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  25 
  26 /**
  27  * {@Incubating}
  28  * <p>
  29  * Classes to express vector computations that, given suitable hardware
  30  * and runtime ability, are accelerated using vector hardware instructions.
  31  * <p>
  32  * Vector computations consist of a sequence of operations on vectors.
  33  * A vector is a fixed sequence of scalar values; a scalar value is
  34  * a single unit of value such as an int, a long, a float and so on.
  35  * Operations on vectors typically perform the equivalent scalar operation on all
  36  * scalar values of the participating vectors, usually generating a vector result.
  37  * When run on a supporting platform, these operations can be
  38  * executed in parallel by the hardware.
  39  * This style of parallelism is called <em>Single Instruction Multiple Data</em> (SIMD)
  40  * parallelism.
  41  *
  42  * <p>The abstract class {@link jdk.incubator.vector.Vector} represents an ordered immutable sequence of
  43  * values of the same element type 'e' that is one of the following primitive types -
  44  * byte, short, int, long, float, or double. The type variable E corresponds to the
  45  * boxed element type, specifically the class that wraps a value of e in an object
  46  * (such as Integer class that wraps a value of int).
  47  *
  48  * <p>Vector declares a set of vector operations (methods) that are common to
  49  * all element types (such as addition). Subclasses of Vector corresponding to
  50  * a specific element type declare further operations that are specific to that element type
  51  * (such as access to element values in lanes, logical operations on values of integral
  52  * elements types, or transcendental operations on values of floating point element
  53  * types). There are six abstract subclasses of {@link jdk.incubator.vector.Vector} corresponding to the supported set of
  54  * element types: {@link jdk.incubator.vector.ByteVector}, {@link jdk.incubator.vector.ShortVector},
  55  * {@link jdk.incubator.vector.IntVector}, {@link jdk.incubator.vector.LongVector},
  56  * {@link jdk.incubator.vector.FloatVector}, and {@link jdk.incubator.vector.DoubleVector}.
  57  *
  58  * In addition to element type, vectors are parameterized by their <em>shape</em>,
  59  * which is their length.  The supported shapes are
  60  * represented by the enum {@link jdk.incubator.vector.VectorShape}.
  61  * The combination of element type and shape determines a <em>vector species</em>,
  62  * represented by {@link jdk.incubator.vector.VectorSpecies}.  The various typed
  63  * vector classes expose static constants corresponding to the supported species,
  64  * and static methods on these types generally take a species as a parameter.
  65  * For example,
  66  * {@link jdk.incubator.vector.FloatVector#fromArray(VectorSpecies, float[], int) FloatVector.fromArray()}
  67  * creates and returns a float vector of the specified species, with elements
  68  * loaded from the specified float array.
  69  *
  70  * <p>
  71  * The species instance for a specific combination of element type and shape
  72  * can be obtained by reading the appropriate static field, as follows:
  73  * <p>
  74  * {@code VectorSpecies<Float> s = FloatVector.SPECIES_256};
  75  * <p>
  76  *
  77  * Code that is agnostic to species can request the "preferred" species for a
  78  * given element type, where the optimal size is selected for the current platform:
  79  * <p>
  80  * {@code VectorSpecies<Float> s = FloatVector.SPECIES_PREFERRED};
  81  * <p>
  82  *
  83  * <p>
  84  * Here is an example of multiplying elements of two float arrays {@code a and b} using vector computation
  85  * and storing result in array {@code c}.
  86  * <pre>{@code
  87  * static final VectorSpecies<Float> SPECIES = FloatVector.SPECIES_512;
  88  *
  89  * void vectorMultiply(float[] a, float[] b, float[] c) {
  90  *   int i = 0;
  91  *   // It is assumed array arguments are of the same size
  92  *   for (; i < (a.length & ~(SPECIES.length() - 1));
  93  *            i += SPECIES.length()) {
  94  *         FloatVector va = FloatVector.fromArray(SPECIES, a, i);
  95  *         FloatVector vb = FloatVector.fromArray(SPECIES, b, i);
  96  *         FloatVector vc = va.mul(vb)
  97  *         vc.intoArray(c, i);
  98  *   }
  99  *
 100  *   for (; i < a.length; i++) {
 101  *     c[i] = a[i] * b[i];
 102  *   }
 103  * }
 104  * }</pre>
 105  *
 106  * The scalar computation after the vector computation is required to process the tail of
 107  * elements, the length of which is smaller than the species length.
