactly @code{count} bytes of data.} */
char                encoding[];
@end example

@table @code
@item int32 rec_type;
Record type.  Always set to 7.

@item int32 subtype;
Record subtype.  Always set to 20.

@item int32 size;
The size of each element in the @code{encoding} member. Always set to 1.

@item int32 count;
The total number of bytes in @code{encoding}.

@item char encoding[];
The name of the character encoding.  Normally this will be an official
IANA character set name or alias.
See @url{http://www.iana.org/assignments/character-sets}.
Character set names are not case-sensitive, but SPSS appears to write
them in all-uppercase.
@end table

This record is not present in files generated by older software.  See
also the @code{character_code} field in the machine integer info
record (@pxref{character-code}).

When the character encoding record and the machine integer info record
are both present, all system files observed in practice indicate the
same character encoding, e.g.@: 1252 as @code{character_code} and
@code{windows-1252} as @code{encoding}, 65001 and @code{UTF-8}, etc.

If, for testing purposes, a file is crafted with different
@code{character_code} and @code{encoding}, it seems that
@code{character_code} controls the encoding for all strings in the
system file before the dictionary termination record, including
strings in data (e.g.@: string missing values), and @code{encoding}
controls the encoding for strings following the dictionary termination
record.

@node Long String Value Labels Record
@section Long String Value Labels Record

This record, if present, specifies value labels for long string
variables.

@example
/* @r{Header.} */
int32               rec_type;
int32               subtype;
int32               size;
int32               count;

/* @r{Repeated up to exactly @code{count} bytes.} */
int32               var_name_len;
char                var_name[];
int32               var_width;
int32               n_labels;
long_string_label   labels[];
@end example

@table @code
@item int32 rec_type;
Record type.  Always set to 7.

@item int32 subtype;
Record subtype.  Always set to 21.

@item int32 size;
Always set to 1.

@item int32 count;
The number of bytes following the header until the next header.

@item int32 var_name_len;
@itemx char var_name[];
The number of bytes in the name of the variable that has long string
value labels, plus the variable name itself, which consists of exactly
@code{var_name_len} bytes.  The variable name is not padded to any
particular boundary, nor is it null-terminated.

@item int32 var_width;
The width of the variable, in bytes, which will be between 9 and
32767.

@item int32 n_labels;
@itemx long_string_label labels[];
The long string labels themselves.  The @code{labels} array contains
exactly @code{n_labels} elements, each of which has the following
substructure:

@example
int32               value_len;
char                value[];
int32               label_len;
char                label[];
@end example

@table @code
@item int32 value_len;
@itemx char value[];
The string value being labeled.  @code{value_len} is the number of
bytes in @code{value}; it is equal to @code{var_width}.  The
@code{value} array is not padded or null-terminated.

@item int32 label_len;
@itemx char label[];
The label for the string value.  @code{label_len}, which must be
between 0 and 120, is the number of bytes in @code{label}.  The
@code{label} array is not padded or null-terminated.
@end table
@end table

@node Long String Missing Values Record
@section Long String Missing Values Record

This record, if present, specifies missing values for long string
variables.

@example
/* @r{Header.} */
int32               rec_type;
int32               subtype;
int32               size;
int32               count;

/* @r{Repeated up to exactly @code{count} bytes.} */
int32               var_name_len;
char                var_name[];
char                n_missing_values;
long_string_missing_value   values[];
@end example

@table @code
@item int32 rec_type;
Record type.  Always set to 7.

@item int32 subtype;
Record subtype.  Always set to 22.

@item int32 size;
Always set to 1.

@item int32 count;
The number of bytes following the header until the next header.

@item int32 var_name_len;
@itemx char var_name[];
The number of bytes in the name of the long string variable that has
missing values, plus the variable name itself, which consists of
exactly @code{var_name_len} bytes.  The variable name is not padded to
any particular boundary, nor is it null-terminated.

@item char n_missing_values;
The number of missing values, either 1, 2, or 3.  (This is, unusually,
a single byte instead of a 32-bit number.)

@item long_string_missing_value values[];
The missing values themselves.  This array contains exactly
@code{n_missing_values} elements, each of which has the following
substructure:

@example
int32               value_len;
char                value[];
@end example

@table @code
@item int32 value_len;
The length of the missing value string, in bytes.  This value should
be 8, because long string variables are at least 8 bytes wide (by
definition), only the first 8 bytes of a long string variable's
missing values are allowed to be non-spaces, and any spaces within the
first 8 bytes are included in the missing value here.

