Codec for VLQ (variable-length quantity) Base64 algorithm

2.0.1 2023-03-16 11:26 UTC

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Last update: 2024-02-19 12:16:09 UTC


Codec for VLQ (variable-length quantity) Base64 algorithm (PHP).

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VQL + Base64

Base64 allows us to represent a sequence of numbers in a text string that can be stored and transmit in text formats (JSON, XML, etc).

VLQ allows us to represent an integer in a sequence numbers with little digit capacity. For example 6 bit is the limit for Base64. The resulting numbers are called "VLQ digits". Small input number is represented by fewer VLQ-digits than big number. Thus VLQ is most effective if the input sequence is contains mainly the small numbers.

VLQ+Base64 allows us effectively represented a sequence of integers (dominated by a small number of) in the text format.

For example, it used in JavaScript/CSS source map.

The Algorithm

For example, we have a block of numbers: [12345, -12345, 0].

(1). VLQ only works with unsigned integers. Transfer the sign bit to the end of the integer.

12345 in binary is 11000000111001. Added 0 (positive) to the end: 110000001110010.

For -12345 take a positive form and add 1 (negative) to the end: 110000001110011.

Result is [110000001110010, 110000001110011, 0].

(2). Transform to the VLQ-sequence. For Base64 we need a block of 6-bit numbers. Most significant bit is reserved - it is "continuation".

Split numbers to groups of 5 bits: [11000 00011 10010, 11000 00011 10011, 00000]. Output starting from the least significant bits. If the group is not the last in the current number then set the continuation bit.

Result: [110010 100011 011000 110011 100011 011000 000000]. Or decimal [50, 35, 24, 51, 35, 24, 0]. These are VLQ digits.

(3). Replace the numbers on the letters of the Base64-alphabet. The standard alphabet is A..Za..z0..9+/.

Result is yjYzjYA.

How to use the library

use axy\codecs\base64vlq\Encoder;

$encoder = new Encoder();

$encoder->encode([12345, -12345, 0]); // yjYzjYA
$encoder->decode('yjYzjYA'); //  [12345, 012345, 9]

$encoder->decode('Variable+Length+QuantitY'); // [-10, 13, -13349, -13 ... -12797139]

Or default encoder can be obtained as follow:

$encoder = Encoder::getStandardInstance();

In this case, the object creation and preliminary calculations are performed only once.

Custom options

The standard encoder uses standard options:

  1. Transfer the sign bit.
  2. 6-bit VLQ digits.
  3. Standard alphabet: A..Za..z0..9+/.

You can apply your settings:

Encoder::__construct([array|string $alphabet, int $bits, bool $signed = true])
/* Custom alphabet, 4 bits, no sign transfer */
$encoder = new Encoder('My Alphabet', 3, false);

$encoder->encode([12345, 6789]); // phalllApplhhhy

Custom alphabet can be specified as a string (My Alphabet) or as an array ([1 => 'A', 10 => 'B', 15 => 'C', 20 => 'D']).


The error classes are located in the namespace axy\codecs\base64vlq\Encoder\Errors.

  • Error
    • VLQ
      • InvalidVLQSequence
    • Base64
      • InvalidBase64
      • InvalidBase64Input
$encoder->decode('Az'); // VLQ sequence is invalid: [0,51]

z is 51 (the continuation bit = 1). The last digit must have 0 in continuation bit.

$encoder->decode('A*A'); // Base-64 string is invalid: "A*A"

* are not in the standard Base64 alphabet.


For the standard encoder this exception should not occur.

Can occur for incorrect custom options:

$encoder = new Encoder('qwe', 10);
$encoder->encode([10, 20, 30]); // Number 20 is not found in Base64 alphabet

10 bits is 1024 variants, but the alphabet contains only 3 letter.