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 <div class="subTitle">org.apache.calcite.util.mapping</div>
 <h2 title="Class Mappings" class="title">Class Mappings</h2>
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 <pre>public abstract class <span class="typeNameLabel">Mappings</span>
 extends <a href="https://docs.oracle.com/javase/8/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></pre>
 <div class="block">Utility functions related to mappings.</div>
 <dl>
 <dt><span class="seeLabel">See Also:</span></dt>
 <dd><a href="../../../../../org/apache/calcite/util/mapping/MappingType.html" title="enum in org.apache.calcite.util.mapping"><code>MappingType</code></a>,
 <a href="../../../../../org/apache/calcite/util/mapping/Mapping.html" title="interface in org.apache.calcite.util.mapping"><code>Mapping</code></a>,
 <a href="../../../../../org/apache/calcite/util/Permutation.html" title="class in org.apache.calcite.util"><code>Permutation</code></a></dd>
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 <tr>
 <th class="colFirst" scope="col">Modifier and Type</th>
 <th class="colLast" scope="col">Class and Description</th>
 </tr>
 <tr class="altColor">
 <td class="colFirst"><code>static class&nbsp;</code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/calcite/util/mapping/Mappings.AbstractMapping.html" title="class in org.apache.calcite.util.mapping">Mappings.AbstractMapping</a></span></code>
 <div class="block">Abstract implementation of <a href="../../../../../org/apache/calcite/util/mapping/Mapping.html" title="interface in org.apache.calcite.util.mapping"><code>Mapping</code></a>.</div>
 </td>
 </tr>
 <tr class="rowColor">
 <td class="colFirst"><code>static interface&nbsp;</code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/calcite/util/mapping/Mappings.CoreMapping.html" title="interface in org.apache.calcite.util.mapping">Mappings.CoreMapping</a></span></code>
 <div class="block">Core interface of all mappings.</div>
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 <tr class="altColor">
 <td class="colFirst"><code>static class&nbsp;</code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/calcite/util/mapping/Mappings.FiniteAbstractMapping.html" title="class in org.apache.calcite.util.mapping">Mappings.FiniteAbstractMapping</a></span></code>
 <div class="block">Abstract implementation of mapping where both source and target
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 <tr class="rowColor">
 <td class="colFirst"><code>static interface&nbsp;</code></td>
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 <tr class="altColor">
 <td class="colFirst"><code>static class&nbsp;</code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/calcite/util/mapping/Mappings.IdentityMapping.html" title="class in org.apache.calcite.util.mapping">Mappings.IdentityMapping</a></span></code>
 <div class="block">The identity mapping, of a given size, or infinite.</div>
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 <tr class="rowColor">
 <td class="colFirst"><code>static class&nbsp;</code></td>
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 <div class="block">Thrown when a mapping is expected to return one element but returns none.</div>
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 <tr class="altColor">
 <td class="colFirst"><code>static class&nbsp;</code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/calcite/util/mapping/Mappings.OverridingSourceMapping.html" title="class in org.apache.calcite.util.mapping">Mappings.OverridingSourceMapping</a></span></code>
 <div class="block">Source mapping that returns the same result as a parent
  <a href="../../../../../org/apache/calcite/util/mapping/Mappings.SourceMapping.html" title="interface in org.apache.calcite.util.mapping"><code>Mappings.SourceMapping</code></a> except for specific overriding elements.</div>
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 <tr class="rowColor">
 <td class="colFirst"><code>static class&nbsp;</code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/calcite/util/mapping/Mappings.OverridingTargetMapping.html" title="class in org.apache.calcite.util.mapping">Mappings.OverridingTargetMapping</a></span></code>
 <div class="block">Target mapping that returns the same result as a parent
  <a href="../../../../../org/apache/calcite/util/mapping/Mappings.TargetMapping.html" title="interface in org.apache.calcite.util.mapping"><code>Mappings.TargetMapping</code></a> except for specific overriding elements.</div>
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 <tr class="altColor">
 <td class="colFirst"><code>static class&nbsp;</code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/calcite/util/mapping/Mappings.PartialMapping.html" title="class in org.apache.calcite.util.mapping">Mappings.PartialMapping</a></span></code>
 <div class="block">A mapping where a source has at most one target, and every target has at
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 </td>
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 <tr class="rowColor">
 <td class="colFirst"><code>static interface&nbsp;</code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/calcite/util/mapping/Mappings.SourceMapping.html" title="interface in org.apache.calcite.util.mapping">Mappings.SourceMapping</a></span></code>
 <div class="block">Mapping suitable for sourcing columns.</div>
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 <tr class="altColor">
 <td class="colFirst"><code>static interface&nbsp;</code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/calcite/util/mapping/Mappings.TargetMapping.html" title="interface in org.apache.calcite.util.mapping">Mappings.TargetMapping</a></span></code>
 <div class="block">Mapping suitable for mapping columns to a target.</div>
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 <tr class="rowColor">
 <td class="colFirst"><code>static class&nbsp;</code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/calcite/util/mapping/Mappings.TooManyElementsException.html" title="class in org.apache.calcite.util.mapping">Mappings.TooManyElementsException</a></span></code>
 <div class="block">Thrown when a mapping is expected to return one element but returns
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 <td class="colFirst"><code>static <a href="../../../../../org/apache/calcite/util/mapping/Mappings.TargetMapping.html" title="interface in org.apache.calcite.util.mapping">Mappings.TargetMapping</a></code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/calcite/util/mapping/Mappings.html#append-org.apache.calcite.util.mapping.Mappings.TargetMapping-org.apache.calcite.util.mapping.Mappings.TargetMapping-">append</a></span>(<a href="../../../../../org/apache/calcite/util/mapping/Mappings.TargetMapping.html" title="interface in org.apache.calcite.util.mapping">Mappings.TargetMapping</a>&nbsp;mapping0,
       <a href="../../../../../org/apache/calcite/util/mapping/Mappings.TargetMapping.html" title="interface in org.apache.calcite.util.mapping">Mappings.TargetMapping</a>&nbsp;mapping1)</code>
 <div class="block">Creates a mapping by appending two mappings.</div>
 </td>
 </tr>
 <tr id="i1" class="rowColor">
 <td class="colFirst"><code>static <a href="https://docs.oracle.com/javase/8/docs/api/java/util/BitSet.html?is-external=true" title="class or interface in java.util">BitSet</a></code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/calcite/util/mapping/Mappings.html#apply-org.apache.calcite.util.mapping.Mapping-java.util.BitSet-">apply</a></span>(<a href="../../../../../org/apache/calcite/util/mapping/Mapping.html" title="interface in org.apache.calcite.util.mapping">Mapping</a>&nbsp;mapping,
      <a href="https://docs.oracle.com/javase/8/docs/api/java/util/BitSet.html?is-external=true" title="class or interface in java.util">BitSet</a>&nbsp;bitSet)</code>
 <div class="block">Applies a mapping to a BitSet.</div>
 </td>
 </tr>
 <tr id="i2" class="altColor">
 <td class="colFirst"><code>static <a href="../../../../../org/apache/calcite/util/ImmutableBitSet.html" title="class in org.apache.calcite.util">ImmutableBitSet</a></code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/calcite/util/mapping/Mappings.html#apply-org.apache.calcite.util.mapping.Mapping-org.apache.calcite.util.ImmutableBitSet-">apply</a></span>(<a href="../../../../../org/apache/calcite/util/mapping/Mapping.html" title="interface in org.apache.calcite.util.mapping">Mapping</a>&nbsp;mapping,
      <a href="../../../../../org/apache/calcite/util/ImmutableBitSet.html" title="class in org.apache.calcite.util">ImmutableBitSet</a>&nbsp;bitSet)</code>
 <div class="block">Applies a mapping to an <code>ImmutableBitSet</code>.</div>
 </td>
 </tr>
 <tr id="i3" class="rowColor">
 <td class="colFirst"><code>static &lt;T&gt;&nbsp;<a href="https://docs.oracle.com/javase/8/docs/api/java/util/List.html?is-external=true" title="class or interface in java.util">List</a>&lt;T&gt;</code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/calcite/util/mapping/Mappings.html#apply-org.apache.calcite.util.mapping.Mapping-java.util.List-">apply</a></span>(<a href="../../../../../org/apache/calcite/util/mapping/Mapping.html" title="interface in org.apache.calcite.util.mapping">Mapping</a>&nbsp;mapping,
      <a href="https://docs.oracle.com/javase/8/docs/api/java/util/List.html?is-external=true" title="class or interface in java.util">List</a>&lt;T&gt;&nbsp;list)</code>
 <div class="block">Applies a mapping to a list.</div>
 </td>
 </tr>
 <tr id="i4" class="altColor">
