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<title>2/dmn</title>
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<!--Weave of '2/fv' generated by 7-->
<ul class="crumbs"><li><a href="../webs.html">&#9733;</a></li><li><a href="index.html">kinds</a></li><li><a href="index.html#2">Chapter 2: Kinds</a></li><li><b>Floating-Point Values</b></li></ul><p class="purpose">To cope with promotions from integer to floating-point arithmetic.</p>
<ul class="toc"><li><a href="#SP1">&#167;1. Definitions</a></li></ul><hr class="tocbar">
<p class="inwebparagraph"><a id="SP1"></a><b>&#167;1. Definitions. </b></p>
<p class="inwebparagraph"><a id="SP2"></a><b>&#167;2. </b>If we do have floating-point arithmetic available, we need to be able to
play off between real and integer versions of the same kind &mdash; for example,
using real arithmetic to approximately carry out integer calculations, or vice
versa.
</p>
<pre class="display">
<span class="reserved">typedef</span><span class="plain"> </span><span class="reserved">struct</span><span class="plain"> </span><span class="reserved">generalised_kind</span><span class="plain"> {</span>
<span class="reserved">struct</span><span class="plain"> </span><span class="reserved">kind</span><span class="plain"> *</span><span class="identifier">valid_kind</span><span class="plain">; </span> <span class="comment">must be non-null</span>
<span class="reserved">int</span><span class="plain"> </span><span class="identifier">promotion</span><span class="plain">; </span> <span class="comment"><code class="display"><span class="extract">0</span></code> for no change, <code class="display"><span class="extract">1</span></code> for "a real version", <code class="display"><span class="extract">-1</span></code> for "an int version"</span>
<span class="plain">} </span><span class="reserved">generalised_kind</span><span class="plain">;</span>
</pre>
<p class="inwebparagraph"></p>
<p class="endnote">The structure generalised_kind is private to this section.</p>
<p class="inwebparagraph"><a id="SP3"></a><b>&#167;3. </b></p>
<pre class="display">
<span class="reserved">generalised_kind</span><span class="plain"> </span><span class="functiontext">Kinds::FloatingPoint::new_gk</span><span class="plain">(</span><span class="reserved">kind</span><span class="plain"> *</span><span class="identifier">K</span><span class="plain">) {</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">K</span><span class="plain"> == </span><span class="identifier">NULL</span><span class="plain">) </span><span class="identifier">internal_error</span><span class="plain">(</span><span class="string">"can't generalise the null kind"</span><span class="plain">);</span>
<span class="reserved">generalised_kind</span><span class="plain"> </span><span class="identifier">gK</span><span class="plain">;</span>
<span class="identifier">gK</span><span class="element">.valid_kind</span><span class="plain"> = </span><span class="identifier">K</span><span class="plain">;</span>
<span class="identifier">gK</span><span class="element">.promotion</span><span class="plain"> = 0;</span>
<span class="reserved">return</span><span class="plain"> </span><span class="identifier">gK</span><span class="plain">;</span>
<span class="plain">}</span>
<span class="reserved">void</span><span class="plain"> </span><span class="functiontext">Kinds::FloatingPoint::log_gk</span><span class="plain">(</span><span class="reserved">generalised_kind</span><span class="plain"> </span><span class="identifier">gK</span><span class="plain">) {</span>
<span class="identifier">LOG</span><span class="plain">(</span><span class="string">"$u"</span><span class="plain">, </span><span class="identifier">gK</span><span class="element">.valid_kind</span><span class="plain">);</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">gK</span><span class="element">.promotion</span><span class="plain"> == 1) { </span><span class="identifier">LOG</span><span class="plain">(</span><span class="string">"=&gt;real"</span><span class="plain">); }</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">gK</span><span class="element">.promotion</span><span class="plain"> == -1) { </span><span class="identifier">LOG</span><span class="plain">(</span><span class="string">"=&gt;int"</span><span class="plain">); }</span>
<span class="plain">}</span>
