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authorsanine <sanine.not@pm.me>2023-03-11 15:58:20 -0600
committersanine <sanine.not@pm.me>2023-03-11 15:58:20 -0600
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+<!DOCTYPE html>
+<html>
+<head>
+<title>ffi.* API Functions</title>
+<meta charset="utf-8">
+<meta name="Copyright" content="Copyright (C) 2005-2022">
+<meta name="Language" content="en">
+<link rel="stylesheet" type="text/css" href="bluequad.css" media="screen">
+<link rel="stylesheet" type="text/css" href="bluequad-print.css" media="print">
+<style type="text/css">
+table.abitable { width: 30em; line-height: 1.2; }
+tr.abihead td { font-weight: bold; }
+td.abiparam { font-weight: bold; width: 6em; }
+</style>
+</head>
+<body>
+<div id="site">
+<a href="https://luajit.org"><span>Lua<span id="logo">JIT</span></span></a>
+</div>
+<div id="head">
+<h1><tt>ffi.*</tt> API Functions</h1>
+</div>
+<div id="nav">
+<ul><li>
+<a href="luajit.html">LuaJIT</a>
+<ul><li>
+<a href="https://luajit.org/download.html">Download <span class="ext">&raquo;</span></a>
+</li><li>
+<a href="install.html">Installation</a>
+</li><li>
+<a href="running.html">Running</a>
+</li></ul>
+</li><li>
+<a href="extensions.html">Extensions</a>
+<ul><li>
+<a href="ext_ffi.html">FFI Library</a>
+<ul><li>
+<a href="ext_ffi_tutorial.html">FFI Tutorial</a>
+</li><li>
+<a class="current" href="ext_ffi_api.html">ffi.* API</a>
+</li><li>
+<a href="ext_ffi_semantics.html">FFI Semantics</a>
+</li></ul>
+</li><li>
+<a href="ext_buffer.html">String Buffers</a>
+</li><li>
+<a href="ext_jit.html">jit.* Library</a>
+</li><li>
+<a href="ext_c_api.html">Lua/C API</a>
+</li><li>
+<a href="ext_profiler.html">Profiler</a>
+</li></ul>
+</li><li>
+<a href="status.html">Status</a>
+</li><li>
+<a href="faq.html">FAQ</a>
+</li><li>
+<a href="https://luajit.org/list.html">Mailing List <span class="ext">&raquo;</span></a>
+</li></ul>
+</div>
+<div id="main">
+<p>
+This page describes the API functions provided by the FFI library in
+detail. It's recommended to read through the
+<a href="ext_ffi.html">introduction</a> and the
+<a href="ext_ffi_tutorial.html">FFI tutorial</a> first.
+</p>
+
+<h2 id="glossary">Glossary</h2>
+<ul>
+<li><b>cdecl</b> &mdash; An abstract C&nbsp;type declaration (a Lua
+string).</li>
+<li><b>ctype</b> &mdash; A C&nbsp;type object. This is a special kind of
+<b>cdata</b> returned by <tt>ffi.typeof()</tt>. It serves as a
+<b>cdata</b> <a href="#ffi_new">constructor</a> when called.</li>
+<li><b>cdata</b> &mdash; A C&nbsp;data object. It holds a value of the
+corresponding <b>ctype</b>.</li>
+<li><b>ct</b> &mdash; A C&nbsp;type specification which can be used for
+most of the API functions. Either a <b>cdecl</b>, a <b>ctype</b> or a
+<b>cdata</b> serving as a template type.</li>
+<li><b>cb</b> &mdash; A callback object. This is a C&nbsp;data object
+holding a special function pointer. Calling this function from
+C&nbsp;code runs an associated Lua function.</li>
+<li><b>VLA</b> &mdash; A variable-length array is declared with a
+<tt>?</tt> instead of the number of elements, e.g. <tt>"int[?]"</tt>.
+The number of elements (<tt>nelem</tt>) must be given when it's
+<a href="#ffi_new">created</a>.</li>
+<li><b>VLS</b> &mdash; A variable-length struct is a <tt>struct</tt> C
+type where the last element is a <b>VLA</b>. The same rules for
+declaration and creation apply.</li>
+</ul>
+
+<h2 id="decl">Declaring and Accessing External Symbols</h2>
+<p>
+External symbols must be declared first and can then be accessed by
+indexing a <a href="ext_ffi_semantics.html#clib">C&nbsp;library
+namespace</a>, which automatically binds the symbol to a specific
+library.
