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<div class="section">
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<div class="titlepage"><div><div><h3 class="title">
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<a name="math_toolkit.logs_and_tables.all_table"></a><a class="link" href="all_table.html" title="Tables of Error Rates for all Functions">Tables of Error
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Rates for all Functions</a>
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</h3></div></div></div>
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<div class="table">
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<a name="math_toolkit.logs_and_tables.all_table.table_beta"></a><p class="title"><b>Table 17.3. Error rates for beta</b></p>
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<div class="table-contents"><table class="table" summary="Error rates for beta">
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<colgroup>
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<col>
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<col>
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<col>
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<col>
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<col>
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</colgroup>
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<thead><tr>
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<th>
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</th>
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<th>
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<p>
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Microsoft Visual C++ version 12.0<br> Win32<br> double
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</p>
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</th>
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<th>
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<p>
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GNU C++ version 5.1.0<br> linux<br> long double
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</p>
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</th>
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<th>
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<p>
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GNU C++ version 5.1.0<br> linux<br> double
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</p>
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</th>
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<th>
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<p>
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Sun compiler version 0x5130<br> Sun Solaris<br> long double
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</p>
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</th>
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</tr></thead>
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<tbody>
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<tr>
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<td>
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<p>
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Beta Function: Small Values
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</p>
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</td>
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<td>
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<p>
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<span class="blue">Max = 1.75ε (Mean = 0.828ε)</span>
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</p>
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</td>
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<td>
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<p>
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<span class="blue">Max = 2.65ε (Mean = 1.22ε)</span><br> <br>
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(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 11.9ε (Mean = 7.03ε))
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</p>
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</td>
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<td>
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<p>
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<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
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1.16:</em></span> Max = 3.94ε (Mean = 1.44ε))<br> (<span class="emphasis"><em>Rmath
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3.0.2:</em></span> Max = 1.14ε (Mean = 0.601ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
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Max = 1.97ε (Mean = 0.934ε))
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</p>
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</td>
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<td>
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<p>
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<span class="blue">Max = 2.86ε (Mean = 1.31ε)</span>
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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Beta Function: Medium Values
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</p>
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</td>
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<td>
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<p>
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<span class="blue">Max = 99.1ε (Mean = 22.4ε)</span>
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</p>
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</td>
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<td>
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<p>
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<span class="blue">Max = 60.4ε (Mean = 19.4ε)</span><br> <br>
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(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1.07e+03ε (Mean =
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264ε))
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</p>
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</td>
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<td>
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<p>
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<span class="blue">Max = 0.978ε (Mean = 0.0578ε)</span><br>
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<br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 1.18e+03ε (Mean = 238ε))<br>
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(<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 1.09e+03ε (Mean = 265ε))<br>
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(<span class="emphasis"><em>Cephes:</em></span> Max = 1.5e+03ε (Mean = 329ε))
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</p>
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</td>
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<td>
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<p>
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<span class="blue">Max = 107ε (Mean = 24.5ε)</span>
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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Beta Function: Divergent Values
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</p>
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</td>
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<td>
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<p>
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<span class="blue">Max = 10.7ε (Mean = 2.22ε)</span>
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</p>
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</td>
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<td>
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<p>
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<span class="blue">Max = 10.3ε (Mean = 2.41ε)</span><br> <br>
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(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 128ε (Mean = 23.8ε))
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</p>
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</td>
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<td>
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<p>
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<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
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1.16:</em></span> Max = 12.1ε (Mean = 1.99ε))<br> (<span class="emphasis"><em>Rmath
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3.0.2:</em></span> Max = 176ε (Mean = 28ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
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Max = 175ε (Mean = 22ε))
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</p>
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</td>
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<td>
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<p>
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<span class="blue">Max = 19.7ε (Mean = 2.75ε)</span>
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</p>
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</td>
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</tr>
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</tbody>
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</table></div>
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</div>
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<br class="table-break"><div class="table">
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<a name="math_toolkit.logs_and_tables.all_table.table_beta_incomplete_"></a><p class="title"><b>Table 17.4. Error rates for beta (incomplete)</b></p>
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<div class="table-contents"><table class="table" summary="Error rates for beta (incomplete)">
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<colgroup>
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<col>
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<col>
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<col>
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<col>
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<col>
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</colgroup>
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<thead><tr>
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<th>
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</th>
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<th>
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<p>
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Microsoft Visual C++ version 12.0<br> Win32<br> double
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</p>
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</th>
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<th>
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<p>
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GNU C++ version 5.1.0<br> linux<br> double
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</p>
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</th>
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<th>
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<p>
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GNU C++ version 5.1.0<br> linux<br> long double
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</p>
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</th>
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<th>
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<p>
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Sun compiler version 0x5130<br> Sun Solaris<br> long double
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</p>
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</th>
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</tr></thead>
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<tbody>
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<tr>
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<td>
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<p>
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Incomplete Beta Function: Small Values
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</p>
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</td>
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<td>
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<p>
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<span class="blue">Max = 11.1ε (Mean = 2.28ε)</span>
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</p>
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</td>
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<td>
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<p>
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<span class="blue">Max = 0ε (Mean = 0ε)</span>
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</p>
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</td>
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<td>
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<p>
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<span class="blue">Max = 12.5ε (Mean = 2.01ε)</span>
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</p>
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</td>
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<td>
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<p>
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<span class="blue">Max = 18.7ε (Mean = 3.19ε)</span>
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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Incomplete Beta Function: Medium Values
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</p>
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</td>
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<td>
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<p>
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<span class="blue">Max = 91.1ε (Mean = 12.7ε)</span>
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</p>
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</td>
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<td>
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<p>
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<span class="blue">Max = 0.568ε (Mean = 0.0342ε)</span>
|
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</p>
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</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 67.1ε (Mean = 13.3ε)</span>
|
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</p>
|
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</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 174ε (Mean = 25ε)</span>
|
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</p>
|
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</td>
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</tr>
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<tr>
|
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<td>
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<p>
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Incomplete Beta Function: Large and Diverse Values
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</p>
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</td>
|
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<td>
|
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<p>
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<span class="blue">Max = 635ε (Mean = 29.5ε)</span>
|
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</p>
|
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</td>
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<td>
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<p>
|
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<span class="blue">Max = 0.999ε (Mean = 0.0399ε)</span>
|
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</p>
|
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</td>
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|
<td>
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<p>
|
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<span class="blue">Max = 6.84e+04ε (Mean = 2.76e+03ε)</span>
|
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</p>
|
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</td>
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|
<td>
|
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<p>
|
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<span class="blue">Max = 6.86e+04ε (Mean = 2.79e+03ε)</span>
|
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</p>
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</td>
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</tr>
|
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<tr>
|
|
<td>
|
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<p>
|
|
Incomplete Beta Function: Small Integer Values
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</p>
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</td>
|
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<td>
|
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<p>
|
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<span class="blue">Max = 26.8ε (Mean = 6.61ε)</span>
|
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</p>
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</td>
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|
<td>
|
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<p>
|
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<span class="blue">Max = 0.786ε (Mean = 0.0248ε)</span>
|
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</p>
|
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</td>
|
|
<td>
|
|
<p>
|
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<span class="blue">Max = 10.2ε (Mean = 3.49ε)</span>
|
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</p>
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</td>
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|
<td>
|
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<p>
|
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<span class="blue">Max = 51.8ε (Mean = 11ε)</span>
|
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</p>
|
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</td>
|
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</tr>
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</tbody>
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</table></div>
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</div>
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<br class="table-break"><div class="table">
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<a name="math_toolkit.logs_and_tables.all_table.table_betac"></a><p class="title"><b>Table 17.5. Error rates for betac</b></p>
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<div class="table-contents"><table class="table" summary="Error rates for betac">
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<colgroup>
|
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<col>
|
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<col>
|
|
<col>
|
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<col>
|
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<col>
|
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</colgroup>
|
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<thead><tr>
|
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<th>
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</th>
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<th>
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<p>
|
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Microsoft Visual C++ version 12.0<br> Win32<br> double
|
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</p>
|
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</th>
|
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<th>
|
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<p>
|
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GNU C++ version 5.1.0<br> linux<br> double
|
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</p>
|
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</th>
|
|
<th>
|
|
<p>
|
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GNU C++ version 5.1.0<br> linux<br> long double
|
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</p>
|
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</th>
|
|
<th>
|
|
<p>
|
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Sun compiler version 0x5130<br> Sun Solaris<br> long double
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</p>
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</th>
|
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</tr></thead>
|
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<tbody>
|
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<tr>
|
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<td>
|
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<p>
|
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Incomplete Beta Function: Small Values
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</p>
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</td>
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<td>
|
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<p>
|
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<span class="blue">Max = 12ε (Mean = 2.43ε)</span>
|
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</p>
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</td>
|
|
<td>
|
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<p>
|
|
<span class="blue">Max = 0.676ε (Mean = 0.0302ε)</span>
|
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</p>
|
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</td>
|
|
<td>
|
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<p>
|
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<span class="blue">Max = 7.75ε (Mean = 1.91ε)</span>
|
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</p>
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</td>
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|
<td>
|
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<p>
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<span class="blue">Max = 12.6ε (Mean = 3.02ε)</span>
|
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</p>
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</td>
|
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</tr>
|
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<tr>
|
|
<td>
|
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<p>
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Incomplete Beta Function: Medium Values
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</p>
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</td>
|
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<td>
|
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<p>
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<span class="blue">Max = 91.3ε (Mean = 14.8ε)</span>
|
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</p>
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</td>
|
|
<td>
|
|
<p>
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<span class="blue">Max = 0.949ε (Mean = 0.0944ε)</span>
|
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</p>
|
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</td>
|
|
<td>
|
|
<p>
|
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<span class="blue">Max = 63.5ε (Mean = 13.4ε)</span>
|
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</p>
|
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</td>
|
|
<td>
|
|
<p>
|
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<span class="blue">Max = 97.6ε (Mean = 24.3ε)</span>
|
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</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
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Incomplete Beta Function: Large and Diverse Values
|
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</p>
|
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</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.72e+003ε (Mean = 113ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.12ε (Mean = 0.0458ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
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<span class="blue">Max = 1.05e+05ε (Mean = 5.45e+03ε)</span>
|
