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Posted to pr@cassandra.apache.org by GitBox <gi...@apache.org> on 2022/05/19 09:14:01 UTC
[GitHub] [cassandra] blambov commented on a diff in pull request #1294: CASSANDRA-6936: Byte-comparable API
blambov commented on code in PR #1294:
URL: https://github.com/apache/cassandra/pull/1294#discussion_r876817286
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src/java/org/apache/cassandra/utils/bytecomparable/ByteComparable.md:
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+ to you under the Apache License, Version 2.0 (the
+ "License"); you may not use this file except in compliance
+ with the License. You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+ Unless required by applicable law or agreed to in writing, software
+ distributed under the License is distributed on an "AS IS" BASIS,
+ WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ See the License for the specific language governing permissions and
+ limitations under the License.
+-->
+
+# Byte-comparable translation of types (ByteComparable/ByteSource)
+
+## Problem / Motivation
+
+Cassandra has a very heavy reliance on comparisons — they are used throughout read and write paths, coordination,
+compaction, etc. to be able to order and merge results. It also supports a range of types which often require the
+compared object to be completely in memory to order correctly, which in turn has necessitated interfaces where
+comparisons can only be applied if the compared objects are completely loaded.
+
+This has some rather painful implications on the performance of the database, both in terms of the time it takes to load,
+compare and garbage collect, as well as in terms of the space required to hold complete keys in on-disk indices and
+deserialized versions in in-memory data structures. In addition to this, the reliance on comparisons forces Cassandra to
+use only comparison-based structures, which aren’t the most efficient.
+
+There is no way to escape the need to compare and order objects in Cassandra, but the machinery for doing this can be
+done much more smartly if we impose some simple structure in the objects we deal with — byte ordering.
+
+The term “byte order” as used in this document refers to the property of being ordered via lexicographic compare on the
+unsigned values of the byte contents. Some of the types in Cassandra already have this property (e.g. strings, blobs),
+but other most heavily used ones (e.g. integers, uuids) don’t.
+
+When byte order is universally available for the types used for keys, several key advantages can be put to use:
+- Comparisons can be done using a single simple method, core machinery doesn’t need to know anything about types.
+- Prefix differences are enough to define order; unique prefixes can be used instead of complete keys.
+- Tries can be used to store, query and iterate over ranges of keys, providing fast lookup and prefix compression.
+- Merging can be performed by merging tries, significantly reducing the number of necessary comparisons.
+
+## Ordering the types
+
+As we want to keep all existing functionality in Cassandra, we need to be able to deal with existing
+non-byte-order-comparable types. This requires some form of conversion of each value to a sequence of bytes that can be
+byte-order compared (also called "byte-comparable"), as well as the inverse conversion from byte-comparable to value.
+
+As one of the main advantages of byte order is the ability to decide comparisons early, without having to read the whole
+of the input sequence, byte-ordered interpretations of values are represented as sources of bytes with unknown length,
+using the interface `ByteSource`. The interface declares one method, `next()` which produces the next byte of the
+stream, or `ByteSource.END_OF_STREAM` if the stream is exhausted.
+
+`END_OF_STREAM` is chosen as `-1` (`(int) -1`, which is outside the range of possible byte values), to make comparing
+two byte sources as trivial (and thus fast) as possible.
+
+To be able to completely abstract type information away from the storage machinery, we also flatten complex types into
+single byte sequences. To do this, we add separator bytes in front, between components, and at the end and do some
+encoding of variable-length sequences.
+
+The other interface provided by this package `ByteComparable`, is an entity whose byte-ordered interpretation can be
+requested. The interface is implemented by `DecoratedKey`, and can be requested for clustering keys and bounds using
+`ClusteringComparator.asByteComparable`. The inverse translation is provided by
+`Buffer/NativeDecoratedKey.fromByteComparable` and `ClusteringComparator.clustering/bound/boundaryFromByteComparable`.
+
+The (rather technical) paragraphs below detail the encoding we have chosen for the various types. For simplicity we
+only discuss the bidirectional `OSS41` version of the translation. The implementations in code of the various mappings
+are in the releavant `AbstractType` subclass.
