Geant4 10.7.0
Toolkit for the simulation of the passage of particles through matter
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G4ErrorFunction.cc
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1//
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5// * The Geant4 software is copyright of the Copyright Holders of *
6// * the Geant4 Collaboration. It is provided under the terms and *
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18// * This code implementation is the result of the scientific and *
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25//
26/*
27 * G4ErrorFunction.cc
28 *
29 * Created on: Jul 23, 2019
30 * Author: W. G. Shin
31 * J. Ramos-Mendez and B. Faddegon
32*/
33
34/*
35 Extracted from http://ab-initio.mit.edu/Faddeeva
36 Steven G. Johnson, October 2012.
37
38 Copyright © 2012 Massachusetts Institute of Technology
39
40 Permission is hereby granted, free of charge, to any person
41 obtaining a copy of this software and associated documentation
42 files (the "Software"), to deal in the Software without restriction,
43 including without limitation the rights to use, copy, modify, merge,
44 publish, distribute, sublicense, and/or sell copies of the Software,
45 and to permit persons to whom the Software is furnished to do so,
46 subject to the following conditions:
47
48 The above copyright notice and this permission notice shall be
49 included in all copies or substantial portions of the Software.
50*/
51
52#include "G4ErrorFunction.hh"
53#include "globals.hh"
54#include "G4SystemOfUnits.hh"
55#include "Randomize.hh"
56#include <vector>
57
58
59G4ErrorFunction::G4ErrorFunction() {;}
60
61G4ErrorFunction::~G4ErrorFunction() {;}
62
63
64
65G4double G4ErrorFunction::erfcx_y100(G4double y100)
66
67{
68 switch ((int) y100) {
69 case 0: {
70 G4double t = 2*y100 - 1;
71 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;
72 }
73 case 1: {
74 G4double t = 2*y100 - 3;
75 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;
76 }
77 case 2: {
78 G4double t = 2*y100 - 5;
79 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;
80 }
81 case 3: {
82 G4double t = 2*y100 - 7;
83 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;
84 }
85 case 4: {
86 G4double t = 2*y100 - 9;
87 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;
88 }
89 case 5: {
90 G4double t = 2*y100 - 11;
91 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;
92 }
93 case 6: {
94 G4double t = 2*y100 - 13;
95 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;
96 }
97 case 7: {
98 G4double t = 2*y100 - 15;
99 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;
100 }
101 case 8: {
102 G4double t = 2*y100 - 17;
103 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;
104 }
105 case 9: {
106 G4double t = 2*y100 - 19;
107 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;
108 }
109 case 10: {
110 G4double t = 2*y100 - 21;
111 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;
112 }
113 case 11: {
114 G4double t = 2*y100 - 23;
115 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;
116 }
117 case 12: {
118 G4double t = 2*y100 - 25;
119 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;
120 }
121 case 13: {
122 G4double t = 2*y100 - 27;
123 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;
124 }
125 case 14: {
126 G4double t = 2*y100 - 29;
127 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;
128 }
129 case 15: {
130 G4double t = 2*y100 - 31;
131 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;
132 }
133 case 16: {
134 G4double t = 2*y100 - 33;
135 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;
136 }
137 case 17: {
138 G4double t = 2*y100 - 35;
139 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;
140 }
141 case 18: {
142 G4double t = 2*y100 - 37;
143 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;
144 }
145 case 19: {
146 G4double t = 2*y100 - 39;
147 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;
148 }
149 case 20: {
150 G4double t = 2*y100 - 41;
151 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;
152 }
153 case 21: {
154 G4double t = 2*y100 - 43;
155 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;
156 }
157 case 22: {
158 G4double t = 2*y100 - 45;
159 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;
160 }
161 case 23: {
162 G4double t = 2*y100 - 47;
163 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;
164 }
165 case 24: {
166 G4double t = 2*y100 - 49;
167 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;
168 }
169 case 25: {
170 G4double t = 2*y100 - 51;
