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- /* specfunc/sinint.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 3 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 "gsl__config.h"
- #include "gsl_math.h"
- #include "gsl_errno.h"
- #include "gsl_sf_trig.h"
- #include "gsl_sf_expint.h"
- #include "gsl_specfunc__error.h"
- #include "gsl_specfunc__chebyshev.h"
- #include "gsl_specfunc__cheb_eval.c"
- /*-*-*-*-*-*-*-*-*-*-*-* Private Section *-*-*-*-*-*-*-*-*-*-*-*/
- /* based on SLATEC r9sifg.f, W. Fullerton */
- /*
- series for f1 on the interval 2.00000e-02 to 6.25000e-02
- with weighted error 2.82e-17
- log weighted error 16.55
- significant figures required 15.36
- decimal places required 17.20
- */
- static double f1_data[20] = {
- -0.1191081969051363610,
- -0.0247823144996236248,
- 0.0011910281453357821,
- -0.0000927027714388562,
- 0.0000093373141568271,
- -0.0000011058287820557,
- 0.0000001464772071460,
- -0.0000000210694496288,
- 0.0000000032293492367,
- -0.0000000005206529618,
- 0.0000000000874878885,
- -0.0000000000152176187,
- 0.0000000000027257192,
- -0.0000000000005007053,
- 0.0000000000000940241,
- -0.0000000000000180014,
- 0.0000000000000035063,
- -0.0000000000000006935,
- 0.0000000000000001391,
- -0.0000000000000000282
- };
- static cheb_series f1_cs = {
- f1_data,
- 19,
- -1, 1,
- 10
- };
- /*
- series for f2 on the interval 0.00000e+00 to 2.00000e-02
- with weighted error 4.32e-17
- log weighted error 16.36
- significant figures required 14.75
- decimal places required 17.10
- */
- static double f2_data[29] = {
- -0.0348409253897013234,
- -0.0166842205677959686,
- 0.0006752901241237738,
- -0.0000535066622544701,
- 0.0000062693421779007,
- -0.0000009526638801991,
- 0.0000001745629224251,
- -0.0000000368795403065,
- 0.0000000087202677705,
- -0.0000000022601970392,
- 0.0000000006324624977,
- -0.0000000001888911889,
- 0.0000000000596774674,
- -0.0000000000198044313,
- 0.0000000000068641396,
- -0.0000000000024731020,
- 0.0000000000009226360,
- -0.0000000000003552364,
- 0.0000000000001407606,
- -0.0000000000000572623,
- 0.0000000000000238654,
- -0.0000000000000101714,
- 0.0000000000000044259,
- -0.0000000000000019634,
- 0.0000000000000008868,
- -0.0000000000000004074,
- 0.0000000000000001901,
- -0.0000000000000000900,
- 0.0000000000000000432
- };
- static cheb_series f2_cs = {
- f2_data,
- 28,
- -1, 1,
- 14
- };
- /*
- series for g1 on the interval 2.00000e-02 to 6.25000e-02
- with weighted error 5.48e-17
- log weighted error 16.26
- significant figures required 15.47
- decimal places required 16.92
- */
- static double g1_data[21] = {
- -0.3040578798253495954,
- -0.0566890984597120588,
- 0.0039046158173275644,
- -0.0003746075959202261,
- 0.0000435431556559844,
- -0.0000057417294453025,
- 0.0000008282552104503,
- -0.0000001278245892595,
- 0.0000000207978352949,
- -0.0000000035313205922,
- 0.0000000006210824236,
- -0.0000000001125215474,
- 0.0000000000209088918,
- -0.0000000000039715832,
- 0.0000000000007690431,
- -0.0000000000001514697,
- 0.0000000000000302892,
- -0.0000000000000061400,
- 0.0000000000000012601,
- -0.0000000000000002615,
- 0.0000000000000000548
