wiki:NumericVectorsCowan

This SRFI provides an API for specialized numeric vectors distinguished by their representation type. The u8 type is the same as the R7RS bytevector type, but the other types are all disjoint from all other Scheme types. It may be useful for Schemes on the JVM or the CLR to use this SRFI to provide access to the platform's native numeric vectors.

This design subsumes SRFI 4. There are many procedures, but many of them can be easily inlined by even a very dumb compiler, providing high efficiency. The procedures provided in the present proposal are the numeric-vector analogues of the R7RS-small vector API plus SRFI 133.

Representation types

The [type] values are:

u1
unsigned 1-bit integer (bit)
u8
unsigned 8-bit integer
s8
signed 8-bit integer
u16
unsigned 16-bit integer
s16
signed 16-bit integer
u32
unsigned 32-bit integer
s32
signed 32-bit integer
u64
unsigned 64-bit integer
s64
signed 64-bit integer
f32
32-bit float
f64
64-bit float
c64
64-bit complex number
c128
128-bit complex number

Constructors

(make-[type]vector k [ fill ])

Returns a newly allocated numeric vector of length k. Fill is converted to a binary value according to [type] and used to fill the vector; if fill is not specified, the values of the elements are unspecified. It is an error if fill cannot be converted to [type].

([type]vector v ... )

Returns a newly allocated numeric vector of length k, where k is the number of arguments to the procedure. It is filled with the binary values resulting from encoding the v arguments according to [type]. It is an error if an argument cannot be converted to [type].

([type]vector-unfold proc length initial-seed)

Returns a newly allocated [type]vector whose length is length and iterates across each index k between 0 and length, applying proc at each iteration to the current index and current seed, in that order, to receive 2 values: first, the element to put in the kth slot of the new vector and a new seed for the next iteration. Note that the termination condition is different from the unfold procedure of SRFI 1.

Examples:

(s8vector-unfold (lambda (i x) (values x (- x 1))) 
                 10 0) 
=> #s8(0 -1 -2 -3 -4 -5 -6 -7 -8 -9)

Construct a vector of the sequence of integers in the range [0,n).

(u8vector-unfold values n) 
=> #u8(0 1 2 ... n-2 n-1)

Copy vector.

(f64vector-unfold (lambda (i) (vector-ref vector i)) 
                 (vector-length vector))

([type]vector-unfold-right proc length initial-seed)

Like [type]vector-unfold, but it uses proc to generate elements from right-to-left, rather than left-to-right. The first index used is length - 1. Note that the termination condition is different from the unfold-right procedure of SRFI 1.

Examples:

Construct a vector of pairs of non-negative integers whose values sum to 4.

(u8vector-unfold-right (lambda (i x) (values (cons i x) (+ x 1))) 5 0) 
=> #u8((0 . 4) (1 . 3) (2 . 2) (3 . 1) (4 . 0)) 

Reverse vector.

(float64-vector-unfold-right (lambda (i x) (values (f64vector-ref vector x) (+ x 1))) 
                       (f64vector-length vector) 
                       0)

([type]vector-copy [type]vec [start [end]])

Allocates a new [type]vector whose length is end - start and fills it with elements from [type]vec. Examples:

([type]vector-reverse-copy [type]vec [start [end]])

Like [type]vector-copy, but it copies the elements in the reverse order from [type]vec.

([type]vector-append [type]vec ...)

Returns a newly allocated vector that contains all elements in order from the locations in the [type]vecs.

([type]vector-concatenate list-of-[type]vectors)

Appends each vector in list-of-[type]vectors. This is equivalent to: (apply [type]vector-append list-of-[type]vectors). However, it may be implemented better.

([type]vector-append-subvectors [ [type]vec start end ] ...)

Returns a vector that contains every element of each [type]vec from start to end in the specified order. This procedure is a generalization of vector-append.

Predicates

([type]vector? obj)

Returns #t if obj is a [type]vector, and #f if it is not.

([type]vector-empty? [type]vector)

Returns #t if [type]vector has length 0, and #f otherwise.

(vector= elt=? [type]vec ...)

Vector structure comparator, generalized across user-specified element comparators. [Type]vectors a and b are considered equal by [type]vector= iff their lengths are the same, and if for each respective element Ea and Eb, (elt=? Ea Eb) returns a true value. The elt= procedure is always applied to two arguments. Element comparison must be consistent with eq; that is, if (eq? Ea Eb) results in a true value, then (elt=? Ea Eb) must also result in a true value. This may be exploited to avoid unnecessary element comparisons.