171 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;
172 }
173 case 26: {
174 G4double t = 2*y100 - 53;
175 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;
176 }
177 case 27: {
178 G4double t = 2*y100 - 55;
179 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;
180 }
181 case 28: {
182 G4double t = 2*y100 - 57;
183 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;
184 }
185 case 29: {
186 G4double t = 2*y100 - 59;
187 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;
188 }
189 case 30: {
190 G4double t = 2*y100 - 61;
191 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;
192 }
193 case 31: {
194 G4double t = 2*y100 - 63;
195 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;
196 }
197 case 32: {
198 G4double t = 2*y100 - 65;
199 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;
200 }
201 case 33: {
202 G4double t = 2*y100 - 67;
203 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;
204 }
205 case 34: {
206 G4double t = 2*y100 - 69;
207 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;
208 }
209 case 35: {
210 G4double t = 2*y100 - 71;
211 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;
212 }
213 case 36: {
214 G4double t = 2*y100 - 73;
215 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;
216 }
217 case 37: {
218 G4double t = 2*y100 - 75;
219 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;
220 }
221 case 38: {
222 G4double t = 2*y100 - 77;
223 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;
224 }
225 case 39: {
226 G4double t = 2*y100 - 79;
227 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;
228 }
229 case 40: {
230 G4double t = 2*y100 - 81;
231 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;
232 }
233 case 41: {
234 G4double t = 2*y100 - 83;
235 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;
236 }
237 case 42: {
238 G4double t = 2*y100 - 85;
239 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;
240 }
241 case 43: {
242 G4double t = 2*y100 - 87;
243 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;
244 }
245 case 44: {
246 G4double t = 2*y100 - 89;
247 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;
248 }
249 case 45: {
250 G4double t = 2*y100 - 91;
251 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;
252 }
253 case 46: {
254 G4double t = 2*y100 - 93;
255 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;
256 }
257 case 47: {
258 G4double t = 2*y100 - 95;
259 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;
260 }
261 case 48: {
262 G4double t = 2*y100 - 97;
263 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;
264 }
265 case 49: {
266 G4double t = 2*y100 - 99;
267 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;
268 }
269 case 50: {
270 G4double t = 2*y100 - 101;
271 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;
272 }
273 case 51: {
274 G4double t = 2*y100 - 103;
275 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;
276 }
277 case 52: {
278 G4double t = 2*y100 - 105;
279 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;
280 }
281 case 53: {
282 G4double t = 2*y100 - 107;
283 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;
284 }
285 case 54: {
286 G4double t = 2*y100 - 109;
287 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;
288 }
289 case 55: {
290 G4double t = 2*y100 - 111;
291 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;
292 }
293 case 56: {
294 G4double t = 2*y100 - 113;
295 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;
296 }
297 case 57: {
298 G4double t = 2*y100 - 115;
299 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;
300 }
301 case 58: {
302 G4double t = 2*y100 - 117;
303 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;
304 }
305 case 59: {
306 G4double t = 2*y100 - 119;
307 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;
308 }
309 case 60: {
310 G4double t = 2*y100 - 121;
311 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;
312 }
313 case 61: {
314 G4double t = 2*y100 - 123;
315 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;
316 }
317 case 62: {
318 G4double t = 2*y100 - 125;
319 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;
320 }
321 case 63: {
322 G4double t = 2*y100 - 127;
323 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;
324 }
325 case 64: {
326 G4double t = 2*y100 - 129;
327 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;
328 }
329 case 65: {
330 G4double t = 2*y100 - 131;
331 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;
332 }
333 case 66: {
334 G4double t = 2*y100 - 133;
335 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;
336 }