 <td class="colFirst"><code>static int</code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/calcite/util/mapping/Mappings.html#apply-org.apache.calcite.util.mapping.Mappings.TargetMapping-int-">apply</a></span>(<a href="../../../../../org/apache/calcite/util/mapping/Mappings.TargetMapping.html" title="interface in org.apache.calcite.util.mapping">Mappings.TargetMapping</a>&nbsp;mapping,
      int&nbsp;i)</code>
 <div class="block">Applies a mapping to an optional integer, returning an optional
  result.</div>
 </td>
 </tr>
 <tr id="i5" class="rowColor">
 <td class="colFirst"><code>static com.google.common.collect.ImmutableList&lt;<a href="../../../../../org/apache/calcite/util/ImmutableBitSet.html" title="class in org.apache.calcite.util">ImmutableBitSet</a>&gt;</code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/calcite/util/mapping/Mappings.html#apply2-org.apache.calcite.util.mapping.Mapping-java.lang.Iterable-">apply2</a></span>(<a href="../../../../../org/apache/calcite/util/mapping/Mapping.html" title="interface in org.apache.calcite.util.mapping">Mapping</a>&nbsp;mapping,
       <a href="https://docs.oracle.com/javase/8/docs/api/java/lang/Iterable.html?is-external=true" title="class or interface in java.lang">Iterable</a>&lt;<a href="../../../../../org/apache/calcite/util/ImmutableBitSet.html" title="class in org.apache.calcite.util">ImmutableBitSet</a>&gt;&nbsp;bitSets)</code>
 <div class="block">Applies a mapping to a collection of <code>ImmutableBitSet</code>s.</div>
 </td>
 </tr>
 <tr id="i6" class="altColor">
 <td class="colFirst"><code>static <a href="https://docs.oracle.com/javase/8/docs/api/java/util/List.html?is-external=true" title="class or interface in java.util">List</a>&lt;<a href="https://docs.oracle.com/javase/8/docs/api/java/lang/Integer.html?is-external=true" title="class or interface in java.lang">Integer</a>&gt;</code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/calcite/util/mapping/Mappings.html#apply2-org.apache.calcite.util.mapping.Mapping-java.util.List-">apply2</a></span>(<a href="../../../../../org/apache/calcite/util/mapping/Mapping.html" title="interface in org.apache.calcite.util.mapping">Mapping</a>&nbsp;mapping,
       <a href="https://docs.oracle.com/javase/8/docs/api/java/util/List.html?is-external=true" title="class or interface in java.util">List</a>&lt;<a href="https://docs.oracle.com/javase/8/docs/api/java/lang/Integer.html?is-external=true" title="class or interface in java.lang">Integer</a>&gt;&nbsp;list)</code>&nbsp;</td>
 </tr>
 <tr id="i7" class="rowColor">
 <td class="colFirst"><code>static &lt;T&gt;&nbsp;<a href="https://docs.oracle.com/javase/8/docs/api/java/util/List.html?is-external=true" title="class or interface in java.util">List</a>&lt;T&gt;</code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/calcite/util/mapping/Mappings.html#apply3-org.apache.calcite.util.mapping.Mapping-java.util.List-">apply3</a></span>(<a href="../../../../../org/apache/calcite/util/mapping/Mapping.html" title="interface in org.apache.calcite.util.mapping">Mapping</a>&nbsp;mapping,
       <a href="https://docs.oracle.com/javase/8/docs/api/java/util/List.html?is-external=true" title="class or interface in java.util">List</a>&lt;T&gt;&nbsp;list)</code>
 <div class="block">Creates a view of a list, permuting according to a mapping.</div>
 </td>
 </tr>
 <tr id="i8" class="altColor">
 <td class="colFirst"><code>static <a href="https://docs.oracle.com/javase/8/docs/api/java/util/List.html?is-external=true" title="class or interface in java.util">List</a>&lt;<a href="https://docs.oracle.com/javase/8/docs/api/java/lang/Integer.html?is-external=true" title="class or interface in java.lang">Integer</a>&gt;</code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/calcite/util/mapping/Mappings.html#asList-org.apache.calcite.util.mapping.Mappings.TargetMapping-">asList</a></span>(<a href="../../../../../org/apache/calcite/util/mapping/Mappings.TargetMapping.html" title="interface in org.apache.calcite.util.mapping">Mappings.TargetMapping</a>&nbsp;mapping)</code>
 <div class="block">Returns a mapping as a list such that <code>list.get(source)</code> is
  <code>mapping.getTarget(source)</code> and <code>list.size()</code> is
  <code>mapping.getSourceCount()</code>.</div>
 </td>
 </tr>
 <tr id="i9" class="rowColor">
 <td class="colFirst"><code>static <a href="../../../../../org/apache/calcite/util/mapping/Mapping.html" title="interface in org.apache.calcite.util.mapping">Mapping</a></code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/calcite/util/mapping/Mappings.html#bijection-java.util.List-">bijection</a></span>(<a href="https://docs.oracle.com/javase/8/docs/api/java/util/List.html?is-external=true" title="class or interface in java.util">List</a>&lt;<a href="https://docs.oracle.com/javase/8/docs/api/java/lang/Integer.html?is-external=true" title="class or interface in java.lang">Integer</a>&gt;&nbsp;targets)</code>
 <div class="block">Creates a bijection.</div>
 </td>
 </tr>
 <tr id="i10" class="altColor">
 <td class="colFirst"><code>static <a href="../../../../../org/apache/calcite/util/mapping/Mapping.html" title="interface in org.apache.calcite.util.mapping">Mapping</a></code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/calcite/util/mapping/Mappings.html#bijection-java.util.Map-">bijection</a></span>(<a href="https://docs.oracle.com/javase/8/docs/api/java/util/Map.html?is-external=true" title="class or interface in java.util">Map</a>&lt;<a href="https://docs.oracle.com/javase/8/docs/api/java/lang/Integer.html?is-external=true" title="class or interface in java.lang">Integer</a>,<a href="https://docs.oracle.com/javase/8/docs/api/java/lang/Integer.html?is-external=true" title="class or interface in java.lang">Integer</a>&gt;&nbsp;targets)</code>
 <div class="block">Creates a bijection.</div>
 </td>
 </tr>
 <tr id="i11" class="rowColor">
 <td class="colFirst"><code>static <a href="../../../../../org/apache/calcite/util/mapping/Mapping.html" title="interface in org.apache.calcite.util.mapping">Mapping</a></code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/calcite/util/mapping/Mappings.html#create-org.apache.calcite.util.mapping.MappingType-int-int-">create</a></span>(<a href="../../../../../org/apache/calcite/util/mapping/MappingType.html" title="enum in org.apache.calcite.util.mapping">MappingType</a>&nbsp;mappingType,
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 <div class="block">Creates a mapping with required properties.</div>
 </td>
 </tr>
 <tr id="i12" class="altColor">
 <td class="colFirst"><code>static <a href="../../../../../org/apache/calcite/util/mapping/Mappings.IdentityMapping.html" title="class in org.apache.calcite.util.mapping">Mappings.IdentityMapping</a></code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/calcite/util/mapping/Mappings.html#createIdentity-int-">createIdentity</a></span>(int&nbsp;fieldCount)</code>
 <div class="block">Creates the identity mapping.</div>
 </td>
 </tr>
 <tr id="i13" class="rowColor">
 <td class="colFirst"><code>static <a href="../../../../../org/apache/calcite/util/mapping/Mappings.TargetMapping.html" title="interface in org.apache.calcite.util.mapping">Mappings.TargetMapping</a></code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/calcite/util/mapping/Mappings.html#createShiftMapping-int-int...-">createShiftMapping</a></span>(int&nbsp;sourceCount,
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 <div class="block">Creates a mapping that consists of a set of contiguous ranges.</div>
 </td>
 </tr>
 <tr id="i14" class="altColor">
 <td class="colFirst"><code>static <a href="../../../../../org/apache/calcite/util/mapping/Mapping.html" title="interface in org.apache.calcite.util.mapping">Mapping</a></code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/calcite/util/mapping/Mappings.html#divide-org.apache.calcite.util.mapping.Mapping-org.apache.calcite.util.mapping.Mapping-">divide</a></span>(<a href="../../../../../org/apache/calcite/util/mapping/Mapping.html" title="interface in org.apache.calcite.util.mapping">Mapping</a>&nbsp;mapping1,
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 <div class="block">Divides one mapping by another.</div>
 </td>
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 <tr id="i15" class="rowColor">
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 <td class="colFirst"><code>static <a href="https://docs.oracle.com/javase/8/docs/api/java/util/Iterator.html?is-external=true" title="class or interface in java.util">Iterator</a>&lt;<a href="../../../../../org/apache/calcite/util/mapping/IntPair.html" title="class in org.apache.calcite.util.mapping">IntPair</a>&gt;</code></td>
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 <div class="block">Inverts an <a href="https://docs.oracle.com/javase/8/docs/api/java/util/Iterator.html?is-external=true" title="class or interface in java.util"><code>Iterator</code></a> over
  <a href="../../../../../org/apache/calcite/util/mapping/IntPair.html" title="class in org.apache.calcite.util.mapping"><code>IntPair</code></a>s.</div>
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 <tr id="i17" class="rowColor">
 <td class="colFirst"><code>static <a href="../../../../../org/apache/calcite/util/mapping/Mapping.html" title="interface in org.apache.calcite.util.mapping">Mapping</a></code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/calcite/util/mapping/Mappings.html#invert-org.apache.calcite.util.mapping.Mapping-">invert</a></span>(<a href="../../../../../org/apache/calcite/util/mapping/Mapping.html" title="interface in org.apache.calcite.util.mapping">Mapping</a>&nbsp;mapping)</code>
