## Definition​

Reduce_aggis the only lambda aggregate Presto function. It allows users to define arbitrary aggregation logic using 2 lambda functions.
``reduce_agg(inputValue T, initialState S, inputFunction(S, T, S), combineFunction(S, S, S)) → SReduces all non-NULL input values into a single value. inputFunction will be invoked foreach non-NULL input value. If all inputs are NULL, the result is NULL. In addition to takingthe input value, inputFunction takes the current state, initially initialState, and returns thenew state. combineFunction will be invoked to combine two states into a new state. The finalstate is returned. Throws an error if initialState is NULL or inputFunction or combineFunctionreturns a NULL.``

Once can think of reduce_agg as using inputFunction to implement partial aggregation and combineFunction to implement final aggregation. Partial aggregation processes a list of input values and produces an intermediate state:

``auto s = initialState;for (auto x : input) {   s = inputFunction(s, x);}return s;``

Final aggregation processes a list of intermediate states and computes the final state.

``auto s = intermediates;for (auto i = 1; i < intermediates.size(); ++i)   s = combineFunction(s, intermediates[i]);}return s;``

For example, one can implement SUM aggregation using reduce_agg as follows:

``reduce_agg(c, 0, (s, x) -> s + x, (s, s2) -> s + s2)``

Implementation of AVG aggregation is a bit trickier. For AVG, state is a tuple of sum and count. Hence, reduce_agg can be used to compute (sum, count) pair, but it cannot compute the actual average. One needs to apply a scalar function on top of reduce_agg to get the average.

``SELECT id, sum_and_count.sum / sum_and_count.count FROM (  SELECT id, reduce_agg(value, CAST(row(0, 0) AS row(sum double, count bigint)),    (s, x) -> CAST(row(s.sum + x, s.count + 1) AS row(sum double, count bigint)),    (s, s2) -> CAST(row(s.sum + s2.sum, s.count + s2.count) AS row(sum double, count bigint))) AS sum_and_count  FROM t  GROUP BY id);``

The examples of using reduce_agg to compute SUM and AVG are for illustrative purposes. One should not use reduce_agg if a specialized aggregation function is available.

One use case for reduce_agg we see in production is to compute a product of input values.

``reduce_agg(c, 1.0, (s, x) -> s * x, (s, s2) -> s * s2)``

Another example is to compute a list of top N distinct values from all input arrays.

``reduce_agg(x, array[],            (a, b) -> slice(reverse(array_sort(array_distinct(concat(a, b)))), 1, 1000),            (a, b) -> slice(reverse(array_sort(array_distinct(concat(a, b)))), 1, 1000))``

Note that this is equivalent to the following query:

``SELECT array_agg(v) FROM (    SELECT DISTINCT v    FROM t, UNNEST(x) AS u(v)    ORDER BY v DESC    LIMIT 1000)``

## Implementation​

Efficient implementation of reduce_agg lambda function is not straightforward. Let’s consider the logic for partial aggregation.

``auto s = initialState;for (auto x : input) {   s = inputFunction(s, x);}``

This is a data-dependent loop, i.e. the next loop iteration depends on the results of the previous iteration. inputFunction needs to be invoked on each input value `x` separately. Since inputFunction is a user-defined lambda, invoking inputFunction means evaluating an expression. And since expression evaluation in Velox is optimized for processing large batches of values at a time, evaluating expressions on one value at a time is very inefficient. To optimize the implementation of reduce_agg we need to reduce the number of times we evaluate user-defined lambdas and increase the number of values we process each time.

One approach is to

1. convert all input values into states by evaluating inputFunction(initialState, x);
2. split states into pairs and evaluate combineFunction on all pairs;
3. repeat step (2) until we have only one state left.

Let’s say we have 1024 values to process. Step 1 evaluates inputFunction expression on 1024 values at once. Step 2 evaluates combineFunction on 512 pairs, then on 256 pairs, then on 128 pairs, 64, 32, 16, 8, 4, 2, finally producing a single state. Step 2 evaluates combineFunction 9 times. In total, this implementation evaluates user-defined expressions 10 times on multiple values each time. This is a lot more efficient than the original implementation that evaluates user-defined expressions 1024 times.

In general, given N inputs, the original implementation evaluates expressions N times while the new one log2(N) times.

