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<h1>stdlib_blas_constants.fypp
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<h2><span class="anchor" id="src"></span>Source Code</h2>
<div class="hl codehilite"><pre><span></span><a id="ln-1" name="ln-1" href="#ln-1"></a><span class="cp">#:include "common.fypp" </span>
<a id="ln-2" name="ln-2" href="#ln-2"></a><span class="cp">#:for ck,ct,ci in REAL_KINDS_TYPES</span>
<a id="ln-3" name="ln-3" href="#ln-3"></a><span class="k">module </span><span class="n">stdlib_blas_constants_$</span><span class="err">{</span><span class="n">ck</span><span class="err">}$</span>
<a id="ln-4" name="ln-4" href="#ln-4"></a><span class="w"> </span><span class="k">use </span><span class="n">stdlib_linalg_constants</span>
<a id="ln-5" name="ln-5" href="#ln-5"></a><span class="w"> </span><span class="k">implicit none</span>
<a id="ln-6" name="ln-6" href="#ln-6"></a><span class="k"> </span>
<a id="ln-7" name="ln-7" href="#ln-7"></a><span class="k"> </span>
<a id="ln-8" name="ln-8" href="#ln-8"></a><span class="k"> </span><span class="kt">real</span><span class="p">(</span><span class="err">${</span><span class="n">ck</span><span class="err">}$</span><span class="p">),</span><span class="w"> </span><span class="k">parameter</span><span class="w"> </span><span class="kd">::</span><span class="w"> </span><span class="n">negone</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">-</span><span class="mf">1.00</span><span class="err">_${</span><span class="n">ck</span><span class="err">}$</span>
<a id="ln-9" name="ln-9" href="#ln-9"></a><span class="w"> </span><span class="kt">real</span><span class="p">(</span><span class="err">${</span><span class="n">ck</span><span class="err">}$</span><span class="p">),</span><span class="w"> </span><span class="k">parameter</span><span class="w"> </span><span class="kd">::</span><span class="w"> </span><span class="n">zero</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0.00</span><span class="err">_${</span><span class="n">ck</span><span class="err">}$</span>
<a id="ln-10" name="ln-10" href="#ln-10"></a><span class="w"> </span><span class="kt">real</span><span class="p">(</span><span class="err">${</span><span class="n">ck</span><span class="err">}$</span><span class="p">),</span><span class="w"> </span><span class="k">parameter</span><span class="w"> </span><span class="kd">::</span><span class="w"> </span><span class="n">half</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0.50</span><span class="err">_${</span><span class="n">ck</span><span class="err">}$</span>
<a id="ln-11" name="ln-11" href="#ln-11"></a><span class="w"> </span><span class="kt">real</span><span class="p">(</span><span class="err">${</span><span class="n">ck</span><span class="err">}$</span><span class="p">),</span><span class="w"> </span><span class="k">parameter</span><span class="w"> </span><span class="kd">::</span><span class="w"> </span><span class="n">one</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1.00</span><span class="err">_${</span><span class="n">ck</span><span class="err">}$</span>
<a id="ln-12" name="ln-12" href="#ln-12"></a><span class="w"> </span><span class="kt">real</span><span class="p">(</span><span class="err">${</span><span class="n">ck</span><span class="err">}$</span><span class="p">),</span><span class="w"> </span><span class="k">parameter</span><span class="w"> </span><span class="kd">::</span><span class="w"> </span><span class="n">two</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2.00</span><span class="err">_${</span><span class="n">ck</span><span class="err">}$</span>
<a id="ln-13" name="ln-13" href="#ln-13"></a><span class="w"> </span><span class="kt">real</span><span class="p">(</span><span class="err">${</span><span class="n">ck</span><span class="err">}$</span><span class="p">),</span><span class="w"> </span><span class="k">parameter</span><span class="w"> </span><span class="kd">::</span><span class="w"> </span><span class="n">three</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">3.00</span><span class="err">_${</span><span class="n">ck</span><span class="err">}$</span>
<a id="ln-14" name="ln-14" href="#ln-14"></a><span class="w"> </span><span class="kt">real</span><span class="p">(</span><span class="err">${</span><span class="n">ck</span><span class="err">}$</span><span class="p">),</span><span class="w"> </span><span class="k">parameter</span><span class="w"> </span><span class="kd">::</span><span class="w"> </span><span class="n">four</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">4.00</span><span class="err">_${</span><span class="n">ck</span><span class="err">}$</span>
