page.title=RenderScript
parent.title=Computation
parent.link=index.html

@jd:body

<div id="qv-wrapper">
  <div id="qv">
    <h2>In this document</h2>

    <ol>
      <li><a href="#writing-an-rs-kernel">Writing a RenderScript Kernel</a></li>
      <li><a href="#access-rs-apis">Accessing RenderScript APIs</a>
        <ol>
          <li><a href="#ide-setup">Setting Up Your Development Environment</a></li>
        </ol>
      </li>
      <li><a href="#using-rs-from-java">Using RenderScript from Java Code</a></li>
      <li><a href="#reduction-in-depth">Reduction Kernels in Depth</a>
        <ol>
          <li><a href="#writing-reduction-kernel">Writing a reduction kernel</a></li>
          <li><a href="#calling-reduction-kernel">Calling a reduction kernel from Java code</a></li>
          <li><a href="#more-example">More example reduction kernels</a></li>
        </ol>
      </li>
    </ol>

    <h2>Related Samples</h2>

    <ol>
      <li><a href="{@docRoot}resources/samples/RenderScript/HelloCompute/index.html">Hello
      Compute</a></li>
    </ol>
  </div>
</div>

<p>RenderScript is a framework for running computationally intensive tasks at high performance on
Android. RenderScript is primarily oriented for use with data-parallel computation, although serial
workloads can benefit as well. The RenderScript runtime parallelizes
work across processors available on a device, such as multi-core CPUs and GPUs. This allows
you to focus on expressing algorithms rather than scheduling work. RenderScript is
especially useful for applications performing image processing, computational photography, or
computer vision.</p>

<p>To begin with RenderScript, there are two main concepts you should understand:</p>
<ul>

<li>High-performance compute kernels are written in a C99-derived language. A <i>compute
    kernel</i> is a function or collection of functions that you can direct the RenderScript runtime
    to execute in parallel across a collection of data.</li>

<li>A Java API is used for managing the lifetime of RenderScript resources and controlling kernel
execution.</li>
</ul>

<h2 id="writing-an-rs-kernel">Writing a RenderScript Kernel</h2>

<p>A RenderScript kernel typically resides in a <code>.rs</code> file in the
<code>&lt;project_root&gt;/src/</code> directory; each <code>.rs</code> file is called a
<i>script</i>. Every script contains its own set of kernels, functions, and variables. A script can
contain:</p>

<ul>
<li>A pragma declaration (<code>#pragma version(1)</code>) that declares the version of the
RenderScript kernel language used in this script. Currently, 1 is the only valid value.</li>

<li>A pragma declaration (<code>#pragma rs java_package_name(com.example.app)</code>) that
declares the package name of the Java classes reflected from this script.
Note that your <code>.rs</code> file must be part of your application package, and not in a
library project.</li>

<li>Zero or more <strong><i>invokable functions</i></strong>. An invokable function is a single-threaded RenderScript
function that you can call from your Java code with arbitrary arguments. These are often useful for
initial setup or serial computations within a larger processing pipeline.</li>

<li><p>Zero or more <strong><i>script globals</i></strong>. A script global is equivalent to a global variable in C. You can
access script globals from Java code, and these are often used for parameter passing to RenderScript
kernels.</p></li>

<li><p>Zero or more <strong><i>compute kernels</i></strong>. There are two kinds of compute
kernels: <i>mapping</i> kernels (also called <i>foreach</i> kernels)
and <i>reduction</i> kernels.</p>

<p>A <em>mapping kernel</em> is a parallel function that operates on a collection of {@link
  android.renderscript.Allocation Allocations} of the same dimensions. By default, it executes
  once for every coordinate in those dimensions. It is typically (but not exclusively) used to
  transform a collection of input {@link android.renderscript.Allocation Allocations} to an
  output {@link android.renderscript.Allocation} one {@link android.renderscript.Element} at a
  time.</p>

<ul>
<li><p>Here is an example of a simple <strong>mapping kernel</strong>:</p>

<pre>uchar4 RS_KERNEL invert(uchar4 in, uint32_t x, uint32_t y) {
  uchar4 out = in;
  out.r = 255 - in.r;
  out.g = 255 - in.g;
  out.b = 255 - in.b;
  return out;
}</pre>

<p>In most respects, this is identical to a standard C
  function. The <a href="#RS_KERNEL"><code>RS_KERNEL</code></a> property applied to the
  function prototype specifies that the function is a RenderScript mapping kernel instead of an
  invokable function. The <code>in</code> argument is automatically filled in based on the
  input {@link android.renderscript.Allocation} passed to the kernel launch. The
  arguments <code>x</code> and <code>y</code> are
  discussed <a href="#special-arguments">below</a>. The value returned from the kernel is
  automatically written to the appropriate location in the output {@link
  android.renderscript.Allocation}. By default, this kernel is run across its entire input
  {@link android.renderscript.Allocation}, with one execution of the kernel function per {@link
  android.renderscript.Element} in the {@link android.renderscript.Allocation}.</p>

<p>A mapping kernel may have one or more input {@link android.renderscript.Allocation
  Allocations}, a single output {@link android.renderscript.Allocation}, or both. The
  RenderScript runtime checks to ensure that all input and output Allocations have the same
  dimensions, and that the {@link android.renderscript.Element} types of the input and output
  Allocations match the kernel's prototype; if either of these checks fails, RenderScript
  throws an exception.</p>

<p class="note"><strong>NOTE:</strong> Before Android 6.0 (API level 23), a mapping kernel may
  not have more than one input {@link android.renderscript.Allocation}.</p>

<p>If you need more input or output {@link android.renderscript.Allocation Allocations} than
  the kernel has, those objects should be bound to <code>rs_allocation</code> script globals
  and accessed from a kernel or invokable function
  via <code>rsGetElementAt_<i>type</i>()</code> or <code>rsSetElementAt_<i>type</i>()</code>.</p>

<p><strong>NOTE:</strong> <a id="RS_KERNEL"><code>RS_KERNEL</code></a> is a macro
  defined automatically by RenderScript for your convenience:</p>
<pre>
#define RS_KERNEL __attribute__((kernel))
</pre>
</li>
</ul>

<p>A <em>reduction kernel</em> is a family of functions that operates on a collection of input
  {@link android.renderscript.Allocation Allocations} of the same dimensions. By default,
  its <a href="#accumulator-function">accumulator function</a> executes once for every
  coordinate in those dimensions.  It is typically (but not exclusively) used to "reduce" a
  collection of input {@link android.renderscript.Allocation Allocations} to a single
  value.</p>

<ul>
<li><p>Here is an <a id="example-addint">example</a> of a simple <strong>reduction
kernel</strong> that adds up the {@link android.renderscript.Element Elements} of its
input:</p>

<pre>#pragma rs reduce(addint) accumulator(addintAccum)

static void addintAccum(int *accum, int val) {
  *accum += val;
}</pre>

<p>A reduction kernel consists of one or more user-written functions.
<code>#pragma rs reduce</code> is used to define the kernel by specifying its name
(<code>addint</code>, in this example) and the names and roles of the functions that make
up the kernel (an <code>accumulator</code> function <code>addintAccum</code>, in this
example). All such functions must be <code>static</code>. A reduction kernel always
requires an <code>accumulator</code> function; it may also have other functions, depending
on what you want the kernel to do.</p>