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</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.04e+05ε (Mean = 5.46e+03ε)</span>
|
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</p>
|
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</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
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<p>
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Incomplete Beta Function: Small Integer Values
|
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</p>
|
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</td>
|
|
<td>
|
|
<p>
|
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<span class="blue">Max = 26.7ε (Mean = 6.67ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.586ε (Mean = 0.0314ε)</span>
|
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</p>
|
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</td>
|
|
<td>
|
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<p>
|
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<span class="blue">Max = 10.4ε (Mean = 3.54ε)</span>
|
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</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 103ε (Mean = 17.4ε)</span>
|
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</p>
|
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</td>
|
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</tr>
|
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</tbody>
|
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</table></div>
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</div>
|
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<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_binomial_coefficient"></a><p class="title"><b>Table 17.6. Error rates for binomial_coefficient</b></p>
|
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<div class="table-contents"><table class="table" summary="Error rates for binomial_coefficient">
|
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<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
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<col>
|
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</colgroup>
|
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<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Binomials: small arguments
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1ε (Mean = 0.369ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1ε (Mean = 0.369ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.5ε (Mean = 0.339ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.5ε (Mean = 0.339ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Binomials: large arguments
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 24.3ε (Mean = 6.3ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.939ε (Mean = 0.314ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 26ε (Mean = 6.09ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 54.1ε (Mean = 10.9ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_cbrt"></a><p class="title"><b>Table 17.7. Error rates for cbrt</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cbrt">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
cbrt Function
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.7ε (Mean = 0.565ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.7ε (Mean = 0.565ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.34ε (Mean = 0.471ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1.34ε (Mean = 0.471ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.34ε (Mean = 0.471ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.11ε (Mean = 0.424ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.11ε (Mean = 0.424ε))
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_cos_pi"></a><p class="title"><b>Table 17.8. Error rates for cos_pi</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cos_pi">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
sin_pi and cos_pi
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.996ε (Mean = 0.281ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.991ε (Mean = 0.302ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.991ε (Mean = 0.302ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
sin_pi and cos_pi near integers and half integers
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.996ε (Mean = 0.298ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.976ε (Mean = 0.28ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.976ε (Mean = 0.28ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_i"></a><p class="title"><b>Table 17.9. Error rates for cyl_bessel_i</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel I0: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.877ε (Mean = 0.549ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.57ε (Mean = 2.1ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 8.49ε (Mean = 3.46ε)
|
|
<a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_i__tr1_cmath__Bessel_I0_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 270ε (Mean = 91.6ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_GSL_1_16_Bessel_I0_Mathworld_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
|
|
<span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_Rmath_3_0_2_Bessel_I0_Mathworld_Data">And
|
|
other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
<span class="red">Max = 2.55e+43ε (Mean = 8.06e+42ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_Cephes_Bessel_I0_Mathworld_Data">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.54ε (Mean = 2.11ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel I1: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.885ε (Mean = 0.55ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.83ε (Mean = 2.79ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 5ε (Mean = 2.15ε)
|
|
<a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_i__tr1_cmath__Bessel_I1_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 128ε (Mean = 41ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_GSL_1_16_Bessel_I1_Mathworld_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
|
|
<span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_Rmath_3_0_2_Bessel_I1_Mathworld_Data">And
|
|
other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
<span class="red">Max = 1.28e+43ε (Mean = 4.05e+42ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_Cephes_Bessel_I1_Mathworld_Data">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.52ε (Mean = 2.25ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel In: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.46ε (Mean = 1.32ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.8ε (Mean = 1.33ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 430ε (Mean = 163ε)
|
|
<a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_i__tr1_cmath__Bessel_In_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 2.31ε (Mean = 0.838ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_GSL_1_16_Bessel_In_Mathworld_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
|
|
<span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_Rmath_3_0_2_Bessel_In_Mathworld_Data">And
|
|
other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
<span class="red">Max = 3.67e+177ε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_Cephes_Bessel_In_Mathworld_Data">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 463ε (Mean = 140ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel Iv: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.97ε (Mean = 1.33ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.12ε (Mean = 1.85ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 616ε (Mean = 221ε)
|
|
<a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_i__tr1_cmath__Bessel_Iv_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 5.95ε (Mean = 2.08ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_GSL_1_16_Bessel_Iv_Mathworld_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
|
|
Max = 1e+04ε (Mean = 3.18e+03ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
<span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_Cephes_Bessel_Iv_Mathworld_Data">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.12ε (Mean = 1.95ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel In: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9.67ε (Mean = 1.89ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.79ε (Mean = 1.15ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 645ε (Mean = 132ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 261ε (Mean = 53.2ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_GSL_1_16_Bessel_In_Random_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
|
|
Max = 7.37ε (Mean = 2.4ε))<br> (<span class="emphasis"><em>Cephes:</em></span> Max
|
|
= 4.22e+06ε (Mean = 2.26e+05ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 176ε (Mean = 39.2ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel Iv: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.46ε (Mean = 1.54ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 8.35ε (Mean = 1.49ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1.05e+03ε (Mean =
|
|
224ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_i__tr1_cmath__Bessel_Iv_Random_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.661ε (Mean = 0.0441ε)</span><br>
|
|
<br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 6.18e+03ε (Mean = 1.55e+03ε)
|
|
<a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_GSL_1_16_Bessel_Iv_Random_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
|
|
<span class="red">Max = 4.28e+08ε (Mean = 2.85e+07ε))</span><br>
|
|
(<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = 6e+30ε (Mean
|
|
= 4e+29ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_Cephes_Bessel_Iv_Random_Data">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 283ε (Mean = 88.4ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel Iv: Mathworld Data (large values)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.67ε (Mean = 1.64ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 14.7ε (Mean = 6.57ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 118ε (Mean = 57.2ε)
|
|
<a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_i__tr1_cmath__Bessel_Iv_Mathworld_Data_large_values_">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 37ε (Mean = 18ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_GSL_1_16_Bessel_Iv_Mathworld_Data_large_values_">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
|
|
<span class="red">Max = 3.77e+168ε (Mean = 2.39e+168ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_Rmath_3_0_2_Bessel_Iv_Mathworld_Data_large_values_">And
|
|
other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
Max = 73.7ε (Mean = 58.5ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 14.7ε (Mean = 6.59ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_i_integer_orders_"></a><p class="title"><b>Table 17.10. Error rates for cyl_bessel_i (integer orders)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i (integer orders)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel I0: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.877ε (Mean = 0.549ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.57ε (Mean = 2.1ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 8.49ε (Mean = 3.46ε)
|
|
<a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_i_integer_orders___tr1_cmath__Bessel_I0_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 0.79ε (Mean = 0.482ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_0_2_Bessel_I0_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
<span class="red">Max = 2.55e+43ε (Mean = 8.06e+42ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_integer_orders__Cephes_Bessel_I0_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.54ε (Mean = 2.11ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel I1: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.885ε (Mean = 0.55ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.83ε (Mean = 2.79ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 5ε (Mean = 2.15ε)
|
|
<a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_i_integer_orders___tr1_cmath__Bessel_I1_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 0.82ε (Mean = 0.456ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_0_2_Bessel_I1_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
<span class="red">Max = 1.28e+43ε (Mean = 4.05e+42ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_integer_orders__Cephes_Bessel_I1_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.52ε (Mean = 2.25ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel In: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.46ε (Mean = 1.32ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.8ε (Mean = 1.33ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 430ε (Mean = 163ε)
|
|
<a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_i_integer_orders___tr1_cmath__Bessel_In_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 5.15ε (Mean = 2.13ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_integer_orders__GSL_1_16_Bessel_In_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
|
|
<span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_0_2_Bessel_In_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
<span class="red">Max = 3.67e+177ε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_integer_orders__Cephes_Bessel_In_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 463ε (Mean = 140ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_i_prime"></a><p class="title"><b>Table 17.11. Error rates for cyl_bessel_i_prime</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i_prime">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel I'0: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.885ε (Mean = 0.567ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.83ε (Mean = 2.84ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.52ε (Mean = 2.26ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel I'1: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.61ε (Mean = 0.786ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.3ε (Mean = 1.28ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.3ε (Mean = 1.29ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel I'n: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.61ε (Mean = 1.22ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.31ε (Mean = 1.41ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 701ε (Mean = 212ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel I'v: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.76e+003ε (Mean = 1.19e+003ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.62ε (Mean = 0.512ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.89e+03ε (Mean = 914ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.89e+03ε (Mean = 914ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel I'n: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9.85ε (Mean = 1.83ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.79ε (Mean = 1.13ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 195ε (Mean = 37.1ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel I'v: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 14ε (Mean = 2.46ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 14.1ε (Mean = 2.93ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 336ε (Mean = 68.5ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel I'v: Mathworld Data (large values)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 59.5ε (Mean = 26.8ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 42.6ε (Mean = 20.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 43.9ε (Mean = 20.7ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_i_prime_integer_orders_"></a><p class="title"><b>Table 17.12. Error rates for cyl_bessel_i_prime (integer orders)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i_prime (integer orders)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel I'0: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.885ε (Mean = 0.567ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.83ε (Mean = 2.84ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.52ε (Mean = 2.26ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel I'1: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.61ε (Mean = 0.786ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.3ε (Mean = 1.28ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.3ε (Mean = 1.29ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel I'n: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.61ε (Mean = 1.22ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.31ε (Mean = 1.41ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 701ε (Mean = 212ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_j"></a><p class="title"><b>Table 17.13. Error rates for cyl_bessel_j</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J0: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.52ε (Mean = 1.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.55ε (Mean = 2.89ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 5.04ε (Mean = 1.78ε)
|
|
<a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_j__tr1_cmath__Bessel_J0_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 0.629ε (Mean = 0.223ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_GSL_1_16_Bessel_J0_Mathworld_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
|
|
<span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_Rmath_3_0_2_Bessel_J0_Mathworld_Data">And
|
|
other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
Max = 1.12ε (Mean = 0.568ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.55ε (Mean = 2.86ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J0: Mathworld Data (Tricky cases)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1e+007ε (Mean = 4.09e+006ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.63e+08ε (Mean = 6.67e+07ε)</span><br>
|
|
<br> (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 4.79e+08ε (Mean
|
|
= 1.96e+08ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.98e+04ε (Mean = 3.26e+04ε)</span><br>
|
|
<br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 6.5e+07ε (Mean = 2.66e+07ε))<br>
|
|
(<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 1.04e+07ε (Mean = 4.29e+06ε))<br>
|
|
(<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = 2.54e+08ε (Mean
|
|
= 1.04e+08ε))</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.64e+08ε (Mean = 6.69e+07ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J1: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.73ε (Mean = 0.976ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.66ε (Mean = 1.38ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 6.1ε (Mean = 2.95ε)
|
|
<a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_j__tr1_cmath__Bessel_J1_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 6.62ε (Mean = 2.35ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_GSL_1_16_Bessel_J1_Mathworld_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
|
|
<span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_Rmath_3_0_2_Bessel_J1_Mathworld_Data">And
|
|
other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
Max = 2.88ε (Mean = 1.12ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.44ε (Mean = 0.637ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J1: Mathworld Data (tricky cases)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.23e+004ε (Mean = 1.45e+004ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.18e+05ε (Mean = 9.76e+04ε)</span><br>
|
|
<br> (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 2.15e+06ε (Mean
|
|
= 1.58e+06ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 106ε (Mean = 47.5ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 1.16:</em></span> Max = 8.75e+05ε (Mean = 5.32e+05ε))<br>
|
|
(<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 2.93e+06ε (Mean = 1.7e+06ε))<br>
|
|
(<span class="emphasis"><em>Cephes:</em></span> Max = 9.56e+05ε (Mean = 4.99e+05ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.18e+05ε (Mean = 9.76e+04ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel JN: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 14.7ε (Mean = 5.4ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.85ε (Mean = 3.41ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> <span class="red">Max
|
|
= 2.13e+19ε (Mean = 5.16e+18ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_j__tr1_cmath__Bessel_JN_Mathworld_Data">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 6.9e+05ε (Mean = 2.15e+05ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_GSL_1_16_Bessel_JN_Mathworld_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
|
|
<span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_Rmath_3_0_2_Bessel_JN_Mathworld_Data">And
|
|
other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
Max = 5.53e+05ε (Mean = 1.9e+05ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 463ε (Mean = 112ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 14.9ε (Mean = 3.82ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 14.7ε (Mean = 4.05ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 3.49e+05ε (Mean =
|
|
7.89e+04ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_j__tr1_cmath__Bessel_J_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 10ε (Mean = 2.19ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.39e+05ε (Mean = 5.24e+04ε)
|
|
<a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_GSL_1_16_Bessel_J_Mathworld_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
|
|
<span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_Rmath_3_0_2_Bessel_J_Mathworld_Data">And
|
|
other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
Max = 5.47e+05ε (Mean = 1.3e+05ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 14.7ε (Mean = 4.12ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J: Mathworld Data (large values)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9.31ε (Mean = 5.52ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 607ε (Mean = 305ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 34.9ε (Mean = 17.4ε)
|
|
<a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_j__tr1_cmath__Bessel_J_Mathworld_Data_large_values_">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.536ε (Mean = 0.268ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 1.16:</em></span> Max = 4.91e+03ε (Mean = 2.46e+03ε)
|
|
<a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_GSL_1_16_Bessel_J_Mathworld_Data_large_values_">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
|
|
Max = 35.9ε (Mean = 18.1ε))<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_Cephes_Bessel_J_Mathworld_Data_large_values_">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 607ε (Mean = 305ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel JN: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 17.5ε (Mean = 1.46ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 50.8ε (Mean = 4.15ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1.12e+03ε (Mean =
|
|
88.7ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 75.7ε (Mean = 5.36ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> Max = 3.93ε (Mean = 1.22ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
Max = 91.4ε (Mean = 6.47ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 99.6ε (Mean = 22ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9.24ε (Mean = 1.36ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9.81ε (Mean = 1.59ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 501ε (Mean = 52.3ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 15.5ε (Mean = 3.33ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_GSL_1_16_Bessel_J_Random_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
|
|
Max = 6.74ε (Mean = 1.3ε))<br> (<span class="emphasis"><em>Cephes:</em></span> Max
|
|
= 16.7ε (Mean = 2.5ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 260ε (Mean = 34ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J: Random Data (Tricky large values)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 59.2ε (Mean = 8.67ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 785ε (Mean = 94.2ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> <span class="red">Max
|
|
= 5.01e+17ε (Mean = 6.23e+16ε))</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 2.48e+05ε (Mean = 5.11e+04ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> Max = 71.6ε (Mean = 11.7ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
