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<title>Rational Type Performance</title>
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<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_multiprecision.perf.rational_performance"></a><a class="link" href="rational_performance.html" title="Rational Type Performance">Rational
      Type Performance</a>
</h3></div></div></div>
<p>
        Note that these tests are carefully designed to test performance of the underlying
        algorithms and not memory allocation or variable copying. As usual, performance
        results should be taken with a healthy dose of scepticism, and real-world
        performance may vary widely depending upon the specifics of the program.
        In each table relative times are given first, with the best performer given
        a score of 1. Total actual times are given in brackets, measured in seconds
        for 500000 operations.
      </p>
<div class="table">
<a name="boost_multiprecision.perf.rational_performance.operator"></a><p class="title"><b>Table&#160;1.66.&#160;Operator +</b></p>
<div class="table-contents"><table class="table" summary="Operator +">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
                <p>
                  Backend
                </p>
              </th>
<th>
                <p>
                  128 Bits
                </p>
              </th>
<th>
                <p>
                  256 Bits
                </p>
              </th>
<th>
                <p>
                  512 Bits
                </p>
              </th>
<th>
                <p>
                  1024 Bits
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  cpp_rational
                </p>
              </td>
<td>
                <p>
                  5.89417 (18.4116s)
                </p>
              </td>
<td>
                <p>
                  6.87256 (47.4698s)
                </p>
              </td>
<td>
                <p>
                  6.65008 (107.715s)
                </p>
              </td>
<td>
                <p>
                  6.53801 (256.244s)
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  mpq_rational
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (3.1237s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (6.90715s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (16.1975s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (39.1929s)
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="boost_multiprecision.perf.rational_performance.operator_int"></a><p class="title"><b>Table&#160;1.67.&#160;Operator +(int)</b></p>
<div class="table-contents"><table class="table" summary="Operator +(int)">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
                <p>
                  Backend
                </p>
              </th>
<th>
                <p>
                  128 Bits
                </p>
              </th>
<th>
                <p>
                  256 Bits
                </p>
              </th>
<th>
                <p>
                  512 Bits
                </p>
              </th>
<th>
                <p>
                  1024 Bits
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  cpp_rational
                </p>
              </td>
<td>
                <p>
                  3.62367 (2.46488s)
                </p>
              </td>
<td>
                <p>
                  4.18291 (2.94603s)
                </p>
              </td>
<td>
                <p>
                  4.726 (3.74866s)
                </p>
              </td>
<td>
                <p>
                  6.1388 (5.56817s)
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  mpq_rational
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (0.680215s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (0.704303s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (0.7932s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (0.907046s)
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="boost_multiprecision.perf.rational_performance.operator_unsigned_long_long"></a><p class="title"><b>Table&#160;1.68.&#160;Operator +(unsigned long long)</b></p>
<div class="table-contents"><table class="table" summary="Operator +(unsigned long long)">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
                <p>
                  Backend
                </p>
              </th>
<th>
                <p>
                  128 Bits
                </p>
              </th>
<th>
                <p>
                  256 Bits
                </p>
              </th>
<th>
                <p>
                  512 Bits
                </p>
              </th>
<th>
                <p>
                  1024 Bits
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  cpp_rational
                </p>
              </td>
<td>
                <p>
                  1.1527 (2.6378s)
                </p>
              </td>
<td>
                <p>
                  1.31751 (3.09863s)
                </p>
              </td>
<td>
                <p>
                  1.58996 (4.00714s)
                </p>
              </td>
<td>
                <p>
                  2.15642 (5.75702s)
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  mpq_rational
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (2.28837s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (2.35189s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (2.52028s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (2.66971s)
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="boost_multiprecision.perf.rational_performance.operator_unsigned_long_long0"></a><p class="title"><b>Table&#160;1.69.&#160;Operator +=(unsigned long long)</b></p>
<div class="table-contents"><table class="table" summary="Operator +=(unsigned long long)">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
                <p>
                  Backend
                </p>
              </th>
<th>
                <p>
                  128 Bits
                </p>
              </th>
<th>
                <p>
                  256 Bits
                </p>
              </th>
<th>
                <p>
                  512 Bits
                </p>
              </th>
<th>
                <p>
                  1024 Bits
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  cpp_rational
                </p>
              </td>
<td>
                <p>
                  1.18436 (2.7059s)
                </p>
              </td>
