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BitVector—Wolfram Language Documentation

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• See Also
  • BitSet
  • BitClear
  • BitGet
  • CreateDataStructure
  • DataStructure
  • Compiled Types
  • Boolean
  • Data Structures
  • BloomFilter
• Related Guides
  • Data Structures
  • Compiled Types
  • Code Compilation
  • Bitwise Operations

"BitVector"

represents a vector of Boolean values or members of a set built from an array of bits.

• A "BitVector" is a very compact representation of data that can only take on two values, such as Boolean data, and can also be an efficient representation of sets.
• The numbering of bits is consistent with other bit operations such as BitSet, so that 0 refers to the first bit.
• For a data structure of type "BitVector", the following operations can be used:
• ds["BitAnd",ds_i] combine the bits in ds and ds_i using bitwise And time: O(n/8) ds["BitClear",k] set the k^th bit in ds to 0 time: O(1) ds["BitClearAll"] set all the bits in ds to 0 time: O(n) ds["BitCount"] return the number of bits in ds that are set to 1 time: O(n) ds["BitGet",k] get the k^th bit in ds time: O(1) ds["BitInvert",k] invert the value of the k^th bit of ds time: O(1) ds["BitList"] return a list of bits that are set to 1 in ds time: O(n) ds["BitNand",ds_i] combine the bits in ds and ds_i using bitwise Nand time: O(n/8) ds["BitNor",ds_i] combine the bits in ds and ds_i using bitwise Nor time: O(n/8) ds["BitNot",ds_i] toggle the bits in ds time: O(n/8) ds["BitOr",ds_i] combine the bits in ds and ds_i using bitwise Or time: O(n/8) ds["BitSet",k] set the k^th bit in ds to 1 time: O(1) ds["BitTest",k] return True if the k^th bit of ds is set to 1 and False otherwise time: O(1) ds["BitXnor",ds_i] combine the bits in ds and ds_i using bitwise Xnor time: O(n/8) ds["BitXor",ds_i] combine the bits in ds and ds_i using bitwise Xor time: O(n/8) ds["Boole"] return a numeric array with ones for the set bits in ds and zeroes elsewhere. time: O(n) ds["Capacity"] return the number of bits that can be stored in ds time: O(1) ds["Copy"] return a copy of ds time: O(n) ds["Length"] return the number of bits that can be stored in ds time: O(1) ds["OffBitList"] return a list of the bits that are off in ds time: O(n/8) ds["OffBitList",ds_i] return a list of the bits that are off in both ds and ds_i time: O(n/8) ds["OnBitList",ds_i] return a list of the bits that are on in both ds and ds_i time: O(n/8) ds["Visualization"] return a visualization of ds time: O(n)
• The following functions are also supported:

A new "BitVector" can be created with CreateDataStructure:

Set the 20th bit to 1:

It is possible to test if a bit is set:

Extract a bit:

Invert a bit:

Get a list of the bits that are set:

Return an expression version of ds:

The normal list can be used to create a new "BitVector" :

Verify that they are equal:

A visualization of the data structure can be generated:

Testing for common bits:

The bits that are on in both:

The bits that are off in both:

Combining:

The "BitVector" only contains bits that were on in both:

A new "BitVector" can be created with CreateDataStructure:

Information about the data structure ds:

The numbering for bits in a "BitVector" is consistent with Power and bit operations such as BitSet.

Create two bit vectors:

Both bit vectors are initialized with zeros:

Equality can be tested with SameQ:

Change one of the bit vectors by setting a bit:

The bit vectors are no longer the same:

Inequality can be tested with UnsameQ:

Create a bit vector:

Get an array of zero/one values corresponding to the bits:

When the bit is set, the array value is one, otherwise zero:

This is equivalent to Boole applied to the Boolean list:

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