by Marc Feeley
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This SRFI describes a set of datatypes for vectors whose elements are
of the same numeric type (signed or unsigned exact integer or inexact
real of a given precision). These datatypes support operations
analogous to the Scheme vector type, but they are distinct datatypes.
An external representation is specified which must be supported by the
read
and write
procedures and by the program
parser (i.e. programs can contain references to literal homogeneous
vectors).
Like lists, Scheme vectors are a heterogeneous datatype which impose no restriction on the type of the elements. This generality is not needed for applications where all the elements are of the same type. The use of Scheme vectors is not ideal for such applications because, in the absence of a compiler with a fancy static analysis, the representation will typically use some form of boxing of the elements which means low space efficiency and slower access to the elements. Moreover, homogeneous vectors are convenient for interfacing with low-level libraries (e.g. binary block I/O) and to interface with foreign languages which support homogeneous vectors. Finally, the use of homogeneous vectors allows certain errors to be caught earlier.
This SRFI specifies a set of homogeneous vector datatypes which cover the most practical case, that is where the type of the elements is numeric (exact integer or inexact real) and the precision and representation is efficiently implemented on the hardware of most current computer architectures (8, 16, 32 and 64 bit integers, either signed or unsigned, and 32 and 64 bit floating point numbers).
There are 8 datatypes of exact integer homogeneous vectors (which will be called integer vectors):
datatype | type of elements | |
s8vector | signed exact integer in the range -(2^7) to (2^7)-1 | |
u8vector | unsigned exact integer in the range 0 to (2^8)-1 | |
s16vector | signed exact integer in the range -(2^15) to (2^15)-1 | |
u16vector | unsigned exact integer in the range 0 to (2^16)-1 | |
s32vector | signed exact integer in the range -(2^31) to (2^31)-1 | |
u32vector | unsigned exact integer in the range 0 to (2^32)-1 | |
s64vector | signed exact integer in the range -(2^63) to (2^63)-1 | |
u64vector | unsigned exact integer in the range 0 to (2^64)-1 |
There are 2 datatypes of inexact real homogeneous vectors (which will be called float vectors):
datatype | type of elements | |
f32vector | inexact real | |
f64vector | inexact real |
The only difference between the two float vector types is that
f64vector
s preserve at least as much precision as
f32vector
s (see the implementation section for details).
A Scheme system that conforms to this SRFI does not have to support
all of these homogeneous vector datatypes. However, a Scheme system
must support f32vector
s and f64vector
s if it
supports Scheme inexact reals (of any precision). A Scheme system
must support a particular integer vector datatype if the system's
exact integer datatype contains all the values that can be stored in
such an integer vector. Thus a Scheme system with bignum support must
implement all the integer vector datatypes and a Scheme system may
only support s8vector
s, u8vector
s,
s16vector
s and u16vector
s if it only
supports small integers in the range -(2^29) to (2^29)-1 (which would
be the case if they are represented as 32 bit fixnums with two bits
for tag). Note that it is possible to test which numeric datatypes
the Scheme system supports by calling the
string->number
procedure (e.g.
(string->number "0.0")
returns #f
if the
Scheme system does not support inexact reals).
Each homogeneous vector datatype has an external representation which
is supported by the read
and write
procedures and by the program parser. Each datatype also has a set of
associated predefined procedures analogous to those available for
Scheme's heterogeneous vectors.
For each value of TAG
in {
s8
, u8
,
s16
, u16
,
s32
, u32
,
s64
, u64
,
f32
, f64
}, if the datatype TAGvector
is supported, then
the external representation of instances of the datatype
TAGvector
is #TAG(
...elements... )
.
For example, #u8(0 #e1e2 #xff)
is an
u8vector
of length 3 containing 0, 100 and 255;
#f64(-1.5)
is an f64vector
of length 1
containing -1.5.
Note that the syntax for float vectors conflicts with Standard Scheme
which parses #f32()
as 3 objects: #f
,
32
and ()
. For this reason, conformance to
this SRFI implies this minor nonconformance to Standard Scheme.
This external representation is also available in program source code.
For example, (set! x '#u8(1 2 3))
will set x
to the object #u8(1 2 3)
. Literal homogeneous vectors
must be quoted just like heterogeneous vectors must be. Homogeneous
vectors can appear in quasiquotations but must not contain
unquote
or unquote-splicing
forms
(i.e. `(,x #u8(1 2))
is legal but `#u8(1 ,x
2)
is not). This restriction is to accommodate the many Scheme
systems that use the read
procedure to parse programs.
the following predefined procedures are available:
(TAGvector? obj)
(make-TAGvector n [ TAGvalue ])
(TAGvector TAGvalue...)
