mirror of
https://github.com/ClickHouse/ClickHouse.git
synced 2024-12-15 19:02:04 +00:00
230fbf76a9
Add `hilbertEncode` and `hilbertDecode` functions
968 lines
23 KiB
Markdown
968 lines
23 KiB
Markdown
---
|
||
slug: /en/sql-reference/functions/encoding-functions
|
||
sidebar_position: 65
|
||
sidebar_label: Encoding
|
||
---
|
||
|
||
# Encoding Functions
|
||
|
||
## char
|
||
|
||
Returns the string with the length as the number of passed arguments and each byte has the value of corresponding argument. Accepts multiple arguments of numeric types. If the value of argument is out of range of UInt8 data type, it is converted to UInt8 with possible rounding and overflow.
|
||
|
||
**Syntax**
|
||
|
||
``` sql
|
||
char(number_1, [number_2, ..., number_n]);
|
||
```
|
||
|
||
**Arguments**
|
||
|
||
- `number_1, number_2, ..., number_n` — Numerical arguments interpreted as integers. Types: [Int](../data-types/int-uint.md), [Float](../data-types/float.md).
|
||
|
||
**Returned value**
|
||
|
||
- a string of given bytes. [String](../data-types/string.md).
|
||
|
||
**Example**
|
||
|
||
Query:
|
||
|
||
``` sql
|
||
SELECT char(104.1, 101, 108.9, 108.9, 111) AS hello;
|
||
```
|
||
|
||
Result:
|
||
|
||
``` text
|
||
┌─hello─┐
|
||
│ hello │
|
||
└───────┘
|
||
```
|
||
|
||
You can construct a string of arbitrary encoding by passing the corresponding bytes. Here is example for UTF-8:
|
||
|
||
Query:
|
||
|
||
``` sql
|
||
SELECT char(0xD0, 0xBF, 0xD1, 0x80, 0xD0, 0xB8, 0xD0, 0xB2, 0xD0, 0xB5, 0xD1, 0x82) AS hello;
|
||
```
|
||
|
||
Result:
|
||
|
||
``` text
|
||
┌─hello──┐
|
||
│ привет │
|
||
└────────┘
|
||
```
|
||
|
||
Query:
|
||
|
||
``` sql
|
||
SELECT char(0xE4, 0xBD, 0xA0, 0xE5, 0xA5, 0xBD) AS hello;
|
||
```
|
||
|
||
Result:
|
||
|
||
``` text
|
||
┌─hello─┐
|
||
│ 你好 │
|
||
└───────┘
|
||
```
|
||
|
||
## hex
|
||
|
||
Returns a string containing the argument’s hexadecimal representation.
|
||
|
||
Alias: `HEX`.
|
||
|
||
**Syntax**
|
||
|
||
``` sql
|
||
hex(arg)
|
||
```
|
||
|
||
The function is using uppercase letters `A-F` and not using any prefixes (like `0x`) or suffixes (like `h`).
|
||
|
||
For integer arguments, it prints hex digits (“nibbles”) from the most significant to least significant (big-endian or “human-readable” order). It starts with the most significant non-zero byte (leading zero bytes are omitted) but always prints both digits of every byte even if the leading digit is zero.
|
||
|
||
Values of type [Date](../data-types/date.md) and [DateTime](../data-types/datetime.md) are formatted as corresponding integers (the number of days since Epoch for Date and the value of Unix Timestamp for DateTime).
|
||
|
||
For [String](../data-types/string.md) and [FixedString](../data-types/fixedstring.md), all bytes are simply encoded as two hexadecimal numbers. Zero bytes are not omitted.
|
||
|
||
Values of [Float](../data-types/float.md) and [Decimal](../data-types/decimal.md) types are encoded as their representation in memory. As we support little-endian architecture, they are encoded in little-endian. Zero leading/trailing bytes are not omitted.
|
||
|
||
Values of [UUID](../data-types/uuid.md) type are encoded as big-endian order string.
