Printed axes help you understand a graph. They convey scale. In an earlier chapter (see section Readying a Graph), we wrote the code to print the body of a graph. Here we write the code for print and labelling vertical and horizontal axes, along with the body itself.
let expression in print-graph.
Since insertions fill a buffer to the right and below point, the new graph printing function should first print the Y or vertical axis, then the body of the graph, and finally the X or horizontal axis. This sequence lays out for us the contents of the function:
Here is an example of how a finished graph should look:
10 -
*
* *
* **
* ***
5 - * *******
* *** *******
*************
***************
1 - ****************
| | | |
1 5 10 15
In this graph, both the vertical and the horizontal axes are labeled with numbers. However, in some graphs, the horizontal axis is time and would be better labeled with months, like this:
5 - *
* ** *
*******
********** **
1 - **************
| ^ |
Jan June Jan
Indeed, with a little thought, we can easily come up with a variety of vertical and horizontal labelling schemes. Our task could become complicated. But complications breed confusion. Rather than permit this, it is better choose a simple labelling scheme for our first effort, and to modify or replace it later.
These considerations suggest the following outline for the
print-graph function:
(defun print-graph (numbers-list)
"documentation..."
(let ((height ...
...))
(print-Y-axis height ... )
(graph-body-print numbers-list)
(print-X-axis ... )))
We can work on each part of the print-graph function definition
in turn.
print-graph Varlist
In writing the print-graph function, the first task is to write
the varlist in the let expression. (We will leave aside for the
moment any thoughts about making the function interactive or about the
contents of its documentation string.)
The varlist should set several values. Clearly, the top of the label
for the vertical axis must be at least the height of the graph, which
means that we must obtain this information here. Note that the
print-graph-body function also requires this information. There
is no reason to calculate the height of the graph in two different
places, so we should change for print-graph-body from the way we
defined it earlier to take advantage of the calculation.
Similarly, both the function for printing the X axis labels and the
print-graph-body function need to learn the value of the width of
each symbol. We can perform the calculation here and change the
definition for print-graph-body from the way we defined it in the
previous chapter.
The length of the label for the horizontal axis must be at least as long as the graph. However, this information is used only in the function that prints the horizontal axis, so it does not need to be calculated here.
These thoughts lead us directly to the following form for the varlist
in the let for print-graph:
(let ((height (apply 'max numbers-list)) ; First version.
(symbol-width (length graph-blank)))
As we shall see, this expression is not quite right.
print-Y-axis Function
The job of the print-Y-axis function is to print a label for
the vertical axis that looks like this:
10 -
5 -
1 -
The function should be passed the height of the graph, and then should construct and insert the appropriate numbers and marks.
It is easy enough to see in the figure what the Y axis label should look like; but to say in words, and then to write a function definition to do the job is another matter. It is not quite true to say that we want a number and a tick every five lines: there are only three lines between the `1' and the `5' (lines 2, 3, and 4), but four lines between the `5' and the `10' (lines 6, 7, 8, and 9). It is better to say that we want a number and a tick mark on the base line (number 1) and then that we want a number and a tick on the fifth line from the bottom and on every line that is a multiple of five.
The next issue is what height the label should be. Suppose the maximum
height of tallest column of the graph is seven. Should the highest
label on the Y axis be `5 -', and should the graph stick up above
the label? Or should the highest label be `7 -', and mark the peak
of the graph? Or should the highest label be 10 -, which is a
multiple of five, and be higher than the topmost value of the graph?
The latter form is preferred. Most graphs are drawn within rectangles
whose sides are an integral number of steps long--5, 10, 15, and so
on for a step distance of five. But as soon as we decide to use a
step height for the vertical axis, we discover that the simple
expression in the varlist for computing the height is wrong. The
expression is (apply 'max numbers-list). This returns the
precise height, not the maximum height plus whatever is necessary to
round up to the nearest multiple of five. A more complex expression
is required.
As usual in cases like this, a complex problem becomes simpler if it is divided into several smaller problems.
First, consider the case when the highest value of the graph is an integral multiple of five--when it is 5, 10, 15 ,or some higher multiple of five. In this case, we can use this value as the Y axis height.
