From d385f2b6da1d69f383416e19ab622975b994964a Mon Sep 17 00:00:00 2001
From: Florian Schanda <florian@schanda.org.uk>
Date: Thu, 14 Mar 2019 13:41:52 +0100
Subject: [PATCH] Add lots of documentation.

---
 docs/.doctrees/environment.pickle | Bin 3635 -> 194818 bytes
 docs/.doctrees/index.doctree      | Bin 7359 -> 142561 bytes
 docs/_sources/index.txt           |   9 +
 docs/genindex.html                | 482 +++++++++++++++++++-
 docs/index.html                   | 715 +++++++++++++++++++++++++++++-
 docs/objects.inv                  | Bin 268 -> 766 bytes
 docs/py-modindex.html             |   5 +
 docs/searchindex.js               |   2 +-
 index.rst                         |   9 +
 mpf/floats.py                     | 279 ++++++++++--
 mpf/rationals.py                  |  70 ++-
 11 files changed, 1529 insertions(+), 42 deletions(-)

diff --git a/docs/.doctrees/environment.pickle b/docs/.doctrees/environment.pickle
index 2cb72334d6c27c6716ba1bf92fe0881bd5d7d4cf..bafb806b8281d9faee9e819ef6e58f333833c394 100644
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diff --git a/docs/.doctrees/index.doctree b/docs/.doctrees/index.doctree
index 624c77004097d698de280ae6db55e45630b7c636..c7a170b8d6ed16fe1986c64ceba84be6f8c8d598 100644
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diff --git a/docs/_sources/index.txt b/docs/_sources/index.txt
index f4d8499..beabcd0 100644
--- a/docs/_sources/index.txt
+++ b/docs/_sources/index.txt
@@ -5,9 +5,18 @@ PyMPF
 .. toctree::
    :maxdepth: 2
 
+=========
+Rationals
+=========
+
+.. automodule:: mpf.rationals
+   :members:
+   :special-members:
+
 ===
 MPF
 ===
 
 .. automodule:: mpf.floats
    :members:
+   :special-members:
diff --git a/docs/genindex.html b/docs/genindex.html
index f79430f..ffcf8c3 100644
--- a/docs/genindex.html
+++ b/docs/genindex.html
@@ -52,10 +52,142 @@ <h3>Navigation</h3>
 <h1 id="index">Index</h1>
 
 <div class="genindex-jumpbox">
- <a href="#F"><strong>F</strong></a>
+ <a href="#_"><strong>_</strong></a>
+ | <a href="#C"><strong>C</strong></a>
+ | <a href="#F"><strong>F</strong></a>
+ | <a href="#I"><strong>I</strong></a>
  | <a href="#M"><strong>M</strong></a>
+ | <a href="#N"><strong>N</strong></a>
+ | <a href="#P"><strong>P</strong></a>
+ | <a href="#Q"><strong>Q</strong></a>
+ | <a href="#R"><strong>R</strong></a>
+ | <a href="#S"><strong>S</strong></a>
+ | <a href="#T"><strong>T</strong></a>
+ | <a href="#U"><strong>U</strong></a>
  
 </div>
+<h2 id="_">_</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%" valign="top"><dl>
+      
+  <dt><a href="index.html#mpf.floats.MPF.__abs__">__abs__() (mpf.floats.MPF method)</a>
+  </dt>
+
+      <dd><dl>
+        
+  <dt><a href="index.html#mpf.rationals.Rational.__abs__">(mpf.rationals.Rational method)</a>
+  </dt>
+
+      </dl></dd>
+      
+  <dt><a href="index.html#mpf.rationals.Rational.__add__">__add__() (mpf.rationals.Rational method)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.floats.MPF.__eq__">__eq__() (mpf.floats.MPF method)</a>
+  </dt>
+
+      <dd><dl>
+        
+  <dt><a href="index.html#mpf.rationals.Rational.__eq__">(mpf.rationals.Rational method)</a>
+  </dt>
+
+      </dl></dd>
+      
+  <dt><a href="index.html#mpf.floats.MPF.__ge__">__ge__() (mpf.floats.MPF method)</a>
+  </dt>
+
+      <dd><dl>
+        
+  <dt><a href="index.html#mpf.rationals.Rational.__ge__">(mpf.rationals.Rational method)</a>
+  </dt>
+
+      </dl></dd>
+      
+  <dt><a href="index.html#mpf.floats.MPF.__gt__">__gt__() (mpf.floats.MPF method)</a>
+  </dt>
+
+      <dd><dl>
+        
+  <dt><a href="index.html#mpf.rationals.Rational.__gt__">(mpf.rationals.Rational method)</a>
+  </dt>
+
+      </dl></dd>
+      
+  <dt><a href="index.html#mpf.floats.MPF.__le__">__le__() (mpf.floats.MPF method)</a>
+  </dt>
+
+      <dd><dl>
+        
+  <dt><a href="index.html#mpf.rationals.Rational.__le__">(mpf.rationals.Rational method)</a>
+  </dt>
+
+      </dl></dd>
+  </dl></td>
+  <td style="width: 33%" valign="top"><dl>
+      
+  <dt><a href="index.html#mpf.floats.MPF.__lt__">__lt__() (mpf.floats.MPF method)</a>
+  </dt>
+
+      <dd><dl>
+        
+  <dt><a href="index.html#mpf.rationals.Rational.__lt__">(mpf.rationals.Rational method)</a>
+  </dt>
+
+      </dl></dd>
+      
+  <dt><a href="index.html#mpf.rationals.Rational.__mul__">__mul__() (mpf.rationals.Rational method)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.rationals.Rational.__ne__">__ne__() (mpf.rationals.Rational method)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.floats.MPF.__neg__">__neg__() (mpf.floats.MPF method)</a>
+  </dt>
+
+      <dd><dl>
+        
+  <dt><a href="index.html#mpf.rationals.Rational.__neg__">(mpf.rationals.Rational method)</a>
+  </dt>
+
+      </dl></dd>
+      
+  <dt><a href="index.html#mpf.rationals.Rational.__pow__">__pow__() (mpf.rationals.Rational method)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.rationals.Rational.__sub__">__sub__() (mpf.rationals.Rational method)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.rationals.Rational.__truediv__">__truediv__() (mpf.rationals.Rational method)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.floats.MPF.__weakref__">__weakref__ (mpf.floats.MPF attribute)</a>
+  </dt>
+
+      <dd><dl>
+        
+  <dt><a href="index.html#mpf.rationals.Rational.__weakref__">(mpf.rationals.Rational attribute)</a>
+  </dt>
+
+      </dl></dd>
+  </dl></td>
+</tr></table>
+
+<h2 id="C">C</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%" valign="top"><dl>
+      
+  <dt><a href="index.html#mpf.floats.MPF.compatible">compatible() (mpf.floats.MPF method)</a>
+  </dt>
+
+  </dl></td>
+</tr></table>
+
 <h2 id="F">F</h2>
 <table style="width: 100%" class="indextable genindextable"><tr>
   <td style="width: 33%" valign="top"><dl>
@@ -63,6 +195,146 @@ <h2 id="F">F</h2>
   <dt><a href="index.html#mpf.floats.fp_add">fp_add() (in module mpf.floats)</a>
   </dt>
 
