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math_special_kokkos.cpp
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rLAMMPS lammps
math_special_kokkos.cpp
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#include <math.h>
#include <stdint.h>
#include "math_special_kokkos.h"
using
namespace
LAMMPS_NS
;
/* Library libcerf:
* Compute complex error functions, based on a new implementation of
* Faddeeva's w_of_z. Also provide Dawson and Voigt functions.
*
* File erfcx.c:
* Compute erfcx(x) = exp(x^2) erfc(x) function, for real x,
* using a novel algorithm that is much faster than DERFC of SLATEC.
* This function is used in the computation of Faddeeva, Dawson, and
* other complex error functions.
*
* Copyright:
* (C) 2012 Massachusetts Institute of Technology
* (C) 2013 Forschungszentrum Jülich GmbH
*
* Licence:
* Permission is hereby granted, free of charge, to any person obtaining
* a copy of this software and associated documentation files (the
* "Software"), to deal in the Software without restriction, including
* without limitation the rights to use, copy, modify, merge, publish,
* distribute, sublicense, and/or sell copies of the Software, and to
* permit persons to whom the Software is furnished to do so, subject to
* the following conditions:
*
* The above copyright notice and this permission notice shall be
* included in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
* LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
* OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
* WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*
* Authors:
* Steven G. Johnson, Massachusetts Institute of Technology, 2012, core author
* Joachim Wuttke, Forschungszentrum Jülich, 2013, package maintainer
*
* Website:
* http://apps.jcns.fz-juelich.de/libcerf
*
* Revision history:
* ../CHANGELOG
*
* Manual page:
* man 3 erfcx
*/
/******************************************************************************/
/* Lookup-table for Chebyshev polynomials for smaller |x| */
/******************************************************************************/
double
MathSpecialKokkos
::
erfcx_y100
(
const
double
y100
)
{
// Steven G. Johnson, October 2012.
// Given y100=100*y, where y = 4/(4+x) for x >= 0, compute erfc(x).
// Uses a look-up table of 100 different Chebyshev polynomials
// for y intervals [0,0.01], [0.01,0.02], ...., [0.99,1], generated
// with the help of Maple and a little shell script. This allows
// the Chebyshev polynomials to be of significantly lower degree (about 1/4)
// compared to fitting the whole [0,1] interval with a single polynomial.
switch
((
int
)
y100
)
{
case
0
:
{
double
t
=
2
*
y100
-
1
;
return
0.70878032454106438663e-3
+
(
0.71234091047026302958e-3
+
(
0.35779077297597742384e-5
+
(
0.17403143962587937815e-7
+
(
0.81710660047307788845e-10
+
(
0.36885022360434957634e-12
+
0.15917038551111111111e-14
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
1
:
{
double
t
=
2
*
y100
-
3
;
return
0.21479143208285144230e-2
+
(
0.72686402367379996033e-3
+
(
0.36843175430938995552e-5
+
(
0.18071841272149201685e-7
+
(
0.85496449296040325555e-10
+
(
0.38852037518534291510e-12
+
0.16868473576888888889e-14
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
2
:
{
double
t
=
2
*
y100
-
5
;
return
0.36165255935630175090e-2
+
(
0.74182092323555510862e-3
+
(
0.37948319957528242260e-5
+
(
0.18771627021793087350e-7
+
(
0.89484715122415089123e-10
+
(
0.40935858517772440862e-12
+
0.17872061464888888889e-14
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
3
:
{
double
t
=
2
*
y100
-
7
;
return
0.51154983860031979264e-2
+
(
0.75722840734791660540e-3
+
(
0.39096425726735703941e-5
+
(
0.19504168704300468210e-7
+
(
0.93687503063178993915e-10
+
(
0.43143925959079664747e-12
+
0.18939926435555555556e-14
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
4
:
{
double
t
=
2
*
y100
-
9
;
return
0.66457513172673049824e-2
+
(
0.77310406054447454920e-3
+
(
0.40289510589399439385e-5
+
(
0.20271233238288381092e-7
+
(
0.98117631321709100264e-10
+
(
0.45484207406017752971e-12
+
0.20076352213333333333e-14
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
5
:
{
double
t
=
2
*
y100
-
11
;
return
0.82082389970241207883e-2
+
(
0.78946629611881710721e-3
+
(
0.41529701552622656574e-5
