GRAP(1)

NAME
grap - Kernighan and Bentley's language for typesetting graphs

SYNOPSIS
grap [-d defines_file] [-D] [-l] [-M include path] [-R] [-r] [-v] [-u] [-C] [-c] [-h] [filename ...]

DESCRIPTION
grap is an implementation of Kernighan and Bentley's language for typesetting graphs, as described in ``Grap-A Language for Typesetting Graphs, Tutorial and User Manual,'' by Jon L. Bentley and Brian W. Kernighan, revised May 1991, which is the primary source for information on how to use grap. As of this writing, it is available electronically at http://www.kohala.com/start/troff/cstr114.ps. Additional documentation and examples, packaged with grap, may have been installed locally as well. If available, paths to them can be displayed using grap -h or grap -v (or grap --help / grap --version)

This version is a black box implementation of grap, and some inconsistencies are to be expected. The remainder of this manual page will briefly outline the grap language as implemented here.

grap is a pic(1) pre-processor. It takes commands embedded in a troff(1) source file which are surrounded by .G1 and .G2 macros, and rewrites them into pic commands to display the graph. Other lines are copied. Output is always to the standard output, which is usually redirected. Input is from the given filenames, which are read in order. A filename of - is the standard input. If no filenames are given, input is read from the standard input.

Because grap is a pic preprocessor, and GNU pic will output TeX, it is possible to use grap with TeX.

The -d option specifies a file of macro definitions to be read at startup, and defaults to /usr/local/share/grap/grap.defines . The -D option inhibits the reading of any initial macros file (the -l flag is a synonym for -D, though I do not remember why). The defines file can also be given using the GRAP_DEFINES environment variable. (See below).

-v prints the version information on the standard output and exits. --version is a synonym for -v.

-u makes labels unaligned by default. This version of grap uses new features of GNU pic to align the left and right labels with the axes, that is that the left and right labels run at right angles to the text of the paper. This may be useful in porting old grap programs. -c makes plot strings unclipped by default. Some versions of grap allow users to place a string anywhere in the coordinate space, rather than only in the frame. By default this version of grap does not plot any string centered outside the frame. -c allows strings to be placed anywhere. See also the clipped and unclipped string modifiers described in the plot statement.

-M is followed by a colon-separated list of directories used to search for relative pathnames included via copy. The path is also used to locate the defines file, so if the -d changes the defines file name to a relative name, it will be searched for in the path given by -M. The search path always includes the current directory, and by default that directory is searched last.

All numbers used internally by grap are double precision floating point values. Sometimes using floating point numbers has unintended consequences. To help avoid these problems, grap can use two thresholds for comparison of floating point numbers, set by -R or -r. The -R flag sets coarse comparison mode, which is suitable for most applications. If you are plotting small values – less than 1e-6 or so – consider using -r which uses very fine comparisons between numbers. You may also want to rescale your plotted values to be larger in magnitude. The coarse comarisons are used by default.

To be precise, the value by which two numbers must differ for grap to consider them not equal is called the comparison limit and the smallest non-zero number is called the minimum value. The values a given version of grap uses for these are included in the output of -v or -h.

All grap commands are included between .G1 and .G2 macros, which are consumed by grap. The output contains pic between .PS and .PE macros. Any arguments to the .G1 macro in the input are arguments to the .PS macro in the output, so graphs can be scaled just like pic diagrams. If -C is given, any macro beginning with .G1 or .G2 is treated as a .G1 or .G2 macro, for compatibility with old versions of troff. Using -C also forces pure troff syntax on embedded font change commands when strings have the size attribute, and all strings to be unclipped.

The -h flag prints a brief help message and exits. --help is a synonym for -h.

It is possible for someone to cause grap to fail by passing a bad format string and data to the sprintf command. If grap is integrated as part of the printing system, this could conceivably provided a path to breaching security on the machine. If you choose to use grap as part of a printing system run by the super-user, you should disable sprintf commands. This can be done by calling grap with the -S flag, setting the GRAP_SAFER environment variable, or compiling with the GRAP_SAFER preprocessor symbol defined. (The GNU configure script included with grap will define that preprocessor symbol if the --with-grap-safe option is given.)