<p>A reduction kernel accumulator function must return <code>void</code> and must have at least
two arguments. The first argument (<code>accum</code>, in this example) is a pointer to
an <i>accumulator data item</i> and the second (<code>val</code>, in this example) is
automatically filled in based on the input {@link android.renderscript.Allocation} passed to
the kernel launch. The accumulator data item is created by the RenderScript runtime; by
default, it is initialized to zero. By default, this kernel is run across its entire input
{@link android.renderscript.Allocation}, with one execution of the accumulator function per
{@link android.renderscript.Element} in the {@link android.renderscript.Allocation}. By
default, the final value of the accumulator data item is treated as the result of the
reduction, and is returned to Java.  The RenderScript runtime checks to ensure that the {@link
android.renderscript.Element} type of the input Allocation matches the accumulator function's
prototype; if it does not match, RenderScript throws an exception.</p>

<p>A reduction kernel has one or more input {@link android.renderscript.Allocation
Allocations} but no output {@link android.renderscript.Allocation Allocations}.</p></li>

<p>Reduction kernels are explained in more detail <a href="#reduction-in-depth">here</a>.</p>

<p>Reduction kernels are supported in Android Nougat (API level 24) and later.</p>
</li>
</ul>

<p>A mapping kernel function or a reduction kernel accumulator function may access the coordinates
of the current execution using the <a id="special-arguments">special arguments</a> <code>x</code>,
<code>y</code>, and <code>z</code>, which must be of type <code>int</code> or <code>uint32_t</code>.
These arguments are optional.</p>

<p>A mapping kernel function or a reduction kernel accumulator
function may also take the optional special argument
<code>context</code> of type <a
href='reference/rs_for_each.html#android_rs:rs_kernel_context'>rs_kernel_context</a>.
It is needed by a family of runtime APIs that are used to query
certain properties of the current execution -- for example, <a
href='reference/rs_for_each.html#android_rs:rsGetDimX'>rsGetDimX</a>.
(The <code>context</code> argument is available in Android 6.0 (API level 23) and later.)</p>
</li>

<li>An optional <code>init()</code> function. An <code>init()</code> function is a special type of
invokable function that RenderScript runs when the script is first instantiated. This allows for some
computation to occur automatically at script creation.</li>

<li>Zero or more <strong><i>static script globals and functions</i></strong>. A static script global is equivalent to a
script global except that it cannot be accessed from Java code. A static function is a standard C
function that can be called from any kernel or invokable function in the script but is not exposed
to the Java API. If a script global or function does not need to be called from Java code, it is
highly recommended that it be declared <code>static</code>.</li> </ul>

<h4>Setting floating point precision</h4>

<p>You can control the required level of floating point precision in a script. This is useful if
full IEEE 754-2008 standard (used by default) is not required. The following pragmas can set a
different level of floating point precision:</p>

<ul>

<li><code>#pragma rs_fp_full</code> (default if nothing is specified): For apps that require
  floating point precision as outlined by the IEEE 754-2008 standard.

</li>

  <li><code>#pragma rs_fp_relaxed</code>: For apps that don’t require strict IEEE 754-2008
    compliance and can tolerate less precision. This mode enables flush-to-zero for denorms and
    round-towards-zero.

</li>

  <li><code>#pragma rs_fp_imprecise</code>: For apps that don’t have stringent precision
    requirements. This mode enables everything in <code>rs_fp_relaxed</code> along with the
    following:

<ul>

  <li>Operations resulting in -0.0 can return +0.0 instead.</li>
  <li>Operations on INF and NAN are undefined.</li>
</ul>
</li>
</ul>

<p>Most applications can use <code>rs_fp_relaxed</code> without any side effects. This may be very
beneficial on some architectures due to additional optimizations only available with relaxed
precision (such as SIMD CPU instructions).</p>


<h2 id="access-rs-apis">Accessing RenderScript APIs</h2>

<p>When developing an Android application that uses RenderScript, you can access its API in
  one of two ways:</p>

<ul>
  <li><strong>{@link android.renderscript}</strong> - The APIs in this class package are
    available on devices running Android 3.0 (API level 11) and higher. </li>
  <li><strong>{@link android.support.v8.renderscript}</strong> - The APIs in this package are
    available through a <a href="{@docRoot}tools/support-library/features.html#v8">Support
    Library</a>, which allows you to use them on devices running Android 2.3 (API level 9) and
    higher.</li>
</ul>

<p>Here are the tradeoffs:</p>

<ul>
<li>If you use the Support Library APIs, the RenderScript portion of your application will be
  compatible with devices running Android 2.3 (API level 9) and higher, regardless of which RenderScript
  features you use. This allows your application to work on more devices than if you use the
  native (<strong>{@link android.renderscript}</strong>) APIs.</li>
<li>Certain RenderScript features are not available through the Support Library APIs.</li>
<li>If you use the Support Library APIs, you will get (possibly significantly) larger APKs than
if you use the native (<strong>{@link android.renderscript}</strong>) APIs.</li>
</ul>

<h3 id="ide-setup">Using the RenderScript Support Library APIs</h3>

<p>In order to use the Support Library RenderScript APIs, you must configure your development
  environment to be able to access them. The following Android SDK tools are required for using
  these APIs:</p>

<ul>
  <li>Android SDK Tools revision 22.2 or higher</li>
  <li>Android SDK Build-tools revision 18.1.0 or higher</li>
</ul>

<p>You can check and update the installed version of these tools in the
  <a href="{@docRoot}tools/help/sdk-manager.html">Android SDK Manager</a>.</p>


<p>To use the Support Library RenderScript APIs:</p>

<ol>
  <li>Make sure you have the required Android SDK version and Build Tools version installed.</li>
  <li> Update the settings for the Android build process to include the RenderScript settings:

    <p><strong>For Android Studio or Gradle-based builds</strong></p>
    <ul>
      <li>Open the {@code build.gradle} file in the app folder of your application module. </li>
      <li>Add the following RenderScript settings to the file:

<pre>
android {
    compileSdkVersion 19
    buildToolsVersion "19.0.3"

    defaultConfig {
        minSdkVersion 9
        targetSdkVersion 16
<strong>
        renderscriptTargetApi 18
        renderscriptSupportModeEnabled true
</strong>
    }
}
</pre>


    <p>The settings listed above control specific behavior in the Android build process:</p>

    <ul>
      <li>{@code renderscriptTargetApi} - Specifies the bytecode version to be generated. We
      recommend you set this value to the highest available API level and set
      {@code renderscriptSupportModeEnabled}
      to {@code true}. Valid values for this setting are any integer value
      from 11 to the most recently released API level. If your minimum SDK version specified in your
      application manifest is set to a different value, that value is ignored and the target value
      in the build file is used to set the minimum SDK version.</li>
      <li>{@code renderscriptSupportModeEnabled} - Specifies that the generated bytecode should fall
      back to a compatible version if the device it is running on does not support the target
      version.
      </li>
      <li>{@code buildToolsVersion} - The version of the Android SDK build tools to use. This value
      should be set to {@code 18.1.0} or higher. If this option is not specified, the highest
      installed build tools version is used. You should always set this value to ensure the
      consistency of builds across development machines with different configurations.</li>
    </ul>

    </li>

    <p><strong>For Eclipse</strong></p>
    <ul>
      <li>Open the {@code project.properties} file in the root folder of your application project.</li>
      <li>Add the following lines to the file:

<pre>
renderscript.target=18
renderscript.support.mode=true
sdk.buildtools=18.1.0
</pre>

      <p>The settings listed above control specific behavior in the Android build process:</p>

      <ul>
        <li>{@code renderscript.target} - Specifies the bytecode version to be generated. We
        recommend you set this value to the highest available API level and set
        {@code renderscript.support.mode} to {@code true}. Valid values for this setting are any
        integer value from 11 to the most recently released API level. If your minimum SDK version
        specified in your application manifest is set to a higher value, this value is ignored and
        the target value is set to the minimum SDK version.</li>
        <li>{@code renderscript.support.mode} - Specifies that the generated bytecode should fall
        back to a compatible version if the device it is running on does not support the target version.
        </li>
        <li>{@code sdk.buildtools} - The version of the Android SDK build tools to use. This value
        should be set to {@code 18.1.0} or higher. If this option is not specified, the highest
        installed build tools version is used. You should always set this value to ensure the
        consistency of builds across development machines with different configurations.</li>
      </ul>
     </li>