|
||
|
||
**Arguments**
|
||
|
||
- `arg` — A value to convert to hexadecimal. Types: [String](../data-types/string.md), [UInt](../data-types/int-uint.md), [Float](../data-types/float.md), [Decimal](../data-types/decimal.md), [Date](../data-types/date.md) or [DateTime](../data-types/datetime.md).
|
||
|
||
**Returned value**
|
||
|
||
- A string with the hexadecimal representation of the argument. [String](../data-types/string.md).
|
||
|
||
**Examples**
|
||
|
||
Query:
|
||
|
||
``` sql
|
||
SELECT hex(1);
|
||
```
|
||
|
||
Result:
|
||
|
||
``` text
|
||
01
|
||
```
|
||
|
||
Query:
|
||
|
||
``` sql
|
||
SELECT hex(toFloat32(number)) AS hex_presentation FROM numbers(15, 2);
|
||
```
|
||
|
||
Result:
|
||
|
||
``` text
|
||
┌─hex_presentation─┐
|
||
│ 00007041 │
|
||
│ 00008041 │
|
||
└──────────────────┘
|
||
```
|
||
|
||
Query:
|
||
|
||
``` sql
|
||
SELECT hex(toFloat64(number)) AS hex_presentation FROM numbers(15, 2);
|
||
```
|
||
|
||
Result:
|
||
|
||
``` text
|
||
┌─hex_presentation─┐
|
||
│ 0000000000002E40 │
|
||
│ 0000000000003040 │
|
||
└──────────────────┘
|
||
```
|
||
|
||
Query:
|
||
|
||
``` sql
|
||
SELECT lower(hex(toUUID('61f0c404-5cb3-11e7-907b-a6006ad3dba0'))) as uuid_hex
|
||
```
|
||
|
||
Result:
|
||
|
||
``` text
|
||
┌─uuid_hex─────────────────────────┐
|
||
│ 61f0c4045cb311e7907ba6006ad3dba0 │
|
||
└──────────────────────────────────┘
|
||
```
|
||
|
||
|
||
## unhex
|
||
|
||
Performs the opposite operation of [hex](#hex). It interprets each pair of hexadecimal digits (in the argument) as a number and converts it to the byte represented by the number. The return value is a binary string (BLOB).
|
||
|
||
If you want to convert the result to a number, you can use the [reverse](../../sql-reference/functions/string-functions.md#reverse) and [reinterpretAs<Type>](../../sql-reference/functions/type-conversion-functions.md#type-conversion-functions) functions.
|
||
|
||
:::note
|
||
If `unhex` is invoked from within the `clickhouse-client`, binary strings display using UTF-8.
|
||
:::
|
||
|
||
Alias: `UNHEX`.
|
||
|
||
**Syntax**
|
||
|
||
``` sql
|
||
unhex(arg)
|
||
```
|
||
|
||
**Arguments**
|
||
|
||
- `arg` — A string containing any number of hexadecimal digits. [String](../data-types/string.md), [FixedString](../data-types/fixedstring.md).
|
||
|
||
Supports both uppercase and lowercase letters `A-F`. The number of hexadecimal digits does not have to be even. If it is odd, the last digit is interpreted as the least significant half of the `00-0F` byte. If the argument string contains anything other than hexadecimal digits, some implementation-defined result is returned (an exception isn’t thrown). For a numeric argument the inverse of hex(N) is not performed by unhex().
|
||
|
||
**Returned value**
|
||
|
||
- A binary string (BLOB). [String](../data-types/string.md).
|
||
|
||
**Example**
|
||
|
||
Query:
|
||
``` sql
|
||
SELECT unhex('303132'), UNHEX('4D7953514C');
|
||
```
|
||
|
||
Result:
|
||
``` text
|
||
┌─unhex('303132')─┬─unhex('4D7953514C')─┐
|
||
│ 012 │ MySQL │
|
||
└─────────────────┴─────────────────────┘
|
||
```
|
||
|
||
Query:
|
||
|
||
``` sql
|
||
SELECT reinterpretAsUInt64(reverse(unhex('FFF'))) AS num;
|
||
```
|
||
|
||
Result:
|
||
|
||
``` text
|
||
┌──num─┐
|
||
│ 4095 │
|
||
└──────┘
|
||
```
|
||
|
||
## bin
|
||
|
||
Returns a string containing the argument’s binary representation.