+      
+  <dt><a href="index.html#mpf.floats.fp_div">fp_div() (in module mpf.floats)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.floats.fp_fma">fp_fma() (in module mpf.floats)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.floats.fp_from_float">fp_from_float() (in module mpf.floats)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.floats.fp_from_int">fp_from_int() (in module mpf.floats)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.floats.fp_from_sbv">fp_from_sbv() (in module mpf.floats)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.floats.fp_from_ubv">fp_from_ubv() (in module mpf.floats)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.floats.fp_max">fp_max() (in module mpf.floats)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.floats.fp_min">fp_min() (in module mpf.floats)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.floats.fp_mul">fp_mul() (in module mpf.floats)</a>
+  </dt>
+
+  </dl></td>
+  <td style="width: 33%" valign="top"><dl>
+      
+  <dt><a href="index.html#mpf.floats.fp_nextDown">fp_nextDown() (in module mpf.floats)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.floats.fp_nextUp">fp_nextUp() (in module mpf.floats)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.floats.fp_rem">fp_rem() (in module mpf.floats)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.floats.fp_roundToIntegral">fp_roundToIntegral() (in module mpf.floats)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.floats.fp_sqrt">fp_sqrt() (in module mpf.floats)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.floats.fp_sub">fp_sub() (in module mpf.floats)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.floats.fp_to_int">fp_to_int() (in module mpf.floats)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.floats.fp_to_sbv">fp_to_sbv() (in module mpf.floats)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.floats.fp_to_ubv">fp_to_ubv() (in module mpf.floats)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.floats.MPF.from_rational">from_rational() (mpf.floats.MPF method)</a>
+  </dt>
+
+  </dl></td>
+</tr></table>
+
+<h2 id="I">I</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%" valign="top"><dl>
+      
+  <dt><a href="index.html#mpf.floats.MPF.isFinite">isFinite() (mpf.floats.MPF method)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.floats.MPF.isInfinite">isInfinite() (mpf.floats.MPF method)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.floats.MPF.isIntegral">isIntegral() (mpf.floats.MPF method)</a>
+  </dt>
+
+      <dd><dl>
+        
+  <dt><a href="index.html#mpf.rationals.Rational.isIntegral">(mpf.rationals.Rational method)</a>
+  </dt>
+
+      </dl></dd>
+      
+  <dt><a href="index.html#mpf.floats.MPF.isNaN">isNaN() (mpf.floats.MPF method)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.floats.MPF.isNegative">isNegative() (mpf.floats.MPF method)</a>
+  </dt>
+
+      <dd><dl>
+        
+  <dt><a href="index.html#mpf.rationals.Rational.isNegative">(mpf.rationals.Rational method)</a>
+  </dt>
+
+      </dl></dd>
+  </dl></td>
+  <td style="width: 33%" valign="top"><dl>
+      
+  <dt><a href="index.html#mpf.floats.MPF.isNormal">isNormal() (mpf.floats.MPF method)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.floats.MPF.isPositive">isPositive() (mpf.floats.MPF method)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.floats.MPF.isSubnormal">isSubnormal() (mpf.floats.MPF method)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.floats.MPF.isZero">isZero() (mpf.floats.MPF method)</a>
+  </dt>
+
+      <dd><dl>
+        
+  <dt><a href="index.html#mpf.rationals.Rational.isZero">(mpf.rationals.Rational method)</a>
+  </dt>
+
+      </dl></dd>
   </dl></td>
 </tr></table>
 
@@ -70,9 +342,217 @@ <h2 id="M">M</h2>
 <table style="width: 100%" class="indextable genindextable"><tr>
   <td style="width: 33%" valign="top"><dl>
       
+  <dt><a href="index.html#mpf.floats.MPF">MPF (class in mpf.floats)</a>
+  </dt>
+
+  </dl></td>
+  <td style="width: 33%" valign="top"><dl>
+      
   <dt><a href="index.html#module-mpf.floats">mpf.floats (module)</a>
   </dt>
 
