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  193.   <section id="complex-number-objects">

  194. <span id="complexobjects"></span><h1>Complex Number Objects<a class="headerlink" href="#complex-number-objects" title="Link to this heading">¶</a></h1>

  195. <p id="index-0">Python’s complex number objects are implemented as two distinct types when

  196. viewed from the C API:  one is the Python object exposed to Python programs, and

  197. the other is a C structure which represents the actual complex number value.

  198. The API provides functions for working with both.</p>

  199. <section id="complex-numbers-as-c-structures">

  200. <h2>Complex Numbers as C Structures<a class="headerlink" href="#complex-numbers-as-c-structures" title="Link to this heading">¶</a></h2>

  201. <p>Note that the functions which accept these structures as parameters and return

  202. them as results do so <em>by value</em> rather than dereferencing them through

  203. pointers.  This is consistent throughout the API.</p>

  204. <dl class="c type">

  205. <dt class="sig sig-object c" id="c.Py_complex">

  206. <span class="k"><span class="pre">type</span></span><span class="w"> </span><span class="sig-name descname"><span class="n"><span class="pre">Py_complex</span></span></span><a class="headerlink" href="#c.Py_complex" title="Link to this definition">¶</a><br /></dt>

  207. <dd><p>The C structure which corresponds to the value portion of a Python complex

  208. number object.  Most of the functions for dealing with complex number objects

  209. use structures of this type as input or output values, as appropriate.  It is

  210. defined as:</p>

  211. <div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="k">typedef</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="p">{</span>

  212. <span class="w">   </span><span class="kt">double</span><span class="w"> </span><span class="n">real</span><span class="p">;</span>

  213. <span class="w">   </span><span class="kt">double</span><span class="w"> </span><span class="n">imag</span><span class="p">;</span>

  214. <span class="p">}</span><span class="w"> </span><span class="n">Py_complex</span><span class="p">;</span>

  215. </pre></div>

  216. </div>

  217. </dd></dl>

  218. 

  219. <dl class="c function">

  220. <dt class="sig sig-object c" id="c._Py_c_sum">

  221. <a class="reference internal" href="#c.Py_complex" title="Py_complex"><span class="n"><span class="pre">Py_complex</span></span></a><span class="w"> </span><span class="sig-name descname"><span class="n"><span class="pre">_Py_c_sum</span></span></span><span class="sig-paren">(</span><a class="reference internal" href="#c.Py_complex" title="Py_complex"><span class="n"><span class="pre">Py_complex</span></span></a><span class="w"> </span><span class="n"><span class="pre">left</span></span>, <a class="reference internal" href="#c.Py_complex" title="Py_complex"><span class="n"><span class="pre">Py_complex</span></span></a><span class="w"> </span><span class="n"><span class="pre">right</span></span><span class="sig-paren">)</span><a class="headerlink" href="#c._Py_c_sum" title="Link to this definition">¶</a><br /></dt>

  222. <dd><p>Return the sum of two complex numbers, using the C <a class="reference internal" href="#c.Py_complex" title="Py_complex"><code class="xref c c-type docutils literal notranslate"><span class="pre">Py_complex</span></code></a>

  223. representation.</p>

  224. </dd></dl>

  225. 

  226. <dl class="c function">

  227. <dt class="sig sig-object c" id="c._Py_c_diff">

  228. <a class="reference internal" href="#c.Py_complex" title="Py_complex"><span class="n"><span class="pre">Py_complex</span></span></a><span class="w"> </span><span class="sig-name descname"><span class="n"><span class="pre">_Py_c_diff</span></span></span><span class="sig-paren">(</span><a class="reference internal" href="#c.Py_complex" title="Py_complex"><span class="n"><span class="pre">Py_complex</span></span></a><span class="w"> </span><span class="n"><span class="pre">left</span></span>, <a class="reference internal" href="#c.Py_complex" title="Py_complex"><span class="n"><span class="pre">Py_complex</span></span></a><span class="w"> </span><span class="n"><span class="pre">right</span></span><span class="sig-paren">)</span><a class="headerlink" href="#c._Py_c_diff" title="Link to this definition">¶</a><br /></dt>

  229. <dd><p>Return the difference between two complex numbers, using the C

  230. <a class="reference internal" href="#c.Py_complex" title="Py_complex"><code class="xref c c-type docutils literal notranslate"><span class="pre">Py_complex</span></code></a> representation.</p>

  231. </dd></dl>

  232. 

