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rys_roots.c
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/*
* Rys quadrature
Code is edited based on
* PyQuante quantum chemistry program suite http://pyquante.sourceforge.net
* BDF program package
Coefficients of Chebyshev polynomials are generated based on Toru Shiozaki's
integral project libslater
*/
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <float.h>
#include <math.h>
#include "cint_config.h"
#include "rys_roots.h"
#include "roots_for_x0.dat"
#ifdef HAVE_QUADMATH_H
#include <quadmath.h>
#endif
#define PIE4 0.78539816339744827900
#define THRESHOLD_ZERO (DBL_EPSILON * 8)
#define SMALLX_LIMIT 3e-7
static int rys_root1(double x, double *roots, double *weights);
static int rys_root2(double x, double *roots, double *weights);
static int rys_root3(double x, double *roots, double *weights);
static int rys_root4(double x, double *roots, double *weights);
static int rys_root5(double x, double *roots, double *weights);
typedef int QuadratureFunction(int n, double x, double lower, double *roots, double *weights);
#ifndef HAVE_QUADMATH_H
#define CINTqrys_schmidt CINTlrys_schmidt
#define CINTqrys_laguerre CINTlrys_laguerre
#define CINTqrys_jacobi CINTlrys_jacobi
#endif
int _CINT_polynomial_roots(double *roots, double *cs, int nroots);
static int segment_solve(int n, double x, double lower, double *u, double *w,
double breakpoint, QuadratureFunction fn1, QuadratureFunction fn2)
{
int error;
if (x <= breakpoint) {
error = fn1(n, x, lower, u, w);
} else {
error = fn2(n, x, lower, u, w);
}
if (error) {
error = CINTqrys_schmidt(n, x, lower, u, w);
}
return error;
}
void CINTrys_roots(int nroots, double x, double *u, double *w)
{
if (x <= SMALLX_LIMIT) {
int off = nroots * (nroots - 1) / 2;
int i;
for (i = 0; i < nroots; i++) {
u[i] = POLY_SMALLX_R0[off+i] + POLY_SMALLX_R1[off+i] * x;
w[i] = POLY_SMALLX_W0[off+i] + POLY_SMALLX_W1[off+i] * x;
}
return;
} else if (x >= 35+nroots*5) {
int off = nroots * (nroots - 1) / 2;
int i;
double rt;
double t = sqrt(PIE4/x);
for (i = 0; i < nroots; i++) {
rt = POLY_LARGEX_RT[off+i];
u[i] = rt / (x - rt);
w[i] = POLY_LARGEX_WW[off+i] * t;
}
return;
}
int err;
switch (nroots) {
case 1:
err = rys_root1(x, u, w);
break;
case 2:
err = rys_root2(x, u, w);
break;
case 3:
err = rys_root3(x, u, w);
break;
case 4:
err = rys_root4(x, u, w);
break;
case 5:
err = rys_root5(x, u, w);
break;
case 6: case 7:
err = segment_solve(nroots, x, 0., u, w, 11, CINTrys_jacobi, CINTrys_schmidt);
break;
case 8:
err = segment_solve(nroots, x, 0., u, w, 11, CINTrys_jacobi, CINTlrys_schmidt);
break;
case 9:
err = segment_solve(nroots, x, 0., u, w, 10, CINTlrys_jacobi, CINTlrys_laguerre);
break;
case 10: case 11:
err = segment_solve(nroots, x, 0., u, w, 18, CINTlrys_jacobi, CINTlrys_laguerre);
break;
case 12:
err = segment_solve(nroots, x, 0., u, w, 22, CINTlrys_jacobi, CINTlrys_laguerre);
break;
default:
err = segment_solve(nroots, x, 0., u, w, 50, CINTqrys_jacobi, CINTqrys_laguerre);
}
if (err) {
fprintf(stderr, "rys_roots fails: nroots=%d x=%g\n",
nroots, x);
#ifndef KEEP_GOING
exit(err);
#endif
}
}
/*
* lower is the lower bound of the sr integral
*/
static int segment_solve1(int n, double x, double lower, double *u, double *w,
double lower_bp1, double lower_bp2, double breakpoint,
QuadratureFunction fn1, QuadratureFunction fn2, QuadratureFunction fn3)
{
int error;
if (lower < lower_bp1) {
if (x <= breakpoint) {
error = fn1(n, x, lower, u, w);
} else {
error = fn2(n, x, lower, u, w);
}
} else if (lower < lower_bp2) {
error = fn3(n, x, lower, u, w);
} else {
return 1;
}
if (error) {
error = CINTqrys_schmidt(n, x, lower, u, w);
}
return error;
}
void CINTsr_rys_roots(int nroots, double x, double lower, double *u, double *w)
{
int err = 1;
switch (nroots) {
case 1:
err = CINTrys_schmidt(nroots, x, lower, u, w);
break;
case 2:
if (lower < 0.99) {
err = CINTrys_schmidt(nroots, x, lower, u, w);
} else {
err = CINTqrys_jacobi(nroots, x, lower, u, w);
}
break;
case 3:
#ifdef WITH_POLYNOMIAL_FIT
if (lower < 0.6) {
err = CINTsr_rys_polyfits(nroots, x, lower, u, w);
if (err == 0) {
break;;
}
}
#endif
if (lower < 0.93) {
err = CINTrys_schmidt(nroots, x, lower, u, w);
} else if (lower < 0.97) {
err = segment_solve(nroots, x, lower, u, w, 10, CINTlrys_jacobi, CINTlrys_laguerre);
} else {
err = CINTqrys_jacobi(nroots, x, lower, u, w);
}
break;
case 4:
#ifdef WITH_POLYNOMIAL_FIT
if (lower < 0.6) {
err = CINTsr_rys_polyfits(nroots, x, lower, u, w);
if (err == 0) {
break;;
}
