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<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="math_toolkit.comp_compilers"></a><a class="link" href="comp_compilers.html" title="Comparing Different Compilers">Comparing Different Compilers</a>
</h2></div></div></div>
<p>
By running our performance test suite multiple times, we can compare the effect
of different compilers: as might be expected, the differences are generally
small compared to say disabling internal use of <code class="computeroutput"><span class="keyword">long</span>
<span class="keyword">double</span></code>. However, there are still gains
to be main, particularly from some of the commercial offerings:
</p>
<div class="table">
<a name="math_toolkit.comp_compilers.table_Compiler_Comparison_on_Windows_x64"></a><p class="title"><b>Table 22.12. Compiler Comparison on Windows x64</b></p>
<div class="table-contents"><table class="table" summary="Compiler Comparison on Windows x64">
<colgroup>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
<p>
Function
</p>
</th>
<th>
<p>
Microsoft Visual C++ version 14.2<br> boost 1.73
</p>
</th>
<th>
<p>
GNU C++ version 9.2.0<br> boost 1.73
</p>
</th>
<th>
<p>
GNU C++ version 9.2.0<br> boost 1.73<br> promote_double&lt;false&gt;
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
assoc_laguerre
</p>
</td>
<td>
<p>
<span class="blue">1.41<br> (179ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.08<br> (137ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (127ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
assoc_legendre
</p>
</td>
<td>
<p>
<span class="blue">1.76<br> (248ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.36<br> (192ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (141ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
beta
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (123ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.62<br> (322ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.93<br> (237ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
beta (incomplete)
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (470ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.95<br> (1385ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.58<br> (741ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
cbrt
</p>
</td>
<td>
<p>
<span class="red">3.40<br> (51ns)</span>
</p>
</td>
<td>
<p>
<span class="red">4.67<br> (70ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (15ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
cyl_bessel_i
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (281ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.38<br> (949ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.38<br> (387ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
cyl_bessel_i (integer order)
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (195ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.06<br> (597ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (195ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
cyl_bessel_j
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (371ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.39<br> (886ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.35<br> (499ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
cyl_bessel_j (integer order)
</p>
</td>
<td>
<p>
<span class="blue">1.28<br> (123ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.92<br> (184ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (96ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
cyl_bessel_k
</p>
</td>
<td>
<p>
<span class="green">1.11<br> (385ns)</span>
</p>
</td>
<td>
<p>
<span class="red">19.68<br> (6847ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (348ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
cyl_bessel_k (integer order)
</p>
</td>
<td>
<p>
<span class="green">1.06<br> (217ns)</span>
</p>
</td>
<td>
<p>
<span class="red">18.17<br> (3724ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (205ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
cyl_neumann
</p>
</td>
<td>
<p>
<span class="green">1.17<br> (6696ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.76<br> (10032ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (5715ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
cyl_neumann (integer order)
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (158ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.20<br> (348ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.59<br> (252ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
digamma
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (20ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.45<br> (69ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.30<br> (46ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ellint_1
</p>
</td>
<td>
<p>
<span class="blue">1.57<br> (390ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.41<br> (349ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (248ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ellint_1 (complete)
</p>
</td>
<td>
<p>
<span class="blue">1.64<br> (77ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.64<br> (77ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (47ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ellint_2
</p>
</td>
<td>
<p>
<span class="blue">1.81<br> (702ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.50<br> (583ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (388ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ellint_2 (complete)
</p>
</td>
<td>
<p>
<span class="red">3.11<br> (84ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.11<br> (57ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (27ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ellint_3
</p>
</td>
<td>
<p>
<span class="red">3.47<br> (1381ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.68<br> (670ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (398ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ellint_3 (complete)
</p>
</td>
<td>
<p>
<span class="red">inf<br> (802ns)</span>
</p>
</td>
<td>
<p>
<span class="green">-nan(ind)<br> (0ns)</span>
</p>
</td>
<td>
<p>
<span class="green">-nan(ind)<br> (0ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ellint_rc
</p>
</td>
<td>
<p>
<span class="blue">1.55<br> (59ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.21<br> (84ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (38ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ellint_rd
</p>
</td>
<td>
<p>
<span class="blue">1.32<br> (271ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.26<br> (260ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (206ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ellint_rf
</p>
</td>
<td>
<p>
<span class="blue">1.27<br> (62ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.94<br> (95ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (49ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ellint_rj
</p>
</td>
<td>
<p>
<span class="blue">1.46<br> (264ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.29<br> (414ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (181ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
erf
</p>
</td>
<td>
<p>
<span class="blue">1.30<br> (43ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.85<br> (61ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (33ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
erfc
</p>
</td>
<td>
<p>