+
(
0.21074693344544655714e-7
+
(
0.10278874108587317989e-9
+
(
0.47965201390613339638e-12
+
0.21285907413333333333e-14
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
6
:
{
double
t
=
2
*
y100
-
13
;
return
0.98039537275352193165e-2
+
(
0.80633440108342840956e-3
+
(
0.42819241329736982942e-5
+
(
0.21916534346907168612e-7
+
(
0.10771535136565470914e-9
+
(
0.50595972623692822410e-12
+
0.22573462684444444444e-14
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
7
:
{
double
t
=
2
*
y100
-
15
;
return
0.11433927298290302370e-1
+
(
0.82372858383196561209e-3
+
(
0.44160495311765438816e-5
+
(
0.22798861426211986056e-7
+
(
0.11291291745879239736e-9
+
(
0.53386189365816880454e-12
+
0.23944209546666666667e-14
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
8
:
{
double
t
=
2
*
y100
-
17
;
return
0.13099232878814653979e-1
+
(
0.84167002467906968214e-3
+
(
0.45555958988457506002e-5
+
(
0.23723907357214175198e-7
+
(
0.11839789326602695603e-9
+
(
0.56346163067550237877e-12
+
0.25403679644444444444e-14
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
9
:
{
double
t
=
2
*
y100
-
19
;
return
0.14800987015587535621e-1
+
(
0.86018092946345943214e-3
+
(
0.47008265848816866105e-5
+
(
0.24694040760197315333e-7
+
(
0.12418779768752299093e-9
+
(
0.59486890370320261949e-12
+
0.26957764568888888889e-14
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
10
:
{
double
t
=
2
*
y100
-
21
;
return
0.16540351739394069380e-1
+
(
0.87928458641241463952e-3
+
(
0.48520195793001753903e-5
+
(
0.25711774900881709176e-7
+
(
0.13030128534230822419e-9
+
(
0.62820097586874779402e-12
+
0.28612737351111111111e-14
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
11
:
{
double
t
=
2
*
y100
-
23
;
return
0.18318536789842392647e-1
+
(
0.89900542647891721692e-3
+
(
0.50094684089553365810e-5
+
(
0.26779777074218070482e-7
+
(
0.13675822186304615566e-9
+
(
0.66358287745352705725e-12
+
0.30375273884444444444e-14
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
12
:
{
double
t
=
2
*
y100
-
25
;
return
0.20136801964214276775e-1
+
(
0.91936908737673676012e-3
+
(
0.51734830914104276820e-5
+
(
0.27900878609710432673e-7
+
(
0.14357976402809042257e-9
+
(
0.70114790311043728387e-12
+
0.32252476000000000000e-14
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
13
:
{
double
t
=
2
*
y100
-
27
;
return
0.21996459598282740954e-1
+
(
0.94040248155366777784e-3
+
(
0.53443911508041164739e-5
+
(
0.29078085538049374673e-7
+
(
0.15078844500329731137e-9
+
(
0.74103813647499204269e-12
+
0.34251892320000000000e-14
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
14
:
{
double
t
=
2
*
y100
-
29
;
return
0.23898877187226319502e-1
+
(
0.96213386835900177540e-3
+
(
0.55225386998049012752e-5
+
(
0.30314589961047687059e-7
+
(
0.15840826497296335264e-9
+
(
0.78340500472414454395e-12
+
0.36381553564444444445e-14
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
15
:
{
double
t
=
2
*
y100
-
31
;
return
0.25845480155298518485e-1
+
(
0.98459293067820123389e-3
+
(
0.57082915920051843672e-5
+
(
0.31613782169164830118e-7
+
(
0.16646478745529630813e-9
+
(
0.82840985928785407942e-12
+
0.38649975768888888890e-14
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
16
:
{
double
t
=
2
*
y100
-
33
;
return
0.27837754783474696598e-1
+
(
0.10078108563256892757e-2
+
(
0.59020366493792212221e-5
+
(
0.32979263553246520417e-7
+
(
0.17498524159268458073e-9
+
(
0.87622459124842525110e-12
+
0.41066206488888888890e-14
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
17
:
{
double
t
=
2
*
y100
-
35
;
return
0.29877251304899307550e-1
+
(
0.10318204245057349310e-2
+
(
0.61041829697162055093e-5
+
(
0.34414860359542720579e-7
+
(
0.18399863072934089607e-9
+
(
0.92703227366365046533e-12
+
0.43639844053333333334e-14
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
18
:
{
double
t
=
2
*
y100
-
37
;
return
0.31965587178596443475e-1
+
(
0.10566560976716574401e-2
+
(
0.63151633192414586770e-5
+
(
0.35924638339521924242e-7
+
(
0.19353584758781174038e-9
+
(
0.98102783859889264382e-12
+
0.46381060817777777779e-14
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
19
:
{
double
t
=
2
*
y100
-
39
;
return
0.34104450552588334840e-1
+
(
0.10823541191350532574e-2
+
(
0.65354356159553934436e-5
+
(
0.37512918348533521149e-7
+
(
0.20362979635817883229e-9