}
#endif
if (lower < 0.8) {
err = CINTrys_schmidt(nroots, x, lower, u, w);
} else if (lower < 0.9) {
err = segment_solve(nroots, x, lower, u, w, 10, CINTlrys_jacobi, CINTlrys_laguerre);
} else {
err = CINTqrys_jacobi(nroots, x, lower, u, w);
}
break;
case 5:
#ifdef WITH_POLYNOMIAL_FIT
if (lower < 0.6) {
err = CINTsr_rys_polyfits(nroots, x, lower, u, w);
if (err == 0) {
break;;
}
}
#endif
if (lower < 0.4) {
err = segment_solve(nroots, x, lower, u, w, 50, CINTrys_schmidt, CINTlrys_laguerre);
} else if (lower < 0.8) {
err = segment_solve(nroots, x, lower, u, w, 10, CINTlrys_jacobi, CINTlrys_laguerre);
} else {
err = CINTqrys_jacobi(nroots, x, lower, u, w);
}
break;
case 6:
if (lower < 0.25) {
err = segment_solve(nroots, x, lower, u, w, 60, CINTrys_schmidt, CINTlrys_laguerre);
} else if (lower < 0.8) {
err = segment_solve(nroots, x, lower, u, w, 10, CINTlrys_jacobi, CINTlrys_laguerre);
} else {
err = CINTqrys_jacobi(nroots, x, lower, u, w);
}
break;
case 7:
err = segment_solve1(nroots, x, lower, u, w, 0.5, 1., 60, CINTlrys_jacobi, CINTlrys_laguerre, CINTqrys_jacobi);
break;
case 8: case 9: case 10:
//CINTqrys_jacobi(nroots, x, lower, u, w);
err = segment_solve1(nroots, x, lower, u, w, 0.15, 1., 60, CINTqrys_jacobi, CINTqrys_laguerre, CINTqrys_jacobi);
break;
case 11: case 12:
err = segment_solve1(nroots, x, lower, u, w, 0.15, 1., 60, CINTqrys_jacobi, CINTqrys_laguerre, CINTqrys_jacobi);
break;
case 13: case 14:
err = segment_solve1(nroots, x, lower, u, w, 0.25, 1., 60, CINTqrys_jacobi, CINTqrys_laguerre, CINTqrys_jacobi);
break;
case 15: case 16:
err = segment_solve1(nroots, x, lower, u, w, 0.25, 0.75, 60, CINTqrys_jacobi, CINTqrys_laguerre, CINTqrys_jacobi);
break;
case 17:
segment_solve1(nroots, x, lower, u, w, 0.25, 0.65, 60, CINTqrys_jacobi, CINTqrys_laguerre, CINTqrys_jacobi);
break;
case 18:
segment_solve1(nroots, x, lower, u, w, 0.15, 0.65, 60, CINTqrys_jacobi, CINTqrys_laguerre, CINTqrys_jacobi);
break;
case 19:
err = segment_solve1(nroots, x, lower, u, w, 0.15, 0.55, 60, CINTqrys_jacobi, CINTqrys_laguerre, CINTqrys_jacobi);
break;
case 20: case 21:
err = segment_solve1(nroots, x, lower, u, w, 0.25, 0.45, 60, CINTqrys_jacobi, CINTqrys_laguerre, CINTqrys_jacobi);
break;
case 22: case 23: case 24:
err = segment_solve1(nroots, x, lower, u, w, 0.25, 0.35, 60, CINTqrys_jacobi, CINTqrys_laguerre, CINTqrys_jacobi);
break;
default:
fprintf(stderr, "libcint SR-rys_roots does not support nroots=%d\n", nroots);
#ifndef KEEP_GOING
exit(1);
#endif
}
if (err) {
fprintf(stderr, "sr_rys_roots fails: nroots=%d x=%.15g lower=%.15g\n",
nroots, x, lower);
#ifndef KEEP_GOING
exit(err);
#endif
}
}
static int rys_root1(double X, double *roots, double *weights)
{
double Y, F1;
if (X > 33.) {
weights[0] = sqrt(PIE4/X);
roots[0] = 0.5E+00/(X-0.5E+00);
return 0;
} else if (X < 3.e-7) {
weights[0] = 1.0E+00 -X/3.0E+00;
roots[0] = 0.5E+00 -X/5.0E+00;
return 0;
}
double E = exp(-X);
if (X > 15.) {
Y = 1./X;
F1 = ((( 1.9623264149430E-01*Y-4.9695241464490E-01)*Y -
6.0156581186481E-05)* E + sqrt(PIE4/X) - E)*Y;
F1 *= .5;
} else if (X > 10.) {
Y = 1./X;
F1 = ((((-1.8784686463512E-01*Y+2.2991849164985E-01)*Y -
4.9893752514047E-01)*Y-2.1916512131607E-05)* E
+ sqrt(PIE4/X) - E)*Y;
F1 *= .5;
} else if (X > 5.) {
Y = 1./X;
F1 = ((((((( 4.6897511375022E-01*Y-6.9955602298985E-01)*Y +
5.3689283271887E-01)*Y-3.2883030418398E-01)*Y +
2.4645596956002E-01)*Y-4.9984072848436E-01)*Y -
3.1501078774085E-06)* E + sqrt(PIE4/X) - E)*Y;
F1 *= .5;
} else if (X > 3.){
Y = X-4.0E+00;
F1 = ((((((((((-2.62453564772299E-11*Y+3.24031041623823E-10 )*Y-
3.614965656163E-09)*Y+3.760256799971E-08)*Y-
3.553558319675E-07)*Y+3.022556449731E-06)*Y-
2.290098979647E-05)*Y+1.526537461148E-04)*Y-
8.81947375894379E-04 )*Y+4.33207949514611E-03 )*Y-
1.75257821619926E-02 )*Y+5.28406320615584E-02;
} else if (X > 1.) {
Y = X-2.0E+00;
F1 = ((((((((((-1.61702782425558E-10*Y+1.96215250865776E-09 )*Y-
2.14234468198419E-08 )*Y+2.17216556336318E-07 )*Y-
1.98850171329371E-06 )*Y+1.62429321438911E-05 )*Y-
1.16740298039895E-04 )*Y+7.24888732052332E-04 )*Y-
3.79490003707156E-03 )*Y+1.61723488664661E-02 )*Y-
5.29428148329736E-02 )*Y+1.15702180856167E-01;
} else {
F1 = ((((((((-8.36313918003957E-08*X+1.21222603512827E-06 )*X-
1.15662609053481E-05 )*X+9.25197374512647E-05 )*X-
6.40994113129432E-04 )*X+3.78787044215009E-03 )*X-
1.85185172458485E-02 )*X+7.14285713298222E-02 )*X-
1.99999999997023E-01 )*X+3.33333333333318E-01;
}
double WW1 = 2. * X * F1 + E;
weights[0] = WW1;
roots[0] = F1 / (WW1 - F1);
return 0;
