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<html xmlns="http://www.w3.org/1999/xhtml"><head><title>CCInt64 (containers.CCInt64)</title><link rel="stylesheet" href="../../odoc.css"/><meta charset="utf-8"/><meta name="viewport" content="width=device-width,initial-scale=1.0"/><script src="../../highlight.pack.js"></script><script>hljs.initHighlightingOnLoad();</script></head><body><div class="content"><header><nav><a href="../index.html">Up</a> <a href="../index.html">containers</a> &#x00BB; CCInt64</nav><h1>Module <code>CCInt64</code></h1><h2 id="int64"><a href="#int64" class="anchor"></a>Int64</h2><p>Helpers for 64-bit integers.</p><p>This module provides operations on the type int64 of signed 64-bit integers. Unlike the built-in int type, the type int64 is guaranteed to be exactly 64-bit wide on all platforms. All arithmetic operations over int64 are taken modulo 2<sup>64</sup>.</p><p>Performance notice: values of type int64 occupy more memory space than values of type int, and arithmetic operations on int64 are generally slower than those on int. Use int64 only when the application requires exact 64-bit arithmetic.</p><dl><dt>since</dt><dd>0.13</dd></dl><nav class="toc"><ul><li><a href="#conversion">Conversion</a></li><li><a href="#printing">Printing</a></li><li><a href="#infix-operators">Infix Operators</a></li></ul></nav></header><div><div class="spec include"><div class="doc"><p><a href="https://caml.inria.fr/pub/docs/manual-ocaml/libref/Int64.html">Documentation for the standard Int64 module</a></p><details open="open"><summary><span class="def"><code><span class="keyword">include</span> <span class="keyword">module</span> <span class="keyword">type</span> <span class="keyword">of</span> <span class="keyword">sig</span> ... <span class="keyword">end</span></code></span></summary><dl><dt class="spec value" id="val-zero"><a href="#val-zero" class="anchor"></a><code><span class="keyword">val</span> zero : int64</code></dt><dt class="spec value" id="val-one"><a href="#val-one" class="anchor"></a><code><span class="keyword">val</span> one : int64</code></dt><dt class="spec value" id="val-minus_one"><a href="#val-minus_one" class="anchor"></a><code><span class="keyword">val</span> minus_one : int64</code></dt></dl><dl><dt class="spec external" id="val-neg"><a href="#val-neg" class="anchor"></a><code><span class="keyword">val</span> neg : int64 <span>&#45;&gt;</span> int64</code></dt><dt class="spec external" id="val-add"><a href="#val-add" class="anchor"></a><code><span class="keyword">val</span> add : int64 <span>&#45;&gt;</span> int64 <span>&#45;&gt;</span> int64</code></dt><dt class="spec external" id="val-sub"><a href="#val-sub" class="anchor"></a><code><span class="keyword">val</span> sub : int64 <span>&#45;&gt;</span> int64 <span>&#45;&gt;</span> int64</code></dt><dt class="spec external" id="val-mul"><a href="#val-mul" class="anchor"></a><code><span class="keyword">val</span> mul : int64 <span>&#45;&gt;</span> int64 <span>&#45;&gt;</span> int64</code></dt><dt class="spec external" id="val-div"><a href="#val-div" class="anchor"></a><code><span class="keyword">val</span> div : int64 <span>&#45;&gt;</span> int64 <span>&#45;&gt;</span> int64</code></dt></dl><dl><dt class="spec value" id="val-unsigned_div"><a href="#val-unsigned_div" class="anchor"></a><code><span class="keyword">val</span> unsigned_div : int64 <span>&#45;&gt;</span> int64 <span>&#45;&gt;</span> int64</code></dt></dl><dl><dt class="spec external" id="val-rem"><a href="#val-rem" class="anchor"></a><code><span class="keyword">val</span> rem : int64 <span>&#45;&gt;</span> int64 <span>&#45;&gt;</span> int64</code></dt></dl><dl><dt class="spec value" id="val-unsigned_rem"><a href="#val-unsigned_rem" class="anchor"></a><code><span class="keyword">val</span> unsigned_rem : int64 <span>&#45;&gt;</span> int64 <span>&#45;&gt;</span> int64</code></dt><dt