sysdeps/ieee754/dbl-64/dosincos.c

   1 /*
   2  * IBM Accurate Mathematical Library
   3  * written by International Business Machines Corp.
   4  * Copyright (C) 2001 Free Software Foundation
   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, write to the Free Software
  18  * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
  19  */
  20 /********************************************************************/
  21 /*                                                                  */
  22 /* MODULE_NAME: dosincos.c                                          */
  23 /*                                                                  */
  24 /*                                                                  */
  25 /* FUNCTIONS:   dubsin                                              */
  26 /*              dubcos                                              */
  27 /*              docos                                               */
  28 /* FILES NEEDED: endian.h mydefs.h dla.h dosincos.h                 */
  29 /*               sincos.tbl                                         */
  30 /*                                                                  */
  31 /* Routines compute sin() and cos() as Double-Length numbers         */
  32 /********************************************************************/
  33
  34
  35
  36 #include "endian.h"
  37 #include "mydefs.h"
  38 #include "sincos.tbl"
  39 #include "dla.h"
  40 #include "dosincos.h"
  41 #include "math_private.h"
  42
  43 /***********************************************************************/
  44 /* Routine receive Double-Length number (x+dx) and computing sin(x+dx) */
  45 /* as Double-Length number and store it at array v .It computes it by  */
  46 /* arithmetic action on Double-Length numbers                          */
  47 /*(x+dx) between 0 and PI/4                                            */
  48 /***********************************************************************/
  49
  50 void __dubsin(double x, double dx, double v[]) {
  51   double r,s,p,hx,tx,hy,ty,q,c,cc,d,dd,d2,dd2,e,ee,
  52     sn,ssn,cs,ccs,ds,dss,dc,dcc;
  53 #if 0
  54   double xx,y,yy,z,zz;
  55 #endif
  56   mynumber u;
  57   int4 k;
  58
  59   u.x=x+big.x;
  60   k = u.i[LOW_HALF]<<2;
  61   x=x-(u.x-big.x);
  62   d=x+dx;
  63   dd=(x-d)+dx;
  64          /* sin(x+dx)=sin(Xi+t)=sin(Xi)*cos(t) + cos(Xi)sin(t) where t ->0 */
  65   MUL2(d,dd,d,dd,d2,dd2,p,hx,tx,hy,ty,q,c,cc);
  66   sn=sincos.x[k];     /*                                  */
  67   ssn=sincos.x[k+1];  /*      sin(Xi) and cos(Xi)         */
  68   cs=sincos.x[k+2];   /*                                  */
  69   ccs=sincos.x[k+3];  /*                                  */
  70   MUL2(d2,dd2,s7.x,ss7.x,ds,dss,p,hx,tx,hy,ty,q,c,cc);  /* Taylor    */
  71   ADD2(ds,dss,s5.x,ss5.x,ds,dss,r,s);
  72   MUL2(d2,dd2,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc);      /* series    */
  73   ADD2(ds,dss,s3.x,ss3.x,ds,dss,r,s);
  74   MUL2(d2,dd2,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc);      /* for sin   */
  75   MUL2(d,dd,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc);
  76   ADD2(ds,dss,d,dd,ds,dss,r,s);                         /* ds=sin(t) */
  77
  78   MUL2(d2,dd2,c8.x,cc8.x,dc,dcc,p,hx,tx,hy,ty,q,c,cc); ;/* Taylor    */
  79   ADD2(dc,dcc,c6.x,cc6.x,dc,dcc,r,s);
  80   MUL2(d2,dd2,dc,dcc,dc,dcc,p,hx,tx,hy,ty,q,c,cc);      /* series    */
  81   ADD2(dc,dcc,c4.x,cc4.x,dc,dcc,r,s);
  82   MUL2(d2,dd2,dc,dcc,dc,dcc,p,hx,tx,hy,ty,q,c,cc);      /* for cos   */
  83   ADD2(dc,dcc,c2.x,cc2.x,dc,dcc,r,s);
  84   MUL2(d2,dd2,dc,dcc,dc,dcc,p,hx,tx,hy,ty,q,c,cc);      /* dc=cos(t) */
  85
  86   MUL2(cs,ccs,ds,dss,e,ee,p,hx,tx,hy,ty,q,c,cc);
  87   MUL2(dc,dcc,sn,ssn,dc,dcc,p,hx,tx,hy,ty,q,c,cc);
  88   SUB2(e,ee,dc,dcc,e,ee,r,s);
  89   ADD2(e,ee,sn,ssn,e,ee,r,s);                    /* e+ee=sin(x+dx) */
  90
  91   v[0]=e;
  92   v[1]=ee;
  93 }
  94 /**********************************************************************/
  95 /* Routine receive Double-Length number (x+dx) and computes cos(x+dx) */