Note that in case when N is not a power of two, splitting states into pairs may leave an extra state. For example, splitting 11 states produces 5 pairs + one extra state. In this case, we set aside the extra state, evaluate combineFunction on 5 pairs, then bring extra state back to a total of 6 states and continue.

A benchmark, velox/functions/prestosql/aggregates/benchmarks/ReduceAgg.cpp, shows that initial implementation of reduce_agg is 60x slower than SUM, while the optimized implementation is only 3x slower. A specialized aggregation function will always be more efficient than generic reduce_agg, hence, reduce_agg should be used only when specialized aggregation function is not available.

Finally, a side effect of the optimized implementation is that it doesn't support applying reduce_agg to sorted inputs. I.e. one cannot use reduce_agg to compute an equivalent of

``    SELECT a, array_agg(b ORDER BY b) FROM t GROUP BY 1``

The array_agg computation depends on order of inputs. A comparable implementation using reduce_agg would look like this:

``    SELECT a,        reduce_agg(b, array[],                    (s, x) -> concat(s, array[x]),                    (s, s2) -> concat(s, s2)                    ORDER BY b)    FROM t GROUP BY 1``

To respect ORDER BY b, the reduce_agg would have to apply inputFunction to each input value one at a time using a data-dependent loop from above. As we saw, this is very expensive. The optimization we apply does not preserve the order of inputs, hence, cannot support the query above. Note that

Presto doesn't support applying reduce_agg to sorted inputs either.

Thank you Orri Erling for brainstorming and Xiaoxuan Meng and

Pedro Eugênio Rocha Pedreira for reviewing the code.
Tags:

## Learnings from optimizing try_cast

One of the queries shadowed internally at Meta was much slower in Velox compared to presto(2 CPU days vs. 4.5 CPU hours). Initial investigation identified that the overhead is related to casting empty strings inside a try_cast.

In this blogpost I summarize my learnings from investigating and optimizing try_cast.

### Start and end results​

Initial benchmark:

``name                                             total timetry_cast(empty_string_col as int)                     4.88stry_cast(valid_string_col as int)                    2.15ms``

The difference between casting a valid and invalid input is huge (>1000X), although ideally casting an invalid string should be just setting a null and should not be that expensive.

Benchmark results after optimization:

``name                                             total timetry_cast(empty_string_col as int)                    1.24mstry_cast(valid_string_col as int)                    2.15ms``

### Sources of regression​

The investigation revealed several factors that contributed to the huge gap, summarized in the points below in addition to their approximate significance.

Whenever a VeloxUserError is thrown an error log used to be generated, however those errors are expected to, (1) either get converted to null if is thrown from within a try, (2) or show up to the user otherwise. Hence, no need for that expensive logging .

Moreover, each failing row used to generate two log message because VELOX_USER_FAIL was called twice. Disabling logging for user error helped save 2.6s of the 4.88s.

Each time a row is casted four exception were thrown:

1. From within Folly library.
2. From Cast in Conversions.h, the function catch the exception thrown by Folly and convert it to Velox exception and throw it.
3. From castToPrimitive function, which catch the exception and threw a new exception with more context.
4. Finally, a forth throw came from applyToSelectedNoThrow which caught an exception and called toVeloxException to check exception type and re-throw.

Those are addressed and avoided using the following:

1. When the input is an empty string, avoid calling folly by directly checking if the input is empty.
2. Remove the catch and re-throw from Conversions.h
3. Introduce setVeloxExceptionError, which can be used to set the error directly in evalContext without throwing (does not call toVeloxException).
4. Optimize applyToSelectedNoThrow to call setVeloxExceptionError if it catches Velox exception.

With all those changes throwing exceptions is completely avoided when casting empty strings. This takes the runtime down to 382.07ms, but its still much higher than 2.15ms.

Constructing Velox exception is expensive, even when there is no throw at all! Luckily this can be avoided for try_cast, since the output can be directly set to null without having to use the errorVector to track errors. By doing so the benchmark runtime goes down to 1.24ms.

After all the changes we have the following performance numbers for other patterns of similar expressions (much better than before but still can be optimized a lot).