+      
+  <dt><a href="index.html#module-mpf.rationals">mpf.rationals (module)</a>
+  </dt>
+
+  </dl></td>
+</tr></table>
+
+<h2 id="N">N</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%" valign="top"><dl>
+      
+  <dt><a href="index.html#mpf.floats.MPF.new_mpf">new_mpf() (mpf.floats.MPF method)</a>
+  </dt>
+
+  </dl></td>
+</tr></table>
+
+<h2 id="P">P</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%" valign="top"><dl>
+      
+  <dt><a href="index.html#mpf.floats.MPF.pack">pack() (mpf.floats.MPF method)</a>
+  </dt>
+
+  </dl></td>
+</tr></table>
+
+<h2 id="Q">Q</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%" valign="top"><dl>
+      
+  <dt><a href="index.html#mpf.rationals.q_from_decimal_fragments">q_from_decimal_fragments() (in module mpf.rationals)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.rationals.q_pow2">q_pow2() (in module mpf.rationals)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.rationals.q_round_rna">q_round_rna() (in module mpf.rationals)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.rationals.q_round_rne">q_round_rne() (in module mpf.rationals)</a>
+  </dt>
+
+  </dl></td>
+  <td style="width: 33%" valign="top"><dl>
+      
+  <dt><a href="index.html#mpf.rationals.q_round_rtn">q_round_rtn() (in module mpf.rationals)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.rationals.q_round_rtp">q_round_rtp() (in module mpf.rationals)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.rationals.q_round_rtz">q_round_rtz() (in module mpf.rationals)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.rationals.q_round_to_nearest">q_round_to_nearest() (in module mpf.rationals)</a>
+  </dt>
+
+  </dl></td>
+</tr></table>
+
+<h2 id="R">R</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%" valign="top"><dl>
+      
+  <dt><a href="index.html#mpf.rationals.Rational">Rational (class in mpf.rationals)</a>
+  </dt>
+
+  </dl></td>
+</tr></table>
+
+<h2 id="S">S</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%" valign="top"><dl>
+      
+  <dt><a href="index.html#mpf.floats.MPF.set_infinite">set_infinite() (mpf.floats.MPF method)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.floats.MPF.set_nan">set_nan() (mpf.floats.MPF method)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.floats.MPF.set_sign_bit">set_sign_bit() (mpf.floats.MPF method)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.floats.MPF.set_zero">set_zero() (mpf.floats.MPF method)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.floats.smtlib_eq">smtlib_eq() (in module mpf.floats)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.floats.MPF.smtlib_from_binary_interchange">smtlib_from_binary_interchange() (mpf.floats.MPF method)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.floats.MPF.smtlib_from_float">smtlib_from_float() (mpf.floats.MPF method)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.floats.MPF.smtlib_from_int">smtlib_from_int() (mpf.floats.MPF method)</a>
+  </dt>
+
+  </dl></td>
+  <td style="width: 33%" valign="top"><dl>
+      
+  <dt><a href="index.html#mpf.floats.MPF.smtlib_from_real">smtlib_from_real() (mpf.floats.MPF method)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.floats.MPF.smtlib_from_sbv">smtlib_from_sbv() (mpf.floats.MPF method)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.floats.MPF.smtlib_from_ubv">smtlib_from_ubv() (mpf.floats.MPF method)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.floats.MPF.smtlib_literal">smtlib_literal() (mpf.floats.MPF method)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.floats.MPF.smtlib_literals">smtlib_literals() (mpf.floats.MPF method)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.floats.MPF.smtlib_random_literal">smtlib_random_literal() (mpf.floats.MPF method)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.floats.MPF.smtlib_sort">smtlib_sort() (mpf.floats.MPF method)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.floats.MPF.smtlib_to_int">smtlib_to_int() (mpf.floats.MPF method)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.floats.MPF.smtlib_to_real">smtlib_to_real() (mpf.floats.MPF method)</a>
+  </dt>
+
+  </dl></td>
+</tr></table>
+
+<h2 id="T">T</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%" valign="top"><dl>
+      
+  <dt><a href="index.html#mpf.rationals.Rational.to_decimal_string">to_decimal_string() (mpf.rationals.Rational method)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.floats.MPF.to_int">to_int() (mpf.floats.MPF method)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.floats.MPF.to_python_float">to_python_float() (mpf.floats.MPF method)</a>
+  </dt>
+
+      <dd><dl>
+        
+  <dt><a href="index.html#mpf.rationals.Rational.to_python_float">(mpf.rationals.Rational method)</a>
+  </dt>
+
+      </dl></dd>
+  </dl></td>
+  <td style="width: 33%" valign="top"><dl>
+      
+  <dt><a href="index.html#mpf.rationals.Rational.to_python_int">to_python_int() (mpf.rationals.Rational method)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.floats.MPF.to_python_string">to_python_string() (mpf.floats.MPF method)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.floats.MPF.to_rational">to_rational() (mpf.floats.MPF method)</a>
+  </dt>
+
+      
+  <dt><a href="index.html#mpf.rationals.Rational.to_smtlib">to_smtlib() (mpf.rationals.Rational method)</a>
+  </dt>
+
+  </dl></td>
+</tr></table>
+
+<h2 id="U">U</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%" valign="top"><dl>
+      
+  <dt><a href="index.html#mpf.floats.MPF.unpack">unpack() (mpf.floats.MPF method)</a>
+  </dt>
+
   </dl></td>
 </tr></table>
 