    </ul>

  </ul>

  <li>In your application classes that use RenderScript, add an import for the Support Library
    classes:

<pre>
import android.support.v8.renderscript.*;
</pre>

  </li>

 </ol>

<h2 id="using-rs-from-java">Using RenderScript from Java Code</h2>

<p>Using RenderScript from Java code relies on the API classes located in the
{@link android.renderscript} or the {@link android.support.v8.renderscript} package. Most
applications follow the same basic usage pattern:</p>

<ol>

<li><strong>Initialize a RenderScript context.</strong> The {@link
android.renderscript.RenderScript} context, created with {@link
android.renderscript.RenderScript#create}, ensures that RenderScript can be used and provides an
object to control the lifetime of all subsequent RenderScript objects. You should consider context
creation to be a potentially long-running operation, since it may create resources on different
pieces of hardware; it should not be in an application's critical path if at all
possible. Typically, an application will have only a single RenderScript context at a time.</li>

<li><strong>Create at least one {@link android.renderscript.Allocation} to be passed to a
script.</strong> An {@link android.renderscript.Allocation} is a RenderScript object that provides
storage for a fixed amount of data. Kernels in scripts take {@link android.renderscript.Allocation}
objects as their input and output, and {@link android.renderscript.Allocation} objects can be
accessed in kernels using <code>rsGetElementAt_<i>type</i>()</code> and
<code>rsSetElementAt_<i>type</i>()</code> when bound as script globals. {@link
android.renderscript.Allocation} objects allow arrays to be passed from Java code to RenderScript
code and vice-versa. {@link android.renderscript.Allocation} objects are typically created using
{@link android.renderscript.Allocation#createTyped createTyped()} or {@link
android.renderscript.Allocation#createFromBitmap createFromBitmap()}.</li>

<li><strong>Create whatever scripts are necessary.</strong> There are two types of scripts available
to you when using RenderScript:

<ul>

<li><strong>ScriptC</strong>: These are the user-defined scripts as described in <a
href="#writing-an-rs-kernel">Writing a RenderScript Kernel</a> above. Every script has a Java class
reflected by the RenderScript compiler in order to make it easy to access the script from Java code;
this class has the name <code>ScriptC_<i>filename</i></code>. For example, if the mapping kernel
above were located in <code>invert.rs</code> and a RenderScript context were already located in
<code>mRenderScript</code>, the Java code to instantiate the script would be:

<pre>ScriptC_invert invert = new ScriptC_invert(mRenderScript);</pre></li>

<li><strong>ScriptIntrinsic</strong>: These are built-in RenderScript kernels for common operations,
such as Gaussian blur, convolution, and image blending. For more information, see the subclasses of
{@link android.renderscript.ScriptIntrinsic}.</li>

</ul></li>

<li><strong>Populate Allocations with data.</strong> Except for Allocations created with {@link
android.renderscript.Allocation#createFromBitmap createFromBitmap()}, an Allocation is populated with empty data when it is
first created. To populate an Allocation, use one of the "copy" methods in {@link
android.renderscript.Allocation}. The "copy" methods are <a href="#asynchronous-model">synchronous</a>.</li>

<li><strong>Set any necessary script globals.</strong> You may set globals using methods in the
  same <code>ScriptC_<i>filename</i></code> class named <code>set_<i>globalname</i></code>. For
  example, in order to set an <code>int</code> variable named <code>threshold</code>, use the
  Java method <code>set_threshold(int)</code>; and in order to set
  an <code>rs_allocation</code> variable named <code>lookup</code>, use the Java
  method <code>set_lookup(Allocation)</code>. The <code>set</code> methods
  are <a href="#asynchronous-model">asynchronous</a>.</li>

<li><strong>Launch the appropriate kernels and invokable functions.</strong>
<p>Methods to launch a given kernel are
reflected in the same <code>ScriptC_<i>filename</i></code> class with methods named
<code>forEach_<i>mappingKernelName</i>()</code>
or <code>reduce_<i>reductionKernelName</i>()</code>.
These launches are <a href="#asynchronous-model">asynchronous</a>.
Depending on the arguments to the kernel, the
method takes one or more Allocations, all of which must have the same dimensions. By default, a
kernel executes over every coordinate in those dimensions; to execute a kernel over a subset of those coordinates,
pass an appropriate {@link
android.renderscript.Script.LaunchOptions} as the last argument to the <code>forEach</code> or <code>reduce</code> method.</p>

<p>Launch invokable functions using the <code>invoke_<i>functionName</i></code> methods
reflected in the same <code>ScriptC_<i>filename</i></code> class.
These launches are <a href="#asynchronous-model">asynchronous</a>.</p></li>

<li><strong>Retrieve data from {@link android.renderscript.Allocation} objects
and <i><a href="#javaFutureType">javaFutureType</a></i> objects.</strong>
In order to
access data from an {@link android.renderscript.Allocation} from Java code, you must copy that data
back to Java using one of the "copy" methods in {@link
android.renderscript.Allocation}.
In order to obtain the result of a reduction kernel, you must use the <code><i>javaFutureType</i>.get()</code> method.
The "copy" and <code>get()</code> methods are <a href="#asynchronous-model">synchronous</a>.</li>

<li><strong>Tear down the RenderScript context.</strong> You can destroy the RenderScript context
with {@link android.renderscript.RenderScript#destroy} or by allowing the RenderScript context
object to be garbage collected. This causes any further use of any object belonging to that
context to throw an exception.</li> </ol>

<h3 id="asynchronous-model">Asynchronous execution model</h3>

<p>The reflected <code>forEach</code>, <code>invoke</code>, <code>reduce</code>,
  and <code>set</code> methods are asynchronous -- each may return to Java before completing the
  requested action.  However, the individual actions are serialized in the order in which they are launched.</p>

<p>The {@link android.renderscript.Allocation} class provides "copy" methods to copy data to
  and from Allocations.  A "copy" method is synchronous, and is serialized with respect to any
  of the asynchronous actions above that touch the same Allocation.</p>

<p>The reflected <i><a href="#javaFutureType">javaFutureType</a></i> classes provide
  a <code>get()</code> method to obtain the result of a reduction. <code>get()</code> is
  synchronous, and is serialized with respect to the reduction (which is asynchronous).</p>

<h2 id="reduction-in-depth">Reduction Kernels in Depth</h2>

<p><i>Reduction</i> is the process of combining a collection of data into a single
value. This is a useful primitive in parallel programming, with applications such as the
following:</p>
<ul>
  <li>computing the sum or product over all the data</li>
  <li>computing logical operations (<code>and</code>, <code>or</code>, <code>xor</code>)
  over all the data</li>
  <li>finding the minimum or maximum value within the data</li>
  <li>searching for a specific value or for the coordinate of a specific value within the data</li>
</ul>

<p>In Android Nougat (API level 24) and later, RenderScript supports <i>reduction kernels</i> to allow
efficient user-written reduction algorithms. You may launch reduction kernels on inputs with
1, 2, or 3 dimensions.<p>

<p>An example above shows a simple <a href="#example-addint">addint</a> reduction kernel.
Here is a more complicated <a id="example-findMinAndMax">findMinAndMax</a> reduction kernel
that finds the locations of the minimum and maximum <code>long</code> values in a
1-dimensional {@link android.renderscript.Allocation}:</p>

