--- title: "nextafter" slug: "dev-database-reference-sql-functions-numeric-nextafter" updated: 2026-10-30T18:18:51Z published: 2026-10-30T18:18:51Z canonical: "docs.vastdata.com/dev-database-reference-sql-functions-numeric-nextafter" --- > ## 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. # nextafter *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) › Floating-point values.* Returns the floating-point value next to `x` in the direction of `y`: the smallest step up or down that a `DOUBLE` (or, for two `FLOAT` arguments, a `FLOAT`) can take from `x`. ## Syntax ``` nextafter(x, y) ``` | Argument | Type | Description | | --- | --- | --- | | `x` | `DOUBLE` or `FLOAT` | The value to step from. | | `y` | `DOUBLE` or `FLOAT` | The direction: the result is the value next to `x` on the side of `y`. | **Returns:** `FLOAT` if both arguments are `FLOAT`, otherwise `DOUBLE`. Integers and `DECIMAL` values are converted to `DOUBLE`, and so is a `FLOAT` paired with a `DOUBLE`. ## 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_nextafter`. 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 five thresholds, stored both as a `DOUBLE` (`x`) and as a `FLOAT` (`f`). Row 3 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_nextafter"' 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}.thresholds" run(f"CREATE SCHEMA IF NOT EXISTS {SCHEMA}") run(f"CREATE TABLE IF NOT EXISTS {TABLE} (id BIGINT, x DOUBLE, f FLOAT)") run(f"INSERT INTO {TABLE} VALUES " "(1, 2.5, 2.5), (2, -1.25, -1.25), (3, NULL, NULL), (4, 0.0, 0.0), (5, 1.0, 1.0)") ``` ``` [] [] [(5,)] ``` ## What it does Floating-point numbers are spaced apart: between `1.0` and the next `DOUBLE` above it there's nothing. `nextafter(x, y)` returns that neighbour of `x`, on the side of `y`: - If `y` is greater than `x`, the next value up: `nextafter(1.0, 2.0)` is `1.0000000000000002`. - If `y` is less than `x`, the next value down: `nextafter(1.0, 0.0)` is `0.9999999999999999`. - If `y` equals `x`, `x` itself: `nextafter(1.0, 1.0)` is `1.0`. The size of the step depends on the type and on the size of `x`. At 1 it's `2.220446049250313e-16` for a `DOUBLE` (`nextafter(1.0, 2.0) - 1.0`) and `1.1920928955078125e-07` for a `FLOAT`. Next to 0 it's the smallest value the type can hold: `nextafter(0.0::DOUBLE, 1)` is `5e-324`. Use it to turn a strict bound into an inclusive one (on a `DOUBLE` column, `x > 1.0` is `x >= nextafter(1.0, 'inf'::DOUBLE)`), or to find how precisely a value can be stored. ## NULLs and edge cases | Input | Result | | --- | --- | | `NULL` as either argument | `NULL` | | `nextafter(1.0, 2.0)`, `nextafter(1.0, 0.0)`, `nextafter(1.0, 1.0)` | `1.0000000000000002`, `0.9999999999999999`, `1.0` | | `nextafter(0.0::DOUBLE, 1)`, `nextafter(0.0::DOUBLE, -1)` | `5e-324`, `-5e-324` | | `nextafter(-0.0::DOUBLE, 0)`, `nextafter(5e-324::DOUBLE, 0)` | `0.0`, `0.0` | | `nextafter(1.7976931348623157e308, 'inf'::DOUBLE)` (from the largest `DOUBLE`) | `inf` | | `nextafter('inf'::DOUBLE, 0)`, `nextafter('-inf'::DOUBLE, 0)` | `1.7976931348623157e+308`, `-1.7976931348623157e+308` | | NaN as either argument | `nan` | | `nextafter(1::FLOAT, 2::FLOAT)` | `1.0000001192092896`, a `FLOAT` | | `nextafter(1::FLOAT, 2::DOUBLE)` | `1.0000000000000002`, a `DOUBLE` | | `nextafter(2.45, 