sysdeps/ieee754/dbl-64/dosincos.c

   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 /*                                                                  */
  21 /* MODULE_NAME: dosincos.c                                          */
  22 /*                                                                  */
  23 /*                                                                  */
  24 /* FUNCTIONS:   dubsin                                              */
  25 /*              dubcos                                              */
  26 /*              docos                                               */
  27 /* FILES NEEDED: endian.h mydefs.h dla.h dosincos.h                 */
  28 /*               sincos.tbl                                         */
  29 /*                                                                  */
  30 /* Routines compute sin() and cos() as Double-Length numbers         */
  31 /********************************************************************/
  32
  33
  34
  35 #include "endian.h"
  36 #include "mydefs.h"
  37 #include <dla.h>
  38 #include "dosincos.h"
  39 #include <math_private.h>
  40
  41 #ifndef SECTION
  42 # define SECTION
  43 #endif
  44
  45 extern const union
  46 {
  47   int4 i[880];
  48   double x[440];
  49 } __sincostab attribute_hidden;
  50
  51 /***********************************************************************/
  52 /* Routine receive Double-Length number (x+dx) and computing sin(x+dx) */
  53 /* as Double-Length number and store it at array v .It computes it by  */
  54 /* arithmetic action on Double-Length numbers                          */
  55 /*(x+dx) between 0 and PI/4                                            */
  56 /***********************************************************************/
  57
  58 void
  59 SECTION
  60 __dubsin (double x, double dx, double v[])
  61 {
  62   double r, s, c, cc, d, dd, d2, dd2, e, ee,
  63          sn, ssn, cs, ccs, ds, dss, dc, dcc;
  64   mynumber u;
  65   int4 k;
  66
  67   u.x = x + big.x;
  68   k = u.i[LOW_HALF] << 2;
  69   x = x - (u.x - big.x);
  70   d = x + dx;
  71   dd = (x - d) + dx;
  72   /* sin(x+dx)=sin(Xi+t)=sin(Xi)*cos(t) + cos(Xi)sin(t) where t ->0 */
  73   MUL2 (d, dd, d, dd, d2, dd2, c, cc);
  74   sn = __sincostab.x[k];       /*                                  */
  75   ssn = __sincostab.x[k + 1];  /*      sin(Xi) and cos(Xi)         */
  76   cs = __sincostab.x[k + 2];   /*                                  */
  77   ccs = __sincostab.x[k + 3];  /*                                  */
  78   /* Taylor series for sin ds=sin(t) */
  79   MUL2 (d2, dd2, s7.x, ss7.x, ds, dss, c, cc);
  80   ADD2 (ds, dss, s5.x, ss5.x, ds, dss, r, s);
  81   MUL2 (d2, dd2, ds, dss, ds, dss, c, cc);
  82   ADD2 (ds, dss, s3.x, ss3.x, ds, dss, r, s);
  83   MUL2 (d2, dd2, ds, dss, ds, dss, c, cc);
  84   MUL2 (d, dd, ds, dss, ds, dss, c, cc);
  85   ADD2 (ds, dss, d, dd, ds, dss, r, s);
  86
  87   /* Taylor series for cos dc=cos(t) */
  88   MUL2 (d2, dd2, c8.x, cc8.x, dc, dcc, c, cc);
  89   ADD2 (dc, dcc, c6.x, cc6.x, dc, dcc, r, s);
  90   MUL2 (d2, dd2, dc, dcc, dc, dcc, c, cc);
  91   ADD2 (dc, dcc, c4.x, cc4.x, dc, dcc, r, s);
  92   MUL2 (d2, dd2, dc, dcc, dc, dcc, c, cc);
  93   ADD2 (dc, dcc, c2.x, cc2.x, dc, dcc, r, s);
  94   MUL2 (d2, dd2, dc, dcc, dc, dcc, c, cc);
  95
  96   MUL2 (cs, ccs, ds, dss, e, ee, c, cc);
  97   MUL2 (dc, dcc, sn, ssn, dc, dcc, c, cc);
  98   SUB2 (e, ee, dc, dcc, e, ee, r, s);
  99   ADD2 (e, ee, sn, ssn, e, ee, r, s);                    /* e+ee=sin(x+dx) */
 100
 101   v[0] = e;
 102   v[1] = ee;
 103 }
 104 /**********************************************************************/
 105 /* Routine receive Double-Length number (x+dx) and computes cos(x+dx) */
 106 /* as Double-Length number and store it in array v .It computes it by */
 107 /* arithmetic action on Double-Length numbers                         */
 108 /*(x+dx) between 0 and PI/4                                           */