``try_cast(empty_string_col as int)                     1.24ms    808.79try_cast(invalid_string_col as int)                  393.61ms     2.54try(cast(empty_string_col as int))                   375.82ms     2.66try(cast(invalid_string_col as int))                767.74ms      1.30``

All these can be optimized to have the same runtime cost of the first expression 1.24ms.

To do that two thing are needed:

1) Tracking errors for try, should not require constructing exceptions

The way errors are tracked when evaluating a try expression is by setting values in an ErrorVector; which is a vector of VeloxException pointers. This forces the construction of a Velox exception for each row, but that is not needed (for try expressions) since only row numbers need to be tracked to be converted eventually to nulls, but not the actual errors.

This can be changed such that errors are tracked using a selectivity vector. Its worth noting that for other expressions such as conjunct expressions this tracking is needed, hence we need to distinguish between both.

This would help optimize any try(x) expression where x throws for large number of rows.

2)Use throw-free cast library

Avoiding throw and instead returning a boolean should allow us to directly set null in try_cast and avoid construction of exceptions completely.

While this is done now for empty strings, its not done for all other types of errors. Folly provides a non-throwing API (folly::tryTo) that can be tried for that purpose. folly::tryTo. According to the folly documentation On the error path, you can expect tryTo to be roughly three orders of magnitude faster than the throwing to and to completely avoid any lock contention arising from stack unwinding.

Tags:

## array_sort lambda function

Presto provides an array_sort function to sort arrays in ascending order with nulls placed at the end.

``presto> select array_sort(array[2, 5, null, 1, -1]);        _col0--------------------- [-1, 1, 2, 5, null]``

There is also an array_sort_desc function that sorts arrays in descending order with nulls placed at the end.

``presto> select array_sort_desc(array[2, 5, null, 1, -1]);        _col0--------------------- [5, 2, 1, -1, null]``

Both array_sort and array_sort_desc place nulls at the end of the array.

There is also a version of array_sort function that takes a comparator lambda function and uses it to sort the array.

``array_sort(array(T), function(T, T, int)) -> array(T)``

A common use case is to sort an array of structs using one of the struct fields as the sorting key.

``presto> select array_sort(array[row('apples', 23), row('bananas', 12), row('grapes', 44)],        -> (x, y) -> if (x < y, -1, if(x > y, 1, 0)));                                         _col0--------------------------------------------------------------------------------------- [{f0=bananas, f1=12}, {f0=apples, f1=23}, {f0=grapes, f1=44}]``

This is all very nice and convenient, but there is a catch.

The documentation says that the "comparator will take two nullable arguments representing two nullable elements of the array."" Did you notice the word "nullable" in "nullable arguments" and "nullable elements"? Do you think it is important? It is Ok if the answer is No or Not Really. Turns out this "nullable" thing is very important. The comparator is expected to handle null inputs and should not assume that inputs are not null or that nulls are handled automatically.

Why is it important to handle null inputs? Let’s see what happens if the comparator doesn’t handle nulls.

``presto> select array_sort(array[2, 3, null, 1],                            (x, y) -> if (x < y, -1, if (x > y, 1, 0)));      _col0----------------- [2, 3, null, 1]``

The result array is not sorted! If subsequent logic relies on the array to be sorted the query will silently return wrong results. And if there is no logic that relies on the sortedness of the array then why waste CPU cycles on sorting?

Why is the array not sorted? That’s because the comparator returns 0 whenever x or y is null.

``    x < y  returns null if x or y is null, then    x > y  returns null if x or y is null, then    result is 0``

This confuses the sorting algorithm as it sees that 1 == null, 2 == null, 3 == null, but 1 != 2 and 1 != 3. The algorithm assumes that the comparator function is written correctly, e.g. if a < b then b > a and if a == b and b == c then a == c. Comparator function that doesn’t handle nulls does not satisfy these rules and causes unpredictable results.

To handle null inputs, the comparator function needs to be modified, for example, like so:

``    (x, y) -> CASE WHEN x IS NULL THEN 1                                WHEN y IS NULL THEN -1                                WHEN x < y THEN -1                                WHEN x > y THEN 1                                ELSE 0 END``
``presto> select array_sort(array[2, 3, null, 1],        -> (x, y) -> CASE WHEN x IS NULL THEN 1        -> WHEN y IS NULL THEN -1        -> WHEN x < y THEN -1        -> WHEN x > y THEN 1        -> ELSE 0 END        -> );      _col0----------------- [1, 2, 3, null]``

This is longer and harder to read, but the result array is sorted properly. The new comparator says that null is greater than any other value, so null is placed at the end of the array.

