--- title: "ln" slug: "dev-database-reference-sql-functions-numeric-ln" updated: 2026-10-30T18:18:51Z published: 2026-10-30T18:18:51Z canonical: "docs.vastdata.com/dev-database-reference-sql-functions-numeric-ln" --- > ## 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. # ln *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 natural logarithm (base e) of a number, as a `DOUBLE`. It's the inverse of [exp](/develop/docs/dev-database-reference-sql-functions-numeric-exp). Zero and negative numbers fail the query. ## Syntax ``` ln(x) ``` | Argument | Type | Description | | --- | --- | --- | | `x` | `DOUBLE` (any number) | The number to take the logarithm of. It must be greater than 0. | **Returns:** `DOUBLE`, whatever the argument type. ## 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_ln`. 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 three days of trading in one share: the opening and closing prices and the number of shares traded. On one day, no shares were traded; 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_ln"' 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}.trades" run(f"CREATE SCHEMA IF NOT EXISTS {SCHEMA}") run(f"CREATE TABLE IF NOT EXISTS {TABLE} (id BIGINT, open_price DOUBLE, close_price DOUBLE, volume BIGINT)") run(f"INSERT INTO {TABLE} VALUES " "(1, 100.0, 110.0, 5000), " "(2, 50.0, 45.0, 0), " "(3, 20.0, 20.0, 120), " "(4, NULL, NULL, NULL)") ``` ``` [] [] [(4,)] ``` ## What it does `ln(x)` returns the power that e must be raised to to give `x`: `ln(1)` is `0.0`, `ln(exp(1))` is `1.0`, and `ln(100)` is `4.605170185988092`. The argument is 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. **Zero and negative numbers are errors,** not infinity or NaN: `ln(0)` fails with `cannot take logarithm of zero`, and `ln(-1)` with `cannot take logarithm of a negative number`. The error stops the whole query: if one row of a column is 0 or negative, `ln()` of that column fails for every row. A negative zero (`-0.0::DOUBLE`) counts as zero, and `'-inf'::DOUBLE` as negative. Keep those values away from `ln()` with `WHERE` or `CASE`; see [Limitations and errors](/develop/docs/dev-database-reference-sql-functions-numeric-ln#limitations-and-errors). `ln('inf'::DOUBLE)` is `inf` and `ln('nan'::DOUBLE)` is `nan`. Very small positive numbers work: `ln(5e-324::DOUBLE)`, the smallest `DOUBLE` above 0, is `-744.4400719213812`. **`log(x)` isn't the natural logarithm.** In the VAST Query Engine, `log(x)` with one argument is the base-10 logarithm: `log(exp(1))` is `0.4342944819032518`. Use `ln` for base e. ## NULLs and edge cases | Input | Result | | --- | --- | | `NULL` | `NULL` | | `ln(1)` | `0.0` | | `ln(exp(1))` | `1.0` | | `ln(100)` | `4.605170185988092` | | `ln(1e308)` | `709.1962086421661` | | `ln(5e-324::DOUBLE)` | `-744.4400719213812` | | `ln('inf'::DOUBLE)`, `ln('nan'::DOUBLE)` | `inf`, `nan` | | `ln(100::INTEGER)` | a `DOUBLE` | | `ln('12')` | `2.4849066497880004` | | `ln(0)`, `ln(-0.0::DOUBLE)` | Error: `cannot take logarithm of zero` | | `ln(-1)`, `ln('-inf'::DOUBLE)` | Error: `cannot take logarithm of a negative number` | | `ln('abc')` | Error: `Could not convert string 'abc' to DOUBLE` | | A boolean, date, interval, `BLOB` or list | Error: `No function matches the given name and argument types`, for example `'ln(BOOLEAN)'` | 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-ln#set-up-the-examples): ``` run("SELECT