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N_DEV_LTRA_Faddeeva.C
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1 //-------------------------------------------------------------------------
2 // Copyright Notice
3 //
4 // Copyright 2002 Sandia Corporation. Under the terms
5 // of Contract DE-AC04-94AL85000 with Sandia Corporation, the U.S.
6 // Government retains certain rights in this software.
7 //
8 // Xyce(TM) Parallel Electrical Simulator
9 // Copyright (C) 2002-2014 Sandia Corporation
10 //
11 // This program is free software: you can redistribute it and/or modify
12 // it under the terms of the GNU General Public License as published by
13 // the Free Software Foundation, either version 3 of the License, or
14 // (at your option) any later version.
15 //
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17 // but WITHOUT ANY WARRANTY; without even the implied warranty of
18 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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22 // along with this program. If not, see <http://www.gnu.org/licenses/>.
23 //-------------------------------------------------------------------------
24 
25 //-------------------------------------------------------------------------
26 // Filename : $RCSfile: N_DEV_LTRA_Faddeeva.C,v $
27 //
28 // Purpose :
29 //
30 // Special Notes :
31 //
32 // Creator : Gary Hennigan
33 //
34 // Creation Date : 12/07/2012
35 //
36 // Revision Information:
37 // ---------------------
38 //
39 // Revision Number: $Revision: 1.8 $
40 //
41 // Revision Date : $Date: 2014/03/19 17:23:29 $
42 //
43 // Current Owner : $Author: tvrusso $
44 //-------------------------------------------------------------------------
45 
46 // Copyright (c) 2012, 2013 Massachusetts Institute of Technology
47 //
48 // Permission is hereby granted, free of charge, to any person obtaining
49 // a copy of this software and associated documentation files (the
50 // "Software"), to deal in the Software without restriction, including
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53 // permit persons to whom the Software is furnished to do so, subject to
54 // the following conditions:
55 //
56 // The above copyright notice and this permission notice shall be
57 // included in all copies or substantial portions of the Software.
58 //
59 // THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
60 // EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
61 // MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
62 // NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
63 // LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
64 // OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
65 // WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
66 //
67 
68 // XYCE-NOTE: This file is, at present, only exists because of the Intel
69 // compilers on Windows not putting erfc() in the standard math library.
70 // Note also that this is a VERY stripped down version of what's
71 // available at the referenced website below.
72 //
73 
74 #include "N_DEV_LTRA_Faddeeva.h"
75 
76 // Available at: http://ab-initio.mit.edu/Faddeeva
77 
78 // Computes various error functions (erf, erfc, erfi, erfcx),
79 // including the Dawson integral, in the complex plane, based
80 // on algorithms for the computation of the Faddeeva function
81 // w(z) = exp(-z^2) * erfc(-i*z).
82 // Given w(z), the error functions are mostly straightforward
83 // to compute, except for certain regions where we have to
84 // switch to Taylor expansions to avoid cancellation errors
85 // [e.g. near the origin for erf(z)].
86 
87 // To compute the Faddeeva function, we use a combination of two
88 // algorithms:
89 
90 // For sufficiently large |z|, we use a continued-fraction expansion
91 // for w(z) similar to those described in:
92 
93 // Walter Gautschi, "Efficient computation of the complex error
94 // function," SIAM J. Numer. Anal. 7(1), pp. 187-198 (1970)
95 
96 // G. P. M. Poppe and C. M. J. Wijers, "More efficient computation
97 // of the complex error function," ACM Trans. Math. Soft. 16(1),
98 // pp. 38-46 (1990).
99 
100 // Unlike those papers, however, we switch to a completely different
101 // algorithm for smaller |z|:
102 
103 // Mofreh R. Zaghloul and Ahmed N. Ali, "Algorithm 916: Computing the
104 // Faddeyeva and Voigt Functions," ACM Trans. Math. Soft. 38(2), 15
105 // (2011).
106 
107 // (I initially used this algorithm for all z, but it turned out to be
108 // significantly slower than the continued-fraction expansion for
109 // larger |z|. On the other hand, it is competitive for smaller |z|,
110 // and is significantly more accurate than the Poppe & Wijers code
111 // in some regions, e.g. in the vicinity of z=1+1i.)