+</p>
+
+<h3 id="ffi_cdef"><tt>ffi.cdef(def)</tt></h3>
+<p>
+Adds multiple C&nbsp;declarations for types or external symbols (named
+variables or functions). <tt>def</tt> must be a Lua string. It's
+recommended to use the syntactic sugar for string arguments as
+follows:
+</p>
+<pre class="code">
+ffi.cdef[[
+<span style="color:#00a000;">typedef struct foo { int a, b; } foo_t; // Declare a struct and typedef.
+int dofoo(foo_t *f, int n); /* Declare an external C function. */</span>
+]]
+</pre>
+<p>
+The contents of the string (the part in green above) must be a
+sequence of
+<a href="ext_ffi_semantics.html#clang">C&nbsp;declarations</a>,
+separated by semicolons. The trailing semicolon for a single
+declaration may be omitted.
+</p>
+<p>
+Please note, that external symbols are only <em>declared</em>, but they
+are <em>not bound</em> to any specific address, yet. Binding is
+achieved with C&nbsp;library namespaces (see below).
+</p>
+<p style="color: #c00000;">
+C&nbsp;declarations are not passed through a C&nbsp;pre-processor,
+yet. No pre-processor tokens are allowed, except for
+<tt>#pragma&nbsp;pack</tt>. Replace <tt>#define</tt> in existing
+C&nbsp;header files with <tt>enum</tt>, <tt>static&nbsp;const</tt>
+or <tt>typedef</tt> and/or pass the files through an external
+C&nbsp;pre-processor (once). Be careful not to include unneeded or
+redundant declarations from unrelated header files.
+</p>
+
+<h3 id="ffi_C"><tt>ffi.C</tt></h3>
+<p>
+This is the default C&nbsp;library namespace &mdash; note the
+uppercase <tt>'C'</tt>. It binds to the default set of symbols or
+libraries on the target system. These are more or less the same as a
+C&nbsp;compiler would offer by default, without specifying extra link
+libraries.
+</p>
+<p>
+On POSIX systems, this binds to symbols in the default or global
+namespace. This includes all exported symbols from the executable and
+any libraries loaded into the global namespace. This includes at least
+<tt>libc</tt>, <tt>libm</tt>, <tt>libdl</tt> (on Linux),
+<tt>libgcc</tt> (if compiled with GCC), as well as any exported
+symbols from the Lua/C&nbsp;API provided by LuaJIT itself.
+</p>
+<p>
+On Windows systems, this binds to symbols exported from the
+<tt>*.exe</tt>, the <tt>lua51.dll</tt> (i.e. the Lua/C&nbsp;API
+provided by LuaJIT itself), the C&nbsp;runtime library LuaJIT was linked
+with (<tt>msvcrt*.dll</tt>), <tt>kernel32.dll</tt>,
+<tt>user32.dll</tt> and <tt>gdi32.dll</tt>.
+</p>
+
+<h3 id="ffi_load"><tt>clib = ffi.load(name [,global])</tt></h3>
+<p>
+This loads the dynamic library given by <tt>name</tt> and returns
+a new C&nbsp;library namespace which binds to its symbols. On POSIX
+systems, if <tt>global</tt> is <tt>true</tt>, the library symbols are
+loaded into the global namespace, too.
+</p>
+<p>
+If <tt>name</tt> is a path, the library is loaded from this path.
+Otherwise <tt>name</tt> is canonicalized in a system-dependent way and
+searched in the default search path for dynamic libraries:
+</p>
+<p>
+On POSIX systems, if the name contains no dot, the extension
+<tt>.so</tt> is appended. Also, the <tt>lib</tt> prefix is prepended
+if necessary. So <tt>ffi.load("z")</tt> looks for <tt>"libz.so"</tt>
+in the default shared library search path.
+</p>
+<p>
+On Windows systems, if the name contains no dot, the extension
+<tt>.dll</tt> is appended. So <tt>ffi.load("ws2_32")</tt> looks for
+<tt>"ws2_32.dll"</tt> in the default DLL search path.
+</p>
+
+<h2 id="create">Creating cdata Objects</h2>
+<p>
+The following API functions create cdata objects (<tt>type()</tt>
+returns <tt>"cdata"</tt>). All created cdata objects are
+<a href="ext_ffi_semantics.html#gc">garbage collected</a>.
