--- title: "atan" slug: "dev-database-reference-sql-functions-numeric-atan" updated: 2026-10-30T18:18:51Z published: 2026-10-30T18:18:51Z canonical: "docs.vastdata.com/dev-database-reference-sql-functions-numeric-atan" --- > ## 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. # atan *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) › Inverse trigonometry.* Returns the arc tangent of a number: the angle, in radians from -pi/2 to pi/2, whose tangent is that number. It takes any number, including infinity. To get the angle of a point, with the right quadrant, use [atan2](/develop/docs/dev-database-reference-sql-functions-numeric-atan2). ## Syntax ``` atan(x) ``` | Argument | Type | Description | | --- | --- | --- | | `x` | Any number (`DOUBLE`, `REAL`, an integer or a `DECIMAL`) | The tangent: any value, including `inf` and `-inf`. | **Returns:** `DOUBLE`, from -pi/2 to pi/2. ## 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_atan`. 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 six road segments with their gradient (rise over run). Row 3 has no value: ``` 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_atan"' 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}.segments" run(f"CREATE SCHEMA IF NOT EXISTS {SCHEMA}") run(f"CREATE TABLE IF NOT EXISTS {TABLE} (id BIGINT, gradient DOUBLE)") run(f"INSERT INTO {TABLE} VALUES " "(1, 0.05), (2, -0.12), (3, NULL), (4, 0.0), (5, 1.0), (6, 2.5)") ``` ``` [] [] [(6,)] ``` ## What it does `atan(x)` is the inverse of [tan](/develop/docs/dev-database-reference-sql-functions-numeric-tan) on the range -pi/2 to pi/2: it returns the angle `a`, in radians, for which `tan(a) = x`. It takes any number. As `x` grows, the result approaches pi/2, and `atan` of infinity is pi/2 (`1.5707963267948966`). To get degrees, wrap it in [degrees](/develop/docs/dev-database-reference-sql-functions-numeric-degrees). | Call | Result | | --- | --- | | `atan(0)` | `0.0` | | `atan(1)` | `0.7853981633974483` (pi/4) | | `atan(-1)` | `-0.7853981633974483` | | `atan(1e308)` | `1.5707963267948966` (pi/2) | | `atan(-1e308)` | `-1.5707963267948966` | The result is a `DOUBLE` for every numeric argument type: an integer, a `REAL`, a `DECIMAL` or a `DOUBLE`. ``` run("SELECT atan(0), atan(1), atan(-1), atan(1e308), atan(-1e308)") run("SELECT typeof(atan(1::INTEGER)), typeof(atan(0.5::FLOAT)), typeof(atan(0.5))") ``` ``` [(0.0, 0.7853981633974483, -0.7853981633974483, 1.5707963267948966, -1.5707963267948966)] [('DOUBLE', 'DOUBLE', 'DOUBLE')] ``` ## NULLs and edge cases | Input | Result | | --- | --- | | `NULL` | `NULL` | | `'inf'::DOUBLE` | `1.5707963267948966` (pi/2) | | `'-inf'::DOUBLE` | `-1.5707963267948966` | | `'nan'::DOUBLE` | `nan` | | `-0.0::DOUBLE` | `-0.0`: the sign of zero is kept | | The smallest positive `DOUBLE` (`5e-324`) | `5e-324` | | `'12'` (a string literal holding a number) | Converted to `DOUBLE`: `1.4876550949064553` | | `'abc'` (a string that isn't a number) | 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 `'atan(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-atan#set-up-the-examples): ``` run("SELECT atan(NULL), atan('inf'::DOUBLE), atan('-inf'::DOUBLE), atan('nan'::DOUBLE)") run("SELECT atan(-0.0::DOUBLE), atan(5e-324::DOUBLE), atan('12')") run("SELECT atan('abc')") run("SELECT atan(DATE '2026-10-16')") ``` ``` [(None, 1.5707963267948966, -1.5707963267948966, nan)] [(-0.0, 5e-324, 1.4876550949064553)] OSError: Could not convert string 'abc' to DOUBLE InternalError: Binder Error: No function matches the given name and argument types 'atan(DATE)'. You might need to add explicit type casts. ``` ## Examples The angle of each segment, in radians and in degrees. A gradient of 1 (one metre up for each metre along) is 45 degrees: ``` run(f"SELECT id, gradient, atan(gradient), degrees(atan(gradient)) FROM {TABLE} ORDER BY id LIMIT 10") ``` ``` [(1, 0.05, 0.049958395721942765, 2.862405226111748), (2, -0.12, -0.11942892601833845, -6.84277341263094), (3, None, None, None), (4, 0.0, 0.0, 0.0), (5, 1.0, 0.7853981633974483, 45.0), (6, 2.5, 1.1902899496825317, 68.19859051364818)] ``` Keep only the segments steeper than 30 degrees: ``` run(f"SELECT id, gradient FROM {TABLE} WHERE degrees(atan(gradient)) > 30 ORDER BY id LIMIT 10") ``` ``` [(5, 1.0), (6, 