}
static int rys_root2(double X, double *roots, double *weights)
{
double R12, R22, W22;
double RT1, RT2, WW1, WW2;
double F1, E, Y;
R12 = 2.75255128608411E-01;
R22 = 2.72474487139158E+00;
W22 = 9.17517095361369E-02;
if (X < 3.e-7){
RT1 = 1.30693606237085E-01 -2.90430236082028E-02 *X;
RT2 = 2.86930639376291E+00 -6.37623643058102E-01 *X;
WW1 = 6.52145154862545E-01 -1.22713621927067E-01 *X;
WW2 = 3.47854845137453E-01 -2.10619711404725E-01 *X;
} else if (X < 1.) {
F1 = ((((((((-8.36313918003957E-08*X+1.21222603512827E-06 )*X-
1.15662609053481E-05 )*X+9.25197374512647E-05 )*X-
6.40994113129432E-04 )*X+3.78787044215009E-03 )*X-
1.85185172458485E-02 )*X+7.14285713298222E-02 )*X-
1.99999999997023E-01 )*X+3.33333333333318E-01;
WW1 = (X+X)*F1+exp(-X);
RT1 = (((((((-2.35234358048491E-09*X+2.49173650389842E-08)*X-
4.558315364581E-08)*X-2.447252174587E-06)*X+
4.743292959463E-05)*X-5.33184749432408E-04 )*X+
4.44654947116579E-03 )*X-2.90430236084697E-02 )*X+
1.30693606237085E-01;
RT2 = (((((((-2.47404902329170E-08*X+2.36809910635906E-07)*X+
1.835367736310E-06)*X-2.066168802076E-05)*X-
1.345693393936E-04)*X-5.88154362858038E-05 )*X+
5.32735082098139E-02 )*X-6.37623643056745E-01 )*X+
2.86930639376289E+00;
WW2 = ((F1-WW1)*RT1+F1)*(1.0E+00+RT2)/(RT2-RT1);
WW1 = WW1-WW2;
} else if (X < 3.) {
Y = X-2.0E+00;
F1 = ((((((((((-1.61702782425558E-10*Y+1.96215250865776E-09 )*Y-
2.14234468198419E-08 )*Y+2.17216556336318E-07 )*Y-
1.98850171329371E-06 )*Y+1.62429321438911E-05 )*Y-
1.16740298039895E-04 )*Y+7.24888732052332E-04 )*Y-
3.79490003707156E-03 )*Y+1.61723488664661E-02 )*Y-
5.29428148329736E-02 )*Y+1.15702180856167E-01;
WW1 = (X+X)*F1+exp(-X);
RT1 = (((((((((-6.36859636616415E-12*Y+8.47417064776270E-11)*Y-
5.152207846962E-10)*Y-3.846389873308E-10)*Y+
8.472253388380E-08)*Y-1.85306035634293E-06 )*Y+
2.47191693238413E-05 )*Y-2.49018321709815E-04 )*Y+
2.19173220020161E-03 )*Y-1.63329339286794E-02 )*Y+
8.68085688285261E-02;
RT2 = ((((((((( 1.45331350488343E-10*Y+2.07111465297976E-09)*Y-
1.878920917404E-08)*Y-1.725838516261E-07)*Y+
2.247389642339E-06)*Y+9.76783813082564E-06 )*Y-
1.93160765581969E-04 )*Y-1.58064140671893E-03 )*Y+
4.85928174507904E-02 )*Y-4.30761584997596E-01 )*Y+
1.80400974537950E+00;
WW2 = ((F1-WW1)*RT1+F1)*(1.0E+00+RT2)/(RT2-RT1);
WW1 = WW1-WW2;
} else if (X < 5.){
Y = X-4.0E+00;
F1 = ((((((((((-2.62453564772299E-11*Y+3.24031041623823E-10 )*Y-
3.614965656163E-09)*Y+3.760256799971E-08)*Y-
3.553558319675E-07)*Y+3.022556449731E-06)*Y-
2.290098979647E-05)*Y+1.526537461148E-04)*Y-
8.81947375894379E-04 )*Y+4.33207949514611E-03 )*Y-
1.75257821619926E-02 )*Y+5.28406320615584E-02;
WW1 = (X+X)*F1+exp(-X);
RT1 = ((((((((-4.11560117487296E-12*Y+7.10910223886747E-11)*Y-
1.73508862390291E-09 )*Y+5.93066856324744E-08 )*Y-
9.76085576741771E-07 )*Y+1.08484384385679E-05 )*Y-
1.12608004981982E-04 )*Y+1.16210907653515E-03 )*Y-
9.89572595720351E-03 )*Y+6.12589701086408E-02;
RT2 = (((((((((-1.80555625241001E-10*Y+5.44072475994123E-10)*Y+
1.603498045240E-08)*Y-1.497986283037E-07)*Y-
7.017002532106E-07)*Y+1.85882653064034E-05 )*Y-
2.04685420150802E-05 )*Y-2.49327728643089E-03 )*Y+
3.56550690684281E-02 )*Y-2.60417417692375E-01 )*Y+
1.12155283108289E+00;
WW2 = ((F1-WW1)*RT1+F1)*(1.0E+00+RT2)/(RT2-RT1);
WW1 = WW1-WW2;
} else if (X < 10) {
E = exp(-X);
WW1 = (((((( 4.6897511375022E-01/X-6.9955602298985E-01)/X +
5.3689283271887E-01)/X-3.2883030418398E-01)/X +
2.4645596956002E-01)/X-4.9984072848436E-01)/X -
3.1501078774085E-06)*E + sqrt(PIE4/X);
F1 = (WW1-E)/(X+X);
Y = X-7.5E+00;
RT1 = (((((((((((((-1.43632730148572E-16*Y+2.38198922570405E-16)*
Y+1.358319618800E-14)*Y-7.064522786879E-14)*Y-
7.719300212748E-13)*Y+7.802544789997E-12)*Y+
6.628721099436E-11)*Y-1.775564159743E-09)*Y+
1.713828823990E-08)*Y-1.497500187053E-07)*Y+
2.283485114279E-06)*Y-3.76953869614706E-05 )*Y+
4.74791204651451E-04 )*Y-4.60448960876139E-03 )*Y+
3.72458587837249E-02;
RT2 = (((((((((((( 2.48791622798900E-14*Y-1.36113510175724E-13)*Y-
2.224334349799E-12)*Y+4.190559455515E-11)*Y-
2.222722579924E-10)*Y-2.624183464275E-09)*Y+
6.128153450169E-08)*Y-4.383376014528E-07)*Y-
2.49952200232910E-06 )*Y+1.03236647888320E-04 )*Y-
1.44614664924989E-03 )*Y+1.35094294917224E-02 )*Y-
9.53478510453887E-02 )*Y+5.44765245686790E-01;
WW2 = ((F1-WW1)*RT1+F1)*(1.0E+00+RT2)/(RT2-RT1);
WW1 = WW1-WW2;
} else if (X < 15) {
E = exp(-X);
WW1 = (((-1.8784686463512E-01/X+2.2991849164985E-01)/X -
4.9893752514047E-01)/X-2.1916512131607E-05)*E
+ sqrt(PIE4/X);
F1 = (WW1-E)/(X+X);
RT1 = ((((-1.01041157064226E-05*X+1.19483054115173E-03)*X -