 <div class="block">Converts a mapping to its inverse.</div>
 </td>
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 <tr id="i18" class="altColor">
 <td class="colFirst"><code>static boolean</code></td>
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           int&nbsp;count)</code>
 <div class="block">Returns whether a list of integers is the identity mapping
  [0, ..., n - 1].</div>
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 <tr id="i19" class="rowColor">
 <td class="colFirst"><code>static boolean</code></td>
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 <tr id="i20" class="altColor">
 <td class="colFirst"><code>static boolean</code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/calcite/util/mapping/Mappings.html#keepsOrdering-org.apache.calcite.util.mapping.Mappings.TargetMapping-">keepsOrdering</a></span>(<a href="../../../../../org/apache/calcite/util/mapping/Mappings.TargetMapping.html" title="interface in org.apache.calcite.util.mapping">Mappings.TargetMapping</a>&nbsp;mapping)</code>
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 <tr id="i21" class="rowColor">
 <td class="colFirst"><code>static <a href="../../../../../org/apache/calcite/util/mapping/Mappings.TargetMapping.html" title="interface in org.apache.calcite.util.mapping">Mappings.TargetMapping</a></code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/calcite/util/mapping/Mappings.html#merge-org.apache.calcite.util.mapping.Mappings.TargetMapping-org.apache.calcite.util.mapping.Mappings.TargetMapping-">merge</a></span>(<a href="../../../../../org/apache/calcite/util/mapping/Mappings.TargetMapping.html" title="interface in org.apache.calcite.util.mapping">Mappings.TargetMapping</a>&nbsp;mapping0,
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 <div class="block">Creates a mapping by merging two mappings.</div>
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 <tr id="i22" class="altColor">
 <td class="colFirst"><code>static <a href="../../../../../org/apache/calcite/util/mapping/Mapping.html" title="interface in org.apache.calcite.util.mapping">Mapping</a></code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/calcite/util/mapping/Mappings.html#multiply-org.apache.calcite.util.mapping.Mapping-org.apache.calcite.util.mapping.Mapping-">multiply</a></span>(<a href="../../../../../org/apache/calcite/util/mapping/Mapping.html" title="interface in org.apache.calcite.util.mapping">Mapping</a>&nbsp;mapping1,
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 <div class="block">Multiplies one mapping by another.</div>
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 <tr id="i23" class="rowColor">
 <td class="colFirst"><code>static <a href="../../../../../org/apache/calcite/util/mapping/Mappings.TargetMapping.html" title="interface in org.apache.calcite.util.mapping">Mappings.TargetMapping</a></code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/calcite/util/mapping/Mappings.html#offset-org.apache.calcite.util.mapping.Mappings.TargetMapping-int-int-">offset</a></span>(<a href="../../../../../org/apache/calcite/util/mapping/Mappings.TargetMapping.html" title="interface in org.apache.calcite.util.mapping">Mappings.TargetMapping</a>&nbsp;mapping,
       int&nbsp;offset,
       int&nbsp;sourceCount)</code>
 <div class="block">Returns a mapping that shifts a given mapping's source and target by a
  given offset.</div>
 </td>
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 <tr id="i24" class="altColor">
 <td class="colFirst"><code>static <a href="../../../../../org/apache/calcite/util/mapping/Mappings.TargetMapping.html" title="interface in org.apache.calcite.util.mapping">Mappings.TargetMapping</a></code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/calcite/util/mapping/Mappings.html#offsetSource-org.apache.calcite.util.mapping.Mappings.TargetMapping-int-">offsetSource</a></span>(<a href="../../../../../org/apache/calcite/util/mapping/Mappings.TargetMapping.html" title="interface in org.apache.calcite.util.mapping">Mappings.TargetMapping</a>&nbsp;mapping,
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 <div class="block">Returns a mapping that shifts a given mapping's source by a given
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 <td class="colFirst"><code>static <a href="../../../../../org/apache/calcite/util/mapping/Mappings.TargetMapping.html" title="interface in org.apache.calcite.util.mapping">Mappings.TargetMapping</a></code></td>
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 <tr id="i26" class="altColor">
 <td class="colFirst"><code>static <a href="../../../../../org/apache/calcite/util/mapping/Mappings.TargetMapping.html" title="interface in org.apache.calcite.util.mapping">Mappings.TargetMapping</a></code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/calcite/util/mapping/Mappings.html#offsetTarget-org.apache.calcite.util.mapping.Mappings.TargetMapping-int-">offsetTarget</a></span>(<a href="../../../../../org/apache/calcite/util/mapping/Mappings.TargetMapping.html" title="interface in org.apache.calcite.util.mapping">Mappings.TargetMapping</a>&nbsp;mapping,
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 <div class="block">Returns a mapping that shifts a given mapping's target by a given
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 <tr id="i27" class="rowColor">
 <td class="colFirst"><code>static <a href="../../../../../org/apache/calcite/util/mapping/Mappings.TargetMapping.html" title="interface in org.apache.calcite.util.mapping">Mappings.TargetMapping</a></code></td>
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             int&nbsp;targetCount)</code>
 <div class="block">Returns a mapping that shifts a given mapping's target by a given
  offset.</div>
 </td>
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 <tr id="i28" class="altColor">
 <td class="colFirst"><code>static &lt;T&gt;&nbsp;<a href="https://docs.oracle.com/javase/8/docs/api/java/util/List.html?is-external=true" title="class or interface in java.util">List</a>&lt;T&gt;</code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/calcite/util/mapping/Mappings.html#permute-java.util.List-org.apache.calcite.util.mapping.Mappings.TargetMapping-">permute</a></span>(<a href="https://docs.oracle.com/javase/8/docs/api/java/util/List.html?is-external=true" title="class or interface in java.util">List</a>&lt;T&gt;&nbsp;list,
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 <tr id="i29" class="rowColor">
 <td class="colFirst"><code>static <a href="../../../../../org/apache/calcite/util/mapping/Mapping.html" title="interface in org.apache.calcite.util.mapping">Mapping</a></code></td>
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 <td class="colFirst"><code>static <a href="../../../../../org/apache/calcite/util/mapping/Mappings.TargetMapping.html" title="interface in org.apache.calcite.util.mapping">Mappings.TargetMapping</a></code></td>
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 <tr id="i31" class="rowColor">
 <td class="colFirst"><code>static <a href="../../../../../org/apache/calcite/util/mapping/Mapping.html" title="interface in org.apache.calcite.util.mapping">Mapping</a></code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/calcite/util/mapping/Mappings.html#target-java.lang.Iterable-int-int-">target</a></span>(<a href="https://docs.oracle.com/javase/8/docs/api/java/lang/Iterable.html?is-external=true" title="class or interface in java.lang">Iterable</a>&lt;<a href="../../../../../org/apache/calcite/util/mapping/IntPair.html" title="class in org.apache.calcite.util.mapping">IntPair</a>&gt;&nbsp;pairs,
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 <tr id="i32" class="altColor">
 <td class="colFirst"><code>static <a href="../../../../../org/apache/calcite/util/mapping/Mapping.html" title="interface in org.apache.calcite.util.mapping">Mapping</a></code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/calcite/util/mapping/Mappings.html#target-java.util.List-int-">target</a></span>(<a href="https://docs.oracle.com/javase/8/docs/api/java/util/List.html?is-external=true" title="class or interface in java.util">List</a>&lt;<a href="https://docs.oracle.com/javase/8/docs/api/java/lang/Integer.html?is-external=true" title="class or interface in java.lang">Integer</a>&gt;&nbsp;sources,
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 <tr id="i33" class="rowColor">
 <td class="colFirst"><code>static <a href="../../../../../org/apache/calcite/util/mapping/Mappings.TargetMapping.html" title="interface in org.apache.calcite.util.mapping">Mappings.TargetMapping</a></code></td>
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       int&nbsp;sourceCount,
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 <div class="block">Converts a <a href="https://docs.oracle.com/javase/8/docs/api/java/util/Map.html?is-external=true" title="class or interface in java.util"><code>Map</code></a> of integers to a <a href="../../../../../org/apache/calcite/util/mapping/Mappings.TargetMapping.html" title="interface in org.apache.calcite.util.mapping"><code>Mappings.TargetMapping</code></a>.</div>
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 <h4>create</h4>
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                              int&nbsp;targetCount)</pre>
 <div class="block">Creates a mapping with required properties.</div>
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 <div class="block">Creates the identity mapping.