class="spec value" id="val-succ"><a href="#val-succ" class="anchor"></a><code><span class="keyword">val</span> succ : int64 <span>&#45;&gt;</span> int64</code></dt><dt class="spec value" id="val-pred"><a href="#val-pred" class="anchor"></a><code><span class="keyword">val</span> pred : int64 <span>&#45;&gt;</span> int64</code></dt><dt class="spec value" id="val-abs"><a href="#val-abs" class="anchor"></a><code><span class="keyword">val</span> abs : int64 <span>&#45;&gt;</span> int64</code></dt><dt class="spec value" id="val-max_int"><a href="#val-max_int" class="anchor"></a><code><span class="keyword">val</span> max_int : int64</code></dt><dt class="spec value" id="val-min_int"><a href="#val-min_int" class="anchor"></a><code><span class="keyword">val</span> min_int : int64</code></dt></dl><dl><dt class="spec external" id="val-logand"><a href="#val-logand" class="anchor"></a><code><span class="keyword">val</span> logand : int64 <span>&#45;&gt;</span> int64 <span>&#45;&gt;</span> int64</code></dt><dt class="spec external" id="val-logor"><a href="#val-logor" class="anchor"></a><code><span class="keyword">val</span> logor : int64 <span>&#45;&gt;</span> int64 <span>&#45;&gt;</span> int64</code></dt><dt class="spec external" id="val-logxor"><a href="#val-logxor" class="anchor"></a><code><span class="keyword">val</span> logxor : int64 <span>&#45;&gt;</span> int64 <span>&#45;&gt;</span> int64</code></dt></dl><dl><dt class="spec value" id="val-lognot"><a href="#val-lognot" class="anchor"></a><code><span class="keyword">val</span> lognot : int64 <span>&#45;&gt;</span> int64</code></dt></dl><dl><dt class="spec external" id="val-shift_left"><a href="#val-shift_left" class="anchor"></a><code><span class="keyword">val</span> shift_left : int64 <span>&#45;&gt;</span> int <span>&#45;&gt;</span> int64</code></dt><dt class="spec external" id="val-shift_right"><a href="#val-shift_right" class="anchor"></a><code><span class="keyword">val</span> shift_right : int64 <span>&#45;&gt;</span> int <span>&#45;&gt;</span> int64</code></dt><dt class="spec external" id="val-shift_right_logical"><a href="#val-shift_right_logical" class="anchor"></a><code><span class="keyword">val</span> shift_right_logical : int64 <span>&#45;&gt;</span> int <span>&#45;&gt;</span> int64</code></dt><dt class="spec external" id="val-of_int"><a href="#val-of_int" class="anchor"></a><code><span class="keyword">val</span> of_int : int <span>&#45;&gt;</span> int64</code></dt><dt class="spec external" id="val-to_int"><a href="#val-to_int" class="anchor"></a><code><span class="keyword">val</span> to_int : int64 <span>&#45;&gt;</span> int</code></dt></dl><dl><dt class="spec value" id="val-unsigned_to_int"><a href="#val-unsigned_to_int" class="anchor"></a><code><span class="keyword">val</span> unsigned_to_int : int64 <span>&#45;&gt;</span> int option</code></dt></dl><dl><dt class="spec external" id="val-of_float"><a href="#val-of_float" class="anchor"></a><code><span class="keyword">val</span> of_float : float <span>&#45;&gt;</span> int64</code></dt><dt class="spec external" id="val-to_float"><a href="#val-to_float" class="anchor"></a><code><span class="keyword">val</span> to_float : int64 <span>&#45;&gt;</span> float</code></dt><dt class="spec external" id="val-of_int32"><a href="#val-of_int32" class="anchor"></a><code><span class="keyword">val</span> of_int32 : int32 <span>&#45;&gt;</span> int64</code></dt><dt class="spec external" id="val-to_int32"><a href="#val-to_int32" class="anchor"></a><code><span class="keyword">val</span> to_int32 : int64 <span>&#45;&gt;</span> int32</code></dt><dt class="spec external" id="val-of_nativeint"><a href="#val-of_nativeint" class="anchor"></a><code><span class="keyword">val</span> of_nativeint : nativeint <span>&#45;&gt;</span> int64</code></dt><dt class="spec external" id="val-to_nativeint"><a href="#val-to_nativeint" class="anchor"></a><code><span