|
||
|
||
**Syntax**
|
||
|
||
``` sql
|
||
bin(arg)
|
||
```
|
||
|
||
Alias: `BIN`.
|
||
|
||
For integer arguments, it prints bin digits from the most significant to least significant (big-endian or “human-readable” order). It starts with the most significant non-zero byte (leading zero bytes are omitted) but always prints eight digits of every byte if the leading digit is zero.
|
||
|
||
Values of type [Date](../data-types/date.md) and [DateTime](../data-types/datetime.md) are formatted as corresponding integers (the number of days since Epoch for `Date` and the value of Unix Timestamp for `DateTime`).
|
||
|
||
For [String](../data-types/string.md) and [FixedString](../data-types/fixedstring.md), all bytes are simply encoded as eight binary numbers. Zero bytes are not omitted.
|
||
|
||
Values of [Float](../data-types/float.md) and [Decimal](../data-types/decimal.md) types are encoded as their representation in memory. As we support little-endian architecture, they are encoded in little-endian. Zero leading/trailing bytes are not omitted.
|
||
|
||
Values of [UUID](../data-types/uuid.md) type are encoded as big-endian order string.
|
||
|
||
**Arguments**
|
||
|
||
- `arg` — A value to convert to binary. [String](../data-types/string.md), [FixedString](../data-types/fixedstring.md), [UInt](../data-types/int-uint.md), [Float](../data-types/float.md), [Decimal](../data-types/decimal.md), [Date](../data-types/date.md), or [DateTime](../data-types/datetime.md).
|
||
|
||
**Returned value**
|
||
|
||
- A string with the binary representation of the argument. [String](../data-types/string.md).
|
||
|
||
**Examples**
|
||
|
||
Query:
|
||
|
||
``` sql
|
||
SELECT bin(14);
|
||
```
|
||
|
||
Result:
|
||
|
||
``` text
|
||
┌─bin(14)──┐
|
||
│ 00001110 │
|
||
└──────────┘
|
||
```
|
||
|
||
Query:
|
||
|
||
``` sql
|
||
SELECT bin(toFloat32(number)) AS bin_presentation FROM numbers(15, 2);
|
||
```
|
||
|
||
Result:
|
||
|
||
``` text
|
||
┌─bin_presentation─────────────────┐
|
||
│ 00000000000000000111000001000001 │
|
||
│ 00000000000000001000000001000001 │
|
||
└──────────────────────────────────┘
|
||
```
|
||
|
||
Query:
|
||
|
||
``` sql
|
||
SELECT bin(toFloat64(number)) AS bin_presentation FROM numbers(15, 2);
|
||
```
|
||
|
||
Result:
|
||
|
||
``` text
|
||
┌─bin_presentation─────────────────────────────────────────────────┐
|
||
│ 0000000000000000000000000000000000000000000000000010111001000000 │
|
||
│ 0000000000000000000000000000000000000000000000000011000001000000 │
|
||
└──────────────────────────────────────────────────────────────────┘
|
||
```
|
||
|
||
Query:
|
||
|
||
``` sql
|
||
SELECT bin(toUUID('61f0c404-5cb3-11e7-907b-a6006ad3dba0')) as bin_uuid
|
||
```
|
||
|
||
Result:
|
||
|
||
``` text
|
||
┌─bin_uuid─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┐
|
||
│ 01100001111100001100010000000100010111001011001100010001111001111001000001111011101001100000000001101010110100111101101110100000 │
|
||
└──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┘
|
||
```
|
||
|
||
|
||
## unbin
|
||
|
||
Interprets each pair of binary digits (in the argument) as a number and converts it to the byte represented by the number. The functions performs the opposite operation to [bin](#bin).
|
||
|
||
**Syntax**
|
||
|
||
``` sql
|
||
unbin(arg)
|
||
```
|
||
|
||
Alias: `UNBIN`.