<pre>
#define LONG_MAX (long)((1UL << 63) - 1)
#define LONG_MIN (long)(1UL << 63)

#pragma rs reduce(findMinAndMax) \
  initializer(fMMInit) accumulator(fMMAccumulator) \
  combiner(fMMCombiner) outconverter(fMMOutConverter)

// Either a value and the location where it was found, or <a href="#INITVAL">INITVAL</a>.
typedef struct {
  long val;
  int idx;     // -1 indicates <a href="#INITVAL">INITVAL</a>
} IndexedVal;

typedef struct {
  IndexedVal min, max;
} MinAndMax;

// In discussion below, this initial value { { LONG_MAX, -1 }, { LONG_MIN, -1 } }
// is called <a id="INITVAL">INITVAL</a>.
static void fMMInit(MinAndMax *accum) {
  accum->min.val = LONG_MAX;
  accum->min.idx = -1;
  accum->max.val = LONG_MIN;
  accum->max.idx = -1;
}

//----------------------------------------------------------------------
// In describing the behavior of the accumulator and combiner functions,
// it is helpful to describe hypothetical functions
//   IndexedVal min(IndexedVal a, IndexedVal b)
//   IndexedVal max(IndexedVal a, IndexedVal b)
//   MinAndMax  minmax(MinAndMax a, MinAndMax b)
//   MinAndMax  minmax(MinAndMax accum, IndexedVal val)
//
// The effect of
//   IndexedVal min(IndexedVal a, IndexedVal b)
// is to return the IndexedVal from among the two arguments
// whose val is lesser, except that when an IndexedVal
// has a negative index, that IndexedVal is never less than
// any other IndexedVal; therefore, if exactly one of the
// two arguments has a negative index, the min is the other
// argument. Like ordinary arithmetic min and max, this function
// is commutative and associative; that is,
//
//   min(A, B) == min(B, A)               // commutative
//   min(A, min(B, C)) == min((A, B), C)  // associative
//
// The effect of
//   IndexedVal max(IndexedVal a, IndexedVal b)
// is analogous (greater . . . never greater than).
//
// Then there is
//
//   MinAndMax minmax(MinAndMax a, MinAndMax b) {
//     return MinAndMax(min(a.min, b.min), max(a.max, b.max));
//   }
//
// Like ordinary arithmetic min and max, the above function
// is commutative and associative; that is:
//
//   minmax(A, B) == minmax(B, A)                  // commutative
//   minmax(A, minmax(B, C)) == minmax((A, B), C)  // associative
//
// Finally define
//
//   MinAndMax minmax(MinAndMax accum, IndexedVal val) {
//     return minmax(accum, MinAndMax(val, val));
//   }
//----------------------------------------------------------------------

// This function can be explained as doing:
//   *accum = minmax(*accum, IndexedVal(in, x))
//
// This function simply computes minimum and maximum values as if
// INITVAL.min were greater than any other minimum value and
// INITVAL.max were less than any other maximum value.  Note that if
// *accum is INITVAL, then this function sets
//   *accum = IndexedVal(in, x)
//
// After this function is called, both accum->min.idx and accum->max.idx
// will have nonnegative values:
// - x is always nonnegative, so if this function ever sets one of the
//   idx fields, it will set it to a nonnegative value
// - if one of the idx fields is negative, then the corresponding
//   val field must be LONG_MAX or LONG_MIN, so the function will always
//   set both the val and idx fields
static void fMMAccumulator(MinAndMax *accum, long in, int x) {
  IndexedVal me;
  me.val = in;
  me.idx = x;

  if (me.val <= accum->min.val)
    accum->min = me;
  if (me.val >= accum->max.val)
    accum->max = me;
}

// This function can be explained as doing:
//   *accum = minmax(*accum, *val)
//
// This function simply computes minimum and maximum values as if
// INITVAL.min were greater than any other minimum value and
// INITVAL.max were less than any other maximum value.  Note that if
// one of the two accumulator data items is INITVAL, then this
// function sets *accum to the other one.
static void fMMCombiner(MinAndMax *accum,
                        const MinAndMax *val) {
  if ((accum->min.idx < 0) || (val->min.val < accum->min.val))
    accum->min = val->min;
  if ((accum->max.idx < 0) || (val->max.val > accum->max.val))
    accum->max = val->max;
}

static void fMMOutConverter(int2 *result,
                            const MinAndMax *val) {
  result->x = val->min.idx;
  result->y = val->max.idx;
}
</pre>

<p class="note"><strong>NOTE:</strong> There are more example reduction
  kernels <a href="#more-example">here</a>.</p>

<p>In order to run a reduction kernel, the RenderScript runtime creates <em>one or more</em>
variables called <a id="accumulator-data-items"><strong><i>accumulator data
items</i></strong></a> to hold the state of the reduction process. The RenderScript runtime
picks the number of accumulator data items in such a way as to maximize performance. The type
of the accumulator data items (<i>accumType</i>) is determined by the kernel's <i>accumulator
function</i> -- the first argument to that function is a pointer to an accumulator data
item. By default, every accumulator data item is initialized to zero (as if
by <code>memset</code>); however, you may write an <i>initializer function</i> to do something
different.</p>

<p class="note"><strong>Example:</strong> In the <a href="#example-addint">addint</a>
kernel, the accumulator data items (of type <code>int</code>) are used to add up input
values. There is no initializer function, so each accumulator data item is initialized to
zero.</p>

<p class="note"><strong>Example:</strong> In
the <a href="#example-findMinAndMax">findMinAndMax</a> kernel, the accumulator data items
(of type <code>MinAndMax</code>) are used to keep track of the minimum and maximum values
found so far. There is an initializer function to set these to <code>LONG_MAX</code> and
<code>LONG_MIN</code>, respectively; and to set the locations of these values to -1, indicating that
the values are not actually present in the (empty) portion of the input that has been
processed.</p>

<p>RenderScript calls your accumulator function once for every coordinate in the
input(s). Typically, your function should update the accumulator data item in some way
according to the input.</p>

<p class="note"><strong>Example:</strong> In the <a href="#example-addint">addint</a>
kernel, the accumulator function adds the value of an input Element to the accumulator
data item.</p>

<p class="note"><strong>Example:</strong> In
the <a href="#example-findMinAndMax">findMinAndMax</a> kernel, the accumulator function
checks to see whether the value of an input Element is less than or equal to the minimum
value recorded in the accumulator data item and/or greater than or equal to the maximum
value recorded in the accumulator data item, and updates the accumulator data item
accordingly.</p>

<p>After the accumulator function has been called once for every coordinate in the input(s),
RenderScript must <strong>combine</strong> the <a href="#accumulator-data-items">accumulator
data items</a> together into a single accumulator data item. You may write a <i>combiner
function</i> to do this. If the accumulator function has a single input and
no <a href="#special-arguments">special arguments</a>, then you do not need to write a combiner
function; RenderScript will use the accumulator function to combine the accumulator data
items. (You may still write a combiner function if this default behavior is not what you
want.)</p>

<p class="note"><strong>Example:</strong> In the <a href="#example-addint">addint</a>
kernel, there is no combiner function, so the accumulator function will be used. This is
the correct behavior, because if we split a collection of values into two pieces, and we
add up the values in those two pieces separately, adding up those two sums is the same as
adding up the entire collection.</p>

<p class="note"><strong>Example:</strong> In
the <a href="#example-findMinAndMax">findMinAndMax</a> kernel, the combiner function
checks to see whether the minimum value recorded in the "source" accumulator data
item <code>*val</code> is less then the minimum value recorded in the "destination"
accumulator data item <code>*accum</code>, and updates <code>*accum</code>
accordingly. It does similar work for the maximum value. This updates <code>*accum</code>
to the state it would have had if all of the input values had been accumulated into
<code>*accum</code> rather than some into <code>*accum</code> and some into
<code>*val</code>.</p>