class="keyword">val</span> to_nativeint : int64 <span>&#45;&gt;</span> nativeint</code></dt><dt class="spec external" id="val-of_string"><a href="#val-of_string" class="anchor"></a><code><span class="keyword">val</span> of_string : string <span>&#45;&gt;</span> int64</code></dt></dl><dl><dt class="spec value" id="val-of_string_opt"><a href="#val-of_string_opt" class="anchor"></a><code><span class="keyword">val</span> of_string_opt : string <span>&#45;&gt;</span> int64 option</code></dt><dt class="spec value" id="val-to_string"><a href="#val-to_string" class="anchor"></a><code><span class="keyword">val</span> to_string : int64 <span>&#45;&gt;</span> string</code></dt></dl><dl><dt class="spec external" id="val-bits_of_float"><a href="#val-bits_of_float" class="anchor"></a><code><span class="keyword">val</span> bits_of_float : float <span>&#45;&gt;</span> int64</code></dt><dt class="spec external" id="val-float_of_bits"><a href="#val-float_of_bits" class="anchor"></a><code><span class="keyword">val</span> float_of_bits : int64 <span>&#45;&gt;</span> float</code></dt></dl><dl><dt class="spec type" id="type-t"><a href="#type-t" class="anchor"></a><code><span class="keyword">type</span> t</code><code> = int64</code></dt></dl><dl><dt class="spec value" id="val-compare"><a href="#val-compare" class="anchor"></a><code><span class="keyword">val</span> compare : <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> int</code></dt><dt class="spec value" id="val-unsigned_compare"><a href="#val-unsigned_compare" class="anchor"></a><code><span class="keyword">val</span> unsigned_compare : <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> int</code></dt><dt class="spec value" id="val-equal"><a href="#val-equal" class="anchor"></a><code><span class="keyword">val</span> equal : <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> bool</code></dt></dl><dl><dt class="spec external" id="val-format"><a href="#val-format" class="anchor"></a><code><span class="keyword">val</span> format : string <span>&#45;&gt;</span> int64 <span>&#45;&gt;</span> string</code></dt></dl></details></div></div></div><dl><dt class="spec value" id="val-min"><a href="#val-min" class="anchor"></a><code><span class="keyword">val</span> min : <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a></code></dt><dd><p><code>min x y</code> returns the minimum of the two integers <code>x</code> and <code>y</code>.</p><dl><dt>since</dt><dd>3.0</dd></dl></dd></dl><dl><dt class="spec value" id="val-max"><a href="#val-max" class="anchor"></a><code><span class="keyword">val</span> max : <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a></code></dt><dd><p><code>max x y</code> returns the maximum of the two integers <code>x</code> and <code>y</code>.</p><dl><dt>since</dt><dd>3.0</dd></dl></dd></dl><dl><dt class="spec value" id="val-hash"><a href="#val-hash" class="anchor"></a><code><span class="keyword">val</span> hash : <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> int</code></dt><dd><p><code>hash x</code> computes the hash of <code>x</code>. Like <span class="xref-unresolved" title="unresolved reference to &quot;Stdlib.abs (to_int x)&quot;"><code>Stdlib</code>.abs (to_int x)</span>.</p></dd></dl><dl><dt class="spec value" id="val-sign"><a href="#val-sign" class="anchor"></a><code><span class="keyword">val</span> sign : <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> int</code></dt><dd><p><code>sign x</code> return <code>0</code> if <code>x = 0</code>, <code>-1</code> if <code>x &lt; 0</code> and <code>1</code> if <code>x &gt; 0</code>. Same as <code>compare x zero</code>.</p><dl><dt>since</dt><dd>3.0</dd></dl></dd></dl><dl><dt class="spec value" id="val-pow"><a href="#val-pow" class="anchor"></a><code><span class="keyword">val</span> pow : <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a></code></dt><dd><p><code>pow base exponent</code> returns <code>base</code> raised to the power of <code>exponent</code>. <code>pow x y = x^y</code> for positive integers <code>x</code> and <code>y</code>. Raises <code>Invalid_argument</code> if <code>x = y = 0</code> or <code>y</code> &lt; 0.