A fairly simply way to determine whether a number is a multiple of five is to divide it by five and see if the division results in a remainder. If there is no remainder, the number is a multiple of five. Thus, seven divided by five has a remainder of two, and seven is not an integral multiple of five. Put in slightly different language, more reminiscent of the classroom, five goes into seven once, with a remainder of two. However, five goes into ten twice, with no remainder: ten is an integral multiple of five.
In Lisp, the function for computing a remainder is %. The
function returns the remainder of its first argument divided by its
second argument. As it happens, % is a function in Emacs Lisp
that you cannot discover using apropos: you find nothing if you
type M-x apropos RET remainder RET. The only way to
learn of the existence of % is to read about it in a book such
as this or in the Emacs Lisp sources. The % function is used
in the code for rotate-yank-pointer, which is described in an
appendix. (See section The Body of rotate-yank-pointer.)
You can try the % function by evaluating the following two
expressions:
(% 7 5) (% 10 5)
The first expression returns 2 and the second expression returns 0.
To test whether the returned value is zero or some other number, we
can use the zerop function. This function returns t if
its argument, which must be a number, is zero.
(zerop (% 7 5))
=> nil
(zerop (% 10 5))
=> t
Thus, the following expression will return t if the height
of the graph is evenly divisible by five:
(zerop (% height 5))
(The value of height, of course, can be found from (apply
'max numbers-list).)
On the other hand, if the value of height is not a multiple of
five, we want to reset the value to the next higher multiple of five.
This is straightforward arithmetic using functions with which we are
already familiar. First, we divide the value of height by five
to determine how many times five goes into the number. Thus, five
goes into twelve twice. If we add one to this quotient and multiply by
five, we will obtain the value of the next multiple of five that is
larger than the height. Five goes into twelve twice. Add one to two,
and multiply by five; the result is fifteen, with is the next multiple
of five that is higher than twelve. The Lisp expression for this is:
(* (1+ (/ height 5)) 5)
For example, if you evaluate the following, the result is 15:
(* (1+ (/ 12 5)) 5)
All through this discussion, we have been using `five' as the value
for spacing labels on the Y axis; but we may want to use some other
value. For generality, we should replace `five' with a variable to
which we can assign a value. The best name I can think of for this
variable is Y-axis-label-spacing. Using this term, and an
if expression, we produce the following:
(if (zerop (% height Y-axis-label-spacing))
height
;; else
(* (1+ (/ height Y-axis-label-spacing))
Y-axis-label-spacing))
This expression returns the value of height itself if the height
is an even multiple of the value of the Y-axis-label-spacing or
else it computes and returns a value of height that is equal to
the next higher multiple of the value of the Y-axis-label-spacing.
We can now include this expression in the let expression of the
print-graph function (after first setting the value of
Y-axis-label-spacing):
(defvar Y-axis-label-spacing 5
"Number of lines from one Y axis label to next.")
...
(let* ((height (apply 'max numbers-list))
(height-of-top-line
(if (zerop (% height Y-axis-label-spacing))
height
;; else
(* (1+ (/ height Y-axis-label-spacing))
Y-axis-label-spacing)))
(symbol-width (length graph-blank))))
...
(Note use of the let* function: the initial value of height is
computed once by the (apply 'max numbers-list) expression and
then the resulting value of height is used to compute its
final value. See section The let* expression, for
more about let*.)
When we print the vertical axis, we want to insert strings such as `5 -' and `10 - ' every five lines. Moreover, we want the numbers and dashes to line up, so shorter numbers must be padded with leading spaces. If some of the strings use two digit numbers, the strings with single digit numbers must include a leading blank space before the number.
To figure out the length of the number, the length function is
used. But the length function works only with a string, not with
a number. So the number has to be converted from being a number to
being a string. This is done with the int-to-string function.
For example,
(length (int-to-string 35))
=> 2
(length (int-to-string 100))
=> 3
In addition, in each label, each number is followed by a string such
as ` - ', which we will call the Y-axis-tic marker.
This variable is defined with defvar:
(defvar Y-axis-tic " - " "String that follows number in a Y axis label.")
The length of the Y label is the sum of the length of the Y axis tick mark and the length of the number of the top of the graph.
(length (concat (int-to-string height) Y-axis-tic)))
This value will be calculated by the print-graph function in
its varlist as full-Y-label-width and passed on. (Note that we
did not think to include this in the varlist when we first proposed it.)