<span class="reserved">kind</span><span class="plain"> *</span><span class="functiontext">Kinds::FloatingPoint::underlying</span><span class="plain">(</span><span class="reserved">generalised_kind</span><span class="plain"> </span><span class="identifier">gK</span><span class="plain">) {</span>
<span class="reserved">return</span><span class="plain"> </span><span class="identifier">gK</span><span class="element">.valid_kind</span><span class="plain">;</span>
<span class="plain">}</span>
<span class="reserved">int</span><span class="plain"> </span><span class="functiontext">Kinds::FloatingPoint::is_real</span><span class="plain">(</span><span class="reserved">generalised_kind</span><span class="plain"> </span><span class="identifier">gK</span><span class="plain">) {</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">gK</span><span class="element">.promotion</span><span class="plain"> == 1) </span><span class="reserved">return</span><span class="plain"> </span><span class="identifier">TRUE</span><span class="plain">;</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="functiontext">Kinds::FloatingPoint::uses_floating_point</span><span class="plain">(</span><span class="identifier">gK</span><span class="element">.valid_kind</span><span class="plain">)) </span><span class="reserved">return</span><span class="plain"> </span><span class="identifier">TRUE</span><span class="plain">;</span>
<span class="reserved">return</span><span class="plain"> </span><span class="identifier">FALSE</span><span class="plain">;</span>
<span class="plain">}</span>
<span class="reserved">generalised_kind</span><span class="plain"> </span><span class="functiontext">Kinds::FloatingPoint::to_integer</span><span class="plain">(</span><span class="reserved">generalised_kind</span><span class="plain"> </span><span class="identifier">gK</span><span class="plain">) {</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="functiontext">Kinds::FloatingPoint::is_real</span><span class="plain">(</span><span class="identifier">gK</span><span class="plain">)) {</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">gK</span><span class="element">.promotion</span><span class="plain"> == 1) </span><span class="identifier">gK</span><span class="element">.promotion</span><span class="plain"> = 0;</span>
<span class="reserved">else</span><span class="plain"> {</span>
<span class="reserved">kind</span><span class="plain"> *</span><span class="identifier">K</span><span class="plain"> = </span><span class="functiontext">Kinds::FloatingPoint::integer_equivalent</span><span class="plain">(</span><span class="identifier">gK</span><span class="element">.valid_kind</span><span class="plain">);</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="functiontext">Kinds::FloatingPoint::uses_floating_point</span><span class="plain">(</span><span class="identifier">K</span><span class="plain">) == </span><span class="identifier">FALSE</span><span class="plain">) </span><span class="identifier">gK</span><span class="element">.valid_kind</span><span class="plain"> = </span><span class="identifier">K</span><span class="plain">;</span>
<span class="reserved">else</span><span class="plain"> </span><span class="identifier">gK</span><span class="element">.promotion</span><span class="plain"> = -1;</span>
<span class="plain">}</span>
<span class="plain">}</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="functiontext">Kinds::FloatingPoint::is_real</span><span class="plain">(</span><span class="identifier">gK</span><span class="plain">))</span>
<span class="identifier">internal_error</span><span class="plain">(</span><span class="string">"gK inconsistent"</span><span class="plain">);</span>
<span class="reserved">return</span><span class="plain"> </span><span class="identifier">gK</span><span class="plain">;</span>
<span class="plain">}</span>
<span class="reserved">generalised_kind</span><span class="plain"> </span><span class="functiontext">Kinds::FloatingPoint::to_real</span><span class="plain">(</span><span class="reserved">generalised_kind</span><span class="plain"> </span><span class="identifier">gK</span><span class="plain">) {</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="functiontext">Kinds::FloatingPoint::is_real</span><span class="plain">(</span><span class="identifier">gK</span><span class="plain">) == </span><span class="identifier">FALSE</span><span class="plain">) {</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">gK</span><span class="element">.promotion</span><span class="plain"> == -1) </span><span class="identifier">gK</span><span class="element">.promotion</span><span class="plain"> = 0;</span>
