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<div class="section" id="pympf">
<h1>PyMPF<a class="headerlink" href="#pympf" title="Permalink to this headline">¶</a></h1>
<div class="toctree-wrapper compound">
</div>
<p>The PyMPF library contains two modules intended for most users:</p>
<ul class="simple">
<li>floats (arbitrary precision IEEE-754 floating point, see
<a class="reference internal" href="#mpf.floats.MPF" title="mpf.floats.MPF"><code class="xref py py-class docutils literal"><span class="pre">mpf.floats.MPF</span></code></a>)</li>
<li>rationals (rational numbers, see <a class="reference internal" href="#mpf.rationals.Rational" title="mpf.rationals.Rational"><code class="xref py py-class docutils literal"><span class="pre">mpf.rationals.Rational</span></code></a>)</li>
</ul>
<p>It also contains the following modules indended for internal use and
the SMT-LIB testcase generator:</p>
<ul class="simple">
<li>bitvectors (very simple bitvector support, only literal printing currently)</li>
<li>interval_q (rational intervals)</li>
<li>bisect (binary search)</li>
</ul>
<div class="section" id="fast-tutorial">
<h2>Fast tutorial<a class="headerlink" href="#fast-tutorial" title="Permalink to this headline">¶</a></h2>
<p>Import the relevant classes. Most likely you want to do this:</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">mpf.rationals</span> <span class="k">import</span> <span class="n">Rational</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">mpf.floats</span> <span class="k">import</span> <span class="o">*</span>
</pre></div>
</div>
<p>You can now create a float like this (here we create a single
precision float):</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">x</span> <span class="o">=</span> <span class="n">MPF</span><span class="p">(</span><span class="mi">8</span><span class="p">,</span> <span class="mi">24</span><span class="p">)</span>
</pre></div>
</div>
<p>To quickly see what we have we can use the
<a class="reference internal" href="#mpf.floats.MPF.to_python_string" title="mpf.floats.MPF.to_python_string"><code class="xref py py-func docutils literal"><span class="pre">mpf.floats.MPF.to_python_string()</span></code></a> member function.</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">x</span><span class="o">.</span><span class="n">to_python_string</span><span class="p">()</span>
<span class="go">'0.0'</span>
</pre></div>
</div>
<p>To set the float to a specific value, such as <span class="math">\(\frac{1}{3}\)</span> we
can use the <a class="reference internal" href="#mpf.floats.MPF.from_rational" title="mpf.floats.MPF.from_rational"><code class="xref py py-func docutils literal"><span class="pre">mpf.floats.MPF.from_rational()</span></code></a> member
function. Since we convert from rationals to floats we might need to
round.</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">x</span><span class="o">.</span><span class="n">from_rational</span><span class="p">(</span><span class="n">RM_RNE</span><span class="p">,</span> <span class="n">Rational</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">))</span>
<span class="gp">>>> </span><span class="n">x</span><span class="o">.</span><span class="n">to_python_string</span><span class="p">()</span>
<span class="go">'0.3333333432674407958984375'</span>
</pre></div>
</div>
<p>PyMPF supports all rounding modes defined by IEEE-754:</p>
<ul class="simple">
<li>RM_RNE (Round nearest even: to break ties, round to the nearest
floating point number whos bit-pattern is even. This is the default
on most desktop processors and programming languages.)</li>
<li>RM_RNA (Round nearest away: to break ties, round to the floating
point number furthest away from zero. Note that this is unsupported
on most hardware (including i686 and amd64), other floating point
libraries (e.g. MPFR).</li>
<li>RM_RTZ (Round to zero: always round towards zero)</li>
<li>RM_RTP (Round to positive: always round towards <span class="math">\(+\infty\)</span>)</li>
<li>RM_RTN (Round to negative: always round towards <span class="math">\(-\infty\)</span>)</li>
</ul>
<p>One of the main use-cases for this library is to generate test-cases
for SMT-LIB. To create an SMT-LIB literal you can use the
<a class="reference internal" href="#mpf.floats.MPF.smtlib_literal" title="mpf.floats.MPF.smtlib_literal"><code class="xref py py-func docutils literal"><span class="pre">mpf.floats.MPF.smtlib_literal()</span></code></a> function:</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">x</span><span class="o">.</span><span class="n">smtlib_literal</span><span class="p">()</span>
<span class="go">'(fp #b0 #b01111101 #b01010101010101010101011)'</span>
</pre></div>
</div>
<p>The MPF class supports all floating-point comparisons:</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">y</span> <span class="o">=</span> <span class="n">MPF</span><span class="p">(</span><span class="mi">8</span><span class="p">,</span> <span class="mi">24</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">x</span> <span class="o">></span> <span class="n">y</span>
<span class="go">True</span>
</pre></div>
</div>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">y</span><span class="o">.</span><span class="n">set_nan</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">x</span> <span class="o">></span> <span class="n">y</span>
<span class="go">False</span>
</pre></div>
</div>
<p>Note that equality considers +0 and -0 to be equal. You can use the
<a class="reference internal" href="#mpf.floats.smtlib_eq" title="mpf.floats.smtlib_eq"><code class="xref py py-func docutils literal"><span class="pre">mpf.floats.smtlib_eq()</span></code></a> if you want bitwise equality:</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">z</span> <span class="o">=</span> <span class="n">MPF</span><span class="p">(</span><span class="mi">8</span><span class="p">,</span> <span class="mi">24</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">z</span><span class="o">.</span><span class="n">set_zero</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">y</span><span class="o">.</span><span class="n">set_zero</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">y</span> <span class="o">==</span> <span class="n">z</span>
<span class="go">True</span>
