--- title: "lgamma" slug: "dev-database-reference-sql-functions-numeric-lgamma" updated: 2026-10-30T18:18:51Z published: 2026-10-30T18:18:51Z canonical: "docs.vastdata.com/dev-database-reference-sql-functions-numeric-lgamma" --- > ## 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. # lgamma *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 of the absolute value of the gamma function: `ln(abs(gamma(x)))`, computed directly, so it stays finite where `gamma(x)` itself is too large for a `DOUBLE`. `lgamma(172)` is `711.71472580229`, while `gamma(172)` is `inf`. It has no aliases. ## Syntax ``` lgamma(x) ``` | Argument | Type | Description | | --- | --- | --- | | `x` | `DOUBLE` (any integer, `DECIMAL` or `FLOAT` is converted) | The number to take the log-gamma of. It can't be 0. | **Returns:** `DOUBLE`. **Aliases:** none. ## 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_lgamma`. 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 group sizes `n`, each with a number `k` of members to choose from it. 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_lgamma"' 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}.groups" run(f"CREATE SCHEMA IF NOT EXISTS {SCHEMA}") run(f"CREATE TABLE IF NOT EXISTS {TABLE} (id BIGINT, n DOUBLE, k DOUBLE)") run(f"INSERT INTO {TABLE} VALUES " "(1, 5, 2), " "(2, 52, 5), " "(3, 200, 2), " "(4, NULL, NULL)") ``` ``` [] [] [(4,)] ``` ## What it does `lgamma(x)` is the natural logarithm of the absolute value of [gamma](/develop/docs/dev-database-reference-sql-functions-numeric-gamma)`(x)`. For a positive whole number `n`, that's the logarithm of (n − 1)!: `lgamma(5)` is `3.1780538303479458`, the logarithm of 24, and `exp(lgamma(5))` gives back `24.000000000000004`. `lgamma(1)` and `lgamma(2)` are both `0.0`, because 0! and 1! are 1. Because it computes the logarithm directly, `lgamma()` stays finite far beyond the range of `gamma()`: `lgamma(172)` is `711.71472580229` and `lgamma(1e300)` is `6.897755278982137e+302`, where `gamma()` returns `inf`. Use it when you need ratios or products of large factorials: subtract and add logarithms, then take [exp](/develop/docs/dev-database-reference-sql-functions-numeric-exp) of the result. It takes the absolute value first, so it doesn't show the sign of a negative `gamma()`: `gamma(-0.5)` is `-3.5449077018110318`, and `lgamma(-0.5)` is `1.2655121234846454`, the logarithm of 3.5449… At a negative whole number, where the gamma function isn't defined, `lgamma()` returns `inf`. At 0 it is an error. The argument is converted to `DOUBLE`, and so is the result. A string of digits is converted too: `lgamma('12')` returns `17.502307845873887`. ## NULLs and edge cases | Input | Result | | --- | --- | | `NULL` | `NULL` | | `1`, `2` | `0.0` | | `0.5` | `0.5723649429247001` | | `172` | `711.71472580229` | | `1e300` | `6.897755278982137e+302` | | `-0.5` | `1.2655121234846454` | | `-1`, `-2` (negative whole numbers) | `inf` | | `'inf'::DOUBLE`, `'-inf'::DOUBLE` | `inf` | | `'nan'::DOUBLE` | `nan` | | `'12'` (a string of digits) | `17.502307845873887` | | `0` or `-0.0::DOUBLE` | Error: `cannot take log gamma of zero` | | `'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 `'lgamma(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-lgamma#set-up-the-examples): ``` run("SELECT lgamma(NULL), lgamma(1), lgamma(2), lgamma(0.5), lgamma(172), lgamma(1e300)") run("SELECT lgamma(-0.5), lgamma(-1), lgamma(-2)") run("SELECT lgamma('inf'::DOUBLE), lgamma('-inf'::DOUBLE), lgamma('nan'::DOUBLE)") run("SELECT lgamma('12')") run("SELECT lgamma(0)") run("SELECT lgamma(-0.0::DOUBLE)") run("SELECT lgamma('abc')") run("SELECT lgamma('\\xAA'::BLOB)") run("SELECT lgamma(DATE '2026-10-16')") run("SELECT lgamma(true)") run("SELECT lgamma([1, 2])") run("SELECT lgamma(INTERVAL 1 DAY)") ``` ``` [(None, 0.0, 0.0, 0.5723649429247001, 711.71472580229, 6.897755278982137e+302)] [(1.2655121234846454, inf, inf)] [(inf, inf, nan)] [(17.502307845873887,)] OSError: cannot take log gamma of zero OSError: cannot take log gamma of zero OSError: Could not convert string 'abc' to DOUBLE InternalError: Binder Error: No function matches the given name and argument types 'lgamma(BLOB)'. You might need to add explicit type casts. InternalError: Binder Error: No function matches the given name and argument types 'lgamma(DATE)'. You might need to add explicit type casts. InternalError: Binder Error: No function matches the given name and argument types 'lgamma(BOOLEAN)'. You might need to add explicit type casts. InternalError: Binder Error: No function matches the given name and argument types 'lgamma(INTEGER[])'. You might need to add explicit type casts. InternalError: Binder Error: No function matches the given name and argument types 'lgamma(INTERVAL)'. You might need to add explicit type casts. ``` ## Examples The number of ways to choose `k` members of a group of `n`, n! / (k! (n − k)!), computed from logarithms so that no factorial has to fit in a `DOUBLE` on its own. `lgamma(n + 1)` is the logarithm of n!: ``` run(f"SELECT