+</p>
+
+<h3 id="ffi_new"><tt>cdata = ffi.new(ct [,nelem] [,init...])<br>
+cdata = <em>ctype</em>([nelem,] [init...])</tt></h3>
+<p>
+Creates a cdata object for the given <tt>ct</tt>. VLA/VLS types
+require the <tt>nelem</tt> argument. The second syntax uses a ctype as
+a constructor and is otherwise fully equivalent.
+</p>
+<p>
+The cdata object is initialized according to the
+<a href="ext_ffi_semantics.html#init">rules for initializers</a>,
+using the optional <tt>init</tt> arguments. Excess initializers cause
+an error.
+</p>
+<p>
+Performance notice: if you want to create many objects of one kind,
+parse the cdecl only once and get its ctype with
+<tt>ffi.typeof()</tt>. Then use the ctype as a constructor repeatedly.
+</p>
+<p style="font-size: 8pt;">
+Please note, that an anonymous <tt>struct</tt> declaration implicitly
+creates a new and distinguished ctype every time you use it for
+<tt>ffi.new()</tt>. This is probably <b>not</b> what you want,
+especially if you create more than one cdata object. Different anonymous
+<tt>structs</tt> are not considered assignment-compatible by the
+C&nbsp;standard, even though they may have the same fields! Also, they
+are considered different types by the JIT-compiler, which may cause an
+excessive number of traces. It's strongly suggested to either declare
+a named <tt>struct</tt> or <tt>typedef</tt> with <tt>ffi.cdef()</tt>
+or to create a single ctype object for an anonymous <tt>struct</tt>
+with <tt>ffi.typeof()</tt>.
+</p>
+
+<h3 id="ffi_typeof"><tt>ctype = ffi.typeof(ct)</tt></h3>
+<p>
+Creates a ctype object for the given <tt>ct</tt>.
+</p>
+<p>
+This function is especially useful to parse a cdecl only once and then
+use the resulting ctype object as a <a href="#ffi_new">constructor</a>.
+</p>
+
+<h3 id="ffi_cast"><tt>cdata = ffi.cast(ct, init)</tt></h3>
+<p>
+Creates a scalar cdata object for the given <tt>ct</tt>. The cdata
+object is initialized with <tt>init</tt> using the "cast" variant of
+the <a href="ext_ffi_semantics.html#convert">C&nbsp;type conversion
+rules</a>.
+</p>
+<p>
+This functions is mainly useful to override the pointer compatibility
+checks or to convert pointers to addresses or vice versa.
+</p>
+
+<h3 id="ffi_metatype"><tt>ctype = ffi.metatype(ct, metatable)</tt></h3>
+<p>
+Creates a ctype object for the given <tt>ct</tt> and associates it with
+a metatable. Only <tt>struct</tt>/<tt>union</tt> types, complex numbers
+and vectors are allowed. Other types may be wrapped in a
+<tt>struct</tt>, if needed.
+</p>
+<p>
+The association with a metatable is permanent and cannot be changed
+afterwards. Neither the contents of the <tt>metatable</tt> nor the
+contents of an <tt>__index</tt> table (if any) may be modified
+afterwards. The associated metatable automatically applies to all uses
+of this type, no matter how the objects are created or where they
+originate from. Note that predefined operations on types have
+precedence (e.g. declared field names cannot be overridden).
+</p>
+<p>
+All standard Lua metamethods are implemented. These are called directly,
+without shortcuts, and on any mix of types. For binary operations, the
+left operand is checked first for a valid ctype metamethod. The
+<tt>__gc</tt> metamethod only applies to <tt>struct</tt>/<tt>union</tt>
+types and performs an implicit <a href="#ffi_gc"><tt>ffi.gc()</tt></a>
+call during creation of an instance.
+</p>
+
+<h3 id="ffi_gc"><tt>cdata = ffi.gc(cdata, finalizer)</tt></h3>
+<p>
+Associates a finalizer with a pointer or aggregate cdata object. The
+cdata object is returned unchanged.
+</p>
+<p>
+This function allows safe integration of unmanaged resources into the
+automatic memory management of the LuaJIT garbage collector. Typical
+usage:
+</p>
+<pre class="code">
+local p = ffi.gc(ffi.C.malloc(n), ffi.C.free)
+...