Max = 2.48e+05ε (Mean = 3.02e+04ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 785ε (Mean = 97.4ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_j_integer_orders_"></a><p class="title"><b>Table 17.14. Error rates for cyl_bessel_j (integer orders)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j (integer orders)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J0: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.52ε (Mean = 1.2ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.89ε (Mean = 0.988ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.55ε (Mean = 2.89ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 5.04ε (Mean = 1.78ε)
|
|
<a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_j_integer_orders___tr1_cmath__Bessel_J0_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 1.12ε (Mean = 0.488ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_0_2_Bessel_J0_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
Max = 1.12ε (Mean = 0.568ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.55ε (Mean = 2.86ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J0: Mathworld Data (Tricky cases) (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1e+007ε (Mean = 4.09e+006ε)</span><br>
|
|
<br> (<span class="emphasis"><em><math.h>:</em></span> <span class="red">Max
|
|
= 2.54e+008ε (Mean = 1.04e+008ε))</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.63e+08ε (Mean = 6.67e+07ε)</span><br>
|
|
<br> (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 4.79e+08ε (Mean
|
|
= 1.96e+08ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.98e+04ε (Mean = 3.26e+04ε)</span><br>
|
|
<br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 1e+07ε (Mean = 4.11e+06ε))<br>
|
|
(<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 1.04e+07ε (Mean = 4.29e+06ε))<br>
|
|
(<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = 2.54e+08ε (Mean
|
|
= 1.04e+08ε))</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.64e+08ε (Mean = 6.69e+07ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J1: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.73ε (Mean = 0.976ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 11.4ε (Mean = 4.15ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.66ε (Mean = 1.38ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 6.1ε (Mean = 2.95ε)
|
|
<a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_j_integer_orders___tr1_cmath__Bessel_J1_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 1.89ε (Mean = 0.721ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_0_2_Bessel_J1_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
Max = 2.88ε (Mean = 1.12ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.44ε (Mean = 0.637ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J1: Mathworld Data (tricky cases) (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.23e+004ε (Mean = 1.45e+004ε)</span><br>
|
|
<br> (<span class="emphasis"><em><math.h>:</em></span> Max = 1.44e+007ε (Mean
|
|
= 6.5e+006ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.18e+05ε (Mean = 9.76e+04ε)</span><br>
|
|
<br> (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 2.15e+06ε (Mean
|
|
= 1.58e+06ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 106ε (Mean = 47.5ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 1.16:</em></span> Max = 1.26e+06ε (Mean = 6.28e+05ε))<br>
|
|
(<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 2.93e+06ε (Mean = 1.7e+06ε))<br>
|
|
(<span class="emphasis"><em>Cephes:</em></span> Max = 9.56e+05ε (Mean = 4.99e+05ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.18e+05ε (Mean = 9.76e+04ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel JN: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 14.7ε (Mean = 5.4ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> <span class="red">Max =
|
|
+INFε (Mean = +INFε) <a class="link" href="logs.html#errors_Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_integer_orders___math_h__Bessel_JN_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.85ε (Mean = 3.41ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> <span class="red">Max
|
|
= 2.13e+19ε (Mean = 5.16e+18ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_j_integer_orders___tr1_cmath__Bessel_JN_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 6.9e+05ε (Mean = 2.53e+05ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_integer_orders__GSL_1_16_Bessel_JN_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
|
|
<span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_0_2_Bessel_JN_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
<span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_integer_orders__Cephes_Bessel_JN_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 463ε (Mean = 112ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_j_prime"></a><p class="title"><b>Table 17.15. Error rates for cyl_bessel_j_prime</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j_prime">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J0': Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.62ε (Mean = 2.55ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 18.9ε (Mean = 6.81ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 18.9ε (Mean = 6.72ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J0': Mathworld Data (Tricky cases)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.67ε (Mean = 1.74ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 8.08ε (Mean = 4.57ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.44ε (Mean = 3.31ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J1': Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.999ε (Mean = 0.627ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.9ε (Mean = 3.37ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.9ε (Mean = 3.37ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J1': Mathworld Data (tricky cases)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 288ε (Mean = 129ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 287ε (Mean = 129ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.88e+05ε (Mean = 2.63e+05ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.88e+05ε (Mean = 2.63e+05ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel JN': Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 14ε (Mean = 6.13ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.527ε (Mean = 0.128ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.29e+03ε (Mean = 312ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.29e+03ε (Mean = 355ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J': Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 23.7ε (Mean = 8.01ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 21.5ε (Mean = 4.7ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 42.5ε (Mean = 9.31ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 42.5ε (Mean = 9.32ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J': Mathworld Data (large values)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.9ε (Mean = 1.61ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 989ε (Mean = 495ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 989ε (Mean = 495ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel JN': Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.34ε (Mean = 0.997ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.593ε (Mean = 0.0396ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 17.3ε (Mean = 2.47ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 79.4ε (Mean = 16.2ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J': Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 176ε (Mean = 9.76ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.885ε (Mean = 0.0457ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 139ε (Mean = 6.47ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 279ε (Mean = 27.2ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J': Random Data (Tricky large values)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 379ε (Mean = 45.4ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 474ε (Mean = 62.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 474ε (Mean = 64.5ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_j_prime_integer_orders_"></a><p class="title"><b>Table 17.16. Error rates for cyl_bessel_j_prime (integer orders)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j_prime (integer orders)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J0': Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.62ε (Mean = 2.55ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 18.9ε (Mean = 6.81ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 18.9ε (Mean = 6.72ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J0': Mathworld Data (Tricky cases) (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.67ε (Mean = 1.74ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 8.08ε (Mean = 4.57ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.44ε (Mean = 3.31ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J1': Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.999ε (Mean = 0.627ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.9ε (Mean = 3.37ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.9ε (Mean = 3.37ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel J1': Mathworld Data (tricky cases) (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 288ε (Mean = 129ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 287ε (Mean = 129ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.88e+05ε (Mean = 2.63e+05ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.88e+05ε (Mean = 2.63e+05ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel JN': Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 14ε (Mean = 6.13ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.527ε (Mean = 0.128ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.29e+03ε (Mean = 312ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.29e+03ε (Mean = 355ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_k"></a><p class="title"><b>Table 17.17. Error rates for cyl_bessel_k</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel K0: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.55ε (Mean = 0.837ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.16ε (Mean = 1.46ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 9.33ε (Mean = 3.25ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 6.04ε (Mean = 2.16ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> Max = 0.833ε (Mean = 0.601ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.16ε (Mean = 1.49ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel K1: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1ε (Mean = 0.573ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.8ε (Mean = 1.02ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 8.94ε (Mean = 3.19ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 6.26ε (Mean = 2.21ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> Max = 0.894ε (Mean = 0.516ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.8ε (Mean = 1.02ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel Kn: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.63ε (Mean = 1.46ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.48ε (Mean = 2.14ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 12.9ε (Mean = 4.91ε)
|
|
<a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_k__tr1_cmath__Bessel_Kn_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 3.36ε (Mean = 1.43ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_k_GSL_1_16_Bessel_Kn_Mathworld_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
|
|
Max = 8.48ε (Mean = 2.98ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.48ε (Mean = 1.98ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel Kv: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.78ε (Mean = 2.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.58ε (Mean = 2.44ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 13ε (Mean = 4.81ε)
|
|
<a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_k__tr1_cmath__Bessel_Kv_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 5.47ε (Mean = 2.04ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_k_GSL_1_16_Bessel_Kv_Mathworld_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
|
|
Max = 3.15ε (Mean = 1.35ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.58ε (Mean = 2.29ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel Kv: Mathworld Data (large values)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 59.8ε (Mean = 26.9ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 42.3ε (Mean = 21ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 42.3ε (Mean = 19.8ε)
|
|
<a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_k__tr1_cmath__Bessel_Kv_Mathworld_Data_large_values_">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 308ε (Mean = 142ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_k_GSL_1_16_Bessel_Kv_Mathworld_Data_large_values_">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
|
|
Max = 84.6ε (Mean = 37.8ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 43.1ε (Mean = 21.3ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel Kn: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.47ε (Mean = 1.4ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.55ε (Mean = 1.09ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 13.9ε (Mean = 2.91ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.764ε (Mean = 0.0348ε)</span><br>
|
|
<br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 8.71ε (Mean = 1.76ε)
|
|
<a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_k_GSL_1_16_Bessel_Kn_Random_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
|
|
Max = 7.47ε (Mean = 1.34ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.55ε (Mean = 1.21ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel Kv: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 8.33ε (Mean = 1.62ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.88ε (Mean = 1.48ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 13.6ε (Mean = 2.68ε)
|
|
<a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_k__tr1_cmath__Bessel_Kv_Random_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.507ε (Mean = 0.0313ε)</span><br>
|
|
<br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 9.71ε (Mean = 1.47ε)
|
|
<a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_k_GSL_1_16_Bessel_Kv_Random_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
|
|
Max = 7.37ε (Mean = 1.49ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.88ε (Mean = 1.49ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_k_integer_orders_"></a><p class="title"><b>Table 17.18. Error rates for cyl_bessel_k (integer orders)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k (integer orders)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel K0: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.55ε (Mean = 0.837ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.16ε (Mean = 1.46ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 9.33ε (Mean = 3.25ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 1.2ε (Mean = 0.733ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> Max = 0.833ε (Mean = 0.601ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
Max = 1.1e+06ε (Mean = 3.68e+05ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.16ε (Mean = 1.49ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel K1: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1ε (Mean = 0.573ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.8ε (Mean = 1.02ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 8.94ε (Mean = 3.19ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 0.626ε (Mean = 0.333ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> Max = 0.894ε (Mean = 0.516ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
Max = 5.38e+05ε (Mean = 1.79e+05ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.8ε (Mean = 1.02ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel Kn: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.63ε (Mean = 1.46ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.48ε (Mean = 2.14ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 12.9ε (Mean = 4.91ε)
|
|
<a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_k_integer_orders___tr1_cmath__Bessel_Kn_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 168ε (Mean = 59.5ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> Max = 8.48ε (Mean = 2.98ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
<span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_k_integer_orders__Cephes_Bessel_Kn_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.48ε (Mean = 1.98ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_k_prime"></a><p class="title"><b>Table 17.19. Error rates for cyl_bessel_k_prime</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k_prime">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel K'0: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1ε (Mean = 0.573ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.8ε (Mean = 1.02ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.8ε (Mean = 1.02ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel K'1: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.09ε (Mean = 0.607ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.96ε (Mean = 1ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.96ε (Mean = 1.04ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel K'n: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.17ε (Mean = 1.74ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.47ε (Mean = 2.05ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.47ε (Mean = 1.93ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel K'v: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.94ε (Mean = 1.43ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.94ε (Mean = 2.49ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.94ε (Mean = 2.35ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel K'v: Mathworld Data (large values)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 18.6ε (Mean = 12.1ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 59.2ε (Mean = 42.9ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 59.8ε (Mean = 43.4ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel K'n: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 8.18ε (Mean = 1.45ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.53ε (Mean = 1.12ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.45ε (Mean = 1.23ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel K'v: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 8.32ε (Mean = 1.65ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.95ε (Mean = 1.53ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.95ε (Mean = 1.55ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_k_prime_integer_orders_"></a><p class="title"><b>Table 17.20. Error rates for cyl_bessel_k_prime (integer orders)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k_prime (integer orders)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel K'0: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1ε (Mean = 0.573ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.8ε (Mean = 1.02ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.8ε (Mean = 1.02ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel K'1: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.09ε (Mean = 0.607ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.96ε (Mean = 1ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.96ε (Mean = 1.04ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Bessel K'n: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.17ε (Mean = 1.74ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.47ε (Mean = 2.05ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.47ε (Mean = 1.93ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_cyl_neumann"></a><p class="title"><b>Table 17.21. Error rates for cyl_neumann</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cyl_neumann">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Y0: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.61ε (Mean = 2.29ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 60.9ε (Mean = 20.4ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> Max = 167ε (Mean = 56.5ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.59ε (Mean = 2.54ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 2.05e+05ε (Mean =
|
|
6.87e+04ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.53ε (Mean = 2.4ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Y1: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.75ε (Mean = 1.72ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 23.4ε (Mean = 8.1ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> Max = 193ε (Mean = 64.4ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 12.7ε (Mean = 4.34ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 9.71e+03ε (Mean =
|
|
4.08e+03ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.33ε (Mean = 2.29ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Yn: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 35ε (Mean = 11.8ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.993ε (Mean = 0.314ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.41e+05ε (Mean = 7.62e+04ε)
|
|
<a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_neumann_GSL_1_16_Yn_Mathworld_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
|
|
Max = 1.24e+04ε (Mean = 4e+03ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 55.2ε (Mean = 17.7ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> <span class="red">Max
|
|
= 2.2e+20ε (Mean = 6.97e+19ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_neumann__tr1_cmath__Yn_Mathworld_Data">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 55.2ε (Mean = 17.8ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Yv: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.89ε (Mean = 3.27ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 10ε (Mean = 3.02ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 1.16:</em></span> Max = 1.07e+05ε (Mean = 3.22e+04ε)
|
|
<a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_neumann_GSL_1_16_Yv_Mathworld_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
|
|
Max = 1.05e+03ε (Mean = 326ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 10.7ε (Mean = 4.92ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> <span class="red">Max
|
|
= 3.49e+15ε (Mean = 1.05e+15ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_neumann__tr1_cmath__Yv_Mathworld_Data">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 10.7ε (Mean = 5.1ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Yv: Mathworld Data (large values)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.682ε (Mean = 0.35ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 60.8ε (Mean = 23ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_neumann_GSL_1_16_Yv_Mathworld_Data_large_values_">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
|
|
<span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_neumann_Rmath_3_0_2_Yv_Mathworld_Data_large_values_">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.57ε (Mean = 1.17ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 43.2ε (Mean = 16.3ε)
|
|
<a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_neumann__tr1_cmath__Yv_Mathworld_Data_large_values_">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.57ε (Mean = 1.24ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Y0 and Y1: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.17ε (Mean = 1.24ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 34.4ε (Mean = 8.9ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> Max = 83ε (Mean = 14.2ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 11.8ε (Mean = 3.28ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 2.59e+03ε (Mean =
|
|
500ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 10.8ε (Mean = 3.04ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Yn: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 117ε (Mean = 10.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 500ε (Mean = 47.8ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> Max = 691ε (Mean = 67.9ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 338ε (Mean = 28.2ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 4.01e+03ε (Mean =
|
|
348ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 338ε (Mean = 27.5ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Yv: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.23e+003ε (Mean = 69.9ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.53ε (Mean = 0.102ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 1.16:</em></span> Max = 1.41e+06ε (Mean = 7.67e+04ε))<br>
|
|
(<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 1.79e+05ε (Mean = 9.64e+03ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.08e+03ε (Mean = 149ε)</span><br>