+
+### Desired properties
+
+Generally, we desire the following two properties from the byte-ordered translations of values we use in the database:
+- Comparison equivalence (1):
+ <math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics>
+ <mstyle displaystyle="true">
+ <mo>∀</mo>
+ <mi>x</mi>
+ <mo>,</mo>
+ <mi>y</mi>
+ <mo>∈</mo>
+ <mi>T</mi>
+ <mo>,</mo>
+ <mrow>
+ <mtext>compareBytesUnsigned</mtext>
+ </mrow>
+ <mrow>
+ <mo>(</mo>
+ <mi>T</mi>
+ <mo>.</mo>
+ <mrow>
+ <mtext>byteOrdered</mtext>
+ </mrow>
+ <mrow>
+ <mo>(</mo>
+ <mi>x</mi>
+ <mo>)</mo>
+ </mrow>
+ <mo>,</mo>
+ <mi>T</mi>
+ <mo>.</mo>
+ <mrow>
+ <mtext>byteOrdered</mtext>
+ </mrow>
+ <mrow>
+ <mo>(</mo>
+ <mi>y</mi>
+ <mo>)</mo>
+ </mrow>
+ <mo>)</mo>
+ </mrow>
+ <mo>=</mo>
+ <mi>T</mi>
+ <mo>.</mo>
+ <mrow>
+ <mtext>compare</mtext>
+ </mrow>
+ <mrow>
+ <mo>(</mo>
+ <mi>x</mi>
+ <mo>,</mo>
+ <mi>y</mi>
+ <mo>)</mo>
+ </mrow>
+ </mstyle>
+ <!-- <annotation encoding="text/x-asciimath">forall x,y in T, "compareBytesUnsigned"(T."byteOrdered"(x), T."byteOrdered"(y))=T."compare"(x, y)</annotation> -->
+ </semantics>
+ </math>
+- Prefix-freedom (2):
+ <math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics>
+ <mstyle displaystyle="true">
+ <mo>∀</mo>
+ <mi>x</mi>
+ <mo>,</mo>
+ <mi>y</mi>
+ <mo>∈</mo>
+ <mi>T</mi>
+ <mo>,</mo>
+ <mi>T</mi>
+ <mo>.</mo>
+ <mrow>
+ <mtext>byteOrdered</mtext>
+ </mrow>
+ <mrow>
+ <mo>(</mo>
+ <mi>x</mi>
+ <mo>)</mo>
+ </mrow>
+ <mrow>
+ <mspace width="1ex" />
+ <mtext> is not a prefix of </mtext>
+ <mspace width="1ex" />
+ </mrow>
+ <mi>T</mi>
+ <mo>.</mo>
+ <mrow>
+ <mtext>byteOrdered</mtext>
+ </mrow>
+ <mrow>
+ <mo>(</mo>
+ <mi>y</mi>
+ <mo>)</mo>
+ </mrow>
+ </mstyle>
+ <!-- <annotation encoding="text/x-asciimath">forall x,y in T, T."byteOrdered"(x) " is not a prefix of " T."byteOrdered"(y)</annotation> -->
+ </semantics>
+ </math>
+
+The former is the essential requirement, and the latter allows construction of encodings of sequences of multiple
+values, as well as a little more efficiency in the data structures.