</p><dl><dt>since</dt><dd>0.11</dd></dl></dd></dl><dl><dt class="spec value" id="val-floor_div"><a href="#val-floor_div" class="anchor"></a><code><span class="keyword">val</span> floor_div : <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a></code></dt><dd><p><code>floor_div x n</code> is integer division rounding towards negative infinity. It satisfies <code>x = m * floor_div x n + rem x n</code>.</p><dl><dt>since</dt><dd>3.0</dd></dl></dd></dl><dl><dt class="spec type" id="type-printer"><a href="#type-printer" class="anchor"></a><code><span class="keyword">type</span> 'a printer</code><code> = Stdlib.Format.formatter <span>&#45;&gt;</span> <span class="type-var">'a</span> <span>&#45;&gt;</span> unit</code></dt><dt class="spec type" id="type-random_gen"><a href="#type-random_gen" class="anchor"></a><code><span class="keyword">type</span> 'a random_gen</code><code> = Stdlib.Random.State.t <span>&#45;&gt;</span> <span class="type-var">'a</span></code></dt><dt class="spec type" id="type-iter"><a href="#type-iter" class="anchor"></a><code><span class="keyword">type</span> 'a iter</code><code> = (<span class="type-var">'a</span> <span>&#45;&gt;</span> unit) <span>&#45;&gt;</span> unit</code></dt></dl><dl><dt class="spec value" id="val-range_by"><a href="#val-range_by" class="anchor"></a><code><span class="keyword">val</span> range_by : step:<a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a> <a href="index.html#type-iter">iter</a></code></dt><dd><p><code>range_by ~step i j</code> iterates on integers from <code>i</code> to <code>j</code> included, where the difference between successive elements is <code>step</code>. Use a negative <code>step</code> for a decreasing list.</p><dl><dt>raises Invalid_argument</dt><dd><p>if <code>step=0</code>.</p></dd></dl><dl><dt>since</dt><dd>3.0</dd></dl></dd></dl><dl><dt class="spec value" id="val-range"><a href="#val-range" class="anchor"></a><code><span class="keyword">val</span> range : <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a> <a href="index.html#type-iter">iter</a></code></dt><dd><p><code>range i j</code> iterates on integers from <code>i</code> to <code>j</code> included . It works both for decreasing and increasing ranges.</p><dl><dt>since</dt><dd>3.0</dd></dl></dd></dl><dl><dt class="spec value" id="val-range'"><a href="#val-range'" class="anchor"></a><code><span class="keyword">val</span> range' : <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a> <a href="index.html#type-iter">iter</a></code></dt><dd><p><code>range' i j</code> is like <a href="index.html#val-range"><code>range</code></a> but the second bound <code>j</code> is excluded. For instance <code>range' 0 5 = Iter.of_list [0;1;2;3;4]</code>.</p><dl><dt>since</dt><dd>3.0</dd></dl></dd></dl><dl><dt class="spec value" id="val-random"><a href="#val-random" class="anchor"></a><code><span class="keyword">val</span> random : <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a> <a href="index.html#type-random_gen">random_gen</a></code></dt><dt class="spec value" id="val-random_small"><a href="#val-random_small" class="anchor"></a><code><span class="keyword">val</span> random_small : <a href="index.html#type-t">t</a> <a href="index.html#type-random_gen">random_gen</a></code></dt><dt class="spec value" id="val-random_range"><a href="#val-random_range" class="anchor"></a><code><span class="keyword">val</span> random_range : <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a> <a href="index.html#type-random_gen">random_gen</a></code></dt></dl><section><header><h3 id="conversion"><a href="#conversion" class="anchor"></a>Conversion</h3></header><dl><dt class="spec value" id="val-of_string"><a href="#val-of_string" class="anchor"></a><code><span class="keyword">val</span> of_string : string <span>&#45;&gt;</span> <a href="index.html#type-t">t</a> option</code></dt><dd><p><code>of_string s</code> is the safe version of <a href="index.html#val-of_string_exn"><code>of_string_exn</code></a>. Like <a href="index.html#val-of_string_exn"><code>of_string_exn</code></a>, but return <code>None</code> instead of raising.