--- title: "log" slug: "dev-database-reference-sql-functions-numeric-log" updated: 2026-10-30T18:18:51Z published: 2026-10-30T18:18:51Z canonical: "docs.vastdata.com/dev-database-reference-sql-functions-numeric-log" --- > ## 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. # log *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.* With one argument, returns the base-10 logarithm of a number; with two, `log(b, x)` returns the logarithm of `x` to base `b`. The result is a `DOUBLE`. Zero and negative numbers fail the query. ## Syntax ``` log(x) log(b, x) ``` | Argument | Type | Description | | --- | --- | --- | | `x` | `DOUBLE` (any number) | The number to take the logarithm of. It must be greater than 0. | | `b` | `DOUBLE` (any number) | In `log(b, x)`, the base. It comes first, and must be greater than 0 and not 1. | **Returns:** `DOUBLE`, whatever the argument types. ## 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_log`. 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 values `x`, each with a base `b`. 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_log"' 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}.measures" run(f"CREATE SCHEMA IF NOT EXISTS {SCHEMA}") run(f"CREATE TABLE IF NOT EXISTS {TABLE} (id BIGINT, b DOUBLE, x DOUBLE)") run(f"INSERT INTO {TABLE} VALUES " "(1, 2.0, 8.0), " "(2, 10.0, 1000.0), " "(3, 0.5, 8.0), " "(4, 3.0, 1.0), " "(5, NULL, NULL)") ``` ``` [] [] [(5,)] ``` ## What it does **`log(x)` is the base-10 logarithm,** the same as [log10](/develop/docs/dev-database-reference-sql-functions-numeric-log10): `log(100)` is `2.0` and `log(1e308)` is `308.0`. It isn't the natural logarithm, as it is in some other SQL dialects: `log(exp(1))` is `0.4342944819032518`. For base e, use [ln](/develop/docs/dev-database-reference-sql-functions-numeric-ln). **`log(b, x)` takes the base first.** `log(2, 8)` is `3.0`, because 23 is 8; `log(8, 2)` is `0.33333333333333337`. A base between 0 and 1 gives the opposite sign: `log(0.5, 8)` is `-3.0`. The arguments are converted to `DOUBLE` first, so integers, `DECIMAL` and `FLOAT` values all work and all give a `DOUBLE`; so does a string that holds a number. **Values a logarithm can't take are errors,** not infinity or NaN, and they stop the whole query: - 0 as `x` or as the base fails with `cannot take logarithm of zero`. A negative zero (`-0.0::DOUBLE`) counts as zero. - A negative number as `x` or as the base fails with `cannot take logarithm of a negative number`; so does `'-inf'::DOUBLE`. - A base of 1 fails with `divison by zero in based logarithm` (the server's spelling). `log('inf'::DOUBLE)` is `inf`, and `nan` as either argument gives `nan`. An infinite base gives 0: `log('inf'::DOUBLE, 2)` is `0.0`. ## NULLs and edge cases | Input | Result | | --- | --- | | `log(NULL)`, `log(2, NULL)`, `log(NULL, 8)` | `NULL` | | `log(1)` | `0.0` | | `log(100)` | `2.0` | | `log(1e308)` | `308.0` | | `log(5e-324::DOUBLE)` | `-323.3062153431158` | | `log('inf'::DOUBLE)`, `log('nan'::DOUBLE)` | `inf`, `nan` | | `log(2, 8)` | `3.0` | | `log(8, 2)` | `0.33333333333333337` | | `log(10, 1000)` | `3.0` | | `log(0.5, 8)` | `-3.0` | | `log(2, 1)` | `0.0` | | `log(2, 'inf'::DOUBLE)` | `inf` | | `log('inf'::DOUBLE, 2)` | `0.0` | | `log(2, 'nan'::DOUBLE)`, `log('nan'::DOUBLE, 2)` | `nan` | | `log(0)`, `log(-0.0::DOUBLE)`, `log(2, 0)`, `log(0, 8)` | Error: `cannot take logarithm of zero` | | `log(-1)`, `log(2, -1)`, `log(-2, 8)` | Error: `cannot take logarithm of a negative number` | | `log(1, 8)`, `log(1, 1)` | Error: `divison by zero in based logarithm` | | `log(2, 8, 3)` | Error: `No function matches the given name and argument types 'log(INTEGER_LITERAL, INTEGER_LITERAL, INTEGER_LITERAL)'` | | `log('abc')` | Error: `Could not convert string 'abc' to DOUBLE` | The same cases, as the cluster returns them. They use the table and helpers from [Set up the examples](/develop/docs/dev-database-reference-sql-functions-numeric-log#set-up-the-examples): ``` run("SELECT log(NULL), log(2, NULL), log(NULL, 8), log(1), log(100), log(1e308), log(5e-324::DOUBLE)") run("SELECT log('inf'::DOUBLE), log('nan'::DOUBLE), log(2, 8), log(8, 2), log(10, 1000), log(0.5, 8), log(2, 1)") run("SELECT log(2, 'inf'::DOUBLE), log('inf'::DOUBLE, 2), log(2, 'nan'::DOUBLE), log('nan'::DOUBLE, 2)") run("SELECT log(0)") run("SELECT log(2, 0)") run("SELECT log(0, 8)") run("SELECT log(-1)") run("SELECT log(-2, 8)") run("SELECT log(1, 8)") run("SELECT log(2, 8, 3)") run(f"SELECT log('abc') FROM {TABLE} LIMIT 1") ``` ``` [(None, None, None, 0.0, 2.0, 308.0, -323.3062153431158)] [(inf, nan, 3.0, 0.33333333333333337, 3.0, -3.0, 0.0)] [(inf, 0.0, nan, nan)] OSError: cannot take logarithm of zero 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: divison by zero in based logarithm InternalError: Binder Error: No function matches the