diff --git a/docs/index.html b/docs/index.html
index 17644be..3f9e6f5 100644
--- a/docs/index.html
+++ b/docs/index.html
@@ -51,33 +51,727 @@ <h3>Navigation</h3>
 <h1>PyMPF<a class="headerlink" href="#pympf" title="Permalink to this headline">¶</a></h1>
 <div class="toctree-wrapper compound">
 </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>&gt;=</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>&gt;</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>&lt;=</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>&lt;</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. &#8220;1.0&#8221;.</p>
+<p>Returns an s-expression otherwise, e.g. &#8220;(- (/ 1.0 3.0))&#8221;.</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 &#8220;1.23E-1&#8221; we have fragments for</dt>
+<dd>sign          =   &#8220;&#8221;
+integer_part  =  &#8220;1&#8221;
+fraction_part = &#8220;23&#8221;
+exp_part      = &#8220;-1&#8221;</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 &#8220;hidden bit&#8221;, 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">&gt;&gt;&gt; </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">\(0 \le bitvec &lt; 2^{eb+sb}\)</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">&gt;&gt;&gt; </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">&gt;&gt;&gt; </span><span class="n">x</span><span class="o">.</span><span class="n">to_python_string</span><span class="p">()</span>
+<span class="go">&#39;1.0&#39;</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 &#8220;Float16&#8221;, &#8220;Float32&#8221;, &#8220;Float64&#8221;, or &#8220;Float128&#8221; if
+possible.</p>
+<p>Returns &#8220;(_ FloatingPoint <em>eb</em> <em>sb</em>)&#8221; 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. &#8216;0.25&#8217;), except for the following special cases:
+&#8216;-0&#8217;, &#8216;Infinity&#8217;, &#8216;-Infinity&#8217;, and &#8216;NaN&#8217;.</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>
-<li><p class="first">NaN propagates</p>
-</li>
-<li><p class="first">Adding opposite infinities results in NaN, otherwise infinities propagate</p>
-</li>
-<li><p class="first">If the precise result is exactly 0 then we special case
-according to Section 6.3 in IEEE-754:</p>
-<blockquote>
-<div><ul class="simple">
+<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>
-</div></blockquote>
 </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>
 
 
@@ -89,6 +783,7 @@ <h1>PyMPF<a class="headerlink" href="#pympf" title="Permalink to this headline">
   <h3><a href="#">Table Of Contents</a></h3>
   <ul>
 <li><a class="reference internal" href="#">PyMPF</a></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>
 </ul>
 
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diff --git a/docs/py-modindex.html b/docs/py-modindex.html
index 2532f57..0e236d5 100644
--- a/docs/py-modindex.html
+++ b/docs/py-modindex.html
@@ -72,6 +72,11 @@ <h1>Python Module Index</h1>
        <td>&#160;&#160;&#160;
        <a href="index.html#module-mpf.floats"><code class="xref">mpf.floats</code></a></td><td>
        <em></em></td></tr>
+     <tr class="cg-1">
+       <td></td>
+       <td>&#160;&#160;&#160;
+       <a href="index.html#module-mpf.rationals"><code class="xref">mpf.rationals</code></a></td><td>
+       <em></em></td></tr>
    </table>
 
 
diff --git a/docs/searchindex.js b/docs/searchindex.js
index f599677..9c5711d 100644
--- a/docs/searchindex.js
+++ b/docs/searchindex.js
@@ -1 +1 @@
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\ No newline at end of file
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\ No newline at end of file
diff --git a/index.rst b/index.rst
index f4d8499..beabcd0 100644
--- a/index.rst
+++ b/index.rst
@@ -5,9 +5,18 @@ PyMPF
 .. toctree::
    :maxdepth: 2
 
+=========
+Rationals
+=========
+
+.. automodule:: mpf.rationals
+   :members:
+   :special-members:
+
 ===
 MPF
 ===
 
 .. automodule:: mpf.floats
    :members:
+   :special-members:
diff --git a/mpf/floats.py b/mpf/floats.py
index aec8ff9..c09f484 100644
--- a/mpf/floats.py
+++ b/mpf/floats.py
@@ -24,19 +24,21 @@
 ##                                                                          ##
 ##############################################################################
 
-# 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.
-#
-# 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).
+"""
+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.
+
+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).
+"""
 
 # TODO: Implement RNA in intervals
 
@@ -63,7 +65,30 @@ class Unspecified(Exception):
 RM_RTN = "RTN"
 RM_RTZ = "RTZ"
 
-class MPF(object):
+class MPF:
+    """Arbitrary precision IEEE-754 floating point number
+
+    *eb* is the number of bits for the exponent.
+
+    *sb* is the number of bits for the significand.
+
+    This includes the "hidden bit", so for example to create a
+    single-precision floating point number we use:
+
+    >>> x = MPF(8, 24)
+
+    By default the created float is +0, however *bitvec* can be used
+    to set the initial value. The expected format is an integer
+    :math:`0 \le bitvec < 2^{eb+sb}` corresponding to the binary
+    interchange format. For example to create the single precision
+    float representing +1:
+
+    >>> x = MPF(8, 24, 0x3f800000)
+    >>> x.to_python_string()
+    '1.0'
+
+    """
+
     ROUNDING_MODES          = (RM_RNE, RM_RNA, RM_RTP, RM_RTN, RM_RTZ)
     ROUNDING_MODES_NEAREST  = (RM_RNE, RM_RNA)
     ROUNDING_MODES_DIRECTED = (RM_RTP, RM_RTN, RM_RTZ)
@@ -87,20 +112,37 @@ def __init__(self, eb, sb, bitvec=0):
 
         self.bv   = bitvec
 
+    def __repr__(self):
+        return "MPF(%u, %u, 0x%x)" % (self.w, self.p, self.bv)
+
     ######################################################################
     # Constructors
 
     def new_mpf(self):
+        """Copy constructor
+
+        Returns a new MPF with the same precision and value.
+        """
         return MPF(self.w, self.p, self.bv)
 