<span class="reserved">else</span><span class="plain"> {</span>
<span class="reserved">kind</span><span class="plain"> *</span><span class="identifier">K</span><span class="plain"> = </span><span class="functiontext">Kinds::FloatingPoint::real_equivalent</span><span class="plain">(</span><span class="identifier">gK</span><span class="element">.valid_kind</span><span class="plain">);</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="functiontext">Kinds::FloatingPoint::uses_floating_point</span><span class="plain">(</span><span class="identifier">K</span><span class="plain">)) </span><span class="identifier">gK</span><span class="element">.valid_kind</span><span class="plain"> = </span><span class="identifier">K</span><span class="plain">;</span>
<span class="reserved">else</span><span class="plain"> </span><span class="identifier">gK</span><span class="element">.promotion</span><span class="plain"> = 1;</span>
<span class="plain">}</span>
<span class="plain">}</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="functiontext">Kinds::FloatingPoint::is_real</span><span class="plain">(</span><span class="identifier">gK</span><span class="plain">) == </span><span class="identifier">FALSE</span><span class="plain">)</span>
<span class="identifier">internal_error</span><span class="plain">(</span><span class="string">"gK inconsistent"</span><span class="plain">);</span>
<span class="reserved">return</span><span class="plain"> </span><span class="identifier">gK</span><span class="plain">;</span>
<span class="plain">}</span>
</pre>
<p class="inwebparagraph"></p>
<p class="endnote">The function Kinds::FloatingPoint::new_gk appears nowhere else.</p>
<p class="endnote">The function Kinds::FloatingPoint::log_gk appears nowhere else.</p>
<p class="endnote">The function Kinds::FloatingPoint::underlying appears nowhere else.</p>
<p class="endnote">The function Kinds::FloatingPoint::is_real appears nowhere else.</p>
<p class="endnote">The function Kinds::FloatingPoint::to_integer appears nowhere else.</p>
<p class="endnote">The function Kinds::FloatingPoint::to_real appears nowhere else.</p>
<p class="inwebparagraph"><a id="SP4"></a><b>&#167;4. </b></p>
<pre class="display">
<span class="reserved">void</span><span class="plain"> </span><span class="functiontext">Kinds::FloatingPoint::begin_flotation</span><span class="plain">(</span><span class="identifier">OUTPUT_STREAM</span><span class="plain">, </span><span class="reserved">kind</span><span class="plain"> *</span><span class="identifier">K</span><span class="plain">) {</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="functiontext">Kinds::Behaviour::scale_factor</span><span class="plain">(</span><span class="identifier">K</span><span class="plain">) != 1) </span><span class="identifier">WRITE</span><span class="plain">(</span><span class="string">"REAL_NUMBER_TY_Divide("</span><span class="plain">);</span>
<span class="identifier">WRITE</span><span class="plain">(</span><span class="string">"NUMBER_TY_to_REAL_NUMBER_TY"</span><span class="plain">);</span>
<span class="identifier">WRITE</span><span class="plain">(</span><span class="string">"("</span><span class="plain">);</span>
<span class="plain">}</span>
<span class="reserved">void</span><span class="plain"> </span><span class="functiontext">Kinds::FloatingPoint::end_flotation</span><span class="plain">(</span><span class="identifier">OUTPUT_STREAM</span><span class="plain">, </span><span class="reserved">kind</span><span class="plain"> *</span><span class="identifier">K</span><span class="plain">) {</span>
<span class="identifier">WRITE</span><span class="plain">(</span><span class="string">")"</span><span class="plain">);</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="functiontext">Kinds::Behaviour::scale_factor</span><span class="plain">(</span><span class="identifier">K</span><span class="plain">) != 1)</span>
<span class="identifier">WRITE</span><span class="plain">(</span><span class="string">", NUMBER_TY_to_REAL_NUMBER_TY(%d))"</span><span class="plain">,</span>