If there are only zero or one [type]vector arguments, #t is automatically returned. The dynamic order in which comparisons of elements and of [type]vectors are performed is left completely unspecified; do not rely on a particular order.

Selectors

([type]vector-ref [type]vector k)

Returns a Scheme number corresponding to the kth element of [type]vector. Note that u8vector-ref is the same as the R7RS-small procedure bytevector-u8-ref.

([type]vector-length [type]vector)

Returns the length of [type]vector.

Iteration

([type]vector-fold kons knil vec1 vec2 ...)

The fundamental [type]vector iterator. Kons is iterated over each value in all of the [type]vectors, stopping at the end of the shortest; kons is applied as (''kons state'' (''[type]vector-ref vec,,1,, i'') (''[type]vector-ref vec,,2,, i'') ...)` where state is the current state value — the current state begins with knil, and becomes whatever kons returned on the previous iteration — and i is the current index.

The iteration is strictly left-to-right.

([type]vector-fold kons knil [type]vec1 [type]vec2 ...)

Similar to [type]vector-fold, but it iterates right to left instead of left to right.

([type]vector-map proc [type]vector ...)

Returns a newly allocated [type]vector which contains the results of applying proc to the elements of the [type]vectors in an unspecified order.

([type]vector-map! proc output-[type]vector [type]vector ...)

Writes the results of applying proc to the elements of the [type]vectors into the corresponding elements of output-[type]vector in an unspecified order. It is not an error for output-[type]vector to be the same as one of the [type]vectors. Returns an unspecified value.

([type]vector-for-each proc [type]vector ...)

Applies proc to the elements of the [type]vectors in order from first to last and discards the results. Returns an unspecified value.

([type]vector-count pred? vec1 vec2 ...)

Counts the number of parallel elements in the [type]vectors that satisfy pred?, which is applied, for each index i in the range [0, length) where length is the length of the smallest vector argument, to each parallel element in the [type]vectors, in order.

([type]vector-cumulate f vec knil)

Returns a newly allocated [type]vector new with the same length as [type]vec. Each element i of new is set to the result of invoking f on newi-1 and veci. However, for the first call on f, the first argument is knil. The new [type]vector is returned.

Searching

FIXME: markup

(vector-index pred? vec1 vec2 ...)

Finds & returns the index of the first elements in vec1 vec2 ... that satisfy pred?. If no matching element is found by the end of the shortest vector, #f is returned.

(vector-index-right pred? vec1 vec2 ...)

Like vector-index, but it searches right-to-left, rather than left-to-right, and all of the vectors must have the same length.

(vector-skip pred? vec1 vec2 ...)

Finds & returns the index of the first elements in vec1 vec2 ... that do not satisfy pred?. If all the values in the vectors satisfy pred? until the end of the shortest vector, this returns #f.

(vector-skip-right pred? vec1 vec2 ...)

Like vector-skip, but it searches for a non-matching element right-to-left, rather than left-to-right, and it is an error if all of the vectors do not have the same length.

(vector-binary-search vec value cmp)

Similar to vector-index and vector-index-right, but instead of searching left to right or right to left, this performs a binary search. If there is more than one element of vec that matches value in the sense of cmp, vector-binary-search may return the index of any of them.

cmp should be a procedure of two arguments and return a negative integer, which indicates that its first argument is less than its second, zero, which indicates that they are equal, or a positive integer, which indicates that the first argument is greater than the second argument.

(vector-any pred? vec1 vec2 ...)

Finds the first set of elements in parallel from vec1 vec2 ... for which pred? returns a true value. If such a parallel set of elements exists, vector-any returns the value that pred? returned for that set of elements. The iteration is strictly left-to-right.

(vector-every pred? vec1 vec2 ...)

If, for every index i between 0 and the length of the shortest vector argument, the set of elements (vector-ref vec1 i) (vector-ref vec2 i) ... satisfies pred?, vector-every returns the value that pred? returned for the last set of elements, at the last index of the shortest vector. The iteration is strictly left-to-right.

(vector-partition pred? vec)

A vector the same size as vec is newly allocated and filled with all the elements of vec that satisfy pred? in their original order followed by all the elements that do not satisfy pred, also in their original order. Two values are returned, the newly allocated vector and the index of the leftmost element that does not satisfy pred.

Mutators

These procedures return an unspecified value.

([type]vector-set! [type]vector k v)

Converts v to a binary value encoded according to [type] and places it into the kth element of [type]vector. It is an error if v cannot be converted to [type]. Note that u8vector-set! is the same as the R7RS-small procedure bytevector-u8-set!.