Note: When (x, y) return -1, the algorithm assumes that x <= y.

Writing comparators correctly is not easy. Writing comparators that handle null inputs is even harder. Having no feedback when a comparator is written incorrectly makes it yet harder to spot bugs and fix them before a query lands in production and starts producing wrong results.

I feel that Presto’s array_sort function with a custom comparator is dangerous and hard to use and I wonder if it makes sense to replace it with a safer, easier to use alternative.

``array_sort(array(T), function(T, U)) -> array(T)``

This version takes an array and a transform lambda function that specifies how to compute sorting keys from the array elements.

To sort array of structs by one of the struct fields, one would write

``presto> select array_sort(array[row('apples', 23), row('bananas', 12), row('grapes', 44)],                            x -> x)                                         _col0--------------------------------------------------------------------------------------- [{f0=bananas, f1=12}, {f0=apples, f1=23}, {f0=grapes, f1=44}]``

This version would sort the array by the sorting keys computed using the specified lambda in ascending order placing nulls at the end of the array.

A matching array_sort_desc function would sort in descending order placing nulls at the end of the array.

These functions would be easier to write and read and null handling will happen automatically.

We implemented these functions in Velox.

We also added partial support for array_sort with a comparator lambda function. Expression compiler in Velox analyzes the comparator expression to determine whether it can be re-written to the alternative version of array_sort. If so, it re-writes the expression and evaluates it. Otherwise, it throws an unsupported exception.

For example,

``    array_sort(a, (x, y) -> if (x < y, -1, if(x > y, 1, 0)))``

is re-written to

``    array_sort(a, x -> x)``

This rewrite allows Prestissimo and Presto-on-Spark-on-Velox to support common use cases and do so efficiently.

The rewrite handles a few different ways to express the same comparator. Some examples:

``    // becomes array_sort(a, f(x))    (x, y) -> if(f(x) < f(y), -1, if(f(x) > f(y), 1, 0))    // becomes array_sort_desc(a, f(x))    (x, y) -> if(f(x) < f(y), 1, if(f(x) > f(y), -1, 0))    // becomes array_sort(a, f(x))    (x, y) -> if(f(x) < f(y), -1, if(f(x) = f(y), 0, 1))    // becomes array_sort(a, f(x))    (x, y) -> if(f(x) = f(y), 0, if(f(x) < f(y), -1, 1))    // becomes array_sort(a, f(x))    (x, y) -> if(f(y) < f(x), 1, if(f(x) < f(y), -1, 0))``

Why didn’t we implement full support for comparator lambda functions in array_sort? Actually, we couldn’t think of an efficient way to do that in a vectorized engine. Velox doesn’t use code generation and interprets expressions. It can do that efficiently if it can process data in large batches. array_sort with custom comparator doesn’t lend itself well to such processing.

array_sort with a transform lambda works well in a vectorized engine. To process a batch of arrays, Velox first evaluates the transform lambda on all the elements of the arrays, then sorts the results.

For further reading, consider the Vectorized and performance-portable Quicksort blog post from Google.

Thank you Orri Erling for brainstorming and Xiaoxuan Meng for reviewing the code.

Tags:

## Simple Functions: Efficient Complex Types

This blogpost is part of a series of blog posts that discuss different features and optimizations of the simple function interface.

## Efficient Complex Types​

In this blogpost, we will discuss two major recent changes to the simple function interface to make its performance comparable to the vector function implementations for functions that produce or consume complex types (Arrays, Maps and Rows).

To show how much simpler simple functions are. The figure below shows a function NestedMapSum written in both the simple and vector interfaces. The function consumes a nested map and computes the summations of all values and keys. Note that the vector function implementation is minimal without any special optimization (ex: vector reuse, fast path for flat inputs ..etc). Adding optimizations will make it even longer.

### View types for inputs​

The previous representations of input complex types in the simple function interface were computationally expensive. Data from vectors used to be copied into std containers and passed to simple functions to process it. Arrays, Maps and Structs used to be materialized into std::vectors, folly::F14FastMap and std::tuples. The graph below illustrates the previous approach.

