JEP 448: Vector API (Sixth Incubator)

Summary

Introduce an API to express vector computations that reliably compile at runtime to optimal vector instructions on supported CPU architectures, thus achieving performance superior to equivalent scalar computations.

History

The Vector API was first proposed by JEP 338 and integrated into JDK 16 as an incubating API. Further rounds of incubation were proposed by JEP 414 (integrated into JDK 17), JEP 417 (JDK 18), JEP 426 (JDK 19), and JEP 438 (JDK 20).

This JEP proposes to re-incubate the API in JDK 21, with minor enhancements in the API relative to JDK 20. The implementation includes bug fixes and performance enhancements. We include the following notable changes:

• Add the exclusive or (xor) operation to vector masks.

• Improve the performance of vector shuffles, especially when used to rearrange the elements of a vector and when converting between vectors.

Goals

• Clear and concise API — The API should be capable of clearly and concisely expressing a wide range of vector computations consisting of sequences of vector operations composed within loops and possibly with control flow. It should be possible to express a computation that is generic with respect to vector size, or the number of lanes per vector, thus enabling such computations to be portable across hardware supporting different vector sizes.

• Platform agnostic — The API should be CPU architecture agnostic, enabling implementations on multiple architectures supporting vector instructions. As is usual in Java APIs, where platform optimization and portability conflict then we will bias toward making the API portable, even if that results in some platform-specific idioms not being expressible in portable code.

• Reliable runtime compilation and performance on x64 and AArch64 architectures — On capable x64 architectures the Java runtime, specifically the HotSpot C2 compiler, should compile vector operations to corresponding efficient and performant vector instructions, such as those supported by Streaming SIMD Extensions (SSE) and Advanced Vector Extensions (AVX). Developers should have confidence that the vector operations they express will reliably map closely to relevant vector instructions. On capable ARM AArch64 architectures C2 will, similarly, compile vector operations to the vector instructions supported by NEON and SVE.

• Graceful degradation — Sometimes a vector computation cannot be fully expressed at runtime as a sequence of vector instructions, perhaps because the architecture does not support some of the required instructions. In such cases the Vector API implementation should degrade gracefully and still function. This may involve issuing warnings if a vector computation cannot be efficiently compiled to vector instructions. On platforms without vectors, graceful degradation will yield code competitive with manually-unrolled loops, where the unroll factor is the number of lanes in the selected vector.

• Alignment with Project Valhalla — The long-term goal of the Vector API is to leverage Project Valhalla's enhancements to the Java object model. Primarily this will mean changing the Vector API's current value-based classes to be value classes so that programs can work with value objects, i.e., class instances that lack object identity. Accordingly, the Vector API will incubate over multiple releases until the necessary features of Project Valhalla become available as preview features. Once these Valhalla features are available we will adapt the Vector API and implementation to use them and then promote the Vector API itself to a preview feature. For further details, see the sections on run-time compilation and future work.

Non-Goals

• It is not a goal to enhance the existing auto-vectorization algorithm in HotSpot.

• It is not a goal to support vector instructions on CPU architectures other than x64 and AArch64. However it is important to state, as expressed in the goals, that the API must not rule out such implementations.

• It is not a goal to support the C1 compiler.

• It is not a goal to guarantee support for strict floating point calculations as is required by the Java platform for scalar operations. The results of floating point operations performed on floating point scalars may differ from equivalent floating point operations performed on vectors of floating point scalars. Any deviations will be clearly documented. This non-goal does not rule out options to express or control the desired precision or reproducibility of floating point vector computations.

Motivation

A vector computation consists of a sequence of operations on vectors. A vector comprises a (usually) fixed sequence of scalar values, where the scalar values correspond to the number of hardware-defined vector lanes. A binary operation applied to two vectors with the same number of lanes would, for each lane, apply the equivalent scalar operation on the corresponding two scalar values from each vector. This is commonly referred to as Single Instruction Multiple Data (SIMD).

Vector operations express a degree of parallelism that enables more work to be performed in a single CPU cycle and thus can result in significant performance gains. For example, given two vectors, each containing a sequence of eight integers (i.e., eight lanes), the two vectors can be added together using a single hardware instruction. The vector addition instruction operates on sixteen integers, performing eight integer additions, in the time it would ordinarily take to operate on two integers, performing one integer addition.

HotSpot already supports auto-vectorization, which transforms scalar operations into superword operations which are then mapped to vector instructions. The set of transformable scalar operations is limited, and also fragile with respect to changes in code shape. Furthermore, only a subset of the available vector instructions might be utilized, limiting the performance of generated code.