+
(
0.10384187833037282363e-11
+
0.49300625262222222221e-14
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
20
:
{
double
t
=
2
*
y100
-
41
;
return
0.36295603928292425716e-1
+
(
0.11089526167995268200e-2
+
(
0.67654845095518363577e-5
+
(
0.39184292949913591646e-7
+
(
0.21431552202133775150e-9
+
(
0.10994259106646731797e-11
+
0.52409949102222222221e-14
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
21
:
{
double
t
=
2
*
y100
-
43
;
return
0.38540888038840509795e-1
+
(
0.11364917134175420009e-2
+
(
0.70058230641246312003e-5
+
(
0.40943644083718586939e-7
+
(
0.22563034723692881631e-9
+
(
0.11642841011361992885e-11
+
0.55721092871111111110e-14
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
22
:
{
double
t
=
2
*
y100
-
45
;
return
0.40842225954785960651e-1
+
(
0.11650136437945673891e-2
+
(
0.72569945502343006619e-5
+
(
0.42796161861855042273e-7
+
(
0.23761401711005024162e-9
+
(
0.12332431172381557035e-11
+
0.59246802364444444445e-14
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
23
:
{
double
t
=
2
*
y100
-
47
;
return
0.43201627431540222422e-1
+
(
0.11945628793917272199e-2
+
(
0.75195743532849206263e-5
+
(
0.44747364553960993492e-7
+
(
0.25030885216472953674e-9
+
(
0.13065684400300476484e-11
+
0.63000532853333333334e-14
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
24
:
{
double
t
=
2
*
y100
-
49
;
return
0.45621193513810471438e-1
+
(
0.12251862608067529503e-2
+
(
0.77941720055551920319e-5
+
(
0.46803119830954460212e-7
+
(
0.26375990983978426273e-9
+
(
0.13845421370977119765e-11
+
0.66996477404444444445e-14
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
25
:
{
double
t
=
2
*
y100
-
51
;
return
0.48103121413299865517e-1
+
(
0.12569331386432195113e-2
+
(
0.80814333496367673980e-5
+
(
0.48969667335682018324e-7
+
(
0.27801515481905748484e-9
+
(
0.14674637611609884208e-11
+
0.71249589351111111110e-14
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
26
:
{
double
t
=
2
*
y100
-
53
;
return
0.50649709676983338501e-1
+
(
0.12898555233099055810e-2
+
(
0.83820428414568799654e-5
+
(
0.51253642652551838659e-7
+
(
0.29312563849675507232e-9
+
(
0.15556512782814827846e-11
+
0.75775607822222222221e-14
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
27
:
{
double
t
=
2
*
y100
-
55
;
return
0.53263363664388864181e-1
+
(
0.13240082443256975769e-2
+
(
0.86967260015007658418e-5
+
(
0.53662102750396795566e-7
+
(
0.30914568786634796807e-9
+
(
0.16494420240828493176e-11
+
0.80591079644444444445e-14
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
28
:
{
double
t
=
2
*
y100
-
57
;
return
0.55946601353500013794e-1
+
(
0.13594491197408190706e-2
+
(
0.90262520233016380987e-5
+
(
0.56202552975056695376e-7
+
(
0.32613310410503135996e-9
+
(
0.17491936862246367398e-11
+
0.85713381688888888890e-14
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
29
:
{
double
t
=
2
*
y100
-
59
;
return
0.58702059496154081813e-1
+
(
0.13962391363223647892e-2
+
(
0.93714365487312784270e-5
+
(
0.58882975670265286526e-7
+
(
0.34414937110591753387e-9
+
(
0.18552853109751857859e-11
+
0.91160736711111111110e-14
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
30
:
{
double
t
=
2
*
y100
-
61
;
return
0.61532500145144778048e-1
+
(
0.14344426411912015247e-2
+
(
0.97331446201016809696e-5
+
(
0.61711860507347175097e-7
+
(
0.36325987418295300221e-9
+
(
0.19681183310134518232e-11
+
0.96952238400000000000e-14
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
31
:
{
double
t
=
2
*
y100
-
63
;
return
0.64440817576653297993e-1
+
(
0.14741275456383131151e-2
+
(
0.10112293819576437838e-4
+
(
0.64698236605933246196e-7
+
(
0.38353412915303665586e-9
+
(
0.20881176114385120186e-11
+
0.10310784480000000000e-13
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
32
:
{
double
t
=
2
*
y100
-
65
;
return
0.67430045633130393282e-1
+
(
0.15153655418916540370e-2
+
(
0.10509857606888328667e-4
+
(
0.67851706529363332855e-7
+
(
0.40504602194811140006e-9
+
(
0.22157325110542534469e-11
+
0.10964842115555555556e-13
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
33
:
{
double
t
=
2
*
y100
-
67
;
return
0.70503365513338850709e-1
+
(
0.15582323336495709827e-2
+
(
0.10926868866865231089e-4
+
(
0.71182482239613507542e-7
+
(
0.42787405890153386710e-9
+
(
0.23514379522274416437e-11
+