 109 /**********************************************************************/
 110
 111 void
 112 SECTION
 113 __dubcos (double x, double dx, double v[])
 114 {
 115   double r, s, c, cc, d, dd, d2, dd2, e, ee,
 116          sn, ssn, cs, ccs, ds, dss, dc, dcc;
 117   mynumber u;
 118   int4 k;
 119   u.x = x + big.x;
 120   k = u.i[LOW_HALF] << 2;
 121   x = x - (u.x - big.x);
 122   d = x + dx;
 123   dd = (x - d) + dx;  /* cos(x+dx)=cos(Xi+t)=cos(Xi)cos(t) - sin(Xi)sin(t) */
 124   MUL2 (d, dd, d, dd, d2, dd2, c, cc);
 125   sn = __sincostab.x[k];     /*                                  */
 126   ssn = __sincostab.x[k + 1];  /*      sin(Xi) and cos(Xi)         */
 127   cs = __sincostab.x[k + 2];   /*                                  */
 128   ccs = __sincostab.x[k + 3];  /*                                  */
 129   MUL2 (d2, dd2, s7.x, ss7.x, ds, dss, c, cc);
 130   ADD2 (ds, dss, s5.x, ss5.x, ds, dss, r, s);
 131   MUL2 (d2, dd2, ds, dss, ds, dss, c, cc);
 132   ADD2 (ds, dss, s3.x, ss3.x, ds, dss, r, s);
 133   MUL2 (d2, dd2, ds, dss, ds, dss, c, cc);
 134   MUL2 (d, dd, ds, dss, ds, dss, c, cc);
 135   ADD2 (ds, dss, d, dd, ds, dss, r, s);
 136
 137   MUL2 (d2, dd2, c8.x, cc8.x, dc, dcc, c, cc);
 138   ADD2 (dc, dcc, c6.x, cc6.x, dc, dcc, r, s);
 139   MUL2 (d2, dd2, dc, dcc, dc, dcc, c, cc);
 140   ADD2 (dc, dcc, c4.x, cc4.x, dc, dcc, r, s);
 141   MUL2 (d2, dd2, dc, dcc, dc, dcc, c, cc);
 142   ADD2 (dc, dcc, c2.x, cc2.x, dc, dcc, r, s);
 143   MUL2 (d2, dd2, dc, dcc, dc, dcc, c, cc);
 144
 145   MUL2 (cs, ccs, ds, dss, e, ee, c, cc);
 146   MUL2 (dc, dcc, sn, ssn, dc, dcc, c, cc);
 147
 148   MUL2 (d2, dd2, s7.x, ss7.x, ds, dss, c, cc);
 149   ADD2 (ds, dss, s5.x, ss5.x, ds, dss, r, s);
 150   MUL2 (d2, dd2, ds, dss, ds, dss, c, cc);
 151   ADD2 (ds, dss, s3.x, ss3.x, ds, dss, r, s);
 152   MUL2 (d2, dd2, ds, dss, ds, dss, c, cc);
 153   MUL2 (d, dd, ds, dss, ds, dss, c, cc);
 154   ADD2 (ds, dss, d, dd, ds, dss, r, s);
 155   MUL2 (d2, dd2, c8.x, cc8.x, dc, dcc, c, cc);
 156   ADD2 (dc, dcc, c6.x, cc6.x, dc, dcc, r, s);
 157   MUL2 (d2, dd2, dc, dcc, dc, dcc, c, cc);
 158   ADD2 (dc, dcc, c4.x, cc4.x, dc, dcc, r, s);
 159   MUL2 (d2, dd2, dc, dcc, dc, dcc, c, cc);
 160   ADD2 (dc, dcc, c2.x, cc2.x, dc, dcc, r, s);
 161   MUL2 (d2, dd2, dc, dcc, dc, dcc, c, cc);
 162   MUL2 (sn, ssn, ds, dss, e, ee, c, cc);
 163   MUL2 (dc, dcc, cs, ccs, dc, dcc, c, cc);
 164   ADD2 (e, ee, dc, dcc, e, ee, r, s);
 165   SUB2 (cs, ccs, e, ee, e, ee, r, s);
 166
 167   v[0] = e;
 168   v[1] = ee;
 169 }
 170 /**********************************************************************/
 171 /* Routine receive Double-Length number (x+dx) and computes cos(x+dx) */
 172 /* as Double-Length number and store it in array v                    */
 173 /**********************************************************************/
 174 void
 175 SECTION
 176 __docos (double x, double dx, double v[])
 177 {
 178   double y, yy, p, w[2];
 179   if (x > 0)
 180     {
 181       y = x; yy = dx;
 182     }
 183   else
 184     {
 185       y = -x; yy = -dx;
 186     }
 187   if (y < 0.5 * hp0.x)                                 /*  y< PI/4    */
 188     {
 189       __dubcos (y, yy, w); v[0] = w[0]; v[1] = w[1];
 190     }
 191   else if (y < 1.5 * hp0.x)                        /* y< 3/4 * PI */
 192     {
 193       p = hp0.x - y; /* p = PI/2 - y */
 194       yy = hp1.x - yy;
 195       y = p + yy;
 196       yy = (p - y) + yy;
 197       if (y > 0)
 198         {
 199           __dubsin (y, yy, w); v[0] = w[0]; v[1] = w[1];
 200         }
 201       /* cos(x) = sin ( 90 -  x ) */
 202       else
 203         {
 204           __dubsin (-y, -yy, w); v[0] = -w[0]; v[1] = -w[1];
 205         }
 206     }
 207   else   /* y>= 3/4 * PI */
 208     {
 209       p = 2.0 * hp0.x - y; /* p = PI- y */
 210       yy = 2.0 * hp1.x - yy;
 211       y = p + yy;
 212       yy = (p - y) + yy;
 213       __dubcos (y, yy, w);
 214       v[0] = -w[0];
 215       v[1] = -w[1];
 216     }
 217 }