<a id="ln-15" name="ln-15" href="#ln-15"></a><span class="w"> </span><span class="kt">real</span><span class="p">(</span><span class="err">${</span><span class="n">ck</span><span class="err">}$</span><span class="p">),</span><span class="w"> </span><span class="k">parameter</span><span class="w"> </span><span class="kd">::</span><span class="w"> </span><span class="n">eight</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">8.00</span><span class="err">_${</span><span class="n">ck</span><span class="err">}$</span>
<a id="ln-16" name="ln-16" href="#ln-16"></a><span class="w"> </span><span class="kt">real</span><span class="p">(</span><span class="err">${</span><span class="n">ck</span><span class="err">}$</span><span class="p">),</span><span class="w"> </span><span class="k">parameter</span><span class="w"> </span><span class="kd">::</span><span class="w"> </span><span class="n">ten</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="mf">0.00</span><span class="err">_${</span><span class="n">ck</span><span class="err">}$</span>
<a id="ln-17" name="ln-17" href="#ln-17"></a><span class="w"> </span>
<a id="ln-18" name="ln-18" href="#ln-18"></a><span class="w"> </span><span class="kt">complex</span><span class="p">(</span><span class="err">${</span><span class="n">ck</span><span class="err">}$</span><span class="p">),</span><span class="w"> </span><span class="k">parameter</span><span class="w"> </span><span class="kd">::</span><span class="w"> </span><span class="n">czero</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="w"> </span><span class="mf">0.0</span><span class="err">_${</span><span class="n">ck</span><span class="err">}$</span><span class="p">,</span><span class="mf">0.0</span><span class="err">_${</span><span class="n">ck</span><span class="err">}$</span><span class="p">)</span>
<a id="ln-19" name="ln-19" href="#ln-19"></a><span class="w"> </span><span class="kt">complex</span><span class="p">(</span><span class="err">${</span><span class="n">ck</span><span class="err">}$</span><span class="p">),</span><span class="w"> </span><span class="k">parameter</span><span class="w"> </span><span class="kd">::</span><span class="w"> </span><span class="n">chalf</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="w"> </span><span class="mf">0.5</span><span class="err">_${</span><span class="n">ck</span><span class="err">}$</span><span class="p">,</span><span class="mf">0.0</span><span class="err">_${</span><span class="n">ck</span><span class="err">}$</span><span class="p">)</span>
<a id="ln-20" name="ln-20" href="#ln-20"></a><span class="w"> </span><span class="kt">complex</span><span class="p">(</span><span class="err">${</span><span class="n">ck</span><span class="err">}$</span><span class="p">),</span><span class="w"> </span><span class="k">parameter</span><span class="w"> </span><span class="kd">::</span><span class="w"> </span><span class="n">cone</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="w"> </span><span class="mf">1.0</span><span class="err">_${</span><span class="n">ck</span><span class="err">}$</span><span class="p">,</span><span class="mf">0.0</span><span class="err">_${</span><span class="n">ck</span><span class="err">}$</span><span class="p">)</span>
<a id="ln-21" name="ln-21" href="#ln-21"></a><span class="w"> </span><span class="kt">complex</span><span class="p">(</span><span class="err">${</span><span class="n">ck</span><span class="err">}$</span><span class="p">),</span><span class="w"> </span><span class="k">parameter</span><span class="w"> </span><span class="kd">::</span><span class="w"> </span><span class="n">cnegone</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="o">-</span><span class="mf">1.0</span><span class="err">_${</span><span class="n">ck</span><span class="err">}$</span><span class="p">,</span><span class="mf">0.0</span><span class="err">_${</span><span class="n">ck</span><span class="err">}$</span><span class="p">)</span>
<a id="ln-22" name="ln-22" href="#ln-22"></a>
<a id="ln-23" name="ln-23" href="#ln-23"></a><span class="w"> </span><span class="c">! scaling constants </span>
<a id="ln-24" name="ln-24" href="#ln-24"></a><span class="w"> </span><span class="kt">integer</span><span class="p">,</span><span class="w"> </span><span class="k">parameter</span><span class="w"> </span><span class="kd">::</span><span class="w"> </span><span class="n">maxexp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">maxexponent</span><span class="p">(</span><span class="n">zero</span><span class="p">)</span><span class="w"> </span>