The grap commands are sketched below. Refer to Kernighan and Bentley's paper for the details.

New versions of groff(1) will invoke grap if -G is given.

  Commands

Commands are separated from one another by newlines or semicolons (;).

frame [line_description] [ ht height | wid width] [ [ (top|bottom| left| right) line_description] ...]

frame [ ht height | wid width] [line_description] [ [ (top|bottom| left| right) line_description] ...]

This describes how the axes for the graph are drawn. A line_description is a pic line description, e.g., dashed 0.5, or the literal solid. It may also include a color keyword followed by the color to draw the string in double quotes. Any color understood by the underlying groff system can be used. Color can only be used under GNU pic, and is not available in compatibility mode. Similarly, for pic implementations that understand thickness, that attribute may be used with a real valued parameter. Thickness is not available in compatibility mode.

If the first line_description is given, the frame is drawn with that style. The default is solid. The height and width of the frame can also be specified in inches. The default line style can be over-ridden for sides of the frame by specifying additional parameters to frame.

If no plotting commands have been given before the frame command is issued, the frame will be output at that point in the plotting stream relative to embedded troff or pic commands. Otherwise the frame is output before the first plotted object (even invisible ones).

ht and wid are in inches by default, but can be any groff unit. If omitted, the dimensions are 2 inches high by 3 inches wide.

coord [name] [x expr, expr] [y expr, expr] [ log x | log y | log log]

The coord command specifies a new coordinate system or sets limits on the default system. It defines the largest and smallest values that can be plotted, and therefore the scale of the data in the frame. The limits for the x and y coordinate systems can be given separately. If a name is given, that coordinate system is defined, if not the default system is modified.

A coordinate system created by one coord command may be modified by subsequent coord commands. A grap program may declare a coordinate space using coord, copy a file of data through a macro that plots the data and finds its maxima and minima, and then define the size of the coordinate system with a second coord statement.

This command also determines if a scale is plotted logarithmically. log log means the same thing as log x log y.

draw [line_name] [line_description] [plot_string]

The draw command defines the style with which a given line will be plotted. If line_name is given, the style is associated with that name, otherwise the default style is set. line_description is a pic line description, and the optional plot_string is a string to be centered at each point. The default line description is invis, and the default plotting string is a centered bullet, so by default each point is a filled circle, and they are unconnected. If points are being connected, each draw command ends any current line and begins a new one.

When defining a line style, that is the first draw command for a given line name, specifying no plot string means that there are to be no plot strings. Omitting the plot string on subsequent draw commands addressing the same named line means not to change the plot string. If a line has been defined with a plot string, and the format is changed by a subsequent draw statement, the plot string can be removed by specifying "" in the draw statement.

The plot string can have its format changed through several string_modifiers. String_modifiers are described in the description of the plot command.

The standard defines file includes several macros useful as plot strings, including bullet, square, and delta.

new is a synonym for draw.

next [line_name] at [coordinates_name] expr, expr [line_description]

The next command plots the given point using the line style given by line_name, or the default if none is given. If line_name is given, it should have been defined by an earlier draw command, if not a new line style with that name is created, initialized the same way as the default style. The two expressions give the point's x and y values, relative to the optional coordinate system. That system should have been defined by an earlier coord command, if not, grap will exit. If the optional line_description is given, it overrides the style's default line description. You cannot over-ride the plotting string. To use a different plotting string use the plot command.

The coordinates may optionally be enclosed in parentheses: (expr, expr)

quoted_string [string_modifiers] [, quoted_string [ string_modifiers]] ... at [coordinates_name] expr, expr

plot expr [format_string] at [coordinates_name] expr, expr

These commands both plot a string at the given point. In the first case the literal strings are stacked above each other. The string_modifiers include the pic justification modifiers (ljust, rjust, above, and below), and absolute and relative size modifiers. See the pic documentation for the description of the justification modifiers. grap also supports the aligned and unaligned modifiers which are briefly noted in the description of the label command.