<p>After all of the accumulator data items have been combined, RenderScript determines
the result of the reduction to return to Java. You may write an <i>outconverter
function</i> to do this. You do not need to write an outconverter function if you want
the final value of the combined accumulator data items to be the result of the reduction.</p>

<p class="note"><strong>Example:</strong> In the <a href="#example-addint">addint</a> kernel,
there is no outconverter function.  The final value of the combined data items is the sum of
all Elements of the input, which is the value we want to return.</p>

<p class="note"><strong>Example:</strong> In
the <a href="#example-findMinAndMax">findMinAndMax</a> kernel, the outconverter function
initializes an <code>int2</code> result value to hold the locations of the minimum and
maximum values resulting from the combination of all of the accumulator data items.</p>

<h3 id="writing-reduction-kernel">Writing a reduction kernel</h3>

<p><code>#pragma rs reduce</code> defines a reduction kernel by
specifying its name and the names and roles of the functions that make
up the kernel.  All such functions must be
<code>static</code>. A reduction kernel always requires an <code>accumulator</code>
function; you can omit some or all of the other functions, depending on what you want the
kernel to do.</p>

<pre>#pragma rs reduce(<i>kernelName</i>) \
  initializer(<i>initializerName</i>) \
  accumulator(<i>accumulatorName</i>) \
  combiner(<i>combinerName</i>) \
  outconverter(<i>outconverterName</i>)
</pre>

<p>The meaning of the items in the <code>#pragma</code> is as follows:</p>
<ul>

<li><code>reduce(<i>kernelName</i>)</code> (mandatory): Specifies that a reduction kernel is
being defined. A reflected Java method <code>reduce_<i>kernelName</i></code> will launch the
kernel.</li>

<li><p><code>initializer(<i>initializerName</i>)</code> (optional): Specifies the name of the
initializer function for this reduction kernel. When you launch the kernel, RenderScript calls
this function once for each <a href="#accumulator-data-items">accumulator data item</a>. The
function must be defined like this:</p>

<pre>static void <i>initializerName</i>(<i>accumType</i> *accum) { … }</pre>

<p><code>accum</code> is a pointer to an accumulator data item for this function to
initialize.</p>

<p>If you do not provide an initializer function, RenderScript initializes every accumulator
data item to zero (as if by <code>memset</code>), behaving as if there were an initializer
function that looks like this:</p>
<pre>static void <i>initializerName</i>(<i>accumType</i> *accum) {
  memset(accum, 0, sizeof(*accum));
}</pre>
</li>

<li><p><code><a id="accumulator-function">accumulator(<i>accumulatorName</i>)</a></code>
(mandatory): Specifies the name of the accumulator function for this
reduction kernel. When you launch the kernel, RenderScript calls
this function once for every coordinate in the input(s), to update an
accumulator data item in some way according to the input(s). The function
must be defined like this:</p>

<pre>
static void <i>accumulatorName</i>(<i>accumType</i> *accum,
                            <i>in1Type</i> in1, <i>&hellip;,</i> <i>inNType</i> in<i>N</i>
                            <i>[, specialArguments]</i>) { &hellip; }
</pre>

<p><code>accum</code> is a pointer to an accumulator data item for this function to
modify. <code>in1</code> through <code>in<i>N</i></code> are one <em>or more</em> arguments that
are automatically filled in based on the inputs passed to the kernel launch, one argument
per input. The accumulator function may optionally take any of the <a
href="#special-arguments">special arguments</a>.</p>

<p>An example kernel with multiple inputs is <a href="#dot-product"><code>dotProduct</code></a>.</p>
</li>

<li><code><a id="combiner-function">combiner(<i>combinerName</i>)</a></code>
(optional): Specifies the name of the combiner function for this
reduction kernel. After RenderScript calls the accumulator function
once for every coordinate in the input(s), it calls this function as many
times as necessary to combine all accumulator data items into a single
accumulator data item. The function must be defined like this:</p>

<pre>static void <i>combinerName</i>(<i>accumType</i> *accum, const <i>accumType</i> *other) { … }</pre>

<p><code>accum</code> is a pointer to a "destination" accumulator data item for this
function to modify. <code>other</code> is a pointer to a "source" accumulator data item
for this function to "combine" into <code>*accum</code>.</p>

<p class="note"><strong>NOTE:</strong> It is possible
  that <code>*accum</code>, <code>*other</code>, or both have been initialized but have never
  been passed to the accumulator function; that is, one or both have never been updated
  according to any input data. For example, in
  the <a href="#example-findMinAndMax">findMinAndMax</a> kernel, the combiner
  function <code>fMMCombiner</code> explicitly checks for <code>idx &lt; 0</code> because that
  indicates such an accumulator data item, whose value is <a href="#INITVAL">INITVAL</a>.</p>

<p>If you do not provide a combiner function, RenderScript uses the accumulator function in its
place, behaving as if there were a combiner function that looks like this:</p>

<pre>static void <i>combinerName</i>(<i>accumType</i> *accum, const <i>accumType</i> *other) {
  <i>accumulatorName</i>(accum, *other);
}</pre>

<p>A combiner function is mandatory if the kernel has more than one input, if the input data
  type is not the same as the accumulator data type, or if the accumulator function takes one
  or more <a href="#special-arguments">special arguments</a>.</p>
</li>

<li><p><code><a id="outconverter-function">outconverter(<i>outconverterName</i>)</a></code>
(optional): Specifies the name of the outconverter function for this
reduction kernel. After RenderScript combines all of the accumulator
data items, it calls this function to determine the result of the
reduction to return to Java. The function must be defined like
this:</p>

<pre>static void <i>outconverterName</i>(<i>resultType</i> *result, const <i>accumType</i> *accum) { … }</pre>

<p><code>result</code> is a pointer to a result data item (allocated but not initialized
by the RenderScript runtime) for this function to initialize with the result of the
reduction. <i>resultType</i> is the type of that data item, which need not be the same
as <i>accumType</i>. <code>accum</code> is a pointer to the final accumulator data item
computed by the <a href="#combiner-function">combiner function</a>.</p>

<p>If you do not provide an outconverter function, RenderScript copies the final accumulator
data item to the result data item, behaving as if there were an outconverter function that
looks like this:</p>

<pre>static void <i>outconverterName</i>(<i>accumType</i> *result, const <i>accumType</i> *accum) {
  *result = *accum;
}</pre>

<p>If you want a different result type than the accumulator data type, then the outconverter function is mandatory.</p>
</li>

</ul>

<p>Note that a kernel has input types, an accumulator data item type, and a result type,
  none of which need to be the same. For example, in
  the <a href="#example-findMinAndMax">findMinAndMax</a> kernel, the input
  type <code>long</code>, accumulator data item type <code>MinAndMax</code>, and result
  type <code>int2</code> are all different.</p>

<h4 id="assume">What can't you assume?</h4>

<p>You must not rely on the number of accumulator data items created by RenderScript for a
  given kernel launch.  There is no guarantee that two launches of the same kernel with the
  same input(s) will create the same number of accumulator data items.</p>

<p>You must not rely on the order in which RenderScript calls the initializer, accumulator, and
  combiner functions; it may even call some of them in parallel.  There is no guarantee that
  two launches of the same kernel with the same input will follow the same order.  The only
  guarantee is that only the initializer function will ever see an uninitialized accumulator
  data item. For example:</p>
<ul>
<li>There is no guarantee that all accumulator data items will be initialized before the
  accumulator function is called, although it will only be called on an initialized accumulator
  data item.</li>
<li>There is no guarantee on the order in which input Elements are passed to the accumulator
  function.</li>
<li>There is no guarantee that the accumulator function has been called for all input Elements
  before the combiner function is called.</li>
</ul>