|
|
<br> (<span class="emphasis"><em><tr1/cmath>:</em></span> <span class="red">Max
|
|
= +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_neumann__tr1_cmath__Yv_Random_Data">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.08e+03ε (Mean = 149ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_cyl_neumann_integer_orders_"></a><p class="title"><b>Table 17.22. Error rates for cyl_neumann (integer orders)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cyl_neumann (integer orders)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Y0: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.61ε (Mean = 2.29ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 5.37e+003ε (Mean = 1.81e+003ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 6.46ε (Mean = 2.38ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> Max = 167ε (Mean = 56.5ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
Max = 5.37e+03ε (Mean = 1.81e+03ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.59ε (Mean = 2.54ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 2.05e+05ε (Mean =
|
|
6.87e+04ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.53ε (Mean = 2.4ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Y1: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.75ε (Mean = 1.72ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.86e+004ε (Mean = 6.2e+003ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 1.51ε (Mean = 0.839ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> Max = 193ε (Mean = 64.4ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
Max = 1.86e+04ε (Mean = 6.2e+03ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 12.7ε (Mean = 4.34ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 9.71e+03ε (Mean =
|
|
4.08e+03ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.33ε (Mean = 2.29ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Yn: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 35ε (Mean = 11.8ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 2.49e+005ε (Mean = 8.14e+004ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.993ε (Mean = 0.314ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.41e+05ε (Mean = 7.62e+04ε))<br>
|
|
(<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 1.24e+04ε (Mean = 4e+03ε))<br>
|
|
(<span class="emphasis"><em>Cephes:</em></span> Max = 2.49e+05ε (Mean = 8.14e+04ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 55.2ε (Mean = 17.7ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> <span class="red">Max
|
|
= 2.2e+20ε (Mean = 6.97e+19ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_neumann_integer_orders___tr1_cmath__Yn_Mathworld_Data_Integer_Version_">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 55.2ε (Mean = 17.8ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_cyl_neumann_prime"></a><p class="title"><b>Table 17.23. Error rates for cyl_neumann_prime</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cyl_neumann_prime">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Y'0: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.75ε (Mean = 1.75ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 12.7ε (Mean = 4.85ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.33ε (Mean = 3.14ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Y'1: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.08ε (Mean = 1.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.58ε (Mean = 0.193ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 36.6ε (Mean = 12.7ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 34ε (Mean = 11.8ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Y'n: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 563ε (Mean = 178ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.05ε (Mean = 0.677ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 56ε (Mean = 18.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 56ε (Mean = 18.2ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Y'v: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 23.7ε (Mean = 10.1ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 21.5ε (Mean = 6.49ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 42.5ε (Mean = 13.4ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 42.5ε (Mean = 13.6ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Y'v: Mathworld Data (large values)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.627ε (Mean = 0.237ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.57ε (Mean = 1.24ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.57ε (Mean = 1.24ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Y'0 and Y'1: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.95ε (Mean = 1.36ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 23.8ε (Mean = 3.84ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 23.8ε (Mean = 3.69ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Y'n: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 621ε (Mean = 36ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.53ε (Mean = 0.0885ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.35e+03ε (Mean = 136ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.35e+03ε (Mean = 136ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Y'v: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.23e+004ε (Mean = 1.13e+003ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 56.8ε (Mean = 2.59ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.16e+05ε (Mean = 5.28e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.16e+05ε (Mean = 5.28e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_cyl_neumann_prime_integer_orders_"></a><p class="title"><b>Table 17.24. Error rates for cyl_neumann_prime (integer orders)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for cyl_neumann_prime (integer orders)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Y'0: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.75ε (Mean = 1.75ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 12.7ε (Mean = 4.85ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.33ε (Mean = 3.14ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Y'1: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.08ε (Mean = 1.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.58ε (Mean = 0.193ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 36.6ε (Mean = 12.7ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 34ε (Mean = 11.8ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Y'n: Mathworld Data (Integer Version)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 563ε (Mean = 178ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.05ε (Mean = 0.677ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 56ε (Mean = 18.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 56ε (Mean = 18.2ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_digamma"></a><p class="title"><b>Table 17.25. Error rates for digamma</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for digamma">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Digamma Function: Large Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.98ε (Mean = 0.369ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 1.84ε (Mean = 0.71ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> Max = 1.18ε (Mean = 0.331ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
Max = 0.919ε (Mean = 0.394ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.39ε (Mean = 0.413ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.39ε (Mean = 0.413ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Digamma Function: Near the Positive Root
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.997ε (Mean = 0.527ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.891ε (Mean = 0.0995ε)</span><br>
|
|
<br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 135ε (Mean = 11.9ε))<br>
|
|
(<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 2.02e+03ε (Mean = 256ε))<br>
|
|
(<span class="emphasis"><em>Cephes:</em></span> Max = 1.42e+04ε (Mean = 1.14e+03ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.37ε (Mean = 0.477ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.31ε (Mean = 0.451ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Digamma Function: Near Zero
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.953ε (Mean = 0.337ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 0.953ε (Mean = 0.348ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> Max = 1.17ε (Mean = 0.564ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
Max = 3.5ε (Mean = 1.04ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.984ε (Mean = 0.361ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.984ε (Mean = 0.361ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Digamma Function: Negative Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 214ε (Mean = 16.1ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 4.56e+04ε (Mean = 3.91e+03ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> Max = 4.6e+04ε (Mean = 3.94e+03ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
Max = 214ε (Mean = 16.4ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 180ε (Mean = 13ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 180ε (Mean = 13ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Digamma Function: Values near 0
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 0.866ε (Mean = 0.387ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> Max = 3.58e+05ε (Mean = 1.6e+05ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
Max = 0.5ε (Mean = 0.224ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1ε (Mean = 0.592ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1ε (Mean = 0.592ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Digamma Function: Integer arguments
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.992ε (Mean = 0.452ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.992ε (Mean = 0.215ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 1.16:</em></span> Max = 1.18ε (Mean = 0.607ε))<br>
|
|
(<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 4.33ε (Mean = 0.982ε))<br>
|
|
(<span class="emphasis"><em>Cephes:</em></span> Max = 0.992ε (Mean = 0.383ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.888ε (Mean = 0.403ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.888ε (Mean = 0.403ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Digamma Function: Half integer arguments
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.78ε (Mean = 0.314ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 1.09ε (Mean = 0.531ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> Max = 46.2ε (Mean = 7.24ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
Max = 8.56ε (Mean = 1.44ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.906ε (Mean = 0.409ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.906ε (Mean = 0.409ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_ellint_1"></a><p class="title"><b>Table 17.26. Error rates for ellint_1</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ellint_1">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral F: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.919ε (Mean = 0.542ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.94ε (Mean = 0.509ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> <span class="red">Max
|
|
= +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_ellint_1__tr1_cmath__Elliptic_Integral_F_Mathworld_Data">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 0.919ε (Mean = 0.544ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
<span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_ellint_1_Cephes_Elliptic_Integral_F_Mathworld_Data">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.94ε (Mean = 0.509ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral F: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.26ε (Mean = 0.631ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.57ε (Mean = 0.56ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 2.56ε (Mean = 0.816ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 2.99ε (Mean = 0.797ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
Max = 2.18ε (Mean = 0.535ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.57ε (Mean = 0.561ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_ellint_1_complete_"></a><p class="title"><b>Table 17.27. Error rates for ellint_1 (complete)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ellint_1 (complete)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral K: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.915ε (Mean = 0.547ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.887ε (Mean = 0.296ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1.19ε (Mean = 0.765ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 0.623ε (Mean = 0.393ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.887ε (Mean = 0.296ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral K: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.958ε (Mean = 0.408ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.27ε (Mean = 0.473ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 2.19ε (Mean = 0.694ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.851ε (Mean = 0.0851ε)</span><br>
|
|
<br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.32ε (Mean = 0.688ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.27ε (Mean = 0.473ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_ellint_2"></a><p class="title"><b>Table 17.28. Error rates for ellint_2</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ellint_2">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral E: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.31ε (Mean = 0.727ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.656ε (Mean = 0.317ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> <span class="red">Max
|
|
= +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_ellint_2__tr1_cmath__Elliptic_Integral_E_Mathworld_Data">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 0.63ε (Mean = 0.325ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
<span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_ellint_2_Cephes_Elliptic_Integral_E_Mathworld_Data">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.656ε (Mean = 0.317ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral E: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.23ε (Mean = 0.639ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.05ε (Mean = 0.632ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 3.08e+04ε (Mean =
|
|
3.84e+03ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 4.4ε (Mean = 1.16ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
Max = 8.92ε (Mean = 1.48ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.05ε (Mean = 0.632ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_ellint_2_complete_"></a><p class="title"><b>Table 17.29. Error rates for ellint_2 (complete)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ellint_2 (complete)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral E: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.3ε (Mean = 0.615ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.836ε (Mean = 0.469ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 170ε (Mean = 55.1ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 3.09ε (Mean = 1.04ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_ellint_2_complete__GSL_1_16_Elliptic_Integral_E_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.836ε (Mean = 0.469ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral E: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.71ε (Mean = 0.553ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.97ε (Mean = 0.629ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 2.49e+04ε (Mean =
|
|
3.39e+03ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 4.34ε (Mean = 1.18ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.97ε (Mean = 0.629ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_ellint_3"></a><p class="title"><b>Table 17.30. Error rates for ellint_3</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ellint_3">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral PI: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 565ε (Mean = 102ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 475ε (Mean = 86.3ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> <span class="red">Max
|
|
= +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_ellint_3__tr1_cmath__Elliptic_Integral_PI_Mathworld_Data">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 1.48e+05ε (Mean = 2.54e+04ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_ellint_3_GSL_1_16_Elliptic_Integral_PI_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 475ε (Mean = 86.3ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral PI: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9.08ε (Mean = 0.99ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.54ε (Mean = 0.895ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> <span class="red">Max
|
|
= 3.37e+20ε (Mean = 3.47e+19ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_ellint_3__tr1_cmath__Elliptic_Integral_PI_Random_Data">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 633ε (Mean = 50.1ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.49ε (Mean = 0.891ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral PI: Large Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.86ε (Mean = 0.944ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.7ε (Mean = 0.893ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> <span class="red">Max
|
|
= 2.52e+18ε (Mean = 4.83e+17ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_ellint_3__tr1_cmath__Elliptic_Integral_PI_Large_Random_Data">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.557ε (Mean = 0.0389ε)</span><br>
|
|
<br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 40.1ε (Mean = 7.77ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.7ε (Mean = 0.892ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_ellint_3_complete_"></a><p class="title"><b>Table 17.31. Error rates for ellint_3 (complete)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ellint_3 (complete)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Complete Elliptic Integral PI: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.971ε (Mean = 0.464ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.4ε (Mean = 0.575ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> <span class="red">Max
|
|
= 6.31e+20ε (Mean = 1.53e+20ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_ellint_3_complete___tr1_cmath__Complete_Elliptic_Integral_PI_Mathworld_Data">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 6.33e+04ε (Mean = 1.54e+04ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_ellint_3_complete__GSL_1_16_Complete_Elliptic_Integral_PI_Mathworld_Data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.4ε (Mean = 0.575ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Complete Elliptic Integral PI: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.46ε (Mean = 0.654ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.45ε (Mean = 0.696ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> <span class="red">Max
|
|
= 8.78e+20ε (Mean = 1.02e+20ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_ellint_3_complete___tr1_cmath__Complete_Elliptic_Integral_PI_Random_Data">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 24ε (Mean = 2.99ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.4ε (Mean = 0.681ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_ellint_d"></a><p class="title"><b>Table 17.32. Error rates for ellint_d</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ellint_d">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral E: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.862ε (Mean = 0.457ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 0.862ε (Mean = 0.568ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.3ε (Mean = 0.813ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.3ε (Mean = 0.813ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral D: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.87ε (Mean = 0.805ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 3.01ε (Mean = 0.928ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.51ε (Mean = 0.883ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.51ε (Mean = 0.883ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_ellint_d_complete_"></a><p class="title"><b>Table 17.33. Error rates for ellint_d (complete)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ellint_d (complete)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral E: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.637ε (Mean = 0.368ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.637ε (Mean = 0.368ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.27ε (Mean = 0.735ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.27ε (Mean = 0.735ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral D: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.27ε (Mean = 0.355ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.27ε (Mean = 0.334ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.27ε (Mean = 0.334ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_ellint_rc"></a><p class="title"><b>Table 17.34. Error rates for ellint_rc</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ellint_rc">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
RC: Random data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.962ε (Mean = 0.407ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 2.4ε (Mean = 0.624ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.995ε (Mean = 0.433ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.995ε (Mean = 0.438ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_ellint_rd"></a><p class="title"><b>Table 17.35. Error rates for ellint_rd</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ellint_rd">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RD: Random data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.16ε (Mean = 0.803ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 2.59ε (Mean = 0.878ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.73ε (Mean = 0.831ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.73ε (Mean = 0.829ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RD: y = z
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 16.5ε (Mean = 0.843ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.896ε (Mean = 0.022ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.88ε (Mean = 0.839ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.65ε (Mean = 0.82ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.65ε (Mean = 0.819ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RD: x = y
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.51ε (Mean = 0.816ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.824ε (Mean = 0.0272ε)</span><br>
|
|
<br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 3.74ε (Mean = 0.84ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.85ε (Mean = 0.865ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.85ε (Mean = 0.865ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RD: x = 0, y = z
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.16ε (Mean = 0.493ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 2ε (Mean = 0.656ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.19ε (Mean = 0.522ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.19ε (Mean = 0.522ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RD: x = y = z
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.03ε (Mean = 0.418ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 1.03ε (Mean = 0.418ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.998ε (Mean = 0.387ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.998ε (Mean = 0.387ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RD: x = 0
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.64ε (Mean = 0.894ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 2.85ε (Mean = 0.781ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.79ε (Mean = 0.883ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.79ε (Mean = 0.883ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_ellint_rf"></a><p class="title"><b>Table 17.36. Error rates for ellint_rf</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ellint_rf">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RF: Random data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.02ε (Mean = 0.677ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 2.73ε (Mean = 0.804ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.54ε (Mean = 0.674ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.54ε (Mean = 0.674ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RF: x = y = z