Today, a developer who wishes to write scalar operations that are reliably transformed into superword operations needs to understand HotSpot's auto-vectorization algorithm and its limitations in order to achieve reliable and sustainable performance. In some cases it may not be possible to write scalar operations that are transformable. For example, HotSpot does not transform the simple scalar operations for calculating the hash code of an array (the Arrays::hashCode methods), nor can it auto-vectorize code to lexicographically compare two arrays (thus we added an intrinsic for lexicographic comparison).

The Vector API aims to improve the situation by providing a way to write complex vector algorithms in Java, using the existing HotSpot auto-vectorizer but with a user model which makes vectorization far more predictable and robust. Hand-coded vector loops can express high-performance algorithms, such as vectorized hashCode or specialized array comparisons, which an auto-vectorizer may never optimize. Numerous domains can benefit from this explicit vector API including machine learning, linear algebra, cryptography, finance, and code within the JDK itself.

Description

A vector is represented by the abstract class Vector<E>. The type variable E is instantiated as the boxed type of the scalar primitive integral or floating point element types covered by the vector. A vector also has a shape which defines the size, in bits, of the vector. The shape of a vector governs how an instance of Vector<E> is mapped to a hardware vector register when vector computations are compiled by the HotSpot C2 compiler. The length of a vector, i.e., the number of lanes or elements, is the vector size divided by the element size.

The set of element types (E) supported is Byte, Short, Integer, Long, Float and Double, corresponding to the scalar primitive types byte, short, int, long, float and double, respectively.

The set of shapes supported correspond to vector sizes of 64, 128, 256, and 512 bits, as well as max bits. A 512-bit shape can pack bytes into 64 lanes or pack ints into 16 lanes, and a vector of such a shape can operate on 64 bytes at a time or 16 ints at a time. A max-bits shape supports the maximum vector size of the current architecture. This enables support for the ARM SVE platform, where platform implementations can support any fixed size ranging from 128 to 2048 bits, in increments of 128 bits.

We believe that these simple shapes are generic enough to be useful on all relevant platforms. However, as we experiment with future platforms during the incubation of this API we may further modify the design of the shape parameter. Such work is not in the early scope of this project, but these possibilities partly inform the present role of shapes in the Vector API. (For further discussion see the future work section, below.)

The combination of element type and shape determines a vector's species, represented by VectorSpecies<E>.

Operations on vectors are classified as either lane-wise or cross-lane.

• A lane-wise operation applies a scalar operator, such as addition, to each lane of one or more vectors in parallel. A lane-wise operation usually, but not always, produces a vector of the same length and shape. Lane-wise operations are further classified as unary, binary, ternary, test, or conversion operations.

• A cross-lane operation applies an operation across an entire vector. A cross-lane operation produces either a scalar or a vector of possibly a different shape. Cross-lane operations are further classified as permutation or reduction operations.

To reduce the surface of the API, we define collective methods for each class of operation. These methods take operator constants as input; these constants are instances of the VectorOperator.Operator class and are defined in static final fields in the VectorOperators class. For convenience we define dedicated methods, which can be used in place of the generic methods, for some common full-service operations such as addition and multiplication.

Certain operations on vectors, such conversion and reinterpretation, are inherently shape-changing; i.e., they produce vectors whose shapes are different from the shapes of their inputs. Shape-changing operations in a vector computation can negatively impact portability and performance. For this reason the API defines a shape-invariant flavor of each shape-changing operation when applicable. For best performance, developers should write shape-invariant code using shape-invariant operations insofar as possible. Shape-changing operations are identified as such in the API specification.

The Vector<E> class declares a set of methods for common vector operations supported by all element types. For operations specific to an element type there are six abstract subclasses of Vector<E>, one for each supported element type: ByteVector, ShortVector, IntVector, LongVector, FloatVector, and DoubleVector. These type-specific subclasses define additional operations that are bound to the element type since the method signature refers either to the element type or to the related array type. Examples of such operations include reduction (e.g., summing all lanes to a scalar value), and copying a vector's elements into an array. These subclasses also define additional full-service operations specific to the integral subtypes (e.g., bitwise operations such as logical or), as well as operations specific to the floating point types (e.g., transcendental mathematical functions such as exponentiation).

