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jzmaddock 3287c922ea Fix some corner cases in the beta functions. 
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<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&#160;16.7.&#160;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>
<col>
</colgroup>
<thead><tr>
<th>
<p>
Function
</p>
</th>
<th>
<p>
Microsoft Visual C++ version 14.0<br> boost 1.59
</p>
</th>
<th>
<p>
Intel C++ C++0x mode version 1500<br> boost 1.59
</p>
</th>
<th>
<p>
GNU C++ version 4.9.2<br> boost 1.59
</p>
</th>
<th>
<p>
GNU C++ version 4.9.2<br> boost 1.59<br> promote_double&lt;false&gt;
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
assoc_laguerre
</p>
</td>
<td>
<p>
<span class="green">1.09<br> (190ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (175ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.29<br> (225ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.09<br> (190ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
assoc_legendre
</p>
</td>
<td>
<p>
<span class="blue">1.64<br> (159ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (97ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.84<br> (178ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.15<br> (112ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
beta
</p>
</td>
<td>
<p>
<span class="blue">1.97<br> (217ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (110ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.64<br> (400ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.01<br> (221ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
beta (incomplete)
</p>
</td>
<td>
<p>
<span class="blue">1.41<br> (520ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (368ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.42<br> (1259ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.74<br> (640ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
cbrt
</p>
</td>
<td>
<p>
<span class="red">3.86<br> (54ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (14ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.43<br> (48ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.29<br> (46ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
cyl_bessel_i
</p>
</td>
<td>
<p>
<span class="green">1.12<br> (402ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (360ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.90<br> (1045ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.23<br> (444ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
cyl_bessel_i (integer order)
</p>
</td>
<td>
<p>
<span class="blue">1.30<br> (257ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (198ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.29<br> (652ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.31<br> (259ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
cyl_bessel_j
</p>
</td>
<td>
<p>
<span class="blue">1.38<br> (544ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (395ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.10<br> (828ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.32<br> (520ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
cyl_bessel_j (integer order)
</p>
</td>
<td>
<p>
<span class="blue">1.33<br> (105ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (79ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.23<br> (176ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.19<br> (94ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
cyl_bessel_k
</p>
</td>
<td>
<p>
<span class="green">1.18<br> (754ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (641ns)</span>
</p>
</td>
<td>
<p>
<span class="red">10.67<br> (6841ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.14<br> (730ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
cyl_bessel_k (integer order)
</p>
</td>
<td>
<p>
<span class="blue">1.26<br> (419ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (332ns)</span>
</p>
</td>
<td>
<p>
<span class="red">10.84<br> (3600ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.14<br> (379ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
cyl_neumann
</p>
</td>
<td>
<p>
<span class="red">17.34<br> (11495ns)</span>
</p>
</td>
<td>
<p>
<span class="red">15.24<br> (10105ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.09<br> (1384ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (663ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
cyl_neumann (integer order)
</p>
</td>
<td>
<p>
<span class="blue">1.21<br> (328ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (270ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.03<br> (547ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.29<br> (348ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
digamma
</p>
</td>
<td>
<p>
<span class="blue">1.33<br> (28ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (21ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.76<br> (79ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.19<br> (46ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ellint_1
</p>
</td>
<td>
<p>
<span class="red">2.23<br> (386ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (173ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.25<br> (389ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.45<br> (251ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ellint_1 (complete)
</p>
</td>
<td>
<p>
<span class="blue">1.78<br> (57ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (32ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.47<br> (79ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.53<br> (49ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ellint_2
</p>
</td>
<td>
<p>
<span class="blue">1.91<br> (554ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (290ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.35<br> (681ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.66<br> (480ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ellint_2 (complete)
</p>
</td>
<td>
<p>
<span class="blue">1.94<br> (64ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (33ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.09<br> (69ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (33ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ellint_3
</p>
</td>
<td>
<p>
<span class="red">2.12<br> (1279ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (602ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.04<br> (1828ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.63<br> (982ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ellint_3 (complete)
</p>
</td>
<td>
<p>
<span class="blue">1.97<br> (691ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (350ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.21<br> (1122ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.65<br> (577ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ellint_rc
</p>
</td>
<td>
<p>
<span class="blue">1.47<br> (47ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (32ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.66<br> (85ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.53<br> (49ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ellint_rd
</p>
</td>
<td>
<p>
<span class="blue">1.62<br> (318ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (196ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.85<br> (362ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.34<br> (262ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ellint_rf
</p>
</td>
<td>
<p>
<span class="blue">1.47<br> (66ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (45ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.33<br> (105ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.40<br> (63ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ellint_rj
</p>
</td>
<td>
<p>
<span class="blue">2.00<br> (352ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (176ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.62<br> (461ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.45<br> (255ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