<span class="gp">>>> </span><span class="n">smtlib_eq</span><span class="p">(</span><span class="n">y</span><span class="p">,</span> <span class="n">z</span><span class="p">)</span>
<span class="go">False</span>
</pre></div>
</div>
<p>To set values you can use the following functions:</p>
<ul class="simple">
<li><a class="reference internal" href="#mpf.floats.MPF.from_rational" title="mpf.floats.MPF.from_rational"><code class="xref py py-func docutils literal"><span class="pre">mpf.floats.MPF.from_rational()</span></code></a> set to value closest to given rational</li>
<li><a class="reference internal" href="#mpf.floats.MPF.set_zero" title="mpf.floats.MPF.set_zero"><code class="xref py py-func docutils literal"><span class="pre">mpf.floats.MPF.set_zero()</span></code></a> set to +0 (if sign is 0) or -0 (if
sign is 1)</li>
<li><a class="reference internal" href="#mpf.floats.MPF.set_infinite" title="mpf.floats.MPF.set_infinite"><code class="xref py py-func docutils literal"><span class="pre">mpf.floats.MPF.set_infinite()</span></code></a> set to <span class="math">\(+\infty\)</span> (if sign
is 0) or <span class="math">\(-\infty\)</span> (if sign is 1)</li>
<li><a class="reference internal" href="#mpf.floats.MPF.set_nan" title="mpf.floats.MPF.set_nan"><code class="xref py py-func docutils literal"><span class="pre">mpf.floats.MPF.set_nan()</span></code></a> set to NaN. PyMPF does not support
the distinction between signalling and non-signalling NaNs,
similarly to SMT-LIB.</li>
</ul>
<p>Finally, to do arithmetic, you can use the fp_* functions. Most take a
rounding mode and two parameters:</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">x</span><span class="o">.</span><span class="n">from_rational</span><span class="p">(</span><span class="n">RM_RNE</span><span class="p">,</span> <span class="n">Rational</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">10</span><span class="p">))</span>
<span class="gp">>>> </span><span class="n">y</span><span class="o">.</span><span class="n">from_rational</span><span class="p">(</span><span class="n">RM_RNE</span><span class="p">,</span> <span class="n">Rational</span><span class="p">(</span><span class="mi">10</span><span class="p">))</span>
<span class="gp">>>> </span><span class="n">z</span> <span class="o">=</span> <span class="n">fp_mul</span><span class="p">(</span><span class="n">RM_RNE</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">z</span><span class="o">.</span><span class="n">to_python_string</span><span class="p">()</span>
<span class="go">'1.0'</span>
</pre></div>
</div>
<p>Here an example demonstrating accumulated rounding errors:</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">y</span><span class="o">.</span><span class="n">set_zero</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<span class="gp">>>> </span><span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">10</span><span class="p">):</span>
<span class="gp">>>> </span> <span class="n">y</span> <span class="o">=</span> <span class="n">fp_add</span><span class="p">(</span><span class="n">RM_RNE</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
<span class="gp">>>> </span> <span class="nb">print</span><span class="p">(</span><span class="n">y</span><span class="o">.</span><span class="n">to_python_string</span><span class="p">())</span>
<span class="go">0.100000001490116119384765625</span>
<span class="go">0.20000000298023223876953125</span>
<span class="go">0.300000011920928955078125</span>
<span class="go">0.4000000059604644775390625</span>
<span class="go">0.5</span>
<span class="go">0.60000002384185791015625</span>
<span class="go">0.7000000476837158203125</span>
<span class="go">0.80000007152557373046875</span>
<span class="go">0.900000095367431640625</span>
<span class="go">1.00000011920928955078125</span>
</pre></div>
</div>
</div>
</div>
<div class="section" id="module-mpf.rationals">
<span id="rationals"></span><h1>Rationals<a class="headerlink" href="#module-mpf.rationals" title="Permalink to this headline">¶</a></h1>
<p>This module defines class to deal with Rational numbers.</p>
<div class="admonition-todo admonition" id="index-0">
<p class="first admonition-title">Todo</p>
<p class="last">This should be a subclass of fractions.Fraction.</p>
</div>
<dl class="class">
<dt id="mpf.rationals.Rational">
<em class="property">class </em><code class="descclassname">mpf.rationals.</code><code class="descname">Rational</code><span class="sig-paren">(</span><em>a=0</em>, <em>b=1</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.rationals.Rational" title="Permalink to this definition">¶</a></dt>
<dd><p>Rational number</p>
<p><em>a</em> is the numerator</p>
<p><em>b</em> is the denominator</p>
<dl class="method">
<dt id="mpf.rationals.Rational.__abs__">
<code class="descname">__abs__</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#mpf.rationals.Rational.__abs__" title="Permalink to this definition">¶</a></dt>
<dd><p>Absolute value</p>
</dd></dl>
<dl class="method">
<dt id="mpf.rationals.Rational.__add__">
<code class="descname">__add__</code><span class="sig-paren">(</span><em>other</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.rationals.Rational.__add__" title="Permalink to this definition">¶</a></dt>
<dd><p>Addition</p>
</dd></dl>
<dl class="method">
<dt id="mpf.rationals.Rational.__eq__">
<code class="descname">__eq__</code><span class="sig-paren">(</span><em>other</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.rationals.Rational.__eq__" title="Permalink to this definition">¶</a></dt>
<dd><p>Equality</p>
</dd></dl>
<dl class="method">
<dt id="mpf.rationals.Rational.__ge__">
<code class="descname">__ge__</code><span class="sig-paren">(</span><em>other</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.rationals.Rational.__ge__" title="Permalink to this definition">¶</a></dt>
<dd><p>>=</p>
</dd></dl>
<dl class="method">
<dt id="mpf.rationals.Rational.__gt__">
<code class="descname">__gt__</code><span class="sig-paren">(</span><em>other</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.rationals.Rational.__gt__" title="Permalink to this definition">¶</a></dt>
<dd><p>></p>
</dd></dl>
<dl class="method">
<dt id="mpf.rationals.Rational.__le__">