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.999ε (Mean = 0.335ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 0.999ε (Mean = 0.34ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.991ε (Mean = 0.345ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.991ε (Mean = 0.345ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RF: x = y or y = z or x = z
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.21ε (Mean = 0.394ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.536ε (Mean = 0.00658ε)</span><br>
|
|
<br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.89ε (Mean = 0.749ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.95ε (Mean = 0.418ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.57ε (Mean = 0.418ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RF: x = 0, y = z
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.999ε (Mean = 0.407ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 1.29ε (Mean = 0.527ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.894ε (Mean = 0.338ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.894ε (Mean = 0.338ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RF: z = 0
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.89ε (Mean = 0.587ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 2.54ε (Mean = 0.781ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.7ε (Mean = 0.539ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.7ε (Mean = 0.539ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_ellint_rg"></a><p class="title"><b>Table 17.37. Error rates for ellint_rg</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ellint_rg">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RG: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.65ε (Mean = 0.929ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.983ε (Mean = 0.0172ε)</span><br>
|
|
<br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 0.983ε (Mean = 0.0172ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.95ε (Mean = 0.951ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.95ε (Mean = 0.951ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RG: two values 0
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RG: All values the same or zero
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.06ε (Mean = 0.348ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.992ε (Mean = 0.288ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.992ε (Mean = 0.288ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RG: two values the same
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.96ε (Mean = 0.374ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.594ε (Mean = 0.0103ε)</span><br>
|
|
<br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 0.594ε (Mean = 0.0103ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.51ε (Mean = 0.404ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.51ε (Mean = 0.404ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RG: one value zero
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.96ε (Mean = 0.674ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.14ε (Mean = 0.722ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.14ε (Mean = 0.722ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_ellint_rj"></a><p class="title"><b>Table 17.38. Error rates for ellint_rj</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ellint_rj">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RJ: Random data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 119ε (Mean = 4.32ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.52ε (Mean = 0.0184ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 1.16:</em></span> Max = 3.57ε (Mean = 0.704ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_ellint_rj_GSL_1_16_RJ_Random_data">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 186ε (Mean = 6.67ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 186ε (Mean = 6.7ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RJ: 4 Equal Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.03ε (Mean = 0.418ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 1.03ε (Mean = 0.418ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.998ε (Mean = 0.387ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.998ε (Mean = 0.387ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RJ: 3 Equal Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 39.9ε (Mean = 1.12ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 3.96ε (Mean = 1.06ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 20.8ε (Mean = 0.986ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 18.2ε (Mean = 0.917ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RJ: 2 Equal Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 214ε (Mean = 5.05ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.6ε (Mean = 0.0228ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.57ε (Mean = 0.754ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 220ε (Mean = 6.64ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 135ε (Mean = 5.3ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
RJ: Equal z and p
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 15.4ε (Mean = 1.05ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.742ε (Mean = 0.0166ε)</span><br>
|
|
<br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.62ε (Mean = 0.699ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 17.2ε (Mean = 1.16ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 16.6ε (Mean = 1.15ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_erf"></a><p class="title"><b>Table 17.39. Error rates for erf</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for erf">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Erf Function: Small Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.996ε (Mean = 0.182ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.57ε (Mean = 0.317ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.925ε (Mean = 0.193ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 0.944ε (Mean = 0.191ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.944ε (Mean = 0.191ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.841ε (Mean = 0.0687ε)</span><br>
|
|
<br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.06ε (Mean = 0.319ε))<br>
|
|
(<span class="emphasis"><em>Cephes:</em></span> Max = 1.13ε (Mean = 0.442ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.925ε (Mean = 0.193ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.944ε (Mean = 0.194ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Erf Function: Medium Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1ε (Mean = 0.169ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.19ε (Mean = 0.244ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.5ε (Mean = 0.193ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 0.921ε (Mean = 0.0723ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.921ε (Mean = 0.0723ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1ε (Mean = 0.119ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.31ε (Mean = 0.368ε))<br>
|
|
(<span class="emphasis"><em>Cephes:</em></span> Max = 1.34ε (Mean = 0.279ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.5ε (Mean = 0.202ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.921ε (Mean = 0.071ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Erf Function: Large Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span>
|
|
Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><tr1/cmath>:</em></span>
|
|
Max = 0ε (Mean = 0ε))<br> (<span class="emphasis"><em><math.h>:</em></span>
|
|
Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 0ε (Mean = 0ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span>
|
|
Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_erf_inv"></a><p class="title"><b>Table 17.40. Error rates for erf_inv</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for erf_inv">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Inverse Erf Function
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.09ε (Mean = 0.502ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.996ε (Mean = 0.389ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.996ε (Mean = 0.385ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_erfc"></a><p class="title"><b>Table 17.41. Error rates for erfc</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for erfc">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Erf Function: Small Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span>
|
|
Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><tr1/cmath>:</em></span>
|
|
Max = 0ε (Mean = 0ε))<br> (<span class="emphasis"><em><math.h>:</em></span>
|
|
Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.658ε (Mean = 0.0537ε)</span><br>
|
|
<br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 1.01ε (Mean = 0.485ε))<br>
|
|
(<span class="emphasis"><em>Cephes:</em></span> Max = 0.786ε (Mean = 0.0642ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span>
|
|
Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Erf Function: Medium Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.65ε (Mean = 0.373ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 2.36ε (Mean = 0.539ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.76ε (Mean = 0.365ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1.35ε (Mean = 0.307ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.35ε (Mean = 0.307ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.983ε (Mean = 0.213ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.64ε (Mean = 0.662ε))<br>
|
|
(<span class="emphasis"><em>Cephes:</em></span> Max = 3.59ε (Mean = 0.779ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.76ε (Mean = 0.383ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 2.81ε (Mean = 0.739ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Erf Function: Large Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.14ε (Mean = 0.248ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.84ε (Mean = 0.331ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.57ε (Mean = 0.542ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1.26ε (Mean = 0.441ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.26ε (Mean = 0.441ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.868ε (Mean = 0.147ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 1.16:</em></span> Max = 3.9ε (Mean = 0.472ε))<br>
|
|
(<span class="emphasis"><em>Cephes:</em></span> Max = 2.74ε (Mean = 0.413ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.57ε (Mean = 0.564ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 4.91ε (Mean = 1.54ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_erfc_inv"></a><p class="title"><b>Table 17.42. Error rates for erfc_inv</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for erfc_inv">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Inverse Erfc Function
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1ε (Mean = 0.491ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.996ε (Mean = 0.397ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.996ε (Mean = 0.397ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Inverse Erfc Function: extreme values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.62ε (Mean = 0.383ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.62ε (Mean = 0.385ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_expint_Ei_"></a><p class="title"><b>Table 17.43. Error rates for expint (Ei)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for expint (Ei)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Exponential Integral Ei
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.43ε (Mean = 0.541ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.05ε (Mean = 0.821ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 14.1ε (Mean = 2.43ε)
|
|
<a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_expint_Ei___tr1_cmath__Exponential_Integral_Ei">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.994ε (Mean = 0.142ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 1.16:</em></span> Max = 8.96ε (Mean = 0.703ε))<br>
|
|
(<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INFε (Mean
|
|
= +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_expint_Ei__Cephes_Exponential_Integral_Ei">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.34ε (Mean = 0.631ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Exponential Integral Ei: double exponent range
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.7ε (Mean = 0.66ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.72ε (Mean = 0.593ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 3.11ε (Mean = 1.13ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.998ε (Mean = 0.156ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 1.16:</em></span> Max = 1.5ε (Mean = 0.612ε))<br>
|
|
(<span class="emphasis"><em>Cephes:</em></span> Max = 1.77ε (Mean = 0.644ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.72ε (Mean = 0.618ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Exponential Integral Ei: long exponent range
|
|
</p>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.98ε (Mean = 0.595ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1.93ε (Mean = 0.855ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.98ε (Mean = 0.575ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_expint_En_"></a><p class="title"><b>Table 17.44. Error rates for expint (En)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for expint (En)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Exponential Integral En
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.16ε (Mean = 1.85ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.589ε (Mean = 0.0331ε)</span><br>
|
|
<br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 58.5ε (Mean = 17.1ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9.97ε (Mean = 2.13ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9.97ε (Mean = 2.13ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Exponential Integral En: small z values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.62ε (Mean = 0.531ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 115ε (Mean = 23.6ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.99ε (Mean = 0.559ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.99ε (Mean = 0.559ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Exponential Integral E1
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.988ε (Mean = 0.486ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.556ε (Mean = 0.0625ε)</span><br>
|
|
<br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 0.988ε (Mean = 0.469ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.965ε (Mean = 0.414ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.965ε (Mean = 0.409ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_expm1"></a><p class="title"><b>Table 17.45. Error rates for expm1</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for expm1">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Random test data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.996ε (Mean = 0.283ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.31ε (Mean = 0.496ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.793ε (Mean = 0.126ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 0.793ε (Mean = 0.126ε))<br>
|
|
(<span class="emphasis"><em>Cephes:</em></span> Max = 1.53ε (Mean = 0.535ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.992ε (Mean = 0.402ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> <span class="red">Max
|
|
= 1.26e+19ε (Mean = 4.89e+18ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_expm1__tr1_cmath__Random_test_data">And
|
|
other failures.</a>)</span><br> (<span class="emphasis"><em><math.h>:</em></span>
|
|
Max = 0.992ε (Mean = 0.402ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.31ε (Mean = 0.406ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.996ε (Mean = 0.426ε))
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_gamma_p"></a><p class="title"><b>Table 17.46. Error rates for gamma_p</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for gamma_p">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma(a, z) medium values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 35.1ε (Mean = 6.97ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.955ε (Mean = 0.05ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 1.16:</em></span> Max = 342ε (Mean = 45.8ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> Max = 389ε (Mean = 44ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
Max = 492ε (Mean = 101ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 41ε (Mean = 8.09ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 239ε (Mean = 30.2ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma(a, z) small values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.54ε (Mean = 0.439ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 4.82ε (Mean = 0.758ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> Max = 1.01ε (Mean = 0.306ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
Max = 21ε (Mean = 5.65ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2ε (Mean = 0.461ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2ε (Mean = 0.472ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma(a, z) large values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 244ε (Mean = 20.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 1.02e+03ε (Mean = 105ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> Max = 1.11e+03ε (Mean = 67.5ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
Max = 8.18e+06ε (Mean = 7.69e+05ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.08e+04ε (Mean = 1.86e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.02e+04ε (Mean = 1.91e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma(a, z) integer and half integer values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 13ε (Mean = 2.93ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 128ε (Mean = 22.6ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> Max = 66.2ε (Mean = 12.2ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
Max = 83.6ε (Mean = 22.2ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 11.8ε (Mean = 2.65ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 71.6ε (Mean = 9.47ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_gamma_p_inv"></a><p class="title"><b>Table 17.47. Error rates for gamma_p_inv</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for gamma_p_inv">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
incomplete gamma inverse(a, z) medium values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.01ε (Mean = 0.307ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.993ε (Mean = 0.15ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 4.88ε (Mean = 0.868ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.62ε (Mean = 0.365ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.86ε (Mean = 0.405ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
incomplete gamma inverse(a, z) large values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.924ε (Mean = 0.118ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> Max = 0.816ε (Mean = 0.0874ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.509ε (Mean = 0.0447ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.509ε (Mean = 0.0447ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
incomplete gamma inverse(a, z) small values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.1e+003ε (Mean = 108ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 441ε (Mean = 53.9ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 547ε (Mean = 61.6ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9.17e+03ε (Mean = 1.32e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.09e+04ε (Mean = 1.46e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_gamma_p_inva"></a><p class="title"><b>Table 17.48. Error rates for gamma_p_inva</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for gamma_p_inva">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Incomplete gamma inverses.
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.52ε (Mean = 0.997ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.44ε (Mean = 1.1ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.08ε (Mean = 1.12ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_gamma_q"></a><p class="title"><b>Table 17.49. Error rates for gamma_q</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for gamma_q">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma(a, z) medium values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 23.7ε (Mean = 4.03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.927ε (Mean = 0.035ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 1.16:</em></span> Max = 201ε (Mean = 13.5ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> Max = 131ε (Mean = 12.7ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
Max = 388ε (Mean = 93.8ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 31.3ε (Mean = 6.56ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 199ε (Mean = 26.6ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma(a, z) small values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.26ε (Mean = 0.732ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> <span class="red">Max = 1.38e+10ε (Mean = 1.05e+09ε))</span><br>
|
|
(<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 65.6ε (Mean = 11ε))<br>
|
|
(<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = 3.42e+11ε (Mean
|
|
= 4.1e+10ε))</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.45ε (Mean = 0.832ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.25ε (Mean = 0.81ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma(a, z) large values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 470ε (Mean = 31.5ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 2.71e+04ε (Mean = 2.16e+03ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> Max = 1.02e+03ε (Mean = 62.7ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
Max = 8.17e+06ε (Mean = 7.7e+05ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.82e+03ε (Mean = 414ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.15e+04ε (Mean = 733ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma(a, z) integer and half integer values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 8.48ε (Mean = 1.42ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 118ε (Mean = 12.5ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> Max = 138ε (Mean = 16.9ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
Max = 129ε (Mean = 26.5ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 11.1ε (Mean = 2.09ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 54.7ε (Mean = 6.16ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_gamma_q_inv"></a><p class="title"><b>Table 17.50. Error rates for gamma_q_inv</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for gamma_q_inv">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
incomplete gamma inverse(a, z) medium values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.46ε (Mean = 0.475ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.912ε (Mean = 0.154ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 4.66ε (Mean = 0.792ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.2ε (Mean = 0.659ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.2ε (Mean = 0.661ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
incomplete gamma inverse(a, z) large values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.814ε (Mean = 0.0856ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.894ε (Mean = 0.0915ε)</span><br>
|
|
<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 0.894ε (Mean = 0.106ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
incomplete gamma inverse(a, z) small values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 451ε (Mean = 65ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 292ε (Mean = 36.4ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 415ε (Mean = 48.7ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 8.28e+03ε (Mean = 963ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 8.98e+03ε (Mean = 877ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_gamma_q_inva"></a><p class="title"><b>Table 17.51. Error rates for gamma_q_inva</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for gamma_q_inva">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Incomplete gamma inverses.