<a id="ln-25" name="ln-25" href="#ln-25"></a><span class="w"> </span><span class="kt">integer</span><span class="p">,</span><span class="w"> </span><span class="k">parameter</span><span class="w"> </span><span class="kd">::</span><span class="w"> </span><span class="n">minexp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">minexponent</span><span class="p">(</span><span class="n">zero</span><span class="p">)</span><span class="w"> </span>
<a id="ln-26" name="ln-26" href="#ln-26"></a><span class="w"> </span>
<a id="ln-27" name="ln-27" href="#ln-27"></a><span class="w"> </span><span class="kt">real</span><span class="p">(</span><span class="err">${</span><span class="n">ck</span><span class="err">}$</span><span class="p">),</span><span class="w"> </span><span class="k">parameter</span><span class="w"> </span><span class="kd">::</span><span class="w"> </span><span class="n">rradix</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kt">real</span><span class="p">(</span><span class="nb">radix</span><span class="p">(</span><span class="n">zero</span><span class="p">),</span><span class="err">${</span><span class="n">ck</span><span class="err">}$</span><span class="p">)</span><span class="w"> </span>
<a id="ln-28" name="ln-28" href="#ln-28"></a><span class="w"> </span><span class="kt">real</span><span class="p">(</span><span class="err">${</span><span class="n">ck</span><span class="err">}$</span><span class="p">),</span><span class="w"> </span><span class="k">parameter</span><span class="w"> </span><span class="kd">::</span><span class="w"> </span><span class="n">ulp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">epsilon</span><span class="p">(</span><span class="n">zero</span><span class="p">)</span><span class="w"> </span>
<a id="ln-29" name="ln-29" href="#ln-29"></a><span class="w"> </span><span class="kt">real</span><span class="p">(</span><span class="err">${</span><span class="n">ck</span><span class="err">}$</span><span class="p">),</span><span class="w"> </span><span class="k">parameter</span><span class="w"> </span><span class="kd">::</span><span class="w"> </span><span class="n">eps</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ulp</span><span class="o">*</span><span class="n">half</span>
<a id="ln-30" name="ln-30" href="#ln-30"></a><span class="w"> </span><span class="kt">real</span><span class="p">(</span><span class="err">${</span><span class="n">ck</span><span class="err">}$</span><span class="p">),</span><span class="w"> </span><span class="k">parameter</span><span class="w"> </span><span class="kd">::</span><span class="w"> </span><span class="n">safmin</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rradix</span><span class="o">**</span><span class="nb">max</span><span class="p">(</span><span class="n">minexp</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="o">-</span><span class="n">maxexp</span><span class="p">)</span><span class="w"> </span>
<a id="ln-31" name="ln-31" href="#ln-31"></a><span class="w"> </span><span class="kt">real</span><span class="p">(</span><span class="err">${</span><span class="n">ck</span><span class="err">}$</span><span class="p">),</span><span class="w"> </span><span class="k">parameter</span><span class="w"> </span><span class="kd">::</span><span class="w"> </span><span class="n">safmax</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">one</span><span class="o">/</span><span class="n">safmin</span><span class="w"> </span>
<a id="ln-32" name="ln-32" href="#ln-32"></a><span class="w"> </span><span class="kt">real</span><span class="p">(</span><span class="err">${</span><span class="n">ck</span><span class="err">}$</span><span class="p">),</span><span class="w"> </span><span class="k">parameter</span><span class="w"> </span><span class="kd">::</span><span class="w"> </span><span class="n">smlnum</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">safmin</span><span class="o">/</span><span class="n">ulp</span>
<a id="ln-33" name="ln-33" href="#ln-33"></a><span class="w"> </span><span class="kt">real</span><span class="p">(</span><span class="err">${</span><span class="n">ck</span><span class="err">}$</span><span class="p">),</span><span class="w"> </span><span class="k">parameter</span><span class="w"> </span><span class="kd">::</span><span class="w"> </span><span class="n">bignum</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">safmax</span><span class="o">*</span><span class="n">ulp</span><span class="w"> </span>
<a id="ln-34" name="ln-34" href="#ln-34"></a><span class="w"> </span><span class="kt">real</span><span class="p">(</span><span class="err">${</span><span class="n">ck</span><span class="err">}$</span><span class="p">),</span><span class="w"> </span><span class="k">parameter</span><span class="w"> </span><span class="kd">::</span><span class="w"> </span><span class="n">rtmin</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">sqrt</span><span class="p">(</span><span class="n">smlnum</span><span class="p">)</span><span class="w"> </span>