0.11659571751111111111e-13
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
34
:
{
double
t
=
2
*
y100
-
69
;
return
0.73664114037944596353e-1
+
(
0.16028078812438820413e-2
+
(
0.11364423678778207991e-4
+
(
0.74701423097423182009e-7
+
(
0.45210162777476488324e-9
+
(
0.24957355004088569134e-11
+
0.12397238257777777778e-13
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
35
:
{
double
t
=
2
*
y100
-
71
;
return
0.76915792420819562379e-1
+
(
0.16491766623447889354e-2
+
(
0.11823685320041302169e-4
+
(
0.78420075993781544386e-7
+
(
0.47781726956916478925e-9
+
(
0.26491544403815724749e-11
+
0.13180196462222222222e-13
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
36
:
{
double
t
=
2
*
y100
-
73
;
return
0.80262075578094612819e-1
+
(
0.16974279491709504117e-2
+
(
0.12305888517309891674e-4
+
(
0.82350717698979042290e-7
+
(
0.50511496109857113929e-9
+
(
0.28122528497626897696e-11
+
0.14010889635555555556e-13
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
37
:
{
double
t
=
2
*
y100
-
75
;
return
0.83706822008980357446e-1
+
(
0.17476561032212656962e-2
+
(
0.12812343958540763368e-4
+
(
0.86506399515036435592e-7
+
(
0.53409440823869467453e-9
+
(
0.29856186620887555043e-11
+
0.14891851591111111111e-13
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
38
:
{
double
t
=
2
*
y100
-
77
;
return
0.87254084284461718231e-1
+
(
0.17999608886001962327e-2
+
(
0.13344443080089492218e-4
+
(
0.90900994316429008631e-7
+
(
0.56486134972616465316e-9
+
(
0.31698707080033956934e-11
+
0.15825697795555555556e-13
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
39
:
{
double
t
=
2
*
y100
-
79
;
return
0.90908120182172748487e-1
+
(
0.18544478050657699758e-2
+
(
0.13903663143426120077e-4
+
(
0.95549246062549906177e-7
+
(
0.59752787125242054315e-9
+
(
0.33656597366099099413e-11
+
0.16815130613333333333e-13
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
40
:
{
double
t
=
2
*
y100
-
81
;
return
0.94673404508075481121e-1
+
(
0.19112284419887303347e-2
+
(
0.14491572616545004930e-4
+
(
0.10046682186333613697e-6
+
(
0.63221272959791000515e-9
+
(
0.35736693975589130818e-11
+
0.17862931591111111111e-13
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
41
:
{
double
t
=
2
*
y100
-
83
;
return
0.98554641648004456555e-1
+
(
0.19704208544725622126e-2
+
(
0.15109836875625443935e-4
+
(
0.10567036667675984067e-6
+
(
0.66904168640019354565e-9
+
(
0.37946171850824333014e-11
+
0.18971959040000000000e-13
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
42
:
{
double
t
=
2
*
y100
-
85
;
return
0.10255677889470089531e0
+
(
0.20321499629472857418e-2
+
(
0.15760224242962179564e-4
+
(
0.11117756071353507391e-6
+
(
0.70814785110097658502e-9
+
(
0.40292553276632563925e-11
+
0.20145143075555555556e-13
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
43
:
{
double
t
=
2
*
y100
-
87
;
return
0.10668502059865093318e0
+
(
0.20965479776148731610e-2
+
(
0.16444612377624983565e-4
+
(
0.11700717962026152749e-6
+
(
0.74967203250938418991e-9
+
(
0.42783716186085922176e-11
+
0.21385479360000000000e-13
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
44
:
{
double
t
=
2
*
y100
-
89
;
return
0.11094484319386444474e0
+
(
0.21637548491908170841e-2
+
(
0.17164995035719657111e-4
+
(
0.12317915750735938089e-6
+
(
0.79376309831499633734e-9
+
(
0.45427901763106353914e-11
+
0.22696025653333333333e-13
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
45
:
{
double
t
=
2
*
y100
-
91
;
return
0.11534201115268804714e0
+
(
0.22339187474546420375e-2
+
(
0.17923489217504226813e-4
+
(
0.12971465288245997681e-6
+
(
0.84057834180389073587e-9
+
(
0.48233721206418027227e-11
+
0.24079890062222222222e-13
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
46
:
{
double
t
=
2
*
y100
-
93
;
return
0.11988259392684094740e0
+
(
0.23071965691918689601e-2
+
(
0.18722342718958935446e-4
+
(
0.13663611754337957520e-6
+
(
0.89028385488493287005e-9
+
(
0.51210161569225846701e-11
+
0.25540227111111111111e-13
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
47
:
{
double
t
=
2
*
y100
-
95
;
return
0.12457298393509812907e0
+
(
0.23837544771809575380e-2
+
(
0.19563942105711612475e-4
+
(
0.14396736847739470782e-6
+
(
0.94305490646459247016e-9
+
(
0.54366590583134218096e-11
+
0.27080225920000000000e-13
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