The previous approach has two key inefficiencies; Eager materialization : For each row, all the data in the input vector is decoded and read before calling the function. And Double reading, the data is read twice once when the input is constructed, and again in the function when it's used.

In order to mitigate those regressions, Velox introduced View types: ArraViews, MapViews ...etc. The goal is to keep the authoring simple but achieve at least the performance of a basic vector implementation that decodes input and applies some logic for every row without any special optimizations.

The view types are Lazy, very cheap to construct and do not materialize the underlying data unless the code accesses it.For example, the function array_first only needs to read the first element in every array, moreover the cardinality function does not need to read any elements in the array. They view types have interfaces similar to those of std::containers.

In a simplified form, an ArrayView stores the length and the offset of the array within the vector, in addition to a pointer to the elements array. Only when an element is accessed then an OptionalAccessor is created, which contains the index of the accessed element and a pointer to the containing vector. Only when the user calls value() or has_value() on that accessor then the nullity or the value is read. Other view types are implemented in a similar way, The graph below illustrates the process.

The graph below compares the runtime of some functions written in the simple interface before and after the introduction of the view types. The speedup for arrays is around 2X, for maps the speed is much higher > `10X` because materializing the intermediate representation previously involves hashing the elements while constructing the hashmap. Furthermore, the overhead of materialization for nested complex types is very high as well, as reflected in row_arrays_sum. Runtimes of functions before and after the introduction of view types, normalized to the runtime of the version that uses the view types.

The graph below compares the runtimes of some functions written using the simple interface, a basic vector function implementation with no special optimizations for the non general case, and a vector implementation that is specialized for flat and null free. The bars are annotated with the line of codes (LOC) used to implement each function.

We can see that LOC are significantly lower for simple functions. ArraySum with flat and null free optimization is faster because the summation can be optimized much better when it's performed over a sequential array of data. The reason the simple is faster than the vector for some benchmarks is because we have several optimizations in the simple interface that are not implemented in the basic vector versions.

### Writer types for outputs​

A similar pattern of inefficiency existed for functions with complex output types. The graph below shows the previous path of writing complex types through the simple function interface. In the previous path, for each row, the result is first written to a temporary object (std::vector, folly::f14FastMap<>, etc.), then serialized into the Velox vector.

We changed the writing path so that the data is written directly into the Velox vector during the function evaluation. By introducing writer types: ArrayWriter, MapWriter, RowWriter. This avoids the double materialization and the unnecessary sorting and hashing for maps.

Consider the function below for example that constructs an array [0, n-1).

outerArray is an array writer and whenever push_back is called, the underlying vector array is updated directly and a new element is written to it.

In order & final elements writing: Unlike the previous interface, the new writer interface needs to write things in order, since it directly serializes elements into Velox vector buffers. Written elements also can not be modified.

For example, for a function with an Array<Map> output , we can't add three maps, and write to them concurrently. The new interface should enforce that one map is written completely before the next one starts. This is because we are serializing things directly in the map vector, and to determine the offset of the new map we need first to know the end offset of the previous one.

The code below shows a function with Array<Map> output:

Compatibility with std::like containers.: Unfortunately, the new interface is not completely compatible with std::like interfaces, in fact, it deviates syntactically and semantically (for example a std::map enforces unique keys and ordering of elements) while map writer does not. When the element type is primitive (ex: Array<int>) we enable std::like APIs (push_back, emplace()).

But we can not do that for nested complex types (ex:Array<Array<int>>) since it breaks the in-order & final elements writing rule mentioned above.

The figure below shows the performance gain achieved by this change, functions' performance is evaluated before and after the change.

The chart below compares the performance of those functions with vector functions implementations, a vector function with an optimization that precomputes the total size needed for the output vector and a single resize is also added. Note that those functions do almost no computation other than constructing the output map. Hence the resize cost becomes very critical, if those were doing more work, then its effect would be less. Furthermore, the gap indicates that it might be worth it to add a way in the simple interface that enables pre-computing/resizing the output vector size.

### Examples:​

For full documentation of the view and writer types, APIs, and how to write simple functions follow thelink.

## Improving the Velox Build Experience

When Velox was open sourced in August 2021, it was not nearly as easily usable and portable as it is today. In order for Velox to become the unified execution engine blurring the boundaries for data analytics and ML, we needed Velox to be easy to build and package on multiple platforms, and support a wide range of hardware architectures. If we are supporting all these platforms, we also need to ensure that Velox remains fast and regressions are caught early.