2.5)] ``` ## 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 `atan()` is always computed by the Query Engine: - **In the `SELECT` list,** the scan reads the column and the Query Engine computes `atan()` for each row it returns. - **In `WHERE`,** the scan sends the column for every row, and a `FILTER` step in the Query Engine computes `atan()` 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 degrees(atan(gradient)) > 30") ``` ``` ┌───────────────────────────┐ │ PROJECTION │ │ ──────────────────── │ │ #1 │ │ │ └─────────────┬─────────────┘ ┌─────────────┴─────────────┐ │ FILTER │ │ ──────────────────── │ │ (degrees(atan(gradient)) >│ │ 30.0) │ │ │ └─────────────┬─────────────┘ ┌─────────────┴─────────────┐ │ VAST_SCAN │ │ ──────────────────── │ │ Function: VAST_SCAN │ │ │ │ Projections: │ │ gradient │ │ id │ │ │ └───────────────────────────┘ ``` ## Make it faster - **Compare the raw column with the tangent of the angle.** `atan()` grows as its argument grows, so `degrees(atan(gradient)) > 30` is the same condition as `gradient > tan(radians(30))`. A function on constants is computed once, before the scan, so the second form is a comparison of the column with a constant, which is pushed down to VAST DataBase. Its plan has no `FILTER` step: ``` plan(f"SELECT id FROM {TABLE} WHERE gradient > tan(radians(30))") run(f"SELECT id, gradient FROM {TABLE} WHERE gradient > tan(radians(30)) ORDER BY id LIMIT 10") ``` ``` ┌───────────────────────────┐ │ VAST_SCAN │ │ ──────────────────── │ │ Function: VAST_SCAN │ │ Projections: id │ │ │ └───────────────────────────┘ [(5, 1.0), (6, 2.5)] ``` - **Store the angle if you filter on it often.** Compute it when you write the rows and keep it in its own column: a condition on that column is pushed down, a condition on `atan()` isn't. ## Limitations and errors - **One argument: no quadrant.** `atan(y / x)` can't tell the point (1, 1) from (-1, -1), because both ratios are 1. Use [atan2](/develop/docs/dev-database-reference-sql-functions-numeric-atan2)`(y, x)`, which takes the two coordinates separately: ``` run("SELECT atan(-1 / -1), atan2(-1, -1), atan(1 / -1), atan2(1, -1)") ``` ``` [(0.7853981633974483, -2.356194490192345, -0.7853981633974483, 2.356194490192345)] ``` - **Numbers only.** A `BLOB`, a date, a boolean, a list or an interval fails with `No function matches the given name and argument types`; the error lists the one form `atan` has, `atan(DOUBLE) -> DOUBLE`. A string literal is converted to `DOUBLE` if it holds a number, and otherwise fails with `Could not convert string 'abc' to DOUBLE`. - **Two arguments aren't accepted.** `atan(1, 2)` fails with `No function matches the given name and argument types 'atan(INTEGER_LITERAL, INTEGER_LITERAL)'`; the two-argument form is `atan2`. - **Radians only.** There's no degrees variant; use `degrees(atan(x))`. ## Similar functions | Function | Returns | Result for `0.5` | | --- | --- | --- | | `atan(x)` | the angle whose tangent is `x`, from -pi/2 to pi/2 | `0.4636476090008061` | | [atan2](/develop/docs/dev-database-reference-sql-functions-numeric-atan2) | the angle of the point (x, y), from -pi to pi | `atan2(0.5, 1)` and `atan2(1, 2)`: `0.4636476090008061` | | [asin](/develop/docs/dev-database-reference-sql-functions-numeric-asin) | the angle whose sine is `x` | `0.5235987755982989` | | [acos](/develop/docs/dev-database-reference-sql-functions-numeric-acos) | the angle whose cosine is `x` | `1.0471975511965979` | | [tan](/develop/docs/dev-database-reference-sql-functions-numeric-tan) | the tangent of an angle: the inverse of `atan` | `tan(atan(0.5))` gives back about `0.5` | | [atanh](/develop/docs/dev-database-reference-sql-functions-numeric-atanh) | the inverse hyperbolic tangent, for -1 to 1 | | | [pi](/develop/docs/dev-database-reference-sql-functions-numeric-pi) | pi; `pi() = 4 * atan(1)` is true | | ``` run("SELECT atan(0.5), atan2(0.5, 1), atan2(1, 2), asin(0.5), acos(0.5), tan(atan(0.5)), atanh(0.5)") run("SELECT pi() = 4 * atan(1)") ``` ``` [(0.4636476090008061, 0.4636476090008061, 0.4636476090008061, 0.5235987755982989, 1.0471975511965979, 0.49999999999999994, 0.5493061443340548)] [(True,)] ``` 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. - [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.