     ######################################################################
     # Internal utilities
 
     def compatible(self, other):
+        """Test if another MPF has the same precision"""
         return (self.w == other.w and
                 self.p == other.p)
 
     def unpack(self):
+        """Unpack into sign, exponent, and significand
+
+        Returns a tuple of integers (S, E, T) where *S* is the sign
+        bit, *E* is the exponent, and *T* is the significand.
+
+        This is the inverse of :func:`pack`.
+
+        """
+
         # TODO: remove ugly hack to convert via strings
         bits = "{0:b}".format(self.bv)
         assert len(bits) <= self.k
@@ -113,6 +155,16 @@ def unpack(self):
         return (S, E, T)
 
     def pack(self, S, E, T):
+        """Pack sign, exponent, and significand
+
+        Sets the value of the floating point number, such that
+
+        The sign corresponds to *S*, the exponent is *E*, and the
+        significand is *T*.
+
+        This is the inverse of :func:`unpack`.
+
+        """
         assert 0 <= S <= 1
         assert 0 <= E <= 2 ** self.w - 1
         assert 0 <= T <= 2 ** self.t - 1
@@ -142,6 +194,12 @@ def inf_boundary(self):
         return inf.to_python_int()
 
     def from_rational(self, rm, q):
+        """Convert from rational to MPF
+
+        Sets the value to the nearest representable floating-point
+        value described by *q*, rounded according to *rm*.
+
+        """
         assert rm in MPF.ROUNDING_MODES
 
         inf = Rational(self.inf_boundary())
@@ -255,6 +313,10 @@ def from_rational(self, rm, q):
         self.set_sign_bit(sign)
 
     def to_rational(self):
+        """Convert from MPF to :class:`.Rational`
+
+        Raises AssertionError for infinities or NaN.
+        """
         S, E, T = self.unpack()
 
         if E == 2 ** self.w - 1:
@@ -280,6 +342,13 @@ def to_rational(self):
         return v
 
     def to_int(self, rm):
+        """Convert from MPF to Python int`
+
+        Raises AssertionError for infinities and NaN. Returns the
+        integer closest to the floating point, rounded according to
+        *rm*.
+
+        """
         assert rm in MPF.ROUNDING_MODES
         assert self.isFinite()
 
@@ -289,6 +358,17 @@ def to_int(self, rm):
         return q.a
 
     def to_python_float(self):
+        """Convert from MPF to Python float`
+
+        Convert to python float. Do not rely on this to be precise for
+        now.
+
+        .. todo:: Use sys.float_info to first convert to the correct
+          format and then directly interpret the bit-pattern.
+
+        If you want something precise, then use
+        :func:`to_python_string` instead.
+        """
         if self.isNaN():
             return float("NaN")
         elif self.isInfinite():
@@ -300,6 +380,17 @@ def to_python_float(self):
             return self.to_rational().to_python_float()
 
     def to_python_string(self):
+        """Convert from MPF to Python string`
+
+        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'.
+
+        The decimal string might be very long (but precise), so if you
+        want something compact then :func:`to_python_float` might be
+        more appropriate.
+
+        """
         if self.isNaN():
             return "NaN"
         elif self.isInfinite():
@@ -316,19 +407,22 @@ def to_python_string(self):
     # Setters
 
     def set_zero(self, sign):
+        """Set value to zero with the given sign bit"""
         assert 0 <= sign <= 1
         self.pack(sign, 0, 0)
 
     def set_infinite(self, sign):
+        """Set value to infinite with the given sign bit"""
         assert 0 <= sign <= 1
         self.pack(sign, 2 ** self.w - 1, 0)
 
     def set_nan(self):
+        """Set value to NaN"""
         self.pack(1, 2 ** self.w - 1, 2 ** self.t - 1)
 
     def set_sign_bit(self, sign):
-        assert type(sign) is bool
-
+        """Set sign bit"""
+        assert 0 <= sign <= 1
         S, E, T = self.unpack()
         S = (1 if sign else 0)
         self.pack(S, E, T)
@@ -367,6 +461,7 @@ def __str__(self):
         return rv
 
     def __abs__(self):
+        """Compute absolute value"""
         rv = self.new_mpf()
         S, E, T = rv.unpack()
         if not rv.isNaN():
@@ -375,6 +470,7 @@ def __abs__(self):
         return rv
 
     def __neg__(self):
+        """Compute inverse"""
         rv = self.new_mpf()
         S, E, T = rv.unpack()
         if not rv.isNaN():
@@ -383,6 +479,7 @@ def __neg__(self):
         return rv
 
     def __le__(self, other):
+        """Test floating-point less than or equal"""
         assert self.compatible(other)
         if self.isNaN() or other.isNaN():
             return False
@@ -390,6 +487,7 @@ def __le__(self, other):
             return self.partial_order() <= other.partial_order()
 
     def __lt__(self, other):
+        """Test floating-point less than"""
         assert self.compatible(other)
         if self.isNaN() or other.isNaN():
             return False
@@ -397,6 +495,7 @@ def __lt__(self, other):
             return self.partial_order() < other.partial_order()
 
     def __ge__(self, other):
+        """Test floating-point greater than or equal"""
         assert self.compatible(other)
         if self.isNaN() or other.isNaN():
             return False
@@ -404,6 +503,7 @@ def __ge__(self, other):
             return self.partial_order() >= other.partial_order()
 
     def __gt__(self, other):
+        """Test floating-point greater than"""
         assert self.compatible(other)
         if self.isNaN() or other.isNaN():
             return False
@@ -411,6 +511,14 @@ def __gt__(self, other):
             return self.partial_order() > other.partial_order()
 
     def __eq__(self, other):
+        """Test floating-point equality
+
+        Note that this is floating-point equality, so comparisons to
+        NaN always fail and -0 and +0 are considered equal.
+
+        If you want true equality, use :func:`smtlib_eq`
+
+        """
         assert self.compatible(other)
         if self.isNaN() or other.isNaN():
             return False
@@ -421,37 +529,63 @@ def __eq__(self, other):
     # Queries
 
     def isZero(self):
+        """Test if value is zero"""
         S, E, T = self.unpack()
         return E == 0 and T == 0
 
     def isSubnormal(self):
+        """Test if value is subnormal"""
         S, E, T = self.unpack()
         return E == 0 and T != 0
 
     def isNormal(self):
+        """Test if value is normal"""
         S, E, T = self.unpack()
         return 1 <= E <= 2 ** self.w - 2
 