6.73760231824074E-02)*X+1.25705571069895E+00)*X +
(((-8.57609422987199E+03/X+5.91005939591842E+03)/X -
1.70807677109425E+03)/X+2.64536689959503E+02)/X -
2.38570496490846E+01)*E + R12/(X-R12);
RT2 = ((( 3.39024225137123E-04*X-9.34976436343509E-02)*X -
4.22216483306320E+00)*X +
(((-2.08457050986847E+03/X -
1.04999071905664E+03)/X+3.39891508992661E+02)/X -
1.56184800325063E+02)/X+8.00839033297501E+00)*E + R22/(X-R22);
WW2 = ((F1-WW1)*RT1+F1)*(1.0E+00+RT2)/(RT2-RT1);
WW1 = WW1-WW2;
} else if (X < 33) {
E = exp(-X);
WW1 = (( 1.9623264149430E-01/X-4.9695241464490E-01)/X -
6.0156581186481E-05)*E + sqrt(PIE4/X);
F1 = (WW1-E)/(X+X);
RT1 = ((((-1.14906395546354E-06*X+1.76003409708332E-04)*X -
1.71984023644904E-02)*X-1.37292644149838E-01)*X +
(-4.75742064274859E+01/X+9.21005186542857E+00)/X -
2.31080873898939E-02)*E + R12/(X-R12);
RT2 = ((( 3.64921633404158E-04*X-9.71850973831558E-02)*X -
4.02886174850252E+00)*X +
(-1.35831002139173E+02/X -
8.66891724287962E+01)/X+2.98011277766958E+00)*E + R22/(X-R22);
WW2 = ((F1-WW1)*RT1+F1)*(1.0E+00+RT2)/(RT2-RT1);
WW1 = WW1-WW2;
} else if (X < 40) {
WW1 = sqrt(PIE4/X);
E = exp(-X);
RT1 = (-8.78947307498880E-01*X+1.09243702330261E+01)*E + R12/(X-R12);
RT2 = (-9.28903924275977E+00*X+8.10642367843811E+01)*E + R22/(X-R22);
WW2 = ( 4.46857389308400E+00*X-7.79250653461045E+01)*E + W22*WW1;
WW1 = WW1-WW2;
} else {
WW1 = sqrt(PIE4/X);
RT1 = R12/(X-R12);
RT2 = R22/(X-R22);
WW2 = W22*WW1;
WW1 = WW1-WW2;
}
roots[0] = RT1;
roots[1] = RT2;
weights[0] = WW1;
weights[1] = WW2;
return 0;
}
static int rys_root3(double X, double *roots, double *weights)
{
double R13, R23, W23, R33, W33;
double RT1, RT2, RT3, WW1, WW2, WW3;
double F1, F2, E, T1, T2, T3, A1, A2, Y;
R13 = 1.90163509193487E-01;
R23 = 1.78449274854325E+00;
W23 = 1.77231492083829E-01;
R33 = 5.52534374226326E+00;
W33 = 5.11156880411248E-03;
if (X < 3.e-7){
RT1 = 6.03769246832797E-02 -9.28875764357368E-03 *X;
RT2 = 7.76823355931043E-01 -1.19511285527878E-01 *X;
RT3 = 6.66279971938567E+00 -1.02504611068957E+00 *X;
WW1 = 4.67913934572691E-01 -5.64876917232519E-02 *X;
WW2 = 3.60761573048137E-01 -1.49077186455208E-01 *X;
WW3 = 1.71324492379169E-01 -1.27768455150979E-01 *X;
} else if (X < 1.) {
RT1 = ((((((-5.10186691538870E-10*X+2.40134415703450E-08)*X-
5.01081057744427E-07 )*X+7.58291285499256E-06 )*X-
9.55085533670919E-05 )*X+1.02893039315878E-03 )*X-
9.28875764374337E-03 )*X+6.03769246832810E-02;
RT2 = ((((((-1.29646524960555E-08*X+7.74602292865683E-08)*X+
1.56022811158727E-06 )*X-1.58051990661661E-05 )*X-
3.30447806384059E-04 )*X+9.74266885190267E-03 )*X-
1.19511285526388E-01 )*X+7.76823355931033E-01;
RT3 = ((((((-9.28536484109606E-09*X-3.02786290067014E-07)*X-
2.50734477064200E-06 )*X-7.32728109752881E-06 )*X+
2.44217481700129E-04 )*X+4.94758452357327E-02 )*X-
1.02504611065774E+00 )*X+6.66279971938553E+00;
F2 = ((((((((-7.60911486098850E-08*X+1.09552870123182E-06 )*X-
1.03463270693454E-05 )*X+8.16324851790106E-05 )*X-
5.55526624875562E-04 )*X+3.20512054753924E-03 )*X-
1.51515139838540E-02 )*X+5.55555554649585E-02 )*X-
1.42857142854412E-01 )*X+1.99999999999986E-01;
E = exp(-X);
F1 = ((X+X)*F2+E)/3.0E+00;
WW1 = (X+X)*F1+E;
T1 = RT1/(RT1+1.0E+00);
T2 = RT2/(RT2+1.0E+00);
T3 = RT3/(RT3+1.0E+00);
A2 = F2-T1*F1;
A1 = F1-T1*WW1;
WW3 = (A2-T2*A1)/((T3-T2)*(T3-T1));
WW2 = (T3*A1-A2)/((T3-T2)*(T2-T1));
WW1 = WW1-WW2-WW3;
} else if (X < 3.) {
Y = X-2.0E+00;
RT1 = (((((((( 1.44687969563318E-12*Y+4.85300143926755E-12)*Y-
6.55098264095516E-10 )*Y+1.56592951656828E-08 )*Y-
2.60122498274734E-07 )*Y+3.86118485517386E-06 )*Y-
5.13430986707889E-05 )*Y+6.03194524398109E-04 )*Y-
6.11219349825090E-03 )*Y+4.52578254679079E-02;
RT2 = ((((((( 6.95964248788138E-10*Y-5.35281831445517E-09)*Y-
6.745205954533E-08)*Y+1.502366784525E-06)*Y+
9.923326947376E-07)*Y-3.89147469249594E-04 )*Y+
7.51549330892401E-03 )*Y-8.48778120363400E-02 )*Y+
5.73928229597613E-01;
RT3 = ((((((((-2.81496588401439E-10*Y+3.61058041895031E-09)*Y+
4.53631789436255E-08 )*Y-1.40971837780847E-07 )*Y-
6.05865557561067E-06 )*Y-5.15964042227127E-05 )*Y+
3.34761560498171E-05 )*Y+5.04871005319119E-02 )*Y-
8.24708946991557E-01 )*Y+4.81234667357205E+00;
F2 = ((((((((((-1.48044231072140E-10*Y+1.78157031325097E-09 )*Y-
1.92514145088973E-08 )*Y+1.92804632038796E-07 )*Y-
1.73806555021045E-06 )*Y+1.39195169625425E-05 )*Y-
9.74574633246452E-05 )*Y+5.83701488646511E-04 )*Y-
2.89955494844975E-03 )*Y+1.13847001113810E-02 )*Y-
3.23446977320647E-02 )*Y+5.29428148329709E-02;
E = exp(-X);
F1 = ((X+X)*F2+E)/3.0E+00;