48
:
{
double
t
=
2
*
y100
-
97
;
return
0.12941991566142438816e0
+
(
0.24637684719508859484e-2
+
(
0.20450821127475879816e-4
+
(
0.15173366280523906622e-6
+
(
0.99907632506389027739e-9
+
(
0.57712760311351625221e-11
+
0.28703099555555555556e-13
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
49
:
{
double
t
=
2
*
y100
-
99
;
return
0.13443048593088696613e0
+
(
0.25474249981080823877e-2
+
(
0.21385669591362915223e-4
+
(
0.15996177579900443030e-6
+
(
0.10585428844575134013e-8
+
(
0.61258809536787882989e-11
+
0.30412080142222222222e-13
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
50
:
{
double
t
=
2
*
y100
-
101
;
return
0.13961217543434561353e0
+
(
0.26349215871051761416e-2
+
(
0.22371342712572567744e-4
+
(
0.16868008199296822247e-6
+
(
0.11216596910444996246e-8
+
(
0.65015264753090890662e-11
+
0.32210394506666666666e-13
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
51
:
{
double
t
=
2
*
y100
-
103
;
return
0.14497287157673800690e0
+
(
0.27264675383982439814e-2
+
(
0.23410870961050950197e-4
+
(
0.17791863939526376477e-6
+
(
0.11886425714330958106e-8
+
(
0.68993039665054288034e-11
+
0.34101266222222222221e-13
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
52
:
{
double
t
=
2
*
y100
-
105
;
return
0.15052089272774618151e0
+
(
0.28222846410136238008e-2
+
(
0.24507470422713397006e-4
+
(
0.18770927679626136909e-6
+
(
0.12597184587583370712e-8
+
(
0.73203433049229821618e-11
+
0.36087889048888888890e-13
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
53
:
{
double
t
=
2
*
y100
-
107
;
return
0.15626501395774612325e0
+
(
0.29226079376196624949e-2
+
(
0.25664553693768450545e-4
+
(
0.19808568415654461964e-6
+
(
0.13351257759815557897e-8
+
(
0.77658124891046760667e-11
+
0.38173420035555555555e-13
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
54
:
{
double
t
=
2
*
y100
-
109
;
return
0.16221449434620737567e0
+
(
0.30276865332726475672e-2
+
(
0.26885741326534564336e-4
+
(
0.20908350604346384143e-6
+
(
0.14151148144240728728e-8
+
(
0.82369170665974313027e-11
+
0.40360957457777777779e-13
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
55
:
{
double
t
=
2
*
y100
-
111
;
return
0.16837910595412130659e0
+
(
0.31377844510793082301e-2
+
(
0.28174873844911175026e-4
+
(
0.22074043807045782387e-6
+
(
0.14999481055996090039e-8
+
(
0.87348993661930809254e-11
+
0.42653528977777777779e-13
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
56
:
{
double
t
=
2
*
y100
-
113
;
return
0.17476916455659369953e0
+
(
0.32531815370903068316e-2
+
(
0.29536024347344364074e-4
+
(
0.23309632627767074202e-6
+
(
0.15899007843582444846e-8
+
(
0.92610375235427359475e-11
+
0.45054073102222222221e-13
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
57
:
{
double
t
=
2
*
y100
-
115
;
return
0.18139556223643701364e0
+
(
0.33741744168096996041e-2
+
(
0.30973511714709500836e-4
+
(
0.24619326937592290996e-6
+
(
0.16852609412267750744e-8
+
(
0.98166442942854895573e-11
+
0.47565418097777777779e-13
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
58
:
{
double
t
=
2
*
y100
-
117
;
return
0.18826980194443664549e0
+
(
0.35010775057740317997e-2
+
(
0.32491914440014267480e-4
+
(
0.26007572375886319028e-6
+
(
0.17863299617388376116e-8
+
(
0.10403065638343878679e-10
+
0.50190265831111111110e-13
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
59
:
{
double
t
=
2
*
y100
-
119
;
return
0.19540403413693967350e0
+
(
0.36342240767211326315e-2
+
(
0.34096085096200907289e-4
+
(
0.27479061117017637474e-6
+
(
0.18934228504790032826e-8
+
(
0.11021679075323598664e-10
+
0.52931171733333333334e-13
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
60
:
{
double
t
=
2
*
y100
-
121
;
return
0.20281109560651886959e0
+
(
0.37739673859323597060e-2
+
(
0.35791165457592409054e-4
+
(
0.29038742889416172404e-6
+
(
0.20068685374849001770e-8
+
(
0.11673891799578381999e-10
+
0.55790523093333333334e-13
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
61
:
{
double
t
=
2
*
y100
-
123
;
return
0.21050455062669334978e0
+
(
0.39206818613925652425e-2
+
(
0.37582602289680101704e-4
+
(
0.30691836231886877385e-6
+
(
0.21270101645763677824e-8
+
(
0.12361138551062899455e-10
+
0.58770520160000000000e-13
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
62
:
{
double
t
=
2
*
y100
-
