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Diffstat (limited to 'gsl-1.9/specfunc/synchrotron.c')
-rw-r--r-- | gsl-1.9/specfunc/synchrotron.c | 285 |
1 files changed, 285 insertions, 0 deletions
diff --git a/gsl-1.9/specfunc/synchrotron.c b/gsl-1.9/specfunc/synchrotron.c new file mode 100644 index 0000000..d52b7b3 --- /dev/null +++ b/gsl-1.9/specfunc/synchrotron.c @@ -0,0 +1,285 @@ +/* specfunc/synchrotron.c + * + * Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU General Public License as published by + * the Free Software Foundation; either version 2 of the License, or (at + * your option) any later version. + * + * This program is distributed in the hope that it will be useful, but + * WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + * General Public License for more details. + * + * You should have received a copy of the GNU General Public License + * along with this program; if not, write to the Free Software + * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. + */ + +/* Author: G. Jungman */ + +#include <config.h> +#include <gsl/gsl_math.h> +#include <gsl/gsl_errno.h> +#include <gsl/gsl_sf_exp.h> +#include <gsl/gsl_sf_pow_int.h> +#include <gsl/gsl_sf_synchrotron.h> + +#include "error.h" + +#include "chebyshev.h" +#include "cheb_eval.c" + +static double synchrotron1_data[13] = { + 30.364682982501076273, + 17.079395277408394574, + 4.560132133545072889, + 0.549281246730419979, + 0.372976075069301172e-01, + 0.161362430201041242e-02, + 0.481916772120371e-04, + 0.10512425288938e-05, + 0.174638504670e-07, + 0.22815486544e-09, + 0.240443082e-11, + 0.2086588e-13, + 0.15167e-15 +}; +static cheb_series synchrotron1_cs = { + synchrotron1_data, + 12, + -1.0, 1.0, + 9 +}; + +static double synchrotron2_data[12] = { + 0.4490721623532660844, + 0.898353677994187218e-01, + 0.81044573772151290e-02, + 0.4261716991089162e-03, + 0.147609631270746e-04, + 0.3628633615300e-06, + 0.66634807498e-08, + 0.949077166e-10, + 0.1079125e-11, + 0.10022e-13, + 0.77e-16, + 0.5e-18 +}; +static cheb_series synchrotron2_cs = { + synchrotron2_data, + 11, + -1.0, 1.0, + 7 +}; + +static double synchrotron1a_data[23] = { + 2.1329305161355000985, + 0.741352864954200240e-01, + 0.86968099909964198e-02, + 0.11703826248775692e-02, + 0.1645105798619192e-03, + 0.240201021420640e-04, + 0.35827756389389e-05, + 0.5447747626984e-06, + 0.838802856196e-07, + 0.13069882684e-07, + 0.2053099071e-08, + 0.325187537e-09, + 0.517914041e-10, + 0.83002988e-11, + 0.13352728e-11, + 0.2159150e-12, + 0.349967e-13, + 0.56994e-14, + 0.9291e-15, + 0.152e-15, + 0.249e-16, + 0.41e-17, + 0.7e-18 +}; +static cheb_series synchrotron1a_cs = { + synchrotron1a_data, + 22, + -1.0, 1.0, + 11 +}; + +static double synchrotron21_data[13] = { + 38.617839923843085480, + 23.037715594963734597, + 5.3802499868335705968, + 0.6156793806995710776, + 0.406688004668895584e-01, + 0.17296274552648414e-02, + 0.51061258836577e-04, + 0.110459595022e-05, + 0.18235530206e-07, + 0.2370769803e-09, + 0.24887296e-11, + 0.21529e-13, + 0.156e-15 +}; +static cheb_series synchrotron21_cs = { + synchrotron21_data, + 12, + -1.0, 1.0, + 9 +}; + +static double synchrotron22_data[13] = { + 7.9063148270660804288, + 3.1353463612853425684, + 0.4854879477453714538, + 0.394816675827237234e-01, + 0.19661622334808802e-02, + 0.659078932293042e-04, + 0.15857561349856e-05, + 0.286865301123e-07, + 0.4041202360e-09, + 0.45568444e-11, + 0.420459e-13, + 0.3232e-15, + 0.21e-17 +}; +static cheb_series synchrotron22_cs = { + synchrotron22_data, + 12, + -1.0, 1.0, + 8 +}; + +static double synchrotron2a_data[17] = { + 2.020337094170713600, + 0.10956237121807404e-01, + 0.8542384730114676e-03, + 0.723430242132822e-04, + 0.63124427962699e-05, + 