doc/guide/localhost/ShareZeroVec

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  26 <h1>ShareZeroVec</h1>
  27 </div>
  28 <div id="content">
  29 <div id="preamble">
  30 <div class="sectionbody">
  31 <div class="paragraph"><p><a href="ShareZeroVec">ShareZeroVec</a> is an optimization pass for the <a href="SSA">SSA</a>
  32 <a href="IntermediateLanguage">IntermediateLanguage</a>, invoked from <a href="SSASimplify">SSASimplify</a>.</p></div>
  33 </div>
  34 </div>
  35 <div class="sect1">
  36 <h2 id="_description">Description</h2>
  37 <div class="sectionbody">
  38 <div class="paragraph"><p>An SSA optimization to share zero-length vectors.</p></div>
  39 <div class="paragraph"><p>From <a href="https://github.com/MLton/mlton/commit/be8c5f576"><span class="monospaced">be8c5f576</span></a>, which replaced the use of the
  40 <span class="monospaced">Array_array0Const</span> primitive in the Basis Library implementation with a
  41 (nullary) <span class="monospaced">Vector_vector</span> primitive:</p></div>
  42 <div class="quoteblock">
  43 <div class="content">
  44 <div class="paragraph"><p>The original motivation for the <span class="monospaced">Array_array0Const</span> primitive was to share the
  45 heap space required for zero-length vectors among all vectors (of a given type).
  46 It was claimed that this optimization is important, e.g., in a self-compile,
  47 where vectors are used for lots of syntax tree elements and many of those
  48 vectors are empty. See:
  49 <a href="http://www.mlton.org/pipermail/mlton-devel/2002-February/021523.html">http://www.mlton.org/pipermail/mlton-devel/2002-February/021523.html</a></p></div>
  50 <div class="paragraph"><p>Curiously, the full effect of this optimization has been missing for quite some
  51 time (perhaps since the port of <a href="ConstantPropagation">ConstantPropagation</a> to the SSA IL).  While
  52 <a href="ConstantPropagation">ConstantPropagation</a> has "globalized" the nullary application of the
  53 <span class="monospaced">Array_array0Const</span> primitive, it also simultaneously transformed it to an
  54 application of the <span class="monospaced">Array_uninit</span> (previously, the <span class="monospaced">Array_array</span>) primitive to
  55 the zero constant.  The hash-consing of globals, meant to create exactly one
  56 global for each distinct constant, treats <span class="monospaced">Array_uninit</span> primitives as unequal
  57 (appropriately, since <span class="monospaced">Array_uninit</span> allocates an array with identity (though
  58 the identity may be supressed by a subsequent <span class="monospaced">Array_toVector</span>)), hence each
  59 distinct <span class="monospaced">Array_array0Const</span> primitive in the program remained as distinct
  60 globals.  The limited amount of inlining prior to <a href="ConstantPropagation">ConstantPropagation</a> meant
  61 that there were typically fewer than a dozen "copies" of the same empty vector
  62 in a program for a given type.</p></div>
  63 <div class="paragraph"><p>As a "functional" primitive, a nullary <span class="monospaced">Vector_vector</span> is globalized by
  64 ClosureConvert, but is further recognized by ConstantPropagation and hash-consed
  65 into a unique instance for each type.</p></div>
  66 </div>
  67 <div class="attribution">
  68 </div></div>
  69 <div class="paragraph"><p>However, a single, shared, global <span class="monospaced">Vector_vector ()</span> inhibits the
  70 coercion-based optimizations of <span class="monospaced">Useless</span>.  For example, consider the
  71 following program:</p></div>
  72 <div class="listingblock">
  73 <div class="content"><div class="highlight"><pre><span class="w">    </span><span class="k">val</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">valOf</span><span class="w"> </span><span class="p">(</span><span class="n">Int</span><span class="p">.</span><span class="n">fromString</span><span class="w"> </span><span class="p">(</span><span class="n">hd</span><span class="w"> </span><span class="p">(</span><span class="n">CommandLine</span><span class="p">.</span><span class="n">arguments</span><span class="w"> </span><span class="p">())))</span><span class="w"></span>
  74