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.64ε (Mean = 1.09ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.91ε (Mean = 1.17ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.86ε (Mean = 1.25ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_hermite"></a><p class="title"><b>Table 17.52. Error rates for hermite</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for hermite">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Hermite Polynomials
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.46ε (Mean = 1.41ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.24ε (Mean = 2.07ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.24ε (Mean = 2.07ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_heuman_lambda"></a><p class="title"><b>Table 17.53. Error rates for heuman_lambda</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for heuman_lambda">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral Jacobi Zeta: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.08ε (Mean = 0.734ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.89ε (Mean = 0.887ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.89ε (Mean = 0.887ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral Heuman Lambda: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.12ε (Mean = 0.59ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.82ε (Mean = 0.609ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.82ε (Mean = 0.608ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_ibeta"></a><p class="title"><b>Table 17.54. Error rates for ibeta</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ibeta">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Incomplete Beta Function: Small Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9.42ε (Mean = 2.24ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 682ε (Mean = 32.6ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> Max = 22.9ε (Mean = 3.35ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
Max = 22.7ε (Mean = 1.69ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.27ε (Mean = 1.7ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 21.3ε (Mean = 2.74ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Incomplete Beta Function: Medium Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 108ε (Mean = 16.3ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 690ε (Mean = 151ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> Max = 232ε (Mean = 27.9ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
Max = 1.55e+03ε (Mean = 121ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 51.4ε (Mean = 12ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 124ε (Mean = 18.4ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Incomplete Beta Function: Large and Diverse Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.19e+003ε (Mean = 59.5ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.26ε (Mean = 0.063ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 1.16:</em></span> Max = 3.9e+05ε (Mean = 1.82e+04ε)
|
|
<a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_ibeta_GSL_1_16_Incomplete_Beta_Function_Large_and_Diverse_Values">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
|
|
Max = 574ε (Mean = 49.4ε))<br> (<span class="emphasis"><em>Cephes:</em></span> Max
|
|
= 5.92e+05ε (Mean = 2.17e+04ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.96e+04ε (Mean = 997ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.98e+04ε (Mean = 2.07e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Incomplete Beta Function: Small Integer Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.69ε (Mean = 0.765ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 254ε (Mean = 50.9ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> Max = 62.2ε (Mean = 8.95ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
Max = 7.96ε (Mean = 1.3ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.45ε (Mean = 0.814ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 44.5ε (Mean = 10.1ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_ibeta_inv"></a><p class="title"><b>Table 17.55. Error rates for ibeta_inv</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ibeta_inv">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Inverse incomplete beta
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.08e+003ε (Mean = 244ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.21ε (Mean = 0.158ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max = +INFε (Mean
|
|
= +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_ibeta_inv_Rmath_3_0_2_Inverse_incomplete_beta">And
|
|
other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
<span class="red">Max = 1.28e+10ε (Mean = 5.17e+08ε))</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.53e+04ε (Mean = 2.93e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.22e+04ε (Mean = 2.8e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_ibeta_inva"></a><p class="title"><b>Table 17.56. Error rates for ibeta_inva</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ibeta_inva">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Inverse incomplete beta
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 395ε (Mean = 24.7ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.602ε (Mean = 0.0239ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 377ε (Mean = 25.1ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 438ε (Mean = 31.6ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_ibeta_invb"></a><p class="title"><b>Table 17.57. Error rates for ibeta_invb</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ibeta_invb">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Inverse incomplete beta
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 409ε (Mean = 17.9ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.836ε (Mean = 0.0491ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 407ε (Mean = 27.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 407ε (Mean = 24.4ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_ibetac"></a><p class="title"><b>Table 17.58. Error rates for ibetac</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ibetac">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Incomplete Beta Function: Small Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.56ε (Mean = 1.88ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> Max = 22.4ε (Mean = 3.67ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 8.47ε (Mean = 1.68ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 13.8ε (Mean = 2.69ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Incomplete Beta Function: Medium Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 56.2ε (Mean = 14.1ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> Max = 204ε (Mean = 25.8ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 75.3ε (Mean = 11.3ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 132ε (Mean = 19.8ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Incomplete Beta Function: Large and Diverse Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.87e+003ε (Mean = 93.8ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.981ε (Mean = 0.0638ε)</span><br>
|
|
<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 889ε (Mean = 68.4ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.45e+04ε (Mean = 1.32e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.26e+04ε (Mean = 1.54e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Incomplete Beta Function: Small Integer Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.37ε (Mean = 1.03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> Max = 84.6ε (Mean = 18ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.34ε (Mean = 1.11ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 107ε (Mean = 17.1ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_ibetac_inv"></a><p class="title"><b>Table 17.59. Error rates for ibetac_inv</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ibetac_inv">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Inverse incomplete beta
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.53e+003ε (Mean = 220ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.71ε (Mean = 0.108ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max = +INFε (Mean
|
|
= +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_ibetac_inv_Rmath_3_0_2_Inverse_incomplete_beta">And
|
|
other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
Max = 1.71ε (Mean = 0.108ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.17e+04ε (Mean = 3.77e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.15e+04ε (Mean = 3.51e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_ibetac_inva"></a><p class="title"><b>Table 17.60. Error rates for ibetac_inva</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ibetac_inva">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Inverse incomplete beta
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 408ε (Mean = 27.8ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.683ε (Mean = 0.0271ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 382ε (Mean = 22.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 315ε (Mean = 23.7ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_ibetac_invb"></a><p class="title"><b>Table 17.61. Error rates for ibetac_invb</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for ibetac_invb">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Inverse incomplete beta
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 329ε (Mean = 18.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.724ε (Mean = 0.0303ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 317ε (Mean = 19.7ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 369ε (Mean = 21.7ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_jacobi_cn"></a><p class="title"><b>Table 17.62. Error rates for jacobi_cn</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for jacobi_cn">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Jacobi Elliptic: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 45.8ε (Mean = 11.4ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 17.3ε (Mean = 4.29ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_cn_GSL_1_16_Jacobi_Elliptic_Mathworld_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_cn_Cephes_Jacobi_Elliptic_Mathworld_Data">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 71.6ε (Mean = 19.3ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 71.6ε (Mean = 19.4ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Jacobi Elliptic: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.83ε (Mean = 0.455ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.816ε (Mean = 0.0563ε)</span><br>
|
|
<br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.43ε (Mean = 0.803ε))<br>
|
|
(<span class="emphasis"><em>Cephes:</em></span> Max = 1.83ε (Mean = 0.437ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.68ε (Mean = 0.443ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.68ε (Mean = 0.454ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Jacobi Elliptic: Random Small Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 26.2ε (Mean = 1.17ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 55.2ε (Mean = 1.64ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_cn_GSL_1_16_Jacobi_Elliptic_Random_Small_Values">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_cn_Cephes_Jacobi_Elliptic_Random_Small_Values">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 10.4ε (Mean = 0.594ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 10.4ε (Mean = 0.602ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Jacobi Elliptic: Modulus near 1
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 513ε (Mean = 126ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.919ε (Mean = 0.127ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 1.16:</em></span> Max = 0ε (Mean = 0ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_cn_GSL_1_16_Jacobi_Elliptic_Modulus_near_1">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_cn_Cephes_Jacobi_Elliptic_Modulus_near_1">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 675ε (Mean = 87.1ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 675ε (Mean = 86.8ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Jacobi Elliptic: Large Phi
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.27e+004ε (Mean = 1.93e+003ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 14.2ε (Mean = 0.927ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 1.16:</em></span> Max = 5.92e+03ε (Mean = 477ε))<br>
|
|
(<span class="emphasis"><em>Cephes:</em></span> Max = 3.27e+04ε (Mean = 1.93e+03ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.97e+04ε (Mean = 1.9e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.97e+04ε (Mean = 1.9e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_jacobi_dn"></a><p class="title"><b>Table 17.63. Error rates for jacobi_dn</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for jacobi_dn">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Jacobi Elliptic: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 34.3ε (Mean = 8.71ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 2.82ε (Mean = 1.18ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_dn_GSL_1_16_Jacobi_Elliptic_Mathworld_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_dn_Cephes_Jacobi_Elliptic_Mathworld_Data">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 49ε (Mean = 14ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 49ε (Mean = 14ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Jacobi Elliptic: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.52ε (Mean = 0.466ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 3ε (Mean = 0.61ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
Max = 1.49ε (Mean = 0.321ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.53ε (Mean = 0.473ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.53ε (Mean = 0.481ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Jacobi Elliptic: Random Small Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 16.1ε (Mean = 0.685ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.5ε (Mean = 0.0122ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 1.16:</em></span> Max = 1.5ε (Mean = 0.391ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_dn_GSL_1_16_Jacobi_Elliptic_Random_Small_Values">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_dn_Cephes_Jacobi_Elliptic_Random_Small_Values">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 22.4ε (Mean = 0.777ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 22.4ε (Mean = 0.763ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Jacobi Elliptic: Modulus near 1
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.24e+003ε (Mean = 482ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.28ε (Mean = 0.194ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 1.16:</em></span> Max = 0ε (Mean = 0ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_dn_GSL_1_16_Jacobi_Elliptic_Modulus_near_1">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_dn_Cephes_Jacobi_Elliptic_Modulus_near_1">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.75e+03ε (Mean = 293ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.75e+03ε (Mean = 293ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Jacobi Elliptic: Large Phi
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.67e+004ε (Mean = 1e+003ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 14.1ε (Mean = 0.897ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 1.16:</em></span> Max = 121ε (Mean = 22ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
Max = 196ε (Mean = 30.2ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.82e+04ε (Mean = 1.79e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.82e+04ε (Mean = 1.79e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_jacobi_sn"></a><p class="title"><b>Table 17.64. Error rates for jacobi_sn</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for jacobi_sn">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Jacobi Elliptic: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 481ε (Mean = 113ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 588ε (Mean = 146ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_sn_GSL_1_16_Jacobi_Elliptic_Mathworld_Data">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_sn_Cephes_Jacobi_Elliptic_Mathworld_Data">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 341ε (Mean = 80.7ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 341ε (Mean = 80.7ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Jacobi Elliptic: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.92ε (Mean = 0.567ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 4.02ε (Mean = 1.07ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
Max = 1.92ε (Mean = 0.567ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.01ε (Mean = 0.584ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.01ε (Mean = 0.593ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Jacobi Elliptic: Random Small Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.11ε (Mean = 0.385ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 11.7ε (Mean = 1.65ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_sn_GSL_1_16_Jacobi_Elliptic_Random_Small_Values">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_sn_Cephes_Jacobi_Elliptic_Random_Small_Values">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.99ε (Mean = 0.347ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.99ε (Mean = 0.347ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Jacobi Elliptic: Modulus near 1
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 23.2ε (Mean = 1.85ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 0ε (Mean = 0ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_sn_GSL_1_16_Jacobi_Elliptic_Modulus_near_1">And
|
|
other failures.</a>)<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_sn_Cephes_Jacobi_Elliptic_Modulus_near_1">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 109ε (Mean = 7.35ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 109ε (Mean = 7.38ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Jacobi Elliptic: Large Phi
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.36e+004ε (Mean = 2.54e+003ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 12ε (Mean = 0.771ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 1.16:</em></span> Max = 4.54e+04ε (Mean = 2.63e+03ε))<br>
|
|
(<span class="emphasis"><em>Cephes:</em></span> Max = 4.36e+04ε (Mean = 2.54e+03ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.45e+04ε (Mean = 1.51e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.45e+04ε (Mean = 1.51e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_jacobi_zeta"></a><p class="title"><b>Table 17.65. Error rates for jacobi_zeta</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for jacobi_zeta">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral Jacobi Zeta: Mathworld Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.505ε (Mean = 0.119ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.66ε (Mean = 0.48ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.66ε (Mean = 0.48ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral Jacobi Zeta: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.89ε (Mean = 0.818ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.99ε (Mean = 0.824ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.96ε (Mean = 1.06ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Elliptic Integral Jacobi Zeta: Large Phi Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.92ε (Mean = 0.964ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.92ε (Mean = 0.951ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.05ε (Mean = 1.13ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_laguerre_n_m_x_"></a><p class="title"><b>Table 17.66. Error rates for laguerre(n, m, x)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for laguerre(n, m, x)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Associated Laguerre Polynomials
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 434ε (Mean = 11.1ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.84ε (Mean = 0.0358ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 1.16:</em></span> Max = 434ε (Mean = 10.7ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 167ε (Mean = 6.38ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 206ε (Mean = 6.86ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 167ε (Mean = 6.38ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_laguerre_n_x_"></a><p class="title"><b>Table 17.67. Error rates for laguerre(n, x)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for laguerre(n, x)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Laguerre Polynomials
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.1e+003ε (Mean = 185ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.82ε (Mean = 0.408ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 1.16:</em></span> Max = 3.1e+03ε (Mean = 185ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.39e+04ε (Mean = 828ε)</span><br>
|
|
<br> (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 4.2e+03ε (Mean
|
|
= 251ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.39e+04ε (Mean = 828ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_legendre_p"></a><p class="title"><b>Table 17.68. Error rates for legendre_p</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for legendre_p">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Legendre Polynomials: Small Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 211ε (Mean = 20.4ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.732ε (Mean = 0.0619ε)</span><br>
|
|