<td>
                <p>
                  1.32279 (3.11099s)
                </p>
              </td>
<td>
                <p>
                  1.61398 (4.05389s)
                </p>
              </td>
<td>
                <p>
                  2.20048 (5.84623s)
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  mpq_rational
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (2.2847s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (2.35183s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (2.51174s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (2.6568s)
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="boost_multiprecision.perf.rational_performance.operator0"></a><p class="title"><b>Table&#160;1.70.&#160;Operator -</b></p>
<div class="table-contents"><table class="table" summary="Operator -">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
                <p>
                  Backend
                </p>
              </th>
<th>
                <p>
                  128 Bits
                </p>
              </th>
<th>
                <p>
                  256 Bits
                </p>
              </th>
<th>
                <p>
                  512 Bits
                </p>
              </th>
<th>
                <p>
                  1024 Bits
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  cpp_rational
                </p>
              </td>
<td>
                <p>
                  5.81893 (18.3457s)
                </p>
              </td>
<td>
                <p>
                  6.82209 (47.1928s)
                </p>
              </td>
<td>
                <p>
                  6.64143 (107.498s)
                </p>
              </td>
<td>
                <p>
                  6.51362 (255.137s)
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  mpq_rational
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (3.15277s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (6.91765s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (16.1859s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (39.1698s)
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="boost_multiprecision.perf.rational_performance.operator_int0"></a><p class="title"><b>Table&#160;1.71.&#160;Operator -(int)</b></p>
<div class="table-contents"><table class="table" summary="Operator -(int)">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
                <p>
                  Backend
                </p>
              </th>
<th>
                <p>
                  128 Bits
                </p>
              </th>
<th>
                <p>
                  256 Bits
                </p>
              </th>
<th>
                <p>
                  512 Bits
                </p>
              </th>
<th>
                <p>
                  1024 Bits
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  cpp_rational
                </p>
              </td>
<td>
                <p>
                  3.72441 (2.48756s)
                </p>
              </td>
<td>
                <p>
                  4.27663 (2.98713s)
                </p>
              </td>
<td>
                <p>
                  4.62109 (3.72114s)
                </p>
              </td>
<td>
                <p>
                  6.17605 (5.56503s)
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  mpq_rational
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (0.667908s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (0.698479s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (0.805252s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (0.901066s)
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="boost_multiprecision.perf.rational_performance.operator_unsigned_long_long1"></a><p class="title"><b>Table&#160;1.72.&#160;Operator -(unsigned long long)</b></p>
<div class="table-contents"><table class="table" summary="Operator -(unsigned long long)">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
                <p>
                  Backend
                </p>
              </th>
<th>
                <p>
                  128 Bits
                </p>
              </th>
<th>
                <p>
                  256 Bits
                </p>
              </th>
<th>
                <p>
                  512 Bits
                </p>
              </th>
<th>
                <p>
                  1024 Bits
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  cpp_rational
                </p>
              </td>
<td>
                <p>
                  1.15627 (2.63239s)
                </p>
              </td>
<td>
                <p>
                  1.32096 (3.12092s)
                </p>
              </td>
<td>
                <p>
                  1.61044 (4.00106s)
                </p>
              </td>
<td>
                <p>
                  2.19378 (5.7644s)
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  mpq_rational
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (2.27663s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (2.36262s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (2.48445s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (2.62761s)
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="boost_multiprecision.perf.rational_performance.operator_unsigned_long_long2"></a><p class="title"><b>Table&#160;1.73.&#160;Operator -=(unsigned long long)</b></p>
<div class="table-contents"><table class="table" summary="Operator -=(unsigned long long)">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
                <p>
                  Backend
                </p>
              </th>
<th>
                <p>
                  128 Bits
                </p>
              </th>
<th>
                <p>
                  256 Bits
                </p>
              </th>
<th>
                <p>
                  512 Bits
                </p>
              </th>
<th>
                <p>
                  1024 Bits
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  cpp_rational
                </p>
              </td>
<td>
                <p>
                  1.1984 (2.73444s)
                </p>
              </td>
<td>
                <p>
                  1.34141 (3.15698s)
                </p>
              </td>
<td>
                <p>
                  1.64159 (4.06997s)
                </p>
              </td>
<td>
                <p>
                  2.23017 (5.88108s)
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  mpq_rational
