Relational Data - Functions - Bit Functions

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Bit functions work for any pair of types from UInt8, UInt16, UInt32, UInt64, Int8, Int16, Int32, Int64, Float32, or Float64. Some functions support String and FixedString types.

The result type is an integer with bits equal to the maximum bits of its arguments. If at least one of the arguments is signed, the result is a signed number. If an argument is a floating-point number, it is cast to Int64.

bitAnd(a, b)

bitOr(a, b)

bitXor(a, b)

bitNot(a)

bitShiftLeft(a, b)

Shifts the binary representation of a value to the left by a specified number of bit positions.

A FixedString or a String is treated as a single multibyte value.

Bits of a FixedString value are lost as they are shifted out. On the contrary, a String value is extended with additional bytes, so no bits are lost.

Syntax 

bitShiftLeft(a, b)

Arguments

Returned value

  • Shifted value.

The type of the returned value is the same as the type of the input value.

Example

In the following queries bin and hex functions are used to show bits of shifted values. 

SELECT 99 AS a, bin(a), bitShiftLeft(a, 2) AS a_shifted, bin(a_shifted);
SELECT 'abc' AS a, hex(a), bitShiftLeft(a, 4) AS a_shifted, hex(a_shifted);
SELECT toFixedString('abc', 3) AS a, hex(a), bitShiftLeft(a, 4) AS a_shifted, hex(a_shifted);

Result: 

┌──a─┬─bin(99)──┬─a_shifted─┬─bin(bitShiftLeft(99, 2))─┐
│ 99 │ 01100011 │       140 │ 10001100                 │
└────┴──────────┴───────────┴──────────────────────────┘
┌─a───┬─hex('abc')─┬─a_shifted─┬─hex(bitShiftLeft('abc', 4))─┐
│ abc │ 616263     │ &0        │ 06162630                    │
└─────┴────────────┴───────────┴─────────────────────────────┘
┌─a───┬─hex(toFixedString('abc', 3))─┬─a_shifted─┬─hex(bitShiftLeft(toFixedString('abc', 3), 4))─┐
│ abc │ 616263                       │ &0        │ 162630                                        │
└─────┴──────────────────────────────┴───────────┴───────────────────────────────────────────────┘

bitShiftRight(a, b)

Shifts the binary representation of a value to the right by a specified number of bit positions.

A FixedString or a String is treated as a single multibyte value. Note that the length of a String value is reduced as bits are shifted out.

Syntax 

bitShiftRight(a, b)

Arguments

Returned value

  • Shifted value.

The type of the returned value is the same as the type of the input value.

Example

Query: 

SELECT 101 AS a, bin(a), bitShiftRight(a, 2) AS a_shifted, bin(a_shifted);
SELECT 'abc' AS a, hex(a), bitShiftRight(a, 12) AS a_shifted, hex(a_shifted);
SELECT toFixedString('abc', 3) AS a, hex(a), bitShiftRight(a, 12) AS a_shifted, hex(a_shifted);

Result: 

┌───a─┬─bin(101)─┬─a_shifted─┬─bin(bitShiftRight(101, 2))─┐
│ 101 │ 01100101 │        25 │ 00011001                   │
└─────┴──────────┴───────────┴────────────────────────────┘
┌─a───┬─hex('abc')─┬─a_shifted─┬─hex(bitShiftRight('abc', 12))─┐
│ abc │ 616263     │           │ 0616                          │
└─────┴────────────┴───────────┴───────────────────────────────┘
┌─a───┬─hex(toFixedString('abc', 3))─┬─a_shifted─┬─hex(bitShiftRight(toFixedString('abc', 3), 12))─┐
│ abc │ 616263                       │           │ 000616                                          │
└─────┴──────────────────────────────┴───────────┴─────────────────────────────────────────────────┘

bitRotateLeft(a, b)

bitRotateRight(a, b)

bitSlice(s, offset, length)

Returns a substring starting with the bit from the ‘offset’ index that is ‘length’ bits long. bits indexing starts from 1

Syntax 

bitSlice(s, offset[, length])

Arguments

  • s — s is String or FixedString.
  • offset — The start index with bit, A positive value indicates an offset on the left, and a negative value is an indent on the right. Numbering of the bits begins with 1.
  • length — The length of substring with bit. If you specify a negative value, the function returns an open substring [offset, array_length - length]. If you omit the value, the function returns the substring [offset, the_end_string]. If length exceeds s, it will be truncate.If length isn’t multiple of 8, will fill 0 on the right.

