SortSupport: Sorting in Postgres at Speed

Most often, there’s a trade off involved in optimizing software. The cost of better performance is the opportunity cost of the time that it took to write the optimization, and the additional cost of maintenance for code that becomes more complex and more difficult to understand.

Many projects prioritize product development over improving runtime speed. Time is spent building new things instead of making existing things faster. Code is kept simpler and easier to understand so that adding new features and fixing bugs stays easy, even as particular people rotate in and out and institutional knowledge is lost.

But that’s certainly not the case in all domains. Game code is often an interesting read because it comes from an industry where speed is a competitive advantage, and it’s common practice to optimize liberally even at some cost to modularity and maintainability. One technique for that is to inline code in critical sections even to the point of absurdity. CryEngine, open-sourced a few years ago, has a few examples of this, with “tick” functions like this one that are 800+ lines long with 14 levels of indentation.

Another common place to find optimizations is in databases. While games optimize because they have to, databases optimize because they’re an example of software that’s extremely leveraged – if there’s a way to make running select queries or building indexes 10% faster, it’s not an improvement that affects just a couple users, it’s one that’ll potentially invigorate millions of installations around the world. That’s enough of an advantage that the enhancement is very often worth it, even if the price is a challenging implementation or some additional code complexity.

Postgres contains a wide breadth of optimizations, and happily they’ve been written conscientiously so that the source code stays readable. The one that we’ll look at today is SortSupport, a technique for localizing the information needed to compare data into places where it can be accessed very quickly, thereby making sorting data much faster. Sorting for types that have had Sortsupport implemented usually gets twice as fast or more, a speedup that transfers directly into common database operations like ORDER BY, DISTINCT, and CREATE INDEX.

Sorting with abbreviated keys

While sorting, Postgres builds a series of tiny structures that represent the data set being sorted. These tuples have space for a value the size of a native pointer (i.e. 64 bits on a 64-bit machine) which is enough to fit the entirety of some common types like booleans or integers (known as pass-by-value types), but not for others that are larger than 64 bits or arbitrarily large. In their case, Postgres will follow a references back to the heap when comparing values (they’re appropriately called pass-by-reference types). Postgres is very fast, so that still happens quickly, but it’s slower than comparing values readily available in memory.

An array of sort tuples.

SortSupport augments pass-by-reference types by bringing a representative part of their value into the sort tuple to save trips to the heap. Because sort tuples usually don’t have the space to store the entirety of the value, SortSupport generates a digest of the full value called an abbreviated key, and stores it instead. The contents of an abbreviated key vary by type, but they’ll aim to store as much sorting-relevant information as possible while remaining faithful to pre-existing sorting rules.

Abbreviated keys should never produce an incorrect comparison, but it’s okay if they can’t fully resolve one. If two abbreviated keys look equal, Postgres will fall back to comparing their full heap values to make sure it gets the right result (called an “authoritative comparison”).

A sort tuple with an abbreviated key and pointer to the heap.

Implementing an abbreviated key is straightforward in many cases. UUIDs are a good example of that: at 128 bits long they’re always larger than the pointer size even on a 64-bit machine, but we can get a very good proxy of their full value just by sampling their first 64 bits (or 32 on a 32-bit machine). Especially for V4 UUIDs which are almost entirely random 1, the first 64 bits will be enough to definitively determine the order for all but unimaginably large data sets. Indeed, the patch that brought in SortSupport for UUIDs made sorting them about twice as fast!

String-like types (e.g. text, varchar) aren’t too much harder: just pack as many characters from the front of the string in as possible (although made somewhat more complicated by locales). Adding SortSupport for them made operations like CREATE INDEX about three times faster. My only ever patch to Postgres was implementing SortSupport for the macaddr type, which was fairly easy because although it’s pass-by-reference, its values are only six bytes long 2. On a 64-bit machine we have room for all six bytes, and on 32-bit we sample the MAC address’ first four bytes.

Some abbreviated keys are more complex. The implementation for the numeric type, which allows arbitrary scale and precision, involves excess-K coding and breaking available bits into multiple parts to store sort-relevant fields.

A glance at the implementation

Let’s try to get a basic idea of how SortSupport is implemented by examining a narrow slice of source code. Sorting in Postgres is extremely complex and involves thousands of lines of code, so fair warning that I’m going to simplify some things and skip a lot of others.