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (2.28174s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (2.35348s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (2.47929s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (2.63706s)
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="boost_multiprecision.perf.rational_performance.operator1"></a><p class="title"><b>Table&#160;1.74.&#160;Operator *</b></p>
<div class="table-contents"><table class="table" summary="Operator *">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
                <p>
                  Backend
                </p>
              </th>
<th>
                <p>
                  128 Bits
                </p>
              </th>
<th>
                <p>
                  256 Bits
                </p>
              </th>
<th>
                <p>
                  512 Bits
                </p>
              </th>
<th>
                <p>
                  1024 Bits
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  cpp_rational
                </p>
              </td>
<td>
                <p>
                  5.4306 (32.5882s)
                </p>
              </td>
<td>
                <p>
                  6.91805 (89.9436s)
                </p>
              </td>
<td>
                <p>
                  6.94556 (207.307s)
                </p>
              </td>
<td>
                <p>
                  6.88704 (492.151s)
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  mpq_rational
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (6.00084s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (13.0013s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (29.8475s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (71.4604s)
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="boost_multiprecision.perf.rational_performance.operator_int1"></a><p class="title"><b>Table&#160;1.75.&#160;Operator *(int)</b></p>
<div class="table-contents"><table class="table" summary="Operator *(int)">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
                <p>
                  Backend
                </p>
              </th>
<th>
                <p>
                  128 Bits
                </p>
              </th>
<th>
                <p>
                  256 Bits
                </p>
              </th>
<th>
                <p>
                  512 Bits
                </p>
              </th>
<th>
                <p>
                  1024 Bits
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  cpp_rational
                </p>
              </td>
<td>
                <p>
                  2.12892 (2.51376s)
                </p>
              </td>
<td>
                <p>
                  2.47245 (3.07841s)
                </p>
              </td>
<td>
                <p>
                  2.86832 (3.93619s)
                </p>
              </td>
<td>
                <p>
                  3.94086 (6.02565s)
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  mpq_rational
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (1.18077s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (1.24508s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (1.3723s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (1.52902s)
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="boost_multiprecision.perf.rational_performance.operator_unsigned_long_long3"></a><p class="title"><b>Table&#160;1.76.&#160;Operator *(unsigned long long)</b></p>
<div class="table-contents"><table class="table" summary="Operator *(unsigned long long)">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
                <p>
                  Backend
                </p>
              </th>
<th>
                <p>
                  128 Bits
                </p>
              </th>
<th>
                <p>
                  256 Bits
                </p>
              </th>
<th>
                <p>
                  512 Bits
                </p>
              </th>
<th>
                <p>
                  1024 Bits
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  cpp_rational
                </p>
              </td>
<td>
                <p>
                  1.32254 (5.43565s)
                </p>
              </td>
<td>
                <p>
                  1.56078 (6.73163s)
                </p>
              </td>
<td>
                <p>
                  1.97701 (9.32522s)
                </p>
              </td>
<td>
                <p>
                  2.85404 (15.1573s)
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  mpq_rational
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (4.11002s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (4.313s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (4.71682s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (5.31082s)
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="boost_multiprecision.perf.rational_performance.operator_unsigned_long_long4"></a><p class="title"><b>Table&#160;1.77.&#160;Operator *=(unsigned long long)</b></p>
<div class="table-contents"><table class="table" summary="Operator *=(unsigned long long)">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
                <p>
                  Backend
                </p>
              </th>
<th>
                <p>
                  128 Bits
                </p>
              </th>
<th>
                <p>
                  256 Bits
                </p>
              </th>
<th>
                <p>
                  512 Bits
                </p>
              </th>
<th>
                <p>
                  1024 Bits
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  cpp_rational
                </p>
              </td>
<td>
                <p>
                  6.29806 (58.1188s)
                </p>
              </td>
<td>
                <p>
                  6.30556 (59.5076s)
                </p>
              </td>
<td>
                <p>
                  6.3385 (62.1007s)
                </p>
              </td>
<td>
                <p>
                  6.55345 (67.6905s)
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  mpq_rational
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (9.22804s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (9.43733s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (9.79739s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (10.329s)