|
||
|
||
For a numeric argument `unbin()` does not return the inverse of `bin()`. If you want to convert the result to a number, you can use the [reverse](../../sql-reference/functions/string-functions.md#reverse) and [reinterpretAs<Type>](../../sql-reference/functions/type-conversion-functions.md#reinterpretasuint8163264) functions.
|
||
|
||
:::note
|
||
If `unbin` is invoked from within the `clickhouse-client`, binary strings are displayed using UTF-8.
|
||
:::
|
||
|
||
Supports binary digits `0` and `1`. The number of binary digits does not have to be multiples of eight. If the argument string contains anything other than binary digits, some implementation-defined result is returned (an exception isn’t thrown).
|
||
|
||
**Arguments**
|
||
|
||
- `arg` — A string containing any number of binary digits. [String](../data-types/string.md).
|
||
|
||
**Returned value**
|
||
|
||
- A binary string (BLOB). [String](../data-types/string.md).
|
||
|
||
**Examples**
|
||
|
||
Query:
|
||
|
||
``` sql
|
||
SELECT UNBIN('001100000011000100110010'), UNBIN('0100110101111001010100110101000101001100');
|
||
```
|
||
|
||
Result:
|
||
|
||
``` text
|
||
┌─unbin('001100000011000100110010')─┬─unbin('0100110101111001010100110101000101001100')─┐
|
||
│ 012 │ MySQL │
|
||
└───────────────────────────────────┴───────────────────────────────────────────────────┘
|
||
```
|
||
|
||
Query:
|
||
|
||
``` sql
|
||
SELECT reinterpretAsUInt64(reverse(unbin('1110'))) AS num;
|
||
```
|
||
|
||
Result:
|
||
|
||
``` text
|
||
┌─num─┐
|
||
│ 14 │
|
||
└─────┘
|
||
```
|
||
|
||
## bitmaskToList(num)
|
||
|
||
Accepts an integer. Returns a string containing the list of powers of two that total the source number when summed. They are comma-separated without spaces in text format, in ascending order.
|
||
|
||
## bitmaskToArray(num)
|
||
|
||
Accepts an integer. Returns an array of UInt64 numbers containing the list of powers of two that total the source number when summed. Numbers in the array are in ascending order.
|
||
|
||
## bitPositionsToArray(num)
|
||
|
||
Accepts an integer and converts it to an unsigned integer. Returns an array of `UInt64` numbers containing the list of positions of bits of `arg` that equal `1`, in ascending order.
|
||
|
||
**Syntax**
|
||
|
||
```sql
|
||
bitPositionsToArray(arg)
|
||
```
|
||
|
||
**Arguments**
|
||
|
||
- `arg` — Integer value. [Int/UInt](../data-types/int-uint.md).
|
||
|
||
**Returned value**
|
||
|
||
- An array containing a list of positions of bits that equal `1`, in ascending order. [Array](../data-types/array.md)([UInt64](../data-types/int-uint.md)).
|
||
|
||
**Example**
|
||
|
||
Query:
|
||
|
||
``` sql
|
||
SELECT bitPositionsToArray(toInt8(1)) AS bit_positions;
|
||
```
|
||
|
||
Result:
|
||
|
||
``` text
|
||
┌─bit_positions─┐
|
||
│ [0] │
|
||
└───────────────┘
|
||
```
|
||
|
||
Query:
|
||
|
||
``` sql
|
||
SELECT bitPositionsToArray(toInt8(-1)) AS bit_positions;
|
||
```
|
||
|
||
Result:
|
||
|
||
``` text
|
||
┌─bit_positions─────┐
|
||
│ [0,1,2,3,4,5,6,7] │
|
||
└───────────────────┘
|
||
```
|
||
|
||
## mortonEncode
|
||
|
||
Calculates the Morton encoding (ZCurve) for a list of unsigned integers.
|
||
|
||
The function has two modes of operation:
|
||
- Simple
|
||
- Expanded
|
||
|
||
### Simple mode
|
||
|
||
Accepts up to 8 unsigned integers as arguments and produces a UInt64 code.