<code class="descname">__le__</code><span class="sig-paren">(</span><em>other</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.rationals.Rational.__le__" title="Permalink to this definition">¶</a></dt>
<dd><p><=</p>
</dd></dl>
<dl class="method">
<dt id="mpf.rationals.Rational.__lt__">
<code class="descname">__lt__</code><span class="sig-paren">(</span><em>other</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.rationals.Rational.__lt__" title="Permalink to this definition">¶</a></dt>
<dd><p><</p>
</dd></dl>
<dl class="method">
<dt id="mpf.rationals.Rational.__mul__">
<code class="descname">__mul__</code><span class="sig-paren">(</span><em>other</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.rationals.Rational.__mul__" title="Permalink to this definition">¶</a></dt>
<dd><p>Multiplication</p>
</dd></dl>
<dl class="method">
<dt id="mpf.rationals.Rational.__ne__">
<code class="descname">__ne__</code><span class="sig-paren">(</span><em>other</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.rationals.Rational.__ne__" title="Permalink to this definition">¶</a></dt>
<dd><p>Inequality</p>
</dd></dl>
<dl class="method">
<dt id="mpf.rationals.Rational.__neg__">
<code class="descname">__neg__</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#mpf.rationals.Rational.__neg__" title="Permalink to this definition">¶</a></dt>
<dd><p>Negation</p>
</dd></dl>
<dl class="method">
<dt id="mpf.rationals.Rational.__pow__">
<code class="descname">__pow__</code><span class="sig-paren">(</span><em>other</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.rationals.Rational.__pow__" title="Permalink to this definition">¶</a></dt>
<dd><p>Exponentiation</p>
<p>The right-hand side must be an integral Rational, otherwise
AssertionError is raised.</p>
</dd></dl>
<dl class="method">
<dt id="mpf.rationals.Rational.__sub__">
<code class="descname">__sub__</code><span class="sig-paren">(</span><em>other</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.rationals.Rational.__sub__" title="Permalink to this definition">¶</a></dt>
<dd><p>Substraction</p>
</dd></dl>
<dl class="method">
<dt id="mpf.rationals.Rational.__truediv__">
<code class="descname">__truediv__</code><span class="sig-paren">(</span><em>other</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.rationals.Rational.__truediv__" title="Permalink to this definition">¶</a></dt>
<dd><p>Division</p>
</dd></dl>
<dl class="attribute">
<dt id="mpf.rationals.Rational.__weakref__">
<code class="descname">__weakref__</code><a class="headerlink" href="#mpf.rationals.Rational.__weakref__" title="Permalink to this definition">¶</a></dt>
<dd><p>list of weak references to the object (if defined)</p>
</dd></dl>
<dl class="method">
<dt id="mpf.rationals.Rational.isIntegral">
<code class="descname">isIntegral</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#mpf.rationals.Rational.isIntegral" title="Permalink to this definition">¶</a></dt>
<dd><p>Test if integral</p>
</dd></dl>
<dl class="method">
<dt id="mpf.rationals.Rational.isNegative">
<code class="descname">isNegative</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#mpf.rationals.Rational.isNegative" title="Permalink to this definition">¶</a></dt>
<dd><p>Test if negative</p>
<p>Returns false for 0.</p>
</dd></dl>
<dl class="method">
<dt id="mpf.rationals.Rational.isZero">
<code class="descname">isZero</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#mpf.rationals.Rational.isZero" title="Permalink to this definition">¶</a></dt>
<dd><p>Test if zero</p>
</dd></dl>
<dl class="method">
<dt id="mpf.rationals.Rational.to_decimal_string">
<code class="descname">to_decimal_string</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#mpf.rationals.Rational.to_decimal_string" title="Permalink to this definition">¶</a></dt>
<dd><p>Convert to decimal string</p>
<p>If the fraction does not terminate (e.g. for 1 / 3), an
exception is thrown.</p>
</dd></dl>
<dl class="method">
<dt id="mpf.rationals.Rational.to_python_float">
<code class="descname">to_python_float</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#mpf.rationals.Rational.to_python_float" title="Permalink to this definition">¶</a></dt>
<dd><p>Convert to python float</p>
</dd></dl>
<dl class="method">
<dt id="mpf.rationals.Rational.to_python_int">
<code class="descname">to_python_int</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#mpf.rationals.Rational.to_python_int" title="Permalink to this definition">¶</a></dt>
<dd><p>Convert to python int</p>
</dd></dl>
<dl class="method">
<dt id="mpf.rationals.Rational.to_smtlib">
<code class="descname">to_smtlib</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#mpf.rationals.Rational.to_smtlib" title="Permalink to this definition">¶</a></dt>
<dd><p>Convert to SMT-LIB Real expression</p>
<p>Returns literal for integrals, e.g. “1.0”.</p>
<p>Returns an s-expression otherwise, e.g. “(- (/ 1.0 3.0))”.</p>
</dd></dl>
</dd></dl>
<dl class="function">
<dt id="mpf.rationals.q_from_decimal_fragments">
<code class="descclassname">mpf.rationals.</code><code class="descname">q_from_decimal_fragments</code><span class="sig-paren">(</span><em>sign</em>, <em>integer_part</em>, <em>fraction_part</em>, <em>exp_part</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.rationals.q_from_decimal_fragments" title="Permalink to this definition">¶</a></dt>
<dd><p>Build a rational from string fragments of a decimal number.</p>
<dl class="docutils">
<dt>E.g. for “1.23E-1” we have fragments for</dt>
<dd>sign = “”
integer_part = “1”
fraction_part = “23”
exp_part = “-1”</dd>
</dl>
</dd></dl>
<dl class="function">
<dt id="mpf.rationals.q_pow2">
<code class="descclassname">mpf.rationals.</code><code class="descname">q_pow2</code><span class="sig-paren">(</span><em>n</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.rationals.q_pow2" title="Permalink to this definition">¶</a></dt>
<dd><p>Create rational for 2^n</p>
<p><em>n</em> can be negative</p>
</dd></dl>
<dl class="function">
<dt id="mpf.rationals.q_round_rna">
<code class="descclassname">mpf.rationals.</code><code class="descname">q_round_rna</code><span class="sig-paren">(</span><em>n</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.rationals.q_round_rna" title="Permalink to this definition">¶</a></dt>
<dd><p>Round to nearest integer, away from zero</p>