(TAGvector-length TAGvect)
(TAGvector-ref TAGvect i)
(TAGvector-set! TAGvect i TAGvalue)
(TAGvector->list TAGvect)
(list->TAGvector TAGlist)
where obj
is any Scheme object, n
is a
nonnegative exact integer, i
is a nonnegative exact
integer less than the length of the vector, TAGvect
is an
instance of the TAGvector
datatype, TAGvalue
is a number of the type acceptable for elements of the
TAGvector
datatype, and TAGlist
is a proper
list of numbers of the type acceptable for elements of the
TAGvector
datatype.
It is an error if TAGvalue
is not the same type as the
elements of the TAGvector
datatype (for example if an
exact integer is passed to f64vector
). If the fill
value is not specified, the content of the vector is unspecified
but individual elements of the vector are guaranteed to be in the
range of values permitted for that type of vector.
The homogeneous vector datatypes described here suggest a concrete
implementation as a sequence of 8, 16, 32 or 64 bit elements, using
two's complement representation for the signed exact integers, and
single and double precision IEEE-754 floating point representation for
the inexact reals. Although this is a practical implementation on
many modern byte-addressed machines, a different implementation is
possible for machines which don't support these concrete numeric types
(the CRAY-T90 for example does not have a 32 bit floating point
representation and the 64 bit floating point representation does not
conform to IEEE-754, so both the f32vector
and
f64vector
datatypes could be represented the same way
with 64 bit floating point numbers).
A portable implementation of the homogeneous vector predefined
procedures can be based on Scheme's heterogeneous vectors.
Here is for example an implementation of s8vector
s
which is exempt of error checking:
(define s8vector? #f) (define make-s8vector #f) (define s8vector #f) (define s8vector-length #f) (define s8vector-ref #f) (define s8vector-set! #f) (define s8vector->list #f) (define list->s8vector #f) (let ((orig-vector? vector?) (orig-make-vector make-vector) (orig-vector vector) (orig-vector-length vector-length) (orig-vector-ref vector-ref) (orig-vector-set! vector-set!) (orig-vector->list vector->list) (orig-list->vector list->vector) (orig-> >) (orig-eq? eq?) (orig-+ +) (orig-null? null?) (orig-cons cons) (orig-car car) (orig-cdr cdr) (orig-not not) (tag (list 's8))) (set! s8vector? (lambda (obj) (and (orig-vector? obj) (orig-> (orig-vector-length obj) 0) (orig-eq? (orig-vector-ref obj 0) tag)))) (set! make-s8vector (lambda (n . opt-fill) (let ((v (orig-make-vector (orig-+ n 1) (if (orig-null? opt-fill) 123 (orig-car opt-fill))))) (orig-vector-set! v 0 tag) v))) (set! s8vector (lambda s8list (orig-list->vector (orig-cons tag s8list)))) (set! s8vector-length (lambda (s8vect) (orig-+ (orig-vector-length s8vect) -1))) (set! s8vector-ref (lambda (s8vect i) (orig-vector-ref s8vect (orig-+ i 1)))) (set! s8vector-set! (lambda (s8vect i s8value) (orig-vector-set! s8vect (orig-+ i 1) s8value))) (set! s8vector->list (lambda (s8vect) (orig-cdr (orig-vector->list s8vect)))) (set! list->s8vector (lambda (s8list) (orig-list->vector (orig-cons tag s8list)))) (set! vector? (lambda (obj) (and (orig-vector? obj) (orig-not (and (orig-> (orig-vector-length obj) 0) (orig-eq? (orig-vector-ref obj 0) tag)))))))
The Scheme system's read
and write
procedures and the program parser also need to be extended to handle
the homogeneous vector external representations. The implementation
is very similar to heterogeneous vectors except that read
and the program parser must recognize the prefixes #s8
,
#f32
, etc. (this can be done by checking if the sharp
sign is followed by a character that can start a symbol, and if this
is the case, parse a symbol and check if it is t
,
f
, s8
, f32
, and so on, and in
the case of a homogeneous vector prefix, check if the next character
is an opening parenthesis).
Copyright (C) Marc Feeley (1999). All Rights Reserved.
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