ln(NULL), ln(1), ln(exp(1)), ln(100), ln(1e308), ln(5e-324::DOUBLE)") run("SELECT ln('inf'::DOUBLE), ln('nan'::DOUBLE), typeof(ln(100::INTEGER))") run(f"SELECT ln('12') FROM {TABLE} LIMIT 1") run("SELECT ln(0)") run("SELECT ln(-0.0::DOUBLE)") run("SELECT ln(-1)") run("SELECT ln('-inf'::DOUBLE)") run(f"SELECT ln('abc') FROM {TABLE} LIMIT 1") run("SELECT ln(true)") ``` ``` [(None, 0.0, 1.0, 4.605170185988092, 709.1962086421661, -744.4400719213812)] [(inf, nan, 'DOUBLE')] [(2.4849066497880004,)] 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 'ln(BOOLEAN)'. You might need to add explicit type casts. ``` ## Examples The log return of each day, `ln(close_price / open_price)`: positive when the price rose, negative when it fell, and 0 when it didn't move: ``` run(f"SELECT id, open_price, close_price, ln(close_price / open_price) FROM {TABLE} ORDER BY id LIMIT 10") ``` ``` [(1, 100.0, 110.0, 0.09531017980432493), (2, 50.0, 45.0, -0.10536051565782628), (3, 20.0, 20.0, 0.0), (4, None, None, None)] ``` Keep only the days on which the price rose: ``` run(f"SELECT id, open_price, close_price FROM {TABLE} WHERE ln(close_price / open_price) > 0 ORDER BY id LIMIT 10") ``` ``` [(1, 100.0, 110.0)] ``` ## 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 `ln()` of a column is always computed by the Query Engine: - **In the `SELECT` list,** the scan reads the column and the Query Engine computes `ln()` for each row it returns. - **In `WHERE`,** the scan sends the column for every row, and a `FILTER` step in the Query Engine computes `ln()` and keeps the rows that match. No rows are skipped in storage, so every row's value reaches `ln()`, including a zero that fails the query. A function of a constant is different: it's computed once, before the scan, so `volume > exp(5)` compares `volume` with the constant `148.4131591025766` (see the plan in [Make it faster](/develop/docs/dev-database-reference-sql-functions-numeric-ln#make-it-faster)). The plan of the `WHERE` example shows the `FILTER` step above the scan: ``` plan(f"SELECT id FROM {TABLE} WHERE ln(close_price / open_price) > 0") ``` ``` ┌───────────────────────────┐ │ PROJECTION │ │ ──────────────────── │ │ #2 │ │ │ └─────────────┬─────────────┘ ┌─────────────┴─────────────┐ │ FILTER │ │ ──────────────────── │ │ (ln((close_price / │ │ open_price)) > 0.0) │ │ │ └─────────────┬─────────────┘ ┌─────────────┴─────────────┐ │ VAST_SCAN │ │ ──────────────────── │ │ Function: VAST_SCAN │ │ │ │ Projections: │ │ close_price │ │ open_price │ │ id │ │ │ └───────────────────────────┘ ``` ## Make it faster - **Apply `exp` to the constant instead.** A larger number always has a larger logarithm, so `ln(volume) > 5` is the same as `volume > exp(5)` for positive values. The second form doesn't call `ln()` on any row, so it also keeps the zero volume away from it: in `WHERE`, `ln(volume) > 5` fails on that row, and `volume > exp(5)` doesn't. On a `DOUBLE` column, such a comparison with a constant is pushed down to VAST DataBase (as `score > 0` is on the [exp](/develop/docs/dev-database-reference-sql-functions-numeric-exp#make-it-faster) page). `volume` is a `BIGINT`, though, so the plan casts it to `DOUBLE` to compare it with `148.4131591025766`, and that comparison runs in a `FILTER` step: ``` run(f"SELECT id FROM {TABLE} WHERE ln(volume) > 5 ORDER BY id LIMIT 10") run(f"SELECT id FROM {TABLE} WHERE volume > exp(5) ORDER BY id LIMIT 