--- title: "log2" slug: "dev-database-reference-sql-functions-numeric-log2" updated: 2026-10-30T18:18:51Z published: 2026-10-30T18:18:51Z canonical: "docs.vastdata.com/dev-database-reference-sql-functions-numeric-log2" --- > ## Documentation Index > Fetch the complete documentation index at: https://docs.vastdata.com/llms.txt > Use this file to discover all available pages before exploring further. # log2 *Applies to VAST Cluster 5.5.* *[Functions](/develop/docs/dev-database-reference-sql-functions-index) › [Numeric and math functions](/develop/docs/dev-database-reference-sql-functions-numeric) › Powers and logarithms.* Returns the base-2 logarithm of a number: the power you raise 2 to in order to get it. `log2(8)` is `3.0`. It has no aliases; `log(2, x)` gives the same result. ## Syntax ``` log2(x) ``` | Argument | Type | Description | | --- | --- | --- | | `x` | `DOUBLE` (any integer, `DECIMAL` or `FLOAT` is converted) | The number to take the logarithm of. It must be greater than 0. | **Returns:** `DOUBLE`. **Aliases:** none. `log(2, x)` returns the same value. ## Set up the examples The examples connect with the ADBC driver, as in [VAST Query Engine (ADBC)](/develop/docs/dev-database-integrations-adbc), and work in a schema called `docs_sql_fn_numeric_log2`. Set `QE_ENDPOINT`, `AWS_ACCESS_KEY_ID`, `AWS_SECRET_ACCESS_KEY` and `VASTDB_BUCKET` ([SQL reference](/develop/docs/dev-database-reference-sql-index#example-connect-and-use-a-transaction)), and run the blocks in order in one Python session. Below each block is the output you should see. This block connects, defines the `run()` and `plan()` helpers, and creates a table of four codes, each with the number of distinct values it has to tell apart. The last row has no values: ``` import os import re import adbc_driver_manager import adbc_driver_manager.dbapi as dbapi import adbc_driver_vastdb BUCKET = os.environ["VASTDB_BUCKET"] SCHEMA = f'"{BUCKET}/docs_sql_fn_numeric_log2"' conn = dbapi.connect( driver=adbc_driver_vastdb.get_driver_path(), db_kwargs={ "vast.db.endpoint": os.environ["QE_ENDPOINT"], "vast.db.access_key": os.environ["AWS_ACCESS_KEY_ID"], "vast.db.secret_key": os.environ["AWS_SECRET_ACCESS_KEY"], }, autocommit=True, ) def server_message(e): """The server's message in a driver error, without the request ID or the echoed statement.""" text = re.sub(r"\[req=0x[0-9a-f]+\]: ", "", str(e)) found = (re.search(r'message: "(.*?)", request_id', text, re.S) or re.search(r"description: (.*)\)", text, re.S)) message = found.group(1) if found else text.strip().splitlines()[-1] message = re.sub(r"^Plan query: '.*?' failed with: ", "", message, flags=re.S) message = re.split(r"\\n|\n", message)[0].replace('\\"', '"') return message.replace(BUCKET, "") def run(sql): """Run one statement. Print the rows it returns, or the error.""" try: with conn.cursor() as cur: cur.execute(sql) rows = cur.fetchall() if cur.description else [] except (adbc_driver_manager.Error, OSError) as e: print(f"{type(e).__name__}: {server_message(e)}") else: print(rows) def plan(sql): """Print the plan without its ~N Rows lines: the table's row count, which can still be 0 just after an insert.""" with conn.cursor() as cur: cur.execute("EXPLAIN " + sql) steps = cur.fetchall()[0][1] print("\n".join(line for line in steps.splitlines() if "Rows" not in line)) TABLE = f"{SCHEMA}.codes" run(f"CREATE SCHEMA IF NOT EXISTS {SCHEMA}") run(f"CREATE TABLE IF NOT EXISTS {TABLE} (id BIGINT, name VARCHAR, distinct_values DOUBLE)") run(f"INSERT INTO {TABLE} VALUES " "(1, 'shift', 3), " "(2, 'weekday', 8), " "(3, 'sensor', 1024), " "(4, NULL, NULL)") ``` ``` [] [] [(4,)] ``` ## What it does `log2(x)` returns the `y` for which 2 to the power `y` is `x`. Every power of 2 gives a whole number: `log2(8)` is `3.0`, `log2(1024)` is `10.0` and `log2(0.5)` is `-1.0`. Other numbers give a fraction: `log2(3)` is `1.584962500721156`. The argument is converted to `DOUBLE`, and so is the result, whatever the argument's type: `log2(100::INTEGER)` and `log2(100::FLOAT)` both return a `DOUBLE`. A string of digits is converted