To make a complete vertical axis label, a tick mark is concatenated
with a number; and the two together may be preceded by one or more
spaces depending on how long the number is. The label consists of
three parts: the (optional) leading spaces, the number, and the tic
mark. The function is passed the value of the number for the specific
row, and the value of the width of the top line, which is calculated
(just once) by print-graph.
(defun Y-axis-element (number full-Y-label-width)
"Construct a NUMBERed label element.
A numbered element looks like this ` 5 - ',
and is padded as needed so all line up with
the element for the largest number."
(let* ((leading-spaces
(- full-Y-label-width
(length
(concat (int-to-string number)
Y-axis-tic)))))
(concat
(make-string leading-spaces ? )
(int-to-string number)
Y-axis-tic)))
The Y-axis-element function concatenates together the leading
spaces, if any; the number, as a string; and the tick mark.
To figure out how many leading spaces the label will need, the function subtracts the actual length of the label--the length of the number plus the length of the tic mark--from the desired label width.
Blank spaces are inserted using the make-string function.
This function takes two arguments: the first tells it how long the
string will be and the second is a symbol for the character to insert,
in a special format. In this case, the format is a question mark
followed by a blank space, like this, `? '.
See section `Character Type' in The GNU Emacs Lisp Reference Manual, for a description of the syntax for characters.
The int-to-string function is used in the concatenation
expression, to convert the number to a string that is concatenated
with the leading spaces and the tic mark.
The preceding functions provide all the tools needed to construct a function that generates a list of numbered and blank strings to insert as the label for the vertical axis:
(defun Y-axis-column (height width-of-label)
"Construct list of Y axis labels and blank strings.
For HEIGHT of line above base and WIDTH-OF-LABEL."
(let (Y-axis)
(while (> height 1)
(if (zerop (% height Y-axis-label-spacing))
;; Insert label.
(setq Y-axis
(cons
(Y-axis-element height width-of-label)
Y-axis))
;; Else, insert blanks.
(setq Y-axis
(cons
(make-string width-of-label ? )
Y-axis)))
(setq height (1- height)))
;; Insert base line.
(setq Y-axis
(cons (Y-axis-element 1 width-of-label) Y-axis))
(nreverse Y-axis)))
In this function, we start with the value of height and
repetitively subtract one from its value. After each subtraction, we
test to see whether the value is an integral multiple of the
Y-axis-label-spacing. If it is, we construct a numbered label
using the Y-axis-element function; if not, we construct a
blank label using the make-string function. The base line
consists of the number one followed by a tic mark.
print-Y-axis
The list constructed by the Y-axis-column function is passed to
the print-Y-axis function, which inserts the list as a column.
(defun print-Y-axis
(height full-Y-label-width &optional vertical-step)
"Insert Y axis using HEIGHT and FULL-Y-LABEL-WIDTH.
Height must be the maximum height of the graph.
Full width is the width of the highest label element.
Optionally, print according to VERTICAL-STEP."
;; Value of height and full-Y-label-width
;; are passed by `print-graph'.
(let ((start (point)))
(insert-rectangle
(Y-axis-column height full-Y-label-width vertical-step))
;; Place point ready for inserting graph.
(goto-char start)
;; Move point forward by value of full-Y-label-width
(forward-char full-Y-label-width)))
The print-Y-axis uses the insert-rectangle function to
insert the Y axis labels created by the Y-axis-column function.
In addition, it places point at the correct position for printing the body of
the graph.
You can test print-Y-axis:
Y-axis-label-spacing Y-axis-tic Y-axis-element Y-axis-columnprint-Y-axis
(print-Y-axis 12 5)
eval-expression).
graph-body-print expression into the minibuffer
with C-y (yank).
Emacs will print labels vertically, the top one being
`10 - '. (The print-graph function
will pass the value of height-of-top-line, which
in this case would be 15.)
print-X-axis FunctionX axis labels are much like Y axis labels, except that the tics are on a line above the numbers. Labels should look like this:
| | | |
1 5 10 15
The first tic is under the first column of the graph and is preceded by
several blank spaces. These spaces provide room in rows above for the Y
axis labels. The second, third, fourth, and subsequent tics are all
spaced equally, according to the value of X-axis-label-spacing.
The second row of the X axis consists of numbers, preceded by several
blank spaces and also separated according to the value of the variable
X-axis-label-spacing.