  75 <span class="w">    </span><span class="k">val</span><span class="w"> </span><span class="n">v1</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">Vector</span><span class="p">.</span><span class="n">tabulate</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"></span>
  76 <span class="w">                              </span><span class="k">let</span><span class="w"> </span><span class="k">val</span><span class="w"> </span><span class="n">w</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">Word16</span><span class="p">.</span><span class="n">fromInt</span><span class="w"> </span><span class="n">i</span><span class="w"></span>
  77 <span class="w">                              </span><span class="k">in</span><span class="w"> </span><span class="p">(</span><span class="n">w</span><span class="w"> </span><span class="n">-</span><span class="w"> </span><span class="mh">0wx1</span><span class="p">,</span><span class="w"> </span><span class="n">w</span><span class="p">,</span><span class="w"> </span><span class="n">w</span><span class="w"> </span><span class="n">+</span><span class="w"> </span><span class="mh">0wx1</span><span class="w"> </span><span class="n">+</span><span class="w"> </span><span class="n">w</span><span class="p">)</span><span class="w"></span>
  78 <span class="w">                              </span><span class="k">end</span><span class="p">)</span><span class="w"></span>
  79 <span class="w">    </span><span class="k">val</span><span class="w"> </span><span class="n">v2</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">Vector</span><span class="p">.</span><span class="n">map</span><span class="w"> </span><span class="p">(</span><span class="k">fn</span><span class="w"> </span><span class="p">(</span><span class="n">w1</span><span class="p">,</span><span class="w"> </span><span class="n">w2</span><span class="p">,</span><span class="w"> </span><span class="n">w3</span><span class="p">)</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="p">(</span><span class="n">w1</span><span class="p">,</span><span class="w"> </span><span class="mh">0wx2</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="n">w2</span><span class="p">,</span><span class="w"> </span><span class="mh">0wx3</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="n">w3</span><span class="p">))</span><span class="w"> </span><span class="n">v1</span><span class="w"></span>
  80 <span class="w">    </span><span class="k">val</span><span class="w"> </span><span class="n">v3</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">VectorSlice</span><span class="p">.</span><span class="n">vector</span><span class="w"> </span><span class="p">(</span><span class="n">VectorSlice</span><span class="p">.</span><span class="n">slice</span><span class="w"> </span><span class="p">(</span><span class="n">v1</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">SOME</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="n">-</span><span class="w"> </span><span class="mi">2</span><span class="p">)))</span><span class="w"></span>
  81 <span class="w">    </span><span class="k">val</span><span class="w"> </span><span class="n">ans1</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">Vector</span><span class="p">.</span><span class="n">foldl</span><span class="w"> </span><span class="p">(</span><span class="k">fn</span><span class="w"> </span><span class="p">((</span><span class="n">w1</span><span class="p">,</span><span class="n">w2</span><span class="p">,</span><span class="n">w3</span><span class="p">),</span><span class="n">w</span><span class="p">)</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="n">w</span><span class="w"> </span><span class="n">+</span><span class="w"> </span><span class="n">w1</span><span class="w"> </span><span class="n">+</span><span class="w"> </span><span class="n">w2</span><span class="w"> </span><span class="n">+</span><span class="w"> </span><span class="n">w3</span><span class="p">)</span><span class="w"> </span><span class="mh">0wx0</span><span class="w"> </span><span class="n">v1</span><span class="w"></span>
