Fractional Indexing

This is based on Implementing Fractional Indexing by David Greenspan. Fractional indexing is a technique to create an ordering that can be used for Realtime Editing of Ordered Sequences. This implementation includes variable-length integers and the prepend/append optimization described in David's article.

[!NOTE] This is a Python port of the original JavaScript implementation from rocicorp/fractional-indexing. The current version is compatible with v4 of the original (see changelog).

Installation

$ pip install fractional-indexing

Usage

Generate a single key

from fractional_indexing import generate_key_between


# Insert at the beginning
first = generate_key_between(None, None)
assert first == 'a0'

# Insert after 1st
second = generate_key_between(first, None)
assert second == 'a1'

# Insert after 2nd
third = generate_key_between(second, None)
assert third == 'a2'

# Insert before 1st
zeroth = generate_key_between(None, first)
assert zeroth == 'Zz'

# Insert in between 2nd and 3rd (midpoint)
second_and_half = generate_key_between(second, third)
assert second_and_half == 'a1V'

Generate multiple keys

Use this when generating multiple keys at some known position, as it spaces out indexes more evenly and leads to shorter keys.

from fractional_indexing import generate_n_keys_between


# Insert 3 at the beginning
keys = generate_n_keys_between(None, None, n=3)
assert keys == ['a0', 'a1', 'a2']

# Insert 3 after 1st
keys = generate_n_keys_between('a0', None, n=3)
assert keys == ['a1', 'a2', 'a3']

# Insert 3 before 1st
keys = generate_n_keys_between(None, 'a0', n=3)
assert keys == ['Zx', 'Zy', 'Zz']

# Insert 3 in between 2nd and 3rd (midpoint)
keys = generate_n_keys_between('a1', 'a2', n=3)
assert keys == ['a1G', 'a1V', 'a1l']

Validate a key

from fractional_indexing import validate_order_key, FIError


validate_order_key('a0')

try:
    validate_order_key('foo')
except FIError as e:
    print(e)  # fractional_indexing.FIError: invalid order key: foo

Use custom base digits

By default, this library uses Base62 character encoding. To use a different set of digits, pass them in as the digits argument to generate_key_between(), generate_n_keys_between(), and validate_order_key().

Every key starts with a "head" character that encodes the length of its integer part. Since v4.0.0 (matching the JS reference v4.0.0), the head alphabet (int_digits) defaults to digits itself, so a custom alphabet produces self-contained keys drawn only from that alphabet:

from fractional_indexing import generate_key_between


assert generate_key_between(None, None, digits='0123456789') == '50'
assert generate_key_between('50', None, digits='0123456789') == '51'

To keep the pre-0.2 behaviour (A-Z/a-z head markers, e.g. a0), pass BASE_52_DIGITS as int_digits. An odd-length alphabet such as Base95 cannot supply its own (even-length) head alphabet, so it must be paired with an explicit int_digits:

from fractional_indexing import BASE_52_DIGITS, generate_key_between, generate_n_keys_between, validate_order_key


BASE_95_DIGITS = ' !"#$%&\'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijklmnopqrstuvwxyz{|}~'

assert generate_key_between(None, None, digits=BASE_95_DIGITS, int_digits=BASE_52_DIGITS) == 'a '
assert generate_key_between('a ', None, digits=BASE_95_DIGITS, int_digits=BASE_52_DIGITS) == 'a!'
assert generate_key_between(None, 'a ', digits=BASE_95_DIGITS, int_digits=BASE_52_DIGITS) == 'Z~'

assert generate_n_keys_between('a ', 'a!', n=3, digits=BASE_95_DIGITS, int_digits=BASE_52_DIGITS) == ['a 8', 'a P', 'a h']

validate_order_key('a ', digits=BASE_95_DIGITS, int_digits=BASE_52_DIGITS)

Alphabets are validated: they must be at least two characters, single-byte (char code 0-255), and in strictly ascending character-code order; int_digits must also have even length. Invalid alphabets raise FIError.

Other Languages

[!IMPORTANT] See changelog for version compatibility.

This is a Python port of the original JavaScript implementation by @rocicorp. That means that this implementation is byte-for-byte compatible with:

Changelog

[!NOTE] Starting with v4, we mirror the major version number of the original JS implementation to indicate compatibility.

4.0.0 (2026-08-06)

Brings the library to parity with rocicorp/fractional-indexing v4.0.0:

• Breaking: the head alphabet now defaults to digits itself, so custom alphabets produce self-contained keys (e.g. generate_key_between(None, None, digits='0123456789') returns '50', not 'a0'). Pass int_digits=BASE_52_DIGITS to restore the previous A-Z/a-z head markers. Keys generated with the default Base62 alphabet are unchanged.
• New int_digits argument on generate_key_between(), generate_n_keys_between(), and validate_order_key() to customise the head alphabet, plus a new BASE_52_DIGITS export.
• generate_key_between() now accepts its bounds in either order and swaps them, instead of raising FIError.
• Alphabets are validated (length, ascending character-code order, single-byte); invalid alphabets and unknown digits now raise FIError consistently instead of leaking ValueError.
• Digit lookups are cached per alphabet, and the midpoint calculation uses integer arithmetic (the decimal dependency is gone).

0.1.2 (2023-08-03)

Bug fixes.

0.1.0 (2022-02-02)

Initial release.