112 
113 // Note that this is an INDEPENDENT RE-IMPLEMENTATION of these algorithms,
114 // based on the description in the papers ONLY. In particular, I did
115 // not refer to the authors' Fortran or Matlab implementations, respectively,
116 // (which are under restrictive ACM copyright terms and therefore unusable
117 // in free/open-source software).
118 
119 // Steven G. Johnson, Massachusetts Institute of Technology
120 // http://math.mit.edu/~stevenj
121 // October 2012.
122 
123 // -- Note that Algorithm 916 assumes that the erfc(x) function,
124 // or rather the scaled function erfcx(x) = exp(x*x)*erfc(x),
125 // is supplied for REAL arguments x. I originally used an
126 // erfcx routine derived from DERFC in SLATEC, but I have
127 // since replaced it with a much faster routine written by
128 // me which uses a combination of continued-fraction expansions
129 // and a lookup table of Chebyshev polynomials. For speed,
130 // I implemented a similar algorithm for Im[w(x)] of real x,
131 // since this comes up frequently in the other error functions.
132 
133 // A small test program is included the end, which checks
134 // the w(z) etc. results against several known values. To compile
135 // the test function, compile with -DTEST_FADDEEVA (that is,
136 // #define TEST_FADDEEVA).
137 
138 // REVISION HISTORY:
139 // 4 October 2012: Initial public release (SGJ)
140 // 5 October 2012: Revised (SGJ) to fix spelling error,
141 // start summation for large x at round(x/a) (> 1)
142 // rather than ceil(x/a) as in the original
143 // paper, which should slightly improve performance
144 // (and, apparently, slightly improves accuracy)
145 // 19 October 2012: Revised (SGJ) to fix bugs for large x, large -y,
146 // and 15<x<26. Performance improvements. Prototype
147 // now supplies default value for relerr.
148 // 24 October 2012: Switch to continued-fraction expansion for
149 // sufficiently large z, for performance reasons.
150 // Also, avoid spurious overflow for |z| > 1e154.
151 // Set relerr argument to min(relerr,0.1).
152 // 27 October 2012: Enhance accuracy in Re[w(z)] taken by itself,
153 // by switching to Alg. 916 in a region near
154 // the real-z axis where continued fractions
155 // have poor relative accuracy in Re[w(z)]. Thanks
156 // to M. Zaghloul for the tip.
157 // 29 October 2012: Replace SLATEC-derived erfcx routine with
158 // completely rewritten code by me, using a very
159 // different algorithm which is much faster.
160 // 30 October 2012: Implemented special-case code for real z
161 // (where real part is exp(-x^2) and imag part is
162 // Dawson integral), using algorithm similar to erfx.
163 // Export ImFaddeeva_w function to make Dawson's
164 // integral directly accessible.
165 // 3 November 2012: Provide implementations of erf, erfc, erfcx,
166 // and Dawson functions in N_DEV_LTRA_Faddeeva:: namespace,
167 // in addition to N_DEV_LTRA_Faddeeva::w. Provide header
168 // file Faddeeva.hh.
169 // 4 November 2012: Slightly faster erf for real arguments.
170 // Updated MATLAB and Octave plugins.
171 
172 #include <cfloat>
173 #include <cmath>
174 
175 namespace Xyce {
176 namespace Device {
177 namespace Faddeeva {
178 
179 using namespace std;
180 
181 /////////////////////////////////////////////////////////////////////////
182 // Auxiliary routines to compute other special functions based on w(z)
183 
184 // compute the error function erf(x)
185 double erf(double x)
186 {
187  double mx2 = -x*x;
188  if (mx2 < -750) // underflow
189  return (x >= 0 ? 1.0 : -1.0);
190 
191  if (x >= 0) {
192  if (x < 5e-3) goto taylor;
193  return 1.0 - exp(mx2) * erfcx(x);
194  }
195  else { // x < 0
196  if (x > -5e-3) goto taylor;
197  return exp(mx2) * erfcx(-x) - 1.0;
198  }
199 
200  // Use Taylor series for small |x|, to avoid cancellation inaccuracy
201  // erf(x) = 2/sqrt(pi) * x * (1 - x^2/3 + x^4/10 - ...)