</p></dd></dl><dl><dt class="spec value" id="val-of_string_opt"><a href="#val-of_string_opt" class="anchor"></a><code><span class="keyword">val</span> of_string_opt : string <span>&#45;&gt;</span> <a href="index.html#type-t">t</a> option</code></dt><dd><p><code>of_string_opt s</code> is an alias to <a href="index.html#val-of_string"><code>of_string</code></a>.</p><dl><dt>since</dt><dd>2.1</dd></dl></dd></dl><dl><dt class="spec value" id="val-of_string_exn"><a href="#val-of_string_exn" class="anchor"></a><code><span class="keyword">val</span> of_string_exn : string <span>&#45;&gt;</span> <a href="index.html#type-t">t</a></code></dt><dd><p><code>of_string_exn s</code> converts the given string <code>s</code> into a 64-bit integer. Alias to <span class="xref-unresolved" title="unresolved reference to &quot;Int64.of_string&quot;"><code>Int64</code>.of_string</span>. The string is read in decimal (by default, or if the string begins with <code>0u</code>) or in hexadecimal, octal or binary if the string begins with <code>0x</code>, <code>0o</code> or <code>0b</code> respectively.</p><p>The <code>0u</code> prefix reads the input as an unsigned integer in the range <code>[0, 2*CCInt64.max_int+1]</code>. If the input exceeds <a href="index.html#val-max_int"><code>CCInt64.max_int</code></a> it is converted to the signed integer <code>CCInt64.min_int + input - CCInt64.max_int - 1</code>.</p><p>The <code>_</code> (underscore) character can appear anywhere in the string and is ignored. Raise <code>Failure &quot;Int64.of_string&quot;</code> if the given string is not a valid representation of an integer, or if the integer represented exceeds the range of integers representable in type <code>int64</code>.</p></dd></dl><dl><dt class="spec value" id="val-to_string_binary"><a href="#val-to_string_binary" class="anchor"></a><code><span class="keyword">val</span> to_string_binary : <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> string</code></dt><dd><p><code>to_string_binary x</code> returns the string representation of the integer <code>x</code>, in binary.</p><dl><dt>since</dt><dd>3.0</dd></dl></dd></dl></section><section><header><h3 id="printing"><a href="#printing" class="anchor"></a>Printing</h3></header><dl><dt class="spec value" id="val-pp"><a href="#val-pp" class="anchor"></a><code><span class="keyword">val</span> pp : <a href="index.html#type-t">t</a> <a href="index.html#type-printer">printer</a></code></dt><dd><p><code>pp ppf x</code> prints the integer <code>x</code> on <code>ppf</code>.</p><dl><dt>since</dt><dd>3.0</dd></dl></dd></dl><dl><dt class="spec value" id="val-pp_binary"><a href="#val-pp_binary" class="anchor"></a><code><span class="keyword">val</span> pp_binary : <a href="index.html#type-t">t</a> <a href="index.html#type-printer">printer</a></code></dt><dd><p><code>pp_binary ppf x</code> prints <code>x</code> on <code>ppf</code>. Print as &quot;0b00101010&quot;.