A good place start is with Datum, the pointer-sized type (32 or 64 bits, depending on the CPU) used for sort comparisons. It stores entire values for pass-by-value types, abbreviated keys for pass-by-reference types that implement SortSupport, and a pointer for those that don’t. You can find it defined in postgres.h:

/*
 * A Datum contains either a value of a pass-by-value type or a pointer
 * to a value of a pass-by-reference type.  Therefore, we require:
 *
 * sizeof(Datum) == sizeof(void *) == 4 or 8
 */

typedef uintptr_t Datum;

#define SIZEOF_DATUM SIZEOF_VOID_P

Building abbreviated keys for UUID

The format of abbreviated keys for the uuid type is one of the easiest to understand, so let’s look at that. In Postgres, the struct pg_uuid_t defines how UUIDs are physically stored in the heap (from uuid.h):

/* uuid size in bytes */
#define UUID_LEN 16

typedef struct pg_uuid_t
{
    unsigned char data[UUID_LEN];
} pg_uuid_t;

You might be used to seeing UUIDs represented in string format like 123e4567-e89b-12d3-a456-426655440000, but remember that this is Postgres which likes to be as efficient as possible! A UUID contains 16 bytes worth of information, so pg_uuid_t above defines an array of exactly 16 bytes. No wastefulness to be found.

SortSupport implementations define a conversion routine which takes the original value and produces a datum containing an abbreviated key. Here’s the one for UUIDs (from uuid.c):

static Datum
uuid_abbrev_convert(Datum original, SortSupport ssup)
{
    pg_uuid_t *authoritative = DatumGetUUIDP(original);
    Datum      res;

    memcpy(&res, authoritative->data, sizeof(Datum));

    ...

    /*
     * Byteswap on little-endian machines.
     *
     * This is needed so that uuid_cmp_abbrev() (an unsigned integer 3-way
     * comparator) works correctly on all platforms.  If we didn't do this,
     * the comparator would have to call memcmp() with a pair of pointers to
     * the first byte of each abbreviated key, which is slower.
     */
    res = DatumBigEndianToNative(res);

    return res;
}

memcpy (“memory copy”) extracts a datum worth of bytes from a pg_uuid_t and places it into res. We can’t take the whole UUID, but we’ll be taking its 4 or 8 most significant bytes, which will be enough information for most comparisons.

Abbreviated key formats for the `uuid` type.

The call DatumBigEndianToNative is there to help with an optimization. When comparing our abbreviated keys, we could do so with memcmp (“memory compare”) which would compare each byte in the datum one at a time. That’s perfectly functional of course, but because our datums are the same size as native integers, we can instead choose to take advantage of the fact that CPUs are optimized to compare integers really, really quickly, and arrange the datums in memory as if they were integers. You can see this integer comparison taking place in the UUID abbreviated key comparison function:

static int
uuid_cmp_abbrev(Datum x, Datum y, SortSupport ssup)
{
    if (x > y)
        return 1;
    else if (x == y)
        return 0;
    else
        return -1;
}

However, pretending that some consecutive bytes in memory are integers introduces some complication. Integers might be stored like data in pg_uuid_t with the most significant byte first, but that depends on the architecture of the CPU. We call architectures that store numerical values this way big-endian. Big-endian machines exist, but the chances are that the CPU you’re using to read this article stores bytes in the reverse order of their significance, with the most significant at the highest address. This layout is called little-endian, and is in use by Intel’s X86, as well as being the default mode for ARM chips like the ones in Android and iOS devices.

If we left the big-endian result of the memcpy unchanged on little-endian systems, the resulting integer would be wrong. The answer is to byteswap, which reverses the order of the bytes, and corrects the integer.

Example placement of integer bytes on little and big endian architectures.