WW1 = (X+X)*F1+E;
T1 = RT1/(RT1+1.0E+00);
T2 = RT2/(RT2+1.0E+00);
T3 = RT3/(RT3+1.0E+00);
A2 = F2-T1*F1;
A1 = F1-T1*WW1;
WW3 = (A2-T2*A1)/((T3-T2)*(T3-T1));
WW2 = (T3*A1-A2)/((T3-T2)*(T2-T1));
WW1 = WW1-WW2-WW3;
} else if (X < 5.){
Y = X-4.0E+00;
RT1 = ((((((( 1.44265709189601E-11*Y-4.66622033006074E-10)*Y+
7.649155832025E-09)*Y-1.229940017368E-07)*Y+
2.026002142457E-06)*Y-2.87048671521677E-05 )*Y+
3.70326938096287E-04 )*Y-4.21006346373634E-03 )*Y+
3.50898470729044E-02;
RT2 = ((((((((-2.65526039155651E-11*Y+1.97549041402552E-10)*Y+
2.15971131403034E-09 )*Y-7.95045680685193E-08 )*Y+
5.15021914287057E-07 )*Y+1.11788717230514E-05 )*Y-
3.33739312603632E-04 )*Y+5.30601428208358E-03 )*Y-
5.93483267268959E-02 )*Y+4.31180523260239E-01;
RT3 = ((((((((-3.92833750584041E-10*Y-4.16423229782280E-09)*Y+
4.42413039572867E-08 )*Y+6.40574545989551E-07 )*Y-
3.05512456576552E-06 )*Y-1.05296443527943E-04 )*Y-
6.14120969315617E-04 )*Y+4.89665802767005E-02 )*Y-
6.24498381002855E-01 )*Y+3.36412312243724E+00;
F2 = ((((((((((-2.36788772599074E-11*Y+2.89147476459092E-10 )*Y-
3.18111322308846E-09 )*Y+3.25336816562485E-08 )*Y-
3.00873821471489E-07 )*Y+2.48749160874431E-06 )*Y-
1.81353179793672E-05 )*Y+1.14504948737066E-04 )*Y-
6.10614987696677E-04 )*Y+2.64584212770942E-03 )*Y-
8.66415899015349E-03 )*Y+1.75257821619922E-02;
E = exp(-X);
F1 = ((X+X)*F2+E)/3.0E+00;
WW1 = (X+X)*F1+E;
T1 = RT1/(RT1+1.0E+00);
T2 = RT2/(RT2+1.0E+00);
T3 = RT3/(RT3+1.0E+00);
A2 = F2-T1*F1;
A1 = F1-T1*WW1;
WW3 = (A2-T2*A1)/((T3-T2)*(T3-T1));
WW2 = (T3*A1-A2)/((T3-T2)*(T2-T1));
WW1 = WW1-WW2-WW3;
} else if (X < 10) {
E = exp(-X);
WW1 = (((((( 4.6897511375022E-01/X-6.9955602298985E-01)/X +
5.3689283271887E-01)/X-3.2883030418398E-01)/X +
2.4645596956002E-01)/X-4.9984072848436E-01)/X -
3.1501078774085E-06)*E + sqrt(PIE4/X);
F1 = (WW1-E)/(X+X);
F2 = (F1+F1+F1-E)/(X+X);
Y = X-7.5E+00;
RT1 = ((((((((((( 5.74429401360115E-16*Y+7.11884203790984E-16)*Y-
6.736701449826E-14)*Y-6.264613873998E-13)*Y+
1.315418927040E-11)*Y-4.23879635610964E-11 )*Y+
1.39032379769474E-09 )*Y-4.65449552856856E-08 )*Y+
7.34609900170759E-07 )*Y-1.08656008854077E-05 )*Y+
1.77930381549953E-04 )*Y-2.39864911618015E-03 )*Y+
2.39112249488821E-02;
RT2 = ((((((((((( 1.13464096209120E-14*Y+6.99375313934242E-15)*Y-
8.595618132088E-13)*Y-5.293620408757E-12)*Y-
2.492175211635E-11)*Y+2.73681574882729E-09 )*Y-
1.06656985608482E-08 )*Y-4.40252529648056E-07 )*Y+
9.68100917793911E-06 )*Y-1.68211091755327E-04 )*Y+
2.69443611274173E-03 )*Y-3.23845035189063E-02 )*Y+
2.75969447451882E-01;
RT3 = (((((((((((( 6.66339416996191E-15*Y+1.84955640200794E-13)*Y-
1.985141104444E-12)*Y-2.309293727603E-11)*Y+
3.917984522103E-10)*Y+1.663165279876E-09)*Y-
6.205591993923E-08)*Y+8.769581622041E-09)*Y+
8.97224398620038E-06 )*Y-3.14232666170796E-05 )*Y-
1.83917335649633E-03 )*Y+3.51246831672571E-02 )*Y-
3.22335051270860E-01 )*Y+1.73582831755430E+00;
T1 = RT1/(RT1+1.0E+00);
T2 = RT2/(RT2+1.0E+00);
T3 = RT3/(RT3+1.0E+00);
A2 = F2-T1*F1;
A1 = F1-T1*WW1;
WW3 = (A2-T2*A1)/((T3-T2)*(T3-T1));
WW2 = (T3*A1-A2)/((T3-T2)*(T2-T1));
WW1 = WW1-WW2-WW3;
} else if (X < 15) {
E = exp(-X);
WW1 = (((-1.8784686463512E-01/X+2.2991849164985E-01)/X -
4.9893752514047E-01)/X-2.1916512131607E-05)*E
+ sqrt(PIE4/X);
F1 = (WW1-E)/(X+X);
F2 = (F1+F1+F1-E)/(X+X);
Y = X-12.5E+00;
RT1 = ((((((((((( 4.42133001283090E-16*Y-2.77189767070441E-15)*Y-
4.084026087887E-14)*Y+5.379885121517E-13)*Y+
1.882093066702E-12)*Y-8.67286219861085E-11 )*Y+
7.11372337079797E-10 )*Y-3.55578027040563E-09 )*Y+
1.29454702851936E-07 )*Y-4.14222202791434E-06 )*Y+
8.04427643593792E-05 )*Y-1.18587782909876E-03 )*Y+
1.53435577063174E-02;
RT2 = ((((((((((( 6.85146742119357E-15*Y-1.08257654410279E-14)*Y-
8.579165965128E-13)*Y+6.642452485783E-12)*Y+
4.798806828724E-11)*Y-1.13413908163831E-09 )*Y+
7.08558457182751E-09 )*Y-5.59678576054633E-08 )*Y+
2.51020389884249E-06 )*Y-6.63678914608681E-05 )*Y+
1.11888323089714E-03 )*Y-1.45361636398178E-02 )*Y+
1.65077877454402E-01;
RT3 = (((((((((((( 3.20622388697743E-15*Y-2.73458804864628E-14)*Y-
3.157134329361E-13)*Y+8.654129268056E-12)*Y-
5.625235879301E-11)*Y-7.718080513708E-10)*Y+
2.064664199164E-08)*Y-1.567725007761E-07)*Y-
1.57938204115055E-06 )*Y+6.27436306915967E-05 )*Y-
1.01308723606946E-03 )*Y+1.13901881430697E-02 )*Y-
1.01449652899450E-01 )*Y+7.77203937334739E-01;
T1 = RT1/(RT1+1.0E+00);
T2 = RT2/(RT2+1.0E+00);
T3 = RT3/(RT3+1.0E+00);
A2 = F2-T1*F1;
A1 = F1-T1*WW1;
WW3 = (A2-T2*A1)/((T3-T2)*(T3-T1));
WW2 = (T3*A1-A2)/((T3-T2)*(T2-T1));
WW1 = WW1-WW2-WW3;