202  taylor:
203  return x * (1.1283791670955125739
204  + mx2 * (0.37612638903183752464
205  + mx2 * 0.11283791670955125739));
206 }
207 
208 // erfc(x) = 1 - erf(x)
209 double erfc(double x)
210 {
211  if (x*x > 750) // underflow
212  return (x >= 0 ? 0.0 : 2.0);
213  return x >= 0 ? exp(-x*x) * erfcx(x)
214  : 2. - exp(-x*x) * erfcx(-x);
215 }
216 
217 
218 
219 /////////////////////////////////////////////////////////////////////////
220 
221 // erfcx(x) = exp(x^2) erfc(x) function, for real x, written by
222 // Steven G. Johnson, October 2012.
223 
224 // This function combines a few different ideas.
225 
226 // First, for x > 50, it uses a continued-fraction expansion (same as
227 // for the Faddeeva function, but with algebraic simplifications for z=i*x).
228 
229 // Second, for 0 <= x <= 50, it uses Chebyshev polynomial approximations,
230 // but with two twists:
231 
232 // a) It maps x to y = 4 / (4+x) in [0,1]. This simple transformation,
233 // inspired by a similar transformation in the octave-forge/specfun
234 // erfcx by Soren Hauberg, results in much faster Chebyshev convergence
235 // than other simple transformations I have examined.
236 
237 // b) Instead of using a single Chebyshev polynomial for the entire
238 // [0,1] y interval, we break the interval up into 100 equal
239 // subintervals, with a switch/lookup table, and use much lower
240 // degree Chebyshev polynomials in each subinterval. This greatly
241 // improves performance in my tests.
242 
243 // For x < 0, we use the relationship erfcx(-x) = 2 exp(x^2) - erfc(x),
244 // with the usual checks for overflow etcetera.
245 
246 // Performance-wise, it seems to be substantially faster than either
247 // the SLATEC DERFC function [or an erfcx function derived therefrom]
248 // or Cody's CALERF function (from netlib.org/specfun), while
249 // retaining near machine precision in accuracy.
250 
251 // Given y100=100*y, where y = 4/(4+x) for x >= 0, compute erfc(x).
252 
253 // Uses a look-up table of 100 different Chebyshev polynomials
254 // for y intervals [0,0.01], [0.01,0.02], ...., [0.99,1], generated
255 // with the help of Maple and a little shell script. This allows
256 // the Chebyshev polynomials to be of significantly lower degree (about 1/4)
257 // compared to fitting the whole [0,1] interval with a single polynomial.
258 static double erfcx_y100(double y100)
259 {
260  switch ((int) y100) {
261 case 0: {
262 double t = 2*y100 - 1;
263 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;
264 }
265 case 1: {
266 double t = 2*y100 - 3;
267 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;
268 }
269 case 2: {
270 double t = 2*y100 - 5;
271 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;
272 }
273 case 3: {
274 double t = 2*y100 - 7;
275 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;
276 }
277 case 4: {
278 double t = 2*y100 - 9;
279 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;
280 }
281 case 5: {
282 double t = 2*y100 - 11;
283 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;
284 }
285 case 6: {
286 double t = 2*y100 - 13;
287 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;
288 }
289 case 7: {
290 double t = 2*y100 - 15;
291 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;
292 }
293 case 8: {
294 double t = 2*y100 - 17;
295 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;
296 }
297 case 9: {
298 double t = 2*y100 - 19;
299 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;
300 }
301 case 10: {
302 double t = 2*y100 - 21;
303 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;
304 }
305 case 11: {
306 double t = 2*y100 - 23;
307 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;
308 }
309 case 12: {
310 double t = 2*y100 - 25;
311 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;
312 }
313 case 13: {
314 double t = 2*y100 - 27;
315 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;
316 }
317 case 14: {
318 double t = 2*y100 - 29;
319 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;
320 }
321 case 15: {
322 double t = 2*y100 - 31;
323 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;
324 }
325 case 16: {
326 double t = 2*y100 - 33;
327 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;
328 }
329 case 17: {
330 double t = 2*y100 - 35;
331 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;
332 }
333 case 18: {
334 double t = 2*y100 - 37;
335 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;
336 }
337 case 19: {
338 double t = 2*y100 - 39;
339 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;
340 }
341 case 20: {
342 double t = 2*y100 - 41;
343 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;
344 }
345 case 21: {
346 double t = 2*y100 - 43;