<p>One consequence of this is that the <a href="#example-findMinAndMax">findMinAndMax</a>
  kernel is not deterministic: If the input contains more than one occurrence of the same
  minimum or maximum value, you have no way of knowing which occurrence the kernel will
  find.</p>

<h4 id="guarantee">What must you guarantee?</h4>

<p>Because the RenderScript system can choose to execute a kernel <a href="#assume">in many
    different ways</a>, you must follow certain rules to ensure that your kernel behaves the
    way you want. If you do not follow these rules, you may get incorrect results,
    nondeterministic behavior, or runtime errors.</p>

<p>The rules below often say that two accumulator data items must have "<a id="the-same">the
  same value"</a>.  What does this mean?  That depends on what you want the kernel to do.  For
  a mathematical reduction such as <a href="#example-addint">addint</a>, it usually makes sense
  for "the same" to mean mathematical equality.  For a "pick any" search such
  as <a href="#example-findMinAndMax">findMinAndMax</a> ("find the location of minimum and
  maximum input values") where there might be more than one occurrence of identical input
  values, all locations of a given input value must be considered "the same".  You could write
  a similar kernel to "find the location of <em>leftmost</em> minimum and maximum input values"
  where (say) a minimum value at location 100 is preferred over an identical minimum value at location
  200; for this kernel, "the same" would mean identical <em>location</em>, not merely
  identical <em>value</em>, and the accumulator and combiner functions would have to be
  different than those for <a href="#example-findMinAndMax">findMinAndMax</a>.</p>

<strong>The initializer function must create an <i>identity value</i>.</strong>  That is,
  if <code><i>I</i></code> and <code><i>A</i></code> are accumulator data items initialized
  by the initializer function, and <code><i>I</i></code> has never been passed to the
  accumulator function (but <code><i>A</i></code> may have been), then
<ul>
<li><code><i>combinerName</i>(&<i>A</i>, &<i>I</i>)</code> must
  leave <code><i>A</i></code> <a href="#the-same">the same</a></li>
<li><code><i>combinerName</i>(&<i>I</i>, &<i>A</i>)</code> must
  leave <code><i>I</i></code> <a href="#the-same">the same</a> as <code><i>A</i></code></li>
</ul>
<p class="note"><strong>Example:</strong> In the <a href="#example-addint">addint</a>
  kernel, an accumulator data item is initialized to zero. The combiner function for this
  kernel performs addition; zero is the identity value for addition.</p>
<div class="note">
<p><strong>Example:</strong> In the <a href="#example-findMinAndMax">findMinAndMax</a>
  kernel, an accumulator data item is initialized
  to <a href="#INITVAL"><code>INITVAL</code></a>.
<ul>
<li><code>fMMCombiner(&<i>A</i>, &<i>I</i>)</code> leaves <code><i>A</i></code> the same,
  because <code><i>I</i></code> is <code>INITVAL</code>.</li>
<li><code>fMMCombiner(&<i>I</i>, &<i>A</i>)</code> sets <code><i>I</i></code>
  to <code><i>A</i></code>, because <code><i>I</i></code> is <code>INITVAL</code>.</li>
</ul>
Therefore, <code>INITVAL</code> is indeed an identity value.
</p></div>

<p><strong>The combiner function must be <i>commutative</i>.</strong>  That is,
  if <code><i>A</i></code> and <code><i>B</i></code> are accumulator data items initialized
  by the initializer function, and that may have been passed to the accumulator function zero
  or more times, then <code><i>combinerName</i>(&<i>A</i>, &<i>B</i>)</code> must
  set <code><i>A</i></code> to <a href="#the-same">the same value</a>
  that <code><i>combinerName</i>(&<i>B</i>, &<i>A</i>)</code>
  sets <code><i>B</i></code>.</p>
<p class="note"><strong>Example:</strong> In the <a href="#example-addint">addint</a>
  kernel, the combiner function adds the two accumulator data item values; addition is
  commutative.</p>
<div class="note">
<p><strong>Example:</strong> In the <a href="#example-findMinAndMax">findMinAndMax</a> kernel,
<pre>
fMMCombiner(&<i>A</i>, &<i>B</i>)
</pre>
is the same as
<pre>
<i>A</i> = minmax(<i>A</i>, <i>B</i>)
</pre>
and <code>minmax</code> is commutative, so <code>fMMCombiner</code> is also.
</p>
</div>

<p><strong>The combiner function must be <i>associative</i>.</strong>  That is,
  if <code><i>A</i></code>, <code><i>B</i></code>, and <code><i>C</i></code> are
  accumulator data items initialized by the initializer function, and that may have been passed
  to the accumulator function zero or more times, then the following two code sequences must
  set <code><i>A</i></code> to <a href="#the-same">the same value</a>:</p>
<ul>
<li><pre>
<i>combinerName</i>(&<i>A</i>, &<i>B</i>);
<i>combinerName</i>(&<i>A</i>, &<i>C</i>);
</pre></li>
<li><pre>
<i>combinerName</i>(&<i>B</i>, &<i>C</i>);
<i>combinerName</i>(&<i>A</i>, &<i>B</i>);
</pre></li>
</ul>
<div class="note">
<p><strong>Example:</strong> In the <a href="#example-addint">addint</a> kernel, the
  combiner function adds the two accumulator data item values:
<ul>
<li><pre>
<i>A</i> = <i>A</i> + <i>B</i>
<i>A</i> = <i>A</i> + <i>C</i>
// Same as
//   <i>A</i> = (<i>A</i> + <i>B</i>) + <i>C</i>
</pre></li>
<li><pre>
<i>B</i> = <i>B</i> + <i>C</i>
<i>A</i> = <i>A</i> + <i>B</i>
// Same as
//   <i>A</i> = <i>A</i> + (<i>B</i> + <i>C</i>)
//   <i>B</i> = <i>B</i> + <i>C</i>
</li>
</ul>
Addition is associative, and so the combiner function is also.
</p>
</div>
<div class="note">
<p><strong>Example:</strong> In the <a href="#example-findMinAndMax">findMinAndMax</a> kernel,
<pre>
fMMCombiner(&<i>A</i>, &<i>B</i>)
</pre>
is the same as
<pre>
<i>A</i> = minmax(<i>A</i>, <i>B</i>)
</pre>
So the two sequences are
<ul>
<li><pre>
<i>A</i> = minmax(<i>A</i>, <i>B</i>)
<i>A</i> = minmax(<i>A</i>, <i>C</i>)
// Same as
//   <i>A</i> = minmax(minmax(<i>A</i>, <i>B</i>), <i>C</i>)
</pre></li>
<li><pre>
<i>B</i> = minmax(<i>B</i>, <i>C</i>)
<i>A</i> = minmax(<i>A</i>, <i>B</i>)
// Same as
//   <i>A</i> = minmax(<i>A</i>, minmax(<i>B</i>, <i>C</i>))
//   <i>B</i> = minmax(<i>B</i>, <i>C</i>)
</pre></li>
<code>minmax</code> is associative, and so <code>fMMCombiner</code> is also.
</p>
</div>