  <p>For example, <code>createIdentity(2)</code> returns the mapping
  {0:0, 1:1, 2:2}.</div>
 <dl>
 <dt><span class="paramLabel">Parameters:</span></dt>
 <dd><code>fieldCount</code> - Number of sources/targets</dd>
 <dt><span class="returnLabel">Returns:</span></dt>
 <dd>Identity mapping</dd>
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 <h4>invert</h4>
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 <div class="block">Converts a mapping to its inverse.</div>
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 <h4>divide</h4>
 <pre>public static&nbsp;<a href="../../../../../org/apache/calcite/util/mapping/Mapping.html" title="interface in org.apache.calcite.util.mapping">Mapping</a>&nbsp;divide(<a href="../../../../../org/apache/calcite/util/mapping/Mapping.html" title="interface in org.apache.calcite.util.mapping">Mapping</a>&nbsp;mapping1,
                              <a href="../../../../../org/apache/calcite/util/mapping/Mapping.html" title="interface in org.apache.calcite.util.mapping">Mapping</a>&nbsp;mapping2)</pre>
 <div class="block">Divides one mapping by another.

  <p><code>divide(A, B)</code> returns a mapping C such that B . C (the mapping
  B followed by the mapping C) is equivalent to A.</div>
 <dl>
 <dt><span class="paramLabel">Parameters:</span></dt>
 <dd><code>mapping1</code> - First mapping</dd>
 <dd><code>mapping2</code> - Second mapping</dd>
 <dt><span class="returnLabel">Returns:</span></dt>
 <dd>Mapping mapping3 such that mapping1 = mapping2 . mapping3</dd>
 </dl>
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 <pre>public static&nbsp;<a href="../../../../../org/apache/calcite/util/mapping/Mapping.html" title="interface in org.apache.calcite.util.mapping">Mapping</a>&nbsp;multiply(<a href="../../../../../org/apache/calcite/util/mapping/Mapping.html" title="interface in org.apache.calcite.util.mapping">Mapping</a>&nbsp;mapping1,
                                <a href="../../../../../org/apache/calcite/util/mapping/Mapping.html" title="interface in org.apache.calcite.util.mapping">Mapping</a>&nbsp;mapping2)</pre>
 <div class="block">Multiplies one mapping by another.