The value of the variable X-axis-label-spacing should itself be
measured in units of symbol-width, since you may want to change
the width of the symbols that you are using to print the body of the
graph without changing the ways the graph is labeled.
The print-X-axis function is constructed in more or less the
same fashion as the print-Y-axis function except that it has
two lines: the line of tic marks and the numbers. We will write a
separate function to print each line and then combine them within the
print-X-axis function.
This is a three step process:
print-X-axis-tic-line.
print-X-axis-numbered-line.
print-X-axis function,
using print-X-axis-tic-line and
print-X-axis-numbered-line.
The first function should print the X axis tic marks. We must specify the tic marks themselves and their spacing:
(defvar X-axis-label-spacing
(if (boundp 'graph-blank)
(* 5 (length graph-blank)) 5)
"Number of units from one X axis label to next.")
(Note that the value of graph-blank is set by another
defvar. The boundp predicate checks whether it has
already been set; boundp returns nil if it has not. If
graph-blank were unbound and we did not use this conditional
construction, we would receive an error message saying `Symbol's
value as variable is void'.)
(defvar X-axis-tic-symbol "|" "String to insert to point to a column in X axis.")
The goal is to make a line that looks like this:
| | | |
The first tic is indented so that it is under the first column, which is indented to provide space for the Y axis labels.
A tic element consists of the blank spaces that stretch from one tic to
the next plus a tic symbol. The number of blanks is determined by the
width of the tic symbol and the X-axis-label-spacing.
The code looks like this:
;;; X-axis-tic-element
...
(concat
(make-string
;; Make a string of blanks.
(- (* symbol-width X-axis-label-spacing)
(length X-axis-tic-symbol))
? )
;; Concatenate blanks with tic symbol.
X-axis-tic-symbol)
...
Next, we determine how many blanks are needed to indent the first tic
mark to the first column of the graph. This uses the value of
full-Y-label-width passed it by the print-graph function.
The code to make X-axis-leading-spaces
looks like this:
;; X-axis-leading-spaces ... (make-string full-Y-label-width ? ) ...
We also need to determine the length of the horizontal axis, which is the length of the numbers list, and the number of tics in the horizontal axis:
;; X-length
...
(length numbers-list)
;; tic-width
...
(* symbol-width X-axis-label-spacing)
;; number-of-X-tics
(if (zerop (% (X-length tic-width)))
(/ (X-length tic-width))
(1+ (/ (X-length tic-width))))
All this leads us directly to the function for printing the X axis tic line:
(defun print-X-axis-tic-line
(number-of-X-tics X-axis-leading-spaces X-axis-tic-element)
"Print tics for X axis."
(insert X-axis-leading-spaces)
(insert X-axis-tic-symbol) ; Under first column.
;; Insert second tic in the right spot.
(insert (concat
(make-string
(- (* symbol-width X-axis-label-spacing)
;; Insert white space up to second tic symbol.
(* 2 (length X-axis-tic-symbol)))
? )
X-axis-tic-symbol))
;; Insert remaining tics.
(while (> number-of-X-tics 1)
(insert X-axis-tic-element)
(setq number-of-X-tics (1- number-of-X-tics))))
The line of numbers is equally straightforward:
First, we create a numbered element with blank spaces before each number:
(defun X-axis-element (number)
"Construct a numbered X axis element."
(let ((leading-spaces
(- (* symbol-width X-axis-label-spacing)
(length (int-to-string number)))))
(concat (make-string leading-spaces ? )
(int-to-string number))))
Next, we create the function to print the numbered line, starting with the number "1" under the first column:
(defun print-X-axis-numbered-line
(number-of-X-tics X-axis-leading-spaces)
"Print line of X-axis numbers"
(let ((number X-axis-label-spacing))
(insert X-axis-leading-spaces)
(insert "1")
(insert (concat
(make-string
;; Insert white space up to next number.
(- (* symbol-width X-axis-label-spacing) 2)
? )
(int-to-string number)))
;; Insert remaining numbers.
(setq number (+ number X-axis-label-spacing))
(while (> number-of-X-tics 1)
(insert (X-axis-element number))
(setq number (+ number X-axis-label-spacing))
(setq number-of-X-tics (1- number-of-X-tics)))))
Finally, we need to write the print-X-axis that uses
print-X-axis-tic-line and
print-X-axis-numbered-line.