  233. <dl class="c function">

  234. <dt class="sig sig-object c" id="c._Py_c_neg">

  235. <a class="reference internal" href="#c.Py_complex" title="Py_complex"><span class="n"><span class="pre">Py_complex</span></span></a><span class="w"> </span><span class="sig-name descname"><span class="n"><span class="pre">_Py_c_neg</span></span></span><span class="sig-paren">(</span><a class="reference internal" href="#c.Py_complex" title="Py_complex"><span class="n"><span class="pre">Py_complex</span></span></a><span class="w"> </span><span class="n"><span class="pre">num</span></span><span class="sig-paren">)</span><a class="headerlink" href="#c._Py_c_neg" title="Link to this definition">¶</a><br /></dt>

  236. <dd><p>Return the negation of the complex number <em>num</em>, using the C

  237. <a class="reference internal" href="#c.Py_complex" title="Py_complex"><code class="xref c c-type docutils literal notranslate"><span class="pre">Py_complex</span></code></a> representation.</p>

  238. </dd></dl>

  239. 

  240. <dl class="c function">

  241. <dt class="sig sig-object c" id="c._Py_c_prod">

  242. <a class="reference internal" href="#c.Py_complex" title="Py_complex"><span class="n"><span class="pre">Py_complex</span></span></a><span class="w"> </span><span class="sig-name descname"><span class="n"><span class="pre">_Py_c_prod</span></span></span><span class="sig-paren">(</span><a class="reference internal" href="#c.Py_complex" title="Py_complex"><span class="n"><span class="pre">Py_complex</span></span></a><span class="w"> </span><span class="n"><span class="pre">left</span></span>, <a class="reference internal" href="#c.Py_complex" title="Py_complex"><span class="n"><span class="pre">Py_complex</span></span></a><span class="w"> </span><span class="n"><span class="pre">right</span></span><span class="sig-paren">)</span><a class="headerlink" href="#c._Py_c_prod" title="Link to this definition">¶</a><br /></dt>

  243. <dd><p>Return the product of two complex numbers, using the C <a class="reference internal" href="#c.Py_complex" title="Py_complex"><code class="xref c c-type docutils literal notranslate"><span class="pre">Py_complex</span></code></a>

  244. representation.</p>

  245. </dd></dl>

  246. 

  247. <dl class="c function">

  248. <dt class="sig sig-object c" id="c._Py_c_quot">

  249. <a class="reference internal" href="#c.Py_complex" title="Py_complex"><span class="n"><span class="pre">Py_complex</span></span></a><span class="w"> </span><span class="sig-name descname"><span class="n"><span class="pre">_Py_c_quot</span></span></span><span class="sig-paren">(</span><a class="reference internal" href="#c.Py_complex" title="Py_complex"><span class="n"><span class="pre">Py_complex</span></span></a><span class="w"> </span><span class="n"><span class="pre">dividend</span></span>, <a class="reference internal" href="#c.Py_complex" title="Py_complex"><span class="n"><span class="pre">Py_complex</span></span></a><span class="w"> </span><span class="n"><span class="pre">divisor</span></span><span class="sig-paren">)</span><a class="headerlink" href="#c._Py_c_quot" title="Link to this definition">¶</a><br /></dt>

  250. <dd><p>Return the quotient of two complex numbers, using the C <a class="reference internal" href="#c.Py_complex" title="Py_complex"><code class="xref c c-type docutils literal notranslate"><span class="pre">Py_complex</span></code></a>

  251. representation.</p>

  252. <p>If <em>divisor</em> is null, this method returns zero and sets

  253. <code class="xref c c-data docutils literal notranslate"><span class="pre">errno</span></code> to <code class="xref c c-macro docutils literal notranslate"><span class="pre">EDOM</span></code>.</p>

  254. </dd></dl>

  255. 

