asin

Applies to VAST Cluster 5.5.

Functions › Numeric and math functions › Inverse trigonometry. Returns the arcsine of a number: the angle, in radians from -π/2 to π/2, whose sine is that number. The number must be from -1 to 1. For the angle in degrees, wrap it in degrees: degrees(asin(x)). It has no aliases.

Syntax

asin(x)

Returns: DOUBLE: an angle in radians, from -π/2 to π/2.

Aliases: none.

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_asin. 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 five slopes, each with the height it rises (negative for a drop) divided by its length along the slope: the sine of its angle. 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_asin"'

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}.slopes"
run(f"CREATE SCHEMA IF NOT EXISTS {SCHEMA}")
run(f"CREATE TABLE IF NOT EXISTS {TABLE} (id BIGINT, slope VARCHAR, rise_ratio DOUBLE)")
run(f"INSERT INTO {TABLE} VALUES "
    "(1, 'ski run', 0.5), "
    "(2, 'cliff', 1.0), "
    "(3, 'meadow', 0.0), "
    "(4, 'descent', -0.5), "
    "(5, NULL, NULL)")

[]
[]
[(5,)]

What it does

asin(x) is the inverse of sin for angles from -π/2 to π/2: it returns the angle whose sine is x. asin(0) is 0.0, asin(0.5) is 0.5235987755982989 (π/6), asin(1) is 1.5707963267948966 (π/2) and asin(-1) is -1.5707963267948966. The argument is converted to DOUBLE, and so is the result, whatever the argument's type.

The result is in radians. In degrees, degrees(asin(0.5)) is 30.000000000000004: the result carries the rounding of floating-point numbers, so round it with round for display.

A sine is never less than -1 or more than 1, so asin() is only defined from -1 to 1. Anything outside that range is an error, even by a little: asin(1.0000000001) fails with ASIN is undefined outside [-1,1]. A ratio you compute yourself can land just outside the range through rounding; clamp it first with least(greatest(x, -1), 1).

NULLs and edge cases

The same cases, as the cluster returns them. They use the helpers from Set up the examples:

run("SELECT asin(NULL), asin(0), asin(-0.0::DOUBLE), asin(0.5), asin(1), asin(-1)")
run("SELECT asin(5e-324::DOUBLE), asin('nan'::DOUBLE)")
run("SELECT asin(1.0000000001)")
run("SELECT asin(-1.0000000001)")
run("SELECT asin(2)")
run("SELECT asin('12')")
run("SELECT asin('inf'::DOUBLE)")
run("SELECT asin('-inf'::DOUBLE)")
run("SELECT asin('abc')")
run("SELECT asin('\\xAA'::BLOB)")
run("SELECT asin(DATE '2026-10-16')")
run("SELECT asin(true)")
run("SELECT asin([1, 2])")
run("SELECT asin(INTERVAL 1 DAY)")

[(None, 0.0, -0.0, 0.5235987755982989, 1.5707963267948966, -1.5707963267948966)]
[(5e-324, nan)]
OSError: ASIN is undefined outside [-1,1]
OSError: ASIN is undefined outside [-1,1]
OSError: ASIN is undefined outside [-1,1]
OSError: ASIN is undefined outside [-1,1]
OSError: input value inf is out of range for numeric function
OSError: input value -inf is out of range for numeric function
OSError: Could not convert string 'abc' to DOUBLE
InternalError: Binder Error: No function matches the given name and argument types 'asin(BLOB)'. You might need to add explicit type casts.
InternalError: Binder Error: No function matches the given name and argument types 'asin(DATE)'. You might need to add explicit type casts.
InternalError: Binder Error: No function matches the given name and argument types 'asin(BOOLEAN)'. You might need to add explicit type casts.
InternalError: Binder Error: No function matches the given name and argument types 'asin(INTEGER[])'. You might need to add explicit type casts.
InternalError: Binder Error: No function matches the given name and argument types 'asin(INTERVAL)'. You might need to add explicit type casts.