<br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 211ε (Mean = 20.4ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 69.2ε (Mean = 9.58ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 124ε (Mean = 13.2ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 69.2ε (Mean = 9.58ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Legendre Polynomials: Large Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 300ε (Mean = 33.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.632ε (Mean = 0.0693ε)</span><br>
|
|
<br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 300ε (Mean = 33.2ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 699ε (Mean = 59.6ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 343ε (Mean = 32.1ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 699ε (Mean = 59.6ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_legendre_p_associated_"></a><p class="title"><b>Table 17.69. Error rates for legendre_p (associated)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for legendre_p (associated)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Associated Legendre Polynomials: Small Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 121ε (Mean = 7.14ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.999ε (Mean = 0.05ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 1.16:</em></span> Max = 121ε (Mean = 6.75ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_legendre_p_associated__GSL_1_16_Associated_Legendre_Polynomials_Small_Values">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 175ε (Mean = 9.88ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 175ε (Mean = 9.36ε)
|
|
<a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_legendre_p_associated___tr1_cmath__Associated_Legendre_Polynomials_Small_Values">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 77.7ε (Mean = 5.59ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_legendre_q"></a><p class="title"><b>Table 17.70. Error rates for legendre_q</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for legendre_q">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Legendre Polynomials: Small Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 46.4ε (Mean = 7.32ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.612ε (Mean = 0.0517ε)</span><br>
|
|
<br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 46.4ε (Mean = 7.46ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 50.9ε (Mean = 9ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 50.9ε (Mean = 8.98ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Legendre Polynomials: Large Values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.6e+003ε (Mean = 366ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.49ε (Mean = 0.202ε)</span><br> <br>
|
|
(<span class="emphasis"><em>GSL 1.16:</em></span> Max = 4.6e+03ε (Mean = 366ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.98e+03ε (Mean = 478ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.98e+03ε (Mean = 478ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_lgamma"></a><p class="title"><b>Table 17.71. Error rates for lgamma</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for lgamma">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
factorials
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.914ε (Mean = 0.167ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.958ε (Mean = 0.38ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 33.6ε (Mean = 2.78ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> Max = 1.55ε (Mean = 0.592ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
Max = 1.55ε (Mean = 0.512ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.991ε (Mean = 0.311ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1.67ε (Mean = 0.487ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.67ε (Mean = 0.487ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.991ε (Mean = 0.383ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.36ε (Mean = 0.476ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
near 0
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.964ε (Mean = 0.462ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.962ε (Mean = 0.372ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 5.21ε (Mean = 1.57ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> Max = 0ε (Mean = 0ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
Max = 1.16ε (Mean = 0.341ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.42ε (Mean = 0.566ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 0.964ε (Mean = 0.543ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.964ε (Mean = 0.543ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.42ε (Mean = 0.566ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.964ε (Mean = 0.543ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
near 1
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.867ε (Mean = 0.468ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.906ε (Mean = 0.565ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 442ε (Mean = 88.8ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> Max = 7.99e+04ε (Mean = 1.68e+04ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
Max = 1.14e+05ε (Mean = 2.64e+04ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.948ε (Mean = 0.36ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 0.615ε (Mean = 0.096ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.615ε (Mean = 0.096ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.866ε (Mean = 0.355ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.71ε (Mean = 0.581ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
near 2
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.591ε (Mean = 0.159ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.741ε (Mean = 0.473ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 1.17e+03ε (Mean = 274ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> Max = 2.63e+05ε (Mean = 5.84e+04ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
Max = 5.08e+05ε (Mean = 9.04e+04ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.878ε (Mean = 0.242ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 0.741ε (Mean = 0.263ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.741ε (Mean = 0.263ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.878ε (Mean = 0.241ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.598ε (Mean = 0.235ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
near -10
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.22ε (Mean = 1.33ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.997ε (Mean = 0.444ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 24.9ε (Mean = 4.6ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> Max = 2.41e+05ε (Mean = 4.29e+04ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
Max = 0.997ε (Mean = 0.429ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.81ε (Mean = 1.01ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 3.01ε (Mean = 0.86ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 3.01ε (Mean = 0.86ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.81ε (Mean = 1.01ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 3.04ε (Mean = 1.01ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
near -55
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.821ε (Mean = 0.419ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 249ε (Mean = 43.1ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 7.02ε (Mean = 1.47ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> Max = 4.08e+04ε (Mean = 7.26e+03ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
Max = 1.64ε (Mean = 0.693ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.821ε (Mean = 0.513ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1.58ε (Mean = 0.672ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.58ε (Mean = 0.672ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.59ε (Mean = 0.587ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.821ε (Mean = 0.674ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_log1p"></a><p class="title"><b>Table 17.72. Error rates for log1p</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for log1p">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Random test data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.509ε (Mean = 0.057ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.509ε (Mean = 0.057ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.846ε (Mean = 0.153ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 0.846ε (Mean = 0.153ε))<br>
|
|
(<span class="emphasis"><em>Cephes:</em></span> Max = 0.799ε (Mean = 0.122ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.818ε (Mean = 0.227ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 0.818ε (Mean = 0.227ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.818ε (Mean = 0.227ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.53ε (Mean = 0.627ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.818ε (Mean = 0.249ε))
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_non_central_beta_CDF"></a><p class="title"><b>Table 17.73. Error rates for non central beta CDF</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for non central beta CDF">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Non Central Beta, medium parameters
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 240ε (Mean = 31ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.998ε (Mean = 0.0659ε)</span><br>
|
|
<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max
|
|
= 1.46e+26ε (Mean = 3.5e+24ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_non_central_beta_CDF_Rmath_3_0_2_Non_Central_Beta_medium_parameters">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 825ε (Mean = 27.4ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 832ε (Mean = 38.1ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Non Central Beta, large parameters
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.41e+003ε (Mean = 475ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.18ε (Mean = 0.175ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max = 1.01e+36ε (Mean
|
|
= 1.19e+35ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_non_central_beta_CDF_Rmath_3_0_2_Non_Central_Beta_large_parameters">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.5e+04ε (Mean = 3.78e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.57e+04ε (Mean = 4.43e+03ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_non_central_beta_CDF_complement"></a><p class="title"><b>Table 17.74. Error rates for non central beta CDF complement</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for non central beta CDF complement">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Non Central Beta, medium parameters
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 619ε (Mean = 62.7ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.998ε (Mean = 0.0957ε)</span><br>
|
|
<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max
|
|
= 7.5e+97ε (Mean = 1.37e+96ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_non_central_beta_CDF_complement_Rmath_3_0_2_Non_Central_Beta_medium_parameters">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 396ε (Mean = 50.7ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 554ε (Mean = 57.3ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Non Central Beta, large parameters
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 8.67e+003ε (Mean = 1.04e+003ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.986ε (Mean = 0.188ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max = +INFε (Mean
|
|
= +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_non_central_beta_CDF_complement_Rmath_3_0_2_Non_Central_Beta_large_parameters">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.83e+03ε (Mean = 993ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.56e+03ε (Mean = 704ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_non_central_chi_squared_CDF"></a><p class="title"><b>Table 17.75. Error rates for non central chi squared CDF</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for non central chi squared CDF">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Non Central Chi Squared, medium parameters
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 48.9ε (Mean = 10ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.99ε (Mean = 0.0529ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 727ε (Mean = 121ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 46.5ε (Mean = 10.3ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 115ε (Mean = 13.9ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Non Central Chi Squared, large parameters
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9.79e+003ε (Mean = 723ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.07ε (Mean = 0.102ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max = 3.27e+08ε (Mean
|
|
= 2.23e+07ε))</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.07e+03ε (Mean = 336ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.17e+03ε (Mean = 677ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_non_central_chi_squared_CDF_complement"></a><p class="title"><b>Table 17.76. Error rates for non central chi squared CDF complement</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for non central chi squared CDF complement">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Non Central Chi Squared, medium parameters
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 98.6ε (Mean = 15.8ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.96ε (Mean = 0.0635ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max = +INFε (Mean
|
|
= +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_non_central_chi_squared_CDF_complement_Rmath_3_0_2_Non_Central_Chi_Squared_medium_parameters">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 107ε (Mean = 17.1ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 171ε (Mean = 22.8ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Non Central Chi Squared, large parameters
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.43e+003ε (Mean = 705ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.11ε (Mean = 0.278ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max = +INFε (Mean
|
|
= +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_non_central_chi_squared_CDF_complement_Rmath_3_0_2_Non_Central_Chi_Squared_large_parameters">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.02e+03ε (Mean = 630ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.1e+03ε (Mean = 577ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_non_central_t_CDF"></a><p class="title"><b>Table 17.77. Error rates for non central t CDF</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for non central t CDF">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Non Central T
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 138ε (Mean = 31.5ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.796ε (Mean = 0.0691ε)</span><br>
|
|
<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max
|
|
= 5.28e+15ε (Mean = 8.49e+14ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_non_central_t_CDF_Rmath_3_0_2_Non_Central_T">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 141ε (Mean = 31.1ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 145ε (Mean = 30.2ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Non Central T (small non-centrality)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.61ε (Mean = 1.03ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> Max = 2.09e+03ε (Mean = 244ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.86ε (Mean = 1.69ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9.15ε (Mean = 2.25ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Non Central T (large parameters)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 286ε (Mean = 62.8ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 257ε (Mean = 72.1ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 2.46ε (Mean = 0.657ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.26e+05ε (Mean = 1.48e+05ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.24e+05ε (Mean = 1.47e+05ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_non_central_t_CDF_complement"></a><p class="title"><b>Table 17.78. Error rates for non central t CDF complement</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for non central t CDF complement">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Non Central T
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 150ε (Mean = 32.3ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.707ε (Mean = 0.0497ε)</span><br>
|
|
<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max
|
|
= 6.19e+15ε (Mean = 6.72e+14ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_non_central_t_CDF_complement_Rmath_3_0_2_Non_Central_T">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 203ε (Mean = 31.8ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 340ε (Mean = 43.6ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Non Central T (small non-centrality)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.21ε (Mean = 1.43ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> Max = 1.87e+03ε (Mean = 263ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.48ε (Mean = 1.86ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 10.9ε (Mean = 2.43ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Non Central T (large parameters)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 227ε (Mean = 50.4ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 478ε (Mean = 96.3ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 2.24ε (Mean = 0.945ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9.79e+05ε (Mean = 1.97e+05ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9.79e+05ε (Mean = 1.97e+05ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_owens_t"></a><p class="title"><b>Table 17.79. Error rates for owens_t</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for owens_t">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Owens T (medium small values)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.37ε (Mean = 0.973ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.34ε (Mean = 0.942ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.34ε (Mean = 0.91ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Owens T (large and diverse values)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.78ε (Mean = 0.621ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 49ε (Mean = 2.16ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 24.5ε (Mean = 1.38ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_polygamma"></a><p class="title"><b>Table 17.80. Error rates for polygamma</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for polygamma">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Mathematica Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.34ε (Mean = 1.53ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.824ε (Mean = 0.0574ε)</span><br>
|
|
<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 108ε (Mean = 15.2ε))<br>
|
|
(<span class="emphasis"><em>GSL 1.16:</em></span> Max = 62.9ε (Mean = 12.8ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.38ε (Mean = 1.84ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 18.3ε (Mean = 4.16ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Mathematica Data - large arguments
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 150ε (Mean = 15.1ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.998ε (Mean = 0.0592ε)</span><br>
|
|
<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max
|
|
= 1.71e+56ε (Mean = 1.01e+55ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_polygamma_Rmath_3_0_2_Mathematica_Data_large_arguments">And
|
|
other failures.</a>)</span><br> (<span class="emphasis"><em>GSL 1.16:</em></span>
|
|
Max = 244ε (Mean = 32.8ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_polygamma_GSL_1_16_Mathematica_Data_large_arguments">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.23ε (Mean = 0.323ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.35ε (Mean = 0.34ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Mathematica Data - negative arguments
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 497ε (Mean = 129ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.516ε (Mean = 0.022ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max = +INFε (Mean
|
|
= +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_polygamma_Rmath_3_0_2_Mathematica_Data_negative_arguments">And
|
|
other failures.</a>)</span><br> (<span class="emphasis"><em>GSL 1.16:</em></span>
|
|
Max = 36.6ε (Mean = 3.04ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_polygamma_GSL_1_16_Mathematica_Data_negative_arguments">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 269ε (Mean = 87.7ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 269ε (Mean = 87.9ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Mathematica Data - large negative arguments
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 162ε (Mean = 101ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_polygamma_Rmath_3_0_2_Mathematica_Data_large_negative_arguments">And
|
|
other failures.</a>)</span><br> (<span class="emphasis"><em>GSL 1.16:</em></span>
|
|
Max = 1.79ε (Mean = 0.197ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_polygamma_GSL_1_16_Mathematica_Data_large_negative_arguments">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 155ε (Mean = 96.4ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 155ε (Mean = 96.4ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Mathematica Data - small arguments
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3ε (Mean = 0.496ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> Max = 106ε (Mean = 20ε))<br> (<span class="emphasis"><em>GSL 1.16:</em></span>
|
|