  <p><code>divide(A, B)</code> returns a mapping C such that B . C (the mapping
  B followed by the mapping C) is equivalent to A.</div>
 <dl>
 <dt><span class="paramLabel">Parameters:</span></dt>
 <dd><code>mapping1</code> - First mapping</dd>
 <dd><code>mapping2</code> - Second mapping</dd>
 <dt><span class="returnLabel">Returns:</span></dt>
 <dd>Mapping mapping3 such that mapping1 = mapping2 . mapping3</dd>
 </dl>
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 <h4>apply</h4>
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 <div class="block">Applies a mapping to a BitSet.

  <p>If the mapping does not affect the bit set, returns the original.
  Never changes the original.</div>
 <dl>
 <dt><span class="paramLabel">Parameters:</span></dt>
 <dd><code>mapping</code> - Mapping</dd>
 <dd><code>bitSet</code> - Bit set</dd>
 <dt><span class="returnLabel">Returns:</span></dt>
 <dd>Bit set with mapping applied</dd>
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 <pre>public static&nbsp;<a href="../../../../../org/apache/calcite/util/ImmutableBitSet.html" title="class in org.apache.calcite.util">ImmutableBitSet</a>&nbsp;apply(<a href="../../../../../org/apache/calcite/util/mapping/Mapping.html" title="interface in org.apache.calcite.util.mapping">Mapping</a>&nbsp;mapping,
                                     <a href="../../../../../org/apache/calcite/util/ImmutableBitSet.html" title="class in org.apache.calcite.util">ImmutableBitSet</a>&nbsp;bitSet)</pre>
 <div class="block">Applies a mapping to an <code>ImmutableBitSet</code>.