</dd></dl>
<dl class="function">
<dt id="mpf.rationals.q_round_rne">
<code class="descclassname">mpf.rationals.</code><code class="descname">q_round_rne</code><span class="sig-paren">(</span><em>n</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.rationals.q_round_rne" title="Permalink to this definition">¶</a></dt>
<dd><p>Round to nearest even integer</p>
</dd></dl>
<dl class="function">
<dt id="mpf.rationals.q_round_rtn">
<code class="descclassname">mpf.rationals.</code><code class="descname">q_round_rtn</code><span class="sig-paren">(</span><em>n</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.rationals.q_round_rtn" title="Permalink to this definition">¶</a></dt>
<dd><p>Round to nearest integer, towards negative</p>
</dd></dl>
<dl class="function">
<dt id="mpf.rationals.q_round_rtp">
<code class="descclassname">mpf.rationals.</code><code class="descname">q_round_rtp</code><span class="sig-paren">(</span><em>n</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.rationals.q_round_rtp" title="Permalink to this definition">¶</a></dt>
<dd><p>Round to nearest integer, towards positive</p>
</dd></dl>
<dl class="function">
<dt id="mpf.rationals.q_round_rtz">
<code class="descclassname">mpf.rationals.</code><code class="descname">q_round_rtz</code><span class="sig-paren">(</span><em>n</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.rationals.q_round_rtz" title="Permalink to this definition">¶</a></dt>
<dd><p>Round to nearest integer, towards zero</p>
</dd></dl>
<dl class="function">
<dt id="mpf.rationals.q_round_to_nearest">
<code class="descclassname">mpf.rationals.</code><code class="descname">q_round_to_nearest</code><span class="sig-paren">(</span><em>n</em>, <em>tiebreak</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.rationals.q_round_to_nearest" title="Permalink to this definition">¶</a></dt>
<dd><p>Round to nearest integer</p>
<p>Round <em>n</em> to the nearest integer</p>
<p>Calls the <em>tiebreak*(upper, lower) function with the two
alternatives if *n</em> is precisely between two integers.</p>
</dd></dl>
</div>
<div class="section" id="module-mpf.floats">
<span id="mpf"></span><h1>MPF<a class="headerlink" href="#module-mpf.floats" title="Permalink to this headline">¶</a></h1>
<p>This module implements IEEE floats using bitvectors as the in-memory
format, but rationals (plus rounding and special case handling) for
calculation. This allows us to directly implement the semantics
described in IEEE-754 (2008) without having to consider any of the
difficult normalisation problems.</p>
<p>The main objective is that the implementation should be simple and
simple to understand and as close to IEEE-754 and SMTLIB as possible
(as opposed to fast) since the main use is the validation of other
IEEE float implementations in SMT solvers (which have to be
fast). It is also not a replacement for libraries such as MPFR
(which is fast, but complicated and does not totally map onto IEEE
floats).</p>
<dl class="class">
<dt id="mpf.floats.MPF">
<em class="property">class </em><code class="descclassname">mpf.floats.</code><code class="descname">MPF</code><span class="sig-paren">(</span><em>eb</em>, <em>sb</em>, <em>bitvec=0</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.MPF" title="Permalink to this definition">¶</a></dt>
<dd><p>Arbitrary precision IEEE-754 floating point number</p>
<p><em>eb</em> is the number of bits for the exponent.</p>
<p><em>sb</em> is the number of bits for the significand.</p>
<p>This includes the “hidden bit”, so for example to create a
single-precision floating point number we use:</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">x</span> <span class="o">=</span> <span class="n">MPF</span><span class="p">(</span><span class="mi">8</span><span class="p">,</span> <span class="mi">24</span><span class="p">)</span>
</pre></div>
</div>
<p>By default the created float is +0, however <em>bitvec</em> can be used
to set the initial value. The expected format is an integer
<span class="math">\(0 \le bitvec < 2^{eb+sb}\)</span> corresponding to the binary
interchange format. For example to create the single precision
float representing +1:</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">x</span> <span class="o">=</span> <span class="n">MPF</span><span class="p">(</span><span class="mi">8</span><span class="p">,</span> <span class="mi">24</span><span class="p">,</span> <span class="mh">0x3f800000</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">x</span><span class="o">.</span><span class="n">to_python_string</span><span class="p">()</span>
<span class="go">'1.0'</span>
</pre></div>
</div>
<dl class="method">
<dt id="mpf.floats.MPF.__abs__">
<code class="descname">__abs__</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.MPF.__abs__" title="Permalink to this definition">¶</a></dt>
<dd><p>Compute absolute value</p>
</dd></dl>
<dl class="method">
<dt id="mpf.floats.MPF.__eq__">
<code class="descname">__eq__</code><span class="sig-paren">(</span><em>other</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.MPF.__eq__" title="Permalink to this definition">¶</a></dt>
<dd><p>Test floating-point equality</p>
<p>Note that this is floating-point equality, so comparisons to
NaN always fail and -0 and +0 are considered equal.</p>
<p>If you want true equality, use <a class="reference internal" href="#mpf.floats.smtlib_eq" title="mpf.floats.smtlib_eq"><code class="xref py py-func docutils literal"><span class="pre">smtlib_eq()</span></code></a></p>
</dd></dl>
<dl class="method">
<dt id="mpf.floats.MPF.__ge__">
<code class="descname">__ge__</code><span class="sig-paren">(</span><em>other</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.MPF.__ge__" title="Permalink to this definition">¶</a></dt>
<dd><p>Test floating-point greater than or equal</p>
</dd></dl>
<dl class="method">
<dt id="mpf.floats.MPF.__gt__">
<code class="descname">__gt__</code><span class="sig-paren">(</span><em>other</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.MPF.__gt__" title="Permalink to this definition">¶</a></dt>
<dd><p>Test floating-point greater than</p>
</dd></dl>
<dl class="method">
<dt id="mpf.floats.MPF.__le__">