<span class="green">1.06<br> (54ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.76<br> (90ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (51ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
expint
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (27ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.41<br> (92ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.22<br> (60ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
expint (En)
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (106ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.94<br> (206ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.29<br> (137ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
expm1
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (11ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.00<br> (33ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.36<br> (26ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
gamma_p
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (303ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">2.00<br> (605ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.17<br> (355ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
gamma_p_inv
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (1266ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.85<br> (2341ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.15<br> (1460ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
gamma_q
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (294ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.10<br> (618ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.21<br> (356ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
gamma_q_inv
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (1194ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.66<br> (1987ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.14<br> (1357ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ibeta
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (512ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.63<br> (1344ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.31<br> (673ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ibeta_inv
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (1910ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.49<br> (4751ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.48<br> (2822ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ibetac
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (525ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.60<br> (1365ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.27<br> (668ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ibetac_inv
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (1676ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.85<br> (4778ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.74<br> (2910ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
jacobi_cn
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (181ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.10<br> (561ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">2.00<br> (362ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
jacobi_dn
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (203ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.03<br> (616ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.93<br> (392ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
jacobi_sn
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (202ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.81<br> (568ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.73<br> (350ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
laguerre
</p>
</td>
<td>
<p>
<span class="green">1.02<br> (107ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.07<br> (112ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (105ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
legendre
</p>
</td>
<td>
<p>
<span class="green">1.11<br> (283ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.25<br> (320ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (255ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
legendre Q
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (309ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.51<br> (466ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.15<br> (354ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
lgamma
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (80ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.67<br> (214ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">2.00<br> (160ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
log1p
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (14ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.07<br> (29ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.21<br> (17ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
polygamma
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (4193ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.85<br> (7743ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.91<br> (8018ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
sph_bessel
</p>
</td>
<td>
<p>
<span class="green">1.01<br> (668ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.48<br> (975ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (661ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
sph_neumann
</p>
</td>
<td>
<p>
<span class="green">1.07<br> (1138ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.96<br> (3153ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (1064ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
tgamma
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (74ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.50<br> (259ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.14<br> (158ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
tgamma (incomplete)
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (208ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.30<br> (478ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.64<br> (342ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
trigamma
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (12ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.83<br> (34ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.17<br> (14ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
zeta
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (117ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.65<br> (310ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.89<br> (221ns)</span>
</p>
</td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.comp_compilers.table_Compiler_Comparison_on_linux"></a><p class="title"><b>Table 22.13. Compiler Comparison on linux</b></p>
<div class="table-contents"><table class="table" summary="Compiler Comparison on linux">
<colgroup>
<col>
<col>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
<p>
Function
</p>
</th>
<th>
<p>
GNU C++ version 9.2.1 20191008<br> boost 1.73
</p>
</th>
<th>
<p>
GNU C++ version 9.2.1 20191008<br> boost 1.73<br> promote_double&lt;false&gt;
</p>
</th>
<th>
<p>
Clang version 9.0.0 (tags/RELEASE_900/final)<br> boost 1.73
</p>
</th>
<th>
<p>
Clang version 9.0.0 (tags/RELEASE_900/final)<br> boost 1.73<br>
promote_double&lt;false&gt;
</p>
</th>
<th>
<p>
Intel C++ C++0x mode version 1910<br> boost 1.73
</p>
</th>
<th>
<p>
Intel C++ C++0x mode version 1910<br> boost 1.73<br> promote_double&lt;false&gt;
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
assoc_laguerre