     def isNaN(self):
+        """Test if value is not a number"""
         S, E, T = self.unpack()
         return E == 2 ** self.w - 1 and T != 0
 
     def isInfinite(self):
+        """Test if value is infinite"""
         S, E, T = self.unpack()
         return E == 2 ** self.w - 1 and T == 0
 
     def isPositive(self):
+        """Test if value is positive
+
+        Returns always false for NaN.
+        """
         S, E, T = self.unpack()
         return not self.isNaN() and S == 0
 
     def isNegative(self):
+        """Test if value is negative
+
+        Returns always false for NaN.
+        """
         S, E, T = self.unpack()
         return not self.isNaN() and S == 1
 
     def isFinite(self):
+        """Test if value is finite
+
+        Returns true for zero, subnormals, or normal numbers.
+
+        Returns false for infinities, and not a number.
+        """
         return self.isZero() or self.isSubnormal() or self.isNormal()
 
     def isIntegral(self):
+        """Test if value is integral
+
+        Returns true if the floating-point value is an integer, and
+        false in all other cases (including infinities and not a
+        number).
+        """
+
         if self.isFinite():
             return self.to_rational().isIntegral()
         else:
@@ -461,6 +595,14 @@ def isIntegral(self):
     # SMTLIB support
 
     def smtlib_sort(self):
+        """SMT-LIB sort
+
+        Returns "Float16", "Float32", "Float64", or "Float128" if
+        possible.
+
+        Returns "(_ FloatingPoint *eb* *sb*)" otherwise.
+
+        """
         if self.w == 5 and self.p == 11:
             return "Float16"
         elif self.w == 8 and self.p == 24:
@@ -473,30 +615,46 @@ def smtlib_sort(self):
             return "(_ FloatingPoint %u %u)" % (self.w, self.p)
 
     def smtlib_from_binary_interchange(self):
+        """SMT-LIB function for converting from bitvector"""
         return "(_ to_fp %u %u)" % (self.w, self.p)
 
     def smtlib_from_float(self):
+        """SMT-LIB function for converting from FloatingPoint"""
         return "(_ to_fp %u %u)" % (self.w, self.p)
 
     def smtlib_from_real(self):
+        """SMT-LIB function for converting from Real"""
         return "(_ to_fp %u %u)" % (self.w, self.p)
 
     def smtlib_from_int(self):
+        """SMT-LIB function for converting from Int"""
         return "(_ to_fp %u %u)" % (self.w, self.p)
 
     def smtlib_from_ubv(self):
+        """SMT-LIB function for converting from unsigned bitvector"""
         return "(_ to_fp_unsigned %u %u)" % (self.w, self.p)
 
     def smtlib_from_sbv(self):
+        """SMT-LIB function for converting from signed bitvector"""
         return "(_ to_fp %u %u)" % (self.w, self.p)
 
     def smtlib_to_real(self):
+        """SMT-LIB function for converting to Real"""
         return "fp.to_real"
 
     def smtlib_to_int(self):
+        """SMT-LIB function for converting to Int"""
         return "fp.to_int"
 
     def smtlib_literals(self):
+        """Return list of all possible SMTLIB literals
+
+        Includes:
+
+        * Binary interchange conversion, e.g. ((_ to_fp 8 24) #x00000000)
+        * FP literal, e.g. (fp #b0 #b00 #b000)
+        * Special value, e.g. (_ +zero 2 4)
+        """
         choices = []
 
         # Binary interchange
@@ -539,9 +697,19 @@ def smtlib_literals(self):
         return choices
 
     def smtlib_literal(self):
+        """Return an SMT-LIB literal
+
+        Favours special cases, such as (_ +zero 8 24), otherwise
+        returns literals of the form (fp ...).
+
+        """
         return self.smtlib_literals()[-1]
 
     def smtlib_random_literal(self):
+        """Return an SMT-LIB literal (randomly chosen)
+
+        Chooses randomly from :func:`smtlib_literals`.
+        """
         return random.choice(self.smtlib_literals())
 
 def q_round(rm, n):
@@ -560,17 +728,13 @@ def fp_add(rm, left, right):
     cases apply:
 
     * NaN propagates
-
     * Adding opposite infinities results in NaN, otherwise infinities propagate
+    * 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:
 
-    * If the precise result is exactly 0 then we special case
-      according to Section 6.3 in IEEE-754:
-
-        * we preserve the sign if left and right have the same sign
-
-        * otherwise, we return -0 if the rounding mode is RTN
-
-        * otherwise, we return +0
+      * we preserve the sign if left and right have the same sign
+      * otherwise, we return -0 if the rounding mode is RTN
+      * otherwise, we return +0
 
     """
     assert rm in MPF.ROUNDING_MODES
@@ -606,6 +770,14 @@ def fp_add(rm, left, right):
     return rv
 
 def fp_sub(rm, left, right):
+    """Floating-point substraction
+
+    Performs a correctly rounded :math:`left - right`, which is
+    equivalent to :math:`left + -right`.
+
+    See :func:`fp_add` for special cases.
+
+    """
     assert rm in MPF.ROUNDING_MODES
     assert left.compatible(right)
     rv = left.new_mpf() # rv == left
@@ -639,6 +811,19 @@ def fp_sub(rm, left, right):
     return rv
 
 def fp_mul(rm, left, right):
+    """Floating-point multiplication
+
+    Performs a correctly rounded :math:`left * right`. The following
+    special cases apply:
+
+    * NaN propagates
+    * Infinities propagate (for non-zero operands)
+    * Multiplying by zero gives the following results
+
+      * NaN if the other operand is infinite
+      * 0 of the same sign as the 0 operand
+
+    """
     assert rm in MPF.ROUNDING_MODES
     assert left.compatible(right)
     sign = (1 if left.isNegative() ^ right.isNegative() else 0)
@@ -660,6 +845,23 @@ def fp_mul(rm, left, right):
     return rv
 
