Talk:Variable-length integer

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On 21 July 2026, it was proposed that this article be moved from Variable-length quantity to Variable-length integer. The result of the discussion was moved.

It was defined for use in the standard MIDI file format[1] to save additional space for a resource constrained system, and ....

Does this sentence mean that no one considered this encoding of integers (in a verifiable way) before the standard MIDI file format was defined in the early 1980s? If so, I am very surprised. --fcp2007 (talk) 21:06, 13 July 2008 (UTC)Reply

It more likely means that the MIDI standard was the first to define the name Variable-length Quantity for this concept.

Do you know of anyone who encoded quantities in a similar way before the MIDI standard? Please tell us about them. I think this article should mention them, even if they didn't use the exact phrase "variable-length quantity" -- since I agree with the essay WP:REFERS that articles in Wikipedia are about concepts, not particular terms.

According to the byte and 8-bit article, 8-bit microprocessors were first introduced in the 1970s. So I would be surprised (but delighted) to see a wp: reliable reference to anyone encoding integers as a variable number of full bytes before the mid 1970s. --DavidCary (talk) 15:51, 8 November 2013 (UTC)Reply

This page should probably be titled "base-128 encoding" or similar, and more generally describe all variations on the theme. (1 or 0 as stop bit, most significant bit group first or last significant, comparison to UTF-8 etc.) —Preceding unsigned comment added by 213.136.42.60 (talk) 13:49, 18 November 2010 (UTC)Reply

I think the two pages should be merged, but that the merged article should be titled "Var-Int" because that seems to be more commonly used in the wild than "LEB128". It could also be called "Variable-length integer" with redirections from LEB128, VarInt, VLQ, etc. Also see my comment about other names. That's my two cents. Andyjrobb (talk) 01:36, 20 June 2019 (UTC)Reply

Another option is to encode the length n with VLQ and then interpret the following n bytes as a number.

Space usage:

• VLQ: ${\displaystyle \lceil \log _{128}n\rceil }$ bytes
• VLQ-length: ${\displaystyle \lceil \log _{128}\lceil \log _{256}n\rceil \rceil +\lceil \log _{256}n\rceil }$ bytes
• VLQ-length-length: ${\displaystyle \lceil \log _{128}\lceil \log _{256}\lceil \log _{256}n\rceil \rceil \rceil +\lceil \log _{256}\lceil \log _{256}n\rceil \rceil +\lceil \log _{256}n\rceil }$ bytes
• VLQ-length-length-length: ${\displaystyle \lceil \log _{128}\lceil \log _{256}\lceil \log _{256}\lceil \log _{256}n\rceil \rceil \rceil \rceil +\lceil \log _{256}\lceil \log _{256}\lceil \log _{256}n\rceil \rceil \rceil +\lceil \log _{256}\lceil \log _{256}n\rceil \rceil +\lceil \log _{256}n\rceil }$ bytes

Solomon Ucko (talk) 21:59, 4 February 2019 (UTC)Reply

There are countless examples of this format throughout various projects, which should be added to the main article, and related articles linking back somehow:

• W3C Efficient XML Interchange (EXI) Binary Encoding for Unsigned Integer
• Google Protocol Buffers Base 128 Varints
• WebAssembly LEB128
• Bitcoin?
• Sqlite?
• Android Dalvik Java VM Byte Code
• DWARF2 LEB128 also here LEB128

There is currently a template-tag to move LEB128 to this page, but I think this page should be moved to LEB128. Andyjrobb (talk) 22:35, 19 June 2019 (UTC)Reply

LEB128 uses two's complement to represent signed numbers. In this scheme of representation, n bits encodes a range from -2ⁿ to 2ⁿ-1. I guess it should be -2^{n - 1} to 2^{n - 1}-1. 178.64.56.11 (talk) 01:20, 24 September 2021 (UTC)Reply

I think that the table (Variable-length quantity#Examples) needs a review. There appear to be many errors in it (such as 7 digit bytes in the row for 134217728, and a "4" in the varint binary representation of 8192).

I've written a script from first principles to generate what I believe to be the correct values, please see the output below.

0

0x00000000

00000000

0x00

00000000

127

0x0000007F

01111111

0x7F

01111111

128

0x00000080

10000000

0x81 0x00

10000001 00000000

8192

0x00002000

00100000 00000000

0xC0 0x00

11000000 00000000

16383

0x00003FFF

00111111 11111111

0xFF 0x7F

11111111 01111111

16384

0x00004000

01000000 00000000

0x81 0x80 0x00

10000001 10000000 00000000

2097151

0x001FFFFF

00011111 11111111 11111111

0xFF 0xFF 0x7F

11111111 11111111 01111111

2097152

0x00200000

00100000 00000000 00000000

0x81 0x80 0x80 0x00

10000001 10000000 10000000 00000000

134217728

0x08000000

00001000 00000000 00000000 00000000

0xC0 0x80 0x80 0x00

11000000 10000000 10000000 00000000

268435455

0x0FFFFFFF

00001111 11111111 11111111 11111111

0xFF 0xFF 0xFF 0x7F

11111111 11111111 11111111 01111111

JSFiddle with the source that generated it: https://jsfiddle.net/w6jL5qy3/

Additionally, I don't see the value in including the two Hexadecimal columns - its just confusing and detracts from the example. -Chieftain Alex 20:15, 18 April 2023 (UTC)Reply

Replying to User:BarrelProof, thank you for the intro improvement, yes I agree it should only be about encodings using a series of bytes, what I meant was that the article contained a somewhat inconsistent mix of MIDI-specific content and content about other varint encodings and that the article might be in need of a rewrite to cover them generically.

They do most seem to be base-128, but there are some like the QUIC standard which defines a "variable-length integer" encoding [1] that is not (encodes the length in the first two bits).

Above it was suggested that LEB128 might be merged into this article, which seems sensible to me. Marboxil (talk) 16:44, 2 August 2026 (UTC)Reply

I wasn't aware of the QUIC scheme that you describe. As far as I know, it is not currently discussed in the article. —⁠ ⁠BarrelProof (talk) 16:54, 2 August 2026 (UTC)Reply