0.5648193141174e-06, + 0.512832480138e-07, + 0.47196532914e-08, + 0.4380744214e-09, + 0.410268149e-10, + 0.38623072e-11, + 0.3661323e-12, + 0.348023e-13, + 0.33301e-14, + 0.319e-15, + 0.307e-16, + 0.3e-17 +}; +static cheb_series synchrotron2a_cs = { + synchrotron2a_data, + 16, + -1.0, 1.0, + 8 +}; + + +/*-*-*-*-*-*-*-*-*-*-*-* Functions with Error Codes *-*-*-*-*-*-*-*-*-*-*-*/ + +int gsl_sf_synchrotron_1_e(const double x, gsl_sf_result * result) +{ + /* CHECK_POINTER(result) */ + + if(x < 0.0) { + DOMAIN_ERROR(result); + } + else if(x < 2.0*M_SQRT2 * GSL_SQRT_DBL_EPSILON) { + /* BJG: added first order correction term. The taylor series + is S1(x) = ((4pi)/(sqrt(3)gamma(1/3))) * (x/2)^(1/3) + * (1 - (gamma(1/3)/2)*(x/2)^2/3 + (3/4) * (x/2)^2 ....) */ + double z = pow(x, 1.0/3.0); + double cf = 1 - 8.43812762813205e-01 * z * z; + result->val = 2.14952824153447863671 * z * cf; + result->err = GSL_DBL_EPSILON * result->val; + return GSL_SUCCESS; + } + else if(x <= 4.0) { + const double c0 = M_PI/M_SQRT3; + const double px = pow(x,1.0/3.0); + const double px11 = gsl_sf_pow_int(px,11); + const double t = x*x/8.0 - 1.0; + gsl_sf_result result_c1; + gsl_sf_result result_c2; + cheb_eval_e(&synchrotron1_cs, t, &result_c1); + cheb_eval_e(&synchrotron2_cs, t, &result_c2); + result->val = px * result_c1.val - px11 * result_c2.val - c0 * x; + result->err = px * result_c1.err + px11 * result_c2.err + c0 * x * GSL_DBL_EPSILON; + result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val); + return GSL_SUCCESS; + } + else if(x < -8.0*GSL_LOG_DBL_MIN/7.0) { + const double c0 = 0.2257913526447274323630976; /* log(sqrt(pi/2)) */ + const double t = (12.0 - x) / (x + 4.0); + gsl_sf_result result_c1; + cheb_eval_e(&synchrotron1a_cs, t, &result_c1); + result->val = sqrt(x) * result_c1.val * exp(c0 - x); + result->err = 2.0 * GSL_DBL_EPSILON * result->val * (fabs(c0-x)+1.0); + return GSL_SUCCESS; + } + else { + UNDERFLOW_ERROR(result); + } +} + + +int gsl_sf_synchrotron_2_e(const double x, gsl_sf_result * result) +{ + /* CHECK_POINTER(result) */ + + if(x < 0.0) { + DOMAIN_ERROR(result); + } + else if(x < 2.0*M_SQRT2*GSL_SQRT_DBL_EPSILON) { + /* BJG: added first order correction term. The taylor series + is S2(x) = ((2pi)/(sqrt(3)*gamma(1/3))) * (x/2)^(1/3) + * (1 - (gamma(1/3)/gamma(4/3))*(x/2)^(4/3) + (gamma(1/3)/gamma(4/3))*(x/2)^2...) */ + + double z = pow(x, 1.0/3.0); + double cf = 1 - 1.17767156510235e+00 * z * x; + result->val = 1.07476412076723931836 * z * cf ; + result->err = 2.0 * GSL_DBL_EPSILON * result->val; + return GSL_SUCCESS; + } + else if(x <= 4.0) { + const double px = pow(x, 1.0/3.0); + const double px5 = gsl_sf_pow_int(px,5); + const double t = x*x/8.0 - 1.0; + gsl_sf_result cheb1; + gsl_sf_result cheb2; + cheb_eval_e(&synchrotron21_cs, t, &cheb1); + cheb_eval_e(&synchrotron22_cs, t, &cheb2); + result->val = px * cheb1.val - px5 * cheb2.val; + result->err = px * cheb1.err + px5 * cheb2.err; + result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val); + return GSL_SUCCESS; + } + else if(x < -8.0*GSL_LOG_DBL_MIN/7.0) { + const double c0 = 0.22579135264472743236; /* log(sqrt(pi/2)) */ + const double t = (10.0 - x) / (x + 2.0); + gsl_sf_result cheb1; + cheb_eval_e(&synchrotron2a_cs, t, &cheb1); + result->val = sqrt(x) * exp(c0-x) * cheb1.val; + result->err = GSL_DBL_EPSILON * result->val * (fabs(c0-x)+1.0); + return GSL_SUCCESS; + } + else { + UNDERFLOW_ERROR(result); + } +} + +/*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/ + +#include "eval.h" + +double gsl_sf_synchrotron_1(const double x) +{ + EVAL_RESULT(gsl_sf_synchrotron_1_e(x, &result)); +} + +double gsl_sf_synchrotron_2(const double x) +{ + EVAL_RESULT(gsl_sf_synchrotron_2_e(x, &result)); +} |