As an implementation matter, these type-specific subclasses of Vector<E> are further extended by concrete subclasses for different vector shapes. These concrete subclasses are not public since there is no need to provide operations specific to types and shapes. This reduces the API surface to a sum of concerns rather than a product. Instances of concrete Vector classes are obtained via factory methods defined in the base Vector<E> class and its type-specific subclasses. These factories take as input the species of the desired vector instance and produce various kinds of instances, for example the vector instance whose elements are default values (i.e., the zero vector), or a vector instance initialized from a given array.

To support control flow, some vector operations optionally accept masks represented by the public abstract class VectorMask<E>. Each element in a mask is a boolean value corresponding to a vector lane. A mask selects the lanes to which an operation is applied: It is applied if the mask element for the lane is true, and some alternative action is taken if the mask is false.

Similar to vectors, instances of VectorMask<E> are instances of non-public concrete subclasses defined for each element type and length combination. The instance of VectorMask<E> used in an operation should have the same type and length as the vector instances involved in the operation. Vector comparison operations produce masks, which can then be used as input to other operations to selectively operate on certain lanes and thereby emulate flow control. Masks can also be created using static factory methods in the VectorMask<E> class.

We anticipate that masks will play an important role in the development of vector computations that are generic with respect to shape. This expectation is based on the central importance of predicate registers, the equivalent of masks, in the ARM Scalable Vector Extensions and in Intel's AVX-512.

On such platforms an instance of VectorMask<E> is mapped to a predicate register, and a mask-accepting operation is compiled to a predicate-register-accepting vector instruction. On platforms that don't support predicate registers, a less efficient approach is applied: An instance of VectorMask<E>is mapped, where possible, to a compatible vector register, and in general a mask-accepting operation is composed of the equivalent unmasked operation and a blend operation.

To support cross-lane permutation operations, some vector operations accept shuffles represented by the public abstract class VectorShuffle<E>. Each element in a shuffle is an int value corresponding to a lane index. A shuffle is a mapping of lane indexes, describing the movement of lane elements from a given vector to a result vector.

Similar to vectors and masks, instances of VectorShuffle<E> are instances of non-public concrete subclasses defined for each element type and length combination. The instance of VectorShuffle<E> used in an operation should have the same type and length as the vector instances involved in the operation.

Example

Here is a simple scalar computation over elements of arrays:

void scalarComputation(float[] a, float[] b, float[] c) {
   for (int i = 0; i < a.length; i++) {
        c[i] = (a[i] * a[i] + b[i] * b[i]) * -1.0f;
   }
}

(We assume that the array arguments are of the same length.)

Here is an equivalent vector computation, using the Vector API:

static final VectorSpecies<Float> SPECIES = FloatVector.SPECIES_PREFERRED;

void vectorComputation(float[] a, float[] b, float[] c) {
    int i = 0;
    int upperBound = SPECIES.loopBound(a.length);
    for (; i < upperBound; i += SPECIES.length()) {
        // FloatVector va, vb, vc;
        var va = FloatVector.fromArray(SPECIES, a, i);
        var vb = FloatVector.fromArray(SPECIES, b, i);
        var vc = va.mul(va)
                   .add(vb.mul(vb))
                   .neg();
        vc.intoArray(c, i);
    }
    for (; i < a.length; i++) {
        c[i] = (a[i] * a[i] + b[i] * b[i]) * -1.0f;
    }
}

To start, we obtain a preferred species whose shape is optimal for the current architecture from FloatVector. We store it in a static final field so that the runtime compiler treats the value as constant and can therefore better optimize the vector computation. The main loop then iterates over the input arrays in strides of the vector length, i.e., the species length. It loads float vectors of the given species from arrays a and b at the corresponding index, fluently performs the arithmetic operations, and then stores the result into array c. If any array elements are left over after the last iteration then the results for those tail elements are computed with an ordinary scalar loop.

This implementation achieves optimal performance on large arrays. The HotSpot C2 compiler generates machine code similar to the following on an Intel x64 processor supporting AVX:

0.43%  / │  0x0000000113d43890: vmovdqu 0x10(%r8,%rbx,4),%ymm0
  7.38%  │ │  0x0000000113d43897: vmovdqu 0x10(%r10,%rbx,4),%ymm1
  8.70%  │ │  0x0000000113d4389e: vmulps %ymm0,%ymm0,%ymm0
  5.60%  │ │  0x0000000113d438a2: vmulps %ymm1,%ymm1,%ymm1
 13.16%  │ │  0x0000000113d438a6: vaddps %ymm0,%ymm1,%ymm0
 21.86%  │ │  0x0000000113d438aa: vxorps -0x7ad76b2(%rip),%ymm0,%ymm0
  7.66%  │ │  0x0000000113d438b2: vmovdqu %ymm0,0x10(%r9,%rbx,4)
 26.20%  │ │  0x0000000113d438b9: add    $0x8,%ebx
  6.44%  │ │  0x0000000113d438bc: cmp    %r11d,%ebx
         \ │  0x0000000113d438bf: jl     0x0000000113d43890