337 case 67: {
338 G4double t = 2*y100 - 135;
339 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;
340 }
341 case 68: {
342 G4double t = 2*y100 - 137;
343 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;
344 }
345 case 69: {
346 G4double t = 2*y100 - 139;
347 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;
348 }
349 case 70: {
350 G4double t = 2*y100 - 141;
351 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;
352 }
353 case 71: {
354 G4double t = 2*y100 - 143;
355 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;
356 }
357 case 72: {
358 G4double t = 2*y100 - 145;
359 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;
360 }
361 case 73: {
362 G4double t = 2*y100 - 147;
363 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;
364 }
365 case 74: {
366 G4double t = 2*y100 - 149;
367 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;
368 }
369 case 75: {
370 G4double t = 2*y100 - 151;
371 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;
372 }
373 case 76: {
374 G4double t = 2*y100 - 153;
375 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;
376 }
377 case 77: {
378 G4double t = 2*y100 - 155;
379 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;
380 }
381 case 78: {
382 G4double t = 2*y100 - 157;
383 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;
384 }
385 case 79: {
386 G4double t = 2*y100 - 159;
387 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;
388 }
389 case 80: {
390 G4double t = 2*y100 - 161;
391 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;
392 }
393 case 81: {
394 G4double t = 2*y100 - 163;
395 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;
396 }
397 case 82: {
398 G4double t = 2*y100 - 165;
399 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;
400 }
401 case 83: {
402 G4double t = 2*y100 - 167;
403 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;
404 }
405 case 84: {
406 G4double t = 2*y100 - 169;
407 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;
408 }
409 case 85: {
410 G4double t = 2*y100 - 171;
411 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;
412 }
413 case 86: {
414 G4double t = 2*y100 - 173;
415 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;
416 }
417 case 87: {
418 G4double t = 2*y100 - 175;
419 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;
420 }
421 case 88: {
422 G4double t = 2*y100 - 177;
423 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;
424 }
425 case 89: {
426 G4double t = 2*y100 - 179;
427 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;
428 }
429 case 90: {
430 G4double t = 2*y100 - 181;
431 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;
432 }
433 case 91: {
434 G4double t = 2*y100 - 183;
435 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;
436 }
437 case 92: {
438 G4double t = 2*y100 - 185;
439 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;
440 }
441 case 93: {
442 G4double t = 2*y100 - 187;
443 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;
444 }
445 case 94: {
446 G4double t = 2*y100 - 189;
447 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;
448 }
449 case 95: {
450 G4double t = 2*y100 - 191;
451 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;
452 }
453 case 96: {
454 G4double t = 2*y100 - 193;
455 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;
456 }
457 case 97: {
458 G4double t = 2*y100 - 195;
459 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;
460 }
461 case 98: {
462 G4double t = 2*y100 - 197;
463 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;
464 }
465 case 99: {
466 G4double t = 2*y100 - 199;
467 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;
468 }
469 }
470 // we only get here if y = 1, i.e. |x| < 4*eps, in which case
471 // erfcx is within 1e-15 of 1..
472 return 1.0;
473}
474
475
476G4double G4ErrorFunction::NormQuantile(G4double p)
477{
478 G4double a0 = 3.3871328727963666080e0;
479 G4double a1 = 1.3314166789178437745e+2;
480 G4double a2 = 1.9715909503065514427e+3;
481 G4double a3 = 1.3731693765509461125e+4;
482 G4double a4 = 4.5921953931549871457e+4;
483 G4double a5 = 6.7265770927008700853e+4;
484 G4double a6 = 3.3430575583588128105e+4;
485 G4double a7 = 2.5090809287301226727e+3;
486 G4double b1 = 4.2313330701600911252e+1;
487 G4double b2 = 6.8718700749205790830e+2;
488 G4double b3 = 5.3941960214247511077e+3;
489 G4double b4 = 2.1213794301586595867e+4;
490 G4double b5 = 3.9307895800092710610e+4;
491 G4double b6 = 2.8729085735721942674e+4;
492 G4double b7 = 5.2264952788528545610e+3;
493 G4double c0 = 1.42343711074968357734e0;