Returned value

Example

Query: 

select bin('Hello'), bin(bitSlice('Hello', 1, 8))
select bin('Hello'), bin(bitSlice('Hello', 1, 2))
select bin('Hello'), bin(bitSlice('Hello', 1, 9))
select bin('Hello'), bin(bitSlice('Hello', -4, 8))

Result: 

┌─bin('Hello')─────────────────────────────┬─bin(bitSlice('Hello', 1, 8))─┐
│ 0100100001100101011011000110110001101111 │ 01001000                     │
└──────────────────────────────────────────┴──────────────────────────────┘
┌─bin('Hello')─────────────────────────────┬─bin(bitSlice('Hello', 1, 2))─┐
│ 0100100001100101011011000110110001101111 │ 01000000                     │
└──────────────────────────────────────────┴──────────────────────────────┘
┌─bin('Hello')─────────────────────────────┬─bin(bitSlice('Hello', 1, 9))─┐
│ 0100100001100101011011000110110001101111 │ 0100100000000000             │
└──────────────────────────────────────────┴──────────────────────────────┘
┌─bin('Hello')─────────────────────────────┬─bin(bitSlice('Hello', -4, 8))─┐
│ 0100100001100101011011000110110001101111 │ 11110000                      │
└──────────────────────────────────────────┴───────────────────────────────┘

byteSlice(s, offset, length)

See function substring.

bitTest

Takes any integer and converts it into binary form, returns the value of a bit at specified position. Counting is right-to-left, starting at 0.

Syntax 

SELECT bitTest(number, index)

Arguments

  • number – Integer number.
  • index – Position of bit.

Returned value

  • Value of the bit at the specified position. UInt8.

Example

For example, the number 43 in base-2 (binary) numeral system is 101011.

Query: 

SELECT bitTest(43, 1);

Result: 

┌─bitTest(43, 1)─┐
│              1 │
└────────────────┘

Another example:

Query: 

SELECT bitTest(43, 2);

Result: 

┌─bitTest(43, 2)─┐
│              0 │
└────────────────┘

bitTestAll

Returns result of logical conjuction (AND operator) of all bits at given positions. Counting is right-to-left, starting at 0.

The conjuction for bit-wise operations:

0 AND 0 = 0

0 AND 1 = 0

1 AND 0 = 0

1 AND 1 = 1

Syntax 

SELECT bitTestAll(number, index1, index2, index3, index4, ...)

Arguments

  • number – Integer number.
  • index1, index2, index3, index4 – Positions of bit. For example, for set of positions (index1, index2, index3, index4) is true if and only if all of its positions are true (index1 ⋀ index2, ⋀ index3 ⋀ index4).

Returned value

  • Result of the logical conjuction. UInt8.

Example

For example, the number 43 in base-2 (binary) numeral system is 101011.

Query: 

SELECT bitTestAll(43, 0, 1, 3, 5);

Result: 

┌─bitTestAll(43, 0, 1, 3, 5)─┐
│                          1 │
└────────────────────────────┘

Another example:

Query: 

SELECT bitTestAll(43, 0, 1, 3, 5, 2);

Result: 

┌─bitTestAll(43, 0, 1, 3, 5, 2)─┐
│                             0 │
└───────────────────────────────┘

bitTestAny

Returns result of logical disjunction (OR operator) of all bits at given positions. Counting is right-to-left, starting at 0.

The disjunction for bit-wise operations:

0 OR 0 = 0

0 OR 1 = 1

1 OR 0 = 1

1 OR 1 = 1

Syntax 

SELECT bitTestAny(number, index1, index2, index3, index4, ...)

Arguments

  • number – Integer number.
  • index1, index2, index3, index4 – Positions of bit.

Returned value

  • Result of the logical disjunction. UInt8.

Example

For example, the number 43 in base-2 (binary) numeral system is 101011.

Query: 

SELECT bitTestAny(43, 0, 2);

Result: 

┌─bitTestAny(43, 0, 2)─┐
│                    1 │
└──────────────────────┘

Another example:

Query: 

SELECT bitTestAny(43, 4, 2);

Result: 

┌─bitTestAny(43, 4, 2)─┐
│                    0 │
└──────────────────────┘

bitCount

Calculates the number of bits set to one in the binary representation of a number.

Syntax 

bitCount(x)

Arguments

  • x — Integer or floating-point number. The function uses the value representation in memory. It allows supporting floating-point numbers.

Returned value

  • Number of bits set to one in the input number. UInt8.

The function does not convert the input value to a larger type (sign extension). So, for example, bitCount(toUInt8(-1)) = 8.


Example

Take for example the number 333. Its binary representation: 0000000101001101.

Query: 

SELECT bitCount(333);

Result: 

┌─bitCount(333)─┐
│             5 │
└───────────────┘

bitHammingDistance

Returns the Hamming Distance between the bit representations of two integer values. Can be used with SimHash functions for detection of semi-duplicate strings. The smaller is the distance, the more likely those strings are the same.

Syntax 

bitHammingDistance(int1, int2)

Arguments

  • int1 — First integer value. Int64.
  • int2 — Second integer value. Int64.

Returned value

  • The Hamming distance. UInt8.

Examples

Query: 

SELECT bitHammingDistance(111, 121);

Result: 

┌─bitHammingDistance(111, 121)─┐
│                            3 │
└──────────────────────────────┘

With SimHash: 

SELECT bitHammingDistance(ngramSimHash('cat ate rat'), ngramSimHash('rat ate cat'));

Result: 

┌─bitHammingDistance(ngramSimHash('cat ate rat'), ngramSimHash('rat ate cat'))─┐
│                                                                            5 │
└──────────────────────────────────────────────────────────────────────────────┘
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