3)` (a `DECIMAL` and an integer) | `2.4500000000000006`, a `DOUBLE` | | `nextafter('12', 10)` (a string) | Converted to `DOUBLE`: `11.999999999999998` | | `nextafter('abc', 10)` | 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 `'nextafter(DATE, INTEGER_LITERAL)'` | | One argument | Error: `No function matches the given name and argument types 'nextafter(INTEGER_LITERAL)'` | The same cases, as the cluster returns them. They use the table and helpers from [Set up the examples](/develop/docs/dev-database-reference-sql-functions-numeric-nextafter#set-up-the-examples): ``` run("SELECT nextafter(NULL, 1), nextafter(1, NULL), nextafter(1.0, 2.0), nextafter(1.0, 0.0), nextafter(1.0, 1.0)") run("SELECT nextafter(0.0::DOUBLE, 1), nextafter(0.0::DOUBLE, -1), nextafter(-0.0::DOUBLE, 0), " "nextafter(5e-324::DOUBLE, 0)") run("SELECT nextafter(1.7976931348623157e308, 'inf'::DOUBLE), nextafter('inf'::DOUBLE, 0), " "nextafter('-inf'::DOUBLE, 0), nextafter('nan'::DOUBLE, 1), nextafter(1, 'nan'::DOUBLE)") run("SELECT nextafter(1::FLOAT, 2::FLOAT), typeof(nextafter(1::FLOAT, 2::FLOAT)), " "nextafter(1::FLOAT, 2::DOUBLE), typeof(nextafter(1::FLOAT, 2::DOUBLE))") run("SELECT nextafter(2.45, 3), typeof(nextafter(2.45, 3)), nextafter('12', 10)") run("SELECT nextafter('abc', 10)") run("SELECT nextafter(DATE '2026-10-16', 10)") run("SELECT nextafter(1)") ``` ``` [(None, None, 1.0000000000000002, 0.9999999999999999, 1.0)] [(5e-324, -5e-324, 0.0, 0.0)] [(inf, 1.7976931348623157e+308, -1.7976931348623157e+308, nan, nan)] [(1.0000001192092896, 'FLOAT', 1.0000000000000002, 'DOUBLE')] [(2.4500000000000006, 'DOUBLE', 11.999999999999998)] OSError: Could not convert string 'abc' to DOUBLE InternalError: Binder Error: No function matches the given name and argument types 'nextafter(DATE, INTEGER_LITERAL)'. You might need to add explicit type casts. InternalError: Binder Error: No function matches the given name and argument types 'nextafter(INTEGER_LITERAL)'. You might need to add explicit type casts. ``` ## Examples The next value above each threshold, as a `DOUBLE` and as a `FLOAT`. Cast the direction to `FLOAT` (`10::FLOAT`) to get a `FLOAT` result for a `FLOAT` column: ``` run(f"SELECT id, nextafter(x, 10), nextafter(f, 10::FLOAT) FROM {TABLE} ORDER BY id LIMIT 10") ``` ``` [(1, 2.5000000000000004, 2.500000238418579), (2, -1.2499999999999998, -1.2499998807907104), (3, None, None), (4, 5e-324, 1.401298464324817e-45), (5, 1.0000000000000002, 1.0000001192092896)] ``` The step to the next value up at each threshold, for each type. It grows with the size of the value, and it's larger for a `FLOAT`: ``` run(f"SELECT id, x, nextafter(x, 'inf'::DOUBLE) - x, nextafter(f, 'inf'::FLOAT) - f " f"FROM {TABLE} ORDER BY id LIMIT 10") ``` ``` [(1, 2.5, 4.440892098500626e-16, 2.384185791015625e-07), (2, -1.25, 2.220446049250313e-16, 1.1920928955078125e-07), (3, None, None, None), (4, 0.0, 5e-324, 1.401298464324817e-45), (5, 1.0, 2.220446049250313e-16, 1.1920928955078125e-07)] ``` `x >= nextafter(1.0, 'inf'::DOUBLE)` keeps the same rows as `x > 1.0`: ``` run(f"SELECT id FROM {TABLE} WHERE x >= nextafter(1.0, 'inf'::DOUBLE) ORDER BY id LIMIT 10") run(f"SELECT id FROM {TABLE} WHERE x > 1.0 ORDER BY id LIMIT 10") ``` ``` [(1,)] [(1,)] ``` ## 