|
||
|
||
**Syntax**
|
||
|
||
```sql
|
||
mortonEncode(args)
|
||
```
|
||
|
||
**Parameters**
|
||
|
||
- `args`: up to 8 [unsigned integers](../data-types/int-uint.md) or columns of the aforementioned type.
|
||
|
||
**Returned value**
|
||
|
||
- A UInt64 code. [UInt64](../data-types/int-uint.md)
|
||
|
||
**Example**
|
||
|
||
Query:
|
||
|
||
```sql
|
||
SELECT mortonEncode(1, 2, 3);
|
||
```
|
||
Result:
|
||
|
||
```response
|
||
53
|
||
```
|
||
|
||
### Expanded mode
|
||
|
||
Accepts a range mask ([tuple](../data-types/tuple.md)) as a first argument and up to 8 [unsigned integers](../data-types/int-uint.md) as other arguments.
|
||
|
||
Each number in the mask configures the amount of range expansion:<br/>
|
||
1 - no expansion<br/>
|
||
2 - 2x expansion<br/>
|
||
3 - 3x expansion<br/>
|
||
...<br/>
|
||
Up to 8x expansion.<br/>
|
||
|
||
**Syntax**
|
||
|
||
```sql
|
||
mortonEncode(range_mask, args)
|
||
```
|
||
|
||
**Parameters**
|
||
- `range_mask`: 1-8.
|
||
- `args`: up to 8 [unsigned integers](../data-types/int-uint.md) or columns of the aforementioned type.
|
||
|
||
Note: when using columns for `args` the provided `range_mask` tuple should still be a constant.
|
||
|
||
**Returned value**
|
||
|
||
- A UInt64 code. [UInt64](../data-types/int-uint.md)
|
||
|
||
|
||
**Example**
|
||
|
||
Range expansion can be beneficial when you need a similar distribution for arguments with wildly different ranges (or cardinality)
|
||
For example: 'IP Address' (0...FFFFFFFF) and 'Country code' (0...FF).
|
||
|
||
Query:
|
||
|
||
```sql
|
||
SELECT mortonEncode((1,2), 1024, 16);
|
||
```
|
||
|
||
Result:
|
||
|
||
```response
|
||
1572864
|
||
```
|
||
|
||
Note: tuple size must be equal to the number of the other arguments.
|
||
|
||
**Example**
|
||
|
||
Morton encoding for one argument is always the argument itself:
|
||
|
||
Query:
|
||
|
||
```sql
|
||
SELECT mortonEncode(1);
|
||
```
|
||
|
||
Result:
|
||
|
||
```response
|
||
1
|
||
```
|
||
|
||
**Example**
|
||
|
||
It is also possible to expand one argument too:
|
||
|
||
Query:
|
||
|
||
```sql
|
||
SELECT mortonEncode(tuple(2), 128);
|
||
```
|
||
|
||
Result:
|
||
|
||
```response
|
||
32768
|
||
```
|
||
|
||
**Example**
|
||
|
||
You can also use column names in the function.
|
||
|
||
Query:
|
||
|
||
First create the table and insert some data.
|
||
|
||
```sql
|
||
create table morton_numbers(
|
||
n1 UInt32,
|
||
n2 UInt32,
|
||
n3 UInt16,
|
||
n4 UInt16,
|
||
n5 UInt8,
|
||
n6 UInt8,
|
||
n7 UInt8,
|
||
n8 UInt8
|
||
)
|
||
Engine=MergeTree()
|
||
ORDER BY n1 SETTINGS index_granularity = 8192, index_granularity_bytes = '10Mi';
|
||
insert into morton_numbers (*) values(1,2,3,4,5,6,7,8);
|
||
```
|
||
Use column names instead of constants as function arguments to `mortonEncode`
|
||
|
||
Query:
|
||
|
||
```sql
|
||
SELECT mortonEncode(n1, n2, n3, n4, n5, n6, n7, n8) FROM morton_numbers;
|
||
```
|
||
|
||
Result:
|
||
|
||
```response
|
||
2155374165
|
||
```
|
||
|
||
**implementation details**
|
||
|
||
Please note that you can fit only so many bits of information into Morton code as [UInt64](../data-types/int-uint.md) has. Two arguments will have a range of maximum 2^32 (64/2) each, three arguments a range of max 2^21 (64/3) each and so on. All overflow will be clamped to zero.
