--- title: "exp" slug: "dev-database-reference-sql-functions-numeric-exp" updated: 2026-10-30T18:18:51Z published: 2026-10-30T18:18:51Z canonical: "docs.vastdata.com/dev-database-reference-sql-functions-numeric-exp" --- > ## 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. # exp *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 e (2.718281828459045…) raised to the power `x`, as a `DOUBLE`. It's the inverse of [ln](/develop/docs/dev-database-reference-sql-functions-numeric-ln). ## Syntax ``` exp(x) ``` | Argument | Type | Description | | --- | --- | --- | | `x` | `DOUBLE` (any number) | The power to raise e to. | **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_exp`. 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 model scores, one of them very large. 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_exp"' 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}.scores" run(f"CREATE SCHEMA IF NOT EXISTS {SCHEMA}") run(f"CREATE TABLE IF NOT EXISTS {TABLE} (id BIGINT, score DOUBLE)") run(f"INSERT INTO {TABLE} VALUES " "(1, 0.0), " "(2, 2.0), " "(3, -1.5), " "(4, 1000.0), " "(5, NULL)") ``` ``` [] [] [(5,)] ``` ## What it does `exp(x)` computes ex: `exp(0)` is `1.0`, `exp(1)` is `2.718281828459045` and `exp(-1)` is `0.36787944117144233`. 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. The result grows fast. It doesn't fail when it's out of range: a result too big for a `DOUBLE` is infinity, and one too small is 0. - `exp(709)` is `8.218407461554972e+307`; from about `exp(709.8)`, the result is `inf`. - `exp(-745)` is `5e-324`, the smallest `DOUBLE` above 0; `exp(-746)` is `0.0`. - `exp('inf'::DOUBLE)` is `inf`, `exp('-inf'::DOUBLE)` is `0.0`, and `exp('nan'::DOUBLE)` is `nan`. `exp` and [ln](/develop/docs/dev-database-reference-sql-functions-numeric-ln) undo each other, up to rounding: `ln(exp(2))` is `2.0`, and `exp(ln(10))` is `10.000000000000002`. ## NULLs and edge cases | Input | Result | | --- | --- | | `NULL` | `NULL` | | `exp(0)` | `1.0` | | `exp(1)` | `2.718281828459045` | | `exp(-1)` | `0.36787944117144233` | | `exp(709)` | `8.218407461554972e+307` | | `exp(710)`, `exp(1000)` | `inf` | | `exp(-745)` | `5e-324` | | `exp(-746)`, `exp(-1000)` | `0.0` | | `exp('inf'::DOUBLE)`, `exp('-inf'::DOUBLE)`, `exp('nan'::DOUBLE)` | `inf`, `0.0`, `nan` | | `exp(ln(10))` | `10.000000000000002` | | `exp(1::FLOAT)` | a `DOUBLE` | | `exp('12')` | `162754.79141900392` | | `exp('abc')` | Error: `Could not convert string 'abc' to DOUBLE` | | `exp(1, 2)` | Error: `No function matches the given name and argument types 'exp(INTEGER_LITERAL, INTEGER_LITERAL)'` | | A boolean, date, interval, `BLOB` or list | Error: `No function matches the given name and argument types`, for example `'exp(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-exp#set-up-the-examples): ``` run("SELECT exp(NULL), exp(0), exp(1), exp(-1), exp(709), exp(710), exp(1000)") run("SELECT exp(-745), exp(-746), exp(-1000), exp('inf'::DOUBLE), exp('-inf'::DOUBLE), exp('nan'::DOUBLE)") run("SELECT exp(ln(10)), typeof(exp(1::FLOAT))") run(f"SELECT exp('12') FROM {TABLE} LIMIT 1") run(f"SELECT exp('abc') FROM {TABLE} LIMIT 1") run("SELECT exp(1, 2)") run("SELECT exp(true)") ``` ``` [(None, 1.0, 2.718281828459045, 0.36787944117144233, 8.218407461554972e+307, inf, inf)] [(5e-324, 0.0, 0.0, inf, 0.0, nan)] [(10.000000000000002, 'DOUBLE')] [(162754.79141900392,)] OSError: Could not convert string 'abc' to DOUBLE InternalError: Binder Error: No function matches the given name and argument types 'exp(INTEGER_LITERAL, INTEGER_LITERAL)'. You might need to add explicit type casts. InternalError: Binder Error: No function matches the given name and argument types 'exp(BOOLEAN)'. You might need to add explicit type casts. ``` ## Examples e to the power of each score, and the logistic function `1 / (1 + exp(-score))`, which maps any score to a probability between 0 and 1. A score of 1000 overflows `exp(score)` to infinity, while `exp(-score)` goes to 0 and the probability to 1: ``` run(f"SELECT id, exp(score), 1 / (1 + exp(-score)) FROM {TABLE} ORDER BY id LIMIT 10") ``` ``` [(1, 1.0, 0.5), (2, 7.38905609893065, 0.8807970779778823), (3, 0.22313016014842982, 