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." $Header: ch9.n 1.4 83/07/21 21:08:57 sklower Exp $
.Lc Arrays\ and\ Vectors 9
.pp
Arrays and vectors are two means of expressing aggregate
data objects in
.Fr .
Vectors may be thought of as sequences of data.
They are intended as a vehicle for user-defined
data types.
This use of vectors is still experimental and subject
to revision.
As a simple data structure, they are similar to
hunks and strings.
Vectors are used to implement closures,
and are useful to communicate with foreign functions.
Both of these topics were discussed in Chapter 8.
Later in this chapter,
we describe the current implementation of vectors, and will
advise the user what is most likely to change.
.pp
Arrays in 
.Fr
provide a programmable data structure access mechanism.
One possible use for 
.Fr
arrays is to implement Maclisp style arrays which are simple vectors
of fixnums, flonums or general lisp values.
This is described in more detail in \(sc9.3 but first
we will describe how array references are handled by
the lisp system.
.pp
The structure of an array object is given in \(sc1.3.10 and reproduced here
for your convenience.
.sp 1v
.TS
box center ;
c | c | c | c .
Subpart name	Get value	Set value	Type

=
access function	getaccess	putaccess	binary, list
			or symbol
_
auxiliary	getaux	putaux	lispval
_
data	arrayref	replace	block of contiguous
		set	lispval
_
length	getlength	putlength	fixnum
_
delta	getdelta	putdelta	fixnum
.TE
.sh 2 "general arrays" \n(ch 1
Suppose the evaluator is told to evaluate \fI(foo\ a\ b)\fP
and the function cell of the symbol foo contains an array object
(which we will call foo_arr_obj).
First the evaluator will evaluate and stack the values of 
.i a 
and 
.i b .
Next it will stack the array object foo_arr_obj.
Finally it will call the access function of foo_arr_obj.
The access function should be a lexpr\*[\(dg\*]
or a symbol whose 
function cell contains a lexpr.
.(f
\*[\(dg\*]A lexpr is a function which accepts any number of arguments
which are evaluated before the function is called.
.)f
The access function is responsible for locating and returning 
a value from the array.
The array access function is free to interpret the arguments as it wishes.
The Maclisp compatible array access function which is provided 
in the standard
.Fr
system interprets the arguments as subscripts in the same way as 
languages like Fortran and Pascal.
.pp
The array access function will also be called upon to store elements in 
the array.
For example, \fI(store\ (foo\ a\ b)\ c)\fP
will automatically expand to (foo c a b) and when the evaluator is called
to evaluate this, it will evaluate the arguments 
.i c , 
.i b 
and
.i a .
Then it will
stack the array object (which is stored 
in the function cell of foo) and call the array access function
with (now) four arguments.
The array access function must be able to tell this is a store operation,
which it can do by checking the number of arguments it has been
given (a lexpr can do this very easily).
.sh 2 "subparts of an array object"
An array is created by allocating an
array object with
.i marray
and  filling in the fields.
Certain lisp functions interpret the values of the subparts 
of the array object in special
ways as described in the following text.
Placing illegal values in these subparts may cause
the lisp system to fail.
.sh 3 "access function"
The purpose of the access function has been described above.
The contents of the access function should be a lexpr, 
either a binary (compiled function) or a list (interpreted function).
It may also be a symbol whose function cell contains a function 
definition.
This subpart 
is used by 
.i eval , 
.i funcall , 
and 
.i apply
when evaluating array references.
.sh 3 auxiliary
This can be used for any purpose. If it is a list and the first element
of that list is the symbol unmarked_array then the data subpart will
not be marked by the garbage collector (this is used in the Maclisp
compatible array package and has the potential for causing strange errors
if used incorrectly).
.sh 3 data
This is either nil or points to a block of data space allocated by 
.i segment 
or 
.i small-segment.
.sh 3 length
This is a fixnum whose value is the number of elements in the
data block.  This is used by the garbage collector and by 
.i arrayref
to determine if your index is in bounds.