Examples

The angle of each slope, in radians and in degrees:

run(f"SELECT id, slope, asin(rise_ratio), degrees(asin(rise_ratio)) FROM {TABLE} ORDER BY id LIMIT 10")

[(1, 'ski run', 0.5235987755982989, 30.000000000000004), (2, 'cliff', 1.5707963267948966, 90.0), (3, 'meadow', 0.0, 0.0), (4, 'descent', -0.5235987755982989, -30.000000000000004), (5, None, None, None)]

A ratio that rounding has pushed just past 1, clamped to the range before asin():

run("SELECT asin(least(greatest(1.0000000001, -1), 1))")

[(1.5707963267948966,)]

Keep only the slopes steeper than 45 degrees:

run(f"SELECT id, slope FROM {TABLE} WHERE degrees(asin(rise_ratio)) > 45 ORDER BY id LIMIT 10")

[(2, 'cliff')]

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 asin() is always computed by the Query Engine:

• In the SELECT list, the scan reads the column and the Query Engine computes asin() for each row it returns.
• In WHERE, the scan sends the column for every row, and a FILTER step in the Query Engine computes asin() 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(asin(rise_ratio)) > 45")

┌───────────────────────────┐
│         PROJECTION        │
│    ────────────────────   │
│             #1            │
│                           │
└─────────────┬─────────────┘
┌─────────────┴─────────────┐
│           FILTER          │
│    ────────────────────   │
│ (degrees(asin(rise_ratio))│
│           > 45.0)         │
│                           │
└─────────────┬─────────────┘
┌─────────────┴─────────────┐
│         VAST_SCAN         │
│    ────────────────────   │
│    Function: VAST_SCAN    │
│                           │
│        Projections:       │
│         rise_ratio        │
│             id            │
│                           │
└───────────────────────────┘

Make it faster

• Compare the ratio, not its angle. asin() grows with its argument, so a threshold on the angle is a threshold on the ratio: steeper than 45 degrees is rise_ratio > sin(radians(45)). A function of constants is computed once, and the comparison of the raw column is pushed down to VAST DataBase, so rows that don't match never leave storage, and asin() isn't computed at all, so a value outside -1 to 1 can't fail the query. The plan has no FILTER step:

plan(f"SELECT id FROM {TABLE} WHERE rise_ratio > sin(radians(45))")

┌───────────────────────────┐
│         VAST_SCAN         │
│    ────────────────────   │
│    Function: VAST_SCAN    │
│      Projections: id      │
│                           │
└───────────────────────────┘

• Store the angle if you filter on it often. Compute it when you write the rows and keep it in its own column: a comparison of that column is pushed down, asin() in WHERE isn't.
• Combine it with a pushed-down condition. In id > 100 AND asin(rise_ratio) > 0.5, id > 100 is still evaluated in VAST DataBase, so asin() runs only on the rows that pass it.

Limitations and errors

• From -1 to 1 only. Anything else fails with ASIN is undefined outside [-1,1], and an infinite value with input value inf is out of range for numeric function. On a table, one such row fails the whole query, not just that row. Clamp computed ratios with least(greatest(x, -1), 1), or compare the raw column (see Make it faster).
• Thresholds on a rounded angle. degrees(asin(0.5)) is 30.000000000000004, so degrees(asin(x)) > 30 is true for x = 0.5. Compare with a margin, or compare the ratio itself.
• The result is in radians, from -π/2 to π/2. Convert it with degrees. For an angle in the full circle from the two sides of a triangle or a point (x, y), use atan2.
• One argument, numbers only. asin(1, 2), 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 asin(2)")
run("SELECT asin(1, 2)")

OSError: ASIN is undefined outside [-1,1]
InternalError: Binder Error: No function matches the given name and argument types 'asin(INTEGER_LITERAL, INTEGER_LITERAL)'. You might need to add explicit type casts.

Similar functions

run("SELECT asin(0.5), acos(0.5), atan(0.5), atan2(0.5, 1), degrees(asin(0.5))")

[(0.5235987755982989, 1.0471975511965979, 0.4636476090008061, 0.4636476090008061, 30.000000000000004)]

Clean up:

run(f"DROP TABLE IF EXISTS {TABLE}")
run(f"DROP SCHEMA IF EXISTS {SCHEMA}")
conn.close()

[]
[]

See also

• Numeric and math functions: all the trigonometric functions.
• sin, acos, atan, atan2 and degrees.
• Where filters run and pushdowns.
• EXPLAIN: how to read a plan.