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: - **On a column, in the `SELECT` list,** the scan reads the column and the Query Engine computes `nextafter()` for each row it returns. - **On a column, in `WHERE`,** the scan sends the column for every row, and a `FILTER` step in the Query Engine computes `nextafter()` and keeps the rows that match. - **On constants,** as in `x >= nextafter(1.0, 'inf'::DOUBLE)`, the Query Engine computes it once, before the scan. The plan of a `WHERE` condition on `nextafter(x, 10)` shows the `FILTER` step above the scan: ``` plan(f"SELECT id FROM {TABLE} WHERE nextafter(x, 10) > 1") ``` ``` ┌───────────────────────────┐ │ PROJECTION │ │ ──────────────────── │ │ #1 │ │ │ └─────────────┬─────────────┘ ┌─────────────┴─────────────┐ │ FILTER │ │ ──────────────────── │ │ (nextafter(x, 10.0) > 1.0)│ │ │ └─────────────┬─────────────┘ ┌─────────────┴─────────────┐ │ VAST_SCAN │ │ ──────────────────── │ │ Function: VAST_SCAN │ │ │ │ Projections: │ │ x │ │ id │ │ │ └───────────────────────────┘ ``` ## Make it faster - **Apply it to the constant, not the column.** In a bound such as `x >= nextafter(1.0, 'inf'::DOUBLE)`, the right-hand side is a constant, so the scan in VAST DataBase can evaluate the condition: ``` plan(f"SELECT id FROM {TABLE} WHERE x >= nextafter(1.0, 'inf'::DOUBLE)") ``` ``` ┌───────────────────────────┐ │ VAST_SCAN │ │ ──────────────────── │ │ Function: VAST_SCAN │ │ Projections: id │ │ │ └───────────────────────────┘ ``` ## Limitations and errors - **Two arguments, `DOUBLE` or `FLOAT`.** A single argument, a date, a boolean, a `BLOB`, a list or an interval fails with `No function matches the given name and argument types`. A string is converted to `DOUBLE` first, and fails with `Could not convert string ... to DOUBLE` if it isn't a number. - **No `DECIMAL` or integer result.** A `DECIMAL` or integer argument is converted to `DOUBLE`, and the result is a `DOUBLE`. - **A `FLOAT` result needs two `FLOAT` arguments.** A `FLOAT` paired with a `DOUBLE` gives a `DOUBLE` step, which is much smaller than a `FLOAT` step. - **It can overflow.** The next value up from the largest `DOUBLE` is `inf`, with no error. ## Similar functions | Expression | Result | Notes | | --- | --- | --- | | `nextafter(1.0, 2.0) - 1.0` | `2.220446049250313e-16` | the `DOUBLE` step at 1 | | `nextafter(1::FLOAT, 2::FLOAT) - 1::FLOAT` | `1.1920928955078125e-07` | the `FLOAT` step at 1 | | [isfinite](/develop/docs/dev-database-reference-sql-functions-numeric-isfinite)`(nextafter(1.7976931348623157e308, 'inf'::DOUBLE))` | `false` | the step past the largest `DOUBLE` is `inf` | ``` run("SELECT nextafter(1.0, 2.0) - 1.0, nextafter(1::FLOAT, 2::FLOAT) - 1::FLOAT, " "isfinite(nextafter(1.7976931348623157e308, 'inf'::DOUBLE))") ``` ``` [(2.220446049250313e-16, 1.1920928955078125e-07, False)] ``` 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#floating-point-values): nextafter and the other floating-point functions. - [isnan](/develop/docs/dev-database-reference-sql-functions-numeric-isnan), [isinf](/develop/docs/dev-database-reference-sql-functions-numeric-isinf) and [isfinite](/develop/docs/dev-database-reference-sql-functions-numeric-isfinite). - [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.