+p = nil -- Last reference to p is gone.
+-- GC will eventually run finalizer: ffi.C.free(p)
+</pre>
+<p>
+A cdata finalizer works like the <tt>__gc</tt> metamethod for userdata
+objects: when the last reference to a cdata object is gone, the
+associated finalizer is called with the cdata object as an argument. The
+finalizer can be a Lua function or a cdata function or cdata function
+pointer. An existing finalizer can be removed by setting a <tt>nil</tt>
+finalizer, e.g. right before explicitly deleting a resource:
+</p>
+<pre class="code">
+ffi.C.free(ffi.gc(p, nil)) -- Manually free the memory.
+</pre>
+
+<h2 id="info">C&nbsp;Type Information</h2>
+<p>
+The following API functions return information about C&nbsp;types.
+They are most useful for inspecting cdata objects.
+</p>
+
+<h3 id="ffi_sizeof"><tt>size = ffi.sizeof(ct [,nelem])</tt></h3>
+<p>
+Returns the size of <tt>ct</tt> in bytes. Returns <tt>nil</tt> if
+the size is not known (e.g. for <tt>"void"</tt> or function types).
+Requires <tt>nelem</tt> for VLA/VLS types, except for cdata objects.
+</p>
+
+<h3 id="ffi_alignof"><tt>align = ffi.alignof(ct)</tt></h3>
+<p>
+Returns the minimum required alignment for <tt>ct</tt> in bytes.
+</p>
+
+<h3 id="ffi_offsetof"><tt>ofs [,bpos,bsize] = ffi.offsetof(ct, field)</tt></h3>
+<p>
+Returns the offset (in bytes) of <tt>field</tt> relative to the start
+of <tt>ct</tt>, which must be a <tt>struct</tt>. Additionally returns
+the position and the field size (in bits) for bit fields.
+</p>
+
+<h3 id="ffi_istype"><tt>status = ffi.istype(ct, obj)</tt></h3>
+<p>
+Returns <tt>true</tt> if <tt>obj</tt> has the C&nbsp;type given by
+<tt>ct</tt>. Returns <tt>false</tt> otherwise.
+</p>
+<p>
+C&nbsp;type qualifiers (<tt>const</tt> etc.) are ignored. Pointers are
+checked with the standard pointer compatibility rules, but without any
+special treatment for <tt>void&nbsp;*</tt>. If <tt>ct</tt> specifies a
+<tt>struct</tt>/<tt>union</tt>, then a pointer to this type is accepted,
+too. Otherwise the types must match exactly.
+</p>
+<p>
+Note: this function accepts all kinds of Lua objects for the
+<tt>obj</tt> argument, but always returns <tt>false</tt> for non-cdata
+objects.
+</p>
+
+<h2 id="util">Utility Functions</h2>
+
+<h3 id="ffi_errno"><tt>err = ffi.errno([newerr])</tt></h3>
+<p>
+Returns the error number set by the last C&nbsp;function call which
+indicated an error condition. If the optional <tt>newerr</tt> argument
+is present, the error number is set to the new value and the previous
+value is returned.
+</p>
+<p>
+This function offers a portable and OS-independent way to get and set the
+error number. Note that only <em>some</em> C&nbsp;functions set the error
+number. And it's only significant if the function actually indicated an
+error condition (e.g. with a return value of <tt>-1</tt> or
+<tt>NULL</tt>). Otherwise, it may or may not contain any previously set
+value.
+</p>
+<p>
+You're advised to call this function only when needed and as close as
+possible after the return of the related C&nbsp;function. The
+<tt>errno</tt> value is preserved across hooks, memory allocations,
+invocations of the JIT compiler and other internal VM activity. The same
+applies to the value returned by <tt>GetLastError()</tt> on Windows, but
+you need to declare and call it yourself.
+</p>
+
+<h3 id="ffi_string"><tt>str = ffi.string(ptr [,len])</tt></h3>
+<p>
+Creates an interned Lua string from the data pointed to by
+<tt>ptr</tt>.
+</p>
+<p>
+If the optional argument <tt>len</tt> is missing, <tt>ptr</tt> is
+converted to a <tt>"char&nbsp;*"</tt> and the data is assumed to be
+zero-terminated. The length of the string is computed with
+<tt>strlen()</tt>.