</p>
</td>
<td>
<p>
<span class="green">1.17<br> (156ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.08<br> (143ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.72<br> (229ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.31<br> (174ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.15<br> (153ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (133ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
assoc_legendre
</p>
</td>
<td>
<p>
<span class="red">2.91<br> (279ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.78<br> (171ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.86<br> (275ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (96ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.79<br> (268ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.16<br> (207ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
beta
</p>
</td>
<td>
<p>
<span class="red">10.52<br> (789ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.40<br> (105ns)</span>
</p>
</td>
<td>
<p>
<span class="red">10.56<br> (792ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.73<br> (130ns)</span>
</p>
</td>
<td>
<p>
<span class="red">6.07<br> (455ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (75ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
beta (incomplete)
</p>
</td>
<td>
<p>
<span class="red">4.98<br> (2076ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.26<br> (524ns)</span>
</p>
</td>
<td>
<p>
<span class="red">5.44<br> (2267ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (417ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.15<br> (1315ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.16<br> (484ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
cbrt
</p>
</td>
<td>
<p>
<span class="red">2.52<br> (58ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.09<br> (25ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.35<br> (54ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.22<br> (28ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.91<br> (44ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (23ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
cyl_bessel_i
</p>
</td>
<td>
<p>
<span class="red">5.05<br> (1182ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.02<br> (239ns)</span>
</p>
</td>
<td>
<p>
<span class="red">10.73<br> (2511ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.74<br> (406ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.99<br> (933ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (234ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
cyl_bessel_i (integer order)
</p>
</td>
<td>
<p>
<span class="red">4.41<br> (767ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (174ns)</span>
</p>
</td>
<td>
<p>
<span class="red">5.09<br> (886ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.03<br> (179ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.63<br> (631ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.12<br> (195ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
cyl_bessel_j
</p>
</td>
<td>
<p>
<span class="red">3.80<br> (1067ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.28<br> (359ns)</span>
</p>
</td>
<td>
<p>
<span class="red">4.72<br> (1327ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.55<br> (436ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.05<br> (857ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (281ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
cyl_bessel_j (integer order)
</p>
</td>
<td>
<p>
<span class="red">3.10<br> (319ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.05<br> (108ns)</span>
</p>
</td>
<td>
<p>
<span class="red">4.73<br> (487ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (103ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.30<br> (237ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.12<br> (115ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
cyl_bessel_k
</p>
</td>
<td>
<p>
<span class="red">10.37<br> (3962ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (382ns)</span>
</p>
</td>
<td>
<p>
<span class="red">11.55<br> (4414ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.52<br> (582ns)</span>
</p>
</td>
<td>
<p>
<span class="red">12.41<br> (4739ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.09<br> (416ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
cyl_bessel_k (integer order)
</p>
</td>
<td>
<p>
<span class="red">19.23<br> (3289ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.06<br> (181ns)</span>
</p>
</td>
<td>
<p>
<span class="red">19.78<br> (3382ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.27<br> (217ns)</span>
</p>
</td>
<td>
<p>
<span class="red">20.02<br> (3423ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (171ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
cyl_neumann
</p>
</td>
<td>
<p>
<span class="red">2.18<br> (8826ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.19<br> (4814ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.23<br> (13059ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.31<br> (5275ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.35<br> (9503ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (4041ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
cyl_neumann (integer order)
</p>
</td>
<td>
<p>
<span class="red">3.67<br> (466ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.35<br> (172ns)</span>
</p>
</td>
<td>
<p>
<span class="red">4.49<br> (570ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.15<br> (146ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.87<br> (364ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (127ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
digamma
</p>
</td>
<td>
<p>
<span class="red">2.30<br> (62ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.30<br> (35ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.11<br> (84ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.33<br> (36ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.85<br> (50ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (27ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ellint_1
</p>
</td>
<td>
<p>
<span class="red">2.26<br> (310ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.12<br> (154ns)</span>
</p>
</td>
<td>
<p>
<span class="red">6.96<br> (954ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.25<br> (171ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.22<br> (441ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (137ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ellint_1 (complete)
</p>
</td>
<td>
<p>
<span class="red">4.65<br> (93ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.15<br> (63ns)</span>
</p>
</td>
<td>
<p>
<span class="red">6.00<br> (120ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.15<br> (23ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.90<br> (38ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (20ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ellint_2
</p>
</td>
<td>
<p>
<span class="red">3.81<br> (704ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.28<br> (236ns)</span>
</p>
</td>
<td>
<p>
<span class="red">8.95<br> (1655ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.36<br> (251ns)</span>
</p>
</td>
<td>
<p>
<span class="red">4.36<br> (807ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (185ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ellint_2 (complete)
</p>
</td>
<td>
<p>
<span class="blue">1.83<br> (44ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.04<br> (25ns)</span>
