sqrt

Applies to VAST Cluster 5.5.

Functions › Numeric and math functions › Powers and logarithms. Returns the square root of a number, as a DOUBLE. A negative number fails the query.

Syntax

sqrt(x)

Returns: DOUBLE, whatever the argument type.

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_sqrt. 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 three square plots: the area of each, and the offset dx, dy of its corner from a survey point. One dx is negative; 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_sqrt"'

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}.plots"
run(f"CREATE SCHEMA IF NOT EXISTS {SCHEMA}")
run(f"CREATE TABLE IF NOT EXISTS {TABLE} (id BIGINT, area DOUBLE, dx DOUBLE, dy DOUBLE)")
run(f"INSERT INTO {TABLE} VALUES "
    "(1, 16.0, 3.0, 4.0), "
    "(2, 2.0, -6.0, 8.0), "
    "(3, 0.25, 1.0, -1.0), "
    "(4, NULL, NULL, NULL)")

[]
[]
[(4,)]

What it does

sqrt(x) returns the non-negative number whose square is x: sqrt(4) is 2.0 and sqrt(2.25) is 1.5. 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: sqrt('12') is 3.4641016151377544.

A negative number is an error, not NaN: sqrt(-1) fails with cannot take square root of a negative number. The error stops the whole query: if one row of a column is negative, sqrt() of that column fails for every row. Keep negative values away from it with WHERE or CASE; see Limitations and errors.

Floating-point special values pass through: sqrt('inf'::DOUBLE) is inf, sqrt('nan'::DOUBLE) is nan, and sqrt(-0.0::DOUBLE) is -0.0, a negative zero, which isn't an error. '-inf'::DOUBLE is negative and fails.

NULLs and edge cases

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

run("SELECT sqrt(NULL), sqrt(4), sqrt(2), sqrt(2.25), typeof(sqrt(4)), typeof(sqrt(2.25))")
run("SELECT sqrt(-0.0::DOUBLE), sqrt('inf'::DOUBLE), sqrt('nan'::DOUBLE), sqrt(5e-324::DOUBLE)")
run(f"SELECT sqrt('12') FROM {TABLE} LIMIT 1")
run("SELECT sqrt(-1)")
run("SELECT sqrt(-1e-300)")
run("SELECT sqrt('-inf'::DOUBLE)")
run(f"SELECT sqrt('abc') FROM {TABLE} LIMIT 1")
run("SELECT sqrt(true)")

[(None, 2.0, 1.4142135623730951, 1.5, 'DOUBLE', 'DOUBLE')]
[(-0.0, inf, nan, 2.2227587494850775e-162)]
[(3.4641016151377544,)]
OSError: cannot take square root of a negative number
OSError: cannot take square root of a negative number
OSError: cannot take square root of a negative number
OSError: Could not convert string 'abc' to DOUBLE
InternalError: Binder Error: No function matches the given name and argument types 'sqrt(BOOLEAN)'. You might need to add explicit type casts.

Examples

The side of each square plot, and the straight-line distance of its corner from the survey point, sqrt(dx * dx + dy * dy):

run(f"SELECT id, sqrt(area), sqrt(dx * dx + dy * dy) FROM {TABLE} ORDER BY id LIMIT 10")

[(1, 4.0, 5.0), (2, 1.4142135623730951, 10.0), (3, 0.5, 1.4142135623730951), (4, None, None)]

Keep only the plots with a side longer than 1:

run(f"SELECT id, area FROM {TABLE} WHERE sqrt(area) > 1 ORDER BY id LIMIT 10")

[(1, 16.0), (2, 2.0)]

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 sqrt() of a column is always computed by the Query Engine:

• In the SELECT list, the scan reads the column and the Query Engine computes sqrt() for each row it returns.
• In WHERE, the scan sends the column for every row, and a FILTER step in the Query Engine computes sqrt() and keeps the rows that match. No rows are skipped in storage.

sqrt() of a constant is different: it's computed once, before the scan, so area > sqrt(0.25) is a comparison with a constant and is pushed down.

The plan of the WHERE example shows the FILTER step above the scan:

plan(f"SELECT id FROM {TABLE} WHERE sqrt(area) > 1")

┌───────────────────────────┐
│         PROJECTION        │
│    ────────────────────   │
│             #1            │
│                           │
└─────────────┬─────────────┘
┌─────────────┴─────────────┐
│           FILTER          │
│    ────────────────────   │
│     (sqrt(area) > 1.0)    │
│                           │
└─────────────┬─────────────┘
┌─────────────┴─────────────┐
│         VAST_SCAN         │
│    ────────────────────   │
│    Function: VAST_SCAN    │
│                           │
│        Projections:       │
│            area           │
│             id            │
│                           │
└───────────────────────────┘

Make it faster

• Square the constant instead. For a column that isn't negative, sqrt(area) > 2 is the same as area > 4, and that 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 area > 4")

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

• Store the root 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 sqrt(area) > 2, id > 100 is still evaluated in VAST DataBase, so sqrt() runs only on the rows that pass it.

Limitations and errors

• A negative value fails the whole query. sqrt(dx) fails with cannot take square root of a negative number because one row has a negative dx, and returns no rows at all. To skip the negative rows, filter them out with a pushed-down condition such as WHERE dx >= 0. To keep them in the result with a NULL, use CASE WHEN dx >= 0 THEN sqrt(dx) END.
• Numbers only. A boolean, date, interval, BLOB or list fails with No function matches the given name and argument types; the error lists the one form sqrt accepts, sqrt(DOUBLE) -> DOUBLE. A string is converted when the query runs, and one that isn't a number fails with Could not convert string 'abc' to DOUBLE.
• No hypot or square. Both fail with Scalar Function with name ... does not exist!. Write sqrt(x * x + y * y) for hypot(x, y), and x * x for square(x).

run(f"SELECT sqrt(dx) FROM {TABLE}")
run(f"SELECT id, sqrt(dx) FROM {TABLE} WHERE dx >= 0 ORDER BY id LIMIT 10")
run(f"SELECT id, CASE WHEN dx >= 0 THEN sqrt(dx) END FROM {TABLE} ORDER BY id LIMIT 10")
run("SELECT hypot(3, 4)")
run("SELECT sqrt(3 * 3 + 4 * 4)")

OSError: cannot take square root of a negative number
[(1, 1.7320508075688772), (3, 1.0)]
[(1, 1.7320508075688772), (2, None), (3, 1.0), (4, None)]
InternalError: Catalog Error: Scalar Function with name hypot does not exist!
[(5.0,)]

Similar functions

run("SELECT sqrt(2), pow(2, 0.5), 2 ** 0.5, cbrt(2)")
run("SELECT pow(-1, 0.5), pow(-2, 0.5)")

[(1.4142135623730951, 1.4142135623730951, 1.4142135623730951, 1.2599210498948734)]
[(nan, nan)]

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 numeric functions.
• pow and cbrt.
• Where filters run and pushdowns.
• EXPLAIN: how to read a plan.