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="boost_multiprecision.perf.rational_performance.operator2"></a><p class="title"><b>Table&#160;1.78.&#160;Operator /</b></p>
<div class="table-contents"><table class="table" summary="Operator /">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
                <p>
                  Backend
                </p>
              </th>
<th>
                <p>
                  128 Bits
                </p>
              </th>
<th>
                <p>
                  256 Bits
                </p>
              </th>
<th>
                <p>
                  512 Bits
                </p>
              </th>
<th>
                <p>
                  1024 Bits
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  cpp_rational
                </p>
              </td>
<td>
                <p>
                  4.4269 (66.8031s)
                </p>
              </td>
<td>
                <p>
                  6.40103 (173.527s)
                </p>
              </td>
<td>
                <p>
                  6.32347 (348.193s)
                </p>
              </td>
<td>
                <p>
                  6.61148 (824.063s)
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  mpq_rational
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (15.0903s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (27.1093s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (55.0637s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (124.641s)
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="boost_multiprecision.perf.rational_performance.operator_int2"></a><p class="title"><b>Table&#160;1.79.&#160;Operator /(int)</b></p>
<div class="table-contents"><table class="table" summary="Operator /(int)">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
                <p>
                  Backend
                </p>
              </th>
<th>
                <p>
                  128 Bits
                </p>
              </th>
<th>
                <p>
                  256 Bits
                </p>
              </th>
<th>
                <p>
                  512 Bits
                </p>
              </th>
<th>
                <p>
                  1024 Bits
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  cpp_rational
                </p>
              </td>
<td>
                <p>
                  1.78772 (2.50984s)
                </p>
              </td>
<td>
                <p>
                  2.10623 (3.10606s)
                </p>
              </td>
<td>
                <p>
                  2.46986 (3.99358s)
                </p>
              </td>
<td>
                <p>
                  3.37428 (5.96678s)
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  mpq_rational
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (1.40393s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (1.4747s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (1.61693s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (1.76831s)
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="boost_multiprecision.perf.rational_performance.operator_unsigned_long_long5"></a><p class="title"><b>Table&#160;1.80.&#160;Operator /(unsigned long long)</b></p>
<div class="table-contents"><table class="table" summary="Operator /(unsigned long long)">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
                <p>
                  Backend
                </p>
              </th>
<th>
                <p>
                  128 Bits
                </p>
              </th>
<th>
                <p>
                  256 Bits
                </p>
              </th>
<th>
                <p>
                  512 Bits
                </p>
              </th>
<th>
                <p>
                  1024 Bits
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  cpp_rational
                </p>
              </td>
<td>
                <p>
                  1.29695 (5.45454s)
                </p>
              </td>
<td>
                <p>
                  1.55248 (6.85353s)
                </p>
              </td>
<td>
                <p>
                  1.93237 (9.28765s)
                </p>
              </td>
<td>
                <p>
                  2.75211 (14.8541s)
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  mpq_rational
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (4.20568s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (4.41458s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (4.80635s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (5.39734s)
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="boost_multiprecision.perf.rational_performance.operator_unsigned_long_long6"></a><p class="title"><b>Table&#160;1.81.&#160;Operator /=(unsigned long long)</b></p>
<div class="table-contents"><table class="table" summary="Operator /=(unsigned long long)">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
                <p>
                  Backend
                </p>
              </th>
<th>
                <p>
                  128 Bits
                </p>
              </th>
<th>
                <p>
                  256 Bits
                </p>
              </th>
<th>
                <p>
                  512 Bits
                </p>
              </th>
<th>
                <p>
                  1024 Bits
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  cpp_rational
                </p>
              </td>
<td>
                <p>
                  6.19401 (58.4278s)
                </p>
              </td>
<td>
                <p>
                  6.20135 (59.643s)
                </p>
              </td>
<td>
                <p>
                  6.21327 (62.0338s)
                </p>
              </td>
<td>
                <p>
                  6.40576 (67.6778s)
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  mpq_rational
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (9.43295s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (9.61774s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (9.98407s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (10.5652s)
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="boost_multiprecision.perf.rational_performance.operator_construct"></a><p class="title"><b>Table&#160;1.82.&#160;Operator construct</b></p>
<div class="table-contents"><table class="table" summary="Operator construct">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
                <p>
                  Backend
                </p>
