JEP 414: Vector API (Second 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 proposed by JEP 338 and integrated into Java 16 as an incubating API. We propose here to incorporate enhancements in response to feedback as well as performance improvements and other significant implementation enhancements. We include the following notable changes:

• Enhancements to the API to support operations on characters, such as for UTF-8 character decoding. Specifically, we add methods for copying characters between short vectors and char arrays, and new vector comparison operators for unsigned comparisons with integral vectors.

• Enhancements to the API for translating byte vectors to and from boolean arrays.

• Intrinsic support for transcendental and trigonometric lanewise operations on x64 using the Intel's Short Vector Math Library (SVML).

• General performance enhancements to the Intel x64 and ARM NEON implementations.

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 the bias will be 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.

• 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.

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 support strict floating point calculations as defined by the Java strictfp keyword. 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. However, this 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 (thus 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 architectures. 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.

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 in order to make the translation clearer; otherwise, HotSpot would unroll this code using existing C2 loop optimizations. All Java object allocations are elided.

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 new intrinsics support the intrinsification of the entire API.

We expect ultimately to declare vector classes as primitive classes, as proposed by Project Valhalla in JEP 401 (Primitive Objects). 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.

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 will not be 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 primitive classes. We expect, further, to leverage Project Valhalla’s generic specialization of primitive classes so that instances of Vector<E> can be primitive values whose concrete types are primitive types. This will make it easier to optimize and express vector computations. Subtypes of Vector<E> for specific types, such as IntVector, might not be required once we have generic specialization over primitive classes. We intend to incubate the API over multiple releases and adapt it as primitive classes and related facilities become available.

• We hope to improve the performance of vector operations that accept masks on architectures that support masking in hardware. If masks were more efficient then 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);
      }
  }

• We intend to enhance the API to load and store vectors using JEP 412 (Foreign Function & Memory API) when that API transitions out of incubation. Memory layouts that describe vector species may prove useful, for example to stride over a memory segment comprised of vector elements.

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

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.

As a backup to performance tests, we may create white-box tests to force the JIT to report to us that Vector API source code did, in fact, trigger vectorization.

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.