10") plan(f"SELECT id FROM {TABLE} WHERE volume > exp(5)") ``` ``` OSError: cannot take logarithm of zero [(1,)] ┌───────────────────────────┐ │ PROJECTION │ │ ──────────────────── │ │ #1 │ │ │ └─────────────┬─────────────┘ ┌─────────────┴─────────────┐ │ FILTER │ │ ──────────────────── │ │ (CAST(volume AS DOUBLE) > │ │ 148.4131591025766) │ │ │ └─────────────┬─────────────┘ ┌─────────────┴─────────────┐ │ VAST_SCAN │ │ ──────────────────── │ │ Function: VAST_SCAN │ │ │ │ Projections: │ │ volume │ │ 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 ln(close_price / open_price) > 0`, `id > 100` is still evaluated in VAST DataBase, so `ln()` runs only on the rows that pass it. ## Limitations and errors - **Zero or a negative value fails the whole query.** `ln(volume)` fails with `cannot take logarithm of zero` because one day has a volume of 0, and returns no rows at all. To skip those rows, filter them out with a pushed-down condition such as `WHERE volume > 0`. To keep them in the result with a NULL, use `CASE WHEN volume > 0 THEN ln(volume) END`. - **Numbers only.** A boolean, date, interval, `BLOB` or list fails with `No function matches the given name and argument types`; the error lists the one form `ln` accepts, `ln(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`. - **No `log1p` or `naturallog`.** They fail with `Scalar Function with name ... does not exist!`. Use `ln(1 + x)`, but for `x` very close to 0 it loses precision: `ln(1 + 1e-17)` is `0.0`. ``` run(f"SELECT ln(volume) FROM {TABLE}") run(f"SELECT id, ln(volume) FROM {TABLE} WHERE volume > 0 ORDER BY id LIMIT 10") run(f"SELECT id, CASE WHEN volume > 0 THEN ln(volume) END FROM {TABLE} ORDER BY id LIMIT 10") run("SELECT log1p(1)") run("SELECT ln(1 + 1e-10), ln(1 + 1e-17)") ``` ``` OSError: cannot take logarithm of zero [(1, 8.517193191416238), (3, 4.787491742782046)] [(1, 8.517193191416238), (2, None), (3, 4.787491742782046), (4, None)] InternalError: Catalog Error: Scalar Function with name log1p does not exist! [(1.000000082690371e-10, 0.0)] ``` ## Similar functions | Function | Base | Result for 100 (`ln` gives `4.605170185988092`) | | --- | --- | --- | | [log](/develop/docs/dev-database-reference-sql-functions-numeric-log) `(x)` | 10 | `2.0` | | [log10](/develop/docs/dev-database-reference-sql-functions-numeric-log10) | 10 | `2.0` | | [log2](/develop/docs/dev-database-reference-sql-functions-numeric-log2) | 2 | `6.643856189774724` | | [log](/develop/docs/dev-database-reference-sql-functions-numeric-log) `(b, x)` | `b` | `log(2, 100)` is `6.643856189774724`; `log(exp(1), 100)` is `4.605170185988092` | | [exp](/develop/docs/dev-database-reference-sql-functions-numeric-exp) | the inverse of `ln` | `ln(exp(2))` is `2.0` | ``` run("SELECT ln(100), log(100), log10(100), log2(100), log(10, 100), log(2, 100), log(exp(1), 100)") run("SELECT ln(8) / ln(2), log2(8), ln(exp(2))") ``` ``` [(4.605170185988092, 2.0, 2.0, 6.643856189774724, 2.0, 6.643856189774724, 4.605170185988092)] [(3.0, 3.0, 2.0)] ``` 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. - [exp](/develop/docs/dev-database-reference-sql-functions-numeric-exp), [log](/develop/docs/dev-database-reference-sql-functions-numeric-log), [log10](/develop/docs/dev-database-reference-sql-functions-numeric-log10) and [log2](/develop/docs/dev-database-reference-sql-functions-numeric-log2). - [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.