.sh 3 delta
This is a fixnum whose value is the number of bytes in each element of 
the data block.
This will be four for an array of fixnums or value cells, and eight
for an array of flonums.
This is used by the garbage collector and 
.i arrayref
as well.
.sh 2 "The Maclisp compatible array package"
.pp
A Maclisp style array is similar to what is known as arrays in other
languages: a block of homogeneous data elements which
is indexed by one or more integers called subscripts.
The data elements can be all fixnums, flonums or general lisp objects.
An array is created by a call to the function 
.i array 
or \fI*array\fP.
The only difference is that 
.i *array
evaluates its arguments.
This call: 
.i "(array foo t 3 5)"
sets up an array called foo of dimensions 3 by 5.
The subscripts are zero based. 
The first element is \fI(foo\ 0\ 0)\fP, the next is \fI(foo\ 0\ 1)\fP
and so on up to \fI(foo\ 2\ 4)\fP.
The t indicates a general lisp object array which means each element of
foo can be any type.
Each element can be any type since all that is stored in the array is
a pointer to a lisp object, not the object itself.
.i Array 
does this by allocating an array object
with
.i marray
and then allocating a segment of 15 consecutive value cells with
.i small-segment
and storing a pointer to that segment in the data subpart of the array
object.
The length and delta subpart of the array object are filled in (with 15
and 4 respectively) and the access function subpart is set to point to 
the appropriate  array access function.
In this case there is a special access function for two dimensional
value cell arrays called arrac-twoD, and this access function is used.
The auxiliary subpart is set to (t\ 3\ 5) which describes the type of array
and the bounds of the subscripts.  
Finally this array object is placed in the function cell of the symbol foo.
Now when 
.i "(foo 1 3)"
is evaluated, the array access function is invoked with three arguments:
1, 3 and the array object.  From the auxiliary field of the
array object it gets a description of the particular array.
It then determines which element \fI(foo\ 1\ 3)\fP refers to  and 
uses arrayref to extract that element.
Since this is an array of value cells, what arrayref returns is a
value cell whose value is what we want, so we evaluate the value cell
and return it as the value of \fI(foo\ 1\ 3)\fP.
.pp
In Maclisp the call \fI(array\ foo\ fixnum\ 25)\fP
returns an array whose data object is a block of 25 memory words.
When fixnums are stored in this array, the actual numbers are 
stored instead of pointers to the numbers as is done in general lisp
object arrays.
This is efficient under Maclisp but inefficient in
.Fr
since every time a value was referenced from an array it had to be copied
and a pointer to the copy returned to prevent aliasing\*[\(dg\*].
.(f
\*[\(dg\*]Aliasing is when two variables are share the same storage location.
For example if the copying mentioned weren't done then after 
\fI(setq\ x\ (foo\ 2))\fP was done, the value of x and 
(foo\ 2) would share the same 
location.
Then should the value of (foo\ 2) change, x's value would change as well.
This is considered dangerous and as a result pointers are never returned
into the data space of arrays.
.)f
Thus t, fixnum and flonum arrays are all implemented in the same 
manner.
This should not affect the compatibility of Maclisp
and 
.Fr .
If there is an application where a block of fixnums or flonums is required,
then the exact same effect of fixnum and flonum arrays in Maclisp
can be achieved by using fixnum-block and flonum-block arrays.
Such arrays are required if you want to pass a large number of arguments to a 
Fortran or C coded function and then get answers back.
.pp
The Maclisp compatible array package is 
just one example of how a general array scheme can be implemented.
Another type of array you could implement would be hashed arrays.
The subscript could be anything, not just a number.
The access function would hash the subscript and use the result to
select an array element.
With the generality of arrays also comes extra cost; if you just
want a simple aggregate of (less than 128) general lisp objects
you would be wise to look into using hunks.
.sh 2 vectors
Vectors were invented to fix two shortcommings with hunks.
They can be longer than 128 elements.  They also have a
tag associated with them, which is intended to say, for example,
"Think of me as an \fIBlobit\fP."  Thus a \fBvector\fP
is an arbitrary sized hunk with a property list.