+</p>
+<p>
+Otherwise <tt>ptr</tt> is converted to a <tt>"void&nbsp;*"</tt> and
+<tt>len</tt> gives the length of the data. The data may contain
+embedded zeros and need not be byte-oriented (though this may cause
+endianess issues).
+</p>
+<p>
+This function is mainly useful to convert (temporary)
+<tt>"const&nbsp;char&nbsp;*"</tt> pointers returned by
+C&nbsp;functions to Lua strings and store them or pass them to other
+functions expecting a Lua string. The Lua string is an (interned) copy
+of the data and bears no relation to the original data area anymore.
+Lua strings are 8&nbsp;bit clean and may be used to hold arbitrary,
+non-character data.
+</p>
+<p>
+Performance notice: it's faster to pass the length of the string, if
+it's known. E.g. when the length is returned by a C&nbsp;call like
+<tt>sprintf()</tt>.
+</p>
+
+<h3 id="ffi_copy"><tt>ffi.copy(dst, src, len)<br>
+ffi.copy(dst, str)</tt></h3>
+<p>
+Copies the data pointed to by <tt>src</tt> to <tt>dst</tt>.
+<tt>dst</tt> is converted to a <tt>"void&nbsp;*"</tt> and <tt>src</tt>
+is converted to a <tt>"const void&nbsp;*"</tt>.
+</p>
+<p>
+In the first syntax, <tt>len</tt> gives the number of bytes to copy.
+Caveat: if <tt>src</tt> is a Lua string, then <tt>len</tt> must not
+exceed <tt>#src+1</tt>.
+</p>
+<p>
+In the second syntax, the source of the copy must be a Lua string. All
+bytes of the string <em>plus a zero-terminator</em> are copied to
+<tt>dst</tt> (i.e. <tt>#src+1</tt> bytes).
+</p>
+<p>
+Performance notice: <tt>ffi.copy()</tt> may be used as a faster
+(inlinable) replacement for the C&nbsp;library functions
+<tt>memcpy()</tt>, <tt>strcpy()</tt> and <tt>strncpy()</tt>.
+</p>
+
+<h3 id="ffi_fill"><tt>ffi.fill(dst, len [,c])</tt></h3>
+<p>
+Fills the data pointed to by <tt>dst</tt> with <tt>len</tt> constant
+bytes, given by <tt>c</tt>. If <tt>c</tt> is omitted, the data is
+zero-filled.
+</p>
+<p>
+Performance notice: <tt>ffi.fill()</tt> may be used as a faster
+(inlinable) replacement for the C&nbsp;library function
+<tt>memset(dst,&nbsp;c,&nbsp;len)</tt>. Please note the different
+order of arguments!
+</p>
+
+<h2 id="target">Target-specific Information</h2>
+
+<h3 id="ffi_abi"><tt>status = ffi.abi(param)</tt></h3>
+<p>
+Returns <tt>true</tt> if <tt>param</tt> (a Lua string) applies for the
+target ABI (Application Binary Interface). Returns <tt>false</tt>
+otherwise. The following parameters are currently defined:
+</p>
+<table class="abitable">
+<tr class="abihead">
+<td class="abiparam">Parameter</td>
+<td class="abidesc">Description</td>
+</tr>
+<tr class="odd separate">
+<td class="abiparam">32bit</td><td class="abidesc">32 bit architecture</td></tr>
+<tr class="even">
+<td class="abiparam">64bit</td><td class="abidesc">64 bit architecture</td></tr>
+<tr class="odd separate">
+<td class="abiparam">le</td><td class="abidesc">Little-endian architecture</td></tr>
+<tr class="even">
+<td class="abiparam">be</td><td class="abidesc">Big-endian architecture</td></tr>
+<tr class="odd separate">
+<td class="abiparam">fpu</td><td class="abidesc">Target has a hardware FPU</td></tr>
+<tr class="even">
+<td class="abiparam">softfp</td><td class="abidesc">softfp calling conventions</td></tr>
+<tr class="odd">
+<td class="abiparam">hardfp</td><td class="abidesc">hardfp calling conventions</td></tr>
+<tr class="even separate">
+<td class="abiparam">eabi</td><td class="abidesc">EABI variant of the standard ABI</td></tr>
+<tr class="odd">
+<td class="abiparam">win</td><td class="abidesc">Windows variant of the standard ABI</td></tr>
+<tr class="even">
+<td class="abiparam">uwp</td><td class="abidesc">Universal Windows Platform</td></tr>
+<tr class="odd">
+<td class="abiparam">gc64</td><td class="abidesc">64 bit GC references</td></tr>
+</table>
+
+<h3 id="ffi_os"><tt>ffi.os</tt></h3>
+<p>
+Contains the target OS name. Same contents as
+<a href="ext_jit.html#jit_os"><tt>jit.os</tt></a>.