  <p>If the mapping does not affect the bit set, returns the original.
  Never changes the original.</div>
 <dl>
 <dt><span class="paramLabel">Parameters:</span></dt>
 <dd><code>mapping</code> - Mapping</dd>
 <dd><code>bitSet</code> - Bit set</dd>
 <dt><span class="returnLabel">Returns:</span></dt>
 <dd>Bit set with mapping applied</dd>
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 <div class="block">Applies a mapping to a collection of <code>ImmutableBitSet</code>s.</div>
 <dl>
 <dt><span class="paramLabel">Parameters:</span></dt>
 <dd><code>mapping</code> - Mapping</dd>
 <dd><code>bitSets</code> - Collection of bit sets</dd>
 <dt><span class="returnLabel">Returns:</span></dt>
 <dd>Sorted bit sets with mapping applied</dd>
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                                 <a href="https://docs.oracle.com/javase/8/docs/api/java/util/List.html?is-external=true" title="class or interface in java.util">List</a>&lt;T&gt;&nbsp;list)</pre>
 <div class="block">Applies a mapping to a list.</div>
 <dl>
 <dt><span class="paramLabel">Type Parameters:</span></dt>
 <dd><code>T</code> - Element type</dd>
 <dt><span class="paramLabel">Parameters:</span></dt>
 <dd><code>mapping</code> - Mapping</dd>
 <dd><code>list</code> - List</dd>
 <dt><span class="returnLabel">Returns:</span></dt>
 <dd>List with elements permuted according to mapping</dd>
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 <div class="block">Creates a view of a list, permuting according to a mapping.</div>
 <dl>
 <dt><span class="paramLabel">Type Parameters:</span></dt>
 <dd><code>T</code> - Element type</dd>
 <dt><span class="paramLabel">Parameters:</span></dt>
 <dd><code>mapping</code> - Mapping</dd>
 <dd><code>list</code> - List</dd>
 <dt><span class="returnLabel">Returns:</span></dt>
 <dd>Permuted view of list</dd>
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                                   <a href="../../../../../org/apache/calcite/util/mapping/Mappings.TargetMapping.html" title="interface in org.apache.calcite.util.mapping">Mappings.TargetMapping</a>&nbsp;mapping)</pre>
 <div class="block">Creates a view of a list, permuting according to a target mapping.</div>
 <dl>
 <dt><span class="paramLabel">Type Parameters:</span></dt>
 <dd><code>T</code> - Element type</dd>
 <dt><span class="paramLabel">Parameters:</span></dt>
 <dd><code>mapping</code> - Mapping</dd>
 <dd><code>list</code> - List</dd>
 <dt><span class="returnLabel">Returns:</span></dt>
 <dd>Permuted view of list</dd>
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 <div class="block">Returns a mapping as a list such that <code>list.get(source)</code> is
  <code>mapping.getTarget(source)</code> and <code>list.size()</code> is
  <code>mapping.getSourceCount()</code>.