|
||
|
||
## mortonDecode
|
||
|
||
Decodes a Morton encoding (ZCurve) into the corresponding unsigned integer tuple.
|
||
|
||
As with the `mortonEncode` function, this function has two modes of operation:
|
||
- Simple
|
||
- Expanded
|
||
|
||
### Simple mode
|
||
|
||
Accepts a resulting tuple size as the first argument and the code as the second argument.
|
||
|
||
**Syntax**
|
||
|
||
```sql
|
||
mortonDecode(tuple_size, code)
|
||
```
|
||
|
||
**Parameters**
|
||
- `tuple_size`: integer value no more than 8.
|
||
- `code`: [UInt64](../data-types/int-uint.md) code.
|
||
|
||
**Returned value**
|
||
|
||
- [tuple](../data-types/tuple.md) of the specified size. [UInt64](../data-types/int-uint.md)
|
||
|
||
**Example**
|
||
|
||
Query:
|
||
|
||
```sql
|
||
SELECT mortonDecode(3, 53);
|
||
```
|
||
|
||
Result:
|
||
|
||
```response
|
||
["1","2","3"]
|
||
```
|
||
|
||
### Expanded mode
|
||
|
||
Accepts a range mask (tuple) as a first argument and the code as the second argument.
|
||
Each number in the mask configures the amount of range shrink:<br/>
|
||
1 - no shrink<br/>
|
||
2 - 2x shrink<br/>
|
||
3 - 3x shrink<br/>
|
||
...<br/>
|
||
Up to 8x shrink.<br/>
|
||
|
||
Range expansion can be beneficial when you need a similar distribution for arguments with wildly different ranges (or cardinality)
|
||
For example: 'IP Address' (0...FFFFFFFF) and 'Country code' (0...FF).
|
||
As with the encode function, this is limited to 8 numbers at most.
|
||
|
||
**Example**
|
||
|
||
Query:
|
||
|
||
```sql
|
||
SELECT mortonDecode(1, 1);
|
||
```
|
||
|
||
Result:
|
||
|
||
```response
|
||
["1"]
|
||
```
|
||
|
||
**Example**
|
||
|
||
It is also possible to shrink one argument:
|
||
|
||
Query:
|
||
|
||
```sql
|
||
SELECT mortonDecode(tuple(2), 32768);
|
||
```
|
||
|
||
Result:
|
||
|
||
```response
|
||
["128"]
|
||
```
|
||
|
||
**Example**
|
||
|
||
You can also use column names in the function.
|
||
|
||
First create the table and insert some data.
|
||
|
||
Query:
|
||
```sql
|
||
create table morton_numbers(
|
||
n1 UInt32,
|
||
n2 UInt32,
|
||
n3 UInt16,
|
||
n4 UInt16,
|
||
n5 UInt8,
|
||
n6 UInt8,
|
||
n7 UInt8,
|
||
n8 UInt8
|
||
)
|
||
Engine=MergeTree()
|
||
ORDER BY n1 SETTINGS index_granularity = 8192, index_granularity_bytes = '10Mi';
|
||
insert into morton_numbers (*) values(1,2,3,4,5,6,7,8);
|
||
```
|
||
Use column names instead of constants as function arguments to `mortonDecode`
|
||
|
||
Query:
|
||
|
||
```sql
|
||
select untuple(mortonDecode(8, mortonEncode(n1, n2, n3, n4, n5, n6, n7, n8))) from morton_numbers;
|
||
```
|
||
|
||
Result:
|
||
|
||
```response
|
||
1 2 3 4 5 6 7 8
|
||
```
|
||
|
||
## hilbertEncode
|
||
|
||
Calculates code for Hilbert Curve for a list of unsigned integers.