0.18242552380635635), (4, inf, 1.0), (5, None, None)] ``` Keep only the scores whose exponential is above 1: ``` run(f"SELECT id, score FROM {TABLE} WHERE exp(score) > 1 ORDER BY id LIMIT 10") ``` ``` [(2, 2.0), (4, 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 `exp()` of a column is always computed by the Query Engine: - **In the `SELECT` list,** the scan reads the column and the Query Engine computes `exp()` for each row it returns. - **In `WHERE`,** the scan sends the column for every row, and a `FILTER` step in the Query Engine computes `exp()` 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 exp(score) > 1") ``` ``` ┌───────────────────────────┐ │ PROJECTION │ │ ──────────────────── │ │ #1 │ │ │ └─────────────┬─────────────┘ ┌─────────────┴─────────────┐ │ FILTER │ │ ──────────────────── │ │ (exp(score) > 1.0) │ │ │ └─────────────┬─────────────┘ ┌─────────────┴─────────────┐ │ VAST_SCAN │ │ ──────────────────── │ │ Function: VAST_SCAN │ │ │ │ Projections: │ │ score │ │ id │ │ │ └───────────────────────────┘ ``` ## Make it faster - **Take the logarithm of the constant instead.** A larger number always has a larger exponential, so `exp(score) > 1` is the same as `score > 0`, and `exp(score) > c` is the same as `score > ln(c)` for a positive `c`. A comparison of the raw column with a constant is pushed down to VAST DataBase, so rows that don't match never leave storage. Its plan has no `FILTER` step: ``` plan(f"SELECT id FROM {TABLE} WHERE score > 0") ``` ``` ┌───────────────────────────┐ │ VAST_SCAN │ │ ──────────────────── │ │ Function: VAST_SCAN │ │ Projections: id │ │ │ └───────────────────────────┘ ``` - **Store the result 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 exp(score) > 1`, `id > 100` is still evaluated in VAST DataBase, so `exp()` runs only on the rows that pass it. ## Limitations and errors - **Numbers only, one argument.** A boolean, date, interval, `BLOB` or list fails with `No function matches the given name and argument types`; the error lists the one form `exp` accepts, `exp(DOUBLE) -> DOUBLE`. For a power of another base, use [pow](/develop/docs/dev-database-reference-sql-functions-numeric-pow). A string is converted when the query runs, and one that isn't a number fails with `Could not convert string 'abc' to DOUBLE`. - **Overflow gives infinity, not an error.** Test for it with [isinf](/develop/docs/dev-database-reference-sql-functions-numeric-isinf), or keep the input below about 709. - **No `e()`, `exp2` or `expm1`.** They fail with `Scalar Function with name ... does not exist!`. Use `exp(1)` for e, `pow(2, x)` for 2x, and `exp(x) - 1` for `expm1(x)`. ``` run(f"SELECT id, isinf(exp(score)) FROM {TABLE} ORDER BY id LIMIT 10") run("SELECT e()") run("SELECT exp(1), pow(2, 3), exp(1) - 1") ``` ``` [(1, False), (2, False), (3, False), (4, True), (5, None)] InternalError: Catalog Error: Scalar Function with name e does not exist! [(2.718281828459045, 8.0, 1.718281828459045)] ``` ## Similar functions | Function | Computes | Result | | --- | --- | --- | | `exp(2)` | e2 | `7.38905609893065` | | [pow](/develop/docs/dev-database-reference-sql-functions-numeric-pow) `(exp(1), 2)` | the same, through a power; rounded differently | `7.3890560989306495` | | [ln](/develop/docs/dev-database-reference-sql-functions-numeric-ln) | the inverse of `exp`: `ln(exp(2))` | `2.0` | | `exp(y * ln(x))` | `x` to the power `y`, like `pow`: `exp(10 * ln(2))` | `1024.0` | | [sinh](/develop/docs/dev-database-reference-sql-functions-numeric-sinh) | `(exp(x) - exp(-x)) / 2` | `sinh(1)` is `1.1752011936438014` | ``` run("SELECT exp(1), pow(exp(1), 2), exp(2), ln(exp(2))") run("SELECT exp(10 * ln(2)), pow(2, 10)") run("SELECT sinh(1), (exp(1) - exp(-1)) / 2") ``` ``` [(2.718281828459045, 7.3890560989306495, 7.38905609893065, 2.0)] [(1024.0, 1024.0)] [(1.1752011936438014, 1.1752011936438014)] ``` 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. - [ln](/develop/docs/dev-database-reference-sql-functions-numeric-ln), [pow](/develop/docs/dev-database-reference-sql-functions-numeric-pow) and [isinf](/develop/docs/dev-database-reference-sql-functions-numeric-isinf). - [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.