  <p>Converse of <a href="../../../../../org/apache/calcite/util/mapping/Mappings.html#target-java.util.List-int-"><code>target(List, int)</code></a></p></div>
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                                             int&nbsp;sourceCount,
                                             int&nbsp;targetCount)</pre>
 <div class="block">Converts a <a href="https://docs.oracle.com/javase/8/docs/api/java/util/Map.html?is-external=true" title="class or interface in java.util"><code>Map</code></a> of integers to a <a href="../../../../../org/apache/calcite/util/mapping/Mappings.TargetMapping.html" title="interface in org.apache.calcite.util.mapping"><code>Mappings.TargetMapping</code></a>.</div>
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                                             int&nbsp;sourceCount,
                                             int&nbsp;targetCount)</pre>
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                              int&nbsp;sourceCount,
                              int&nbsp;targetCount)</pre>
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 <pre>public static&nbsp;<a href="../../../../../org/apache/calcite/util/mapping/Mapping.html" title="interface in org.apache.calcite.util.mapping">Mapping</a>&nbsp;source(<a href="https://docs.oracle.com/javase/8/docs/api/java/util/List.html?is-external=true" title="class or interface in java.util">List</a>&lt;<a href="https://docs.oracle.com/javase/8/docs/api/java/lang/Integer.html?is-external=true" title="class or interface in java.lang">Integer</a>&gt;&nbsp;targets,
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 <pre>public static&nbsp;<a href="../../../../../org/apache/calcite/util/mapping/Mapping.html" title="interface in org.apache.calcite.util.mapping">Mapping</a>&nbsp;target(<a href="https://docs.oracle.com/javase/8/docs/api/java/util/List.html?is-external=true" title="class or interface in java.util">List</a>&lt;<a href="https://docs.oracle.com/javase/8/docs/api/java/lang/Integer.html?is-external=true" title="class or interface in java.lang">Integer</a>&gt;&nbsp;sources,
                              int&nbsp;sourceCount)</pre>
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 <div class="block">Creates a bijection.

  <p>Throws if sources and targets are not one to one.</p></div>
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 <div class="block">Creates a bijection.

  <p>Throws if sources and targets are not one to one.</div>
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 <div class="block">Returns whether a mapping is the identity.</div>
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 <div class="block">Returns whether a mapping keeps order.

  <p>For example, {0:0, 1:1} and {0:1, 1:1} keeps order,
  and {0:1, 1:0} breaks the initial order.</div>
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 <pre>public static&nbsp;<a href="../../../../../org/apache/calcite/util/mapping/Mappings.TargetMapping.html" title="interface in org.apache.calcite.util.mapping">Mappings.TargetMapping</a>&nbsp;createShiftMapping(int&nbsp;sourceCount,
                                                         int...&nbsp;ints)</pre>
 <div class="block">Creates a mapping that consists of a set of contiguous ranges.

  <p>For example,</p>

  <blockquote><pre>createShiftMapping(60,
      100, 0, 3,
      200, 50, 5);
  </pre></blockquote>

  <p>creates</p>

  <table>
  <caption>Example mapping</caption>
  <tr><th>Source</th><th>Target</th></tr>
  <tr><td>0</td><td>100</td></tr>
  <tr><td>1</td><td>101</td></tr>
  <tr><td>2</td><td>102</td></tr>
  <tr><td>3</td><td>-1</td></tr>
  <tr><td>...</td><td>-1</td></tr>
  <tr><td>50</td><td>200</td></tr>
  <tr><td>51</td><td>201</td></tr>
  <tr><td>52</td><td>202</td></tr>
  <tr><td>53</td><td>203</td></tr>
  <tr><td>54</td><td>204</td></tr>
  <tr><td>55</td><td>-1</td></tr>
  <tr><td>...</td><td>-1</td></tr>
  <tr><td>59</td><td>-1</td></tr>
  </table></div>
 <dl>
 <dt><span class="paramLabel">Parameters:</span></dt>
 <dd><code>sourceCount</code> - Maximum value of <code>source</code></dd>
 <dd><code>ints</code> - Collection of ranges, each
                     <code>(target, source, count)</code></dd>
 <dt><span class="returnLabel">Returns:</span></dt>
 <dd>Mapping that maps from source ranges to target ranges</dd>
 </dl>
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                                             <a href="../../../../../org/apache/calcite/util/mapping/Mappings.TargetMapping.html" title="interface in org.apache.calcite.util.mapping">Mappings.TargetMapping</a>&nbsp;mapping1)</pre>
 <div class="block">Creates a mapping by appending two mappings.

  <p>Sources and targets of the second mapping are shifted to the right.</p>

  <p>For example, <pre>append({0:0, 1:1}, {0:0, 1:1, 2:2})</pre> yields
  <pre>{0:0, 1:1, 2:2, 3:3, 4:4}</pre>.</div>
 <dl>
 <dt><span class="seeLabel">See Also:</span></dt>
 <dd><a href="../../../../../org/apache/calcite/util/mapping/Mappings.html#merge-org.apache.calcite.util.mapping.Mappings.TargetMapping-org.apache.calcite.util.mapping.Mappings.TargetMapping-"><code>merge(org.apache.calcite.util.mapping.Mappings.TargetMapping, org.apache.calcite.util.mapping.Mappings.TargetMapping)</code></a></dd>
 </dl>
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 <pre>public static&nbsp;<a href="../../../../../org/apache/calcite/util/mapping/Mappings.TargetMapping.html" title="interface in org.apache.calcite.util.mapping">Mappings.TargetMapping</a>&nbsp;merge(<a href="../../../../../org/apache/calcite/util/mapping/Mappings.TargetMapping.html" title="interface in org.apache.calcite.util.mapping">Mappings.TargetMapping</a>&nbsp;mapping0,
                                            <a href="../../../../../org/apache/calcite/util/mapping/Mappings.TargetMapping.html" title="interface in org.apache.calcite.util.mapping">Mappings.TargetMapping</a>&nbsp;mapping1)</pre>
 <div class="block">Creates a mapping by merging two mappings. There must be no clashes.

  <p>Unlike <a href="../../../../../org/apache/calcite/util/mapping/Mappings.html#append-org.apache.calcite.util.mapping.Mappings.TargetMapping-org.apache.calcite.util.mapping.Mappings.TargetMapping-"><code>append(org.apache.calcite.util.mapping.Mappings.TargetMapping, org.apache.calcite.util.mapping.Mappings.TargetMapping)</code></a>, sources and targets are not shifted.

