1/*
2 * IBM Accurate Mathematical Library
3 * written by International Business Machines Corp.
4 * Copyright (C) 2001-2020 Free Software Foundation, Inc.
5 *
6 * This program is free software; you can redistribute it and/or modify
7 * it under the terms of the GNU Lesser General Public License as published by
8 * the Free Software Foundation; either version 2.1 of the License, or
9 * (at your option) any later version.
10 *
11 * This program is distributed in the hope that it will be useful,
12 * but WITHOUT ANY WARRANTY; without even the implied warranty of
13 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
14 * GNU Lesser General Public License for more details.
15 *
16 * You should have received a copy of the GNU Lesser General Public License
17 * along with this program; if not, see <https://www.gnu.org/licenses/>.
18 */
19/**********************************************************************/
20/* MODULE_NAME: doasin.c */
21/* */
22/* FUNCTION: doasin */
23/* */
24/* FILES NEEDED:endian.h mydefs.h dla.h doasin.h */
25/* mpa.c */
26/* */
27/* Compute arcsin(x,dx,v) of double-length number (x+dx) the result */
28/* stored in v where v= v[0]+v[1] =arcsin(x+dx) */
29/**********************************************************************/
30
31#include "endian.h"
32#include "mydefs.h"
33#include <dla.h>
34#include <math_private.h>
35
36#ifndef SECTION
37# define SECTION
38#endif
39
40/********************************************************************/
41/* Compute arcsin(x,dx,v) of double-length number (x+dx) the result */
42/* stored in v where v= v[0]+v[1] =arcsin(x+dx) */
43/********************************************************************/
44void
45SECTION
46__doasin(double x, double dx, double v[]) {
47
48#include "doasin.h"
49
50 static const double
51 d5 = 0.22372159090911789889975459505194491E-01,
52 d6 = 0.17352764422456822913014975683014622E-01,
53 d7 = 0.13964843843786693521653681033981614E-01,
54 d8 = 0.11551791438485242609036067259086589E-01,
55 d9 = 0.97622386568166960207425666787248914E-02,
56 d10 = 0.83638737193775788576092749009744976E-02,
57 d11 = 0.79470250400727425881446981833568758E-02;
58
59 double xx,p,pp,u,uu,r,s;
60 double tc,tcc;
61
62
63/* Taylor series for arcsin for Double-Length numbers */
64 xx = x*x+2.0*x*dx;
65 p = ((((((d11*xx+d10)*xx+d9)*xx+d8)*xx+d7)*xx+d6)*xx+d5)*xx;
66 pp = 0;
67
68 MUL2(x,dx,x,dx,u,uu,tc,tcc);
69 ADD2(p,pp,c4.x,cc4.x,p,pp,r,s);
70 MUL2(p,pp,u,uu,p,pp,tc,tcc);
71 ADD2(p,pp,c3.x,cc3.x,p,pp,r,s);
72 MUL2(p,pp,u,uu,p,pp,tc,tcc);
73 ADD2(p,pp,c2.x,cc2.x,p,pp,r,s);
74 MUL2(p,pp,u,uu,p,pp,tc,tcc);
75 ADD2(p,pp,c1.x,cc1.x,p,pp,r,s);
76 MUL2(p,pp,u,uu,p,pp,tc,tcc);
77 MUL2(p,pp,x,dx,p,pp,tc,tcc);
78 ADD2(p,pp,x,dx,p,pp,r,s);
79 v[0]=p;
80 v[1]=pp; /* arcsin(x+dx)=v[0]+v[1] */
81}
82