sysdeps/ieee754/dbl-64/doasin.c

   1 /*
   2  * IBM Accurate Mathematical Library
   3  * written by International Business Machines Corp.
   4  * Copyright (C) 2001-2015 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 <http://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 /********************************************************************/
  44 void
  45 SECTION
  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 #ifndef DLA_FMS
  62   double hx,tx,hy,ty,tp,tq;
  63 #endif
  64
  65
  66 /* Taylor series for arcsin for Double-Length numbers         */
  67   xx = x*x+2.0*x*dx;
  68   p = ((((((d11*xx+d10)*xx+d9)*xx+d8)*xx+d7)*xx+d6)*xx+d5)*xx;
  69   pp = 0;
  70
  71   MUL2(x,dx,x,dx,u,uu,tp,hx,tx,hy,ty,tq,tc,tcc);
  72   ADD2(p,pp,c4.x,cc4.x,p,pp,r,s);
  73   MUL2(p,pp,u,uu,p,pp,tp,hx,tx,hy,ty,tq,tc,tcc);
  74   ADD2(p,pp,c3.x,cc3.x,p,pp,r,s);
  75   MUL2(p,pp,u,uu,p,pp,tp,hx,tx,hy,ty,tq,tc,tcc);
  76   ADD2(p,pp,c2.x,cc2.x,p,pp,r,s);
  77   MUL2(p,pp,u,uu,p,pp,tp,hx,tx,hy,ty,tq,tc,tcc);
  78   ADD2(p,pp,c1.x,cc1.x,p,pp,r,s);
  79   MUL2(p,pp,u,uu,p,pp,tp,hx,tx,hy,ty,tq,tc,tcc);
  80   MUL2(p,pp,x,dx,p,pp,tp,hx,tx,hy,ty,tq,tc,tcc);
  81   ADD2(p,pp,x,dx,p,pp,r,s);
  82   v[0]=p;
  83   v[1]=pp; /* arcsin(x+dx)=v[0]+v[1] */
  84 }