347 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;
348 }
349 case 22: {
350 double t = 2*y100 - 45;
351 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;
352 }
353 case 23: {
354 double t = 2*y100 - 47;
355 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;
356 }
357 case 24: {
358 double t = 2*y100 - 49;
359 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;
360 }
361 case 25: {
362 double t = 2*y100 - 51;
363 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;
364 }
365 case 26: {
366 double t = 2*y100 - 53;
367 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;
368 }
369 case 27: {
370 double t = 2*y100 - 55;
371 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;
372 }
373 case 28: {
374 double t = 2*y100 - 57;
375 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;
376 }
377 case 29: {
378 double t = 2*y100 - 59;
379 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;
380 }
381 case 30: {
382 double t = 2*y100 - 61;
383 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;
384 }
385 case 31: {
386 double t = 2*y100 - 63;
387 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;
388 }
389 case 32: {
390 double t = 2*y100 - 65;
391 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;
392 }
393 case 33: {
394 double t = 2*y100 - 67;
395 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;
396 }
397 case 34: {
398 double t = 2*y100 - 69;
399 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;
400 }
401 case 35: {
402 double t = 2*y100 - 71;
403 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;
404 }
405 case 36: {
406 double t = 2*y100 - 73;
407 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;
408 }
409 case 37: {
410 double t = 2*y100 - 75;
411 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;
412 }
413 case 38: {
414 double t = 2*y100 - 77;
415 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;
416 }
417 case 39: {
418 double t = 2*y100 - 79;
419 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;
420 }
421 case 40: {
422 double t = 2*y100 - 81;
423 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;
424 }
425 case 41: {
426 double t = 2*y100 - 83;
427 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;
428 }
429 case 42: {
430 double t = 2*y100 - 85;
431 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;
432 }
433 case 43: {
434 double t = 2*y100 - 87;
435 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;
436 }
437 case 44: {
438 double t = 2*y100 - 89;
439 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;
440 }
441 case 45: {
442 double t = 2*y100 - 91;
443 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;
444 }
445 case 46: {
446 double t = 2*y100 - 93;
447 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;
448 }
449 case 47: {
450 double t = 2*y100 - 95;
451 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;
452 }
453 case 48: {
454 double t = 2*y100 - 97;
455 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;
456 }
457 case 49: {
458 double t = 2*y100 - 99;
459 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;
460 }
461 case 50: {
462 double t = 2*y100 - 101;
463 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;
464 }
465 case 51: {
466 double t = 2*y100 - 103;
467 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;
468 }
469 case 52: {
470 double t = 2*y100 - 105;
471 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;
472 }
473 case 53: {
474 double t = 2*y100 - 107;
475 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;
476 }
477 case 54: {
478 double t = 2*y100 - 109;
479 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;
480 }
481 case 55: {
482 double t = 2*y100 - 111;
483 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;
484 }
485 case 56: {
486 double t = 2*y100 - 113;
487 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;
488 }
489 case 57: {
490 double t = 2*y100 - 115;
491 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;
492 }
493 case 58: {
494 double t = 2*y100 - 117;
495 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;
496 }
497 case 59: {
498 double t = 2*y100 - 119;
499 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;
500 }
501 case 60: {
502 double t = 2*y100 - 121;
503 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;
504 }
505 case 61: {
506 double t = 2*y100 - 123;
507 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;
508 }
509 case 62: {
510 double t = 2*y100 - 125;
511 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;
512 }
513 case 63: {
514 double t = 2*y100 - 127;
515 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;
516 }
517 case 64: {
518 double t = 2*y100 - 129;
519 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;