</p><dl><dt>since</dt><dd>3.0</dd></dl></dd></dl></section><section><header><h3 id="infix-operators"><a href="#infix-operators" class="anchor"></a>Infix Operators</h3></header><aside><p>Infix operators</p><dl><dt>since</dt><dd>2.1</dd></dl></aside><div class="spec module" id="module-Infix"><a href="#module-Infix" class="anchor"></a><code><span class="keyword">module</span> <a href="Infix/index.html">Infix</a> : <span class="keyword">sig</span> ... <span class="keyword">end</span></code></div><div><div class="spec include"><div class="doc"><details open="open"><summary><span class="def"><code><span class="keyword">include</span> <span class="keyword">module</span> <span class="keyword">type</span> <span class="keyword">of</span> <a href="index.html#module-Infix">Infix</a></code></span></summary><dl><dt class="spec value" id="val-(+)"><a href="#val-(+)" class="anchor"></a><code><span class="keyword">val</span> (+) : <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a></code></dt><dd><p><code>x + y</code> is the sum of <code>x</code> and <code>y</code>. Addition.</p></dd></dl><dl><dt class="spec value" id="val-(-)"><a href="#val-(-)" class="anchor"></a><code><span class="keyword">val</span> (-) : <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a></code></dt><dd><p><code>x - y</code> is the difference of <code>x</code> and <code>y</code>. Subtraction.</p></dd></dl><dl><dt class="spec value" id="val-(~-)"><a href="#val-(~-)" class="anchor"></a><code><span class="keyword">val</span> (~-) : <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a></code></dt><dd><p><code>~- x</code> is the negation of <code>x</code>. Unary negation.</p></dd></dl><dl><dt class="spec value" id="val-(*)"><a href="#val-(*)" class="anchor"></a><code><span class="keyword">val</span> (*) : <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a></code></dt><dd><p><code> x * y</code> is the product of <code>x</code> and <code>y</code>. Multiplication.</p></dd></dl><dl><dt class="spec value" id="val-(/)"><a href="#val-(/)" class="anchor"></a><code><span class="keyword">val</span> (/) : <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a></code></dt><dd><p><code>x / y</code> is the integer quotient of <code>x</code> and <code>y</code>. Integer division. Raise <code>Division_by_zero</code> if the second argument <code>y</code> is zero. This division rounds the real quotient of its arguments towards zero, as specified for <span class="xref-unresolved" title="unresolved reference to &quot;Stdlib.(/)&quot;"><code>Stdlib</code>.(/)</span>.</p></dd></dl><dl><dt class="spec value" id="val-(mod)"><a href="#val-(mod)" class="anchor"></a><code><span class="keyword">val</span> (mod) : <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a></code></dt><dd><p><code>x mod y</code> is the integer remainder of <code>x / y</code>. If <code>y &lt;&gt; zero</code>, the result of <code>x mod y</code> satisfies the following properties: <code>zero &lt;= x mod y &lt; abs y</code> and <code>x = ((x / y) * y) + (x mod y)</code>. If <code>y = 0</code>, <code>x mod y</code> raises <code>Division_by_zero</code>.</p></dd></dl><dl><dt class="spec value" id="val-(**)"><a href="#val-(**)" class="anchor"></a><code><span class="keyword">val</span> (**) : <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a></code></dt><dd><p>Alias to <a href="index.html#val-pow"><code>pow</code></a></p><dl><dt>since</dt><dd>3.0</dd></dl></dd></dl><dl><dt class="spec value" id="val-(--)"><a href="#val-(--)" class="anchor"></a><code><span class="keyword">val</span> (--) : <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a> <a href="index.html#type-iter">iter</a></code></dt><dd><p>Alias to <a href="index.html#val-range"><code>range</code></a>.</p><dl><dt>since</dt><dd>3.0</dd></dl></dd></dl><dl><dt class="spec value" id="val-(--^)"><a href="#val-(--^)" class="anchor"></a><code><span class="keyword">val</span> (--^) : <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a> <a href="index.html#type-iter">iter</a></code></dt><dd><p>Alias to <a href="index.html#val-range'"><code>range'</code></a>.</p><dl><dt>since</dt><dd>3.0</dd></dl></dd></dl><dl><dt class="spec value" id="val-(land)"><a href="#val-(land)" class="anchor"></a><code><span class="keyword">val</span> (land) : <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a></code></dt><dd><p><code>x land y</code> is the bitwise logical and of <code>x</code> and <code>y</code>.