(vector-swap! [type]vec i j)

Swaps or exchanges the values of the locations in [type]vec at i and j.

(vector-fill! [type]vec fill [ start [ end ]])

Assigns the value of every location in [type]vec between start, which defaults to 0 and end, which defaults to the length of vec, to fill. It is an error if fill cannot be converted to [type].

(vector-reverse! [type]vec [ start [ end ]])

Destructively reverses the contents of the sequence of locations in [type]vec between start and end.

(vector-copy! to at from [ start [ end ]])

Copies the elements of [type]vector from between start and end to [type]vector to, starting at at. The order in which elements are copied is unspecified, except that if the source and destination overlap, copying takes place as if the source is first copied into a temporary vector and then into the destination. This can be achieved without allocating storage by making sure to copy in the correct direction in such circumstances.

(vector-reverse-copy! to at from [ start [ end ]])

Like vector-copy`, but the elements appear in to in reverse order.

Conversions to numeric vectors

It is an error if a value being used to fill an element of a [type]vector cannot be converted to [type].

(vector->[type]vector vector [start [ end ] ])

Returns a newly allocated [type]vector of length end - start, filled with the corresponding elements of vector.

(list->[type]vector list)

Returns a newly allocated [type]vector whose length is the length of list, filled with the elements of list.

(vector->[type]vector! [type]vector at vector [start [ end ] ])

Writes the elements of vector from start to end into [type]vector starting at at.

(list->[type]vector! list [type]vector at)

Writes the elements of list into [type]vector starting at at.

Conversions from numeric vectors

([type]vector->vector [type]vector [ start [ end ] ])

([type]vector->list [type]vector [ start [ end ] ])

Returns a newly allocated vector or list of length end - start with the elements of [type]vector from start to end.

([type]vector->vector! vector at [type]vector [start [ end ] ])

Writes the elements of [type]vector from start to end into vector starting at at.

Textual input and output

The external representation of a numeric vector consists of a # character followed by the two- to four-character representation of [type] with no intervening whitespace. This prefix is followed, after optional whitespace, by the representation of a list produced as if by [type]vector->list. The prefix is interpreted case-insensitively.

(array-read [ input-port ])

Reads the external representation of a [type]vector from input-port (the current input port if input-port is not specified) and returns the corresponding [type]vector.

([type]vector-write [type]vector [ stream ])

Writes the external representation of [type]vector from output-port (the current output port if output-port is not specified) and returns an unspecified value.

This SRFI recommends, but does not require, that the standard Scheme procedures read, write, and display be extended to deal with external representations of [type]vectors. On R7RS systems, if read accepts the external representation of [type]vectors, it must also be allowed in Scheme code, in which case array constants are self-quoting.

Binary input and output

For the procedures in this section, b is a constant whose value depends on the type, representing the number of bytes required for the type. Thus it is 1 for types u8 and s8, 2 for types u16 and s16, and so on up to 16 for type c128.

(input-[type]vector k [ port ])

(input-[type]vector-be k [ port ])

(input-[type]vector-le k [ port ])

Read k * b bytes from port into a newly allocated [type]vector using native/big-endian/little-endian order and returns it.

(input-[type]vector! [type]vector [ port [ start [ end ] ] ])

(input-[type]vector-le! [type]vector [ port [ start [ end ] ] ])

(input-[type]vector-be! [type]vector [ port [ start [ end ] ] ])

Read end * b - start * b bytes from port into [type]vector starting at start using native/big-endian/little-endian order. Returns the number of bytes read divided by b, or an eof object if no bytes are available. If the number of bytes available is not a multiple of b, the value of the element of [type]vector for which b bytes are not available is unspecified.

(output-[type]vector [type]vector [ port [ start [ end ] ] ])

(output-[type]vector-le [type]vector [ port [ start [ end ] ] ])

(output-[type]vector-be [type]vector [ port [ start [ end ] ] ])

Write end * b - start * b bytes to port from [type]vector starting at start using native/big-endian/little-endian order. Returns an unspecified value.

Packaging

SRFI 4 provides just 8 procedures per type: the basic and multi-argument constructors, the predicate, the basic accessor, the basic mutator, length, and conversion to and from lists. Since there are many more procedures, it makes sense to factor this into separate libraries. Most programs won't require all the representation types, so factoring horizontally into 12 libraries based on [type] is a simple approach.

Implementation

This syntax-rules macro by Ian Price will be helpful in implementing lots of similar but not identical procedures for the 12 types.

Last modified 5 weeks ago Last modified on 03/24/17 12:18:20