} else if (X < 33) {
E = exp(-X);
WW1 = (( 1.9623264149430E-01/X-4.9695241464490E-01)/X -
6.0156581186481E-05)*E + sqrt(PIE4/X);
F1 = (WW1-E)/(X+X);
F2 = (F1+F1+F1-E)/(X+X);
if (X < 20) {
RT1 = ((((((-2.43270989903742E-06*X+3.57901398988359E-04)*X -
2.34112415981143E-02)*X+7.81425144913975E-01)*X -
1.73209218219175E+01)*X+2.43517435690398E+02)*X +
(-1.97611541576986E+04/X+9.82441363463929E+03)/X -
2.07970687843258E+03)*E + R13/(X-R13);
RT2 = (((((-2.62627010965435E-04*X+3.49187925428138E-02)*X -
3.09337618731880E+00)*X+1.07037141010778E+02)*X -
2.36659637247087E+03)*X +
((-2.91669113681020E+06/X +
1.41129505262758E+06)/X-2.91532335433779E+05)/X +
3.35202872835409E+04)*E + R23/(X-R23);
RT3 = ((((( 9.31856404738601E-05*X-2.87029400759565E-02)*X -
7.83503697918455E-01)*X-1.84338896480695E+01)*X +
4.04996712650414E+02)*X +
(-1.89829509315154E+05/X +
5.11498390849158E+04)/X-6.88145821789955E+03)*E
+ R33/(X-R33);
} else {
RT1 = ((((-4.97561537069643E-04*X-5.00929599665316E-02)*X +
1.31099142238996E+00)*X-1.88336409225481E+01)*X -
6.60344754467191E+02 /X+1.64931462413877E+02)*E
+ R13/(X-R13);
RT2 = ((((-4.48218898474906E-03*X-5.17373211334924E-01)*X +
1.13691058739678E+01)*X-1.65426392885291E+02)*X -
6.30909125686731E+03 /X+1.52231757709236E+03)*E
+ R23/(X-R23);
RT3 = ((((-1.38368602394293E-02*X-1.77293428863008E+00)*X +
1.73639054044562E+01)*X-3.57615122086961E+02)*X -
1.45734701095912E+04 /X+2.69831813951849E+03)*E
+ R33/(X-R33);
}
T1 = RT1/(RT1+1.0E+00);
T2 = RT2/(RT2+1.0E+00);
T3 = RT3/(RT3+1.0E+00);
A2 = F2-T1*F1;
A1 = F1-T1*WW1;
WW3 = (A2-T2*A1)/((T3-T2)*(T3-T1));
WW2 = (T3*A1-A2)/((T3-T2)*(T2-T1));
WW1 = WW1-WW2-WW3;
} else if (X < 47) {
WW1 = sqrt(PIE4/X);
E = exp(-X);
RT1 = ((-7.39058467995275E+00*X+3.21318352526305E+02)*X -
3.99433696473658E+03)*E + R13/(X-R13);
RT2 = ((-7.38726243906513E+01*X+3.13569966333873E+03)*X -
3.86862867311321E+04)*E + R23/(X-R23);
RT3 = ((-2.63750565461336E+02*X+1.04412168692352E+04)*X -
1.28094577915394E+05)*E + R33/(X-R33);
WW3 = ((( 1.52258947224714E-01*X-8.30661900042651E+00)*X +
1.92977367967984E+02)*X-1.67787926005344E+03)*E
+ W33*WW1;
WW2 = (( 6.15072615497811E+01*X-2.91980647450269E+03)*X +
3.80794303087338E+04)*E + W23*WW1;
WW1 = WW1-WW2-WW3;
} else {
WW1 = sqrt(PIE4/X);
RT1 = R13/(X-R13);
RT2 = R23/(X-R23);
RT3 = R33/(X-R33);
WW2 = W23*WW1;
WW3 = W33*WW1;
WW1 = WW1-WW2-WW3;
}
roots[0] = RT1;
roots[1] = RT2;
roots[2] = RT3;
weights[0] = WW1;
weights[1] = WW2;
weights[2] = WW3;
return 0;
}
static int rys_root4(double X, double *roots, double *weights)
{
double R14, R24, W24, R34, W34, R44, W44;
double RT1, RT2, RT3, RT4, WW1, WW2, WW3, WW4;
double Y, E;
R14 = 1.45303521503316E-01;
R24 = 1.33909728812636E+00;
W24 = 2.34479815323517E-01;
R34 = 3.92696350135829E+00;
W34 = 1.92704402415764E-02;
R44 = 8.58863568901199E+00;
W44 = 2.25229076750736E-04;
if (X <= 3.0E-7) {
RT1 = 3.48198973061471E-02 -4.09645850660395E-03 *X;
RT2 = 3.81567185080042E-01 -4.48902570656719E-02 *X;
RT3 = 1.73730726945891E+00 -2.04389090547327E-01 *X;
RT4 = 1.18463056481549E+01 -1.39368301742312E+00 *X;
WW1 = 3.62683783378362E-01 -3.13844305713928E-02 *X;
WW2 = 3.13706645877886E-01 -8.98046242557724E-02 *X;
WW3 = 2.22381034453372E-01 -1.29314370958973E-01 *X;
WW4 = 1.01228536290376E-01 -8.28299075414321E-02 *X;
} else if (X <= 1.0) {
RT1 = ((((((-1.95309614628539E-10*X+5.19765728707592E-09)*X-
1.01756452250573E-07 )*X+1.72365935872131E-06 )*X-
2.61203523522184E-05 )*X+3.52921308769880E-04 )*X-
4.09645850658433E-03 )*X+3.48198973061469E-02;
RT2 = (((((-1.89554881382342E-08*X+3.07583114342365E-07)*X+
1.270981734393E-06)*X-1.417298563884E-04)*X+
3.226979163176E-03)*X-4.48902570678178E-02 )*X+
3.81567185080039E-01;
RT3 = (((((( 1.77280535300416E-09*X+3.36524958870615E-08)*X-
2.58341529013893E-07 )*X-1.13644895662320E-05 )*X-
7.91549618884063E-05 )*X+1.03825827346828E-02 )*X-
2.04389090525137E-01 )*X+1.73730726945889E+00;
RT4 = (((((-5.61188882415248E-08*X-2.49480733072460E-07)*X+
3.428685057114E-06)*X+1.679007454539E-04)*X+
4.722855585715E-02)*X-1.39368301737828E+00 )*X+
1.18463056481543E+01;
WW1 = ((((((-1.14649303201279E-08*X+1.88015570196787E-07)*X-
2.33305875372323E-06 )*X+2.68880044371597E-05 )*X-
2.94268428977387E-04 )*X+3.06548909776613E-03 )*X-
3.13844305680096E-02 )*X+3.62683783378335E-01;
WW2 = ((((((((-4.11720483772634E-09*X+6.54963481852134E-08)*X-
7.20045285129626E-07 )*X+6.93779646721723E-06 )*X-
6.05367572016373E-05 )*X+4.74241566251899E-04 )*X-
3.26956188125316E-03 )*X+1.91883866626681E-02 )*X-
