sysdeps/ieee754/dbl-64/sincos32.c

   1 /*
   2  * IBM Accurate Mathematical Library
   3  * written by International Business Machines Corp.
   4  * Copyright (C) 2001, 2011 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, see <http://www.gnu.org/licenses/>.
  18  */
  19 /****************************************************************/
  20 /*  MODULE_NAME: sincos32.c                                     */
  21 /*                                                              */
  22 /*  FUNCTIONS: ss32                                             */
  23 /*             cc32                                             */
  24 /*             c32                                              */
  25 /*             sin32                                            */
  26 /*             cos32                                            */
  27 /*             mpsin                                            */
  28 /*             mpcos                                            */
  29 /*             mpranred                                         */
  30 /*             mpsin1                                           */
  31 /*             mpcos1                                           */
  32 /*                                                              */
  33 /* FILES NEEDED: endian.h mpa.h sincos32.h                      */
  34 /*               mpa.c                                          */
  35 /*                                                              */
  36 /* Multi Precision sin() and cos() function with p=32  for sin()*/
  37 /* cos() arcsin() and arccos() routines                         */
  38 /* In addition mpranred() routine  performs range  reduction of */
  39 /* a double number x into multi precision number   y,           */
  40 /* such that y=x-n*pi/2, abs(y)<pi/4,  n=0,+-1,+-2,....         */
  41 /****************************************************************/
  42 #include "endian.h"
  43 #include "mpa.h"
  44 #include "sincos32.h"
  45 #include "math_private.h"
  46
  47 #ifndef SECTION
  48 # define SECTION
  49 #endif
  50
  51 /****************************************************************/
  52 /* Compute Multi-Precision sin() function for given p.  Receive */
  53 /* Multi  Precision number x and result stored at y             */
  54 /****************************************************************/
  55 static void
  56 SECTION
  57 ss32(mp_no *x, mp_no *y, int p) {
  58   int i;
  59   double a;
  60 #if 0
  61   double b;
  62   static const mp_no mpone = {1,{1.0,1.0}};
  63 #endif
  64   mp_no mpt1,x2,gor,sum ,mpk={1,{1.0}};
  65 #if 0
  66   mp_no mpt2;
  67 #endif
  68   for (i=1;i<=p;i++) mpk.d[i]=0;
  69
  70   __mul(x,x,&x2,p);
  71   __cpy(&oofac27,&gor,p);
  72   __cpy(&gor,&sum,p);
  73   for (a=27.0;a>1.0;a-=2.0) {
  74     mpk.d[1]=a*(a-1.0);
  75     __mul(&gor,&mpk,&mpt1,p);
  76     __cpy(&mpt1,&gor,p);
  77     __mul(&x2,&sum,&mpt1,p);
  78     __sub(&gor,&mpt1,&sum,p);
  79   }
  80   __mul(x,&sum,y,p);
  81 }
  82
  83 /**********************************************************************/
  84 /* Compute Multi-Precision cos() function for given p. Receive Multi  */
  85 /* Precision number x and result stored at y                          */
  86 /**********************************************************************/
  87 static void
  88 SECTION
  89 cc32(mp_no *x, mp_no *y, int p) {
  90   int i;
  91   double a;
  92 #if 0
  93   double b;
  94   static const mp_no mpone = {1,{1.0,1.0}};
  95 #endif
  96   mp_no mpt1,x2,gor,sum ,mpk={1,{1.0}};
  97 #if 0
  98   mp_no mpt2;
  99 #endif
 100   for (i=1;i<=p;i++) mpk.d[i]=0;
 101
 102   __mul(x,x,&x2,p);
 103   mpk.d[1]=27.0;
 104   __mul(&oofac27,&mpk,&gor,p);
 105   __cpy(&gor,&sum,p);
 106   for (a=26.0;a>2.0;a-=2.0) {
 107     mpk.d[1]=a*(a-1.0);
 108     __mul(&gor,&mpk,&mpt1,p);
 109     __cpy(&mpt1,&gor,p);
 110     __mul(&x2,&sum,&mpt1,p);
 111     __sub(&gor,&mpt1,&sum,p);
 112   }
 113   __mul(&x2,&sum,y,p);
 114 }
 115
 116 /***************************************************************************/
 117 /* c32()   computes both sin(x), cos(x) as Multi precision numbers         */
 118 /***************************************************************************/
 119 void
 120 SECTION
 121 __c32(mp_no *x, mp_no *y, mp_no *z, int p) {
 122   static const mp_no mpt={1,{1.0,2.0}}, one={1,{1.0,1.0}};
 123   mp_no u,t,t1,t2,c,s;
 124   int i;
 125   __cpy(x,&u,p);
 126   u.e=u.e-1;
 127   cc32(&u,&c,p);
 128   ss32(&u,&s,p);
 129   for (i=0;i<24;i++) {
 130     __mul(&c,&s,&t,p);