too, so `log2('12')` returns `3.584962500721156`. The logarithm is only defined for numbers greater than 0: zero and negative numbers are errors, not `NULL`. ## NULLs and edge cases | Input | Result | | --- | --- | | `NULL` | `NULL` | | `1` | `0.0` | | `0.5` | `-1.0` | | `5e-324::DOUBLE` (the smallest `DOUBLE` above 0) | `-1074.0` | | `'inf'::DOUBLE` | `inf` | | `'nan'::DOUBLE` | `nan` | | `'12'` (a string of digits) | `3.584962500721156` | | `0` or `-0.0::DOUBLE` | Error: `cannot take logarithm of zero` | | A negative number, or `'-inf'::DOUBLE` | Error: `cannot take logarithm of a negative number` | | `'abc'` | Error: `Could not convert string 'abc' to DOUBLE` | | A `BLOB`, date, boolean, list or interval | Error: `No function matches the given name and argument types`, for example `'log2(DATE)'` | The same cases, as the cluster returns them. They use the helpers from [Set up the examples](/develop/docs/dev-database-reference-sql-functions-numeric-log2#set-up-the-examples): ``` run("SELECT log2(NULL), log2(1), log2(0.5), log2(5e-324::DOUBLE), log2('inf'::DOUBLE), log2('nan'::DOUBLE)") run("SELECT log2('12')") run("SELECT log2(0)") run("SELECT log2(-0.0::DOUBLE)") run("SELECT log2(-1)") run("SELECT log2('-inf'::DOUBLE)") run("SELECT log2('abc')") run("SELECT log2('\\xAA'::BLOB)") run("SELECT log2(DATE '2026-10-16')") run("SELECT log2(true)") run("SELECT log2([1, 2])") run("SELECT log2(INTERVAL 1 DAY)") ``` ``` [(None, 0.0, -1.0, -1074.0, inf, nan)] [(3.584962500721156,)] OSError: cannot take logarithm of zero OSError: cannot take logarithm of zero OSError: cannot take logarithm of a negative number OSError: cannot take logarithm of a negative number OSError: Could not convert string 'abc' to DOUBLE InternalError: Binder Error: No function matches the given name and argument types 'log2(BLOB)'. You might need to add explicit type casts. InternalError: Binder Error: No function matches the given name and argument types 'log2(DATE)'. You might need to add explicit type casts. InternalError: Binder Error: No function matches the given name and argument types 'log2(BOOLEAN)'. You might need to add explicit type casts. InternalError: Binder Error: No function matches the given name and argument types 'log2(INTEGER[])'. You might need to add explicit type casts. InternalError: Binder Error: No function matches the given name and argument types 'log2(INTERVAL)'. You might need to add explicit type casts. ``` ## Examples The base-2 logarithm of each code's number of distinct values, and, rounded up with [ceil](/develop/docs/dev-database-reference-sql-functions-numeric-ceil), the number of bits it takes to give each value its own number: ``` run(f"SELECT id, name, log2(distinct_values), ceil(log2(distinct_values)) FROM {TABLE} ORDER BY id LIMIT 10") ``` ``` [(1, 'shift', 1.584962500721156, 2.0), (2, 'weekday', 3.0, 3.0), (3, 'sensor', 10.0, 10.0), (4, None, None, None)] ``` Keep only the codes that need more than 2 bits: ``` run(f"SELECT id, name FROM {TABLE} WHERE log2(distinct_values) > 2 ORDER BY id LIMIT 10") ``` ``` [(2, 'weekday'), (3, 'sensor')] ``` ## How it runs in VAST The Query Engine runs on the cluster's CNodes, and a query on a table starts with a scan in VAST DataBase (`VAST_SCAN`). VAST DataBase can evaluate a comparison of a column with a constant, but not a function of a column, so `log2()` is always computed by the Query Engine: - **In the `SELECT` list,** the scan reads the column and the Query Engine computes `log2()` for each row it returns. - **In `WHERE`,** the scan sends the column for every row, and a `FILTER` step in the Query Engine computes `log2()` and keeps the rows that match. No rows are skipped in storage. The plan of the `WHERE` example shows the `FILTER` step above the scan: ``` plan(f"SELECT id FROM {TABLE} WHERE log2(distinct_values) > 2") ``` ``` ┌───────────────────────────┐ │ PROJECTION │ │ ──────────────────── │ │ #1 │ │ │ └─────────────┬─────────────┘ ┌─────────────┴─────────────┐ │ FILTER │ │ ──────────────────── │ │ (log2(distinct_values) > 2│ │ .0) │ │ │ └─────────────┬─────────────┘ ┌─────────────┴─────────────┐ │ VAST_SCAN │ │ ──────────────────── │ │ Function: VAST_SCAN │ │ │ │ Projections: │ │ distinct_values │ │ id │ │ │ └───────────────────────────┘ ``` ## Make it faster - **Compare the column, not its logarithm.