<span class="functiontext">Kinds::Behaviour::scale_factor</span><span class="plain">(</span><span class="identifier">K</span><span class="plain">));</span>
<span class="plain">}</span>
<span class="reserved">void</span><span class="plain"> </span><span class="functiontext">Kinds::FloatingPoint::begin_deflotation</span><span class="plain">(</span><span class="identifier">OUTPUT_STREAM</span><span class="plain">, </span><span class="reserved">kind</span><span class="plain"> *</span><span class="identifier">K</span><span class="plain">) {</span>
<span class="identifier">WRITE</span><span class="plain">(</span><span class="string">"REAL_NUMBER_TY_to_NUMBER_TY("</span><span class="plain">);</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="functiontext">Kinds::Behaviour::scale_factor</span><span class="plain">(</span><span class="identifier">K</span><span class="plain">) != 1) </span><span class="identifier">WRITE</span><span class="plain">(</span><span class="string">"REAL_NUMBER_TY_Times("</span><span class="plain">);</span>
<span class="plain">}</span>
<span class="reserved">void</span><span class="plain"> </span><span class="functiontext">Kinds::FloatingPoint::end_deflotation</span><span class="plain">(</span><span class="identifier">OUTPUT_STREAM</span><span class="plain">, </span><span class="reserved">kind</span><span class="plain"> *</span><span class="identifier">K</span><span class="plain">) {</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="functiontext">Kinds::Behaviour::scale_factor</span><span class="plain">(</span><span class="identifier">K</span><span class="plain">) != 1)</span>
<span class="identifier">WRITE</span><span class="plain">(</span><span class="string">", NUMBER_TY_to_REAL_NUMBER_TY(%d))"</span><span class="plain">,</span>
<span class="functiontext">Kinds::Behaviour::scale_factor</span><span class="plain">(</span><span class="identifier">K</span><span class="plain">));</span>
<span class="identifier">WRITE</span><span class="plain">(</span><span class="string">")"</span><span class="plain">);</span>
<span class="plain">}</span>
<span class="plain">#</span><span class="identifier">ifdef</span><span class="plain"> </span><span class="identifier">CORE_MODULE</span>
<span class="reserved">void</span><span class="plain"> </span><span class="functiontext">Kinds::FloatingPoint::begin_flotation_emit</span><span class="plain">(</span><span class="reserved">kind</span><span class="plain"> *</span><span class="identifier">K</span><span class="plain">) {</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="functiontext">Kinds::Behaviour::scale_factor</span><span class="plain">(</span><span class="identifier">K</span><span class="plain">) != 1) {</span>
<span class="identifier">Produce::inv_call_iname</span><span class="plain">(</span><span class="identifier">Emit::tree</span><span class="plain">(), </span><span class="identifier">Hierarchy::find</span><span class="plain">(</span><span class="identifier">REAL_NUMBER_TY_DIVIDE_HL</span><span class="plain">));</span>
<span class="identifier">Produce::down</span><span class="plain">(</span><span class="identifier">Emit::tree</span><span class="plain">());</span>
<span class="plain">}</span>
<span class="identifier">Produce::inv_call_iname</span><span class="plain">(</span><span class="identifier">Emit::tree</span><span class="plain">(), </span><span class="identifier">Hierarchy::find</span><span class="plain">(</span><span class="identifier">NUMBER_TY_TO_REAL_NUMBER_TY_HL</span><span class="plain">));</span>
<span class="identifier">Produce::down</span><span class="plain">(</span><span class="identifier">Emit::tree</span><span class="plain">());</span>
<span class="plain">}</span>
<span class="reserved">void</span><span class="plain"> </span><span class="functiontext">Kinds::FloatingPoint::end_flotation_emit</span><span class="plain">(</span><span class="reserved">kind</span><span class="plain"> *</span><span class="identifier">K</span><span class="plain">) {</span>
<span class="identifier">Produce::up</span><span class="plain">(</span><span class="identifier">Emit::tree</span><span class="plain">());</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="functiontext">Kinds::Behaviour::scale_factor</span><span class="plain">(</span><span class="identifier">K</span><span class="plain">) != 1) {</span>
