fanum tax 64-bit integers with LEB128

Matthew Kim

Last update: May 22, 2024

Overview

rizz64

Fanum* tax 64-bit integers.

_{* Fanum is a popular streamer who taxes his friends by taking bites of their food.}

This crate provides an efficient and powerful variable-length integer codec using LEB128 compression.

Why rizz64 is helpful

It's super efficient in representing smaller numbers with fewer bytes. Instead of a fixed-size solution like u64, this form of encoding can store values using less space or memory.

Basic metrics:

Decimal	Powers of 2	# of Bytes Needed
0..127	`2^0-1`..`2^7-1`	1
128..16383	`2^7`..`2^14-1`	2
16384..2097151	`2^14`..`2^21-1`	3
2097152..268435455	`2^21`..`2^28-1`	4

and so on... to compute the number of bytes required, you can use the following:

The upper bound of log2(max(x, 1)) / 7, where x is your number. This is derived from the fact that each byte can represent 7 bits. rizz64 uses a base-2 logarithm to determine the magnitude in bits. We call max(x, 1) to ensure this value could never be 0. We take the upper bound and round to the nearest whole number.

How encoding works

For a given u64, we process the number by groups of 7 bits. For every group, if there are more than 7 bits still to be encoded, we loop.

In the loop, the least significant 7 bits are extracted and packed into a buffer. The 8th bit is the most significant bit (MSB); we set the MSB to 1 to indicate there are more groups ahead. Then, we shift right (>>=) by 7 bits and we process the next group.

After looping, the remaining bits of the number are packed into the buffer. This is the last byte and since we're halting, we don't set the MSB to 1.

Literature

LEB128
sqlite variable-length ints
varint.go

Todo

Go outside

Comments

feat: skip bound checks by iterating

Instead of running:

loop {
     unsafe { *buf.get_mut_unchecked(i) = .... } 
}

The rust compiler seems to skip this bound check when shoving this into an iterator that is:

for i in 0..buf.len() {
     // same stuff here
}

compiler explorer: https://godbolt.org/z/49P653o9j

Performance

Running benchmarks indicate significantly faster execution times.

Benchmarking Log/write_u64 1152921504606846976: Collecting 10
Log/write_u64 1152921504606846976
                        time:   [321.67 ps 325.25 ps 329.86 ps]
                        change: [-91.933% -91.871% -91.799%] (p = 0.00 < 0.05)
                        Performance has improved.
Found 12 outliers among 100 measurements (12.00%)

It also seems to beat out the leb128 crate by significant measures:

Benchmarking Log/leb128::write::unsigned 1152921504606846976:
Log/leb128::write::unsigned 1152921504606846976
                        time:   [1.6255 ns 1.6417 ns 1.6615 ns]
Found 11 outliers among 100 measurements (11.00%)
  5 (5.00%) high mild
  6 (6.00%) high severe

Note a more robust benchmarking report is needed to fully assert these claims

opened by friendlymatthew 0

fanum tax 64-bit integers with LEB128

Related tags

Overview

rizz64

Why rizz64 is helpful

How encoding works

Literature

Todo

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Comments

feat: skip bound checks by iterating

Performance

Owner

Matthew Kim

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