SRFI 4: Homogeneous numeric vector datatypes

# Title

SRFI-4: Homogeneous numeric vector datatypes

# Author

Marc Feeley

# Status

This SRFI is currently in ``final'' status. To see an explanation of each status that a SRFI can hold, see here. You can access previous messages via the archive of the mailing list.

- Received: 1998/1/11
- Draft: 1999/1/19-1999/03/19
- Revised: 1999/04/26
- Final: 1999/5/22

# Abstract

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).

# Rationale

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).

# Specification

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

1. 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.

2. the following predefined procedures are available:
   1. `(TAGvector? obj)`
   2. `(make-TAGvector n [ TAGvalue ])`
   3. `(TAGvector TAGvalue...)`
   4. `(TAGvector-length TAGvect)`
   5. `(TAGvector-ref TAGvect i)`
   6. `(TAGvector-set! TAGvect i TAGvalue)`
   7. `(TAGvector->list TAGvect)`
   8. `(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.

# Implementation

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

Copyright (C) Marc Feeley (1999). All Rights Reserved.

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

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