</p>
</td>
<td>
<p>
<span class="red">6.25<br> (150ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.25<br> (30ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">2.00<br> (48ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (24ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ellint_3
</p>
</td>
<td>
<p>
<span class="red">3.27<br> (609ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.17<br> (217ns)</span>
</p>
</td>
<td>
<p>
<span class="red">5.37<br> (998ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.32<br> (245ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.84<br> (528ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (186ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ellint_3 (complete)
</p>
</td>
<td>
<p>
<span class="green">-nan<br> (0ns)</span>
</p>
</td>
<td>
<p>
<span class="green">-nan<br> (0ns)</span>
</p>
</td>
<td>
<p>
<span class="green">-nan<br> (0ns)</span>
</p>
</td>
<td>
<p>
<span class="green">-nan<br> (0ns)</span>
</p>
</td>
<td>
<p>
<span class="green">-nan<br> (0ns)</span>
</p>
</td>
<td>
<p>
<span class="green">-nan<br> (0ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ellint_rc
</p>
</td>
<td>
<p>
<span class="red">2.75<br> (66ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.29<br> (31ns)</span>
</p>
</td>
<td>
<p>
<span class="red">4.71<br> (113ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.42<br> (34ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.83<br> (44ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (24ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ellint_rd
</p>
</td>
<td>
<p>
<span class="red">4.37<br> (428ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.31<br> (128ns)</span>
</p>
</td>
<td>
<p>
<span class="red">9.24<br> (906ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.31<br> (128ns)</span>
</p>
</td>
<td>
<p>
<span class="red">4.17<br> (409ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (98ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ellint_rf
</p>
</td>
<td>
<p>
<span class="red">2.47<br> (84ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.44<br> (49ns)</span>
</p>
</td>
<td>
<p>
<span class="red">4.62<br> (157ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.32<br> (45ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.85<br> (63ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (34ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ellint_rj
</p>
</td>
<td>
<p>
<span class="red">4.14<br> (426ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.36<br> (140ns)</span>
</p>
</td>
<td>
<p>
<span class="red">7.18<br> (740ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.31<br> (135ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.33<br> (343ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (103ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
erf
</p>
</td>
<td>
<p>
<span class="blue">1.69<br> (54ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.28<br> (41ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.56<br> (82ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.38<br> (44ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.34<br> (43ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (32ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
erfc
</p>
</td>
<td>
<p>
<span class="blue">1.65<br> (89ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.20<br> (65ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.46<br> (133ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.26<br> (68ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.22<br> (66ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (54ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
expint
</p>
</td>
<td>
<p>
<span class="red">2.93<br> (85ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.45<br> (42ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.90<br> (84ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.31<br> (38ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.21<br> (64ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (29ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
expint (En)
</p>
</td>
<td>
<p>
<span class="red">2.42<br> (242ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.14<br> (114ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.76<br> (276ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.19<br> (119ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.84<br> (184ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (100ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
expm1
</p>
</td>
<td>
<p>
<span class="blue">1.90<br> (19ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.60<br> (16ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.50<br> (15ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.40<br> (14ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.80<br> (18ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (10ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
gamma_p
</p>
</td>
<td>
<p>
<span class="red">2.43<br> (618ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.02<br> (260ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.95<br> (749ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (254ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.15<br> (545ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.03<br> (262ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
gamma_p_inv
</p>
</td>
<td>
<p>
<span class="red">2.37<br> (2328ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.06<br> (1038ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.73<br> (2676ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.06<br> (1045ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.92<br> (1883ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (982ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
gamma_q
</p>
</td>
<td>
<p>
<span class="red">2.49<br> (629ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (253ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.28<br> (831ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.11<br> (280ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.18<br> (551ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.04<br> (263ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
gamma_q_inv
</p>
</td>
<td>
<p>
<span class="red">2.73<br> (2016ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.30<br> (958ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.22<br> (2381ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.30<br> (962ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.73<br> (1275ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (739ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ibeta
</p>
</td>
<td>
<p>
<span class="red">4.56<br> (1979ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.21<br> (524ns)</span>
</p>
</td>
<td>
<p>
<span class="red">4.60<br> (1996ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (434ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.35<br> (1453ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.13<br> (491ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ibeta_inv
</p>
</td>
<td>
<p>
<span class="red">3.22<br> (5552ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.10<br> (1902ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.49<br> (6013ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.03<br> (1781ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.58<br> (4437ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (1722ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ibetac