<code class="descname">__le__</code><span class="sig-paren">(</span><em>other</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.MPF.__le__" title="Permalink to this definition">¶</a></dt>
<dd><p>Test floating-point less than or equal</p>
</dd></dl>
<dl class="method">
<dt id="mpf.floats.MPF.__lt__">
<code class="descname">__lt__</code><span class="sig-paren">(</span><em>other</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.MPF.__lt__" title="Permalink to this definition">¶</a></dt>
<dd><p>Test floating-point less than</p>
</dd></dl>
<dl class="method">
<dt id="mpf.floats.MPF.__neg__">
<code class="descname">__neg__</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.MPF.__neg__" title="Permalink to this definition">¶</a></dt>
<dd><p>Compute inverse</p>
</dd></dl>
<dl class="attribute">
<dt id="mpf.floats.MPF.__weakref__">
<code class="descname">__weakref__</code><a class="headerlink" href="#mpf.floats.MPF.__weakref__" title="Permalink to this definition">¶</a></dt>
<dd><p>list of weak references to the object (if defined)</p>
</dd></dl>
<dl class="method">
<dt id="mpf.floats.MPF.compatible">
<code class="descname">compatible</code><span class="sig-paren">(</span><em>other</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.MPF.compatible" title="Permalink to this definition">¶</a></dt>
<dd><p>Test if another MPF has the same precision</p>
</dd></dl>
<dl class="method">
<dt id="mpf.floats.MPF.from_rational">
<code class="descname">from_rational</code><span class="sig-paren">(</span><em>rm</em>, <em>q</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.MPF.from_rational" title="Permalink to this definition">¶</a></dt>
<dd><p>Convert from rational to MPF</p>
<p>Sets the value to the nearest representable floating-point
value described by <em>q</em>, rounded according to <em>rm</em>.</p>
</dd></dl>
<dl class="method">
<dt id="mpf.floats.MPF.isFinite">
<code class="descname">isFinite</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.MPF.isFinite" title="Permalink to this definition">¶</a></dt>
<dd><p>Test if value is finite</p>
<p>Returns true for zero, subnormals, or normal numbers.</p>
<p>Returns false for infinities, and not a number.</p>
</dd></dl>
<dl class="method">
<dt id="mpf.floats.MPF.isInfinite">
<code class="descname">isInfinite</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.MPF.isInfinite" title="Permalink to this definition">¶</a></dt>
<dd><p>Test if value is infinite</p>
</dd></dl>
<dl class="method">
<dt id="mpf.floats.MPF.isIntegral">
<code class="descname">isIntegral</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.MPF.isIntegral" title="Permalink to this definition">¶</a></dt>
<dd><p>Test if value is integral</p>
<p>Returns true if the floating-point value is an integer, and
false in all other cases (including infinities and not a
number).</p>
</dd></dl>
<dl class="method">
<dt id="mpf.floats.MPF.isNaN">
<code class="descname">isNaN</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.MPF.isNaN" title="Permalink to this definition">¶</a></dt>
<dd><p>Test if value is not a number</p>
</dd></dl>
<dl class="method">
<dt id="mpf.floats.MPF.isNegative">
<code class="descname">isNegative</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.MPF.isNegative" title="Permalink to this definition">¶</a></dt>
<dd><p>Test if value is negative</p>
<p>Returns always false for NaN.</p>
</dd></dl>
<dl class="method">
<dt id="mpf.floats.MPF.isNormal">
<code class="descname">isNormal</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.MPF.isNormal" title="Permalink to this definition">¶</a></dt>
<dd><p>Test if value is normal</p>
</dd></dl>
<dl class="method">
<dt id="mpf.floats.MPF.isPositive">
<code class="descname">isPositive</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.MPF.isPositive" title="Permalink to this definition">¶</a></dt>
<dd><p>Test if value is positive</p>
<p>Returns always false for NaN.</p>
</dd></dl>
<dl class="method">
<dt id="mpf.floats.MPF.isSubnormal">
<code class="descname">isSubnormal</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.MPF.isSubnormal" title="Permalink to this definition">¶</a></dt>
<dd><p>Test if value is subnormal</p>
</dd></dl>
<dl class="method">
<dt id="mpf.floats.MPF.isZero">
<code class="descname">isZero</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.MPF.isZero" title="Permalink to this definition">¶</a></dt>
<dd><p>Test if value is zero</p>
</dd></dl>
<dl class="method">
<dt id="mpf.floats.MPF.new_mpf">
<code class="descname">new_mpf</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.MPF.new_mpf" title="Permalink to this definition">¶</a></dt>
<dd><p>Copy constructor</p>
<p>Returns a new MPF with the same precision and value.</p>
</dd></dl>
<dl class="method">
<dt id="mpf.floats.MPF.pack">
<code class="descname">pack</code><span class="sig-paren">(</span><em>S</em>, <em>E</em>, <em>T</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.MPF.pack" title="Permalink to this definition">¶</a></dt>
<dd><p>Pack sign, exponent, and significand</p>
<p>Sets the value of the floating point number, such that</p>
<p>The sign corresponds to <em>S</em>, the exponent is <em>E</em>, and the
significand is <em>T</em>.</p>
<p>This is the inverse of <a class="reference internal" href="#mpf.floats.MPF.unpack" title="mpf.floats.MPF.unpack"><code class="xref py py-func docutils literal"><span class="pre">unpack()</span></code></a>.</p>
</dd></dl>
<dl class="method">
<dt id="mpf.floats.MPF.set_infinite">
<code class="descname">set_infinite</code><span class="sig-paren">(</span><em>sign</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.MPF.set_infinite" title="Permalink to this definition">¶</a></dt>
<dd><p>Set value to infinite with the given sign bit</p>
</dd></dl>
<dl class="method">
<dt id="mpf.floats.MPF.set_nan">
<code class="descname">set_nan</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.MPF.set_nan" title="Permalink to this definition">¶</a></dt>
<dd><p>Set value to NaN</p>
</dd></dl>
<dl class="method">
<dt id="mpf.floats.MPF.set_sign_bit">
<code class="descname">set_sign_bit</code><span class="sig-paren">(</span><em>sign</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.MPF.set_sign_bit" title="Permalink to this definition">¶</a></dt>
<dd><p>Set sign bit</p>
</dd></dl>
<dl class="method">
<dt id="mpf.floats.MPF.set_zero">