<span class="identifier">Produce::inv_call_iname</span><span class="plain">(</span><span class="identifier">Emit::tree</span><span class="plain">(), </span><span class="identifier">Hierarchy::find</span><span class="plain">(</span><span class="identifier">NUMBER_TY_TO_REAL_NUMBER_TY_HL</span><span class="plain">));</span>
<span class="identifier">Produce::down</span><span class="plain">(</span><span class="identifier">Emit::tree</span><span class="plain">());</span>
<span class="identifier">Produce::val</span><span class="plain">(</span><span class="identifier">Emit::tree</span><span class="plain">(), </span><span class="identifier">K_number</span><span class="plain">, </span><span class="identifier">LITERAL_IVAL</span><span class="plain">, (</span><span class="identifier">inter_t</span><span class="plain">) </span><span class="functiontext">Kinds::Behaviour::scale_factor</span><span class="plain">(</span><span class="identifier">K</span><span class="plain">));</span>
<span class="identifier">Produce::up</span><span class="plain">(</span><span class="identifier">Emit::tree</span><span class="plain">());</span>
<span class="identifier">Produce::up</span><span class="plain">(</span><span class="identifier">Emit::tree</span><span class="plain">());</span>
<span class="plain">}</span>
<span class="plain">}</span>
<span class="reserved">void</span><span class="plain"> </span><span class="functiontext">Kinds::FloatingPoint::begin_deflotation_emit</span><span class="plain">(</span><span class="reserved">kind</span><span class="plain"> *</span><span class="identifier">K</span><span class="plain">) {</span>
<span class="identifier">Produce::inv_call_iname</span><span class="plain">(</span><span class="identifier">Emit::tree</span><span class="plain">(), </span><span class="identifier">Hierarchy::find</span><span class="plain">(</span><span class="identifier">REAL_NUMBER_TY_TO_NUMBER_TY_HL</span><span class="plain">));</span>
<span class="identifier">Produce::down</span><span class="plain">(</span><span class="identifier">Emit::tree</span><span class="plain">());</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="functiontext">Kinds::Behaviour::scale_factor</span><span class="plain">(</span><span class="identifier">K</span><span class="plain">) != 1) {</span>
<span class="identifier">Produce::inv_call_iname</span><span class="plain">(</span><span class="identifier">Emit::tree</span><span class="plain">(), </span><span class="identifier">Hierarchy::find</span><span class="plain">(</span><span class="identifier">REAL_NUMBER_TY_TIMES_HL</span><span class="plain">));</span>
<span class="identifier">Produce::down</span><span class="plain">(</span><span class="identifier">Emit::tree</span><span class="plain">());</span>
<span class="plain">}</span>
<span class="plain">}</span>
<span class="reserved">void</span><span class="plain"> </span><span class="functiontext">Kinds::FloatingPoint::end_deflotation_emit</span><span class="plain">(</span><span class="reserved">kind</span><span class="plain"> *</span><span class="identifier">K</span><span class="plain">) {</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="functiontext">Kinds::Behaviour::scale_factor</span><span class="plain">(</span><span class="identifier">K</span><span class="plain">) != 1) {</span>
<span class="identifier">Produce::inv_call_iname</span><span class="plain">(</span><span class="identifier">Emit::tree</span><span class="plain">(), </span><span class="identifier">Hierarchy::find</span><span class="plain">(</span><span class="identifier">REAL_NUMBER_TY_TO_NUMBER_TY_HL</span><span class="plain">));</span>
<span class="identifier">Produce::down</span><span class="plain">(</span><span class="identifier">Emit::tree</span><span class="plain">());</span>
<span class="identifier">Produce::val</span><span class="plain">(</span><span class="identifier">Emit::tree</span><span class="plain">(), </span><span class="identifier">K_number</span><span class="plain">, </span><span class="identifier">LITERAL_IVAL</span><span class="plain">, (</span><span class="identifier">inter_t</span><span class="plain">) </span><span class="functiontext">Kinds::Behaviour::scale_factor</span><span class="plain">(</span><span class="identifier">K</span><span class="plain">));</span>
<span class="identifier">Produce::up</span><span class="plain">(</span><span class="identifier">Emit::tree</span><span class="plain">());</span>