+</p>
+
+<h3 id="ffi_arch"><tt>ffi.arch</tt></h3>
+<p>
+Contains the target architecture name. Same contents as
+<a href="ext_jit.html#jit_arch"><tt>jit.arch</tt></a>.
+</p>
+
+<h2 id="callback">Methods for Callbacks</h2>
+<p>
+The C&nbsp;types for <a href="ext_ffi_semantics.html#callback">callbacks</a>
+have some extra methods:
+</p>
+
+<h3 id="callback_free"><tt>cb:free()</tt></h3>
+<p>
+Free the resources associated with a callback. The associated Lua
+function is unanchored and may be garbage collected. The callback
+function pointer is no longer valid and must not be called again
+(it may be reused by a subsequently created callback).
+</p>
+
+<h3 id="callback_set"><tt>cb:set(func)</tt></h3>
+<p>
+Associate a new Lua function with a callback. The C&nbsp;type of the
+callback and the callback function pointer are unchanged.
+</p>
+<p>
+This method is useful to dynamically switch the receiver of callbacks
+without creating a new callback each time and registering it again (e.g.
+with a GUI library).
+</p>
+
+<h2 id="extended">Extended Standard Library Functions</h2>
+<p>
+The following standard library functions have been extended to work
+with cdata objects:
+</p>
+
+<h3 id="tonumber"><tt>n = tonumber(cdata)</tt></h3>
+<p>
+Converts a number cdata object to a <tt>double</tt> and returns it as
+a Lua number. This is particularly useful for boxed 64&nbsp;bit
+integer values. Caveat: this conversion may incur a precision loss.
+</p>
+
+<h3 id="tostring"><tt>s = tostring(cdata)</tt></h3>
+<p>
+Returns a string representation of the value of 64&nbsp;bit integers
+(<tt><b>"</b>nnn<b>LL"</b></tt> or <tt><b>"</b>nnn<b>ULL"</b></tt>) or
+complex numbers (<tt><b>"</b>re&plusmn;im<b>i"</b></tt>). Otherwise
+returns a string representation of the C&nbsp;type of a ctype object
+(<tt><b>"ctype&lt;</b>type<b>&gt;"</b></tt>) or a cdata object
+(<tt><b>"cdata&lt;</b>type<b>&gt;:&nbsp;</b>address"</tt>), unless you
+override it with a <tt>__tostring</tt> metamethod (see
+<a href="#ffi_metatype"><tt>ffi.metatype()</tt></a>).
+</p>
+
+<h3 id="pairs"><tt>iter, obj, start = pairs(cdata)<br>
+iter, obj, start = ipairs(cdata)<br></tt></h3>
+<p>
+Calls the <tt>__pairs</tt> or <tt>__ipairs</tt> metamethod of the
+corresponding ctype.
+</p>
+
+<h2 id="literals">Extensions to the Lua Parser</h2>
+<p>
+The parser for Lua source code treats numeric literals with the
+suffixes <tt>LL</tt> or <tt>ULL</tt> as signed or unsigned 64&nbsp;bit
+integers. Case doesn't matter, but uppercase is recommended for
+readability. It handles decimal (<tt>42LL</tt>), hexadecimal
+(<tt>0x2aLL</tt>) and binary (<tt>0b101010LL</tt>) literals.
+</p>
+<p>
+The imaginary part of complex numbers can be specified by suffixing
+number literals with <tt>i</tt> or <tt>I</tt>, e.g. <tt>12.5i</tt>.
+Caveat: you'll need to use <tt>1i</tt> to get an imaginary part with
+the value one, since <tt>i</tt> itself still refers to a variable
+named <tt>i</tt>.
+</p>
+<br class="flush">
+</div>
+<div id="foot">
+<hr class="hide">
+Copyright &copy; 2005-2022
+<span class="noprint">
+&middot;
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+</span>
+</div>
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