</p>
</td>
<td>
<p>
<span class="red">4.34<br> (2008ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.27<br> (590ns)</span>
</p>
</td>
<td>
<p>
<span class="red">4.34<br> (2008ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (463ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.11<br> (1438ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.17<br> (543ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ibetac_inv
</p>
</td>
<td>
<p>
<span class="red">3.32<br> (5533ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.11<br> (1853ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.55<br> (5915ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.03<br> (1722ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.48<br> (4131ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (1666ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
jacobi_cn
</p>
</td>
<td>
<p>
<span class="red">3.74<br> (483ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.26<br> (163ns)</span>
</p>
</td>
<td>
<p>
<span class="red">4.98<br> (643ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.61<br> (208ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.67<br> (345ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (129ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
jacobi_dn
</p>
</td>
<td>
<p>
<span class="red">3.64<br> (503ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.25<br> (173ns)</span>
</p>
</td>
<td>
<p>
<span class="red">4.70<br> (648ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.49<br> (206ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.72<br> (375ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (138ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
jacobi_sn
</p>
</td>
<td>
<p>
<span class="red">4.99<br> (614ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.46<br> (180ns)</span>
</p>
</td>
<td>
<p>
<span class="red">5.20<br> (640ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.72<br> (212ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.57<br> (316ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (123ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
laguerre
</p>
</td>
<td>
<p>
<span class="green">1.11<br> (92ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.08<br> (90ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.41<br> (117ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.11<br> (92ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.17<br> (97ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (83ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
legendre
</p>
</td>
<td>
<p>
<span class="green">1.12<br> (282ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (251ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.21<br> (304ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.30<br> (326ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.39<br> (349ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.08<br> (270ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
legendre Q
</p>
</td>
<td>
<p>
<span class="blue">1.24<br> (390ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (314ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.29<br> (404ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.14<br> (358ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.42<br> (445ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.11<br> (347ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
lgamma
</p>
</td>
<td>
<p>
<span class="red">2.65<br> (265ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.17<br> (117ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.86<br> (386ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.24<br> (124ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.90<br> (190ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (100ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
log1p
</p>
</td>
<td>
<p>
<span class="green">1.11<br> (20ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.22<br> (22ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.06<br> (19ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (18ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.06<br> (19ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (18ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
polygamma
</p>
</td>
<td>
<p>
<span class="red">16.70<br> (8883ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.42<br> (756ns)</span>
</p>
</td>
<td>
<p>
<span class="red">6.56<br> (3491ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (532ns)</span>
</p>
</td>
<td>
<p>
<span class="red">7.49<br> (3985ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.05<br> (559ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
sph_bessel
</p>
</td>
<td>
<p>
<span class="red">2.36<br> (1122ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.24<br> (588ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.31<br> (1574ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.41<br> (673ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.12<br> (1010ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (476ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
sph_neumann
</p>
</td>
<td>
<p>
<span class="red">3.40<br> (2842ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.21<br> (1015ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.59<br> (3009ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.21<br> (1012ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.14<br> (2627ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (837ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
tgamma
</p>
</td>
<td>
<p>
<span class="red">4.72<br> (472ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.44<br> (144ns)</span>
</p>
</td>
<td>
<p>
<span class="red">5.70<br> (570ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.05<br> (105ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.29<br> (229ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (100ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
tgamma (incomplete)
</p>
</td>
<td>
<p>
<span class="red">3.28<br> (669ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.13<br> (231ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.88<br> (792ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.14<br> (232ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.21<br> (451ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (204ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
trigamma
</p>
</td>
<td>
<p>
<span class="red">2.08<br> (25ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (12ns)</span>
</p>
</td>
<td>
<p>
<span class="red">4.00<br> (48ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.50<br> (18ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">2.00<br> (24ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.08<br> (13ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
zeta
</p>
</td>
<td>
<p>
<span class="red">4.21<br> (455ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (108ns)</span>
</p>
</td>
<td>
<p>
<span class="red">5.77<br> (623ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.20<br> (130ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.98<br> (322ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.08<br> (117ns)</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 © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, 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>
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