<p><strong>The accumulator function and combiner function together must obey the <i>basic
  folding rule</i>.</strong>  That is, if <code><i>A</i></code>
  and <code><i>B</i></code> are accumulator data items, <code><i>A</i></code> has been
  initialized by the initializer function and may have been passed to the accumulator function
  zero or more times, <code><i>B</i></code> has not been initialized, and <i>args</i> is
  the list of input arguments and special arguments for a particular call to the accumulator
  function, then the following two code sequences must set <code><i>A</i></code>
  to <a href="#the-same">the same value</a>:</p>
<ul>
<li><pre>
<i>accumulatorName</i>(&<i>A</i>, <i>args</i>);  // statement 1
</pre></li>
<li><pre>
<i>initializerName</i>(&<i>B</i>);        // statement 2
<i>accumulatorName</i>(&<i>B</i>, <i>args</i>);  // statement 3
<i>combinerName</i>(&<i>A</i>, &<i>B</i>);       // statement 4
</pre></li>
</ul>
<div class="note">
<p><strong>Example:</strong> In the <a href="#example-addint">addint</a> kernel, for an input value <i>V</i>:
<ul>
<li>Statement 1 is the same as <code>A += <i>V</i></code></li>
<li>Statement 2 is the same as <code>B = 0</code></li>
<li>Statement 3 is the same as <code>B += <i>V</i></code>, which is the same as <code>B = <i>V</i></code></li>
<li>Statement 4 is the same as <code>A += B</code>, which is the same as <code>A += <i>V</i></code></li>
</ul>
Statements 1 and 4 set <code><i>A</i></code> to the same value, and so this kernel obeys the
basic folding rule.
</p>
</div>
<div class="note">
<p><strong>Example:</strong> In the <a href="#example-findMinAndMax">findMinAndMax</a> kernel, for an input
  value <i>V</i> at coordinate <i>X</i>:
<ul>
<li>Statement 1 is the same as <code>A = minmax(A, IndexedVal(<i>V</i>, <i>X</i>))</code></li>
<li>Statement 2 is the same as <code>B = <a href="#INITVAL">INITVAL</a></code></li>
<li>Statement 3 is the same as
<pre>
B = minmax(B, IndexedVal(<i>V</i>, <i>X</i>))
</pre>
which, because <i>B</i> is the initial value, is the same as
<pre>
B = IndexedVal(<i>V</i>, <i>X</i>)
</pre>
</li>
<li>Statement 4 is the same as
<pre>
A = minmax(A, B)
</pre>
which is the same as
<pre>
A = minmax(A, IndexedVal(<i>V</i>, <i>X</i>))
</pre>
</ul>
Statements 1 and 4 set <code><i>A</i></code> to the same value, and so this kernel obeys the
basic folding rule.
</p>
</div>

<h3 id="calling-reduction-kernel">Calling a reduction kernel from Java code</h3>

<p>For a reduction kernel named <i>kernelName</i> defined in the
file <code><i>filename</i>.rs</code>, there are three methods reflected in the
class <code>ScriptC_<i>filename</i></code>:</p>

<pre>
// Method 1
public <i>javaFutureType</i> reduce_<i>kernelName</i>(Allocation ain1, <i>&hellip;,</i>
                                        Allocation ain<i>N</i>);

// Method 2
public <i>javaFutureType</i> reduce_<i>kernelName</i>(Allocation ain1, <i>&hellip;,</i>
                                        Allocation ain<i>N</i>,
                                        Script.LaunchOptions sc);

// Method 3
public <i>javaFutureType</i> reduce_<i>kernelName</i>(<i><a href="#devec">devecSiIn1Type</a></i>[] in1, &hellip;,
                                        <i><a href="#devec">devecSiInNType</a></i>[] in<i>N</i>);
</pre>

<p>Here are some examples of calling the <a href="#example-addint">addint</a> kernel:</p>
<pre>
ScriptC_example script = new ScriptC_example(mRenderScript);

// 1D array
//   and obtain answer immediately
int input1[] = <i>&hellip;</i>;
int sum1 = script.reduce_addint(input1).get();  // Method 3

// 2D allocation
//   and do some additional work before obtaining answer
Type.Builder typeBuilder =
  new Type.Builder(RS, Element.I32(RS));
typeBuilder.setX(<i>&hellip;</i>);
typeBuilder.setY(<i>&hellip;</i>);
Allocation input2 = createTyped(RS, typeBuilder.create());
<i>populateSomehow</i>(input2);  // fill in input Allocation with data
script.result_int result2 = script.reduce_addint(input2);  // Method 1
<i>doSomeAdditionalWork</i>(); // might run at same time as reduction
int sum2 = result2.get();
</pre>

<p><strong>Method 1</strong> has one input {@link android.renderscript.Allocation} argument for
  every input argument in the kernel's <a href="#accumulator-function">accumulator
    function</a>. The RenderScript runtime checks to ensure that all of the input Allocations
  have the same dimensions and that the {@link android.renderscript.Element} type of each of
  the input Allocations matches that of the corresponding input argument of the accumulator
  function's prototype. If any of these checks fail, RenderScript throws an exception. The
  kernel executes over every coordinate in those dimensions.</p>

<p><strong>Method 2</strong> is the same as Method 1 except that Method 2 takes an additional
  argument <code>sc</code> that can be used to limit the kernel execution to a subset of the
  coordinates.</p>

<p><strong><a id="reduce-method-3">Method 3</a></strong> is the same as Method 1 except that
  instead of taking Allocation inputs it takes Java array inputs. This is a convenience that
  saves you from having to write code to explicitly create an Allocation and copy data to it
  from a Java array. <em>However, using Method 3 instead of Method 1 does not increase the
  performance of the code</em>. For each input array, Method 3 creates a temporary
  1-dimensional Allocation with the appropriate {@link android.renderscript.Element} type and
  {@link android.renderscript.Allocation#setAutoPadding} enabled, and copies the array to the
  Allocation as if by the appropriate <code>copyFrom()</code> method of {@link
  android.renderscript.Allocation}. It then calls Method 1, passing those temporary
  Allocations.</p>
<p class="note"><strong>NOTE:</strong> If your application will make multiple kernel calls with
  the same array, or with different arrays of the same dimensions and Element type, you may improve
  performance by explicitly creating, populating, and reusing Allocations yourself, instead of
  by using Method 3.</p>
<p><strong><i><a id="javaFutureType">javaFutureType</a></i></strong>,
  the return type of the reflected reduction methods, is a reflected
  static nested class within the <code>ScriptC_<i>filename</i></code>
  class. It represents the future result of a reduction
  kernel run. To obtain the actual result of the run, call
  the <code>get()</code> method of that class, which returns a value
  of type <i>javaResultType</i>. <code>get()</code> is <a href="#asynchronous-model">synchronous</a>.</p>

<pre>
public class ScriptC_<i>filename</i> extends ScriptC {
  public static class <i>javaFutureType</i> {
    public <i>javaResultType</i> get() { &hellip; }
  }
}
</pre>

<p><strong><i>javaResultType</i></strong> is determined from the <i>resultType</i> of the
  <a href="#outconverter-function">outconverter function</a>. Unless <i>resultType</i> is an
  unsigned type (scalar, vector, or array), <i>javaResultType</i> is the directly corresponding
  Java type. If <i>resultType</i> is an unsigned type and there is a larger Java signed type,
  then <i>javaResultType</i> is that larger Java signed type; otherwise, it is the directly
  corresponding Java type. For example:</p>
<ul>
<li>If <i>resultType</i> is <code>int</code>, <code>int2</code>, or <code>int[15]</code>,
  then <i>javaResultType</i> is <code>int</code>, <code>Int2</code>,
  or <code>int[]</code>. All values of <i>resultType</i> can be represented
  by <i>javaResultType</i>.</li>
<li>If <i>resultType</i> is <code>uint</code>, <code>uint2</code>, or <code>uint[15]</code>,
  then <i>javaResultType</i> is <code>long</code>, <code>Long2</code>,
  or <code>long[]</code>.  All values of <i>resultType</i> can be represented
  by <i>javaResultType</i>.</li>
<li>If <i>resultType</i> is <code>ulong</code>, <code>ulong2</code>,
  or <code>ulong[15]</code>, then <i>javaResultType</i>
  is <code>long</code>, <code>Long2</code>, or <code>long[]</code>. There are certain values
  of <i>resultType</i> that cannot be represented by <i>javaResultType</i>.</li>
</ul>