.pp
Continuing the example,
the lisp kernel may not know how to print out
or evaluate \fIblobits\fP, but this is information which will
be common to all \fIblobits\fP.  On the other hand, for each
individual blobits there are particulars which are likely to change,
(height, weight, eye-color).  This is the part that would
previously have been stored in the individual entries in the hunk,
and are stored in the data slots of the vector.
Once again we summarize the structure of a vector in tabular form:
.sp 1v
.TS
box center ;
c | c | c | c .
Subpart name	Get value	Set value	Type

=
datum[\fIi\fP]	vref	vset	lispval
_
property	vprop	vsetprop	lispval
		vputprop
_
size	vsize	\-	fixnum
.TE
Vectors are created specifying size and optional fill value using the
function (\fInew-vector\fP  'x_size ['g_fill ['g_prop]]), or by
initial values: (\fIvector\fP ['g_val ...]).
.sh 2 "anatomy of vectors"
There are some technical details about vectors, that the user should
know:
.sh 3 size
The user is not free to alter this.  It is noted when the vector
is created, and is used by the garbage collector.  The garbage
collector will coallesce two free vectors, which are neighbors
in the heap.  Internally, this is kept as the number of bytes
of data.  Thus, a vector created by (\fIvector\fP 'foo), has a
size of 4.
.sh 3 property
Currently, we expect the property to be either a symbol, or a list
whose first entry is a symbol.  The symbols \fBfclosure\fP and
\fBstructure-value-argument\fP are magic, and their effect is described in
Chapter 8.  If the property is a (non-null) symbol, the vector
will be printed out as <symbol>[<size>].  
Another case is if the property is actually a (disembodied) property-list, which
contains a value for the indicator \fBprint\fP.
The value is taken to be a Lisp function, which the printer
will invoke with two arguments:  the vector and the current output port.
Otherwise, the vector will be printed as vector[<size>].
We have vague (as yet unimplemented) ideas
about similar mechanisms for evaluation properties.
Users are cautioned against putting anything other than nil
in the property entry of a vector.
.sh 3 "internal order"
In memory, vectors start with a longword containing the size
(which is immediate data within the vector).
The next cell contains a pointer to the property.
Any remaining cells (if any) are for data.
Vectors are handled differently from any other object in
.Fr,
in that a pointer to a vector is pointer to the first data
cell, i.e. a pointer to the \fIthird\fP longword of the structure.
This was done for efficiency in compiled code and for uniformity
in referencing immediate-vectors (described below).
The user should never return a pointer to any other part
of a vector, as this may cause the garbage collector to follow an
invalid pointer.
.sh 2 "immediate-vectors"
Immediate-vectors are similar to vectors.  They differ, in
that binary data are stored in space directly within the vector.
Thus the garbage collector will preserve the vector itself (if used),
and will only traverse the property cell.
The data may be referenced as longwords, shortwords, or even bytes.
Shorts and bytes are returned sign-extended.
The compiler open-codes such references,
and will avoid boxing the resulting integer data, where possible.
Thus, immediate vectors may be used for efficiently processing
character data.
They are also useful in storing results from functions written
in other languages.
.sp 1v
.TS
box center ;
c | c | c | c .
Subpart name	Get value	Set value	Type

=
datum[\fIi\fP]	vrefi-byte	vseti-byte	fixnum
	vrefi-word	vseti-word	fixnum
	vrefi-long	vseti-long	fixnum
_
property	vprop	vsetprop	lispval
		vputprop
_
size	vsize	\-	fixnum
	vsize-byte		fixnum
	vsize-word		fixnum
.TE
To create immediate vectors specifying size and fill data,
you can use the functions
\fInew-vectori-byte\fP,
\fInew-vectori-word\fP,
or \fInew-vectori-long\fP.
You can also use the functions
\fIvectori-byte\fP,
\fIvectori-word\fP,
or \fIvectori-long\fP.
All of these functions are described in
chapter 2.