@item char value[];
The missing value string, exactly @code{value_len} bytes, without
any padding or null terminator.
@end table
@end table

@node Data File and Variable Attributes Records
@section Data File and Variable Attributes Records

The data file and variable attributes records represent custom
attributes for the system file or for individual variables in the
system file, as defined on the DATAFILE ATTRIBUTE (@pxref{DATAFILE
ATTRIBUTE,,,pspp, PSPP Users Guide}) and VARIABLE ATTRIBUTE commands
(@pxref{VARIABLE ATTRIBUTE,,,pspp, PSPP Users Guide}), respectively.

@example
/* @r{Header.} */
int32               rec_type;
int32               subtype;
int32               size;
int32               count;

/* @r{Exactly @code{count} bytes of data.} */
char                attributes[];
@end example

@table @code
@item int32 rec_type;
Record type.  Always set to 7.

@item int32 subtype;
Record subtype.  Always set to 17 for a data file attribute record or
to 18 for a variable attributes record.

@item int32 size;
The size of each element in the @code{attributes} member. Always set to 1.

@item int32 count;
The total number of bytes in @code{attributes}.

@item char attributes[];
The attributes, in a text-based format.

In record type 17, this field contains a single attribute set.  An
attribute set is a sequence of one or more attributes concatenated
together.  Each attribute consists of a name, which has the same
syntax as a variable name, followed by, inside parentheses, a sequence
of one or more values.  Each value consists of a string enclosed in
single quotes (@code{'}) followed by a line feed (byte 0x0a).  A value
may contain single quote characters, which are not themselves escaped
or quoted or required to be present in pairs.  There is no apparent
way to embed a line feed in a value.  There is no distinction between
an attribute with a single value and an attribute array with one
element.

In record type 18, this field contains a sequence of one or more
variable attribute sets.  If more than one variable attribute set is
present, each one after the first is delimited from the previous by
@code{/}.  Each variable attribute set consists of a long
variable name,
followed by @code{:}, followed by an attribute set with the same
syntax as on record type 17.

The total length is @code{count} bytes.
@end table

@subheading Example

A system file produced with the following VARIABLE ATTRIBUTE commands
in effect:

@example
VARIABLE ATTRIBUTE VARIABLES=dummy ATTRIBUTE=fred[1]('23') fred[2]('34').
VARIABLE ATTRIBUTE VARIABLES=dummy ATTRIBUTE=bert('123').
@end example

@noindent
will contain a variable attribute record with the following contents:

@example
0000  07 00 00 00 12 00 00 00  01 00 00 00 22 00 00 00  |............"...|
0010  64 75 6d 6d 79 3a 66 72  65 64 28 27 32 33 27 0a  |dummy:fred('23'.|
0020  27 33 34 27 0a 29 62 65  72 74 28 27 31 32 33 27  |'34'.)bert('123'|
0030  0a 29                                             |.)              |
@end example

@menu
* Variable Roles::
@end menu

@node Variable Roles
@subsection Variable Roles

A variable's role is represented as an attribute named @code{$@@Role}.
This attribute has a single element whose values and their meanings
are:

@table @code
@item 0
Input.  This, the default, is the most common role.
@item 1
Output.
@item 2
Both.
@item 3
None.
@item 4
Partition.
@item 5
Split.
@end table

@node Extended Number of Cases Record
@section Extended Number of Cases Record

The file header record expresses the number of cases in the system
file as an int32 (@pxref{File Header Record}).  This record allows the
number of cases in the system file to be expressed as a 64-bit number.

@example
int32               rec_type;
int32               subtype;
int32               size;
int32               count;
int64               unknown;
int64               ncases64;
@end example

@table @code
@item int32 rec_type;
Record type.  Always set to 7.

@item int32 subtype;
Record subtype.  Always set to 16.

@item int32 size;
Size of each element.  Always set to 8.

@item int32 count;
Number of pieces of data in the data part.  Alway set to 2.

@item int64 unknown;
Meaning unknown.  Always set to 1.