<code class="descname">set_zero</code><span class="sig-paren">(</span><em>sign</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.MPF.set_zero" title="Permalink to this definition">¶</a></dt>
<dd><p>Set value to zero with the given sign bit</p>
</dd></dl>
<dl class="method">
<dt id="mpf.floats.MPF.smtlib_from_binary_interchange">
<code class="descname">smtlib_from_binary_interchange</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.MPF.smtlib_from_binary_interchange" title="Permalink to this definition">¶</a></dt>
<dd><p>SMT-LIB function for converting from bitvector</p>
</dd></dl>
<dl class="method">
<dt id="mpf.floats.MPF.smtlib_from_float">
<code class="descname">smtlib_from_float</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.MPF.smtlib_from_float" title="Permalink to this definition">¶</a></dt>
<dd><p>SMT-LIB function for converting from FloatingPoint</p>
</dd></dl>
<dl class="method">
<dt id="mpf.floats.MPF.smtlib_from_int">
<code class="descname">smtlib_from_int</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.MPF.smtlib_from_int" title="Permalink to this definition">¶</a></dt>
<dd><p>SMT-LIB function for converting from Int</p>
</dd></dl>
<dl class="method">
<dt id="mpf.floats.MPF.smtlib_from_real">
<code class="descname">smtlib_from_real</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.MPF.smtlib_from_real" title="Permalink to this definition">¶</a></dt>
<dd><p>SMT-LIB function for converting from Real</p>
</dd></dl>
<dl class="method">
<dt id="mpf.floats.MPF.smtlib_from_sbv">
<code class="descname">smtlib_from_sbv</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.MPF.smtlib_from_sbv" title="Permalink to this definition">¶</a></dt>
<dd><p>SMT-LIB function for converting from signed bitvector</p>
</dd></dl>
<dl class="method">
<dt id="mpf.floats.MPF.smtlib_from_ubv">
<code class="descname">smtlib_from_ubv</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.MPF.smtlib_from_ubv" title="Permalink to this definition">¶</a></dt>
<dd><p>SMT-LIB function for converting from unsigned bitvector</p>
</dd></dl>
<dl class="method">
<dt id="mpf.floats.MPF.smtlib_literal">
<code class="descname">smtlib_literal</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.MPF.smtlib_literal" title="Permalink to this definition">¶</a></dt>
<dd><p>Return an SMT-LIB literal</p>
<p>Favours special cases, such as (_ +zero 8 24), otherwise
returns literals of the form (fp ...).</p>
</dd></dl>
<dl class="method">
<dt id="mpf.floats.MPF.smtlib_literals">
<code class="descname">smtlib_literals</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.MPF.smtlib_literals" title="Permalink to this definition">¶</a></dt>
<dd><p>Return list of all possible SMTLIB literals</p>
<p>Includes:</p>
<ul class="simple">
<li>Binary interchange conversion, e.g. ((_ to_fp 8 24) #x00000000)</li>
<li>FP literal, e.g. (fp #b0 #b00 #b000)</li>
<li>Special value, e.g. (_ +zero 2 4)</li>
</ul>
</dd></dl>
<dl class="method">
<dt id="mpf.floats.MPF.smtlib_random_literal">
<code class="descname">smtlib_random_literal</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.MPF.smtlib_random_literal" title="Permalink to this definition">¶</a></dt>
<dd><p>Return an SMT-LIB literal (randomly chosen)</p>
<p>Chooses randomly from <a class="reference internal" href="#mpf.floats.MPF.smtlib_literals" title="mpf.floats.MPF.smtlib_literals"><code class="xref py py-func docutils literal"><span class="pre">smtlib_literals()</span></code></a>.</p>
</dd></dl>
<dl class="method">
<dt id="mpf.floats.MPF.smtlib_sort">
<code class="descname">smtlib_sort</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.MPF.smtlib_sort" title="Permalink to this definition">¶</a></dt>
<dd><p>SMT-LIB sort</p>
<p>Returns “Float16”, “Float32”, “Float64”, or “Float128” if
possible.</p>
<p>Returns “(_ FloatingPoint <em>eb</em> <em>sb</em>)” otherwise.</p>
</dd></dl>
<dl class="method">
<dt id="mpf.floats.MPF.smtlib_to_int">
<code class="descname">smtlib_to_int</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.MPF.smtlib_to_int" title="Permalink to this definition">¶</a></dt>
<dd><p>SMT-LIB function for converting to Int</p>
</dd></dl>
<dl class="method">
<dt id="mpf.floats.MPF.smtlib_to_real">
<code class="descname">smtlib_to_real</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.MPF.smtlib_to_real" title="Permalink to this definition">¶</a></dt>
<dd><p>SMT-LIB function for converting to Real</p>
</dd></dl>
<dl class="method">
<dt id="mpf.floats.MPF.to_int">
<code class="descname">to_int</code><span class="sig-paren">(</span><em>rm</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.MPF.to_int" title="Permalink to this definition">¶</a></dt>
<dd><p>Convert from MPF to Python int`</p>
<p>Raises AssertionError for infinities and NaN. Returns the
integer closest to the floating point, rounded according to
<em>rm</em>.</p>
</dd></dl>
<dl class="method">
<dt id="mpf.floats.MPF.to_python_float">
<code class="descname">to_python_float</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.MPF.to_python_float" title="Permalink to this definition">¶</a></dt>
<dd><p>Convert from MPF to Python float`</p>
<p>Convert to python float. Do not rely on this to be precise for
now.</p>
<div class="admonition-todo admonition" id="index-1">
<p class="first admonition-title">Todo</p>
<p class="last">Use sys.float_info to first convert to the correct
format and then directly interpret the bit-pattern.</p>
</div>
<p>If you want something precise, then use
<a class="reference internal" href="#mpf.floats.MPF.to_python_string" title="mpf.floats.MPF.to_python_string"><code class="xref py py-func docutils literal"><span class="pre">to_python_string()</span></code></a> instead.</p>
</dd></dl>
<dl class="method">
<dt id="mpf.floats.MPF.to_python_string">
<code class="descname">to_python_string</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.MPF.to_python_string" title="Permalink to this definition">¶</a></dt>
<dd><p>Convert from MPF to Python string`</p>
<p>Return a string describing the float. We return a decimal
string (e.g. ‘0.25’), except for the following special cases:
‘-0’, ‘Infinity’, ‘-Infinity’, and ‘NaN’.</p>
<p>The decimal string might be very long (but precise), so if you