The standard defines file includes several macros useful as plot strings, including bullet, square, and delta.

Strings placed by either format of the plot command are restricted to being within the frame. This can be overridden by using the unclipped attribute, which allows a string to be plotted in or out of the frame. The -c and -C flags set unclipped on all strings, and to prevent a string from being plotted outside the frame when those flags are active, the clipped attribute can be used to retore clipping behavior. Though clipped or unclipped can be applied to any string, it only has meaning for plot statements.

size expr sets the string size to expr points. If expr is preceded by a + or -, the size is increased or decreased by that many points.

If color and a color name in double quotes appears, the string will be rendered in that color under a version of GNU troff that supports color. Color is not available in compatibility mode.

In the second version, the expr is converted to a string and placed on the graph. format_string is a printf(3) format string. Only formatting escapes for printing floating point numbers make sense. The format string is only respected if the sprintf command is also active. See the description of sprintf for the various ways to disable it. Plot and sprintf respond differently when grap is running safely. Sprintf ignores any arguments, passing the format string through without substitution. plot ignores the format string completely, plotting expr using the "%g" format.

Points are specified the same way as for next commands, with the same consequences for undefined coordinate systems.

The second form of this command is because the first form can be used with a grap sprintf expression (See Expressions).

ticks (left|right |top|bottom) [ (in|out) [expr]] [ on|auto coord_name]

ticks (left|right|top|bottom) (in|out) [expr] [ up expr | down expr | left expr | right expr] at [coord_name] expr [format_string] [ [, expr [ format_string]] ...]

ticks (left|right |top|bottom) (in|out) [expr] [ up expr | down expr | left expr | right expr] from [coord_name] start_expr to end_expr [ by [ +|-|*|/] by_expr] [format_string]

ticks [ left|right |top|bottom] off

This command controls the placement of ticks on the frame. By default, ticks are automatically generated on the left and bottom sides of the frame.

The first version of this command turns on the automatic tick generation for a given side. The in or out parameter controls the direction and length of the ticks. If a coord_name is specified, the ticks are automatically generated using that coordinate system. If no system is specified, the default coordinate system is used. As with next and plot, the coordinate system must be declared before the ticks statement that references it. This syntax for requesting automatically generated ticks is an extension, and will not port to older grap implementations.

The second version of the ticks command overrides the automatic placement of the ticks by specifying a list of coordinates at which to place the ticks. If the ticks are not defined with respect to the default coordinate system, the coord_name parameter must be given. For each tick a printf(3) style format string can be given. The format_string defaults to "%g". The format string can also take string modifiers as described in the plot command. To place ticks with no labels, specify format_string as "".

If sprintf is disabled, ticks behaves as plot with respect to the format string.

The labels on the ticks may be shifted by specifying a direction and the distance in inches to offset the label. That is the optional direction and expression immediately preceding the at.

The third format of the ticks command over-rides the default tick generation with a set of ticks ar regular intervals. The syntax is reminiscent of programming language for loops. Ticks are placed starting at start_expr ending at end_expr one unit apart. If the by clause is specified, ticks are by_expr units apart. If an operator appears before by_expr each tick is operated on by that operator instead of +. For example

    ticks left out from 2 to 32 by *2

will put ticks at 2, 4, 8, 16, and 32. If format_string is specified, all ticks are formatted using it.

The parameters preceding the from act as described above.

The at and for forms of tick command may both be issued on the same side of a frame. For example:

    ticks left out from 2 to 32 by *2
    ticks left in 3, 5, 7

will put ticks on the left side of the frame pointing out at 2, 4, 8, 16, and 32 and in at 3, 5, and 7.