erf
</p>
</td>
<td>
<p>
<span class="blue">1.55<br> (17ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (11ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.36<br> (37ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.36<br> (26ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
erfc
</p>
</td>
<td>
<p>
<span class="blue">1.47<br> (25ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (17ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.24<br> (55ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.06<br> (35ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
expint
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (28ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (28ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.18<br> (89ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.21<br> (62ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
expint (En)
</p>
</td>
<td>
<p>
<span class="green">1.12<br> (118ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (105ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.14<br> (225ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.50<br> (157ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
expm1
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (8ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (8ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.75<br> (30ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.00<br> (24ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
gamma_p
</p>
</td>
<td>
<p>
<span class="blue">1.26<br> (187ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (149ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.78<br> (414ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.70<br> (254ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
gamma_p_inv
</p>
</td>
<td>
<p>
<span class="blue">1.26<br> (659ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (524ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.31<br> (1212ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.89<br> (989ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
gamma_q
</p>
</td>
<td>
<p>
<span class="blue">1.27<br> (181ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (143ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.78<br> (398ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.60<br> (229ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
gamma_q_inv
</p>
</td>
<td>
<p>
<span class="blue">1.36<br> (689ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (507ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.38<br> (1208ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.97<br> (1000ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ibeta
</p>
</td>
<td>
<p>
<span class="blue">1.27<br> (520ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (408ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.13<br> (1276ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.72<br> (701ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ibeta_inv
</p>
</td>
<td>
<p>
<span class="blue">1.32<br> (1866ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (1409ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.92<br> (4120ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.79<br> (2520ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ibetac
</p>
</td>
<td>
<p>
<span class="blue">1.51<br> (599ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (397ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.27<br> (1297ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.76<br> (698ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ibetac_inv
</p>
</td>
<td>
<p>
<span class="blue">1.26<br> (1985ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (1576ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.66<br> (4198ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.69<br> (2666ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
jacobi_cn
</p>
</td>
<td>
<p>
<span class="green">1.20<br> (177ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (148ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.67<br> (543ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.15<br> (318ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
jacobi_dn
</p>
</td>
<td>
<p>
<span class="green">1.17<br> (213ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (182ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.19<br> (581ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.84<br> (335ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
jacobi_sn
</p>
</td>
<td>
<p>
<span class="blue">1.31<br> (202ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (154ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.17<br> (488ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.81<br> (279ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
laguerre
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (121ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (121ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.17<br> (142ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.10<br> (133ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
legendre
</p>
</td>
<td>
<p>
<span class="green">1.05<br> (348ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.15<br> (380ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.24<br> (410ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (330ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
legendre Q
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (415ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.12<br> (464ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.23<br> (512ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.05<br> (437ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
lgamma
</p>
</td>
<td>
<p>
<span class="blue">1.28<br> (88ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (69ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.46<br> (239ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.03<br> (140ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
log1p
</p>
</td>
<td>
<p>
<span class="green">1.10<br> (11ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (10ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.00<br> (30ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.60<br> (16ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
polygamma
</p>
</td>
<td>
<p>
<span class="green">1.15<br> (3952ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (3443ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.12<br> (3848ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.24<br> (7699ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
sph_bessel
</p>
</td>
<td>
<p>
<span class="green">1.18<br> (1002ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (852ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.61<br> (1372ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.13<br> (966ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
sph_neumann
</p>
</td>
<td>
<p>
<span class="blue">1.23<br> (1910ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (1557ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.28<br> (3557ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.12<br> (1746ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
tgamma
</p>
</td>
<td>
<p>
<span class="blue">1.70<br> (109ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (64ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.33<br> (213ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.14<br> (137ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
tgamma (incomplete)
</p>
</td>
<td>
<p>
<span class="green">1.13<br> (247ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (219ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.53<br> (553ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.81<br> (396ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
trigamma
</p>