The function must determine the local values of the variables used by both
print-X-axis-tic-line and print-X-axis-numbered-line, and
then it must call them. Also, it must print the carriage return that
separates the two lines.
The function consists of a varlist that specifies five local variables, and calls to each of the two line printing functions:
(defun print-X-axis (numbers-list)
"Print X axis labels to length of NUMBERS-LIST."
(let* ((leading-spaces
(make-string full-Y-label-width ? ))
;; symbol-width is provided by graph-body-print
(tic-width (* symbol-width X-axis-label-spacing))
(X-length (length numbers-list))
(X-tic
(concat
(make-string
;; Make a string of blanks.
(- (* symbol-width X-axis-label-spacing)
(length X-axis-tic-symbol))
? )
;; Concatenate blanks with tic symbol.
X-axis-tic-symbol))
(tic-number
(if (zerop (% X-length tic-width))
(/ X-length tic-width)
(1+ (/ X-length tic-width)))))
(print-X-axis-tic-line tic-number leading-spaces X-tic)
(insert "\n")
(print-X-axis-numbered-line tic-number leading-spaces)))
You can test print-X-axis:
X-axis-tic-symbol, X-axis-label-spacing,
print-X-axis-tic-line, as well as X-axis-element,
print-X-axis-numbered-line, and print-X-axis.
(progn
(let ((full-Y-label-width 5)
(symbol-width 1))
(print-X-axis
'(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16))))
eval-expression).
yank).
Emacs will print the horizontal axis like this:
| | | | |
1 5 10 15 20
Now we are nearly ready to print the whole graph.
The function to print the graph with the proper labels follows the outline we created earlier (see section A Graph with Labelled Axes), but with additions.
Here is the outline:
(defun print-graph (numbers-list)
"documentation..."
(let ((height ...
...))
(print-Y-axis height ... )
(graph-body-print numbers-list)
(print-X-axis ... )))
The final version is different from what we planned in two ways: first, it contains additional values calculated once in the varlist; second, it carries an option to specify the labels' increment per row. This latter feature turns out to be essential; otherwise a graph may have more rows than fit on a display or on a sheet of paper.
This new feature requires a change to the Y-axis-column
function, to add vertical-step to it. The function looks like
this:
;;; Final version.
(defun Y-axis-column
(height width-of-label &optional vertical-step)
"Construct list of labels for Y axis.
HEIGHT is maximum height of graph.
WIDTH-OF-LABEL is maximum width of label.
VERTICAL-STEP, an option, is a positive integer
that specifies how much a Y axis label increments
for each line. For example, a step of 5 means
that each line is five units of the graph."
(let (Y-axis
(number-per-line (or vertical-step 1)))
(while (> height 1)
(if (zerop (% height Y-axis-label-spacing))
;; Insert label.
(setq Y-axis
(cons
(Y-axis-element
(* height number-per-line)
width-of-label)
Y-axis))
;; Else, insert blanks.
(setq Y-axis
(cons
(make-string width-of-label ? )
Y-axis)))
(setq height (1- height)))
;; Insert base line.
(setq Y-axis (cons (Y-axis-element
(or vertical-step 1)
width-of-label)
Y-axis))
(nreverse Y-axis)))
The values for the maximum height of graph and the width of a symbol
are computed by print-graph in its let expression; so
graph-body-print must be changed to accept them.
;;; Final version.
(defun graph-body-print (numbers-list height symbol-width)
"Print a bar graph of the NUMBERS-LIST.
The numbers-list consists of the Y-axis values.
HEIGHT is maximum height of graph.
SYMBOL-WIDTH is number of each column."
(let (from-position)
(while numbers-list
(setq from-position (point))
(insert-rectangle
(column-of-graph height (car numbers-list)))
(goto-char from-position)
(forward-char symbol-width)
;; Draw graph column by column.
(sit-for 0)
(setq numbers-list (cdr numbers-list)))
;; Place point for X axis labels.
(forward-line height)
(insert "\n")))
Finally, the code for the print-graph function:
;;; Final version.
(defun print-graph
(numbers-list &optional vertical-step)
"Print labelled bar graph of the NUMBERS-LIST.
The numbers-list consists of the Y-axis values.
Optionally, VERTICAL-STEP, a positive integer,
specifies how much a Y axis label increments for
each line. For example, a step of 5 means that
each row is five units."