@item int64 ncases64;
Number of cases in the file as a 64-bit integer.  Presumably this
could be -1 to indicate that the number of cases is unknown, for the
same reason as @code{ncases} in the file header record, but this has
not been observed in the wild.
@end table

@node Miscellaneous Informational Records
@section Miscellaneous Informational Records

Some specific types of miscellaneous informational records are
documented here, but others are known to exist.  PSPP ignores unknown
miscellaneous informational records when reading system files.

@example
/* @r{Header.} */
int32               rec_type;
int32               subtype;
int32               size;
int32               count;

/* @r{Exactly @code{size * count} bytes of data.} */
char                data[];
@end example

@table @code
@item int32 rec_type;
Record type.  Always set to 7.

@item int32 subtype;
Record subtype.  May take any value.  According to Aapi
H@"am@"al@"ainen, value 5 indicates a set of grouped variables and 6
indicates date info (probably related to USE).  Subtype 24 appears to
contain XML that describes how data in the file should be displayed
on-screen.

@item int32 size;
Size of each piece of data in the data part.  Should have the value 1,
4, or 8, for @code{char}, @code{int32}, and @code{flt64} format data,
respectively.

@item int32 count;
Number of pieces of data in the data part.

@item char data[];
Arbitrary data.  There must be @code{size} times @code{count} bytes of
data.
@end table

@node Dictionary Termination Record
@section Dictionary Termination Record

The dictionary termination record separates all other records from the
data records.

@example
int32               rec_type;
int32               filler;
@end example

@table @code
@item int32 rec_type;
Record type.  Always set to 999.

@item int32 filler;
Ignored padding.  Should be set to 0.
@end table

@node Data Record
@section Data Record

The data record must follow all other records in the system file.
Every system file must have a data record that specifies data for at
least one case.  The format of the data record varies depending on the
value of @code{compression} in the file header record:

@table @asis
@item 0: no compression
Data is arranged as a series of 8-byte elements.
Each element corresponds to
the variable declared in the respective variable record (@pxref{Variable
Record}).  Numeric values are given in @code{flt64} format; string
values are literal characters string, padded on the right when
necessary to fill out 8-byte units.

@item 1: bytecode compression
The first 8 bytes
of the data record is divided into a series of 1-byte command
codes.  These codes have meanings as described below:

@table @asis
@item 0
Ignored.  If the program writing the system file accumulates compressed
data in blocks of fixed length, 0 bytes can be used to pad out extra
bytes remaining at the end of a fixed-size block.

@item 1 through 251
A number with
value @var{code} - @var{bias}, where
@var{code} is the value of the compression code and @var{bias} is the
variable @code{bias} from the file header.  For example,
code 105 with bias 100.0 (the normal value) indicates a numeric variable
of value 5.
One file has been seen written by SPSS 14 that contained such a code
in a @emph{string} field with the value 0 (after the bias is
subtracted) as a way of encoding null bytes.

@item 252
End of file.  This code may or may not appear at the end of the data
stream.  PSPP always outputs this code but its use is not required.

@item 253
A numeric or string value that is not
compressible.  The value is stored in the 8 bytes following the
current block of command bytes.  If this value appears twice in a block
of command bytes, then it indicates the second group of 8 bytes following the
command bytes, and so on.

@item 254
An 8-byte string value that is all spaces.

@item 255
The system-missing value.
@end table

The end of the 8-byte group of bytecodes is followed by any 8-byte
blocks of non-compressible values indicated by code 253.  After that
follows another 8-byte group of bytecodes, then those bytecodes'
non-compressible values.  The pattern repeats to the end of the file
or a code with value 252.

@item 2: ZLIB compression
The data record consists of the following, in order:

@itemize @bullet
@item
ZLIB data header, 24 bytes long.

@item
One or more variable-length blocks of ZLIB compressed data.

@item
ZLIB data trailer, with a 24-byte fixed header plus an additional 24
bytes for each preceding ZLIB compressed data block.
@end itemize

The ZLIB data header has the following format:

@example
int64               zheader_ofs;
int64               ztrailer_ofs;
int64               ztrailer_len;
@end example

@table @code
@item int64 zheader_ofs;
The offset, in bytes, of the beginning of this structure within the
system file.

@item int64 ztrailer_ofs;
The offset, in bytes, of the first byte of the ZLIB data trailer.