</p></dd></dl><dl><dt class="spec value" id="val-(lor)"><a href="#val-(lor)" class="anchor"></a><code><span class="keyword">val</span> (lor) : <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a></code></dt><dd><p><code>x lor y</code> is the bitwise logical or of <code>x</code> and <code>y</code>.</p></dd></dl><dl><dt class="spec value" id="val-(lxor)"><a href="#val-(lxor)" class="anchor"></a><code><span class="keyword">val</span> (lxor) : <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a></code></dt><dd><p><code>x lxor y</code> is the bitwise logical exclusive or of <code>x</code> and <code>y</code>.</p></dd></dl><dl><dt class="spec value" id="val-(lnot)"><a href="#val-(lnot)" class="anchor"></a><code><span class="keyword">val</span> (lnot) : <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a></code></dt><dd><p><code>lnot x</code> is the bitwise logical negation of <code>x</code> (the bits of <code>x</code> are inverted).</p></dd></dl><dl><dt class="spec value" id="val-(lsl)"><a href="#val-(lsl)" class="anchor"></a><code><span class="keyword">val</span> (lsl) : <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> int <span>&#45;&gt;</span> <a href="index.html#type-t">t</a></code></dt><dd><p><code> x lsl y</code> shifts <code>x</code> to the left by <code>y</code> bits, filling in with zeroes. The result is unspecified if <code>y &lt; 0</code> or <code>y &gt;= 64</code>.</p></dd></dl><dl><dt class="spec value" id="val-(lsr)"><a href="#val-(lsr)" class="anchor"></a><code><span class="keyword">val</span> (lsr) : <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> int <span>&#45;&gt;</span> <a href="index.html#type-t">t</a></code></dt><dd><p><code>x lsr y</code> shifts <code>x</code> to the right by <code>y</code> bits. This is a logical shift: zeroes are inserted in the vacated bits regardless of the sign of <code>x</code>. The result is unspecified if <code>y &lt; 0</code> or <code>y &gt;= 64</code>.</p></dd></dl><dl><dt class="spec value" id="val-(asr)"><a href="#val-(asr)" class="anchor"></a><code><span class="keyword">val</span> (asr) : <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> int <span>&#45;&gt;</span> <a href="index.html#type-t">t</a></code></dt><dd><p><code>x asr y</code> shifts <code>x</code> to the right by <code>y</code> bits. This is an arithmetic shift: the sign bit of <code>x</code> is replicated and inserted in the vacated bits. The result is unspecified if <code>y &lt; 0</code> or <code>y &gt;= 64</code>.</p></dd></dl><dl><dt class="spec value" id="val-(=)"><a href="#val-(=)" class="anchor"></a><code><span class="keyword">val</span> (=) : <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> bool</code></dt><dt class="spec value" id="val-(&lt;&gt;)"><a href="#val-(&lt;&gt;)" class="anchor"></a><code><span class="keyword">val</span> (&lt;&gt;) : <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> bool</code></dt><dt class="spec value" id="val-(&gt;)"><a href="#val-(&gt;)" class="anchor"></a><code><span class="keyword">val</span> (&gt;) : <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> bool</code></dt><dt class="spec value" id="val-(&gt;=)"><a href="#val-(&gt;=)" class="anchor"></a><code><span class="keyword">val</span> (&gt;=) : <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> bool</code></dt><dt class="spec value" id="val-(&lt;=)"><a href="#val-(&lt;=)" class="anchor"></a><code><span class="keyword">val</span> (&lt;=) : <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> bool</code></dt><dt class="spec value" id="val-(&lt;)"><a href="#val-(&lt;)" class="anchor"></a><code><span class="keyword">val</span> (&lt;) : <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> <a href="index.html#type-t">t</a> <span>&#45;&gt;</span> bool</code></dt></dl></details></div></div></div></section></div></body></html>