  <p>For example, <code>merge({0:0, 1:1}, {2:2, 3:3, 4:4})</code> yields
  <code>{0:0, 1:1, 2:2, 3:3, 4:4}</code>.
  <code>merge({0:0, 1:1}, {1:2, 2:3})</code> throws, because there are
  two entries with source=1.</div>
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                                                   int&nbsp;offset)</pre>
 <div class="block">Returns a mapping that shifts a given mapping's source by a given
  offset, incrementing the number of sources by the minimum possible.</div>
 <dl>
 <dt><span class="paramLabel">Parameters:</span></dt>
 <dd><code>mapping</code> - Input mapping</dd>
 <dd><code>offset</code> - Offset to be applied to each source</dd>
 <dt><span class="returnLabel">Returns:</span></dt>
 <dd>Shifted mapping</dd>
 </dl>
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                                                   int&nbsp;offset,
                                                   int&nbsp;sourceCount)</pre>
 <div class="block">Returns a mapping that shifts a given mapping's source by a given
  offset.

  <p>For example, given <code>mapping</code> with sourceCount=2, targetCount=8,
  and (source, target) entries {[0: 5], [1: 7]}, offsetSource(mapping, 3)
  returns a mapping with sourceCount=5, targetCount=8,
  and (source, target) entries {[3: 5], [4: 7]}.</div>
 <dl>
 <dt><span class="paramLabel">Parameters:</span></dt>
 <dd><code>mapping</code> - Input mapping</dd>
 <dd><code>offset</code> - Offset to be applied to each source</dd>
 <dd><code>sourceCount</code> - New source count; must be at least <code>mapping</code>'s
                     source count plus <code>offset</code></dd>
 <dt><span class="returnLabel">Returns:</span></dt>
 <dd>Shifted mapping</dd>
 </dl>
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                                                   int&nbsp;offset)</pre>
 <div class="block">Returns a mapping that shifts a given mapping's target by a given
  offset, incrementing the number of targets by the minimum possible.</div>
 <dl>
 <dt><span class="paramLabel">Parameters:</span></dt>
 <dd><code>mapping</code> - Input mapping</dd>
 <dd><code>offset</code> - Offset to be applied to each target</dd>
 <dt><span class="returnLabel">Returns:</span></dt>
 <dd>Shifted mapping</dd>
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 <pre>public static&nbsp;<a href="../../../../../org/apache/calcite/util/mapping/Mappings.TargetMapping.html" title="interface in org.apache.calcite.util.mapping">Mappings.TargetMapping</a>&nbsp;offsetTarget(<a href="../../../../../org/apache/calcite/util/mapping/Mappings.TargetMapping.html" title="interface in org.apache.calcite.util.mapping">Mappings.TargetMapping</a>&nbsp;mapping,
                                                   int&nbsp;offset,
                                                   int&nbsp;targetCount)</pre>
 <div class="block">Returns a mapping that shifts a given mapping's target by a given
  offset.

  <p>For example, given <code>mapping</code> with sourceCount=2, targetCount=8,
  and (source, target) entries {[0: 5], [1: 7]}, offsetTarget(mapping, 3)
  returns a mapping with sourceCount=2, targetCount=11,
  and (source, target) entries {[0: 8], [1: 10]}.</div>
 <dl>
 <dt><span class="paramLabel">Parameters:</span></dt>
 <dd><code>mapping</code> - Input mapping</dd>
 <dd><code>offset</code> - Offset to be applied to each target</dd>
 <dd><code>targetCount</code> - New target count; must be at least <code>mapping</code>'s
                     target count plus <code>offset</code></dd>
 <dt><span class="returnLabel">Returns:</span></dt>
 <dd>Shifted mapping</dd>
 </dl>
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 <pre>public static&nbsp;<a href="../../../../../org/apache/calcite/util/mapping/Mappings.TargetMapping.html" title="interface in org.apache.calcite.util.mapping">Mappings.TargetMapping</a>&nbsp;offset(<a href="../../../../../org/apache/calcite/util/mapping/Mappings.TargetMapping.html" title="interface in org.apache.calcite.util.mapping">Mappings.TargetMapping</a>&nbsp;mapping,
                                             int&nbsp;offset,
                                             int&nbsp;sourceCount)</pre>
 <div class="block">Returns a mapping that shifts a given mapping's source and target by a
  given offset.

  <p>For example, given <code>mapping</code> with sourceCount=2, targetCount=8,
  and (source, target) entries {[0: 5], [1: 7]}, offsetSource(mapping, 3)
  returns a mapping with sourceCount=5, targetCount=8,
  and (source, target) entries {[3: 8], [4: 10]}.</div>
 <dl>
 <dt><span class="paramLabel">Parameters:</span></dt>
 <dd><code>mapping</code> - Input mapping</dd>
 <dd><code>offset</code> - Offset to be applied to each source</dd>
 <dd><code>sourceCount</code> - New source count; must be at least <code>mapping</code>'s
                     source count plus <code>offset</code></dd>
 <dt><span class="returnLabel">Returns:</span></dt>
 <dd>Shifted mapping</dd>
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                                  int&nbsp;count)</pre>
 <div class="block">Returns whether a list of integers is the identity mapping
  [0, ..., n - 1].</div>
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 <div class="block">Inverts an <a href="https://docs.oracle.com/javase/8/docs/api/java/lang/Iterable.html?is-external=true" title="class or interface in java.lang"><code>Iterable</code></a> over
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 <div class="block">Inverts an <a href="https://docs.oracle.com/javase/8/docs/api/java/util/Iterator.html?is-external=true" title="class or interface in java.util"><code>Iterator</code></a> over
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                         int&nbsp;i)</pre>
 <div class="block">Applies a mapping to an optional integer, returning an optional
  result.</div>
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