+
+To more efficiently encode byte-ordered blobs, however, we use a slightly tweaked version of the above requirements:
+
+- Comparison equivalence (3):
+ <math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics>
+ <mstyle displaystyle="true">
+ <mo>∀</mo>
+ <mi>x</mi>
+ <mo>,</mo>
+ <mi>y</mi>
+ <mo>∈</mo>
+ <mi>T</mi>
+ <mo>,</mo>
+ <mo>∀</mo>
+ <msub>
+ <mi>b</mi>
+ <mn>1</mn>
+ </msub>
+ <mo>,</mo>
+ <msub>
+ <mi>b</mi>
+ <mn>2</mn>
+ </msub>
+ <mo>∈</mo>
+ <mrow>
+ <mo>[</mo>
+ <mn>0x10</mn>
+ <mo>-</mo>
+ <mn>0xEF</mn>
+ <mo>]</mo>
+ </mrow>
+ <mo>,</mo>
+ <mtext><br/></mtext>
+ <mrow>
+ <mtext>compareBytesUnsigned</mtext>
+ </mrow>
+ <mrow>
+ <mo>(</mo>
+ <mi>T</mi>
+ <mo>.</mo>
+ <mrow>
+ <mtext>byteOrdered</mtext>
+ </mrow>
+ <mrow>
+ <mo>(</mo>
+ <mi>x</mi>
+ <mo>)</mo>
+ </mrow>
+ <mo>+</mo>
+ <msub>
+ <mi>b</mi>
+ <mn>1</mn>
+ </msub>
+ <mo>,</mo>
+ <mi>T</mi>
+ <mo>.</mo>
+ <mrow>
+ <mtext>byteOrdered</mtext>
+ </mrow>
+ <mrow>
+ <mo>(</mo>
+ <mi>y</mi>
+ <mo>)</mo>
+ </mrow>
+ <mo>+</mo>
+ <msub>
+ <mi>b</mi>
+ <mn>2</mn>
+ </msub>
+ <mo>)</mo>
+ </mrow>
+ <mo>=</mo>
+ <mi>T</mi>
+ <mo>.</mo>
+ <mrow>
+ <mtext>compare</mtext>
+ </mrow>
+ <mrow>
+ <mo>(</mo>
+ <mi>x</mi>
+ <mo>,</mo>
+ <mi>y</mi>
+ <mo>)</mo>
+ </mrow>
+ </mstyle>
+ <!-- <annotation encoding="text/x-asciimath">forall x,y in T, forall b_1, b_2 in [0x10-0xEF],
+ "compareBytesUnsigned"(T."byteOrdered"(x)+b_1, T."byteOrdered"(y)+b_2)=T."compare"(x, y)</annotation> -->
+ </semantics>
+ </math>
+- Weak prefix-freedom (4):
+ <math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics>
+ <mstyle displaystyle="true">
+ <mo>∀</mo>
+ <mi>x</mi>
+ <mo>,</mo>
+ <mi>y</mi>
+ <mo>∈</mo>
+ <mi>T</mi>
+ <mo>,</mo>
+ <mo>∀</mo>
+ <mi>b</mi>
+ <mo>∈</mo>
+ <mrow>
+ <mo>[</mo>
+ <mn>0x10</mn>
+ <mo>-</mo>
+ <mn>0xEF</mn>
+ <mo>]</mo>
+ </mrow>
+ <mo>,</mo>
+ <mtext><br/></mtext>
+ <mrow>
+ <mo>(</mo>
+ <mi>T</mi>
+ <mo>.</mo>
+ <mrow>
+ <mtext>byteOrdered</mtext>
+ </mrow>
+ <mrow>
+ <mo>(</mo>
+ <mi>x</mi>
+ <mo>)</mo>
+ </mrow>
+ <mo>+</mo>
+ <mi>b</mi>
+ <mo>)</mo>
+ </mrow>
+ <mrow>
+ <mspace width="1ex" />
+ <mtext> is not a prefix of </mtext>
+ <mspace width="1ex" />
+ </mrow>
+ <mi>T</mi>
+ <mo>.</mo>
+ <mrow>
+ <mtext>byteOrdered</mtext>
+ </mrow>
+ <mrow>
+ <mo>(</mo>
+ <mi>y</mi>
+ <mo>)</mo>
+ </mrow>
+ </mstyle>
+ <!-- <annotation encoding="text/x-asciimath">forall x,y in T, forall b in [0x10-0xEF],
+ (T."byteOrdered"(x)+b) " is not a prefix of " T."byteOrdered"(y)</annotation> -->
+ </semantics>
+ </math>
+
+These versions allow the addition of a separator byte after each value, and guarantee that the combination with
+separator fulfills the original requirements. (3) is somewhat stronger than (1) but is necessarily true if (2) is also
+in force, while (4) trivially follows from (2).
+
+## Fixed length unsigned integers (Murmur token, date/time)
+
+This is the trivial case, as we can simply use the input bytes in big-endian order. The comparison result is the same,
+and fixed length values are trivially prefix free, i.e. (1) and (2) are satisfied, and thus (3) and (4) follow from the
+observation above.
+
+## Fixed-length signed integers (byte, short, int, legacy bigint)
+
+As above, but we need to invert the sign bit of the number to put negative numbers before positives. This maps
+`MIN_VALUE` to `0x00`..., `-1` to `0x7F…`, `0` to `0x80…`, and `MAX_VALUE` to `0xFF…`; comparing the resulting number
+as an unsigned integer has the same effect as comparing the source signed.