- };
- static cheb_series g1_cs = {
- g1_data,
- 20,
- -1, 1,
- 13
- };
- /*
- series for g2 on the interval 0.00000e+00 to 2.00000e-02
- with weighted error 5.01e-17
- log weighted error 16.30
- significant figures required 15.12
- decimal places required 17.07
- */
- static double g2_data[34] = {
- -0.0967329367532432218,
- -0.0452077907957459871,
- 0.0028190005352706523,
- -0.0002899167740759160,
- 0.0000407444664601121,
- -0.0000071056382192354,
- 0.0000014534723163019,
- -0.0000003364116512503,
- 0.0000000859774367886,
- -0.0000000238437656302,
- 0.0000000070831906340,
- -0.0000000022318068154,
- 0.0000000007401087359,
- -0.0000000002567171162,
- 0.0000000000926707021,
- -0.0000000000346693311,
- 0.0000000000133950573,
- -0.0000000000053290754,
- 0.0000000000021775312,
- -0.0000000000009118621,
- 0.0000000000003905864,
- -0.0000000000001708459,
- 0.0000000000000762015,
- -0.0000000000000346151,
- 0.0000000000000159996,
- -0.0000000000000075213,
- 0.0000000000000035970,
- -0.0000000000000017530,
- 0.0000000000000008738,
- -0.0000000000000004487,
- 0.0000000000000002397,
- -0.0000000000000001347,
- 0.0000000000000000801,
- -0.0000000000000000501
- };
- static cheb_series g2_cs = {
- g2_data,
- 33,
- -1, 1,
- 20
- };
- /* x >= 4.0 */
- static void fg_asymp(const double x, gsl_sf_result * f, gsl_sf_result * g)
- {
- /*
- xbig = sqrt (1.0/r1mach(3))
- xmaxf = exp (amin1(-alog(r1mach(1)), alog(r1mach(2))) - 0.01)
- xmaxg = 1.0/sqrt(r1mach(1))
- xbnd = sqrt(50.0)
- */
- const double xbig = 1.0/GSL_SQRT_DBL_EPSILON;
- const double xmaxf = 1.0/GSL_DBL_MIN;
- const double xmaxg = 1.0/GSL_SQRT_DBL_MIN;
- const double xbnd = 7.07106781187;
- const double x2 = x*x;
- if(x <= xbnd) {
- gsl_sf_result result_c1;
- gsl_sf_result result_c2;
- cheb_eval_e(&f1_cs, (1.0/x2-0.04125)/0.02125, &result_c1);
- cheb_eval_e(&g1_cs, (1.0/x2-0.04125)/0.02125, &result_c2);
- f->val = (1.0 + result_c1.val)/x;
- g->val = (1.0 + result_c2.val)/x2;
- f->err = result_c1.err/x + 2.0 * GSL_DBL_EPSILON * fabs(f->val);
- g->err = result_c2.err/x2 + 2.0 * GSL_DBL_EPSILON * fabs(g->val);
- }
- else if(x <= xbig) {
- gsl_sf_result result_c1;
- gsl_sf_result result_c2;
- cheb_eval_e(&f2_cs, 100.0/x2-1.0, &result_c1);
- cheb_eval_e(&g2_cs, 100.0/x2-1.0, &result_c2);
- f->val = (1.0 + result_c1.val)/x;
- g->val = (1.0 + result_c2.val)/x2;
- f->err = result_c1.err/x + 2.0 * GSL_DBL_EPSILON * fabs(f->val);
- g->err = result_c2.err/x2 + 2.0 * GSL_DBL_EPSILON * fabs(g->val);
- }
- else {
- f->val = (x < xmaxf ? 1.0/x : 0.0);
- g->val = (x < xmaxg ? 1.0/x2 : 0.0);
- f->err = 2.0 * GSL_DBL_EPSILON * fabs(f->val);
- g->err = 2.0 * GSL_DBL_EPSILON * fabs(g->val);
- }
- return;
- }
- /* based on SLATEC si.f, W. Fullerton
- series for si on the interval 0.00000e+00 to 1.60000e+01
- with weighted error 1.22e-17
- log weighted error 16.91
- significant figures required 16.37
- decimal places required 17.45
- */
- static double si_data[12] = {
- -0.1315646598184841929,
- -0.2776578526973601892,
- 0.0354414054866659180,
- -0.0025631631447933978,
- 0.0001162365390497009,
- -0.0000035904327241606,
- 0.0000000802342123706,
- -0.0000000013562997693,