id, n, k, exp(lgamma(n + 1) - lgamma(k + 1) - lgamma(n - k + 1)) FROM {TABLE} ORDER BY id LIMIT 10") ``` ``` [(1, 5.0, 2.0, 9.999999999999998), (2, 52.0, 5.0, 2598960.000000018), (3, 200.0, 2.0, 19899.999999999513), (4, None, None, None)] ``` The result is a `DOUBLE`, so it carries floating-point rounding: round it with [round](/develop/docs/dev-database-reference-sql-functions-numeric-round) if you need a whole number. Keep only the groups whose log-factorial is more than 10: ``` run(f"SELECT id, n FROM {TABLE} WHERE lgamma(n + 1) > 10 ORDER BY id LIMIT 10") ``` ``` [(2, 52.0), (3, 200.0)] ``` ## 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 `lgamma()` is always computed by the Query Engine: - **In the `SELECT` list,** the scan reads the column and the Query Engine computes `lgamma()` for each row it returns. - **In `WHERE`,** the scan sends the column for every row, and a `FILTER` step in the Query Engine computes `lgamma()` 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 lgamma(n + 1) > 10") ``` ``` ┌───────────────────────────┐ │ PROJECTION │ │ ──────────────────── │ │ #1 │ │ │ └─────────────┬─────────────┘ ┌─────────────┴─────────────┐ │ FILTER │ │ ──────────────────── │ │ (lgamma((n + 1.0)) > 10.0)│ │ │ └─────────────┬─────────────┘ ┌─────────────┴─────────────┐ │ VAST_SCAN │ │ ──────────────────── │ │ Function: VAST_SCAN │ │ │ │ Projections: │ │ n │ │ id │ │ │ └───────────────────────────┘ ``` ## Make it faster - **Compare the column where you can.** For arguments of 2 or more, `lgamma()` grows with its argument, so a threshold on `lgamma(n + 1)` is a threshold on `n`. A comparison of the raw column with a constant is pushed down to VAST DataBase, so rows that don't match never leave storage. The plan for `n > 10` has no `FILTER` step: ``` plan(f"SELECT id FROM {TABLE} WHERE n > 10") ``` ``` ┌───────────────────────────┐ │ VAST_SCAN │ │ ──────────────────── │ │ Function: VAST_SCAN │ │ Projections: id │ │ │ └───────────────────────────┘ ``` - **Store the value if you filter on it often.** Compute `lgamma()` when you write the rows and keep it in its own column: a comparison of that column is pushed down, `lgamma()` in `WHERE` isn't. - **Combine it with a pushed-down condition.** In `id > 100 AND lgamma(n + 1) > 10`, `id > 100` is still evaluated in VAST DataBase, so `lgamma()` runs only on the rows that pass it. ## Limitations and errors - **Zero is an error.** `lgamma(0)` and `lgamma(-0.0::DOUBLE)` fail with `cannot take log gamma of zero`. On a table, one zero fails the whole query, not just that row. Keep zeros out of the column, or filter them out with a condition on the raw column. - **Negative whole numbers give `inf`,** not an error or `NULL`. Test for it with [isinf](/develop/docs/dev-database-reference-sql-functions-numeric-isinf). - **No sign.** `lgamma()` is the logarithm of the absolute value; for the sign of the gamma function of a negative number, use [gamma](/develop/docs/dev-database-reference-sql-functions-numeric-gamma) or [sign](/develop/docs/dev-database-reference-sql-functions-numeric-sign)`(gamma(x))` where `gamma()` doesn't overflow. - **Floating point, not exact.** `exp(lgamma(6))` is `119.99999999999997`, not 120. For exact factorials of an `INTEGER`, use [factorial](/develop/docs/dev-database-reference-sql-functions-numeric-factorial). - **Numbers only.** A `BLOB`, a date, a boolean, a list or an interval fails with `No function matches the given name and argument types`. A string is converted to `DOUBLE`, so a string that isn't a number fails with `Could not convert string ... to DOUBLE`. ``` run("SELECT lgamma(-0.5), gamma(-0.5), exp(lgamma(6))") ``` ``` [(1.2655121234846454, -3.5449077018110318, 119.99999999999997)] ``` ## Similar functions | Function | Computes | Result for `172` | Result for `6` | | --- | --- | --- | --- | | `lgamma(x)` | ln of the absolute value of the gamma function | `711.71472580229` | `4.787491742782046` (the logarithm of 120) | | [gamma](/develop/docs/dev-database-reference-sql-functions-numeric-gamma) | the gamma function | `inf` | `120.0` | | `exp(lgamma(x))` | the gamma function's absolute value, from `lgamma` | | `119.99999999999997` | | [factorial](/develop/docs/dev-database-reference-sql-functions-numeric-factorial) `(x - 1)` | the exact factorial of an `INTEGER` | | `factorial(5)` = `120` | | [ln](/develop/docs/dev-database-reference-sql-functions-numeric-ln) | the natural logarithm | | | ``` run("SELECT lgamma(172), gamma(172)") run("SELECT lgamma(6), gamma(6), exp(lgamma(6)), factorial(5)") ``` ``` [(711.71472580229, inf)] [(4.787491742782046, 120.0, 119.99999999999997, Decimal('120'))] ``` 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. - [gamma](/develop/docs/dev-database-reference-sql-functions-numeric-gamma), [factorial](/develop/docs/dev-database-reference-sql-functions-numeric-factorial), [exp](/develop/docs/dev-database-reference-sql-functions-numeric-exp) and [ln](/develop/docs/dev-database-reference-sql-functions-numeric-ln). - [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.