  82 <span class="w">    </span><span class="k">val</span><span class="w"> </span><span class="n">ans2</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">Vector</span><span class="p">.</span><span class="n">foldl</span><span class="w"> </span><span class="p">(</span><span class="k">fn</span><span class="w"> </span><span class="p">((_,</span><span class="n">w2</span><span class="p">,_),</span><span class="n">w</span><span class="p">)</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="n">w</span><span class="w"> </span><span class="n">+</span><span class="w"> </span><span class="n">w2</span><span class="p">)</span><span class="w"> </span><span class="mh">0wx0</span><span class="w"> </span><span class="n">v2</span><span class="w"></span>
  83 <span class="w">    </span><span class="k">val</span><span class="w"> </span><span class="n">ans3</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">Vector</span><span class="p">.</span><span class="n">foldl</span><span class="w"> </span><span class="p">(</span><span class="k">fn</span><span class="w"> </span><span class="p">((_,</span><span class="n">w2</span><span class="p">,_),</span><span class="n">w</span><span class="p">)</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="n">w</span><span class="w"> </span><span class="n">+</span><span class="w"> </span><span class="n">w2</span><span class="p">)</span><span class="w"> </span><span class="mh">0wx0</span><span class="w"> </span><span class="n">v3</span><span class="w"></span>
  84
  85 <span class="w">    </span><span class="k">val</span><span class="w"> </span><span class="p">_</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">print</span><span class="w"> </span><span class="p">(</span><span class="n">concat</span><span class="w"> </span><span class="p">[</span><span class="s">&quot;ans1 = &quot;</span><span class="p">,</span><span class="w"> </span><span class="n">Word16</span><span class="p">.</span><span class="n">toString</span><span class="w"> </span><span class="n">ans1</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;  &quot;</span><span class="p">,</span><span class="w"></span>
  86 <span class="w">                           </span><span class="s">&quot;ans2 = &quot;</span><span class="p">,</span><span class="w"> </span><span class="n">Word16</span><span class="p">.</span><span class="n">toString</span><span class="w"> </span><span class="n">ans2</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;  &quot;</span><span class="p">,</span><span class="w"></span>
  87 <span class="w">                           </span><span class="s">&quot;ans3 = &quot;</span><span class="p">,</span><span class="w"> </span><span class="n">Word16</span><span class="p">.</span><span class="n">toString</span><span class="w"> </span><span class="n">ans3</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">])</span><span class="w"></span>
  88 </pre></div></div></div>
  89 <div class="paragraph"><p>We would like <span class="monospaced">v2</span> and <span class="monospaced">v3</span> to be optimized from
  90 <span class="monospaced">(word16 * word16 * word16) vector</span> to <span class="monospaced">word16 vector</span> because only
  91 the 2nd component of the elements is needed to compute the answer.</p></div>
  92 <div class="paragraph"><p>With <span class="monospaced">Array_array0Const</span>, each distinct occurrence of
  93 <span class="monospaced">Array_array0Const((word16 * word16 * word16))</span> arising from
  94 polyvariance and inlining remained a distinct
  95 <span class="monospaced">Array_uninit((word16 * word16 * word16)) (0x0)</span> global, which
  96 resulted in distinct occurrences for the
  97 <span class="monospaced">val v1 = Vector.tabulate ...</span> and for the
  98 <span class="monospaced">val v2 = Vector.map ...</span>. The latter could be optimized to
  99 <span class="monospaced">Array_uninit(word16) (0x0)</span> by <span class="monospaced">Useless</span>, because its result only
 100 flows to places requiring the 2nd component of the elements.</p></div>
 101 <div class="paragraph"><p>With <span class="monospaced">Vector_vector ()</span>, the distinct occurrences of
 102 <span class="monospaced">Vector_vector((word16 * word16 * word16)) ()</span> arising from
 103 polyvariance are globalized during <span class="monospaced">ClosureConvert</span>, those global
 104 references may be further duplicated by inlining, but the distinct
 105 occurrences of <span class="monospaced">Vector_vector((word16 * word16 * word16)) ()</span> are