To improve the Velox experience for users and community developers, Velox has partnered with Voltron Data to help make Velox more accessible and user-friendly. In this blog post, we will examine the challenges we faced, the improvements that have already been made, and the ones yet to come.

## Enhancements & Improvements​

Velox was a product of the mono repo and required installation of dependencies on the system via a script. Any change in the state of the host system could cause a build failure and introduce version conflicts of dependencies. Fixing these challenges was a big focus to help the Velox Community and we worked in collaboration with the Voltron Data Team. We wanted to improve the overall Velox user experience by making Velox easy to consume across a wide range of platforms to accelerate its adoption.

We choose hermetic builds as a solution to the aforementioned problems, as they provide a number of benefits. Hermetic builds1 improve reproducibility by providing isolation from the state of the host machine and produce the same result for any given commit in the Velox repository. This requires precise dependency management.

The first major step in moving towards hermetic builds was the integration of a new dependency management system that is able to download, configure and build the necessary dependencies within the Velox build process. This new system also gives users the option to use already installed system dependencies. We hope this work will increase adoption of Velox in downstream projects and make troubleshooting of build issues easier, as well as improve overall reliability and stability.

We also wanted to lower the barrier to entry for contributions to Velox. Therefore, we created Docker Development images for both Ubuntu and CentOS, and we now publish them automatically when changes are merged. We hope this work will help speed up the development process by allowing developers to stand up a development environment quickly, without the requirement of installing third-party dependencies locally. We also use these images in the Velox CI to lower build times and speed up the feedback loop for proposing a PR.

``# Run the development image from the root of the Velox repository# to build and test Veloxdocker compose run --rm ubuntu-cpp``

An important non-technical improvement is the introduction of new issue templates and utility scripts. These will help guide troubleshooting and getting support from the relevant Velox developers via Github. This helps to improve the experience for the community and make it easier for users and contributors to get help and support when they need it.

Lastly, we implemented new nightly builds to increase the overall reliability and stability of Velox, as well as test the integration with downstream community projects.

To enable easy access to Velox from Python, we built CI infrastructure to generate and publish pre-built binary wheels for PyVelox (the Velox Python Bindings). We also improved Conda support by contributing to upstream feedstocks.

``# Try PyVelox today!pip install pyvelox``

## Future Goals​

We will continue the work of moving all dependencies to the new dependency management system to move closer to hermetic builds and make development and usage as smooth as possible.

In the same theme, the next major goal is the refactoring of the existing CMake build system to use a target based "modern" style. This will allow us to properly install Velox as a system library to be used by other projects. This project will improve the development experience overall by creating a stable, reliable build infrastructure, but also allows us to publish Velox as a conda-forge package and make it easier to further improve support for non x86_64 architectures like Apple Silicon, arm64 systems, various compilers and older CPUs that don’t support the currently obligatory instructions sets like BMI2 and make Velox available to an even larger community.

Confidence in the stability and reliability of a project are key when you want to deploy it as part of your stack. Therefore, we are working on a release process and versioning scheme for Velox so that you can deploy with confidence!

In conclusion, the collaboration between Velox and Voltron Data has led to several key improvements in Velox's packaging and CI. Setting up a new environment with Velox has never been this easy! With the new improvements, this new broader community of developers and contributors can expect a smoother and more user-friendly experience when using Velox. The Velox team is continuously working towards further improving the developer and user experience, and we invite you to join us in building the next generation unified execution engine!

1. Hermeticity - why hermetic builds are recommended
Tags:

## Simple Functions: Introduction and Basic Optimizations

This blogpost is part of a series of blog posts that discuss different features and optimizations of the simple function interface in Velox.

## Introduction to Simple Functions​

Scalar functions are one of the most used extension points in Velox. Since Velox is a vectorized engine, by nature functions are "vector functions" that consume Velox vectors (batches of data) and produce vectors. Velox allows users to write functions as vector functions or as single-row operations "simple functions" that are converted to vector functions using template expansion through SimpleFunctionAdapter.

