9 Bit Vectors

▼ |  | Data: Data Structures

1 | Imperative Queues
2 | Growable Vectors
3 | Orders and Ordered Dictionaries
4 | Splay Trees
5 | Skip Lists
6 | Interval Maps
7 | Binary Heaps
8 | Integer Sets
9 | Bit Vectors
10 | Union-Find: Sets with only Canonical Elements
11 | Enumerations

On this page:

make-bit-vector
bit-vector
bit-vector?
bit-vector-ref
bit-vector-set!
bit-vector-length
bit-vector-popcount
bit-vector-copy
in-bit-vector
for/ bit-vector
for*/ bit-vector
bit-vector->list
list->bit-vector
bit-vector->string
string->bit-vector

6.5
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### 9`` Bit Vectors

Jens Axel Søgaard <soegaard@racket-lang.org>

(require data/bit-vector) | package: base

A bit vector is a mutable sequence whose elements are booleans. A bit vector also acts as a dictionary (dict? from racket/dict), where the keys are zero-based indexes and the values are the elements of the bit-vector. A bit-vector has a fixed size.

Two bit-vectors are equal? if they contain the same number of elements and if they contain equal elements at each index.

> procedure (make-bit-vector size [fill]) → bit-vector?
> size : exact-integer?
> fill : boolean? = #f

Creates a new bit-vector of size size. All elements are initialized to fill.

Examples:

> > (bit-vector-ref (make-bit-vector 3) 2)
> #f
> > (bit-vector-ref (make-bit-vector 3 #t) 2)
> #t

> procedure (bit-vector elem ...) → bit-vector?
> elem : boolean?

Creates a new bit-vector containing each elem in order.

Example:

> > (bit-vector-ref (bit-vector #f #t #f) 1)
> #t

> procedure (bit-vector? v) → boolean?
> v : any/c

Returns #t if v is a bit-vector, #f otherwise.

> procedure (bit-vector-ref bv index [default]) → any/c
> bv : bit-vector?
> index : exact-nonnegative-integer?
> default : any/c = (error ....)

Returns the element at index index, if index is less than (bit-vector-length bv). Otherwise, default is invoked if it is a procedure, returned otherwise.

Examples:

> > (bit-vector-ref (bit-vector #f #t) 1)
> #t
> > (bit-vector-ref (bit-vector #f #t) 5 'not-there)
> 'not-there

> procedure (bit-vector-set! bv index value) → void?
> bv : bit-vector?
> | index |  | : |  |
> (and/c exact-nonnegative-integer?
> (</c (+ 1 (bit-vector-length vv))))
> value : boolean?

Sets the value at index index to be value.

Examples:

> > (define bv (bit-vector #f #t))
> > (bit-vector-ref bv 0)
> #f
> > (bit-vector-set! bv 0 #t)
> > (bit-vector-ref bv 0)
> #t

> procedure (bit-vector-length bv) → exact-nonnegative-integer?
> bv : bit-vector?

Returns the number of items in the bit-vector bv.

> procedure (bit-vector-popcount bv) → exact-nonnegative-integer?
> bv : bit-vector?

Returns the number of set bits in the bit-vector bv.

Example:

> > (bit-vector-popcount (bit-vector #f #t #t))
> 2

> procedure (bit-vector-copy bv [start end]) → bit-vector?
> bv : bit-vector?
> start : exact-nonnegative-integer? = 0
> end : exact-nonnegative-integer? = (vector-length v)

Creates a fresh bit-vector with the same elements as bv from start (inclusive) to end (exclusive).

> procedure (in-bit-vector bv) → sequence?
> bv : bit-vector?

Returns a sequence whose elements are the elements of the bit-vector bv. Mutation of bv while the sequence is running changes the elements produced by the sequence. To obtain a sequence from a snapshot of bv, use (in-bit-vector (bit-vector-copy bv)) instead.

Examples:

> > (define bv (bit-vector #f #t #f))
> > (for/list ([x (in-bit-vector bv)]) x)
> '(#f #t #f)

> > syntax
> > (for/bit-vector maybe-length (for-clause ...)
> > body-or-break ... body)
> maybe-length |  | = |  |
> |  | | |  | #:length length-expr
> |  | | |  | #:length length-expr #:fill fill-expr
> | length-expr |  | : |  | exact-nonnegative-integer?

Iterates like for/vector, but results are accumulated into a bit-vector instead of a vector.

If the optional #:length clause is specified, the result of length-expr determines the length of the result bit-vector. In that case, the iteration can be performed more efficiently, and it terminates when the bit-vector is full or the requested number of iterations have been performed, whichever comes first. If length-expr specifies a length longer than the number of iterations, then the remaining slots of the vector are initialized to the value of fill-expr, which defaults to #f (i.e., the default argument of make-bit-vector).

Examples:

> > (bit-vector->list
> (for/bit-vector ([i '(1 2 3)]) (odd? i)))
> '(#t #f #t)
> > (bit-vector->list
> (for/bit-vector #:length 2 ([i '(1 2 3)]) (odd? i)))
> '(#t #f)
> > (bit-vector->list
> (for/bit-vector #:length 4 ([i '(1 2 3)]) (odd? i)))
> '(#t #f #t #f)
> > (bit-vector->list
> (for/bit-vector #:length 4 #:fill #t ([i '(1 2 3)]) (odd? i)))
> '(#t #f #t #t)

The for/bit-vector form may allocate a bit-vector and mutate it after each iteration of body, which means that capturing a continuation during body and applying it multiple times may mutate a shared bit-vector.

> > syntax
> > (for*/bit-vector maybe-length (for-clause ...)
> > body-or-break ... body)

Like for/bit-vector but with the implicit nesting of for*.

> procedure (bit-vector->list bv) → (listof boolean?)
> bv : bit-vector?
> procedure (list->bit-vector bits) → bit-vector?
> bits : (listof boolean?)
> procedure (bit-vector->string bv) → (and/c string? #rx"^[01]*$")
> bv : bit-vector?
> procedure (string->bit-vector s) → bit-vector?
> s : (and/c string? #rx"^[01]*$")

Converts between bit-vectors and their representations as lists and strings.

Examples:

> > (bit-vector->list (string->bit-vector "100111"))
> '(#t #f #f #t #t #t)
> > (bit-vector->string (list->bit-vector '(#t #f #t #t)))
> "1011"

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