This is the output of a JMH micro-benchmark for the above code using the prototype of the Vector API and implementation found on the vectorIntrinsics branch of Project Panama's development repository. These hot areas of generated machine code show a clear translation to vector registers and vector instructions. We disabled loop unrolling (via the HotSpot option -XX:LoopUnrollLimit=0) in order to make the translation clearer; otherwise, HotSpot would unroll this code using existing C2 loop optimizations. All Java object allocations are elided.

(HotSpot is capable of auto-vectorizing the scalar computation in this particular example, and it will generate a similar sequence of vector instructions. The main difference is that the auto-vectorizer generates a vector multiply instruction for the multiplication by -1.0f, whereas the Vector API implementation generates a vector XOR instruction that flips the sign bit. However, the key point of this example is to present the Vector API and show how its implementation generates vector instructions, rather than to compare it to the auto-vectorizer.)

On platforms supporting predicate registers, the example above could be written more simply, without the scalar loop to process the tail elements, while still achieving optimal performance:

void vectorComputation(float[] a, float[] b, float[] c) {
    for (int i = 0; i < a.length; i += SPECIES.length()) {
        // VectorMask<Float>  m;
        var m = SPECIES.indexInRange(i, a.length);
        // FloatVector va, vb, vc;
        var va = FloatVector.fromArray(SPECIES, a, i, m);
        var vb = FloatVector.fromArray(SPECIES, b, i, m);
        var vc = va.mul(va)
                   .add(vb.mul(vb))
                   .neg();
        vc.intoArray(c, i, m);
    }
}

In the loop body we obtain a loop dependent mask for input to the load and store operations. When i < SPECIES.loopBound(a.length) the mask, m, declares all lanes are set. For the last iteration of the loop, when SPECIES.loopBound(a.length) <= i < a.length and (a.length - i) <= SPECIES.length(), the mask may declare a suffix of unset lanes. The load and store operations will not throw out-of-bounds exceptions since the mask prevents access to the array beyond its length.

We would prefer that developers write in the above style for all supported platforms and achieve optimal performance, but today on platforms without predicate registers the above approach is not optimal. In theory the C2 compiler could be enhanced to transform the loop, peeling off the last iteration and removing the mask from the loop body. This remains an area for further investigation.

Run-time compilation

The Vector API has two implementations. The first implements operations in Java, thus it is functional but not optimal. The second defines intrinsic vector operations for the HotSpot C2 run-time compiler so that it can compile vector computations to appropriate hardware registers and vector instructions when available.

To avoid an explosion of C2 intrinsics we define generalized intrinsics corresponding to the various kinds of operations such as unary, binary, conversion, and so on, which take a parameter describing the specific operation to be performed. Approximately twenty-five new intrinsics support the intrinsification of the entire API.

We expect ultimately to declare vector classes as value classes, as proposed by Project Valhalla (see Value Objects and JEP 401 (Implicit Value Object Creation)). In the meantime Vector<E> and its subclasses are considered value-based classes, so identity-sensitive operations on their instances should be avoided. Although vector instances are abstractly composed of elements in lanes, those elements are not scalarized by C2 — a vector’s value is treated as a whole unit, like an int or a long, that maps to a vector register of the appropriate size. Vector instances are treated specially by C2 in order to overcome limitations in escape analysis and avoid boxing. In the future we will align this special treatment with Valhalla's value objects.

Intel SVML intrinsics for transcendental operations

The Vector API supports transcendental and trigonometric lanewise operations on floating point vectors. On x64 we leverage the Intel Short Vector Math Library (SVML) to provide optimized intrinsic implementations for such operations. The intrinsic operations have the same numerical properties as the corresponding scalar operations defined in java.lang.Math.

The assembly source files for SVML operations are in the source code of the jdk.incubator.vector module, under OS-specific directories. The JDK build process compiles these source files for the target operating system into an SVML-specific shared library. This library is fairly large, weighing in at just under a megabyte. If a JDK image, built via jlink, omits the jdk.incubator.vector module then the SVML library is not copied into the image.