<a id="ln-35" name="ln-35" href="#ln-35"></a><span class="w"> </span><span class="kt">real</span><span class="p">(</span><span class="err">${</span><span class="n">ck</span><span class="err">}$</span><span class="p">),</span><span class="w"> </span><span class="k">parameter</span><span class="w"> </span><span class="kd">::</span><span class="w"> </span><span class="n">rtmax</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">sqrt</span><span class="p">(</span><span class="n">bignum</span><span class="p">)</span><span class="w"> </span>
<a id="ln-36" name="ln-36" href="#ln-36"></a>
<a id="ln-37" name="ln-37" href="#ln-37"></a><span class="w"> </span><span class="c">! Blue's scaling constants </span>
<a id="ln-38" name="ln-38" href="#ln-38"></a><span class="w"> </span><span class="c">! ssml>=1/s and sbig==1/S with s,S as defined in https://doi.org/10.1145/355769.355771 </span>
<a id="ln-39" name="ln-39" href="#ln-39"></a><span class="w"> </span><span class="kt">real</span><span class="p">(</span><span class="err">${</span><span class="n">ck</span><span class="err">}$</span><span class="p">),</span><span class="w"> </span><span class="k">parameter</span><span class="w"> </span><span class="kd">::</span><span class="w"> </span><span class="n">tsml</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rradix</span><span class="o">**</span><span class="nb">ceiling</span><span class="p">((</span><span class="n">minexp</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="o">*</span><span class="n">half</span><span class="p">)</span><span class="w"> </span>
<a id="ln-40" name="ln-40" href="#ln-40"></a><span class="w"> </span><span class="kt">real</span><span class="p">(</span><span class="err">${</span><span class="n">ck</span><span class="err">}$</span><span class="p">),</span><span class="w"> </span><span class="k">parameter</span><span class="w"> </span><span class="kd">::</span><span class="w"> </span><span class="n">tbig</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rradix</span><span class="o">**</span><span class="nb">floor</span><span class="p">((</span><span class="n">maxexp</span><span class="o">-</span><span class="nb">digits</span><span class="p">(</span><span class="n">zero</span><span class="p">)</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span><span class="o">*</span><span class="n">half</span><span class="p">)</span><span class="w"> </span>
<a id="ln-41" name="ln-41" href="#ln-41"></a><span class="w"> </span><span class="kt">real</span><span class="p">(</span><span class="err">${</span><span class="n">ck</span><span class="err">}$</span><span class="p">),</span><span class="w"> </span><span class="k">parameter</span><span class="w"> </span><span class="kd">::</span><span class="w"> </span><span class="n">ssml</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rradix</span><span class="o">**</span><span class="p">(</span><span class="o">-</span><span class="nb">floor</span><span class="p">((</span><span class="n">minexp</span><span class="o">-</span><span class="nb">digits</span><span class="p">(</span><span class="n">zero</span><span class="p">))</span><span class="o">*</span><span class="n">half</span><span class="p">))</span><span class="w"> </span>
<a id="ln-42" name="ln-42" href="#ln-42"></a><span class="w"> </span><span class="kt">real</span><span class="p">(</span><span class="err">${</span><span class="n">ck</span><span class="err">}$</span><span class="p">),</span><span class="w"> </span><span class="k">parameter</span><span class="w"> </span><span class="kd">::</span><span class="w"> </span><span class="n">sbig</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rradix</span><span class="o">**</span><span class="p">(</span><span class="o">-</span><span class="nb">ceiling</span><span class="p">((</span><span class="n">maxexp</span><span class="o">+</span><span class="nb">digits</span><span class="p">(</span><span class="n">zero</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="o">*</span><span class="n">half</span><span class="p">))</span>
<a id="ln-43" name="ln-43" href="#ln-43"></a><span class="w"> </span>
<a id="ln-44" name="ln-44" href="#ln-44"></a><span class="k">end module</span>
<a id="ln-45" name="ln-45" href="#ln-45"></a>
<a id="ln-46" name="ln-46" href="#ln-46"></a><span class="cp">#:endfor</span>
</pre></div>
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