 def fp_div(rm, left, right):
+    """Floating-point division
+
+    Performs a correctly rounded :math:`left \div right`. The
+    following special cases apply:
+
+    * NaN propagates
+    * When dividing by infinity
+
+      * NaN when dividing two infinities
+      * 0 otherwise
+
+    * When dividing by zero
+
+      * NaN when dividing zero by zero
+      * Infinity otherwise
+
+    """
     assert rm in MPF.ROUNDING_MODES
     assert left.compatible(right)
     sign = (1 if left.isNegative() ^ right.isNegative() else 0)
@@ -685,7 +887,17 @@ def fp_div(rm, left, right):
     return rv
 
 def fp_fma(rm, x, y, z):
-    # computes (x * y) + z
+    """Floating-point fused multiply add
+
+    Performs a correctly rounded :math:`x * y + z`. The special cases
+    of :func:`fp_mul` and :func:`fp_add` apply, and in addition:
+
+    * On a precise 0 result the sign of zero is:
+
+      * Preserved if the sign of x * y is the same as z
+      * -0 for RTN
+      * +0 otherwise
+    """
     assert rm in MPF.ROUNDING_MODES
     assert x.compatible(y)
     assert x.compatible(z)
@@ -725,6 +937,7 @@ def fp_fma(rm, x, y, z):
     return rv
 
 def fp_sqrt(rm, op):
+    """Floating-point square root"""
     assert rm in MPF.ROUNDING_MODES
     # We can get away with approximating the square root to sufficient
     # precision because of Theorem 19 (p168) of the Handbook of
@@ -779,6 +992,7 @@ def fp_sqrt(rm, op):
     return root
 
 def fp_rem(left, right):
+    """Floating-point remainder"""
     assert left.compatible(right)
 
     rv = left.new_mpf()
@@ -798,6 +1012,7 @@ def fp_rem(left, right):
     return rv
 
 def fp_roundToIntegral(rm, op):
+    """Floating-point round to integer"""
     assert rm in MPF.ROUNDING_MODES
 
     rv = op.new_mpf()
@@ -814,6 +1029,7 @@ def fp_roundToIntegral(rm, op):
     return rv
 
 def fp_min(left, right):
+    """Floating-point minimum"""
     assert left.compatible(right)
     if (left.isZero() and right.isZero() and
         left.isPositive() != right.isPositive()):
@@ -827,6 +1043,7 @@ def fp_min(left, right):
         return left.new_mpf()
 
 def fp_max(left, right):
+    """Floating-point maximum"""
     assert left.compatible(right)
     if (left.isZero() and right.isZero() and
         left.isPositive() != right.isPositive()):
@@ -840,10 +1057,12 @@ def fp_max(left, right):
         return left.new_mpf()
 
 def smtlib_eq(left, right):
+    """Bit-wise equality"""
     assert left.compatible(right)
     return (left.isNaN() and right.isNaN()) or (left.bv == right.bv)
 
 def fp_nextUp(op):
+    """Floating-point successor"""
     rv = op.new_mpf()
 
     if op.isNaN():
@@ -878,15 +1097,18 @@ def fp_nextUp(op):
     return rv
 
 def fp_nextDown(op):
+    """Floating-point predecessor"""
     # This is how it is defined in 5.3.1
     return -fp_nextUp(-op)
 
 def fp_from_ubv(eb, sb, rm, op):
+    """Conversion from unsigned bitvector to MPF"""
     rv = MPF(eb, sb)
     rv.from_rational(rm, op.to_unsigned_int())
     return rv
 
 def fp_to_ubv(op, rm, width):
+    """Conversion from MPF to unsigned bitvector"""
     if op.isInfinite() or op.isNaN():
         raise Unspecified
 
@@ -900,11 +1122,13 @@ def fp_to_ubv(op, rm, width):
         raise Unspecified
 
 def fp_from_sbv(eb, sb, rm, op):
+    """Conversion from signed bitvector to MPF"""
     rv = MPF(eb, sb)
     rv.from_rational(rm, op.to_signed_int())
     return rv
 
 def fp_to_sbv(op, rm, width):
+    """Conversion from MPF to signed bitvector"""
     if op.isInfinite() or op.isNaN():
         raise Unspecified
 
@@ -919,12 +1143,14 @@ def fp_to_sbv(op, rm, width):
 
 # ((_ to_fp eb sb) rm op)
 def fp_from_int(eb, sb, rm, op):
+    """Conversion from Python integer to MPF"""
     rv = MPF(eb, sb)
     rv.from_rational(rm, Rational(op))
     return rv
 
 # (fp.to_int rm op)
 def fp_to_int(rm, op):
+    """Conversion from MPF to Python integer"""
     if op.isInfinite() or op.isNaN():
         raise Unspecified
 
@@ -938,6 +1164,7 @@ def fp_to_int(rm, op):
 # is where you land when you read 5.4.2), but in 6.3 it says it
 # doesn't change.
 def fp_from_float(eb, sb, rm, op):
+    """Conversion from MPF to MPF (of a different precision)"""
     rv = MPF(eb, sb)
     if op.isNaN():
         rv.set_nan()
diff --git a/mpf/rationals.py b/mpf/rationals.py
index b3c084e..1e4dd0a 100644
--- a/mpf/rationals.py
+++ b/mpf/rationals.py
@@ -23,12 +23,21 @@
 ##                                                                          ##
 ##############################################################################
 