Writing functions as vector functions directly gives the user `complete` control over the function implementations and optimizations, however it comes with some cost that can be summarized in three points:

• Complexity : Requires an understanding of Velox vectorized data representation and encodings, which requires additional work for our customers, specially those without DB background. Moreover, Writing optimized vector functions requires even deeper understanding.
• Repetition : Involves repeated efforts and code; in each function, authors have to decode the input vectors, apply the same optimizations, and build the output vectors. For example, most arithmetic functions need benefits from a fast path when all the inputs are flat-encoded, authors need to implement that for every function that benefits from it.
• Reliability : More code means more bugs, especially in such a complex context.

Writing functions through the simple interface mitigates the previously mentioned drawbacks, and significantly simplifies the function authoring process. For example, to add the function plus the user only needs to implement the PlusFunction struct shown in the graph above , which is then expanded using template expansion to a vector function.

However, the simple function interface does not give the user full control over the authoring and has its own limitations, for example the function map_keys can be implemented in O(1) as a vector function by moving the keys vector; this is not possible to express as a simple function.

Another limitation is that when using the simple interface, authors do not have access to the encodings of the input vectors, nor control over the encoding of the result vector. Hence, do not have the power to optimize the code for specific input encodings or optimize it by generating specific output encodings. The array_sort function for instance does not need to re-order the elements and copy them during sorting; instead it can generate a dictionary vector as an output, which is something not expressible as a simple function.

In the ideal world we would like to add most of the optimization that someone can do in a vector function to the simple functions adapter, so it would be enabled automatically. We have identified a number of optimizations that apply to all functions and implemented these generically in the SimpleFunctionAdapter. In this way, we can achieve the best of the two worlds and gain Simplicity, Efficiency and Reliability for most functions.

In the past year, we have been working on several improvements to the simple function interface on both the `expressivity` and `performance` axes that we will discuss in this series of notes.

In this blog post, we will talk about some of the general optimizations that we have in the adapter, the optimizations discussed in this post make the performance of most simple functions that operates on primitive types matches their counter optimized vector function implementations. In the next blog post, we will discuss complex types in simple functions.

## General Optimizations​

#### Vector Reuse​

If the output type matches one of the input types, and the input vector is to die after the function invocation, then it is possible to reuse it for the results instead of allocating a new vector. For example, in the expression plus(a, b), if a is stored in a flat vector that is not used after the invocation of the plus function, then that vevtor can be used to store the reults of the computation instead of allocating a new vevtor for the results.

#### Bulk Null Setting​

Nulls are represented in a bit vector, hence, writing each bit can be expensive specially for primitive operations (like plus and minus). One optimization is to optimize for the `not null` case, and bulk setting the nulls to not null. After that during the computation, only if the results are null, the null bit is set to null.

#### Null Setting Avoidance​

The adapter can statically infer if a function never generates null; In the simple function interface if the `call` function return's type is `void`, it means the output is never null, and if it's `bool`, then the function returns true for not null and false for null).

When the function does not generate nulls, then null setting is completely avoided during the computation (only the previous bulk setting is needed). The consequence of that is that the hot loop applying the function becomes simdizable triggering a huge boost in performance for primitive operations.

Worth to note also that if the simple function happens to be inlined in the adapter, then even if its return type is not void, but it always returns `true` then the compiler will be able to infer that setting nulls is never executed and would remove the null setting code.

#### Encoding Based Fast Path​

Vectors in Velox can have different encodings (flat, constant..etc). The generic way of reading a vector of arbitrary encoding is to use a decoded vector to guarantee correct data access. Even though decoded vectors provide a consistent API and make it easier to handle arbitrarily encoded input data, they translate into an overhead each time an input value is accessed (we need to check the encoding of the vector to know how to read the value for every row).

When the function is a primitive operation like plus or minus, such overhead is expensive! To avoid that, encoding based fast paths can be added, the code snippet below illustrates the idea.

In the code above, the overhead of checking the encoding is switched outside the loop that applies the functions (the plus operation here). And the inner loops are simple operations that are potentially simdizable and free of encoding checks. One issue with this optimization is that the core loop is replicated many times. In general, the numbers of times it will be replicated is `n^m` where `n` is the number of args, and `m` is the number of encodings.

To avoid code size blowing, we only apply this optimization when all input arguments are primitives and the number of input arguments is <=3. The figure below shows the effect of this optimization on the processing time of a query of primitive operations (the expression is a common pattern in ML use cases).