8.98046242565811E-02 )*X+3.13706645877886E-01;
WW3 = ((((((((-3.41688436990215E-08*X+5.07238960340773E-07)*X-
5.01675628408220E-06 )*X+4.20363420922845E-05 )*X-
3.08040221166823E-04 )*X+1.94431864731239E-03 )*X-
1.02477820460278E-02 )*X+4.28670143840073E-02 )*X-
1.29314370962569E-01 )*X+2.22381034453369E-01;
WW4 = ((((((((( 4.99660550769508E-09*X-7.94585963310120E-08)*X+
8.359072409485E-07)*X-7.422369210610E-06)*X+
5.763374308160E-05)*X-3.86645606718233E-04 )*X+
2.18417516259781E-03 )*X-9.99791027771119E-03 )*X+
3.48791097377370E-02 )*X-8.28299075413889E-02 )*X+
1.01228536290376E-01;
} else if (X <= 5) {
Y = X-3.0E+00;
RT1 = (((((((((-1.48570633747284E-15*Y-1.33273068108777E-13)*Y+
4.068543696670E-12)*Y-9.163164161821E-11)*Y+
2.046819017845E-09)*Y-4.03076426299031E-08 )*Y+
7.29407420660149E-07 )*Y-1.23118059980833E-05 )*Y+
1.88796581246938E-04 )*Y-2.53262912046853E-03 )*Y+
2.51198234505021E-02;
RT2 = ((((((((( 1.35830583483312E-13*Y-2.29772605964836E-12)*Y-
3.821500128045E-12)*Y+6.844424214735E-10)*Y-
1.048063352259E-08)*Y+1.50083186233363E-08 )*Y+
3.48848942324454E-06 )*Y-1.08694174399193E-04 )*Y+
2.08048885251999E-03 )*Y-2.91205805373793E-02 )*Y+
2.72276489515713E-01;
RT3 = ((((((((( 5.02799392850289E-13*Y+1.07461812944084E-11)*Y-
1.482277886411E-10)*Y-2.153585661215E-09)*Y+
3.654087802817E-08)*Y+5.15929575830120E-07 )*Y-
9.52388379435709E-06 )*Y-2.16552440036426E-04 )*Y+
9.03551469568320E-03 )*Y-1.45505469175613E-01 )*Y+
1.21449092319186E+00;
RT4 = (((((((((-1.08510370291979E-12*Y+6.41492397277798E-11)*Y+
7.542387436125E-10)*Y-2.213111836647E-09)*Y-
1.448228963549E-07)*Y-1.95670833237101E-06 )*Y-
1.07481314670844E-05 )*Y+1.49335941252765E-04 )*Y+
4.87791531990593E-02 )*Y-1.10559909038653E+00 )*Y+
8.09502028611780E+00;
WW1 = ((((((((((-4.65801912689961E-14*Y+7.58669507106800E-13)*Y-
1.186387548048E-11)*Y+1.862334710665E-10)*Y-
2.799399389539E-09)*Y+4.148972684255E-08)*Y-
5.933568079600E-07)*Y+8.168349266115E-06)*Y-
1.08989176177409E-04 )*Y+1.41357961729531E-03 )*Y-
1.87588361833659E-02 )*Y+2.89898651436026E-01;
WW2 = ((((((((((((-1.46345073267549E-14*Y+2.25644205432182E-13)*Y-
3.116258693847E-12)*Y+4.321908756610E-11)*Y-
5.673270062669E-10)*Y+7.006295962960E-09)*Y-
8.120186517000E-08)*Y+8.775294645770E-07)*Y-
8.77829235749024E-06 )*Y+8.04372147732379E-05 )*Y-
6.64149238804153E-04 )*Y+4.81181506827225E-03 )*Y-
2.88982669486183E-02 )*Y+1.56247249979288E-01;
WW3 = ((((((((((((( 9.06812118895365E-15*Y-1.40541322766087E-13)*
Y+1.919270015269E-12)*Y-2.605135739010E-11)*Y+
3.299685839012E-10)*Y-3.86354139348735E-09 )*Y+
4.16265847927498E-08 )*Y-4.09462835471470E-07 )*Y+
3.64018881086111E-06 )*Y-2.88665153269386E-05 )*Y+
2.00515819789028E-04 )*Y-1.18791896897934E-03 )*Y+
5.75223633388589E-03 )*Y-2.09400418772687E-02 )*Y+
4.85368861938873E-02;
WW4 = ((((((((((((((-9.74835552342257E-16*Y+1.57857099317175E-14)*
Y-2.249993780112E-13)*Y+3.173422008953E-12)*Y-
4.161159459680E-11)*Y+5.021343560166E-10)*Y-
5.545047534808E-09)*Y+5.554146993491E-08)*Y-
4.99048696190133E-07 )*Y+3.96650392371311E-06 )*Y-
2.73816413291214E-05 )*Y+1.60106988333186E-04 )*Y-
7.64560567879592E-04 )*Y+2.81330044426892E-03 )*Y-
7.16227030134947E-03 )*Y+9.66077262223353E-03;
} else if (X <= 10.0) {
Y = X-7.5E+00;
RT1 = ((((((((( 4.64217329776215E-15*Y-6.27892383644164E-15)*Y+
3.462236347446E-13)*Y-2.927229355350E-11)*Y+
5.090355371676E-10)*Y-9.97272656345253E-09 )*Y+
2.37835295639281E-07 )*Y-4.60301761310921E-06 )*Y+
8.42824204233222E-05 )*Y-1.37983082233081E-03 )*Y+
1.66630865869375E-02;
RT2 = ((((((((( 2.93981127919047E-14*Y+8.47635639065744E-13)*Y-
1.446314544774E-11)*Y-6.149155555753E-12)*Y+
8.484275604612E-10)*Y-6.10898827887652E-08 )*Y+
2.39156093611106E-06 )*Y-5.35837089462592E-05 )*Y+
1.00967602595557E-03 )*Y-1.57769317127372E-02 )*Y+
1.74853819464285E-01;
RT3 = (((((((((( 2.93523563363000E-14*Y-6.40041776667020E-14)*Y-
2.695740446312E-12)*Y+1.027082960169E-10)*Y-
5.822038656780E-10)*Y-3.159991002539E-08)*Y+
4.327249251331E-07)*Y+4.856768455119E-06)*Y-
2.54617989427762E-04 )*Y+5.54843378106589E-03 )*Y-
7.95013029486684E-02 )*Y+7.20206142703162E-01;
RT4 = (((((((((((-1.62212382394553E-14*Y+7.68943641360593E-13)*Y+
5.764015756615E-12)*Y-1.380635298784E-10)*Y-
1.476849808675E-09)*Y+1.84347052385605E-08 )*Y+
3.34382940759405E-07 )*Y-1.39428366421645E-06 )*Y-
7.50249313713996E-05 )*Y-6.26495899187507E-04 )*Y+
4.69716410901162E-02 )*Y-6.66871297428209E-01 )*Y+
4.11207530217806E+00;
WW1 = ((((((((((-1.65995045235997E-15*Y+6.91838935879598E-14)*Y-
9.131223418888E-13)*Y+1.403341829454E-11)*Y-