 106 merged to a single occurrence.  Because this result flows to places
 107 requiring all three components of the elements, it remains
 108 <span class="monospaced">Vector_vector((word16 * word16 * word16)) ()</span> after
 109 <span class="monospaced">Useless</span>. Furthermore, because one cannot (in constant time) coerce a
 110 <span class="monospaced">(word16 * word16 * word16) vector</span> to a <span class="monospaced">word16 vector</span>, the <span class="monospaced">v2</span>
 111 value remains of type <span class="monospaced">(word16 * word16 * word16) vector</span>.</p></div>
 112 <div class="paragraph"><p>One option would be to drop the 0-element vector "optimization"
 113 entirely.  This costs some space (no sharing of empty vectors) and
 114 some time (allocation and garbage collection of empty vectors).</p></div>
 115 <div class="paragraph"><p>Another option would be to reinstate the <span class="monospaced">Array_array0Const</span> primitive
 116 and associated <span class="monospaced">ConstantPropagation</span> treatment.  But, the semantics
 117 and purpose of <span class="monospaced">Array_array0Const</span> was poorly understood, resulting in
 118 this break.</p></div>
 119 <div class="paragraph"><p>The <a href="ShareZeroVec">ShareZeroVec</a> pass pursues a different approach: perform the 0-element
 120 vector "optimization" as a separate optimization, after
 121 <span class="monospaced">ConstantPropagation</span> and <span class="monospaced">Useless</span>.  A trivial static analysis is
 122 used to match <span class="monospaced">val v: t vector = Array_toVector(t) (a)</span> with
 123 corresponding <span class="monospaced">val a: array = Array_uninit(t) (l)</span> and the later are
 124 expanded to
 125 <span class="monospaced">val a: t array = if 0 = l then zeroArr_[t] else Array_uninit(t) (l)</span>
 126 with a single global <span class="monospaced">val zeroArr_[t] = Array_uninit(t) (0)</span> created
 127 for each distinct type (after coercion-based optimizations).</p></div>
 128 <div class="paragraph"><p>One disadvantage of this approach, compared to the <span class="monospaced">Vector_vector(t) ()</span>
 129 approach, is that <span class="monospaced">Array_toVector</span> is applied each time a vector
 130 is created, even if it is being applied to the <span class="monospaced">zeroArr_[t]</span>
 131 zero-length array.  (Although, this was the behavior of the
 132 <span class="monospaced">Array_array0Const</span> approach.)  This updates the object header each
 133 time, whereas the <span class="monospaced">Vector_vector(t) ()</span> approach would have updated
 134 the object header once, when the global was created, and the
 135 <span class="monospaced">zeroVec_[t]</span> global and the <span class="monospaced">Array_toVector</span> result would flow to the
 136 join point.</p></div>
 137 <div class="paragraph"><p>It would be possible to properly share zero-length vectors, but doing
 138 so is a more sophisticated analysis and transformation, because there
 139 can be arbitrary code between the
 140 <span class="monospaced">val a: t array = Array_uninit(t) (l)</span> and the corresponding
 141 <span class="monospaced">val v: v vector = Array_toVector(t) (a)</span>, although, in practice,
 142 nothing happens when a zero-length vector is created.  It may be best
 143 to pursue a more general "array to vector" optimization that
 144 transforms creations of static-length vectors (e.g., all the
 145 <span class="monospaced">Vector.new&lt;N&gt;</span> functions) into <span class="monospaced">Vector_vector</span> primitives (some of
 146 which could be globalized).</p></div>
 147 </div>
 148 </div>
 149 <div class="sect1">
 150 <h2 id="_implementation">Implementation</h2>
 151 <div class="sectionbody">
 152 <div class="ulist"><ul>
 153 <li>
 154 <p>
 155 <a href="https://github.com/MLton/mlton/blob/master/mlton/ssa/share-zero-vec.fun"><span class="monospaced">share-zero-vec.fun</span></a>
 156 </p>
 157 </li>
 158 </ul></div>
 159 </div>
 160 </div>
 161 <div class="sect1">
 162 <h2 id="_details_and_notes">Details and Notes</h2>
 163 <div class="sectionbody">
 164 <div class="paragraph"><p></p></div>
 165 </div>
 166 </div>
 167 </div>
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