  256. <dl class="c function">

  257. <dt class="sig sig-object c" id="c._Py_c_pow">

  258. <a class="reference internal" href="#c.Py_complex" title="Py_complex"><span class="n"><span class="pre">Py_complex</span></span></a><span class="w"> </span><span class="sig-name descname"><span class="n"><span class="pre">_Py_c_pow</span></span></span><span class="sig-paren">(</span><a class="reference internal" href="#c.Py_complex" title="Py_complex"><span class="n"><span class="pre">Py_complex</span></span></a><span class="w"> </span><span class="n"><span class="pre">num</span></span>, <a class="reference internal" href="#c.Py_complex" title="Py_complex"><span class="n"><span class="pre">Py_complex</span></span></a><span class="w"> </span><span class="n"><span class="pre">exp</span></span><span class="sig-paren">)</span><a class="headerlink" href="#c._Py_c_pow" title="Link to this definition">¶</a><br /></dt>

  259. <dd><p>Return the exponentiation of <em>num</em> by <em>exp</em>, using the C <a class="reference internal" href="#c.Py_complex" title="Py_complex"><code class="xref c c-type docutils literal notranslate"><span class="pre">Py_complex</span></code></a>

  260. representation.</p>

  261. <p>If <em>num</em> is null and <em>exp</em> is not a positive real number,

  262. this method returns zero and sets <code class="xref c c-data docutils literal notranslate"><span class="pre">errno</span></code> to <code class="xref c c-macro docutils literal notranslate"><span class="pre">EDOM</span></code>.</p>

  263. </dd></dl>

  264. 

  265. </section>

  266. <section id="complex-numbers-as-python-objects">

  267. <h2>Complex Numbers as Python Objects<a class="headerlink" href="#complex-numbers-as-python-objects" title="Link to this heading">¶</a></h2>

  268. <dl class="c type">

  269. <dt class="sig sig-object c" id="c.PyComplexObject">

  270. <span class="k"><span class="pre">type</span></span><span class="w"> </span><span class="sig-name descname"><span class="n"><span class="pre">PyComplexObject</span></span></span><a class="headerlink" href="#c.PyComplexObject" title="Link to this definition">¶</a><br /></dt>

  271. <dd><p>This subtype of <a class="reference internal" href="structures.html#c.PyObject" title="PyObject"><code class="xref c c-type docutils literal notranslate"><span class="pre">PyObject</span></code></a> represents a Python complex number object.</p>

  272. </dd></dl>

  273. 

  274. <dl class="c var">

  275. <dt class="sig sig-object c" id="c.PyComplex_Type">

  276. <a class="reference internal" href="type.html#c.PyTypeObject" title="PyTypeObject"><span class="n"><span class="pre">PyTypeObject</span></span></a><span class="w"> </span><span class="sig-name descname"><span class="n"><span class="pre">PyComplex_Type</span></span></span><a class="headerlink" href="#c.PyComplex_Type" title="Link to this definition">¶</a><br /></dt>

  277. <dd><em class="stableabi"> Part of the <a class="reference internal" href="stable.html#stable"><span class="std std-ref">Stable ABI</span></a>.</em><p>This instance of <a class="reference internal" href="type.html#c.PyTypeObject" title="PyTypeObject"><code class="xref c c-type docutils literal notranslate"><span class="pre">PyTypeObject</span></code></a> represents the Python complex number

  278. type. It is the same object as <a class="reference internal" href="../library/functions.html#complex" title="complex"><code class="xref py py-class docutils literal notranslate"><span class="pre">complex</span></code></a> in the Python layer.</p>

  279. </dd></dl>

  280. 

  281. <dl class="c function">

  282. <dt class="sig sig-object c" id="c.PyComplex_Check">

  283. <span class="kt"><span class="pre">int</span></span><span class="w"> </span><span class="sig-name descname"><span class="n"><span class="pre">PyComplex_Check</span></span></span><span class="sig-paren">(</span><a class="reference internal" href="structures.html#c.PyObject" title="PyObject"><span class="n"><span class="pre">PyObject</span></span></a><span class="w"> </span><span class="p"><span class="pre">*</span></span><span class="n"><span class="pre">p</span></span><span class="sig-paren">)</span><a class="headerlink" href="#c.PyComplex_Check" title="Link to this definition">¶</a><br /></dt>

  284. <dd><p>Return true if its argument is a <a class="reference internal" href="#c.PyComplexObject" title="PyComplexObject"><code class="xref c c-type docutils literal notranslate"><span class="pre">PyComplexObject</span></code></a> or a subtype of

  285. <a class="reference internal" href="#c.PyComplexObject" title="PyComplexObject"><code class="xref c c-type docutils literal notranslate"><span class="pre">PyComplexObject</span></code></a>.  This function always succeeds.</p>

  286. </dd></dl>

  287. 