given name and argument types 'log(INTEGER_LITERAL, INTEGER_LITERAL, INTEGER_LITERAL)'. You might need to add explicit type casts. OSError: Could not convert string 'abc' to DOUBLE ``` ## Examples The base-10 logarithm of each value, its logarithm to the row's own base, and its logarithm to base 2: ``` run(f"SELECT id, b, x, log(x), log(b, x), log(2, x) FROM {TABLE} ORDER BY id LIMIT 10") ``` ``` [(1, 2.0, 8.0, 0.9030899869919435, 3.0, 3.0), (2, 10.0, 1000.0, 3.0, 3.0, 9.965784284662087), (3, 0.5, 8.0, 0.9030899869919435, -3.0, 3.0), (4, 3.0, 1.0, 0.0, 0.0, 0.0), (5, None, None, None, None, None)] ``` Keep only the values of 1,000 or more, by their base-10 logarithm: ``` run(f"SELECT id, x FROM {TABLE} WHERE log(x) >= 3 ORDER BY id LIMIT 10") ``` ``` [(2, 1000.0)] ``` ## 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 `log()` of a column is always computed by the Query Engine: - **In the `SELECT` list,** the scan reads the columns and the Query Engine computes `log()` for each row it returns. - **In `WHERE`,** the scan sends the columns for every row, and a `FILTER` step in the Query Engine computes `log()` and keeps the rows that match. No rows are skipped in storage, so every row's value reaches `log()`: a zero or a negative value fails the query, even in `WHERE`. The plan of the `WHERE` example shows the `FILTER` step above the scan: ``` plan(f"SELECT id FROM {TABLE} WHERE log(x) >= 3") ``` ``` ┌───────────────────────────┐ │ PROJECTION │ │ ──────────────────── │ │ #1 │ │ │ └─────────────┬─────────────┘ ┌─────────────┴─────────────┐ │ FILTER │ │ ──────────────────── │ │ (log(x) >= 3.0) │ │ │ └─────────────┬─────────────┘ ┌─────────────┴─────────────┐ │ VAST_SCAN │ │ ──────────────────── │ │ Function: VAST_SCAN │ │ │ │ Projections: │ │ x │ │ id │ │ │ └───────────────────────────┘ ``` ## Make it faster - **Raise the constant to the power instead.** A larger number always has a larger logarithm, so `log(x) >= 3` is the same as `x >= 1000`. That comparison of the raw column with a constant is pushed down to VAST DataBase, so rows that don't match never leave storage, and zero or negative values never reach a logarithm. Its plan has no `FILTER` step: ``` plan(f"SELECT id FROM {TABLE} WHERE x >= 1000") ``` ``` ┌───────────────────────────┐ │ VAST_SCAN │ │ ──────────────────── │ │ Function: VAST_SCAN │ │ Projections: id │ │ │ └───────────────────────────┘ ``` - **Store the logarithm if you filter on it often.** Compute it when you write the rows and keep it in its own column. - **Combine it with a pushed-down condition.** In `id > 100 AND log(x) >= 3`, `id > 100` is still evaluated in VAST DataBase, so `log()` runs only on the rows that pass it. ## Limitations and errors - **Zero, a negative value or a base of 1 fails the whole query.** One such row in a column stops the query for every row. To skip those rows, filter them out with a pushed-down condition such as `WHERE x > 0`. To keep them in the result with a NULL, use `CASE WHEN x > 0 THEN log(x) END`. - **One or two arguments, numbers only.** `log(2, 8, 3)` fails, and so does a boolean, date, interval, `BLOB` or list, with `No function matches the given name and argument types`. The error lists the two forms `log` accepts: `log(DOUBLE) -> DOUBLE` and `log(DOUBLE, DOUBLE) -> DOUBLE`. A string is converted when the query runs, and one that isn't a number fails with `Could not convert string 'abc' to DOUBLE`. - **The base comes first.** `log(8, 2)` is the logarithm of 2 to base 8, not of 8 to base 2. ``` run(f"SELECT id, CASE WHEN x > 0 THEN log(x) END FROM {TABLE} ORDER BY id LIMIT 10") run("SELECT log(2, 8), log(8, 2)") ``` ``` [(1, 0.9030899869919435), (2, 3.0), (3, 0.9030899869919435), (4, 0.0), (5, None)] [(3.0, 0.33333333333333337)] ``` ## Similar functions | Function | Base | Result for 8 (`log(8)` gives `0.9030899869919435`) | | --- | --- | --- | | [log10](/develop/docs/dev-database-reference-sql-functions-numeric-log10) | 10 | `0.9030899869919435` | | [ln](/develop/docs/dev-database-reference-sql-functions-numeric-ln) | e | `2.0794415416798357` | | [log2](/develop/docs/dev-database-reference-sql-functions-numeric-log2) | 2 | `3.0` | | `log(2, x)` | 2 | `3.0` | | `ln(x) / ln(b)` | `b` | `ln(8) / ln(2)` is `3.0` | ``` run("SELECT log(8), log10(8), ln(8), log2(8), log(2, 8), ln(8) / ln(2)") ``` ``` [(0.9030899869919435, 0.9030899869919435, 2.0794415416798357, 3.0, 3.0, 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): all the numeric functions. - [log10](/develop/docs/dev-database-reference-sql-functions-numeric-log10), [ln](/develop/docs/dev-database-reference-sql-functions-numeric-ln), [log2](/develop/docs/dev-database-reference-sql-functions-numeric-log2) and [exp](/develop/docs/dev-database-reference-sql-functions-numeric-exp). - [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.