** `log2()` grows with its argument, so `log2(x) > 2` keeps the same rows as `x > 4` (2 to the power 2). A comparison of the raw column with a constant is pushed down to VAST DataBase, so rows that don't match never leave storage, and `log2()` isn't computed at all, so a zero or a negative value in the column can't fail the query. The plan for `distinct_values > 4` has no `FILTER` step: ``` plan(f"SELECT id FROM {TABLE} WHERE distinct_values > 4") ``` ``` ┌───────────────────────────┐ │ VAST_SCAN │ │ ──────────────────── │ │ Function: VAST_SCAN │ │ Projections: id │ │ │ └───────────────────────────┘ ``` - **Store the logarithm if you can't rewrite the condition.** Compute it when you write the rows and keep it in its own column: a comparison of that column is pushed down, `log2(x)` in `WHERE` isn't. - **Combine it with a pushed-down condition.** In `id > 100 AND log2(x) > 2`, `id > 100` is still evaluated in VAST DataBase, so `log2()` runs only on the rows that pass it. ## Limitations and errors - **Greater than 0 only.** `log2(0)` fails with `cannot take logarithm of zero` and a negative number with `cannot take logarithm of a negative number`. On a table, one such row fails the whole query, not just that row: `NULL` is the only value that gives a `NULL`. Filter on the raw column (see [Make it faster](/develop/docs/dev-database-reference-sql-functions-numeric-log2#make-it-faster)) or keep zeros and negative numbers out of the column you take the logarithm of. - **Numbers only.** A `BLOB`, a date, a boolean, a list or an interval fails with `No function matches the given name and argument types`; `log2` takes a `DOUBLE`. A string is converted to `DOUBLE`, so a string that isn't a number fails with `Could not convert string ... to DOUBLE`. - **The result is a `DOUBLE`**, whatever the type of the argument. - **No `exp2`.** To raise 2 to a power, the inverse of `log2`, use [pow](/develop/docs/dev-database-reference-sql-functions-numeric-pow): `pow(2, 10)` returns `1024.0`. ``` run("SELECT exp2(10)") run("SELECT pow(2, 10)") ``` ``` InternalError: Catalog Error: Scalar Function with name exp2 does not exist! [(1024.0,)] ``` ## Similar functions | Function | Base | Result for `8` | | --- | --- | --- | | `log2(x)` | 2 | `3.0` | | [log](/develop/docs/dev-database-reference-sql-functions-numeric-log) `(2, x)` | the first argument | `3.0` | | [ln](/develop/docs/dev-database-reference-sql-functions-numeric-ln) | e | `2.0794415416798357` | | [log10](/develop/docs/dev-database-reference-sql-functions-numeric-log10) | 10 | `0.9030899869919435` | | [log](/develop/docs/dev-database-reference-sql-functions-numeric-log) `(x)`, one argument | 10, as `log10` | `0.9030899869919435` | | `ln(x) / ln(2)` | 2, computed from `ln` | `3.0` | | [pow](/develop/docs/dev-database-reference-sql-functions-numeric-pow) `(2, y)` | the inverse: 2 to the power `y` | | ``` run("SELECT log2(8), log(2, 8), ln(8), log10(8), log(8), ln(8) / ln(2)") ``` ``` [(3.0, 3.0, 2.0794415416798357, 0.9030899869919435, 0.9030899869919435, 3.0)] ``` Clean up: ``` run(f"DROP TABLE IF EXISTS {TABLE}") run(f"DROP SCHEMA IF EXISTS {SCHEMA}") conn.close() ``` ``` [] [] ``` ## See also - [Numeric and math functions](/develop/docs/dev-database-reference-sql-functions-numeric#powers-and-logarithms): all the powers and logarithms. - [log](/develop/docs/dev-database-reference-sql-functions-numeric-log), [ln](/develop/docs/dev-database-reference-sql-functions-numeric-ln), [log10](/develop/docs/dev-database-reference-sql-functions-numeric-log10) and [pow](/develop/docs/dev-database-reference-sql-functions-numeric-pow). - [Where filters run](/develop/docs/dev-database-reference-sql-select#where-filters-run) and [pushdowns](/develop/docs/dev-database-reference-pushdowns). - [EXPLAIN](/develop/docs/dev-database-reference-sql-explain): how to read a plan.