@item int64 ztrailer_len;
The number of bytes in the ZLIB data trailer.  This and the previous
field sum to the size of the system file in bytes.
@end table

The data header is followed by @code{(ztrailer_ofs - 24) / 24} ZLIB
compressed data blocks.  Each ZLIB compressed data block begins with a
ZLIB header as specified in RFC@tie{}1950, e.g.@: hex bytes @code{78
01} (the only header yet observed in practice).  Each block
decompresses to a fixed number of bytes (in practice only
@code{0x3ff000}-byte blocks have been observed), except that the last
block of data may be shorter.  The last ZLIB compressed data block
gends just before offset @code{ztrailer_ofs}.

The result of ZLIB decompression is bytecode compressed data as
described above for compression format 1.

The ZLIB data trailer begins with the following 24-byte fixed header:

@example
int64               bias;
int64               zero;
int32               block_size;
int32               n_blocks;
@end example

@table @code
@item int64 int_bias;
The compression bias as a negative integer, e.g.@: if @code{bias} in
the file header record is 100.0, then @code{int_bias} is @minus{}100
(this is the only value yet observed in practice).

@item int64 zero;
Always observed to be zero.

@item int32 block_size;
The number of bytes in each ZLIB compressed data block, except
possibly the last, following decompression.  Only @code{0x3ff000} has
been observed so far.

@item int32 n_blocks;
The number of ZLIB compressed data blocks, always exactly
@code{(ztrailer_ofs - 24) / 24}.
@end table

The fixed header is followed by @code{n_blocks} 24-byte ZLIB data
block descriptors, each of which describes the compressed data block
corresponding to its offset.  Each block descriptor has the following
format:

@example
int64               uncompressed_ofs;
int64               compressed_ofs;
int32               uncompressed_size;
int32               compressed_size;
@end example

@table @code
@item int64 uncompressed_ofs;
The offset, in bytes, that this block of data would have in a similar
system file that uses compression format 1.  This is
@code{zheader_ofs} in the first block descriptor, and in each
succeeding block descriptor it is the sum of the previous desciptor's
@code{uncompressed_ofs} and @code{uncompressed_size}.

@item int64 compressed_ofs;
The offset, in bytes, of the actual beginning of this compressed data
block.  This is @code{zheader_ofs + 24} in the first block descriptor,
and in each succeeding block descriptor it is the sum of the previous
descriptor's @code{compressed_ofs} and @code{compressed_size}.  The
final block descriptor's @code{compressed_ofs} and
@code{compressed_size} sum to @code{ztrailer_ofs}.

@item int32 uncompressed_size;
The number of bytes in this data block, after decompression.  This is
@code{block_size} in every data block except the last, which may be
smaller.

@item int32 compressed_size;
The number of bytes in this data block, as stored compressed in this
system file.
@end table
@end table

@setfilename ignored

@node Encrypted System Files
@section Encrypted System Files

SPSS 21 and later support an encrypted system file format.

@quotation Warning
The SPSS encrypted file format is poorly designed.  It is much cheaper
and faster to decrypt a file encrypted this way than if a well
designed alternative were used.  If you must use this format, use a
10-byte randomly generated password.
@end quotation

@subheading Encrypted File Format

Encrypted system files begin with the following 36-byte fixed header:

@example
0000  1c 00 00 00 00 00 00 00  45 4e 43 52 59 50 54 45  |........ENCRYPTE|
0010  44 53 41 56 15 00 00 00  00 00 00 00 00 00 00 00  |DSAV............|
0020  00 00 00 00                                       |....|
@end example

Following the fixed header is a complete system file in the usual
format, except that each 16-byte block is encrypted with AES-256 in
ECB mode.  The AES-256 key is derived from a password in the following
way:

@enumerate 
@item
Start from the literal password typed by the user.  Truncate it to at
most 10 bytes, then append (between 1 and 22) null bytes until there
are exactly 32 bytes.  Call this @var{password}.