You can see in pg_bswap.h that DatumBigEndianToNative is defined as a no-op on a big-endian machine, and is otherwise connected to a byteswap (“bswap”) routine of the appropriate size:

#ifdef WORDS_BIGENDIAN

        #define        DatumBigEndianToNative(x)    (x)

#else

    #if SIZEOF_DATUM == 8
        #define        DatumBigEndianToNative(x)    pg_bswap64(x)
    #else
        #define        DatumBigEndianToNative(x)    pg_bswap32(x)
    #endif

#endif

Conversion abort & HyperLogLog

Let’s touch upon one more feature of uuid_abbrev_convert. In data sets with very low cardinality (i.e, many duplicated items) SortSupport introduces some danger of worsening performance. With so many duplicates, the contents of abbreviated keys would often show equality, in which cases Postgres would often have to fall back to the authoritative comparator. In effect, by adding SortSupport we would have added a useless additional comparison that wasn’t there before.

To protect against performance regression, SortSupport has a mechanism for aborting abbreviated key conversion. If the data set is found to be below a certain cardinality threshold, Postgres stops abbreviating, reverts any keys that were already abbreviated, and disables further abbreviation for the sort.

Cardinality is estimated with the help of HyperLogLog, an algorithm that estimates the distinct count of a data set in a very memory-efficient way. Here you can see the conversion routine adding new values to the HyperLogLog if an abort is still possible:

uss->input_count += 1;

if (uss->estimating)
{
    uint32        tmp;

#if SIZEOF_DATUM == 8
    tmp = (uint32) res ^ (uint32) ((uint64) res >> 32);
#else
    tmp = (uint32) res;
#endif

    addHyperLogLog(&uss->abbr_card, DatumGetUInt32(hash_uint32(tmp)));
}

And where it makes an abort decision (from uuid.c):

static bool
uuid_abbrev_abort(int memtupcount, SortSupport ssup)
{
    ...

    abbr_card = estimateHyperLogLog(&uss->abbr_card);

    /*
     * If we have >100k distinct values, then even if we were
     * sorting many billion rows we'd likely still break even,
     * and the penalty of undoing that many rows of abbrevs would
     * probably not be worth it. Stop even counting at that point.
     */
    if (abbr_card > 100000.0)
    {
        uss->estimating = false;
        return false;
    }

    /*
     * Target minimum cardinality is 1 per ~2k of non-null inputs.
     * 0.5 row fudge factor allows us to abort earlier on genuinely
     * pathological data where we've had exactly one abbreviated
     * value in the first 2k (non-null) rows.
     */
    if (abbr_card < uss->input_count / 2000.0 + 0.5)
    {
        return true;
    }

    ...
}

It also covers aborting the case where we have a data set that’s poorly suited to the abbreviated key format. For example, imagine a million UUIDs that all shared a common prefix in their first eight bytes, but were distinct in their last eight 3. Realistically this will be extremely unusual, so abbreviated key conversion will rarely abort.

Tuples and data types

Sort tuples are the tiny structures that Postgres sorts in memory. They hold a reference to the “true” tuple, a datum, and a flag to indicate whether or not the first value is NULL (which has its own special sorting semantics). The latter two are named with a 1 suffix as datum1 and isnull1 because they represent only one field worth of information. Postgres will need to fall back to different values in the event of equality in a multi-column comparison. From tuplesort.c:

/*
 * The objects we actually sort are SortTuple structs.  These contain
 * a pointer to the tuple proper (might be a MinimalTuple or IndexTuple),
 * which is a separate palloc chunk --- we assume it is just one chunk and
 * can be freed by a simple pfree() (except during merge, when we use a
 * simple slab allocator).  SortTuples also contain the tuple's first key
 * column in Datum/nullflag format, and an index integer.
 */
typedef struct
{
    void       *tuple;          /* the tuple itself */
    Datum       datum1;         /* value of first key column */
    bool        isnull1;        /* is first key column NULL? */
    int         tupindex;       /* see notes above */
} SortTuple;

In the code we’ll look at below, SortTuple may reference a heap tuple, which has a variety of different struct representations. One used by the sort algorithm is HeapTupleHeaderData (from htup_details.h):

struct HeapTupleHeaderData
{
    union
    {
        HeapTupleFields t_heap;
        DatumTupleFields t_datum;
    }            t_choice;

    ItemPointerData t_ctid; /* current TID of this or newer tuple (or a
                             * speculative insertion token) */

    ...
}

Heap tuples have a pretty complex structure which we won’t cover, but you can see that it contains an ItemPointerData value. This struct is what gives Postgres the precise information it needs to find data in the heap (from itemptr.h):