125
;
return
0.21849873453703332479e0
+
(
0.40747643554689586041e-2
+
(
0.39476163820986711501e-4
+
(
0.32443839970139918836e-6
+
(
0.22542053491518680200e-8
+
(
0.13084879235290858490e-10
+
0.61873153262222222221e-13
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
63
:
{
double
t
=
2
*
y100
-
127
;
return
0.22680879990043229327e0
+
(
0.42366354648628516935e-2
+
(
0.41477956909656896779e-4
+
(
0.34300544894502810002e-6
+
(
0.23888264229264067658e-8
+
(
0.13846596292818514601e-10
+
0.65100183751111111110e-13
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
64
:
{
double
t
=
2
*
y100
-
129
;
return
0.23545076536988703937e0
+
(
0.44067409206365170888e-2
+
(
0.43594444916224700881e-4
+
(
0.36268045617760415178e-6
+
(
0.25312606430853202748e-8
+
(
0.14647791812837903061e-10
+
0.68453122631111111110e-13
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
65
:
{
double
t
=
2
*
y100
-
131
;
return
0.24444156740777432838e0
+
(
0.45855530511605787178e-2
+
(
0.45832466292683085475e-4
+
(
0.38352752590033030472e-6
+
(
0.26819103733055603460e-8
+
(
0.15489984390884756993e-10
+
0.71933206364444444445e-13
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
66
:
{
double
t
=
2
*
y100
-
133
;
return
0.25379911500634264643e0
+
(
0.47735723208650032167e-2
+
(
0.48199253896534185372e-4
+
(
0.40561404245564732314e-6
+
(
0.28411932320871165585e-8
+
(
0.16374705736458320149e-10
+
0.75541379822222222221e-13
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
67
:
{
double
t
=
2
*
y100
-
135
;
return
0.26354234756393613032e0
+
(
0.49713289477083781266e-2
+
(
0.50702455036930367504e-4
+
(
0.42901079254268185722e-6
+
(
0.30095422058900481753e-8
+
(
0.17303497025347342498e-10
+
0.79278273368888888890e-13
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
68
:
{
double
t
=
2
*
y100
-
137
;
return
0.27369129607732343398e0
+
(
0.51793846023052643767e-2
+
(
0.53350152258326602629e-4
+
(
0.45379208848865015485e-6
+
(
0.31874057245814381257e-8
+
(
0.18277905010245111046e-10
+
0.83144182364444444445e-13
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
69
:
{
double
t
=
2
*
y100
-
139
;
return
0.28426714781640316172e0
+
(
0.53983341916695141966e-2
+
(
0.56150884865255810638e-4
+
(
0.48003589196494734238e-6
+
(
0.33752476967570796349e-8
+
(
0.19299477888083469086e-10
+
0.87139049137777777779e-13
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
70
:
{
double
t
=
2
*
y100
-
141
;
return
0.29529231465348519920e0
+
(
0.56288077305420795663e-2
+
(
0.59113671189913307427e-4
+
(
0.50782393781744840482e-6
+
(
0.35735475025851713168e-8
+
(
0.20369760937017070382e-10
+
0.91262442613333333334e-13
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
71
:
{
double
t
=
2
*
y100
-
143
;
return
0.30679050522528838613e0
+
(
0.58714723032745403331e-2
+
(
0.62248031602197686791e-4
+
(
0.53724185766200945789e-6
+
(
0.37827999418960232678e-8
+
(
0.21490291930444538307e-10
+
0.95513539182222222221e-13
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
72
:
{
double
t
=
2
*
y100
-
145
;
return
0.31878680111173319425e0
+
(
0.61270341192339103514e-2
+
(
0.65564012259707640976e-4
+
(
0.56837930287837738996e-6
+
(
0.40035151353392378882e-8
+
(
0.22662596341239294792e-10
+
0.99891109760000000000e-13
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
73
:
{
double
t
=
2
*
y100
-
147
;
return
0.33130773722152622027e0
+
(
0.63962406646798080903e-2
+
(
0.69072209592942396666e-4
+
(
0.60133006661885941812e-6
+
(
0.42362183765883466691e-8
+
(
0.23888182347073698382e-10
+
0.10439349811555555556e-12
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
74
:
{
double
t
=
2
*
y100
-
149
;
return
0.34438138658041336523e0
+
(
0.66798829540414007258e-2
+
(
0.72783795518603561144e-4
+
(
0.63619220443228800680e-6
+
(
0.44814499336514453364e-8
+
(
0.25168535651285475274e-10
+
0.10901861383111111111e-12
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
75
:
{
double
t
=
2
*
y100
-
151
;
return
0.35803744972380175583e0
+
(
0.69787978834882685031e-2
+
(
0.76710543371454822497e-4
+
(
0.67306815308917386747e-6
+
(
0.47397647975845228205e-8
+
(
0.26505114141143050509e-10
+
0.11376390933333333333e-12
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
76
:
{
double
t
=
2
*
y100
-
153
;
return
0.37230734890119724188e0
+
(