|
||
|
||
The function has two modes of operation:
|
||
- Simple
|
||
- Expanded
|
||
|
||
### Simple mode
|
||
|
||
Simple: accepts up to 2 unsigned integers as arguments and produces a UInt64 code.
|
||
|
||
**Syntax**
|
||
|
||
```sql
|
||
hilbertEncode(args)
|
||
```
|
||
|
||
**Parameters**
|
||
|
||
- `args`: up to 2 [unsigned integers](../../sql-reference/data-types/int-uint.md) or columns of the aforementioned type.
|
||
|
||
**Returned value**
|
||
|
||
- A UInt64 code
|
||
|
||
Type: [UInt64](../../sql-reference/data-types/int-uint.md)
|
||
|
||
**Example**
|
||
|
||
Query:
|
||
|
||
```sql
|
||
SELECT hilbertEncode(3, 4);
|
||
```
|
||
Result:
|
||
|
||
```response
|
||
31
|
||
```
|
||
|
||
### Expanded mode
|
||
|
||
Accepts a range mask ([tuple](../../sql-reference/data-types/tuple.md)) as a first argument and up to 2 [unsigned integers](../../sql-reference/data-types/int-uint.md) as other arguments.
|
||
|
||
Each number in the mask configures the number of bits by which the corresponding argument will be shifted left, effectively scaling the argument within its range.
|
||
|
||
**Syntax**
|
||
|
||
```sql
|
||
hilbertEncode(range_mask, args)
|
||
```
|
||
|
||
**Parameters**
|
||
- `range_mask`: ([tuple](../../sql-reference/data-types/tuple.md))
|
||
- `args`: up to 2 [unsigned integers](../../sql-reference/data-types/int-uint.md) or columns of the aforementioned type.
|
||
|
||
Note: when using columns for `args` the provided `range_mask` tuple should still be a constant.
|
||
|
||
**Returned value**
|
||
|
||
- A UInt64 code
|
||
|
||
Type: [UInt64](../../sql-reference/data-types/int-uint.md)
|
||
|
||
|
||
**Example**
|
||
|
||
Range expansion can be beneficial when you need a similar distribution for arguments with wildly different ranges (or cardinality)
|
||
For example: 'IP Address' (0...FFFFFFFF) and 'Country code' (0...FF).
|
||
|
||
Query:
|
||
|
||
```sql
|
||
SELECT hilbertEncode((10,6), 1024, 16);
|
||
```
|
||
|
||
Result:
|
||
|
||
```response
|
||
4031541586602
|
||
```
|
||
|
||
Note: tuple size must be equal to the number of the other arguments.
|
||
|
||
**Example**
|
||
|
||
For a single argument without a tuple, the function returns the argument itself as the Hilbert index, since no dimensional mapping is needed.
|
||
|
||
Query:
|
||
|
||
```sql
|
||
SELECT hilbertEncode(1);
|
||
```
|
||
|
||
Result:
|
||
|
||
```response
|
||
1
|
||
```
|
||
|
||
**Example**
|
||
|
||
If a single argument is provided with a tuple specifying bit shifts, the function shifts the argument left by the specified number of bits.
|
||
|
||
Query:
|
||
|
||
```sql
|
||
SELECT hilbertEncode(tuple(2), 128);
|
||
```
|
||
|
||
Result:
|
||
|
||
```response
|
||
512
|
||
```
|
||
|
||
**Example**
|
||
|
||
The function also accepts columns as arguments:
|
||
|
||
Query:
|
||
|
||
First create the table and insert some data.