  288. <dl class="c function">

  289. <dt class="sig sig-object c" id="c.PyComplex_CheckExact">

  290. <span class="kt"><span class="pre">int</span></span><span class="w"> </span><span class="sig-name descname"><span class="n"><span class="pre">PyComplex_CheckExact</span></span></span><span class="sig-paren">(</span><a class="reference internal" href="structures.html#c.PyObject" title="PyObject"><span class="n"><span class="pre">PyObject</span></span></a><span class="w"> </span><span class="p"><span class="pre">*</span></span><span class="n"><span class="pre">p</span></span><span class="sig-paren">)</span><a class="headerlink" href="#c.PyComplex_CheckExact" title="Link to this definition">¶</a><br /></dt>

  291. <dd><p>Return true if its argument is a <a class="reference internal" href="#c.PyComplexObject" title="PyComplexObject"><code class="xref c c-type docutils literal notranslate"><span class="pre">PyComplexObject</span></code></a>, but not a subtype of

  292. <a class="reference internal" href="#c.PyComplexObject" title="PyComplexObject"><code class="xref c c-type docutils literal notranslate"><span class="pre">PyComplexObject</span></code></a>.  This function always succeeds.</p>

  293. </dd></dl>

  294. 

  295. <dl class="c function">

  296. <dt class="sig sig-object c" id="c.PyComplex_FromCComplex">

  297. <a class="reference internal" href="structures.html#c.PyObject" title="PyObject"><span class="n"><span class="pre">PyObject</span></span></a><span class="w"> </span><span class="p"><span class="pre">*</span></span><span class="sig-name descname"><span class="n"><span class="pre">PyComplex_FromCComplex</span></span></span><span class="sig-paren">(</span><a class="reference internal" href="#c.Py_complex" title="Py_complex"><span class="n"><span class="pre">Py_complex</span></span></a><span class="w"> </span><span class="n"><span class="pre">v</span></span><span class="sig-paren">)</span><a class="headerlink" href="#c.PyComplex_FromCComplex" title="Link to this definition">¶</a><br /></dt>

  298. <dd><em class="refcount">Return value: New reference.</em><p>Create a new Python complex number object from a C <a class="reference internal" href="#c.Py_complex" title="Py_complex"><code class="xref c c-type docutils literal notranslate"><span class="pre">Py_complex</span></code></a> value.</p>

  299. </dd></dl>

  300. 

  301. <dl class="c function">

  302. <dt class="sig sig-object c" id="c.PyComplex_FromDoubles">

  303. <a class="reference internal" href="structures.html#c.PyObject" title="PyObject"><span class="n"><span class="pre">PyObject</span></span></a><span class="w"> </span><span class="p"><span class="pre">*</span></span><span class="sig-name descname"><span class="n"><span class="pre">PyComplex_FromDoubles</span></span></span><span class="sig-paren">(</span><span class="kt"><span class="pre">double</span></span><span class="w"> </span><span class="n"><span class="pre">real</span></span>, <span class="kt"><span class="pre">double</span></span><span class="w"> </span><span class="n"><span class="pre">imag</span></span><span class="sig-paren">)</span><a class="headerlink" href="#c.PyComplex_FromDoubles" title="Link to this definition">¶</a><br /></dt>

  304. <dd><em class="refcount">Return value: New reference.</em><em class="stableabi"> Part of the <a class="reference internal" href="stable.html#stable"><span class="std std-ref">Stable ABI</span></a>.</em><p>Return a new <a class="reference internal" href="#c.PyComplexObject" title="PyComplexObject"><code class="xref c c-type docutils literal notranslate"><span class="pre">PyComplexObject</span></code></a> object from <em>real</em> and <em>imag</em>.</p>

  305. </dd></dl>

  306. 