want something compact then <a class="reference internal" href="#mpf.floats.MPF.to_python_float" title="mpf.floats.MPF.to_python_float"><code class="xref py py-func docutils literal"><span class="pre">to_python_float()</span></code></a> might be
more appropriate.</p>
</dd></dl>
<dl class="method">
<dt id="mpf.floats.MPF.to_rational">
<code class="descname">to_rational</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.MPF.to_rational" title="Permalink to this definition">¶</a></dt>
<dd><p>Convert from MPF to <a class="reference internal" href="#mpf.rationals.Rational" title="mpf.rationals.Rational"><code class="xref py py-class docutils literal"><span class="pre">Rational</span></code></a></p>
<p>Raises AssertionError for infinities or NaN.</p>
</dd></dl>
<dl class="method">
<dt id="mpf.floats.MPF.unpack">
<code class="descname">unpack</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.MPF.unpack" title="Permalink to this definition">¶</a></dt>
<dd><p>Unpack into sign, exponent, and significand</p>
<p>Returns a tuple of integers (S, E, T) where <em>S</em> is the sign
bit, <em>E</em> is the exponent, and <em>T</em> is the significand.</p>
<p>This is the inverse of <a class="reference internal" href="#mpf.floats.MPF.pack" title="mpf.floats.MPF.pack"><code class="xref py py-func docutils literal"><span class="pre">pack()</span></code></a>.</p>
</dd></dl>
</dd></dl>
<dl class="function">
<dt id="mpf.floats.fp_add">
<code class="descclassname">mpf.floats.</code><code class="descname">fp_add</code><span class="sig-paren">(</span><em>rm</em>, <em>left</em>, <em>right</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.fp_add" title="Permalink to this definition">¶</a></dt>
<dd><p>Floating-point addition</p>
<p>Performs a correctly rounded <span class="math">\(left + right\)</span>. The following special
cases apply:</p>
<ul class="simple">
<li>NaN propagates</li>
<li>Adding opposite infinities results in NaN, otherwise infinities propagate</li>
<li>If the precise result is exactly 0 (i.e. 0 + 0 or a + -a) then we
special case according to Section 6.3 in IEEE-754:<ul>
<li>we preserve the sign if left and right have the same sign</li>
<li>otherwise, we return -0 if the rounding mode is RTN</li>
<li>otherwise, we return +0</li>
</ul>
</li>
</ul>
</dd></dl>
<dl class="function">
<dt id="mpf.floats.fp_div">
<code class="descclassname">mpf.floats.</code><code class="descname">fp_div</code><span class="sig-paren">(</span><em>rm</em>, <em>left</em>, <em>right</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.fp_div" title="Permalink to this definition">¶</a></dt>
<dd><p>Floating-point division</p>
<p>Performs a correctly rounded <span class="math">\(left \div right\)</span>. The
following special cases apply:</p>
<ul class="simple">
<li>NaN propagates</li>
<li>When dividing by infinity<ul>
<li>NaN when dividing two infinities</li>
<li>0 otherwise</li>
</ul>
</li>
<li>When dividing by zero<ul>
<li>NaN when dividing zero by zero</li>
<li>Infinity otherwise</li>
</ul>
</li>
</ul>
</dd></dl>
<dl class="function">
<dt id="mpf.floats.fp_fma">
<code class="descclassname">mpf.floats.</code><code class="descname">fp_fma</code><span class="sig-paren">(</span><em>rm</em>, <em>x</em>, <em>y</em>, <em>z</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.fp_fma" title="Permalink to this definition">¶</a></dt>
<dd><p>Floating-point fused multiply add</p>
<p>Performs a correctly rounded <span class="math">\(x * y + z\)</span>. The special cases
of <a class="reference internal" href="#mpf.floats.fp_mul" title="mpf.floats.fp_mul"><code class="xref py py-func docutils literal"><span class="pre">fp_mul()</span></code></a> and <a class="reference internal" href="#mpf.floats.fp_add" title="mpf.floats.fp_add"><code class="xref py py-func docutils literal"><span class="pre">fp_add()</span></code></a> apply, and in addition:</p>
<ul class="simple">
<li>On a precise 0 result the sign of zero is:<ul>
<li>Preserved if the sign of x * y is the same as z</li>
<li>-0 for RTN</li>
<li>+0 otherwise</li>
</ul>
</li>
</ul>
</dd></dl>
<dl class="function">
<dt id="mpf.floats.fp_from_float">
<code class="descclassname">mpf.floats.</code><code class="descname">fp_from_float</code><span class="sig-paren">(</span><em>eb</em>, <em>sb</em>, <em>rm</em>, <em>op</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.fp_from_float" title="Permalink to this definition">¶</a></dt>
<dd><p>Conversion from MPF to MPF (of a different precision)</p>
</dd></dl>
<dl class="function">
<dt id="mpf.floats.fp_from_int">
<code class="descclassname">mpf.floats.</code><code class="descname">fp_from_int</code><span class="sig-paren">(</span><em>eb</em>, <em>sb</em>, <em>rm</em>, <em>op</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.fp_from_int" title="Permalink to this definition">¶</a></dt>
<dd><p>Conversion from Python integer to MPF</p>
</dd></dl>
<dl class="function">
<dt id="mpf.floats.fp_from_sbv">
<code class="descclassname">mpf.floats.</code><code class="descname">fp_from_sbv</code><span class="sig-paren">(</span><em>eb</em>, <em>sb</em>, <em>rm</em>, <em>op</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.fp_from_sbv" title="Permalink to this definition">¶</a></dt>
<dd><p>Conversion from signed bitvector to MPF</p>
</dd></dl>
<dl class="function">
<dt id="mpf.floats.fp_from_ubv">
<code class="descclassname">mpf.floats.</code><code class="descname">fp_from_ubv</code><span class="sig-paren">(</span><em>eb</em>, <em>sb</em>, <em>rm</em>, <em>op</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.fp_from_ubv" title="Permalink to this definition">¶</a></dt>
<dd><p>Conversion from unsigned bitvector to MPF</p>
</dd></dl>
<dl class="function">
<dt id="mpf.floats.fp_max">
<code class="descclassname">mpf.floats.</code><code class="descname">fp_max</code><span class="sig-paren">(</span><em>left</em>, <em>right</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.fp_max" title="Permalink to this definition">¶</a></dt>
<dd><p>Floating-point maximum</p>
</dd></dl>
<dl class="function">
<dt id="mpf.floats.fp_min">
<code class="descclassname">mpf.floats.</code><code class="descname">fp_min</code><span class="sig-paren">(</span><em>left</em>, <em>right</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.fp_min" title="Permalink to this definition">¶</a></dt>