- 0.0000000000179440722,
- -0.0000000000001908387,
- 0.0000000000000016670,
- -0.0000000000000000122
- };
- static cheb_series si_cs = {
- si_data,
- 11,
- -1, 1,
- 9
- };
- /*
- series for ci on the interval 0.00000e+00 to 1.60000e+01
- with weighted error 1.94e-18
- log weighted error 17.71
- significant figures required 17.74
- decimal places required 18.27
- */
- static double ci_data[13] = {
- -0.34004281856055363156,
- -1.03302166401177456807,
- 0.19388222659917082877,
- -0.01918260436019865894,
- 0.00110789252584784967,
- -0.00004157234558247209,
- 0.00000109278524300229,
- -0.00000002123285954183,
- 0.00000000031733482164,
- -0.00000000000376141548,
- 0.00000000000003622653,
- -0.00000000000000028912,
- 0.00000000000000000194
- };
- static cheb_series ci_cs = {
- ci_data,
- 12,
- -1, 1,
- 9
- };
- /*-*-*-*-*-*-*-*-*-*-*-* Functions with Error Codes *-*-*-*-*-*-*-*-*-*-*-*/
- int gsl_sf_Si_e(const double x, gsl_sf_result * result)
- {
- double ax = fabs(x);
-
- /* CHECK_POINTER(result) */
- if(ax < GSL_SQRT_DBL_EPSILON) {
- result->val = x;
- result->err = 0.0;
- return GSL_SUCCESS;
- }
- else if(ax <= 4.0) {
- gsl_sf_result result_c;
- cheb_eval_e(&si_cs, (x*x-8.0)*0.125, &result_c);
- result->val = x * (0.75 + result_c.val);
- result->err = ax * result_c.err;
- result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
- return GSL_SUCCESS;
- }
- else {
- /* Note there is no loss of precision
- * here bcause of the leading constant.
- */
- gsl_sf_result f;
- gsl_sf_result g;
- fg_asymp(ax, &f, &g);
- result->val = 0.5 * M_PI - f.val*cos(ax) - g.val*sin(ax);
- result->err = f.err + g.err;
- result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
- if(x < 0.0) result->val = -result->val;
- return GSL_SUCCESS;
- }
- }
- int gsl_sf_Ci_e(const double x, gsl_sf_result * result)
- {
- /* CHECK_POINTER(result) */
- if(x <= 0.0) {
- DOMAIN_ERROR(result);
- }
- else if(x <= 4.0) {
- const double lx = log(x);
- const double y = (x*x-8.0)*0.125;
- gsl_sf_result result_c;
- cheb_eval_e(&ci_cs, y, &result_c);
- result->val = lx - 0.5 + result_c.val;
- result->err = 2.0 * GSL_DBL_EPSILON * (fabs(lx) + 0.5) + result_c.err;
- result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
- return GSL_SUCCESS;
- }
- else {
- gsl_sf_result sin_result;
- gsl_sf_result cos_result;
- int stat_sin = gsl_sf_sin_e(x, &sin_result);
- int stat_cos = gsl_sf_cos_e(x, &cos_result);
- gsl_sf_result f;
- gsl_sf_result g;
- fg_asymp(x, &f, &g);
- result->val = f.val*sin_result.val - g.val*cos_result.val;
- result->err = fabs(f.err*sin_result.val);
- result->err += fabs(g.err*cos_result.val);
- result->err += fabs(f.val*sin_result.err);
- result->err += fabs(g.val*cos_result.err);
- result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
- return GSL_ERROR_SELECT_2(stat_sin, stat_cos);
- }
- }
- /*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/
- #include "gsl_specfunc__eval.h"
- double gsl_sf_Si(const double x)
- {
- EVAL_RESULT(gsl_sf_Si_e(x, &result));
- }
- double gsl_sf_Ci(const double x)
- {
- EVAL_RESULT(gsl_sf_Ci_e(x, &result));
- }
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