520 }
521 case 65: {
522 double t = 2*y100 - 131;
523 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;
524 }
525 case 66: {
526 double t = 2*y100 - 133;
527 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;
528 }
529 case 67: {
530 double t = 2*y100 - 135;
531 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;
532 }
533 case 68: {
534 double t = 2*y100 - 137;
535 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;
536 }
537 case 69: {
538 double t = 2*y100 - 139;
539 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;
540 }
541 case 70: {
542 double t = 2*y100 - 141;
543 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;
544 }
545 case 71: {
546 double t = 2*y100 - 143;
547 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;
548 }
549 case 72: {
550 double t = 2*y100 - 145;
551 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;
552 }
553 case 73: {
554 double t = 2*y100 - 147;
555 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;
556 }
557 case 74: {
558 double t = 2*y100 - 149;
559 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;
560 }
561 case 75: {
562 double t = 2*y100 - 151;
563 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;
564 }
565 case 76: {
566 double t = 2*y100 - 153;
567 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;
568 }
569 case 77: {
570 double t = 2*y100 - 155;
571 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;
572 }
573 case 78: {
574 double t = 2*y100 - 157;
575 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;
576 }
577 case 79: {
578 double t = 2*y100 - 159;
579 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;
580 }
581 case 80: {
582 double t = 2*y100 - 161;
583 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;
584 }
585 case 81: {
586 double t = 2*y100 - 163;
587 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;
588 }
589 case 82: {
590 double t = 2*y100 - 165;
591 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;
592 }
593 case 83: {
594 double t = 2*y100 - 167;
595 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;
596 }
597 case 84: {
598 double t = 2*y100 - 169;
599 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;
600 }
601 case 85: {
602 double t = 2*y100 - 171;
603 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;
604 }
605 case 86: {
606 double t = 2*y100 - 173;
607 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;
608 }
609 case 87: {
610 double t = 2*y100 - 175;
611 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;
612 }
613 case 88: {
614 double t = 2*y100 - 177;
615 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;
616 }
617 case 89: {
618 double t = 2*y100 - 179;
619 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;
620 }
621 case 90: {
622 double t = 2*y100 - 181;
623 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;
624 }
625 case 91: {
626 double t = 2*y100 - 183;
627 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;
628 }
629 case 92: {
630 double t = 2*y100 - 185;
631 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;
632 }
633 case 93: {
634 double t = 2*y100 - 187;
635 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;
636 }
637 case 94: {
638 double t = 2*y100 - 189;
639 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;
640 }
641 case 95: {
642 double t = 2*y100 - 191;
643 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;
644 }
645 case 96: {
646 double t = 2*y100 - 193;
647 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;
648 }
649 case 97: {
650 double t = 2*y100 - 195;
651 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;
652 }
653 case 98: {
654 double t = 2*y100 - 197;
655 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;
656 }
657 case 99: {
658 double t = 2*y100 - 199;
659 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;
660 }
661  }
662  // we only get here if y = 1, i.e. |x| < 4*eps, in which case
663  // erfcx is within 1e-15 of 1..
664  return 1.0;
665 }
666 
667 double erfcx(double x)
668 {
669  if (x >= 0) {
670  if (x > 50) { // continued-fraction expansion is faster
671  const double ispi = 0.56418958354775628694807945156; // 1 / sqrt(pi)
672  if (x > 5e7) // 1-term expansion, important to avoid overflow
673  return ispi / x;
674  // 5-term expansion (rely on compiler for CSE), simplified from:
675  // ispi / (x+0.5/(x+1/(x+1.5/(x+2/x))))
676  return ispi*((x*x) * (x*x+4.5) + 2) / (x * ((x*x) * (x*x+5) + 3.75));
677  }
678  return erfcx_y100(400/(4+x));
679  }
680  else
681  return x < -26.7 ? HUGE_VAL : (x < -6.1 ? 2*exp(x*x)
682  : 2*exp(x*x) - erfcx_y100(400/(4-x)));
683 }
684 
685 } // namespace Faddeeva
686 } // namespace Device
687 } // namespace Xyce