</td>
<td>
<p>
<span class="red">2.12<br> (36ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (17ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.88<br> (49ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.76<br> (30ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
zeta
</p>
</td>
<td>
<p>
<span class="blue">1.81<br> (161ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (89ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.93<br> (350ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.60<br> (231ns)</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&#160;16.8.&#160;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 5.1.0<br> boost 1.59
</p>
</th>
<th>
<p>
GNU C++ version 5.1.0<br> boost 1.59<br> promote_double&lt;false&gt;
</p>
</th>
<th>
<p>
Intel C++ C++0x mode version 1500<br> boost 1.59
</p>
</th>
<th>
<p>
Intel C++ C++0x mode version 1500<br> boost 1.59<br> promote_double&lt;false&gt;
</p>
</th>
<th>
<p>
Clang version 3.7.0 (trunk 236512)<br> boost 1.59
</p>
</th>
<th>
<p>
Clang version 3.7.0 (trunk 236512)<br> boost 1.59<br> promote_double&lt;false&gt;
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
assoc_laguerre
</p>
</td>
<td>
<p>
<span class="blue">1.23<br> (218ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.05<br> (186ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.21<br> (215ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (177ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.23<br> (217ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.25<br> (222ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
assoc_legendre
</p>
</td>
<td>
<p>
<span class="red">2.84<br> (241ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.14<br> (97ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.92<br> (163ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (85ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.98<br> (253ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.18<br> (100ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
beta
</p>
</td>
<td>
<p>
<span class="red">8.62<br> (698ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.86<br> (151ns)</span>
</p>
</td>
<td>
<p>
<span class="red">5.99<br> (485ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (81ns)</span>
</p>
</td>
<td>
<p>
<span class="red">9.21<br> (746ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.86<br> (151ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
beta (incomplete)
</p>
</td>
<td>
<p>
<span class="red">4.74<br> (1746ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.51<br> (555ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.36<br> (1235ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (368ns)</span>
</p>
</td>
<td>
<p>
<span class="red">4.97<br> (1828ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.51<br> (554ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
cbrt
</p>
</td>
<td>
<p>
<span class="red">2.56<br> (41ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.06<br> (17ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.31<br> (37ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.12<br> (18ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.81<br> (45ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (16ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
cyl_bessel_i
</p>
</td>
<td>
<p>
<span class="red">4.41<br> (1354ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.24<br> (381ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.72<br> (1142ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (307ns)</span>
</p>
</td>
<td>
<p>
<span class="red">4.76<br> (1461ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.28<br> (394ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
cyl_bessel_i (integer order)
</p>
</td>
<td>
<p>
<span class="red">3.62<br> (752ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.11<br> (231ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.38<br> (702ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (208ns)</span>
</p>
</td>
<td>
<p>
<span class="red">4.13<br> (859ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.17<br> (243ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
cyl_bessel_j
</p>
</td>
<td>
<p>
<span class="red">3.26<br> (1029ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.21<br> (382ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.94<br> (930ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (316ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.55<br> (1123ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.33<br> (420ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
cyl_bessel_j (integer order)
</p>
</td>
<td>
<p>
<span class="red">3.49<br> (258ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.31<br> (97ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.92<br> (216ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (74ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.80<br> (281ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.30<br> (96ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
cyl_bessel_k
</p>
</td>
<td>
<p>
<span class="red">7.29<br> (4416ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.06<br> (643ns)</span>
</p>
</td>
<td>
<p>
<span class="red">7.21<br> (4370ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (606ns)</span>
</p>
</td>
<td>
<p>
<span class="red">7.96<br> (4826ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.22<br> (741ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
cyl_bessel_k (integer order)
</p>
</td>
<td>
<p>
<span class="red">10.29<br> (3456ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (336ns)</span>
</p>
</td>
<td>
<p>
<span class="red">11.07<br> (3721ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.01<br> (338ns)</span>
</p>
</td>
<td>
<p>
<span class="red">15.39<br> (5170ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.12<br> (377ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
cyl_neumann
</p>
</td>
<td>
<p>
<span class="red">2.90<br> (1418ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.17<br> (574ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.74<br> (1338ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (489ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.51<br> (1714ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.21<br> (594ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
cyl_neumann (integer order)
</p>
</td>
<td>
<p>
<span class="red">2.19<br> (532ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.06<br> (258ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.29<br> (557ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (243ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.93<br> (713ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.11<br> (269ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
digamma
</p>
</td>
<td>
<p>
<span class="red">2.79<br> (67ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.50<br> (36ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.21<br> (53ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (24ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.92<br> (70ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.46<br> (35ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ellint_1
</p>
</td>
<td>
<p>
<span class="red">2.03<br> (349ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.04<br> (179ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.19<br> (377ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (172ns)</span>
</p>
</td>
<td>
<p>
<span class="red">4.26<br> (732ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.01<br> (173ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ellint_1 (complete)
</p>
</td>
<td>
<p>
<span class="red">2.52<br> (53ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.19<br> (25ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.95<br> (41ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (21ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.29<br> (48ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.29<br> (27ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ellint_2