The implementation only supports Linux and Windows at this time. We will consider macOS support later, since it is a non-trivial amount of work to provide assembly source files with the required directives.

The HotSpot runtime will attempt to load the SVML library and, if present, bind the operations in the SVML library to named stub routines. The C2 compiler generates code that calls the appropriate stub routine based on the operation and vector species (i.e., element type and shape).

In the future, if Project Panama expands its support of native calling conventions to support vector values then it may be possible for the Vector API implementation to load the SVML library from an external source. If there is no performance impact with this approach then it would no longer be necessary to include SVML in source form and build it into the JDK. Until then we deem the above approach acceptable, given the potential performance gains.

Future work

• As mentioned above, we expect ultimately to declare vector classes as value classes. For ongoing efforts to align the Vector API with Valhalla see the lworld+vector branch of Project Valhalla's code repository. We expect, further, to leverage Project Valhalla’s generic specialization of value classes so that instances of Vector<E> are value objects, where E is a primitive class such as int instead of its boxed class Integer. Subtypes of Vector<E> for specific types, such as IntVector, might not be required once we have generic specialization over primitive classes.

• We may add support for vectors of IEEE floating-point binary16 values (float16 values). This also has a dependency on Project Valhalla, requiring that we represent a float16 value as a value object, with optimized layout in arrays and fields, and enhance the Vector API implementation to leverage vector hardware instructions on vectors of float16 values. For exploratory work see the vectorIntrinsics+fp16 branch of Project Panama's Vector API code repository.

• We anticipate enhancing the implementation to improve the optimization of loops containing vectorized code, and generally improve performance incrementally over time.

• We also anticipate enhancing the combinatorial unit tests to assert that C2 generates vector hardware instructions. The unit tests currently assume, without verification, that repeated execution is sufficient to cause C2 to generate vector hardware instructions. We will explore the use of C2's IR Test Framework to assert, cross-platform, that vector nodes are present in the IR graph (for example, using regex matching). If this approach is problematic we may explore a rudimentary approach that uses the non-product -XX:+TraceNewVectors flag to print vector nodes.

• We will evaluate the definition of synthetic vector shapes to give better control over loop unrolling and matrix operations, and consider appropriate support for sorting and parsing algorithms. (See this presentation for more details.)

Alternatives

HotSpot's auto-vectorization is an alternative approach, but it would require significant work. It would, moreover, still be fragile and limited compared to the Vector API, since auto-vectorization with complex control flow is very hard to perform.

In general, even after decades of research — especially for FORTRAN and C array loops — it seems that auto-vectorization of scalar code is not a reliable tactic for optimizing ad-hoc user-written loops unless the user pays unusually careful attention to unwritten contracts about exactly which loops a compiler is prepared to auto-vectorize. It is too easy to write a loop that fails to auto-vectorize, for a reason that no human reader can detect. Years of work on auto-vectorization, even in HotSpot, have left us with lots of optimization machinery that works only on special occasions. We want to enjoy the use of this machinery more often!

Testing

We will develop combinatorial unit tests to ensure coverage for all operations, for all supported types and shapes, over various data sets.

We will also develop performance tests to ensure that performance goals are met and vector computations map efficiently to vector instructions. This will likely consist of JMH micro-benchmarks, but more realistic examples of useful algorithms will also be required. Such tests may initially reside in a project specific repository. Curation is likely required before integration into the main repository given the proportion of tests and the manner in which they are generated.

Risks and Assumptions

• There is a risk that the API will be biased to the SIMD functionality supported on x64 architectures, but this is mitigated with support for AArch64. This applies mainly to the explicitly fixed set of supported shapes, which bias against coding algorithms in a shape-generic fashion. We consider the majority of other operations of the Vector API to bias toward portable algorithms. To mitigate that risk we will take other architectures into account, specifically the ARM Scalar Vector Extension architecture whose programming model adjusts dynamically to the singular fixed shape supported by the hardware. We welcome and encourage OpenJDK contributors working on the ARM-specific areas of HotSpot to participate in this effort.

• The Vector API uses box types (e.g., Integer) as proxies for primitive types (e.g., int). This decision is forced by the current limitations of Java generics, which are hostile to primitive types. When Project Valhalla eventually introduces more capable generics then the current decision will seem awkward, and will likely need changing. We assume that such changes will be possible without excessive backward incompatibility.