Max = 15.2ε (Mean = 5.03ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.33ε (Mean = 0.75ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.33ε (Mean = 0.75ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Mathematica Data - Large orders and other bug cases
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 200ε (Mean = 57.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_polygamma_Rmath_3_0_2_Mathematica_Data_Large_orders_and_other_bug_cases">And
|
|
other failures.</a>)</span><br> (<span class="emphasis"><em>GSL 1.16:</em></span>
|
|
Max = 151ε (Mean = 39.3ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_polygamma_GSL_1_16_Mathematica_Data_Large_orders_and_other_bug_cases">And
|
|
other failures.</a>)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 54.5ε (Mean = 13.3ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 90.1ε (Mean = 30.6ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_powm1"></a><p class="title"><b>Table 17.81. Error rates for powm1</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for powm1">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
powm1
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.99ε (Mean = 0.461ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.26ε (Mean = 0.428ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.04ε (Mean = 0.521ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.14ε (Mean = 0.498ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_sin_pi"></a><p class="title"><b>Table 17.82. Error rates for sin_pi</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for sin_pi">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
sin_pi and cos_pi
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.99ε (Mean = 0.328ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.996ε (Mean = 0.335ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.996ε (Mean = 0.336ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
sin_pi and cos_pi near integers and half integers
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.996ε (Mean = 0.343ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.976ε (Mean = 0.293ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.976ε (Mean = 0.293ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_sph_bessel"></a><p class="title"><b>Table 17.83. Error rates for sph_bessel</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for sph_bessel">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Bessel j: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 245ε (Mean = 16.3ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 243ε (Mean = 13.3ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1.91e+06ε (Mean =
|
|
1.09e+05ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.978ε (Mean = 0.0539ε)</span><br>
|
|
<br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 1.79e+03ε (Mean = 107ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 243ε (Mean = 33.7ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_sph_bessel_prime"></a><p class="title"><b>Table 17.84. Error rates for sph_bessel_prime</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for sph_bessel_prime">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Bessel j': Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 307ε (Mean = 25.2ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.753ε (Mean = 0.0343ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 167ε (Mean = 12ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 167ε (Mean = 33.2ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_sph_neumann"></a><p class="title"><b>Table 17.85. Error rates for sph_neumann</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for sph_neumann">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
y: Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 281ε (Mean = 31.1ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.995ε (Mean = 0.0665ε)</span><br>
|
|
<br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 8.5e+04ε (Mean = 5.33e+03ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 234ε (Mean = 19.5ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1.6e+06ε (Mean = 1.4e+05ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 234ε (Mean = 19.8ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_sph_neumann_prime"></a><p class="title"><b>Table 17.86. Error rates for sph_neumann_prime</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for sph_neumann_prime">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
y': Random Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 296ε (Mean = 25.6ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.752ε (Mean = 0.062ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 158ε (Mean = 18.8ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 158ε (Mean = 20.2ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_spherical_harmonic_i"></a><p class="title"><b>Table 17.87. Error rates for spherical_harmonic_i</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for spherical_harmonic_i">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Spherical Harmonics
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.27e+004ε (Mean = 725ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.36ε (Mean = 0.0765ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.89e+03ε (Mean = 108ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.03e+04ε (Mean = 327ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_spherical_harmonic_r"></a><p class="title"><b>Table 17.88. Error rates for spherical_harmonic_r</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for spherical_harmonic_r">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Spherical Harmonics
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.27e+004ε (Mean = 725ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.58ε (Mean = 0.0707ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.89e+03ε (Mean = 108ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.03e+04ε (Mean = 327ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_sqrt1pm1"></a><p class="title"><b>Table 17.89. Error rates for sqrt1pm1</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for sqrt1pm1">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
sqrt1pm1
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.36ε (Mean = 0.44ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.3ε (Mean = 0.404ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.33ε (Mean = 0.409ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.54ε (Mean = 0.568ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_tgamma"></a><p class="title"><b>Table 17.90. Error rates for tgamma</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for tgamma">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
factorials
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.85ε (Mean = 0.491ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 3.17ε (Mean = 0.928ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 3.95ε (Mean = 0.783ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> Max = 314ε (Mean = 93.4ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
Max = 3.19ε (Mean = 0.884ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.96ε (Mean = 0.483ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1.66ε (Mean = 0.584ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.66ε (Mean = 0.584ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 172ε (Mean = 41ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
near 0
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.96ε (Mean = 0.684ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1ε (Mean = 0.405ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 4.51ε (Mean = 1.92ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> Max = 1ε (Mean = 0.335ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
Max = 1ε (Mean = 0.548ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2ε (Mean = 0.73ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1ε (Mean = 0.376ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1ε (Mean = 0.376ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2ε (Mean = 0.647ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.5ε (Mean = 0.0791ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
near 1
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2ε (Mean = 0.865ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1ε (Mean = 0.4ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 4.41ε (Mean = 1.81ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> Max = 1ε (Mean = 0.32ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
Max = 1ε (Mean = 0.518ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2ε (Mean = 0.85ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 0.918ε (Mean = 0.203ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.918ε (Mean = 0.203ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.01ε (Mean = 1.06ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1ε (Mean = 0.175ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
near 2
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2ε (Mean = 0.995ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 7.95ε (Mean = 3.12ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> Max = 1ε (Mean = 0.191ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
Max = 1.09ε (Mean = 0.502ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2ε (Mean = 0.913ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 0.558ε (Mean = 0.298ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.558ε (Mean = 0.298ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.01ε (Mean = 1.89ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
near -10
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.73ε (Mean = 0.729ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0.866ε (Mean = 0.445ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 2.6ε (Mean = 1.05ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> Max = 6.34e+05ε (Mean = 1.2e+05ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
Max = 2.6ε (Mean = 0.956ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.6ε (Mean = 0.985ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 2.26ε (Mean = 1.08ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 2.26ε (Mean = 1.08ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.75ε (Mean = 0.819ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
near -55
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.8ε (Mean = 0.817ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 3.87e+004ε (Mean = 6.71e+003ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 1.8ε (Mean = 0.782ε))<br> (<span class="emphasis"><em>Rmath
|
|
3.0.2:</em></span> Max = 6.36e+06ε (Mean = 1.13e+06ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
Max = 2.7ε (Mean = 0.988ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.8ε (Mean = 0.847ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1.79ε (Mean = 0.75ε))<br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 1.79ε (Mean = 0.75ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 98.5ε (Mean = 53.4ε)</span><br> <br>
|
|
(<span class="emphasis"><em><math.h>:</em></span> Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_tgamma1pm1"></a><p class="title"><b>Table 17.91. Error rates for tgamma1pm1</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for tgamma1pm1">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
tgamma1pm1(dz)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.982ε (Mean = 0.399ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.12ε (Mean = 0.49ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.97ε (Mean = 0.713ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_tgamma_delta_ratio"></a><p class="title"><b>Table 17.92. Error rates for tgamma_delta_ratio</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for tgamma_delta_ratio">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma + small delta ratios
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 10.1ε (Mean = 1.25ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.56ε (Mean = 0.969ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 15.4ε (Mean = 2.09ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma + small delta ratios (negative delta)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 8.04ε (Mean = 1.31ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 8.67ε (Mean = 1.29ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 18.3ε (Mean = 2.03ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma + small integer ratios
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.74ε (Mean = 0.736ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.96ε (Mean = 0.677ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.96ε (Mean = 0.677ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma + small integer ratios (negative delta)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.15ε (Mean = 0.685ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.62ε (Mean = 0.451ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.62ε (Mean = 0.451ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
integer tgamma ratios
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.968ε (Mean = 0.386ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.997ε (Mean = 0.4ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.997ε (Mean = 0.4ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
integer tgamma ratios (negative delta)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.974ε (Mean = 0.184ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.853ε (Mean = 0.176ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.853ε (Mean = 0.176ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_tgamma_incomplete_"></a><p class="title"><b>Table 17.93. Error rates for tgamma (incomplete)</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for tgamma (incomplete)">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma(a, z) medium values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 8.14ε (Mean = 1.71ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 200ε (Mean = 13.3ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.35ε (Mean = 1.69ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 412ε (Mean = 95.5ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma(a, z) small values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.53ε (Mean = 0.66ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.753ε (Mean = 0.0474ε)</span><br>
|
|
<br> (<span class="emphasis"><em>GSL 1.16:</em></span> <span class="red">Max =
|
|
1.38e+10ε (Mean = 1.05e+09ε))</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.13ε (Mean = 0.717ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.13ε (Mean = 0.712ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma(a, z) integer and half integer values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.16ε (Mean = 1.44ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 117ε (Mean = 12.5ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.52ε (Mean = 1.52ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 79.6ε (Mean = 20.9ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_tgamma_lower"></a><p class="title"><b>Table 17.94. Error rates for tgamma_lower</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for tgamma_lower">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma(a, z) medium values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 5.62ε (Mean = 1.43ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.833ε (Mean = 0.0315ε)</span><br>
|
|
<br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 0.833ε (Mean = 0.0315ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.79ε (Mean = 1.38ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 363ε (Mean = 63.8ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma(a, z) small values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.57ε (Mean = 0.527ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.97ε (Mean = 0.552ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.97ε (Mean = 0.567ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
tgamma(a, z) integer and half integer values
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.69ε (Mean = 0.866ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 0ε (Mean = 0ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 4.83ε (Mean = 1.12ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 84.7ε (Mean = 17.5ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_tgamma_ratio"></a><p class="title"><b>Table 17.95. Error rates for tgamma_ratio</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for tgamma_ratio">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
tgamma ratios
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.66ε (Mean = 1.27ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 3.09ε (Mean = 1.15ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 174ε (Mean = 61.2ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_trigamma"></a><p class="title"><b>Table 17.96. Error rates for trigamma</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for trigamma">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
Mathematica Data
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1ε (Mean = 0.382ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.998ε (Mean = 0.105ε)</span><br> <br>
|
|
(<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 1.34e+04ε (Mean = 1.51e+03ε))<br>
|
|
(<span class="emphasis"><em>GSL 1.16:</em></span> Max = 1.34e+04ε (Mean = 1.49e+03ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.28ε (Mean = 0.449ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.28ε (Mean = 0.447ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="table">
|
|
<a name="math_toolkit.logs_and_tables.all_table.table_zeta"></a><p class="title"><b>Table 17.97. Error rates for zeta</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for zeta">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 12.0<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 5.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5130<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Zeta: Random values greater than 1
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.836ε (Mean = 0.093ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 8.69ε (Mean = 1.03ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
<span class="red">Max = 4.49e+33ε (Mean = 6.85e+32ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_zeta_Cephes_Zeta_Random_values_greater_than_1">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.846ε (Mean = 0.0833ε)</span><br>
|
|
<br> (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 5.45ε (Mean
|
|
= 1ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.846ε (Mean = 0.0743ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Zeta: Random values less than 1
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.03ε (Mean = 2.98ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 137ε (Mean = 13.8ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
<span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_zeta_Cephes_Zeta_Random_values_less_than_1">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 7.03ε (Mean = 2.71ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 538ε (Mean = 59.3ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 70.1ε (Mean = 17.1ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Zeta: Values close to and greater than 1
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.994ε (Mean = 0.421ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 7.73ε (Mean = 4.07ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
<span class="red">Max = 6.77e+15ε (Mean = 1.52e+15ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_zeta_Cephes_Zeta_Values_close_to_and_greater_than_1">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.995ε (Mean = 0.5ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1.9e+06ε (Mean = 5.11e+05ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.995ε (Mean = 0.5ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Zeta: Values close to and less than 1
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.991ε (Mean = 0.375ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 0.991ε (Mean = 0.28ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
<span class="red">Max = 8.66e+15ε (Mean = 1.9e+15ε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_zeta_Cephes_Zeta_Values_close_to_and_less_than_1">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.998ε (Mean = 0.508ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 8.53e+06ε (Mean =
|
|
1.87e+06ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0.998ε (Mean = 0.568ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
Zeta: Integer arguments
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 6.5ε (Mean = 2.17ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
|
1.16:</em></span> Max = 3.75ε (Mean = 1.1ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
|
<span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_zeta_Cephes_Zeta_Integer_arguments">And
|
|
other failures.</a>)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 9ε (Mean = 3.06ε)</span><br> <br>
|
|
(<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 70.3ε (Mean = 17.4ε))
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 21ε (Mean = 7.13ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break">
|
|
</div>
|
|
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
|
<td align="left"></td>
|
|
<td align="right"><div class="copyright-footer">Copyright © 2006-2010, 2012-2014 Nikhar Agrawal,
|
|
Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
|
|
Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan Råde, Gautam Sewani,
|
|
Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
|
|
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
|
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
|
|
</p>
|
|
</div></td>
|
|
</tr></table>
|
|
<hr>
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