(let* ((symbol-width (length graph-blank))
;; height is both the largest number
;; and the number with the most digits.
(height (apply 'max numbers-list))
(height-of-top-line
(if (zerop (% height Y-axis-label-spacing))
height
;; else
(* (1+ (/ height Y-axis-label-spacing))
Y-axis-label-spacing)))
(vertical-step (or vertical-step 1))
(full-Y-label-width
(length
(concat
(int-to-string
(* height-of-top-line vertical-step))
Y-axis-tic))))
(print-Y-axis
height-of-top-line full-Y-label-width vertical-step)
(graph-body-print
numbers-list height-of-top-line symbol-width)
(print-X-axis numbers-list)))
print-graph
We can test the print-graph function with a short list of numbers
Y-axis-column,
graph-body-print, and print-graph (in addition to the
rest of the code.)
(print-graph '(3 2 5 6 7 5 3 4 6 4 3 2 1))
eval-expression).
yank).
Emacs will print a graph that looks like this:
10 -
*
** *
5 - **** *
**** ***
* *********
************
1 - *************
| | | |
1 5 10 15
On the other hand, if you pass print-graph a
vertical-step value of 2, by evaluating this expression:
(print-graph '(3 2 5 6 7 5 3 4 6 4 3 2 1) 2)
The graph looks like this:
20 -
*
** *
10 - **** *
**** ***
* *********
************
2 - *************
| | | |
1 5 10 15
(A question: is the `2' on the bottom of the vertical axis a bug or a feature? If you think it is a bug, and should be a `1' instead, (or even a `0'), you can modify the sources.)
Now for the graph for which all this code was written: a graph that shows how many function definitions contain fewer than 10 words and symbols, how many contain between 10 and 19 words and symbols, how many contain between 20 and 29 words and symbols, and so on.
This is a multi-step process. First make sure you have loaded all the requisit code.
It is a good idea to reset the value of top-of-ranges in case
you have sent it to some different value. You can evaluate the
following:
(setq top-of-ranges '(10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300)
Next create a list of the number of words and symbols in each range.
Evaluate the following:
(setq list-for-graph
(defuns-per-range
(sort
(recursive-lengths-list-many-files
(directory-files "/usr/local/emacs/lisp"
t ".+el$"))
'<)
top-of-ranges))
On my machine, this takes about an hour. It looks though 303 Lisp
files in my copy of Emacs version 19.23. After all that computing,
the list-for-graph has this value:
(537 1027 955 785 594 483 349 292 224 199 166 120 116 99 90 80 67 48 52 45 41 33 28 26 25 20 12 28 11 13 220)
This means that my copy of Emacs has 537 function definitions with fewer than 10 words or symbols in them, 1,027 function definitions with 10 to 19 words or symbols in them, 955 function definitions with 20 to 29 words or symbols in them, and so on.
Clearly, just by looking at this list we can see that most function definitions contain ten to thirty words and symbols.
Now for printing. We do not want to print a graph that is 1,030 lines high ... Instead, we should print a graph that is fewer than twenty-five lines high. A graph that height can be displayed on almost any monitor, and easily printed on a sheet of paper.
This means that each value in list-for-graph must be reduced to
one-fiftieth it present value.
Here is a short function to do just that, using two functions we have
not yet seen, mapcar and lambda.
(defun one-fiftieth (full-range) "Return list, each number one-fiftieth of previous." (mapcar '(lambda (arg) (/ arg 50)) full-range))
lambda Expression
lambda is the symbol for an anonymous function, a function
without a name. Every time you use an anonymous function, you need to
include its whole body.
Thus,
(lambda (arg) (/ arg 50))
is a function definition that says `return the value resulting from
dividing whatever is passed to me as arg by 50'.
Earlier, for example, we had a function multiply-by-seven; it
multiplied its argument by 7. This function is similar, except it
divides its argument by 50; and, it has no name. The anonymous
equivalent of multiply-by-seven is:
(lambda (number) (* 7 number))
(See section The defun Special Form.)
If we want to multiply 3 by 7, we can write:
(multiply-by-seven 3)
\_______________/ ^
| |
function argument
This expression returns 21.
Similarly, we can write:
((lambda (number) (* 7 number)) 3)
\____________________________/ ^
| |
anonymous function argument
If we want to divide 100 by 50, we can write:
((lambda (arg) (/ arg 50)) 100)
\______________________/ \_/
| |
anonymous function argument
This expression returns 2. The 100 is passed to the function, which divides that number by 50.