0.72938706896461381003e-2
+
(
0.80864854542670714092e-4
+
(
0.71206484718062688779e-6
+
(
0.50117323769745883805e-8
+
(
0.27899342394100074165e-10
+
0.11862637614222222222e-12
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
77
:
{
double
t
=
2
*
y100
-
155
;
return
0.38722432730555448223e0
+
(
0.76260375162549802745e-2
+
(
0.85259785810004603848e-4
+
(
0.75329383305171327677e-6
+
(
0.52979361368388119355e-8
+
(
0.29352606054164086709e-10
+
0.12360253370666666667e-12
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
78
:
{
double
t
=
2
*
y100
-
157
;
return
0.40282355354616940667e0
+
(
0.79762880915029728079e-2
+
(
0.89909077342438246452e-4
+
(
0.79687137961956194579e-6
+
(
0.55989731807360403195e-8
+
(
0.30866246101464869050e-10
+
0.12868841946666666667e-12
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
79
:
{
double
t
=
2
*
y100
-
159
;
return
0.41914223158913787649e0
+
(
0.83456685186950463538e-2
+
(
0.94827181359250161335e-4
+
(
0.84291858561783141014e-6
+
(
0.59154537751083485684e-8
+
(
0.32441553034347469291e-10
+
0.13387957943111111111e-12
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
80
:
{
double
t
=
2
*
y100
-
161
;
return
0.43621971639463786896e0
+
(
0.87352841828289495773e-2
+
(
0.10002929142066799966e-3
+
(
0.89156148280219880024e-6
+
(
0.62480008150788597147e-8
+
(
0.34079760983458878910e-10
+
0.13917107176888888889e-12
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
81
:
{
double
t
=
2
*
y100
-
163
;
return
0.45409763548534330981e0
+
(
0.91463027755548240654e-2
+
(
0.10553137232446167258e-3
+
(
0.94293113464638623798e-6
+
(
0.65972492312219959885e-8
+
(
0.35782041795476563662e-10
+
0.14455745872000000000e-12
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
82
:
{
double
t
=
2
*
y100
-
165
;
return
0.47282001668512331468e0
+
(
0.95799574408860463394e-2
+
(
0.11135019058000067469e-3
+
(
0.99716373005509038080e-6
+
(
0.69638453369956970347e-8
+
(
0.37549499088161345850e-10
+
0.15003280712888888889e-12
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
83
:
{
double
t
=
2
*
y100
-
167
;
return
0.49243342227179841649e0
+
(
0.10037550043909497071e-1
+
(
0.11750334542845234952e-3
+
(
0.10544006716188967172e-5
+
(
0.73484461168242224872e-8
+
(
0.39383162326435752965e-10
+
0.15559069118222222222e-12
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
84
:
{
double
t
=
2
*
y100
-
169
;
return
0.51298708979209258326e0
+
(
0.10520454564612427224e-1
+
(
0.12400930037494996655e-3
+
(
0.11147886579371265246e-5
+
(
0.77517184550568711454e-8
+
(
0.41283980931872622611e-10
+
0.16122419680000000000e-12
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
85
:
{
double
t
=
2
*
y100
-
171
;
return
0.53453307979101369843e0
+
(
0.11030120618800726938e-1
+
(
0.13088741519572269581e-3
+
(
0.11784797595374515432e-5
+
(
0.81743383063044825400e-8
+
(
0.43252818449517081051e-10
+
0.16692592640000000000e-12
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
86
:
{
double
t
=
2
*
y100
-
173
;
return
0.55712643071169299478e0
+
(
0.11568077107929735233e-1
+
(
0.13815797838036651289e-3
+
(
0.12456314879260904558e-5
+
(
0.86169898078969313597e-8
+
(
0.45290446811539652525e-10
+
0.17268801084444444444e-12
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
87
:
{
double
t
=
2
*
y100
-
175
;
return
0.58082532122519320968e0
+
(
0.12135935999503877077e-1
+
(
0.14584223996665838559e-3
+
(
0.13164068573095710742e-5
+
(
0.90803643355106020163e-8
+
(
0.47397540713124619155e-10
+
0.17850211608888888889e-12
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
88
:
{
double
t
=
2
*
y100
-
177
;
return
0.60569124025293375554e0
+
(
0.12735396239525550361e-1
+
(
0.15396244472258863344e-3
+
(
0.13909744385382818253e-5
+
(
0.95651595032306228245e-8
+
(
0.49574672127669041550e-10
+
0.18435945564444444444e-12
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
89
:
{
double
t
=
2
*
y100
-
179
;
return
0.63178916494715716894e0
+
(
0.13368247798287030927e-1
+
(
0.16254186562762076141e-3
+
(
0.14695084048334056083e-5
+
(
0.10072078109604152350e-7
+
(
0.51822304995680707483e-10
+
0.19025081422222222222e-12
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
90
:
{
double
t
=
2
*
y100
-
181
;
return
0.65918774689725319200e0
+
(
0.14036375850601992063e-1
+
(
0.17160483760259706354e-3