|
||
|
||
```sql
|
||
create table hilbert_numbers(
|
||
n1 UInt32,
|
||
n2 UInt32
|
||
)
|
||
Engine=MergeTree()
|
||
ORDER BY n1 SETTINGS index_granularity = 8192, index_granularity_bytes = '10Mi';
|
||
insert into hilbert_numbers (*) values(1,2);
|
||
```
|
||
Use column names instead of constants as function arguments to `hilbertEncode`
|
||
|
||
Query:
|
||
|
||
```sql
|
||
SELECT hilbertEncode(n1, n2) FROM hilbert_numbers;
|
||
```
|
||
|
||
Result:
|
||
|
||
```response
|
||
13
|
||
```
|
||
|
||
**implementation details**
|
||
|
||
Please note that you can fit only so many bits of information into Hilbert code as [UInt64](../../sql-reference/data-types/int-uint.md) has. Two arguments will have a range of maximum 2^32 (64/2) each. All overflow will be clamped to zero.
|
||
|
||
## hilbertDecode
|
||
|
||
Decodes a Hilbert curve index back into a tuple of unsigned integers, representing coordinates in multi-dimensional space.
|
||
|
||
As with the `hilbertEncode` function, this function has two modes of operation:
|
||
- Simple
|
||
- Expanded
|
||
|
||
### Simple mode
|
||
|
||
Accepts up to 2 unsigned integers as arguments and produces a UInt64 code.
|
||
|
||
**Syntax**
|
||
|
||
```sql
|
||
hilbertDecode(tuple_size, code)
|
||
```
|
||
|
||
**Parameters**
|
||
- `tuple_size`: integer value no more than 2.
|
||
- `code`: [UInt64](../../sql-reference/data-types/int-uint.md) code.
|
||
|
||
**Returned value**
|
||
|
||
- [tuple](../../sql-reference/data-types/tuple.md) of the specified size.
|
||
|
||
Type: [UInt64](../../sql-reference/data-types/int-uint.md)
|
||
|
||
**Example**
|
||
|
||
Query:
|
||
|
||
```sql
|
||
SELECT hilbertDecode(2, 31);
|
||
```
|
||
|
||
Result:
|
||
|
||
```response
|
||
["3", "4"]
|
||
```
|
||
|
||
### Expanded mode
|
||
|
||
Accepts a range mask (tuple) as a first argument and up to 2 unsigned integers as other arguments.
|
||
Each number in the mask configures the number of bits by which the corresponding argument will be shifted left, effectively scaling the argument within its range.
|
||
|
||
Range expansion can be beneficial when you need a similar distribution for arguments with wildly different ranges (or cardinality)
|
||
For example: 'IP Address' (0...FFFFFFFF) and 'Country code' (0...FF).
|
||
As with the encode function, this is limited to 8 numbers at most.
|
||
|
||
**Example**
|
||
|
||
Hilbert code for one argument is always the argument itself (as a tuple).
|
||
|
||
Query:
|
||
|
||
```sql
|
||
SELECT hilbertDecode(1, 1);
|
||
```
|
||
|
||
Result:
|
||
|
||
```response
|
||
["1"]
|
||
```
|
||
|
||
**Example**
|
||
|
||
A single argument with a tuple specifying bit shifts will be right-shifted accordingly.
|
||
|
||
Query:
|
||
|
||
```sql
|
||
SELECT hilbertDecode(tuple(2), 32768);
|
||
```
|
||
|
||
Result:
|
||
|
||
```response
|
||
["128"]
|
||
```
|
||
|
||
**Example**
|
||
|
||
The function accepts a column of codes as a second argument:
|
||
|
||
First create the table and insert some data.
|
||
|
||
Query:
|
||
```sql
|
||
create table hilbert_numbers(
|
||
n1 UInt32,
|
||
n2 UInt32
|
||
)
|
||
Engine=MergeTree()
|
||
ORDER BY n1 SETTINGS index_granularity = 8192, index_granularity_bytes = '10Mi';
|
||
insert into hilbert_numbers (*) values(1,2);
|
||
```
|
||
Use column names instead of constants as function arguments to `hilbertDecode`
|
||
|
||
Query:
|
||
|
||
```sql
|
||
select untuple(hilbertDecode(2, hilbertEncode(n1, n2))) from hilbert_numbers;
|
||
```
|
||
|
||
Result:
|
||
|
||
```response
|
||
1 2
|
||
```
|