 108  *
 109  * The example above uses vectors hardcoded to a concrete shape (512-bit). Instead, we could use preferred
 110  * species as shown below, to make the code dynamically adapt to optimal shape for the platform on which it runs.
 111  *
 112  * <pre>{@code
 113  * static final VectorSpecies<Float> SPECIES = FloatVector.SPECIES_PREFERRED;
 114  * }</pre>
 115  *
 116  * <h2>Vector operations</h2>
 117  * We use the term <em>lanes</em> when defining operations on vectors. The number of lanes
 118  * in a vector is the number of scalar elements it holds. For example, a vector of
 119  * type {@code Float} and shape {@code VectorShape.S_256_BIT} has eight lanes.
 120  * Vector operations can be grouped into various categories and their behavior
 121  * generally specified as follows:
 122  * <ul>
 123  * <li>
 124  * A lane-wise unary operation operates on one input vector and produce a
 125  * result vector.
 126  * For each lane of the input vector the
 127  * lane element is operated on using the specified scalar unary operation and
 128  * the element result is placed into the vector result at the same lane.
 129  * The following pseudocode expresses the behavior of this operation category,
 130  * where {@code e} is the element type and {@code EVector} corresponds to the
 131  * primitive Vector type:
 132  *
 133  * <pre>{@code
 134  * EVector a = ...;
 135  * e[] ar = new e[a.length()];
 136  * for (int i = 0; i < a.length(); i++) {
 137  *     ar[i] = scalar_unary_op(a.get(i));
 138  * }
 139  * EVector r = EVector.fromArray(a.species(), ar, 0);
 140  * }</pre>
 141  *
 142  * Unless otherwise specified the input and result vectors will have the same
 143  * element type and shape.
 144  *
 145  * <li>
 146  * A lane-wise binary operation operates on two input
 147  * vectors to produce a result vector.
 148  * For each lane of the two input vectors,
 149  * a and b say, the corresponding lane elements from a and b are operated on
 150  * using the specified scalar binary operation and the element result is placed
 151  * into the vector result at the same lane.
 152  * The following pseudocode expresses the behavior of this operation category:
 153  *
 154  * <pre>{@code
 155  * EVector a = ...;
 156  * EVector b = ...;
 157  * e[] ar = new e[a.length()];
 158  * for (int i = 0; i < a.length(); i++) {
 159  *     ar[i] = scalar_binary_op(a.get(i), b.get(i));
 160  * }
 161  * EVector r = EVector.fromArray(a.species(), ar, 0);
 162  * }</pre>
 163  *
 164  * Unless otherwise specified the two input and result vectors will have the
 165  * same element type and shape.
 166  *
 167  * <li>
 168  * Generalizing from unary and binary operations, a lane-wise n-ary
 169  * operation operates on n input vectors to produce a
 170  * result vector.
 171  * N lane elements from each input vector are operated on
 172  * using the specified n-ary scalar operation and the element result is placed
 173  * into the vector result at the same lane.
 174  *
 175  * Unless otherwise specified the n input and result vectors will have the same
 176  * element type and shape.
 177  *
 178  * <li>
 179  * A vector reduction operation operates on all the lane
 180  * elements of an input vector, and applies an accumulation function to all the
 181  * lane elements to produce a scalar result.
 182  * If the reduction operation is associative then the result may be accumulated
 183  * by operating on the lane elements in any order using a specified associative
 184  * scalar binary operation and identity value.  Otherwise, the reduction
 185  * operation specifies the behavior of the accumulation function.
 186  * The following pseudocode expresses the behavior of this operation category
 187  * if it is associative:
 188  * <pre>{@code
 189  * EVector a = ...;
 190  * e r = <identity value>;
 191  * for (int i = 0; i < a.length(); i++) {
 192  *     r = assoc_scalar_binary_op(r, a.get(i));
 193  * }
 194  * }</pre>
 195  *
 196  * Unless otherwise specified the scalar result type and element type will be
 197  * the same.
 198  *
 199  * <li>
 200  * A lane-wise binary test operation operates on two input vectors to produce a
 201  * result mask.  For each lane of the two input vectors, a and b say, the
 202  * the corresponding lane elements from a and b are operated on using the
 203  * specified scalar binary test operation and the boolean result is placed
 204  * into the mask at the same lane.