494 G4double c1 = 4.63033784615654529590e0;
495 G4double c2 = 5.76949722146069140550e0;
496 G4double c3 = 3.64784832476320460504e0;
497 G4double c4 = 1.27045825245236838258e0;
498 G4double c5 = 2.41780725177450611770e-1;
499 G4double c6 = 2.27238449892691845833e-2;
500 G4double c7 = 7.74545014278341407640e-4;
501 G4double d1 = 2.05319162663775882187e0;
502 G4double d2 = 1.67638483018380384940e0;
503 G4double d3 = 6.89767334985100004550e-1;
504 G4double d4 = 1.48103976427480074590e-1;
505 G4double d5 = 1.51986665636164571966e-2;
506 G4double d6 = 5.47593808499534494600e-4;
507 G4double d7 = 1.05075007164441684324e-9;
508 G4double e0 = 6.65790464350110377720e0;
509 G4double e1 = 5.46378491116411436990e0;
510 G4double e2 = 1.78482653991729133580e0;
511 G4double e3 = 2.96560571828504891230e-1;
512 G4double e4 = 2.65321895265761230930e-2;
513 G4double e5 = 1.24266094738807843860e-3;
514 G4double e6 = 2.71155556874348757815e-5;
515 G4double e7 = 2.01033439929228813265e-7;
516 G4double f1 = 5.99832206555887937690e-1;
517 G4double f2 = 1.36929880922735805310e-1;
518 G4double f3 = 1.48753612908506148525e-2;
519 G4double f4 = 7.86869131145613259100e-4;
520 G4double f5 = 1.84631831751005468180e-5;
521 G4double f6 = 1.42151175831644588870e-7;
522 G4double f7 = 2.04426310338993978564e-15;
523
524 G4double split1 = 0.425;
525 G4double split2=5.;
526 G4double konst1=0.180625;
527 G4double konst2=1.6;
528
529 G4double q, r, quantile;
530 q=p-0.5;
531 if (std::abs(q)<split1) {
532 r=konst1-q*q;
533 quantile = q* (((((((a7 * r + a6) * r + a5) * r + a4) * r + a3)
534 * r + a2) * r + a1) * r + a0) /
535 (((((((b7 * r + b6) * r + b5) * r + b4) * r + b3)
536 * r + b2) * r + b1) * r + 1.);
537 } else {
538 if(q<0) r=p;
539 else r=1-p;
540 //error case
541 if (r<=0)
542 quantile=0;
543 else {
544 r=std::sqrt(-std::log(r));
545 if (r<=split2) {
546 r=r-konst2;
547 quantile=(((((((c7 * r + c6) * r + c5) * r + c4) * r + c3)
548 * r + c2) * r + c1) * r + c0) /
549 (((((((d7 * r + d6) * r + d5) * r + d4) * r + d3)
550 * r + d2) * r + d1) * r + 1);
551 } else{
552 r=r-split2;
553 quantile=(((((((e7 * r + e6) * r + e5) * r + e4) * r + e3)
554 * r + e2) * r + e1) * r + e0) /
555 (((((((f7 * r + f6) * r + f5) * r + f4) * r + f3)
556 * r + f2) * r + f1) * r + 1);
557 }
558 if (q<0) quantile=-quantile;
559 }
560 }
561 return quantile;
562}
563
564
565
566
567G4double G4ErrorFunction::erfcx(G4double x)
568{
569 if (x >= 0) {
570 if (x > 50) { // continued-fraction expansion is faster
571 const G4double ispi = 1./std::sqrt(CLHEP::pi); //0.56418958354775628694807945156; // 1 / sqrt(pi)
572 if (x > 5e7) // 1-term expansion, important to avoid overflow
573 return ispi / x;
574 /* 5-term expansion (rely on compiler for CSE), simplified from:
575 ispi / (x+0.5/(x+1/(x+1.5/(x+2/x)))) */
576 return ispi*((x*x) * (x*x+4.5) + 2) / (x * ((x*x) * (x*x+5) + 3.75));
577 }
578 return erfcx_y100(400/(4+x));
579 }
580 else
581 return x < -26.7 ? HUGE_VAL : (x < -6.1 ? 2*std::exp(x*x)
582 : 2*std::exp(x*x) - erfcx_y100(400/(4-x)));
583}
584
585
586G4double G4ErrorFunction::erfc(G4double x) {
587 return 1.0 - std::erf(x);
588}
589
590
591G4double G4ErrorFunction::erfcWxy(G4double c, G4double x, G4double y) {
592 return c * ( erfc(x) - std::exp(-x*x) * erfcx(x+y) );
593}
594
595
596G4double G4ErrorFunction::Lambda(G4double x, G4double beta, G4double alphatilde) {
597 return std::exp(-beta*beta/x) * ( 1.0 - alphatilde * std::sqrt(CLHEP::pi * x) * erfcx(beta/std::sqrt(x) + alphatilde*std::sqrt(x)));
598}
599
600
601G4double G4ErrorFunction::erfcInv(G4double x) {
602 return - 0.70710678118654752440 * NormQuantile( 0.5 * x);
603}
604
605
a0
const G4double a0
Definition: G4IonCoulombCrossSection.cc:68
G4double
double G4double
Definition: G4Types.hh:83
G4ErrorFunction::Lambda
static G4double Lambda(G4double x, G4double beta, G4double alpha)
Definition: G4ErrorFunction.cc:596
G4ErrorFunction::~G4ErrorFunction
virtual ~G4ErrorFunction()
Definition: G4ErrorFunction.cc:61
G4ErrorFunction::erfcx_y100
static G4double erfcx_y100(G4double x)
Definition: G4ErrorFunction.cc:65
G4ErrorFunction::erfcx
static G4double erfcx(G4double x)
Definition: G4ErrorFunction.cc:567
G4ErrorFunction::erfcInv
static G4double erfcInv(G4double x)
Definition: G4ErrorFunction.cc:601
G4ErrorFunction::erfcWxy
static G4double erfcWxy(G4double c, G4double x, G4double y)
Definition: G4ErrorFunction.cc:591
G4ErrorFunction::erfc
static G4double erfc(G4double x)
Definition: G4ErrorFunction.cc:586
G4ErrorFunction::NormQuantile
static G4double NormQuantile(G4double x)
Definition: G4ErrorFunction.cc:476