/*
 * ItemPointer:
 *
 * This is a pointer to an item within a disk page of a known file
 * (for example, a cross-link from an index to its parent table).
 * blkid tells us which block, posid tells us which entry in the linp
 * (ItemIdData) array we want.
 */
typedef struct ItemPointerData
{
    BlockIdData ip_blkid;
    OffsetNumber ip_posid;
}

Tuple comparison

The algorithm to compare abbreviated keys is duplicated in the Postgres source in a number of places depending on the sort operation being carried out. We’ll take a look at comparetup_heap (from tuplesort.c) which is used when sorting based on the heap. This would be invoked for example if you ran an ORDER BY on a field that doesn’t have an index on it.

static int
comparetup_heap(const SortTuple *a, const SortTuple *b, Tuplesortstate *state)
{
    SortSupport sortKey = state->sortKeys;
    HeapTupleData ltup;
    HeapTupleData rtup;
    TupleDesc     tupDesc;
    int           nkey;
    int32         compare;
    AttrNumber    attno;
    Datum         datum1,
                  datum2;
    bool          isnull1,
                  isnull2;


    /* Compare the leading sort key */
    compare = ApplySortComparator(a->datum1, a->isnull1,
                                  b->datum1, b->isnull1,
                                  sortKey);
    if (compare != 0)
        return compare;

ApplySortComparator gets a comparison result between two datum values. It’ll compare two abbreviated keys where appropriate and handles NULL sorting semantics. The return value of a comparison follows the spirit of C’s strcmp: when comparing (a, b), -1 indicates a < b, 0 indicates equality, and 1 indicates a > b.

The algorithm returns immediately if inequality (!= 0) was detected. Otherwise, it checks to see if abbreviated keys were used, and if so applies the authoritative comparison if they were. Because space in abbreviated keys is limited, two being equal doesn’t necessarily indicate that the values that they represent are.

if (sortKey->abbrev_converter)
{
    attno = sortKey->ssup_attno;

    datum1 = heap_getattr(&ltup, attno, tupDesc, &isnull1);
    datum2 = heap_getattr(&rtup, attno, tupDesc, &isnull2);

    compare = ApplySortAbbrevFullComparator(datum1, isnull1,
                                            datum2, isnull2,
                                            sortKey);
    if (compare != 0)
        return compare;
}

Once again, the algorithm returns if inequality was detected. If not, it starts to look beyond the first field (in the case of a multi-column sort):

    ...

    sortKey++;
    for (nkey = 1; nkey < state->nKeys; nkey++, sortKey++)
    {
        attno = sortKey->ssup_attno;

        datum1 = heap_getattr(&ltup, attno, tupDesc, &isnull1);
        datum2 = heap_getattr(&rtup, attno, tupDesc, &isnull2);

        compare = ApplySortComparator(datum1, isnull1,
                                      datum2, isnull2,
                                      sortKey);
        if (compare != 0)
            return compare;
    }

    return 0;
}

After finding abbreviated keys to be equal, full values to be equal, and all additional sort fields to be equal, the last step is to return 0, indicating in classic libc style that the two tuples are really, fully equal.

Fast code and leveraged software

SortSupport is a good example of the type of low-level optimization that most of us probably wouldn’t bother with in our projects, but which makes sense in an extremely leveraged system like a database. As implementations are added for it and Postgres’ tens of thousands of users like myself upgrade, common operations like DISTINCT, ORDER BY, and CREATE INDEX get twice as fast, for free.

Credit to Peter Geoghegan for some of the original exploration of this idea and implementations for UUID and a generalized system for SortSupport on variable-length string types, Robert Haas and Tom Lane for adding the necessary infrastructure, and Andrew Gierth for a difficult implementation for numeric. (I hope I got all that right.)

1 A note for the pedantic that V4 UUIDs usually have only 122 bits of randomness as four bits are used for the version and two for the variant.

2 The new type macaddr8 was later introduced to handle EUI-64 MAC addresses, which are 64 bits long.

3 A data set of UUIDs with common datum-sized prefixes is a pretty unlikely scenario, but it’s a little more realistic for variable-length string types, where users are storing much more free-form data.

Article
SortSupport: Sorting in Postgres at Speed

Published
February 4, 2019

Location
San Francisco

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