<dd><p>Floating-point minimum</p>
</dd></dl>
<dl class="function">
<dt id="mpf.floats.fp_mul">
<code class="descclassname">mpf.floats.</code><code class="descname">fp_mul</code><span class="sig-paren">(</span><em>rm</em>, <em>left</em>, <em>right</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.fp_mul" title="Permalink to this definition">¶</a></dt>
<dd><p>Floating-point multiplication</p>
<p>Performs a correctly rounded <span class="math">\(left * right\)</span>. The following
special cases apply:</p>
<ul class="simple">
<li>NaN propagates</li>
<li>Infinities propagate (for non-zero operands)</li>
<li>Multiplying by zero gives the following results<ul>
<li>NaN if the other operand is infinite</li>
<li>0 of the same sign as the 0 operand</li>
</ul>
</li>
</ul>
</dd></dl>
<dl class="function">
<dt id="mpf.floats.fp_nextDown">
<code class="descclassname">mpf.floats.</code><code class="descname">fp_nextDown</code><span class="sig-paren">(</span><em>op</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.fp_nextDown" title="Permalink to this definition">¶</a></dt>
<dd><p>Floating-point predecessor</p>
</dd></dl>
<dl class="function">
<dt id="mpf.floats.fp_nextUp">
<code class="descclassname">mpf.floats.</code><code class="descname">fp_nextUp</code><span class="sig-paren">(</span><em>op</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.fp_nextUp" title="Permalink to this definition">¶</a></dt>
<dd><p>Floating-point successor</p>
</dd></dl>
<dl class="function">
<dt id="mpf.floats.fp_rem">
<code class="descclassname">mpf.floats.</code><code class="descname">fp_rem</code><span class="sig-paren">(</span><em>left</em>, <em>right</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.fp_rem" title="Permalink to this definition">¶</a></dt>
<dd><p>Floating-point remainder</p>
</dd></dl>
<dl class="function">
<dt id="mpf.floats.fp_roundToIntegral">
<code class="descclassname">mpf.floats.</code><code class="descname">fp_roundToIntegral</code><span class="sig-paren">(</span><em>rm</em>, <em>op</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.fp_roundToIntegral" title="Permalink to this definition">¶</a></dt>
<dd><p>Floating-point round to integer</p>
</dd></dl>
<dl class="function">
<dt id="mpf.floats.fp_sqrt">
<code class="descclassname">mpf.floats.</code><code class="descname">fp_sqrt</code><span class="sig-paren">(</span><em>rm</em>, <em>op</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.fp_sqrt" title="Permalink to this definition">¶</a></dt>
<dd><p>Floating-point square root</p>
</dd></dl>
<dl class="function">
<dt id="mpf.floats.fp_sub">
<code class="descclassname">mpf.floats.</code><code class="descname">fp_sub</code><span class="sig-paren">(</span><em>rm</em>, <em>left</em>, <em>right</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.fp_sub" title="Permalink to this definition">¶</a></dt>
<dd><p>Floating-point substraction</p>
<p>Performs a correctly rounded <span class="math">\(left - right\)</span>, which is
equivalent to <span class="math">\(left + -right\)</span>.</p>
<p>See <a class="reference internal" href="#mpf.floats.fp_add" title="mpf.floats.fp_add"><code class="xref py py-func docutils literal"><span class="pre">fp_add()</span></code></a> for special cases.</p>
</dd></dl>
<dl class="function">
<dt id="mpf.floats.fp_to_int">
<code class="descclassname">mpf.floats.</code><code class="descname">fp_to_int</code><span class="sig-paren">(</span><em>rm</em>, <em>op</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.fp_to_int" title="Permalink to this definition">¶</a></dt>
<dd><p>Conversion from MPF to Python integer</p>
</dd></dl>
<dl class="function">
<dt id="mpf.floats.fp_to_sbv">
<code class="descclassname">mpf.floats.</code><code class="descname">fp_to_sbv</code><span class="sig-paren">(</span><em>op</em>, <em>rm</em>, <em>width</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.fp_to_sbv" title="Permalink to this definition">¶</a></dt>
<dd><p>Conversion from MPF to signed bitvector</p>
</dd></dl>
<dl class="function">
<dt id="mpf.floats.fp_to_ubv">
<code class="descclassname">mpf.floats.</code><code class="descname">fp_to_ubv</code><span class="sig-paren">(</span><em>op</em>, <em>rm</em>, <em>width</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.fp_to_ubv" title="Permalink to this definition">¶</a></dt>
<dd><p>Conversion from MPF to unsigned bitvector</p>
</dd></dl>
<dl class="function">
<dt id="mpf.floats.smtlib_eq">
<code class="descclassname">mpf.floats.</code><code class="descname">smtlib_eq</code><span class="sig-paren">(</span><em>left</em>, <em>right</em><span class="sig-paren">)</span><a class="headerlink" href="#mpf.floats.smtlib_eq" title="Permalink to this definition">¶</a></dt>
<dd><p>Bit-wise equality</p>
</dd></dl>
</div>
<div class="section" id="changelog">
<h1>Changelog<a class="headerlink" href="#changelog" title="Permalink to this headline">¶</a></h1>
<div class="section" id="id1">
<h2>1.0<a class="headerlink" href="#id1" title="Permalink to this headline">¶</a></h2>
<div class="section" id="id2">
<h3>1.0.3<a class="headerlink" href="#id2" title="Permalink to this headline">¶</a></h3>
<ul class="simple">
<li>Add basic documentation (fast tutorial, and basic descriptions of
MPF and Rational classes).</li>
</ul>
</div>
<div class="section" id="id3">
<h3>1.0.2<a class="headerlink" href="#id3" title="Permalink to this headline">¶</a></h3>
<ul class="simple">
<li>First public release on PyPI.</li>
</ul>
</div>
</div>
</div>
</div>
</div>
</div>
<div class="sphinxsidebar" role="navigation" aria-label="main navigation">
<div class="sphinxsidebarwrapper">
<h3><a href="#">Table Of Contents</a></h3>
<ul>
<li><a class="reference internal" href="#">PyMPF</a><ul>
<li><a class="reference internal" href="#fast-tutorial">Fast tutorial</a></li>
</ul>
</li>
<li><a class="reference internal" href="#module-mpf.rationals">Rationals</a></li>
<li><a class="reference internal" href="#module-mpf.floats">MPF</a></li>
<li><a class="reference internal" href="#changelog">Changelog</a><ul>
<li><a class="reference internal" href="#id1">1.0</a><ul>
<li><a class="reference internal" href="#id2">1.0.3</a></li>
<li><a class="reference internal" href="#id3">1.0.2</a></li>
</ul>
</li>
</ul>
</li>
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