--- title: "tanh" slug: "dev-database-reference-sql-functions-numeric-tanh" updated: 2026-10-30T18:18:51Z published: 2026-10-30T18:18:51Z canonical: "docs.vastdata.com/dev-database-reference-sql-functions-numeric-tanh" --- > ## 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. # tanh *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) › Hyperbolic functions.* Returns the hyperbolic tangent of a number, `sinh(x) / cosh(x)`. It takes any number and returns a value from -1 to 1, which makes it a smooth way to squash an unbounded score into that range. ## Syntax ``` tanh(x) ``` | Argument | Type | Description | | --- | --- | --- | | `x` | Any number (`DOUBLE`, `REAL`, an integer or a `DECIMAL`) | Any value, including `inf` and `-inf`. | **Returns:** `DOUBLE`, from -1 to 1. ## 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_tanh`. 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 raw scores. Row 3 has no score: ``` 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_tanh"' 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, 0.5), (2, -1.0), (3, NULL), (4, 0.0), (5, 3.0), (6, 25.0)") ``` ``` [] [] [(6,)] ``` ## What it does `tanh(x)` is the hyperbolic tangent, `sinh(x) / cosh(x)`. It's an odd function (`tanh(-x)` is `-tanh(x)`), it's 0 at 0, and it approaches 1 as `x` grows and -1 as `x` falls. Its inverse is [atanh](/develop/docs/dev-database-reference-sql-functions-numeric-atanh). | Call | Result | | --- | --- | | `tanh(0)` | `0.0` | | `tanh(1)` | `0.7615941559557649` | | `tanh(20)` | `1.0`: the nearest `DOUBLE` to the true value | | `tanh(-20)` | `-1.0` | | `tanh(1e308)` | `1.0` | The result is a `DOUBLE` for every numeric argument type: an integer, a `REAL`, a `DECIMAL` or a `DOUBLE`. ``` run("SELECT tanh(0), tanh(1), tanh(20), tanh(-20), tanh(1e308)") run("SELECT typeof(tanh(1::INTEGER)), typeof(tanh(0.5::FLOAT)), typeof(tanh(0.5))") ``` ``` [(0.0, 0.7615941559557649, 1.0, -1.0, 1.0)] [('DOUBLE', 'DOUBLE', 'DOUBLE')] ``` ## NULLs and edge cases | Input | Result | | --- | --- | | `NULL` | `NULL` | | `'inf'::DOUBLE` | `1.0` | | `'-inf'::DOUBLE` | `-1.0` | | `'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`: `0.9999999999244973` | | `'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 `'tanh(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-tanh#set-up-the-examples): ``` run("SELECT tanh(NULL), tanh('inf'::DOUBLE), tanh('-inf'::DOUBLE), tanh('nan'::DOUBLE)") run("SELECT tanh(-0.0::DOUBLE), tanh(5e-324::DOUBLE), tanh('12')") run("SELECT tanh('abc')") run("SELECT tanh(DATE '2026-10-16')") ``` ``` [(None, 1.0, -1.0, nan)] [(-0.0, 5e-324, 0.9999999999244973)] OSError: Could not convert string 'abc' to DOUBLE InternalError: Binder Error: No function matches the given name and argument types 'tanh(DATE)'. You might need to add explicit type casts. ``` ## Examples Each raw score squashed into the range -1 to 1, and the same squash with the score scaled first, which keeps more of the difference between large scores: ``` run(f"SELECT id, score, tanh(score), tanh(score / 10) FROM {TABLE} ORDER BY id LIMIT 10") ``` ``` [(1, 0.5, 0.46211715726000974, 0.04995837495787998), (2, -1.0, -0.7615941559557649, -0.09966799462495582), (3, None, None, None), (4, 0.0, 0.0, 0.0), (5, 3.0, 0.9950547536867305, 0.2913126124515909), (6, 25.0, 1.0, 0.9866142981514303)] ``` Keep only the rows whose squashed score is above 0.9: ``` run(f"SELECT id, score FROM {TABLE} WHERE tanh(score) > 0.9 ORDER BY id LIMIT 10") ``` ``` [(5, 3.0), (6, 25.0)] ``` ## 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 `tanh()` is always computed by the Query Engine: - **In the `SELECT` list,** the scan reads the column and the Query Engine computes `tanh()` for each row it returns. - **In `WHERE`,** the scan sends the column for every row, and a `FILTER` step in the Query Engine computes `tanh()` 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 tanh(score) > 0.9") ``` ``` ┌───────────────────────────┐ │ PROJECTION │ │ ──────────────────── │ │ #1 │ │ │ └─────────────┬─────────────┘ ┌─────────────┴─────────────┐ │ FILTER │ │ ──────────────────── │ │ (tanh(score) > 0.9) │ │ │ └─────────────┬─────────────┘ ┌─────────────┴─────────────┐ │ VAST_SCAN │ │ ──────────────────── │ │ Function: VAST_SCAN │ │ │ │ Projections: │ │ score │ │ id │ │ │ └───────────────────────────┘ ``` ## Make it faster - **Compare the raw column with the inverse of the constant.** `tanh()` grows as its argument grows, so `tanh(score) > 0.9` is the same condition as `score > atanh(0.9)`. 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. The bound must be between -1 and 1: `atanh(1)` is infinity. ``` plan(f"SELECT id FROM {TABLE} WHERE score > atanh(0.9)") run(f"SELECT id, score FROM {TABLE} WHERE score > atanh(0.9) ORDER BY id LIMIT 10") ``` ``` ┌───────────────────────────┐ │ VAST_SCAN │ │ ──────────────────── │ │ Function: VAST_SCAN │ │ Projections: id │ │ │ └───────────────────────────┘ [(5, 3.0), (6, 25.0)] ``` - **Store the result 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 `tanh()` isn't. ## Limitations and errors - **Large inputs all give 1.** From about 20 up, `tanh()` returns exactly `1.0` (and `-1.0` from about -20 down), so those values can't be told apart or ordered by their `tanh`. Scale the input down first, as in `tanh(score / 10)`, or compare the raw column. - **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 `tanh` has, `tanh(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`. - **One argument.** `tanh(1, 2)` fails with `No function matches the given name and argument types 'tanh(INTEGER_LITERAL, INTEGER_LITERAL)'`. ## Similar functions | Function | Returns | Result for `1` | | --- | --- | --- | | `tanh(x)` | the hyperbolic tangent, from -1 to 1 | `0.7615941559557649` | | [sinh](/develop/docs/dev-database-reference-sql-functions-numeric-sinh) | the hyperbolic sine | `1.1752011936438014` | | [cosh](/develop/docs/dev-database-reference-sql-functions-numeric-cosh) | the hyperbolic cosine | `1.5430806348152437` | | [atanh](/develop/docs/dev-database-reference-sql-functions-numeric-atanh) | the inverse of `tanh`, for -1 to 1 | `atanh(tanh(1))` is `0.9999999999999999` | | [tan](/develop/docs/dev-database-reference-sql-functions-numeric-tan) | the tangent of an angle in radians | | | [atan](/develop/docs/dev-database-reference-sql-functions-numeric-atan) | another S-shaped curve, from -pi/2 to pi/2 | | ``` run("SELECT tanh(1), sinh(1), cosh(1), atanh(tanh(1)), sinh(1) / cosh(1), tan(1), atan(1)") ``` ``` [(0.7615941559557649, 1.1752011936438014, 1.5430806348152437, 0.9999999999999999, 0.7615941559557649, 1.5574077246549023, 0.7853981633974483)] ``` 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.