@item
Let @var{constant} be the following 73-byte constant:

@example
0000  00 00 00 01 35 27 13 cc  53 a7 78 89 87 53 22 11
0010  d6 5b 31 58 dc fe 2e 7e  94 da 2f 00 cc 15 71 80
0020  0a 6c 63 53 00 38 c3 38  ac 22 f3 63 62 0e ce 85
0030  3f b8 07 4c 4e 2b 77 c7  21 f5 1a 80 1d 67 fb e1
0040  e1 83 07 d8 0d 00 00 01  00
@end example

@item
Compute CMAC-AES-256(@var{password}, @var{constant}).  Call the
16-byte result @var{cmac}.

@item
The 32-byte AES-256 key is @var{cmac} || @var{cmac}, that is,
@var{cmac} repeated twice.
@end enumerate

@subsubheading Example

Consider the password @samp{pspp}.  @var{password} is:

@example
0000  70 73 70 70 00 00 00 00  00 00 00 00 00 00 00 00  |pspp............|
0010  00 00 00 00 00 00 00 00  00 00 00 00 00 00 00 00  |................|
@end example

@noindent
@var{cmac} is:

@example
0000  3e da 09 8e 66 04 d4 fd  f9 63 0c 2c a8 6f b0 45
@end example

@noindent
The AES-256 key is:

@example
0000  3e da 09 8e 66 04 d4 fd  f9 63 0c 2c a8 6f b0 45
0010  3e da 09 8e 66 04 d4 fd  f9 63 0c 2c a8 6f b0 45
@end example

@subheading Password Encoding

SPSS also supports what it calls ``encrypted passwords.''  These are
not encrypted.  They are encoded with a simple, fixed scheme.  An
encoded password is always a multiple of 2 characters long, and never
longer than 20 characters.  The characters in an encoded password are
always in the graphic ASCII range 33 through 126.  Each successive
pair of characters in the password encodes a single byte in the
plaintext password.

Use the following algorithm to decode a pair of characters:

@enumerate
@item
Let @var{a} be the ASCII code of the first character, and @var{b} be
the ASCII code of the second character.

@item
Let @var{ah} be the most significant 4 bits of @var{a}.  Find the line
in the table below that has @var{ah} on the left side.  The right side
of the line is a set of possible values for the most significant 4
bits of the decoded byte.

@display
@t{2 } @result{} @t{2367}
@t{3 } @result{} @t{0145}
@t{47} @result{} @t{89cd}
@t{56} @result{} @t{abef}
@end display

@item
Let @var{bh} be the most significant 4 bits of @var{b}.  Find the line
in the second table below that has @var{bh} on the left side.  The
right side of the line is a set of possible values for the most
significant 4 bits of the decoded byte.  Together with the results of
the previous step, only a single possibility is left.

@display
@t{2 } @result{} @t{139b}
@t{3 } @result{} @t{028a}
@t{47} @result{} @t{46ce}
@t{56} @result{} @t{57df}
@end display

@item
Let @var{al} be the least significant 4 bits of @var{a}.  Find the
line in the table below that has @var{al} on the left side.  The right
side of the line is a set of possible values for the least significant
4 bits of the decoded byte.

@display
@t{03cf} @result{} @t{0145}
@t{12de} @result{} @t{2367}
@t{478b} @result{} @t{89cd}
@t{569a} @result{} @t{abef}
@end display

@item
Let @var{bl} be the least significant 4 bits of @var{b}.  Find the
line in the table below that has @var{bl} on the left side.  The right
side of the line is a set of possible values for the least significant
4 bits of the decoded byte.  Together with the results of the previous
step, only a single possibility is left.

@display
@t{03cf} @result{} @t{028a}
@t{12de} @result{} @t{139b}
@t{478b} @result{} @t{46ce}
@t{569a} @result{} @t{57df}
@end display
@end enumerate

@subsubheading Example

Consider the encoded character pair @samp{-|}.  @var{a} is
0x2d and @var{b} is 0x7c, so @var{ah} is 2, @var{bh} is 7, @var{al} is
0xd, and @var{bl} is 0xc.  @var{ah} means that the most significant
four bits of the decoded character is 2, 3, 6, or 7, and @var{bh}
means that they are 4, 6, 0xc, or 0xe.  The single possibility in
common is 6, so the most significant four bits are 6.  Similarly,
@var{al} means that the least significant four bits are 2, 3, 6, or 7,
and @var{bl} means they are 0, 2, 8, or 0xa, so the least significant
four bits are 2.  The decoded character is therefore 0x62, the letter
@samp{b}.