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<center><h1>Module <a href="type_ArrayLabels.html">ArrayLabels</a></h1></center>
<br>
<pre><span class="keyword">module</span> ArrayLabels: <code class="code"><span class="keyword">sig</span></code> <a href="ArrayLabels.html">..</a> <code class="code"><span class="keyword">end</span></code></pre>Array operations.<br>
<hr width="100%">
<pre><span id="VALlength"><span class="keyword">val</span> length</span> : <code class="type">'a array -> int</code></pre><div class="info">
Return the length (number of elements) of the given array.<br>
</div>
<pre><span id="VALget"><span class="keyword">val</span> get</span> : <code class="type">'a array -> int -> 'a</code></pre><div class="info">
<code class="code"><span class="constructor">Array</span>.get a n</code> returns the element number <code class="code">n</code> of array <code class="code">a</code>.
   The first element has number 0.
   The last element has number <code class="code"><span class="constructor">Array</span>.length a - 1</code>.
   You can also write <code class="code">a.(n)</code> instead of <code class="code"><span class="constructor">Array</span>.get a n</code>.
<p>

   Raise <code class="code"><span class="constructor">Invalid_argument</span> <span class="string">"index out of bounds"</span></code>
   if <code class="code">n</code> is outside the range 0 to <code class="code">(<span class="constructor">Array</span>.length a - 1)</code>.<br>
</div>
<pre><span id="VALset"><span class="keyword">val</span> set</span> : <code class="type">'a array -> int -> 'a -> unit</code></pre><div class="info">
<code class="code"><span class="constructor">Array</span>.set a n x</code> modifies array <code class="code">a</code> in place, replacing
   element number <code class="code">n</code> with <code class="code">x</code>.
   You can also write <code class="code">a.(n) &lt;- x</code> instead of <code class="code"><span class="constructor">Array</span>.set a n x</code>.
<p>

   Raise <code class="code"><span class="constructor">Invalid_argument</span> <span class="string">"index out of bounds"</span></code>
   if <code class="code">n</code> is outside the range 0 to <code class="code"><span class="constructor">Array</span>.length a - 1</code>.<br>
</div>
<pre><span id="VALmake"><span class="keyword">val</span> make</span> : <code class="type">int -> 'a -> 'a array</code></pre><div class="info">
<code class="code"><span class="constructor">Array</span>.make n x</code> returns a fresh array of length <code class="code">n</code>,
   initialized with <code class="code">x</code>.
   All the elements of this new array are initially
   physically equal to <code class="code">x</code> (in the sense of the <code class="code">==</code> predicate).
   Consequently, if <code class="code">x</code> is mutable, it is shared among all elements
   of the array, and modifying <code class="code">x</code> through one of the array entries
   will modify all other entries at the same time.
<p>

   Raise <code class="code"><span class="constructor">Invalid_argument</span></code> if <code class="code">n &lt; 0</code> or <code class="code">n &gt; <span class="constructor">Sys</span>.max_array_length</code>.
   If the value of <code class="code">x</code> is a floating-point number, then the maximum
   size is only <code class="code"><span class="constructor">Sys</span>.max_array_length / 2</code>.<br>
</div>
<pre><span id="VALcreate"><span class="keyword">val</span> create</span> : <code class="type">int -> 'a -> 'a array</code></pre><div class="info">
<span class="warning">Deprecated.</span><code class="code"><span class="constructor">Array</span>.create</code> is an alias for <a href="ArrayLabels.html#VALmake"><code class="code"><span class="constructor">ArrayLabels</span>.make</code></a>.<br>
</div>
<pre><span id="VALinit"><span class="keyword">val</span> init</span> : <code class="type">int -> f:(int -> 'a) -> 'a array</code></pre><div class="info">
<code class="code"><span class="constructor">Array</span>.init n f</code> returns a fresh array of length <code class="code">n</code>,
   with element number <code class="code">i</code> initialized to the result of <code class="code">f i</code>.
   In other terms, <code class="code"><span class="constructor">Array</span>.init n f</code> tabulates the results of <code class="code">f</code>
   applied to the integers <code class="code">0</code> to <code class="code">n-1</code>.
<p>