</p>
</td>
<td>
<p>
<span class="red">2.74<br> (779ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.19<br> (339ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.30<br> (936ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (284ns)</span>
</p>
</td>
<td>
<p>
<span class="red">4.79<br> (1359ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.16<br> (329ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ellint_2 (complete)
</p>
</td>
<td>
<p>
<span class="red">2.07<br> (56ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.19<br> (32ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.22<br> (60ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (27ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">2.00<br> (54ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.19<br> (32ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ellint_3
</p>
</td>
<td>
<p>
<span class="red">3.42<br> (2031ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.26<br> (748ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.40<br> (2016ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (593ns)</span>
</p>
</td>
<td>
<p>
<span class="red">4.84<br> (2873ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.22<br> (726ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ellint_3 (complete)
</p>
</td>
<td>
<p>
<span class="red">3.21<br> (1131ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.29<br> (455ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.07<br> (1080ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (352ns)</span>
</p>
</td>
<td>
<p>
<span class="red">4.12<br> (1452ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.27<br> (447ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ellint_rc
</p>
</td>
<td>
<p>
<span class="red">2.34<br> (75ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.44<br> (46ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.59<br> (51ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (32ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.38<br> (76ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.25<br> (40ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ellint_rd
</p>
</td>
<td>
<p>
<span class="red">2.58<br> (488ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.19<br> (225ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.15<br> (407ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (189ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.72<br> (703ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.17<br> (222ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ellint_rf
</p>
</td>
<td>
<p>
<span class="red">2.24<br> (92ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.51<br> (62ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.63<br> (67ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (41ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.51<br> (103ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.37<br> (56ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ellint_rj
</p>
</td>
<td>
<p>
<span class="red">3.03<br> (460ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.30<br> (198ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.95<br> (448ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (152ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.89<br> (591ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.21<br> (184ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
erf
</p>
</td>
<td>
<p>
<span class="red">2.77<br> (36ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (13ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.38<br> (31ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (13ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.77<br> (36ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (13ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
erfc
</p>
</td>
<td>
<p>
<span class="red">2.79<br> (53ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (19ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.37<br> (45ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (19ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.79<br> (53ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (19ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
expint
</p>
</td>
<td>
<p>
<span class="red">2.87<br> (89ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.10<br> (34ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.26<br> (70ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (31ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.71<br> (84ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.10<br> (34ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
expint (En)
</p>
</td>
<td>
<p>
<span class="red">2.20<br> (244ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.20<br> (133ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.95<br> (217ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (111ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.39<br> (265ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.39<br> (154ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
expm1
</p>
</td>
<td>
<p>
<span class="blue">1.50<br> (12ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.25<br> (10ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.50<br> (12ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (8ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.12<br> (9ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.25<br> (10ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
gamma_p
</p>
</td>
<td>
<p>
<span class="red">3.13<br> (454ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.30<br> (189ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.54<br> (369ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (145ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.26<br> (473ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.30<br> (188ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
gamma_p_inv
</p>
</td>
<td>
<p>
<span class="red">3.11<br> (1497ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.42<br> (684ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.29<br> (1100ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (481ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.13<br> (1506ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.41<br> (678ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
gamma_q
</p>
</td>
<td>
<p>
<span class="red">3.43<br> (466ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.38<br> (188ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.66<br> (362ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (136ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.44<br> (468ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.36<br> (185ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
gamma_q_inv
</p>
</td>
<td>
<p>
<span class="red">4.93<br> (1756ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.92<br> (683ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.85<br> (1016ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (356ns)</span>
</p>
</td>
<td>
<p>
<span class="red">4.87<br> (1734ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.94<br> (691ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ibeta
</p>
</td>
<td>
<p>
<span class="red">4.52<br> (1641ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.61<br> (584ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.33<br> (1208ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (363ns)</span>
</p>
</td>
<td>
<p>
<span class="red">4.75<br> (1725ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.56<br> (566ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ibeta_inv
</p>
</td>
<td>
<p>