+
+Examples:
+
+|Type and value|bytes|encodes as|
+|--------------|-----|----------|
+|int 1 |00 00 00 01| 80 00 00 01
+|short -1 |FF FF | 7F FF
+|byte 0 |00 | 80
+|int MAX_VALUE |7F FF FF FF| FF FF FF FF
+|long MIN_VALUE|80 00 00 00 00 00 00 00| 00 00 00 00 00 00 00 00
+
+## Variable-length encoding of integers (current bigint)
+
+Another way to encode integers that may save significant amounts of space when smaller numbers are often in use, but
+still permits large values to be efficiently encoded, is to use an encoding scheme similar to UTF-8.
+
+For unsigned numbers this can be done by starting the number with as many 1s in most significant bits as there are
+additional bytes in the encoding, followed by a 0, and the bits of the number. Numbers between 0 and 127 are encoded
+in one byte, and each additional byte adds 7 more bits. Values that use all 8 bytes do not need a 9th bit of 0 and can
+thus fit 9 bytes. Because longer numbers have more 1s in their MSBs, they compare
+higher than shorter ones (and we always use the shortest representation). Because the length is specified through these
+initial bits, no value can be a prefix of another.
+
+| Value | bytes |encodes as|
+|------------------|-------------------------|----------|
+| 0 | 00 00 00 00 00 00 00 00 | 00
+| 1 | 00 00 00 00 00 00 00 01 | 01
+| 127 (2^7-1) | 00 00 00 00 00 00 00 7F | 7F
+| 128 (2^7) | 00 00 00 00 00 00 00 80 | 80 80
+| 16383 (2^14 - 1) | 00 00 00 00 00 00 3F FF | BF FF
+| 16384 (2^14) | 00 00 00 00 00 00 40 00 | C0 40 00
+| 2^31 - 1 | 00 00 00 00 7F FF FF FF | F0 7F FF FF FF
+| 2^31 | 00 00 00 00 80 00 00 00 | F0 80 00 00 00
+| 2^56 - 1 | 00 FF FF FF FF FF FF FF | FE FF FF FF FF FF FF FF
+| 2^56 | 01 00 00 00 00 00 00 00 | FF 01 00 00 00 00 00 00 00
+| 2^64- 1 | FF FF FF FF FF FF FF FF | FF FF FF FF FF FF FF FF FF
+
+
+To encode signed numbers, we must start with the sign bit, and must also ensure that longer negative numbers sort
+smaller than shorter ones. The first bit of the encoding is the inverted sign (i.e. 1 for positive, 0 for negative),
+followed by the length encoded as a sequence of bits that matches the inverted sign, followed by a bit that differs
+(like above, not necessary for 9-byte encodings) and the bits of the number's two's complement.
+
+| Value | bytes |encodes as|
+|-------------------|--------------------------|----------|
+| 1 | 00 00 00 00 00 00 00 01 | 01
+| -1 | FF FF FF FF FF FF FF FF | 7F
+| 0 | 00 00 00 00 00 00 00 00 | 80
+| 63 | 00 00 00 00 00 00 00 3F | BF
+| -64 | FF FF FF FF FF FF FF C0 | 40
+| 64 | 00 00 00 00 00 00 00 40 | C0 40
+| -65 | FF FF FF FF FF FF FF BF | 3F BF
+| 8191 | 00 00 00 00 00 00 1F FF | DF FF
+| 8192 | 00 00 00 00 00 00 20 00 | E0 20 00
+| Integer.MAX_VALUE | 00 00 00 00 7F FF FF FF | F8 7F FF FF FF
+| Long.MIN_VALUE | 80 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 00
+
+
+## Fixed-size floating-point numbers (float, double)
+
+IEEE-754 was designed with byte-by-byte comparisons in mind, and provides an important guarantee about the bytes of a
+floating point number:
+* If x and y are of the same sign, bytes(x) ≥ bytes(y) ⇔ |x| ≥ |y|.
+
+Thus, to be able to order floating point numbers as unsigned integers, we can:
+* Flip the sign bit so negatives are smaller than positive numbers.
+* If the number was negative, also flip all the other bits so larger magnitudes become smaller integers.