<span class="identifier">Produce::up</span><span class="plain">(</span><span class="identifier">Emit::tree</span><span class="plain">());</span>
<span class="plain">}</span>
<span class="identifier">Produce::up</span><span class="plain">(</span><span class="identifier">Emit::tree</span><span class="plain">());</span>
<span class="plain">}</span>
<span class="plain">#</span><span class="identifier">endif</span>
<span class="reserved">int</span><span class="plain"> </span><span class="functiontext">Kinds::FloatingPoint::uses_floating_point</span><span class="plain">(</span><span class="reserved">kind</span><span class="plain"> *</span><span class="identifier">K</span><span class="plain">) {</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">K</span><span class="plain"> == </span><span class="identifier">NULL</span><span class="plain">) </span><span class="reserved">return</span><span class="plain"> </span><span class="identifier">FALSE</span><span class="plain">;</span>
<span class="reserved">return</span><span class="plain"> </span><span class="functiontext">Kinds::Constructors::is_arithmetic_and_real</span><span class="plain">(</span><span class="identifier">K</span><span class="plain">-</span><span class="element">&gt;construct</span><span class="plain">);</span>
<span class="plain">}</span>
<span class="reserved">kind</span><span class="plain"> *</span><span class="functiontext">Kinds::FloatingPoint::real_equivalent</span><span class="plain">(</span><span class="reserved">kind</span><span class="plain"> *</span><span class="identifier">K</span><span class="plain">) {</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="functiontext">Kinds::Compare::eq</span><span class="plain">(</span><span class="identifier">K</span><span class="plain">, </span><span class="identifier">K_number</span><span class="plain">)) </span><span class="reserved">return</span><span class="plain"> </span><span class="identifier">K_real_number</span><span class="plain">;</span>
<span class="reserved">return</span><span class="plain"> </span><span class="identifier">K</span><span class="plain">;</span>
<span class="plain">}</span>
<span class="reserved">kind</span><span class="plain"> *</span><span class="functiontext">Kinds::FloatingPoint::integer_equivalent</span><span class="plain">(</span><span class="reserved">kind</span><span class="plain"> *</span><span class="identifier">K</span><span class="plain">) {</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="functiontext">Kinds::Compare::eq</span><span class="plain">(</span><span class="identifier">K</span><span class="plain">, </span><span class="identifier">K_real_number</span><span class="plain">)) </span><span class="reserved">return</span><span class="plain"> </span><span class="identifier">K_number</span><span class="plain">;</span>
<span class="reserved">return</span><span class="plain"> </span><span class="identifier">K</span><span class="plain">;</span>
<span class="plain">}</span>
</pre>
<p class="inwebparagraph"></p>
<p class="endnote">The function Kinds::FloatingPoint::begin_flotation appears nowhere else.</p>
<p class="endnote">The function Kinds::FloatingPoint::end_flotation appears nowhere else.</p>
<p class="endnote">The function Kinds::FloatingPoint::begin_deflotation appears nowhere else.</p>
<p class="endnote">The function Kinds::FloatingPoint::end_deflotation appears nowhere else.</p>
<p class="endnote">The function Kinds::FloatingPoint::begin_flotation_emit appears nowhere else.</p>
<p class="endnote">The function Kinds::FloatingPoint::end_flotation_emit appears nowhere else.</p>
<p class="endnote">The function Kinds::FloatingPoint::begin_deflotation_emit appears nowhere else.</p>
<p class="endnote">The function Kinds::FloatingPoint::end_deflotation_emit appears nowhere else.</p>
<p class="endnote">The function Kinds::FloatingPoint::uses_floating_point is used in <a href="#SP3">&#167;3</a>, 2/kc (<a href="2-kc.html#SP12">&#167;12</a>), 2/uk (<a href="2-uk.html#SP18">&#167;18</a>), 2/dmn (<a href="2-dmn.html#SP40_2">&#167;40.2</a>).</p>
<p class="endnote">The function Kinds::FloatingPoint::real_equivalent is used in <a href="#SP3">&#167;3</a>, 2/kc (<a href="2-kc.html#SP12">&#167;12</a>).</p>
<p class="endnote">The function Kinds::FloatingPoint::integer_equivalent is used in <a href="#SP3">&#167;3</a>.</p>
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