   Raise <code class="code"><span class="constructor">Invalid_argument</span></code> if <code class="code">n &lt; 0</code> or <code class="code">n &gt; <span class="constructor">Sys</span>.max_array_length</code>.
   If the return type of <code class="code">f</code> is <code class="code">float</code>, then the maximum
   size is only <code class="code"><span class="constructor">Sys</span>.max_array_length / 2</code>.<br>
</div>
<pre><span id="VALmake_matrix"><span class="keyword">val</span> make_matrix</span> : <code class="type">dimx:int -> dimy:int -> 'a -> 'a array array</code></pre><div class="info">
<code class="code"><span class="constructor">Array</span>.make_matrix dimx dimy e</code> returns a two-dimensional array
   (an array of arrays) with first dimension <code class="code">dimx</code> and
   second dimension <code class="code">dimy</code>. All the elements of this new matrix
   are initially physically equal to <code class="code">e</code>.
   The element (<code class="code">x,y</code>) of a matrix <code class="code">m</code> is accessed
   with the notation <code class="code">m.(x).(y)</code>.
<p>

   Raise <code class="code"><span class="constructor">Invalid_argument</span></code> if <code class="code">dimx</code> or <code class="code">dimy</code> is negative or
   greater than <code class="code"><span class="constructor">Sys</span>.max_array_length</code>.
   If the value of <code class="code">e</code> is a floating-point number, then the maximum
   size is only <code class="code"><span class="constructor">Sys</span>.max_array_length / 2</code>.<br>
</div>
<pre><span id="VALcreate_matrix"><span class="keyword">val</span> create_matrix</span> : <code class="type">dimx:int -> dimy:int -> 'a -> 'a array array</code></pre><div class="info">
<span class="warning">Deprecated.</span><code class="code"><span class="constructor">Array</span>.create_matrix</code> is an alias for
   <a href="ArrayLabels.html#VALmake_matrix"><code class="code"><span class="constructor">ArrayLabels</span>.make_matrix</code></a>.<br>
</div>
<pre><span id="VALappend"><span class="keyword">val</span> append</span> : <code class="type">'a array -> 'a array -> 'a array</code></pre><div class="info">
<code class="code"><span class="constructor">Array</span>.append v1 v2</code> returns a fresh array containing the
   concatenation of the arrays <code class="code">v1</code> and <code class="code">v2</code>.<br>
</div>
<pre><span id="VALconcat"><span class="keyword">val</span> concat</span> : <code class="type">'a array list -> 'a array</code></pre><div class="info">
Same as <code class="code"><span class="constructor">Array</span>.append</code>, but concatenates a list of arrays.<br>
</div>
<pre><span id="VALsub"><span class="keyword">val</span> sub</span> : <code class="type">'a array -> pos:int -> len:int -> 'a array</code></pre><div class="info">
<code class="code"><span class="constructor">Array</span>.sub a start len</code> returns a fresh array of length <code class="code">len</code>,
   containing the elements number <code class="code">start</code> to <code class="code">start + len - 1</code>
   of array <code class="code">a</code>.
<p>

   Raise <code class="code"><span class="constructor">Invalid_argument</span> <span class="string">"Array.sub"</span></code> if <code class="code">start</code> and <code class="code">len</code> do not
   designate a valid subarray of <code class="code">a</code>; that is, if
   <code class="code">start &lt; 0</code>, or <code class="code">len &lt; 0</code>, or <code class="code">start + len &gt; <span class="constructor">Array</span>.length a</code>.<br>
</div>
<pre><span id="VALcopy"><span class="keyword">val</span> copy</span> : <code class="type">'a array -> 'a array</code></pre><div class="info">
<code class="code"><span class="constructor">Array</span>.copy a</code> returns a copy of <code class="code">a</code>, that is, a fresh array
   containing the same elements as <code class="code">a</code>.<br>
</div>
<pre><span id="VALfill"><span class="keyword">val</span> fill</span> : <code class="type">'a array -> pos:int -> len:int -> 'a -> unit</code></pre><div class="info">
<code class="code"><span class="constructor">Array</span>.fill a ofs len x</code> modifies the array <code class="code">a</code> in place,
   storing <code class="code">x</code> in elements number <code class="code">ofs</code> to <code class="code">ofs + len - 1</code>.
<p>