<span class="red">3.57<br> (5230ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.43<br> (2093ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.92<br> (4275ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (1465ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.82<br> (5597ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.43<br> (2098ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ibetac
</p>
</td>
<td>
<p>
<span class="red">4.62<br> (1650ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.64<br> (586ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.30<br> (1177ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (357ns)</span>
</p>
</td>
<td>
<p>
<span class="red">4.83<br> (1724ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.59<br> (566ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
ibetac_inv
</p>
</td>
<td>
<p>
<span class="red">3.58<br> (5308ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.45<br> (2141ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.92<br> (4329ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (1481ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.85<br> (5703ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.42<br> (2106ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
jacobi_cn
</p>
</td>
<td>
<p>
<span class="red">3.73<br> (466ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.33<br> (166ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.76<br> (345ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (125ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.85<br> (481ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.36<br> (170ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
jacobi_dn
</p>
</td>
<td>
<p>
<span class="red">3.46<br> (457ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.25<br> (165ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.74<br> (362ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (132ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.58<br> (472ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.27<br> (167ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
jacobi_sn
</p>
</td>
<td>
<p>
<span class="red">3.75<br> (465ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.34<br> (166ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.55<br> (316ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (124ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.84<br> (476ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.38<br> (171ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
laguerre
</p>
</td>
<td>
<p>
<span class="blue">1.21<br> (142ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.03<br> (121ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.20<br> (140ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (117ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.18<br> (138ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.28<br> (150ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
legendre
</p>
</td>
<td>
<p>
<span class="green">1.16<br> (385ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (332ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.36<br> (450ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.14<br> (377ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.15<br> (381ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.08<br> (358ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
legendre Q
</p>
</td>
<td>
<p>
<span class="blue">1.21<br> (466ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (384ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.39<br> (534ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.19<br> (457ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.21<br> (464ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.03<br> (396ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
lgamma
</p>
</td>
<td>
<p>
<span class="red">3.70<br> (244ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.68<br> (111ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.76<br> (182ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (66ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.95<br> (261ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.67<br> (110ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
log1p
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (11ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (11ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.18<br> (13ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.09<br> (12ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (11ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (11ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
polygamma
</p>
</td>
<td>
<p>
<span class="red">10.22<br> (2791ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.64<br> (722ns)</span>
</p>
</td>
<td>
<p>
<span class="red">5.34<br> (1459ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (273ns)</span>
</p>
</td>
<td>
<p>
<span class="red">10.25<br> (2798ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.65<br> (723ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
sph_bessel
</p>
</td>
<td>
<p>
<span class="blue">1.81<br> (1520ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.05<br> (883ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.69<br> (1413ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (838ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.92<br> (1605ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.05<br> (880ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
sph_neumann
</p>
</td>
<td>
<p>
<span class="red">2.16<br> (3368ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.01<br> (1575ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.25<br> (3514ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (1559ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.42<br> (3772ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.04<br> (1620ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
tgamma
</p>
</td>
<td>
<p>
<span class="red">6.28<br> (333ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.75<br> (93ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.83<br> (203ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (53ns)</span>
</p>
</td>
<td>
<p>
<span class="red">6.68<br> (354ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.77<br> (94ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
tgamma (incomplete)
</p>
</td>
<td>
<p>
<span class="red">3.34<br> (691ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.42<br> (293ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.39<br> (495ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (207ns)</span>
</p>
</td>
<td>
<p>
<span class="red">3.51<br> (726ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.40<br> (289ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
trigamma
</p>
</td>
<td>
<p>
<span class="blue">1.58<br> (30ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (19ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.74<br> (33ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.05<br> (20ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.89<br> (36ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.11<br> (21ns)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
zeta
</p>
</td>
<td>
<p>
<span class="red">4.35<br> (492ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.61<br> (182ns)</span>
</p>
</td>
<td>
<p>
<span class="red">2.98<br> (337ns)</span>
</p>
</td>
<td>
<p>
<span class="green">1.00<br> (113ns)</span>
</p>
</td>
<td>
<p>
<span class="red">4.11<br> (464ns)</span>
</p>
</td>
<td>
<p>
<span class="blue">1.54<br> (174ns)</span>
</p>
</td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break">
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014 Nikhar Agrawal,
Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
Holin, Bruno Lalande, John Maddock, Johan R&#229;de, 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>)
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