The final form of ticks turns off ticks on a given side. If no side is given the ticks for all sides are cancelled.

tick is a synonym for ticks.

grid (left|right |top|bottom) [ticks off] [line_description] [ up expr | down expr | left expr | right expr] [ on|auto [coord_name]]

grid (left|right |top|bottom) [ticks off] [line_description] [ up expr | down expr | left expr | right expr] at [coord_name] expr [format_string] [ [, expr [ format_string]] ...]

grid (left|right |top|bottom) [ticks off] [line_description] [ up expr | down expr | left expr | right expr] from [coord_name] start_expr to end_expr [ by [ +|-|*|/] by_expr] [format_string]

The grid command is similar to the ticks command except that grid specifies the placement of lines in the frame. The syntax is similar to ticks as well.

By specifying ticks off in the command, no ticks are drawn on that side of the frame. If ticks appear on a side by default, or have been declared by an earlier ticks command, grid does not cancel them unless ticks off is specified.

Instead of a direction for ticks, grid allows the user to pick a line description for the grid lines. The usual pic line descriptions are allowed.

Grids are labelled by default. To omit labels, specify the format string as "".

If sprintf is disabled, grid behaves as plot with respect to the format string.

label (left|right |top|bottom) quoted_string [string_modifiers] [, quoted_string [ string_modifiers]] ... [ up expr | down expr | left expr | right expr]

The label command places a label on the given axis. It is possible to specify several labels, which will be stacked over each other as in pic. The final argument, if present, specifies how many inches the label is shifted from the axis.

By default the labels on the left and right labels run parallel to the frame. You can cancel this by specifying unaligned as a string_modifier.

circle at [coordinate_name] expr, expr [radius expr] [linedesc]

This draws an circle at the point indicated. By default, the circle is small, 0.025 inches. This can be over-ridden by specifying a radius. The coordinates of the point are relative to the named coordinate system, or the default system if none is specified.

This command has been extended to take a line description, e.g., dotted. It also accepts the filling extensions described below in the bar command. It will also accept a color keyword that gives the color of the outline of the circle in double quotes and a fillcolor command that sets the color to fill the circle with similarly. Colors are only available when compatibility mode is off, and using a version of GNU pic that supports color.

line [line_description] from [coordinate_name] expr, expr to [coordinate_name] expr, expr [line_description]

arrow [line_description] from [coordinate_name] expr, expr to [coordinate_name] expr, expr [line_description]

This draws a line or arrow from the first point to the second using the given style. The default line style is solid. The line_description can be given either before the from or after the to clause. If both are given the second is used. It is possible to specify one point in one coordinate system and one in another, note that if both points are in a named coordinate system (even if they are in the same named coordinate system), both points must have coordinate_name given.

copy ["filename"] [until "string"] [thru macro]

The copy command imports data from another file into the current graph. The form with only a filename given is a simple file inclusion; the included file is simply read into the input stream and can contain arbitrary grap commands. The more common case is that it is a number list; see Number Lists below.

The second form takes lines from the file, splits them into words delimited by one or more spaces, and calls the given macro with those words as parameters. The macro may either be defined here, or be a macro defined earlier. See Macros for more information on macros.

The filename may be omitted if the until clause is present. If so the current file is treated as the input file until string is encountered at the beginning of the line.

copy is one of the workhorses of grap. Check out the paper and /usr/local/share/examples/grap for more details. Confirm the location of the examples directory using the -v flag.

print (expr|string)

Prints its argument to the standard error.

sh block

This passes block to sh(1). Unlike K&B grap no macro or variable expansion is done. I believe that this is also true for GNU pic version 1.10. See the Macros section for information on defining blocks.

pic pic_statement

This issues the given pic statements in the enclosing .PS and .PE at the point where the command is issued.

Statements that begin with a period are considered to be troff(statements) and are output in the enclosing .PS and .PE at the point where the command appears.