+
+This matches exactly the behaviour of `Double.compare`, which doesn’t fully agree with numerical comparisons (see spec)
+in order to define a natural order over the floating point numbers.
+
+Examples:
+
+|Type and value|bytes|encodes as|
+|---|---|---|
+|float +1.0| 3F 80 00 00| BF 80 00 00|
+|float +0.0| 00 00 00 00| 80 00 00 00|
+|float -0.0| 80 00 00 00| 7F FF FF FF|
+|float -1.0| BF 80 00 00| 40 7F FF FF|
+|double +1.0| 3F F0 00 00 00 00 00 00| BF F0 00 00 00 00 00 00|
+|double +Inf| 7F F0 00 00 00 00 00 00| FF F0 00 00 00 00 00 00|
+|double -Inf| FF F0 00 00 00 00 00 00| 00 0F FF FF FF FF FF FF|
+|double NaN| 7F F8 00 00 00 00 00 00| FF F8 00 00 00 00 00 00|
+
+## UUIDs
+UUIDs are fixed-length unsigned integers, where the UUID version/type is compared first, and where bits need to be
+reordered for the time UUIDs. To create a byte-ordered representation, we reorder the bytes: pull the version digit
+first, then the rest of the digits, using the special time order if the version is equal to one.
+
+Examples:
+
+|Type and value|bytes|encodes as|
+|---|---|---|
+|Random (v4)| cc520882-9507-44fb-8fc9-b349ecdee658 | 4cc52088295074fb8fc9b349ecdee658
+|Time (v1) | 2a92d750-d8dc-11e6-a2de-cf8ecd4cf053 | 11e6d8dc2a92d750a2decf8ecd4cf053
+
+## Multi-component sequences (Partition or Clustering keys, tuples), bounds and nulls
+
+As mentioned above, we encode sequences by adding separator bytes in front, between components, and a terminator at the
+end. The values we chose for the separator and terminator are `0x40` and `0x38`, and they serve several purposes:
+- Permits partially specified bounds, with strict/exclusive or non-strict/inclusive semantics. This is done by finishing
+ a bound with a terminator value that is smaller/greater than the separator and terminator. We can use `0x20` for </≥
+ and `0x60` for ≤/>.
+- Permits encoding of `null` and `empty` values. We use `0x3E` as the separator for nulls and `0x3F` for empty,
+ followed by no value bytes. This is always smaller than a sequence with non-null value for this component, but not
+ smaller than a sequence that ends in this component.
+- Helps identify the ending of variable-length components (see below).
+
+Examples:
+
+|Types and values|bytes|encodes as|
+|---|---|---|
+|(short 1, float 1.0) | 00 01, 3F 80 00 00 | 40·80 01·40·BF 80 00 00·38
+|(short -1, null) | FF FF, — | 40·7F FF·3E·38
+|≥ (short 0, float -Inf) | 00 00, FF 80 00 00, >=| 40·80 00·40·00 7F FF FF·20
+|< (short MIN) | 80 00, <= | 40·00 00·20
+|\> (null) | | 3E·60
+|BOTTOM | | 20
+|TOP | | 60
+
+(The middle dot · doesn't exist in the encoding, it’s just a visualisation of the boundaries in the examples.)
+
+Since:
+- all separators in use are within `0x10`-`0xEF`, and
+- we use the same separator for internal components, with the exception of nulls which we encode with a smaller
+ separator
+- the sequence has a fixed number of components or we use a different trailing value whenever it can be shorter
+
+the properties (3) and (4) guarantee that the byte comparison of the encoding goes in the same direction as the
+lexicographical comparison of the sequence. In combination with the third point above, (4) also ensures that no encoding
+is a prefix of another. Since we have (1) and (2), (3) and (4) are also satisfied.
+
+Note that this means that the encodings of all partition and clustering keys used in the database will be prefix-free.
+
+## Variable-length byte comparables (ASCII, UTF-8 strings, blobs, InetAddress)
+
+In isolation, these can be compared directly without reinterpretation. However, once we place these inside a flattened
+sequence of values we need to clearly define the boundaries between values while maintaining order. To do this we use an
+end-of-value marker; since shorter values must be smaller than longer, this marker must be 0 and we need to find a way
+to encode/escape actual 0s in the input sequence.
+
+The method we chose for this is the following:
+- If the input does not end on `00`, a `00` byte is appended at the end.