              </th>
<th>
                <p>
                  128 Bits
                </p>
              </th>
<th>
                <p>
                  256 Bits
                </p>
              </th>
<th>
                <p>
                  512 Bits
                </p>
              </th>
<th>
                <p>
                  1024 Bits
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  cpp_rational
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (0.00978288s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (0.0100574s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (0.0101393s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (0.0101847s)
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  mpq_rational
                </p>
              </td>
<td>
                <p>
                  39.1516 (0.383015s)
                </p>
              </td>
<td>
                <p>
                  38.3523 (0.385725s)
                </p>
              </td>
<td>
                <p>
                  37.5812 (0.381048s)
                </p>
              </td>
<td>
                <p>
                  37.6007 (0.382953s)
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="boost_multiprecision.perf.rational_performance.operator_construct_unsigned"></a><p class="title"><b>Table&#160;1.83.&#160;Operator construct(unsigned)</b></p>
<div class="table-contents"><table class="table" summary="Operator construct(unsigned)">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
                <p>
                  Backend
                </p>
              </th>
<th>
                <p>
                  128 Bits
                </p>
              </th>
<th>
                <p>
                  256 Bits
                </p>
              </th>
<th>
                <p>
                  512 Bits
                </p>
              </th>
<th>
                <p>
                  1024 Bits
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  cpp_rational
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (0.0548151s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (0.0557542s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (0.055825s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (0.0552808s)
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  mpq_rational
                </p>
              </td>
<td>
                <p>
                  7.21073 (0.395257s)
                </p>
              </td>
<td>
                <p>
                  7.1016 (0.395944s)
                </p>
              </td>
<td>
                <p>
                  7.02046 (0.391917s)
                </p>
              </td>
<td>
                <p>
                  7.16881 (0.396297s)
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="boost_multiprecision.perf.rational_performance.operator_construct_unsigned_long"></a><p class="title"><b>Table&#160;1.84.&#160;Operator construct(unsigned long long)</b></p>
<div class="table-contents"><table class="table" summary="Operator construct(unsigned long long)">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
                <p>
                  Backend
                </p>
              </th>
<th>
                <p>
                  128 Bits
                </p>
              </th>
<th>
                <p>
                  256 Bits
                </p>
              </th>
<th>
                <p>
                  512 Bits
                </p>
              </th>
<th>
                <p>
                  1024 Bits
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  cpp_rational
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (0.0605156s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (0.0616657s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (0.0592056s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (0.0603081s)
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  mpq_rational
                </p>
              </td>
<td>
                <p>
                  35.1604 (2.12775s)
                </p>
              </td>
<td>
                <p>
                  34.7575 (2.14335s)
                </p>
              </td>
<td>
                <p>
                  35.7232 (2.11502s)
                </p>
              </td>
<td>
                <p>
                  35.0437 (2.11342s)
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="boost_multiprecision.perf.rational_performance.operator_str"></a><p class="title"><b>Table&#160;1.85.&#160;Operator str</b></p>
<div class="table-contents"><table class="table" summary="Operator str">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
                <p>
                  Backend
                </p>
              </th>
<th>
                <p>
                  128 Bits
                </p>
              </th>
<th>
                <p>
                  256 Bits
                </p>
              </th>
<th>
                <p>
                  512 Bits
                </p>
              </th>
<th>
                <p>
                  1024 Bits
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  cpp_rational
                </p>
              </td>
<td>
                <p>
                  5.48898 (0.0208949s)
                </p>
              </td>
<td>
                <p>
                  8.49668 (0.0546688s)
                </p>
              </td>
<td>
                <p>
                  10.107 (0.121897s)
                </p>
              </td>
<td>
                <p>
                  10.5339 (0.310584s)
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  mpq_rational
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (0.0038067s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (0.00643413s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (0.0120606s)
                </p>
              </td>
<td>
                <p>
                  <span class="bold"><strong>1</strong></span> (0.0294843s)
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><p>
        Test code was compiled with Microsoft Visual Studio 2010 with all optimisations
        turned on (/Ox), and used MPIR-2.3.0 and <a href="http://www.mpfr.org" target="_top">MPFR</a>-3.0.0.
        The tests were run on 32-bit Windows Vista machine.
      </p>
</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 &#169; 2002-2019 John Maddock
      and Christopher Kormanyos<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>
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