  96 /* as Double-Length number and store it in array v .It computes it by */
  97 /* arithmetic action on Double-Length numbers                         */
  98 /*(x+dx) between 0 and PI/4                                           */
  99 /**********************************************************************/
 100
 101 void __dubcos(double x, double dx, double v[]) {
 102   double r,s,p,hx,tx,hy,ty,q,c,cc,d,dd,d2,dd2,e,ee,
 103     sn,ssn,cs,ccs,ds,dss,dc,dcc;
 104 #if 0
 105   double xx,y,yy,z,zz;
 106 #endif
 107   mynumber u;
 108   int4 k;
 109   u.x=x+big.x;
 110   k = u.i[LOW_HALF]<<2;
 111   x=x-(u.x-big.x);
 112   d=x+dx;
 113   dd=(x-d)+dx;  /* cos(x+dx)=cos(Xi+t)=cos(Xi)cos(t) - sin(Xi)sin(t) */
 114   MUL2(d,dd,d,dd,d2,dd2,p,hx,tx,hy,ty,q,c,cc);
 115   sn=sincos.x[k];     /*                                  */
 116   ssn=sincos.x[k+1];  /*      sin(Xi) and cos(Xi)         */
 117   cs=sincos.x[k+2];   /*                                  */
 118   ccs=sincos.x[k+3];  /*                                  */
 119   MUL2(d2,dd2,s7.x,ss7.x,ds,dss,p,hx,tx,hy,ty,q,c,cc);
 120   ADD2(ds,dss,s5.x,ss5.x,ds,dss,r,s);
 121   MUL2(d2,dd2,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc);
 122   ADD2(ds,dss,s3.x,ss3.x,ds,dss,r,s);
 123   MUL2(d2,dd2,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc);
 124   MUL2(d,dd,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc);
 125   ADD2(ds,dss,d,dd,ds,dss,r,s);
 126
 127   MUL2(d2,dd2,c8.x,cc8.x,dc,dcc,p,hx,tx,hy,ty,q,c,cc);
 128   ADD2(dc,dcc,c6.x,cc6.x,dc,dcc,r,s);
 129   MUL2(d2,dd2,dc,dcc,dc,dcc,p,hx,tx,hy,ty,q,c,cc);
 130   ADD2(dc,dcc,c4.x,cc4.x,dc,dcc,r,s);
 131   MUL2(d2,dd2,dc,dcc,dc,dcc,p,hx,tx,hy,ty,q,c,cc);
 132   ADD2(dc,dcc,c2.x,cc2.x,dc,dcc,r,s);
 133   MUL2(d2,dd2,dc,dcc,dc,dcc,p,hx,tx,hy,ty,q,c,cc);
 134
 135   MUL2(cs,ccs,ds,dss,e,ee,p,hx,tx,hy,ty,q,c,cc);
 136   MUL2(dc,dcc,sn,ssn,dc,dcc,p,hx,tx,hy,ty,q,c,cc);
 137
 138   MUL2(d2,dd2,s7.x,ss7.x,ds,dss,p,hx,tx,hy,ty,q,c,cc);
 139   ADD2(ds,dss,s5.x,ss5.x,ds,dss,r,s);
 140   MUL2(d2,dd2,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc);
 141   ADD2(ds,dss,s3.x,ss3.x,ds,dss,r,s);
 142   MUL2(d2,dd2,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc);
 143   MUL2(d,dd,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc);
 144   ADD2(ds,dss,d,dd,ds,dss,r,s);
 145   MUL2(d2,dd2,c8.x,cc8.x,dc,dcc,p,hx,tx,hy,ty,q,c,cc);
 146   ADD2(dc,dcc,c6.x,cc6.x,dc,dcc,r,s);
 147   MUL2(d2,dd2,dc,dcc,dc,dcc,p,hx,tx,hy,ty,q,c,cc);
 148   ADD2(dc,dcc,c4.x,cc4.x,dc,dcc,r,s);
 149   MUL2(d2,dd2,dc,dcc,dc,dcc,p,hx,tx,hy,ty,q,c,cc);
 150   ADD2(dc,dcc,c2.x,cc2.x,dc,dcc,r,s);
 151   MUL2(d2,dd2,dc,dcc,dc,dcc,p,hx,tx,hy,ty,q,c,cc);
 152   MUL2(sn,ssn,ds,dss,e,ee,p,hx,tx,hy,ty,q,c,cc);
 153   MUL2(dc,dcc,cs,ccs,dc,dcc,p,hx,tx,hy,ty,q,c,cc);
 154   ADD2(e,ee,dc,dcc,e,ee,r,s);
 155   SUB2(cs,ccs,e,ee,e,ee,r,s);
 156
 157   v[0]=e;
 158   v[1]=ee;
 159 }
 160 /**********************************************************************/
 161 /* Routine receive Double-Length number (x+dx) and computes cos(x+dx) */
 162 /* as Double-Length number and store it in array v                    */
 163 /**********************************************************************/
 164 void __docos(double x, double dx, double v[]) {
 165   double y,yy,p,w[2];
 166   if (x>0) {y=x; yy=dx;}
 167      else {y=-x; yy=-dx;}
 168   if (y<0.5*hp0.x)                                 /*  y< PI/4    */
 169            {__dubcos(y,yy,w); v[0]=w[0]; v[1]=w[1];}
 170      else if (y<1.5*hp0.x) {                       /* y< 3/4 * PI */
 171        p=hp0.x-y;  /* p = PI/2 - y */
 172        yy=hp1.x-yy;
 173        y=p+yy;
 174        yy=(p-y)+yy;
 175        if (y>0) {__dubsin(y,yy,w); v[0]=w[0]; v[1]=w[1];}
 176                                        /* cos(x) = sin ( 90 -  x ) */
 177          else {__dubsin(-y,-yy,w); v[0]=-w[0]; v[1]=-w[1];
 178          }
 179      }
 180   else { /* y>= 3/4 * PI */
 181     p=2.0*hp0.x-y;    /* p = PI- y */
 182     yy=2.0*hp1.x-yy;
 183     y=p+yy;
 184     yy=(p-y)+yy;
 185     __dubcos(y,yy,w);
 186     v[0]=-w[0];
 187     v[1]=-w[1];
 188   }
 189 }