  307. <dl class="c function">

  308. <dt class="sig sig-object c" id="c.PyComplex_RealAsDouble">

  309. <span class="kt"><span class="pre">double</span></span><span class="w"> </span><span class="sig-name descname"><span class="n"><span class="pre">PyComplex_RealAsDouble</span></span></span><span class="sig-paren">(</span><a class="reference internal" href="structures.html#c.PyObject" title="PyObject"><span class="n"><span class="pre">PyObject</span></span></a><span class="w"> </span><span class="p"><span class="pre">*</span></span><span class="n"><span class="pre">op</span></span><span class="sig-paren">)</span><a class="headerlink" href="#c.PyComplex_RealAsDouble" title="Link to this definition">¶</a><br /></dt>

  310. <dd><em class="stableabi"> Part of the <a class="reference internal" href="stable.html#stable"><span class="std std-ref">Stable ABI</span></a>.</em><p>Return the real part of <em>op</em> as a C <span class="c-expr sig sig-inline c"><span class="kt">double</span></span>.</p>

  311. </dd></dl>

  312. 

  313. <dl class="c function">

  314. <dt class="sig sig-object c" id="c.PyComplex_ImagAsDouble">

  315. <span class="kt"><span class="pre">double</span></span><span class="w"> </span><span class="sig-name descname"><span class="n"><span class="pre">PyComplex_ImagAsDouble</span></span></span><span class="sig-paren">(</span><a class="reference internal" href="structures.html#c.PyObject" title="PyObject"><span class="n"><span class="pre">PyObject</span></span></a><span class="w"> </span><span class="p"><span class="pre">*</span></span><span class="n"><span class="pre">op</span></span><span class="sig-paren">)</span><a class="headerlink" href="#c.PyComplex_ImagAsDouble" title="Link to this definition">¶</a><br /></dt>

  316. <dd><em class="stableabi"> Part of the <a class="reference internal" href="stable.html#stable"><span class="std std-ref">Stable ABI</span></a>.</em><p>Return the imaginary part of <em>op</em> as a C <span class="c-expr sig sig-inline c"><span class="kt">double</span></span>.</p>

  317. </dd></dl>

  318. 

  319. <dl class="c function">

  320. <dt class="sig sig-object c" id="c.PyComplex_AsCComplex">

  321. <a class="reference internal" href="#c.Py_complex" title="Py_complex"><span class="n"><span class="pre">Py_complex</span></span></a><span class="w"> </span><span class="sig-name descname"><span class="n"><span class="pre">PyComplex_AsCComplex</span></span></span><span class="sig-paren">(</span><a class="reference internal" href="structures.html#c.PyObject" title="PyObject"><span class="n"><span class="pre">PyObject</span></span></a><span class="w"> </span><span class="p"><span class="pre">*</span></span><span class="n"><span class="pre">op</span></span><span class="sig-paren">)</span><a class="headerlink" href="#c.PyComplex_AsCComplex" title="Link to this definition">¶</a><br /></dt>

  322. <dd><p>Return the <a class="reference internal" href="#c.Py_complex" title="Py_complex"><code class="xref c c-type docutils literal notranslate"><span class="pre">Py_complex</span></code></a> value of the complex number <em>op</em>.</p>

  323. <p>If <em>op</em> is not a Python complex number object but has a <a class="reference internal" href="../reference/datamodel.html#object.__complex__" title="object.__complex__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__complex__()</span></code></a>

  324. method, this method will first be called to convert <em>op</em> to a Python complex

  325. number object.  If <code class="xref py py-meth docutils literal notranslate"><span class="pre">__complex__()</span></code> is not defined then it falls back to

  326. <a class="reference internal" href="../reference/datamodel.html#object.__float__" title="object.__float__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__float__()</span></code></a>.  If <code class="xref py py-meth docutils literal notranslate"><span class="pre">__float__()</span></code> is not defined then it falls back

  327. to <a class="reference internal" href="../reference/datamodel.html#object.__index__" title="object.__index__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__index__()</span></code></a>.  Upon failure, this method returns <code class="docutils literal notranslate"><span class="pre">-1.0</span></code> as a real

  328. value.</p>

  329. <div class="versionchanged">

  330. <p><span class="versionmodified changed">Changed in version 3.8: </span>Use <a class="reference internal" href="../reference/datamodel.html#object.__index__" title="object.__index__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__index__()</span></code></a> if available.</p>

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