+- If the input contains a `00` byte, it is encoded as `00 FF`.
+- If the input contains a sequence of *n* `00` bytes, they are encoded as `00` `FE` (*n*-1 times) `FF`
+ (so that we don’t double the size of `00` blobs).
+- If the input ends in `00`, the last `FF` is changed to `FE`
+ (to ensure it’s smaller than the same value with `00` appended).
+
+Examples:
+
+|bytes/sequence|encodes as|
+|---|----|
+|22 00 | 22 00 FE
+|22 00 00 33 | 22 00 FE FF 33 00
+|22 00 11 | 22 00 FF 11 00
+|(blob 22, short 0) | 40·22 00·40·80 00·40
+| ≥ (blob 22 00) | 40·22 00 FE·20
+| ≤ (blob 22 00 00) | 40·22 00 FE FE·60
+
+Within the encoding, a `00` byte can only be followed by a `FE` or `FF` byte, and hence if an encoding is a prefix of
+another, the latter has to have a `FE` or `FF` as the next byte, which ensures both (4) (adding `10`-`EF` to the former
+makes it no longer a prefix of the latter) and (3) (adding `10`-`EF` to the former makes it smaller than the latter; in
+this case the original value of the former is a prefix of the original value of the latter).
+
+## Variable-length integers (varint, RandomPartitioner token), legacy encoding
+
+If integers of unbounded length are guaranteed to start with a non-zero digit, to compare them we can first use a signed
+length, as numbers with longer representations have higher magnitudes. Only if the lengths match we need to compare the
+sequence of digits, which now has a known length.
+
+(Note: The meaning of “digit” here is not the same as “decimal digit”. We operate with numbers stored as bytes, thus it
+makes most sense to treat the numbers as encoded in base-256, where each digit is a byte.)
+
+This translates to the following encoding of varints:
+- Strip any leading zeros. Note that for negative numbers, `BigInteger` encodes leading 0 as `0xFF`.
+- If the length is 128 or greater, lead with a byte of `0xFF` (positive) or `0x00` (negative) for every 128 until there
+ are less than 128 left.
+- Encode the sign and (remaining) length of the number as a byte:
+ - `0x80 + (length - 1)` for positive numbers (so that greater magnitude is higher);
+ - `0x7F - (length - 1)` for negative numbers (so that greater magnitude is lower, and all negatives are lower than
+ positives).
+- Paste the bytes of the number, 2’s complement encoded for negative numbers (`BigInteger` already applies the 2’s
+ complement).
+
+Since when comparing two numbers we either have a difference in the length prefix, or the lengths are the same if we
+need to compare the content bytes, there is no risk that a longer number can be confused with a shorter combined in a
+multi-component sequence. In other words, no value can be a prefix of another, thus we have (1) and (2) and thus (3) and (4)
+as well.
+
+Examples:
+
+| value | bytes |encodes as|
+|--------:|------------------|---|
+| 0 | 00 | 80·00
+| 1 | 01 | 80·01
+| -1 | FF | 7F·FF
+| 255 | 00 FF | 80·FF
+| -256 | FF 00 | 7F·00
+| 256 | 01 00 | 81·01 00
+| 2^16 | 01 00 00 | 82·01 00 00
+| -2^32 | FF 00 00 00 00 | 7C·00 00 00 00
+| 2^1024 | 01 00(128 times) | FF 80·01 00(128 times)
+| -2^2048 | FF 00(256 times) | 00 00 80·00(256 times)
+
+(Middle dot · shows the transition point between length and digits.)
+
+## Variable-length integers, current encoding
+
+Because variable-length integers are also often used to store smaller range integers, it makes sense to also apply
+the variable-length integer encoding. Thus, the current varint scheme chooses to:
+- Strip any leading zeros. Note that for negative numbers, `BigInteger` encodes leading 0 as `0xFF`.
+- Map numbers directly to their variable-length integer encoding, if they have 6 bytes or less.
Review Comment:
There's a [section on this](https://github.com/apache/cassandra/blob/0c78906e85f07468e0ce794838f5807effbb53fd/src/java/org/apache/cassandra/utils/bytecomparable/ByteComparable.md#variable-length-encoding-of-integers-current-bigint) earlier. I'm adding a link to it.
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