<p><strong><i>javaFutureType</i></strong> is the future result type corresponding
  to the <i>resultType</i> of the <a href="#outconverter-function">outconverter
  function</a>.</p>
<ul>
<li>If <i>resultType</i> is not an array type, then <i>javaFutureType</i>
  is <code>result_<i>resultType</i></code>.</li>
<li>If <i>resultType</i> is an array of length <i>Count</i> with members of type <i>memberType</i>,
  then <i>javaFutureType</i> is <code>resultArray<i>Count</i>_<i>memberType</i></code>.</li>
</ul>

<p>For example:</p>

<pre>
public class ScriptC_<i>filename</i> extends ScriptC {
  // for kernels with int result
  public static class result_int {
    public int get() { &hellip; }
  }

  // for kernels with int[10] result
  public static class resultArray10_int {
    public int[] get() { &hellip; }
  }

  // for kernels with int2 result
  //   note that the Java type name "Int2" is not the same as the script type name "int2"
  public static class result_int2 {
    public Int2 get() { &hellip; }
  }

  // for kernels with int2[10] result
  //   note that the Java type name "Int2" is not the same as the script type name "int2"
  public static class resultArray10_int2 {
    public Int2[] get() { &hellip; }
  }

  // for kernels with uint result
  //   note that the Java type "long" is a wider signed type than the unsigned script type "uint"
  public static class result_uint {
    public long get() { &hellip; }
  }

  // for kernels with uint[10] result
  //   note that the Java type "long" is a wider signed type than the unsigned script type "uint"
  public static class resultArray10_uint {
    public long[] get() { &hellip; }
  }

  // for kernels with uint2 result
  //   note that the Java type "Long2" is a wider signed type than the unsigned script type "uint2"
  public static class result_uint2 {
    public Long2 get() { &hellip; }
  }

  // for kernels with uint2[10] result
  //   note that the Java type "Long2" is a wider signed type than the unsigned script type "uint2"
  public static class resultArray10_uint2 {
    public Long2[] get() { &hellip; }
  }
}
</pre>

<p>If <i>javaResultType</i> is an object type (including an array type), each call
  to <code><i>javaFutureType</i>.get()</code> on the same instance will return the same
  object.</p>

<p>If <i>javaResultType</i> cannot represent all values of type <i>resultType</i>, and a
  reduction kernel produces an unrepresentible value,
  then <code><i>javaFutureType</i>.get()</code> throws an exception.</p>

<h4 id="devec">Method 3 and <i>devecSiInXType</i></h4>

<p><strong><i>devecSiInXType</i></strong> is the Java type corresponding to
  the <i>inXType</i> of the corresponding argument of
  the <a href="#accumulator-function">accumulator function</a>. Unless <i>inXType</i> is an
  unsigned type or a vector type, <i>devecSiInXType</i> is the directly corresponding Java
  type. If <i>inXType</i> is an unsigned scalar type, then <i>devecSiInXType</i> is the
  Java type directly corresponding to the signed scalar type of the same
  size. If <i>inXType</i> is a signed vector type, then <i>devecSiInXType</i> is the Java
  type directly corresponding to the vector component type. If <i>inXType</i> is an unsigned
  vector type, then <i>devecSiInXType</i> is the Java type directly corresponding to the
  signed scalar type of the same size as the vector component type. For example:</p>
<ul>
<li>If <i>inXType</i> is <code>int</code>, then <i>devecSiInXType</i>
  is <code>int</code>.</li>
<li>If <i>inXType</i> is <code>int2</code>, then <i>devecSiInXType</i>
  is <code>int</code>. The array is a <em>flattened</em> representation: It has twice as
  many <em>scalar</em> Elements as the Allocation has 2-component <em>vector</em>
  Elements. This is the same way that the <code>copyFrom()</code> methods of {@link
  android.renderscript.Allocation} work.</li>
<li>If <i>inXType</i> is <code>uint</code>, then <i>deviceSiInXType</i>
  is <code>int</code>. A signed value in the Java array is interpreted as an unsigned value of
  the same bitpattern in the Allocation. This is the same way that the <code>copyFrom()</code>
  methods of {@link android.renderscript.Allocation} work.</li>
<li>If <i>inXType</i> is <code>uint2</code>, then <i>deviceSiInXType</i>
  is <code>int</code>. This is a combination of the way <code>int2</code> and <code>uint</code>
  are handled: The array is a flattened representation, and Java array signed values are
  interpreted as RenderScript unsigned Element values.</li>
</ul>

<p>Note that for <a href="#reduce-method-3">Method 3</a>, input types are handled differently
than result types:</p>

<ul>
<li>A script's vector input is flattened on the Java side, whereas a script's vector result is not.</li>
<li>A script's unsigned input is represented as a signed input of the same size on the Java
  side, whereas a script's unsigned result is represented as a widened signed type on the Java
  side (except in the case of <code>ulong</code>).</li>
</ul>

<h3 id="more-example">More example reduction kernels</h3>

<pre id="dot-product">
#pragma rs reduce(dotProduct) \
  accumulator(dotProductAccum) combiner(dotProductSum)

// Note: No initializer function -- therefore,
// each accumulator data item is implicitly initialized to 0.0f.

static void dotProductAccum(float *accum, float in1, float in2) {
  *accum += in1*in2;
}

// combiner function
static void dotProductSum(float *accum, const float *val) {
  *accum += *val;
}
</pre>

<pre>
// Find a zero Element in a 2D allocation; return (-1, -1) if none
#pragma rs reduce(fz2) \
  initializer(fz2Init) \
  accumulator(fz2Accum) combiner(fz2Combine)

static void fz2Init(int2 *accum) { accum->x = accum->y = -1; }

static void fz2Accum(int2 *accum,
                     int inVal,
                     int x /* special arg */,
                     int y /* special arg */) {
  if (inVal==0) {
    accum->x = x;
    accum->y = y;
  }
}

static void fz2Combine(int2 *accum, const int2 *accum2) {
  if (accum2->x >= 0) *accum = *accum2;
}
</pre>

<pre>
// Note that this kernel returns an array to Java
#pragma rs reduce(histogram) \
  accumulator(hsgAccum) combiner(hsgCombine)

#define BUCKETS 256
typedef uint32_t Histogram[BUCKETS];

// Note: No initializer function --
// therefore, each bucket is implicitly initialized to 0.

static void hsgAccum(Histogram *h, uchar in) { ++(*h)[in]; }

static void hsgCombine(Histogram *accum,
                       const Histogram *addend) {
  for (int i = 0; i < BUCKETS; ++i)
    (*accum)[i] += (*addend)[i];
}

// Determines the mode (most frequently occurring value), and returns
// the value and the frequency.
//
// If multiple values have the same highest frequency, returns the lowest
// of those values.
//
// Shares functions with the histogram reduction kernel.
#pragma rs reduce(mode) \
  accumulator(hsgAccum) combiner(hsgCombine) \
  outconverter(modeOutConvert)

static void modeOutConvert(int2 *result, const Histogram *h) {
  uint32_t mode = 0;
  for (int i = 1; i < BUCKETS; ++i)
    if ((*h)[i] > (*h)[mode]) mode = i;
  result->x = mode;
  result->y = (*h)[mode];
}
</pre>