-# Todo: Make this a subclass of Fraction instead of re-inventing the
-# wheel.
+"""
+This module defines class to deal with Rational numbers.
+
+.. todo:: This should be a subclass of fractions.Fraction.
+"""
 
 import fractions
 
 class Rational(object):
+    """Rational number
+
+    *a* is the numerator
+
+    *b* is the denominator
+    """
     def __init__(self, a=0, b=1):
         assert type(a) is int
         assert type(b) is int
@@ -45,22 +54,31 @@ def __init__(self, a=0, b=1):
         assert type(self.b) is int
 
     def __mul__(self, other):
+        """Multiplication"""
         return Rational(self.a*other.a,
                         self.b*other.b)
 
     def __truediv__(self, other):
+        """Division"""
         return Rational(self.a*other.b,
                         self.b*other.a)
 
     def __add__(self, other):
+        """Addition"""
         return Rational(self.a*other.b + other.a*self.b,
                         self.b*other.b)
 
     def __sub__(self, other):
+        """Substraction"""
         return Rational(self.a*other.b - other.a*self.b,
                         self.b*other.b)
 
     def __pow__(self, other):
+        """Exponentiation
+
+        The right-hand side must be an integral Rational, otherwise
+        AssertionError is raised.
+        """
         assert other.isIntegral()
 
         a = fractions.Fraction(self.a, self.b)
@@ -69,9 +87,11 @@ def __pow__(self, other):
         return Rational(p.numerator, p.denominator)
 
     def __abs__(self):
+        """Absolute value"""
         return Rational(abs(self.a), self.b)
 
     def __neg__(self):
+        """Negation"""
         return Rational(-self.a, self.b)
 
     def __repr__(self):
@@ -81,40 +101,60 @@ def __repr__(self):
             return "Rational(%i, %u)" % (self.a, self.b)
 
     def __lt__(self, other):
+        """<"""
         return self.a*other.b < other.a*self.b
 
     def __le__(self, other):
+        """<="""
         return self.a*other.b <= other.a*self.b
 
     def __eq__(self, other):
+        """Equality"""
         return self.a*other.b == other.a*self.b
 
     def __ne__(self, other):
+        """Inequality"""
         return self.a*other.b != other.a*self.b
 
     def __gt__(self, other):
+        """>"""
         return self.a*other.b > other.a*self.b
 
     def __ge__(self, other):
+        """>="""
         return self.a*other.b >= other.a*self.b
 
     def isZero(self):
+        """Test if zero"""
         return self.a == 0
 
     def isNegative(self):
+        """Test if negative
+
+        Returns false for 0.
+        """
         return self.a < 0
 
     def isIntegral(self):
+        """Test if integral"""
         return (self.a % self.b) == 0
 
     def to_python_int(self):
+        """Convert to python int"""
         assert self.isIntegral()
         return self.a
 
     def to_python_float(self):
+        """Convert to python float"""
         return float(fractions.Fraction(self.a, self.b))
 
     def to_smtlib(self):
+        """Convert to SMT-LIB Real expression
+
+        Returns literal for integrals, e.g. "1.0".
+
+        Returns an s-expression otherwise, e.g. "(- (/ 1.0 3.0))".
+        """
         tmp = "%u.0" % abs(self.a)
         if self.b != 1:
             tmp = "(/ %s %u.0)" % (tmp, self.b)
@@ -123,6 +163,12 @@ def to_smtlib(self):
         return tmp
 
     def to_decimal_string(self):
+        """Convert to decimal string
+
+        If the fraction does not terminate (e.g. for 1 / 3), an
+        exception is thrown.
+
+        """
         if self.b > 2:
             b = self.b
             while b > 1:
@@ -154,12 +200,24 @@ def to_decimal_string(self):
             return rv
 
 def q_pow2(n):
+    """Create rational for 2^n
+
+    *n* can be negative
+    """
     if n >= 0:
         return Rational(2**n)
     else:
         return Rational(1, 2**(-n))
 
 def q_round_to_nearest(n, tiebreak):
+    """Round to nearest integer
+
+    Round *n* to the nearest integer
+
+    Calls the *tiebreak*(upper, lower) function with the two
+    alternatives if *n* is precisely between two integers.
+
+    """
     lower = (n.a - (n.a % n.b)) /  n.b
     upper = lower + 1
     assert Rational(lower) <= n <= Rational(upper)
@@ -172,6 +230,7 @@ def q_round_to_nearest(n, tiebreak):
         return Rational(tiebreak(lower, upper))
 
 def q_round_rne(n):
+    """Round to nearest even integer"""
     def tiebreak(lower, upper):
         if lower % 2 == 0:
             return lower
@@ -181,6 +240,7 @@ def tiebreak(lower, upper):
     return q_round_to_nearest(n, tiebreak)
 
 def q_round_rna(n):
+    """Round to nearest integer, away from zero"""
     def tiebreak(lower, upper):
         if abs(lower) > abs(upper):
             return lower
@@ -189,6 +249,7 @@ def tiebreak(lower, upper):
     return q_round_to_nearest(n, tiebreak)
 
 def q_round_rtz(n):
+    """Round to nearest integer, towards zero"""
     i = Rational(abs(n.a) / n.b)
     if n.isNegative():
         return -i
@@ -196,6 +257,7 @@ def q_round_rtz(n):
         return i
 
 def q_round_rtp(n):
+    """Round to nearest integer, towards positive"""
     if n.isIntegral():
         return n
     i = abs(n.a) / n.b
@@ -205,6 +267,7 @@ def q_round_rtp(n):
         return Rational(i + 1)
 
 def q_round_rtn(n):
+    """Round to nearest integer, towards negative"""
     if n.isIntegral():
         return n
     i = abs(n.a) / n.b
@@ -214,8 +277,7 @@ def q_round_rtn(n):
         return Rational(i)
 
 def q_from_decimal_fragments(sign, integer_part, fraction_part, exp_part):
-    """
-    Build a rational from fragments of a decimal number.
+    """Build a rational from string fragments of a decimal number.
 
     E.g. for "1.23E-1" we have fragments for
        sign          =   ""