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9.6. Bit String Functions and Operators
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9.6. Bit String Functions and Operators #

This section describes functions and operators for examining and manipulating bit strings, that is values of the types bit and bit varying. (While only type bit is mentioned in these tables, values of type bit varying can be used interchangeably.) Bit strings support the usual comparison operators shown in Table 9.1, as well as the operators shown in Table 9.14.

Table 9.14. Bit String Operators

Operator Description Example(s)

Operator Description Example(s)
`bit` `+

` `+bit` → `bit` Concatenation `+B'10001'

B'011'` → `+10001011`
`bit` `&` `bit` → `bit` Bitwise AND (inputs must be of equal length) `B'10001' & B'01101'` → `00001`
`bit` `+
` `+bit` → `bit` Bitwise OR (inputs must be of equal length) `+B'10001'
B'01101'` → `+11101`
`bit` `#` `bit` → `bit` Bitwise exclusive OR (inputs must be of equal length) `B'10001' # B'01101'` → `11100`
`~` `bit` → `bit` Bitwise NOT `~ B'10001'` → `01110`
`bit` `<<` `integer` → `bit` Bitwise shift left (string length is preserved) `B'10001' << 3` → `01000`
`bit` `>>` `integer` → `bit` Bitwise shift right (string length is preserved) `B'10001' >> 2` → `00100`

bit `+

` `+bit` → bit

Concatenation

`+B'10001'

B'011'` → `+10001011`

bit & bit → bit

Bitwise AND (inputs must be of equal length)

B'10001' & B'01101' → 00001

bit `+

` `+bit` → bit

Bitwise OR (inputs must be of equal length)

`+B'10001'

B'01101'` → `+11101`

bit # bit → bit

Bitwise exclusive OR (inputs must be of equal length)

B'10001' # B'01101' → 11100

~ bit → bit

Bitwise NOT

~ B'10001' → 01110

bit << integer → bit

Bitwise shift left (string length is preserved)

B'10001' << 3 → 01000

bit >> integer → bit

Bitwise shift right (string length is preserved)

B'10001' >> 2 → 00100

Some of the functions available for binary strings are also available for bit strings, as shown in Table 9.15.

Table 9.15. Bit String Functions

Function Description Example(s)

Function Description Example(s)
`+bit_count+` ( `+bit+` ) → `+bigint+` Returns the number of bits set in the bit string (also known as “[.quote]#popcount”#). `bit_count(B'10111')` → `4`
`+bit_length+` ( `+bit+` ) → `+integer+` Returns number of bits in the bit string. `bit_length(B'10111')` → `5`
`+length+` ( `+bit+` ) → `+integer+` Returns number of bits in the bit string. `length(B'10111')` → `5`
`+octet_length+` ( `+bit+` ) → `+integer+` Returns number of bytes in the bit string. `octet_length(B'1011111011')` → `2`
`+overlay+` ( _`+bits+`_ `+bit+` `+PLACING+` _`+newsubstring+`_ `+bit+` `+FROM+` _`+start+`_ `+integer+` [ [.optional]#`+FOR+` _`+count+`_ `+integer+`# ] ) → `+bit+` Replaces the substring of `bits `that starts at the` start`'th bit and extends for` count `bits with` newsubstring`. If` count `is omitted, it defaults to the length of` newsubstring`. `overlay(B'01010101010101010' placing B'11111' from 2 for 3)` → `0111110101010101010`
`+position+` ( _`+substring+`_ `+bit+` `+IN+` _`+bits+`_ `+bit+` ) → `+integer+` Returns first starting index of the specified `substring `within` bits`, or zero if it’s not present. `position(B'010' in B'000001101011')` → `8`
`+substring+` ( _`+bits+`_ `+bit+` [ [.optional]#`+FROM+` _`+start+`_ `+integer+`# ] [ [.optional]#`+FOR+` _`+count+`_ `+integer+`# ] ) → `+bit+` Extracts the substring of `bits `starting at the` start`'th bit if that is specified, and stopping after` count `bits if that is specified. Provide at least one of` start `and` count`. `substring(B'110010111111' from 3 for 2)` → `00`
`+get_bit+` ( _`+bits+`_ `+bit+`, _`+n+`_ `+integer+` ) → `+integer+` Extracts `n`'th bit from bit string; the first (leftmost) bit is bit 0. `get_bit(B'101010101010101010', 6)` → `1`
`+set_bit+` ( _`+bits+`_ `+bit+`, _`+n+`_ `+integer+`, _`+newvalue+`_ `+integer+` ) → `+bit+` Sets `n`'th bit in bit string to` newvalue`; the first (leftmost) bit is bit 0. `set_bit(B'101010101010101010', 6, 0)` → `101010001010101010`

`+bit_count+` ( `+bit+` ) → `+bigint+`

Returns the number of bits set in the bit string (also known as “[.quote]#popcount”#).

bit_count(B'10111') → 4

`+bit_length+` ( `+bit+` ) → `+integer+`

Returns number of bits in the bit string.

bit_length(B'10111') → 5

`+length+` ( `+bit+` ) → `+integer+`

Returns number of bits in the bit string.

length(B'10111') → 5

`+octet_length+` ( `+bit+` ) → `+integer+`

Returns number of bytes in the bit string.

octet_length(B'1011111011') → 2

`+overlay+` ( _`+bits+`_ `+bit+` `+PLACING+` _`+newsubstring+`_ `+bit+` `+FROM+` _`+start+`_ `+integer+` [ [.optional]#`+FOR+` _`+count+`_ `+integer+`# ] ) → `+bit+`

Replaces the substring of `bits that starts at the start'th bit and extends for count bits with newsubstring. If count is omitted, it defaults to the length of newsubstring`.

overlay(B'01010101010101010' placing B'11111' from 2 for 3) → 0111110101010101010

`+position+` ( _`+substring+`_ `+bit+` `+IN+` _`+bits+`_ `+bit+` ) → `+integer+`

Returns first starting index of the specified `substring within bits`, or zero if it’s not present.

position(B'010' in B'000001101011') → 8

`+substring+` ( _`+bits+`_ `+bit+` [ [.optional]#`+FROM+` _`+start+`_ `+integer+`# ] [ [.optional]#`+FOR+` _`+count+`_ `+integer+`# ] ) → `+bit+`

Extracts the substring of `bits starting at the start'th bit if that is specified, and stopping after count bits if that is specified. Provide at least one of start and count`.

substring(B'110010111111' from 3 for 2) → 00

`+get_bit+` ( _`+bits+`_ `+bit+`, _`+n+`_ `+integer+` ) → `+integer+`

Extracts `n`'th bit from bit string; the first (leftmost) bit is bit 0.

get_bit(B'101010101010101010', 6) → 1

`+set_bit+` ( _`+bits+`_ `+bit+`, _`+n+`_ `+integer+`, _`+newvalue+`_ `+integer+` ) → `+bit+`

Sets `n'th bit in bit string to newvalue`; the first (leftmost) bit is bit 0.

set_bit(B'101010101010101010', 6, 0) → 101010001010101010

In addition, it is possible to cast integral values to and from type bit. Casting an integer to bit(n) copies the rightmost n bits. Casting an integer to a bit string width wider than the integer itself will sign-extend on the left. Some examples:

44::bit(10)                    0000101100
44::bit(3)                     100
cast(-44 as bit(12))           111111010100
'1110'::bit(4)::integer        14

Note that casting to just “[.quote]#bit”# means casting to bit(1), and so will deliver only the least significant bit of the integer.

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