See section `Lambda Expressions' in The GNU Emacs Lisp Reference Manual, for more about lambda. Lisp and lambda
expressions derive from the Lambda Calculus.
mapcar Function
mapcar is a function that calls its first argument with each
element of its second argument, in turn. The second argument must be
a sequence.
For example,
(mapcar '1+ '(2 4 6))
=> (3 5 7)
The function 1+ which adds one to its argument, is executed on
each element of the list, and a new list is returned.
Contrast this with apply, which applies its first argument to
all the remaining.
(See section Readying a Graph, for a explanation of
apply.)
In the definition of one-fiftieth, the first argument is the
anonymous function:
(lambda (arg) (/ arg 50))
and the second argument is full-range, which will be bound to
list-for-graph.
The whole expression looks like this:
(mapcar '(lambda (arg) (/ arg 50)) full-range))
See section `Mapping Functions' in The GNU Emacs Lisp Reference Manual, for more about mapcar.
Using the one-fiftieth function, we can generate a list in
which each element is one-fiftieth the size of the corresponding
element in list-for-graph.
(setq fiftieth-list-for-graph
(one-fiftieth list-for-graph))
The resulting list looks like this:
(10 20 19 15 11 9 6 5 4 3 3 2 2 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 4)
This we are almost ready to print! (We also notice the loss of information: many of the higher ranges are 0, meaning that fewer than 50 defuns had that many words or symbols--but not necessarily meaning that none had that many words or symbols.)
I said `almost ready to print'! Of course, there is a bug in the
print-graph function ... It has a vertical-step
option, but not a horizontal-step option. The
top-of-range scale goes from 10 to 300 by tens. But the
print-graph function will print only by ones.
This is a classic example of what some consider the most insidious type of bug, the bug of omission. This is not the kind of bug you can find by studying the code, for it is not in the code; it is an omitted feature. Your best actions are to try your program early and often; and try to arrange, as much as you can, to write code that is easy to understand and easy to change. Try to be aware, whenever you can, that whatever you have written, will be rewritten, if not soon, eventually. A hard maxim to follow.
It is the print-X-axis-numbered-line function that needs the
work; and then the print-X-axis and the print-graph
functions need to be adapted. Not much needs to be done; there is one
nicety: the numbers ought to line up under the tic marks. This takes
a little thought.
Here is the corrected print-X-axis-numbered-line:
(defun print-X-axis-numbered-line
(number-of-X-tics X-axis-leading-spaces
&optional horizontal-step)
"Print line of X-axis numbers"
(let ((number X-axis-label-spacing)
(horizontal-step (or horizontal-step 1)))
(insert X-axis-leading-spaces)
;; Delete extra leading spaces.
(delete-char
(- (1-
(length (int-to-string horizontal-step)))))
(insert (concat
(make-string
;; Insert white space.
(- (* symbol-width
X-axis-label-spacing)
(1-
(length
(int-to-string horizontal-step)))
2)
? )
(int-to-string
(* number horizontal-step))))
;; Insert remaining numbers.
(setq number (+ number X-axis-label-spacing))
(while (> number-of-X-tics 1)
(insert (X-axis-element
(* number horizontal-step)))
(setq number (+ number X-axis-label-spacing))
(setq number-of-X-tics (1- number-of-X-tics)))))
If you are reading this in Info, you can see the new versions of
print-X-axis print-graph and evaluate them. If you are
reading this in a printed book, you can see the changed lines here
(the full text is too much to print).
(defun print-X-axis (numbers-list horizontal-step)
...
(print-X-axis-numbered-line
tic-number leading-spaces horizontal-step))
(defun print-graph
(numbers-list
&optional vertical-step horizontal-step)
...
(print-X-axis numbers-list horizontal-step))
When made and installed, you can call the print-graph command
like this:
(print-graph fiftieth-list-for-graph 50 10)
Here is the graph:
1000 - *
**
**
**
**
750 - ***
***
***
***
****
500 - *****
******
******
******
*******
250 - ********
********* *
*********** *
************* *
50 - ***************** * *
| | | | | | | |
10 50 100 150 200 250 300 350
The largest group of functions contain 10 -- 19 words and symbols each.