/* 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 <config.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_errno.h>
#include <gsl/gsl_sf_trig.h>
#include <gsl/gsl_sf_expint.h>
#include "error.h"
#include "chebyshev.h"
#include "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 "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));
}