   Raise <code class="code"><span class="constructor">Invalid_argument</span> <span class="string">"Array.fill"</span></code> if <code class="code">ofs</code> and <code class="code">len</code> do not
   designate a valid subarray of <code class="code">a</code>.<br>
</div>
<pre><span id="VALblit"><span class="keyword">val</span> blit</span> : <code class="type">src:'a array -> src_pos:int -> dst:'a array -> dst_pos:int -> len:int -> unit</code></pre><div class="info">
<code class="code"><span class="constructor">Array</span>.blit v1 o1 v2 o2 len</code> copies <code class="code">len</code> elements
   from array <code class="code">v1</code>, starting at element number <code class="code">o1</code>, to array <code class="code">v2</code>,
   starting at element number <code class="code">o2</code>. It works correctly even if
   <code class="code">v1</code> and <code class="code">v2</code> are the same array, and the source and
   destination chunks overlap.
<p>

   Raise <code class="code"><span class="constructor">Invalid_argument</span> <span class="string">"Array.blit"</span></code> if <code class="code">o1</code> and <code class="code">len</code> do not
   designate a valid subarray of <code class="code">v1</code>, or if <code class="code">o2</code> and <code class="code">len</code> do not
   designate a valid subarray of <code class="code">v2</code>.<br>
</div>
<pre><span id="VALto_list"><span class="keyword">val</span> to_list</span> : <code class="type">'a array -> 'a list</code></pre><div class="info">
<code class="code"><span class="constructor">Array</span>.to_list a</code> returns the list of all the elements of <code class="code">a</code>.<br>
</div>
<pre><span id="VALof_list"><span class="keyword">val</span> of_list</span> : <code class="type">'a list -> 'a array</code></pre><div class="info">
<code class="code"><span class="constructor">Array</span>.of_list l</code> returns a fresh array containing the elements
   of <code class="code">l</code>.<br>
</div>
<pre><span id="VALiter"><span class="keyword">val</span> iter</span> : <code class="type">f:('a -> unit) -> 'a array -> unit</code></pre><div class="info">
<code class="code"><span class="constructor">Array</span>.iter f a</code> applies function <code class="code">f</code> in turn to all
   the elements of <code class="code">a</code>.  It is equivalent to
   <code class="code">f a.(0); f a.(1); ...; f a.(<span class="constructor">Array</span>.length a - 1); ()</code>.<br>
</div>
<pre><span id="VALmap"><span class="keyword">val</span> map</span> : <code class="type">f:('a -> 'b) -> 'a array -> 'b array</code></pre><div class="info">
<code class="code"><span class="constructor">Array</span>.map f a</code> applies function <code class="code">f</code> to all the elements of <code class="code">a</code>,
   and builds an array with the results returned by <code class="code">f</code>:
   <code class="code">[| f a.(0); f a.(1); ...; f a.(<span class="constructor">Array</span>.length a - 1) |]</code>.<br>
</div>
<pre><span id="VALiteri"><span class="keyword">val</span> iteri</span> : <code class="type">f:(int -> 'a -> unit) -> 'a array -> unit</code></pre><div class="info">
Same as <a href="ArrayLabels.html#VALiter"><code class="code"><span class="constructor">ArrayLabels</span>.iter</code></a>, but the
   function is applied to the index of the element as first argument,
   and the element itself as second argument.<br>
</div>
<pre><span id="VALmapi"><span class="keyword">val</span> mapi</span> : <code class="type">f:(int -> 'a -> 'b) -> 'a array -> 'b array</code></pre><div class="info">
Same as <a href="ArrayLabels.html#VALmap"><code class="code"><span class="constructor">ArrayLabels</span>.map</code></a>, but the
   function is applied to the index of the element as first argument,
   and the element itself as second argument.<br>
</div>
<pre><span id="VALfold_left"><span class="keyword">val</span> fold_left</span> : <code class="type">f:('a -> 'b -> 'a) -> init:'a -> 'b array -> 'a</code></pre><div class="info">
<code class="code"><span class="constructor">Array</span>.fold_left f x a</code> computes
   <code class="code">f (... (f (f x a.(0)) a.(1)) ...) a.(n-1)</code>,
   where <code class="code">n</code> is the length of the array <code class="code">a</code>.<br>
</div>
<pre><span id="VALfold_right"><span class="keyword">val</span> fold_right</span> : <code class="type">f:('a -> 'b -> 'b) -> 'a array -> init:'b -> 'b</code></pre><div class="info">
<code class="code"><span class="constructor">Array</span>.fold_right f a x</code> computes
   <code class="code">f a.(0) (f a.(1) ( ... (f a.(n-1) x) ...))</code>,
   where <code class="code">n</code> is the length of the array <code class="code">a</code>.<br>
</div>
<br>
<span id="6_Sorting"><h6>Sorting</h6></span><br>
<pre><span id="VALsort"><span class="keyword">val</span> sort</span> : <code class="type">cmp:('a -> 'a -> int) -> 'a array -> unit</code></pre><div class="info">
Sort an array in increasing order according to a comparison
   function.  The comparison function must return 0 if its arguments
   compare as equal, a positive integer if the first is greater,
   and a negative integer if the first is smaller (see below for a
   complete specification).  For example, <a href="Pervasives.html#VALcompare"><code class="code">compare</code></a> is
   a suitable comparison function, provided there are no floating-point
   NaN values in the data.  After calling <code class="code"><span class="constructor">Array</span>.sort</code>, the
   array is sorted in place in increasing order.
   <code class="code"><span class="constructor">Array</span>.sort</code> is guaranteed to run in constant heap space
   and (at most) logarithmic stack space.
<p>