To compromise for both (performance and code size) when the conditions for specializing for all encodings are not met, we have a pseudo specialization mode that does not blow up the code size, but still reduce the overhead of decoding to a single multiplication per argument. This mode is enabled when all the primitive arguments are either flat or constant. The code below illustrates the idea:

When the input vector is constant we can read the value always from index 0 of the values buffer, and when it is flat we can read it from the index row; this can be achieved by assigning a factor to either 0 or 1 and reducing the decoding operation per row into a multiplication with that factor Note that such a multiplication does not prevent simd. The graph above shows that the psudeo specialization makes the program 1.6X fatser wi, while the complete specialization makes the program 2.5X faster.

#### ASCII Fast Path​

Functions with string inputs can be optimized when the inputs are known to be ascii. For example the length function for ascii strings is the size of the StringView O(1). But for non-ascii inputs the computation is a more complicated O(n) operation. Users can define a function `callAscii()` that will be called when all the string input arguments are ascii.

#### Zero-Copy Optimization​

When an input string (or portion of it, reaches the output as is) it does not need to be deep copied. Instead only a StringView needs to be set. Substring is an example of a function that benefits from this. This can be done in the simple function interface in two simple steps.

1. Using setNoCopy(); to set the output results without copying string vectors.
2. Inform the function to make the output vector share ownership of input string buffers, this can be by setting the field reuse_strings_from_arg.

The graph below shows the effect of the previous two optimizations on the performance of the substring function.

#### Constant Inputs Pre-processing​

Users can pre-process constant inputs of functions to avoid repeated computation by defining `initialize` function which is called once during query compilations and receives the constant inputs. For example, a regex function with constant pattern would only needs to compile the pattern expressions only once when its constant.

## Velox: The Unified Execution Engine Now Available We are extremely excited to introduce Velox as an open-source project, with a mission to define common standards for modular data processing systems. Velox provides reusable, extensible, high-performance, and dialect-agnostic data processing components for building execution engines, and enhancing data management systems. We envision Velox to be the defacto execution engine for Arrow-compatible data format powering ML and Analytical workloads.

The Velox team has been partnering with companies such as Ahana, Intel, and Voltron Data as well as various academic institutions to accelerate innovation and development in the data management industry.

Looking at the future, we believe Velox’s unified and modular nature has the potential to disrupt the data management industry. It will allow us to deepen our partnership with hardware vendors and proactively adapt our unified software stack as hardware advances. We believe that modularity and reusability are the future of database system development and hope a vibrant open source community will help us in this journey.

Quick Introduction -

If you are excited to learn what’s under the hood, refer to the Velox research paper.

If you are interested in contributing, visit our Contributing guide on Github. For technical discussions and exploring what’s happening within our community, refer to the discussions section.

We will be publishing a series of technical blogs on various topics on our website soon!

## Documentation​

• Add documentation for :ref:`complex types writers<outputs-write>`.

## Core Library​

• Add support for INTERVAL DAY TO SECOND Presto type.
• Allow cast between DATE and TIMESTAMP types.
• Allow cast from JSON to scalar, ARRAY, and MAP types.
• Add :ref:`GroupIdNode<group-id-node>` and GroupId operator to support aggregations over grouping sets.
• Add support for function signatures with DECIMAL input and return types using flex and bison to evaluate formulas for calculating the return precision and scale based on input precisions and scales.
• Add support for conversion of DuckDB DECIMALS to Velox DECIMALS.
• Fix expression evaluation to disable sub-expression optimization for non-deterministic functions.

## Presto Functions​

• Add :func:`degrees`, :func:`e`, and :func:`sha512` functions.
• Add aggregate function :func:`map_union`.
• Optimize :func:`zip` for the case when all arrays are flat and the same size.
• Extend :func:`plus`, :func:`minus` functions to support DATE, INTERVAL DAY TO SECOND argument types.

## Hive Connector​

• Optimize `NOT IN (<list of integers>)` filters pushed down into DWRF reader.

## TPC-H Connector​

• Add `totalParts` and `partNumber` to TpchSplit.

## Performance and Correctness​

• Add q3 to TPC-H benchmark.
• Add utility to benchmark dataset generation speed to TPC-H connector.