3.672235069444E-10)*Y+6.366962546990E-09)*Y-
1.039220021671E-07)*Y+1.959098751715E-06)*Y-
3.33474893152939E-05 )*Y+5.72164211151013E-04 )*Y-
1.05583210553392E-02 )*Y+2.26696066029591E-01;
WW2 = ((((((((((((-3.57248951192047E-16*Y+6.25708409149331E-15)*Y-
9.657033089714E-14)*Y+1.507864898748E-12)*Y-
2.332522256110E-11)*Y+3.428545616603E-10)*Y-
4.698730937661E-09)*Y+6.219977635130E-08)*Y-
7.83008889613661E-07 )*Y+9.08621687041567E-06 )*Y-
9.86368311253873E-05 )*Y+9.69632496710088E-04 )*Y-
8.14594214284187E-03 )*Y+8.50218447733457E-02;
WW3 = ((((((((((((( 1.64742458534277E-16*Y-2.68512265928410E-15)*
Y+3.788890667676E-14)*Y-5.508918529823E-13)*Y+
7.555896810069E-12)*Y-9.69039768312637E-11 )*Y+
1.16034263529672E-09 )*Y-1.28771698573873E-08 )*Y+
1.31949431805798E-07 )*Y-1.23673915616005E-06 )*Y+
1.04189803544936E-05 )*Y-7.79566003744742E-05 )*Y+
5.03162624754434E-04 )*Y-2.55138844587555E-03 )*Y+
1.13250730954014E-02;
WW4 = ((((((((((((((-1.55714130075679E-17*Y+2.57193722698891E-16)*
Y-3.626606654097E-15)*Y+5.234734676175E-14)*Y-
7.067105402134E-13)*Y+8.793512664890E-12)*Y-
1.006088923498E-10)*Y+1.050565098393E-09)*Y-
9.91517881772662E-09 )*Y+8.35835975882941E-08 )*Y-
6.19785782240693E-07 )*Y+3.95841149373135E-06 )*Y-
2.11366761402403E-05 )*Y+9.00474771229507E-05 )*Y-
2.78777909813289E-04 )*Y+5.26543779837487E-04;
} else if (X <= 15) {
Y = X-12.5E+00;
RT1 = ((((((((((( 4.94869622744119E-17*Y+8.03568805739160E-16)*Y-
5.599125915431E-15)*Y-1.378685560217E-13)*Y+
7.006511663249E-13)*Y+1.30391406991118E-11 )*Y+
8.06987313467541E-11 )*Y-5.20644072732933E-09 )*Y+
7.72794187755457E-08 )*Y-1.61512612564194E-06 )*Y+
4.15083811185831E-05 )*Y-7.87855975560199E-04 )*Y+
1.14189319050009E-02;
RT2 = ((((((((((( 4.89224285522336E-16*Y+1.06390248099712E-14)*Y-
5.446260182933E-14)*Y-1.613630106295E-12)*Y+
3.910179118937E-12)*Y+1.90712434258806E-10 )*Y+
8.78470199094761E-10 )*Y-5.97332993206797E-08 )*Y+
9.25750831481589E-07 )*Y-2.02362185197088E-05 )*Y+
4.92341968336776E-04 )*Y-8.68438439874703E-03 )*Y+
1.15825965127958E-01;
RT3 = (((((((((( 6.12419396208408E-14*Y+1.12328861406073E-13)*Y-
9.051094103059E-12)*Y-4.781797525341E-11)*Y+
1.660828868694E-09)*Y+4.499058798868E-10)*Y-
2.519549641933E-07)*Y+4.977444040180E-06)*Y-
1.25858350034589E-04 )*Y+2.70279176970044E-03 )*Y-
3.99327850801083E-02 )*Y+4.33467200855434E-01;
RT4 = ((((((((((( 4.63414725924048E-14*Y-4.72757262693062E-14)*Y-
1.001926833832E-11)*Y+6.074107718414E-11)*Y+
1.576976911942E-09)*Y-2.01186401974027E-08 )*Y-
1.84530195217118E-07 )*Y+5.02333087806827E-06 )*Y+
9.66961790843006E-06 )*Y-1.58522208889528E-03 )*Y+
2.80539673938339E-02 )*Y-2.78953904330072E-01 )*Y+
1.82835655238235E+00;
WW4 = ((((((((((((( 2.90401781000996E-18*Y-4.63389683098251E-17)*
Y+6.274018198326E-16)*Y-8.936002188168E-15)*Y+
1.194719074934E-13)*Y-1.45501321259466E-12 )*Y+
1.64090830181013E-11 )*Y-1.71987745310181E-10 )*Y+
1.63738403295718E-09 )*Y-1.39237504892842E-08 )*Y+
1.06527318142151E-07 )*Y-7.27634957230524E-07 )*Y+
4.12159381310339E-06 )*Y-1.74648169719173E-05 )*Y+
8.50290130067818E-05;
WW3 = ((((((((((((-4.19569145459480E-17*Y+5.94344180261644E-16)*Y-
1.148797566469E-14)*Y+1.881303962576E-13)*Y-
2.413554618391E-12)*Y+3.372127423047E-11)*Y-
4.933988617784E-10)*Y+6.116545396281E-09)*Y-
6.69965691739299E-08 )*Y+7.52380085447161E-07 )*Y-
8.08708393262321E-06 )*Y+6.88603417296672E-05 )*Y-
4.67067112993427E-04 )*Y+5.42313365864597E-03;
WW2 = ((((((((((-6.22272689880615E-15*Y+1.04126809657554E-13)*Y-
6.842418230913E-13)*Y+1.576841731919E-11)*Y-
4.203948834175E-10)*Y+6.287255934781E-09)*Y-
8.307159819228E-08)*Y+1.356478091922E-06)*Y-
2.08065576105639E-05 )*Y+2.52396730332340E-04 )*Y-
2.94484050194539E-03 )*Y+6.01396183129168E-02;
WW1 = (((-1.8784686463512E-01/X+2.2991849164985E-01)/X -
4.9893752514047E-01)/X-2.1916512131607E-05)*exp(-X) +
sqrt(PIE4/X)-WW4-WW3-WW2;
} else if (X <= 20) {
WW1 = sqrt(PIE4/X);
Y = X-17.5E+00;
RT1 = ((((((((((( 4.36701759531398E-17*Y-1.12860600219889E-16)*Y-
6.149849164164E-15)*Y+5.820231579541E-14)*Y+
4.396602872143E-13)*Y-1.24330365320172E-11 )*Y+
6.71083474044549E-11 )*Y+2.43865205376067E-10 )*Y+
1.67559587099969E-08 )*Y-9.32738632357572E-07 )*Y+
2.39030487004977E-05 )*Y-4.68648206591515E-04 )*Y+
8.34977776583956E-03;
RT2 = ((((((((((( 4.98913142288158E-16*Y-2.60732537093612E-16)*Y-
7.775156445127E-14)*Y+5.766105220086E-13)*Y+
6.432696729600E-12)*Y-1.39571683725792E-10 )*Y+
5.95451479522191E-10 )*Y+2.42471442836205E-09 )*Y+
2.47485710143120E-07 )*Y-1.14710398652091E-05 )*Y+