   The current implementation uses Heap Sort.  It runs in constant
   stack space.
<p>

   Specification of the comparison function:
   Let <code class="code">a</code> be the array and <code class="code">cmp</code> the comparison function.  The following
   must be true for all x, y, z in a :<ul>
<li>  <code class="code">cmp x y</code> &gt; 0 if and only if <code class="code">cmp y x</code> &lt; 0</li>
<li>  if <code class="code">cmp x y</code> &gt;= 0 and <code class="code">cmp y z</code> &gt;= 0 then <code class="code">cmp x z</code> &gt;= 0</li>
</ul>

   When <code class="code"><span class="constructor">Array</span>.sort</code> returns, <code class="code">a</code> contains the same elements as before,
   reordered in such a way that for all i and j valid indices of <code class="code">a</code> :<ul>
<li>  <code class="code">cmp a.(i) a.(j)</code> &gt;= 0 if and only if i &gt;= j</li>
</ul>
<br>
</div>
<pre><span id="VALstable_sort"><span class="keyword">val</span> stable_sort</span> : <code class="type">cmp:('a -> 'a -> int) -> 'a array -> unit</code></pre><div class="info">
Same as <a href="ArrayLabels.html#VALsort"><code class="code"><span class="constructor">ArrayLabels</span>.sort</code></a>, but the sorting algorithm is stable (i.e.
   elements that compare equal are kept in their original order) and
   not guaranteed to run in constant heap space.
<p>

   The current implementation uses Merge Sort. It uses <code class="code">n/2</code>
   words of heap space, where <code class="code">n</code> is the length of the array.
   It is usually faster than the current implementation of <a href="ArrayLabels.html#VALsort"><code class="code"><span class="constructor">ArrayLabels</span>.sort</code></a>.<br>
</div>
<pre><span id="VALfast_sort"><span class="keyword">val</span> fast_sort</span> : <code class="type">cmp:('a -> 'a -> int) -> 'a array -> unit</code></pre><div class="info">
Same as <a href="Array.html#VALsort"><code class="code"><span class="constructor">Array</span>.sort</code></a> or <a href="Array.html#VALstable_sort"><code class="code"><span class="constructor">Array</span>.stable_sort</code></a>, whichever is faster
    on typical input.<br>
</div>
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