For the purposes of relative placement of pic or troff commands, the frame is output immediately before the first plotted object, or the frame statement, if any. If the user specifies pic or troff commands and neither any plotable object nor a frame command, the commands will not be output.

graph Name pic_commands

This command is used to position graphs with respect to each other. The current graph is given the pic name Name (names used by pic begin with capital letters). Any pic commands following the graph are used to position the next graph. The frame of the graph is available for use with pic name Frame. The following places a second graph below the first:

    graph Linear
    [ graph description ]
    graph Exponential with .Frame.n at \
    	Linear.Frame.s - (0, .05)
    [ graph description ]

name = expr

This assigns expr to the variable name. grap has only numeric (double) variables.

Assignment creates a variable if it does not exist. Variables persist across graphs. Assignments can cascade; a = b = 35 assigns 35 to a and b.

bar (up|right) [coordinates_name] offset ht height [wid width] [base base_offset] [line_description]

bar [coordinates_name] expr, expr, [coordinates_name] expr, expr, [line_description]

The bar command facilitates drawing bar graphs. The first form of the command describes the bar somewhat generally and has grap place it. The bar may extend up or to the right, is centered on offset and extends up or right height units (in the given coordinate system). For example

    bar up 3 ht 2

draws a 2 unit high bar sitting on the x axis, centered on x=3. By default bars are 1 unit wide, but this can be changed with the wid keyword. By default bars sit on the base axis, i.e., bars directed up will extend from y=0. That may be overridden by the base keyword. (The bar described above has corners (2.5, 0) and (3.5, 2).)

The line description has been extended to include a fill expr keyword that specifies the shading inside the bar. Bars may be drawn in any line style. They support the color and fillcolor keywords described under circle.

The second form of the command draws a box with the two points as corners. This can be used to draw boxes highlighting certain data as well as bar graphs. Note that filled bars will cover data drawn under them.

  Control Flow

if expr then block [else block]

The if statement provides simple conditional execution. If expr is non-zero, the block after the then statement is executed. If not the block after the else is executed, if present. See Macros for the definition of blocks. Early versions of this implementation of grap treated the blocks as macros that were defined and expanded in place. This led to unnecessary confusion because explicit separators were sometimes called for. Now, grap inserts a separator (;) after the last character in block, so constructs like

    if (x == 3) { y = y + 1 }
    x = x + 1

behave as expected. A separator is also appended to the end of a for block.

for name from from_expr to to_expr [ by [+|-|*|/] by_expr] do block

This command executes block iteratively. The variable name is set to from_expr and incremented by by_expr until it exceeds to_expr. The iteration has the semantics defined in the ticks command. The definition of block is discussed in Macros. See also the note about implicit separators in the description of the if command.

An = can be used in place of from.

  Expressions

grap supports most standard arithmetic operators: + - / * ^. The carat (^) is exponentiation. In an if statement grap also supports the C logical operators ==, !=, &&, || and unary !. Also in an if, == and != are overloaded for the comparison of quoted strings. Parentheses are used for grouping.

Assignment is not allowed in an expression in any context, except for simple cascading of assignments. a = b = 35 works as expected; a = 3.5 * (b = 10) does not execute.

grap supports the following functions that take one argument: log, exp, int, sin, cos, sqrt, rand. The logarithms are base 10 and the trigonometric functions are in radians. eexp returns Euler's number to the given power and ln returns the natural logarithm. The natural log and exponentiation functions are extensions and are probably not available in other grap implementations.

rand returns a random number uniformly distributed on [0,1). The following two-argument functions are supported: atan2, min, max. atan2 works just like atan2(3). The random number generator can be seeded by calling srand with a single parameter (converted internally to an integer). Because its return value is of no use, you must use srand as a separate statement, it is not part of a valid expression. srand is not portable.

The getpid function takes no arguments and returns the process id. This may be used to seed the random number generator, but do not expect cryptographically random values to result.

