tanh

Applies to VAST Cluster 5.5.

Functions › Numeric and math functions › 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)

Returns: DOUBLE, from -1 to 1.

Set up the examples

The examples connect with the ADBC driver, as in VAST Query Engine (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), 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, "<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.

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

The same cases, as the cluster returns them. They use the helpers from 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

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()

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See also

• Numeric and math functions: all the numeric functions.
• Where filters run and pushdowns.
• EXPLAIN: how to read a plan.