+
(
0.15521885688723188371e-5
+
(
0.10601827031535280590e-7
+
(
0.54140790105837520499e-10
+
0.19616655146666666667e-12
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
91
:
{
double
t
=
2
*
y100
-
183
;
return
0.68795950683174433822e0
+
(
0.14741765091365869084e-1
+
(
0.18117679143520433835e-3
+
(
0.16392004108230585213e-5
+
(
0.11155116068018043001e-7
+
(
0.56530360194925690374e-10
+
0.20209663662222222222e-12
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
92
:
{
double
t
=
2
*
y100
-
185
;
return
0.71818103808729967036e0
+
(
0.15486504187117112279e-1
+
(
0.19128428784550923217e-3
+
(
0.17307350969359975848e-5
+
(
0.11732656736113607751e-7
+
(
0.58991125287563833603e-10
+
0.20803065333333333333e-12
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
93
:
{
double
t
=
2
*
y100
-
187
;
return
0.74993321911726254661e0
+
(
0.16272790364044783382e-1
+
(
0.20195505163377912645e-3
+
(
0.18269894883203346953e-5
+
(
0.12335161021630225535e-7
+
(
0.61523068312169087227e-10
+
0.21395783431111111111e-12
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
94
:
{
double
t
=
2
*
y100
-
189
;
return
0.78330143531283492729e0
+
(
0.17102934132652429240e-1
+
(
0.21321800585063327041e-3
+
(
0.19281661395543913713e-5
+
(
0.12963340087354341574e-7
+
(
0.64126040998066348872e-10
+
0.21986708942222222222e-12
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
95
:
{
double
t
=
2
*
y100
-
191
;
return
0.81837581041023811832e0
+
(
0.17979364149044223802e-1
+
(
0.22510330592753129006e-3
+
(
0.20344732868018175389e-5
+
(
0.13617902941839949718e-7
+
(
0.66799760083972474642e-10
+
0.22574701262222222222e-12
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
96
:
{
double
t
=
2
*
y100
-
193
;
return
0.85525144775685126237e0
+
(
0.18904632212547561026e-1
+
(
0.23764237370371255638e-3
+
(
0.21461248251306387979e-5
+
(
0.14299555071870523786e-7
+
(
0.69543803864694171934e-10
+
0.23158593688888888889e-12
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
97
:
{
double
t
=
2
*
y100
-
195
;
return
0.89402868170849933734e0
+
(
0.19881418399127202569e-1
+
(
0.25086793128395995798e-3
+
(
0.22633402747585233180e-5
+
(
0.15008997042116532283e-7
+
(
0.72357609075043941261e-10
+
0.23737194737777777778e-12
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
98
:
{
double
t
=
2
*
y100
-
197
;
return
0.93481333942870796363e0
+
(
0.20912536329780368893e-1
+
(
0.26481403465998477969e-3
+
(
0.23863447359754921676e-5
+
(
0.15746923065472184451e-7
+
(
0.75240468141720143653e-10
+
0.24309291271111111111e-12
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
case
99
:
{
double
t
=
2
*
y100
-
199
;
return
0.97771701335885035464e0
+
(
0.22000938572830479551e-1
+
(
0.27951610702682383001e-3
+
(
0.25153688325245314530e-5
+
(
0.16514019547822821453e-7
+
(
0.78191526829368231251e-10
+
0.24873652355555555556e-12
*
t
)
*
t
)
*
t
)
*
t
)
*
t
)
*
t
;
}
}
/* we only get here if y = 1, i.e. |x| < 4*eps, in which case
* erfcx is within 1e-15 of 1.. */
return
1.0
;
}
/* erfcx_y100 */
/* optimizer friendly implementation of exp2(x).
*
* strategy:
*
* split argument into an integer part and a fraction:
* ipart = floor(x+0.5);
* fpart = x - ipart;
*
* compute exp2(ipart) from setting the ieee754 exponent
* compute exp2(fpart) using a pade' approximation for x in [-0.5;0.5[
*
* the result becomes: exp2(x) = exp2(ipart) * exp2(fpart)
*/
/* IEEE 754 double precision floating point data manipulation */
typedef
union
{
double
f
;
uint64_t
u
;
struct
{
int32_t
i0
,
i1
;}
s
;
}
udi_t
;
static
const
double
fm_exp2_q
[]
=
{
/* 1.00000000000000000000e0, */
2.33184211722314911771e2
,
4.36821166879210612817e3
};
static
const
double
fm_exp2_p
[]
=
{
2.30933477057345225087e-2
,
2.02020656693165307700e1
,
1.51390680115615096133e3
};
double
MathSpecialKokkos
::
exp2_x86
(
double
x
)
{
double
ipart
,
fpart
,
px
,
qx
;
udi_t
epart
;
ipart
=
floor
(
x
+
0.5
);
fpart
=
x
-
ipart
;
epart
.
s
.
i0
=
0
;
epart
.
s
.
i1
=
(((
int
)
ipart
)
+
1023
)
<<
20
;
x
=
fpart
*
fpart
;
px
=
fm_exp2_p
[
0
];
px
=
px
*
x
+
fm_exp2_p
[
1
];
qx
=
x
+
fm_exp2_q
[
0
];
px
=
px
*
x
+
fm_exp2_p
[
2
];
qx
=
qx
*
x
+
fm_exp2_q
[
1
];
px
=
px
*
fpart
;
x
=
1.0
+
2.0
*
(
px
/
(
qx
-
px
));
return
epart
.
f
*
x
;
}
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