Other than string comparison, no expressions can use strings. One string valued function exists: sprintf (format, [ expr [, expr]] ). It operates like sprintf(3), except returning the value. It can be used anywhere a quoted string is used. If grap is run with -S, the environment variable GRAP_SAFER is defined, or grap has been compiled for safer operation, the sprintf command will return the format string. This mode of operation is only intended to be used only if grap is being used as part of a super-user enabled print system.

  Macros
grap has a simple but powerful macro facility. Macros are defined using the define command :

define name block
undefine name

Every occurrence of name in the program text is replaced by the contents of block. block is defined by a series of statements in nested { }'s, or a series of statements surrounded by the same letter. An example of the latter is

    define foo  X coord x 1,3 X

Each time foo appears in the text, it will be replaced by coord x 1,3. Macros are literal, and can contain newlines. If a macro does not span multiple lines, it should end in a semicolon to avoid parsing errors.

Macros can take parameters, too. If a macro call is followed by a parenthesized, comma-separated list the values starting with $1 will be replaced in the macro with the elements of the list. A $ not followed by a digit is left unchanged. This parsing is very rudimentary; no nesting or parentheses or escaping of commas is allowed. Also, there is no way to say argument 1 followed by a digit (${1}0 in sh(1)).

The following will draw a line with slope 1.

    define foo { next at $1, $2 }
    for i from 1 to 5 { foo(i,i) }

Macros persist across graphs. The file /usr/local/share/grap/grap.defines contains simple macros for plotting common characters. The undefine command deletes a macro.

See the directory /usr/local/share/examples/grap for more examples of macros. Confirm the location of the examples directory using the -v flag.

  Number Lists

A whitespace-separated list of numbers is treated specially. The list is taken to be points to be plotted using the default line style on the default coordinate system. If more than two numbers are given, the extra numbers are taken to be additional y values to plot at the first x value. Number lists in DWB grap can be comma-separated, and this grap supports that as well. More precisely, numbers in number lists can be separated by either whitespace, commas, or both.

    1 2 3
    4 5 6

Will plot points using the default line style at (1,2), (1,3),(4,5) and (4,6). A simple way to plot a set of numbers in a file named ./data is:

    .G1
    copy "./data"
    .G2

  Pic Macros

grap defines pic macros that can be used in embedded pic code to place elements in the graph. The macros are x_gg, y_gg, and xy_gg. These macros define pic distances that correspond to the given argument. They can be used to size boxes or to plot pic constructs on the graph. To place a given construct on the graph, you should add Frame.Origin to it. Other coordinate spaces can be used by replacing gg with the name of the coordinate space. A coordinate space named gg cannot be reliably accessed by these macros.

The macros are emitted immediately before the frame is drawn.

DWB grap may use these as part of its implementation. This grap provides them only for compatibility. Note that these are very simple macros, and may not do what you expect under complex conditions.

ENVIRONMENT VARIABLES

If the environment variable GRAP_DEFINES is defined, grap will look for its defines file there. If that value is a relative path name the path specified in the -M option will be searched for it. GRAP_DEFINES overrides the compiled in location of the defines file, but may be overridden by the -d or -D flags.

If GRAP_SAFER is set, sprintf is disabled to prevent forcing grap to core dump or smash the stack.

FILES
/usr/local/share/grap/grap.defines

SEE ALSO
atan2(3), groff(1), pic(1), printf(3), sh(1), sprintf(3), troff(1)

If documentation and examples have been installed, grap --version or grap --help will display the locations.

BUGS

There are several small incompatibilities with K&R grap. They include the sh command not expanding variables and macros, and a more strict adherence to parameter order in the internal commands.

Although much improved, the error reporting code can still be confused. Notably, an error in a macro is not detected until the macro is used, and it produces unusual output in the error message.

Iterating many times over a macro with no newlines can run grap out of memory.

AUTHOR
This implementation was done by Ted Faber <faber@lunabase.org>. Bruce Lilly <blilly@erols.com> contributed many bug fixes, including a considerable revamp of the error reporting code. If you can actually find an error in your grap code, you can probably thank him. grap was designed and specified by Brian Kernighan and Jon Bentley.