 205  * The following pseudocode expresses the behavior of this operation category:
 206  * <pre>{@code
 207  * EVector a = ...;
 208  * EVector b = ...;
 209  * boolean[] ar = new boolean[a.length()];
 210  * for (int i = 0; i < a.length(); i++) {
 211  *     ar[i] = scalar_binary_test_op(a.get(i), b.get(i));
 212  * }
 213  * VectorMask<E> r = VectorMask.fromArray(a.species(), ar, 0);
 214  * }</pre>
 215  *
 216  * Unless otherwise specified the two input vectors and result mask will have
 217  * the same element type and shape.
 218  *
 219  * <li>
 220  * The prior categories of operation can be said to operate within the vector
 221  * lanes, where lane access is uniformly applied to all vectors, specifically
 222  * the scalar operation is applied to elements taken from input vectors at the
 223  * same lane, and if appropriate applied to the result vector at the same lane.
 224  * A further category of operation is a cross-lane vector operation where lane
 225  * access is defined by the arguments to the operation.  Cross-lane operations
 226  * generally rearrange lane elements, for example by permutation (commonly
 227  * controlled by a {@link jdk.incubator.vector.VectorShuffle}) or by blending (commonly controlled by a
 228  * {@link jdk.incubator.vector.VectorMask}). Such an operation explicitly specifies how it rearranges lane
 229  * elements.
 230  * </ul>
 231  *
 232  * <p>
 233  * If a vector operation does not belong to one of the above categories then
 234  * the operation explicitly specifies how it processes the lane elements of
 235  * input vectors, and where appropriate expresses the behavior using
 236  * pseudocode.
 237  *
 238  * <p>
 239  * Many vector operations provide an additional {@link jdk.incubator.vector.VectorMask mask}-accepting
 240  * variant.
 241  * The mask controls which lanes are selected for application of the scalar
 242  * operation.  Masks are a key component for the support of control flow in
 243  * vector computations.
 244  * <p>
 245  * For certain operation categories the mask accepting variants can be specified
 246  * in generic terms.  If a lane of the mask is set then the scalar operation is
 247  * applied to corresponding lane elements, otherwise if a lane of a mask is not
 248  * set then a default scalar operation is applied and its result is placed into
 249  * the vector result at the same lane. The default operation is specified as follows:
 250  * <ul>
 251  * <li>
 252  * For a lane-wise n-ary operation the default operation is a function that returns
 253  * it's first argument, specifically the lane element of the first input vector.
 254  * <li>
 255  * For an associative vector reduction operation the default operation is a
 256  * function that returns the identity value.
 257  * <li>
 258  * For lane-wise binary test operation the default operation is a function that
 259  * returns false.
 260  * </ul>
 261  * Otherwise, the mask accepting variant of the operation explicitly specifies
 262  * how it processes the lane elements of input vectors, and where appropriate
 263  * expresses the behavior using pseudocode.
 264  *
 265  * <p>
 266  * For convenience, many vector operations of arity greater than one provide
 267  * an additional scalar-accepting variant (such as adding a constant scalar
 268  * value to all lanes of a vector).  This variant accepts compatible
 269  * scalar values instead of vectors for the second and subsequent input vectors,
 270  * if any.
 271  * Unless otherwise specified the scalar variant behaves as if each scalar value
 272  * is transformed to a vector using the appropriate vector {@code broadcast} operation, and
 273  * then the vector accepting vector operation is applied using the transformed
 274  * values.
 275  *
 276  * <h2> Performance notes </h2>
 277  * This package depends on the runtime's ability to dynamically compile vector operations
 278  * into optimal vector hardware instructions. There is a default scalar implementation
 279  * for each operation which is used if the operation cannot be compiled to vector instructions.
 280  *
 281  * <p>There are certain things users need to pay attention to for generating optimal vector machine code:
 282  *
 283  * <ul>
 284  * <li>The shape of vectors used should be supported by the underlying platform. For example,
 285  * code written using {@code IntVector} of Shape S_512_BIT will not be compiled to vector
 286  * instructions on a platform which supports only 256 bit vectors. Instead, the default
 287  * scalar implementation will be used.
 288  * For this reason, it is recommended to use the preferred species as shown above to write
 289  * generically sized vector computations.
 290  * <li>Classes defined in this package should be treated as
 291  * <a href="{@docRoot}/java.base/java/lang/doc-files/ValueBased.html">value-based</a> classes.
 292  * Use of identity-sensitive operations (including reference equality
 293  * ({@code ==}), identity hash code, or synchronization) will limit generation of
 294  * optimal vector instructions.
 295  * </ul>
 296  */
 297 package jdk.incubator.vector;