 131     __sub(&s,&t,&t1,p);
 132     __add(&t1,&t1,&s,p);
 133     __sub(&mpt,&c,&t1,p);
 134     __mul(&t1,&c,&t2,p);
 135     __add(&t2,&t2,&c,p);
 136   }
 137   __sub(&one,&c,y,p);
 138   __cpy(&s,z,p);
 139 }
 140
 141 /************************************************************************/
 142 /*Routine receive double x and two double results of sin(x) and return  */
 143 /*result which is more accurate                                         */
 144 /*Computing sin(x) with multi precision routine c32                     */
 145 /************************************************************************/
 146 double
 147 SECTION
 148 __sin32(double x, double res, double res1) {
 149   int p;
 150   mp_no a,b,c;
 151   p=32;
 152   __dbl_mp(res,&a,p);
 153   __dbl_mp(0.5*(res1-res),&b,p);
 154   __add(&a,&b,&c,p);
 155   if (x>0.8)
 156   { __sub(&hp,&c,&a,p);
 157     __c32(&a,&b,&c,p);
 158   }
 159   else __c32(&c,&a,&b,p);     /* b=sin(0.5*(res+res1))  */
 160   __dbl_mp(x,&c,p);           /* c = x                  */
 161   __sub(&b,&c,&a,p);
 162   /* if a>0 return min(res,res1), otherwise return max(res,res1) */
 163   if (a.d[0]>0)  return (res<res1)?res:res1;
 164   else  return (res>res1)?res:res1;
 165 }
 166
 167 /************************************************************************/
 168 /*Routine receive double x and two double results of cos(x) and return  */
 169 /*result which is more accurate                                         */
 170 /*Computing cos(x) with multi precision routine c32                     */
 171 /************************************************************************/
 172 double
 173 SECTION
 174 __cos32(double x, double res, double res1) {
 175   int p;
 176   mp_no a,b,c;
 177   p=32;
 178   __dbl_mp(res,&a,p);
 179   __dbl_mp(0.5*(res1-res),&b,p);
 180   __add(&a,&b,&c,p);
 181   if (x>2.4)
 182   { __sub(&pi,&c,&a,p);
 183     __c32(&a,&b,&c,p);
 184     b.d[0]=-b.d[0];
 185   }
 186   else if (x>0.8)
 187        { __sub(&hp,&c,&a,p);
 188          __c32(&a,&c,&b,p);
 189        }
 190   else __c32(&c,&b,&a,p);     /* b=cos(0.5*(res+res1))  */
 191   __dbl_mp(x,&c,p);    /* c = x                  */
 192   __sub(&b,&c,&a,p);
 193              /* if a>0 return max(res,res1), otherwise return min(res,res1) */
 194   if (a.d[0]>0)  return (res>res1)?res:res1;
 195   else  return (res<res1)?res:res1;
 196 }
 197
 198 /*******************************************************************/
 199 /*Compute sin(x+dx) as Multi Precision number and return result as */
 200 /* double                                                          */
 201 /*******************************************************************/
 202 double
 203 SECTION
 204 __mpsin(double x, double dx) {
 205   int p;
 206   double y;
 207   mp_no a,b,c;
 208   p=32;
 209   __dbl_mp(x,&a,p);
 210   __dbl_mp(dx,&b,p);
 211   __add(&a,&b,&c,p);
 212   if (x>0.8) { __sub(&hp,&c,&a,p); __c32(&a,&b,&c,p); }
 213   else __c32(&c,&a,&b,p);     /* b = sin(x+dx)     */
 214   __mp_dbl(&b,&y,p);
 215   return y;
 216 }
 217
 218 /*******************************************************************/
 219 /* Compute cos()of double-length number (x+dx) as Multi Precision  */
 220 /* number and return result as double                              */
 221 /*******************************************************************/
 222 double
 223 SECTION
 224 __mpcos(double x, double dx) {
 225   int p;
 226   double y;
 227   mp_no a,b,c;
 228   p=32;
 229   __dbl_mp(x,&a,p);
 230   __dbl_mp(dx,&b,p);
 231   __add(&a,&b,&c,p);
 232   if (x>0.8)
 233   { __sub(&hp,&c,&b,p);
 234     __c32(&b,&c,&a,p);
 235   }
 236   else __c32(&c,&a,&b,p);     /* a = cos(x+dx)     */
 237   __mp_dbl(&a,&y,p);
 238   return y;
 239 }
 240
 241 /******************************************************************/
 242 /* mpranred() performs range reduction of a double number x into  */
 243 /* multi precision number y, such that y=x-n*pi/2, abs(y)<pi/4,   */
 244 /* n=0,+-1,+-2,....                                               */
 245 /* Return int which indicates in which quarter of circle x is     */
 246 /******************************************************************/
 247 int
 248 SECTION
 249 __mpranred(double x, mp_no *y, int p)
 250 {
 251   number v;
 252   double t,xn;
 253   int i,k,n;
 254   static const mp_no one = {1,{1.0,1.0}};
 255   mp_no a,b,c;
 256
 257   if (ABS(x) < 2.8e14) {
 258     t = (x*hpinv.d + toint.d);
 259     xn = t - toint.d;
 260     v.d = t;
 261     n =v.i[LOW_HALF]&3;
 262     __dbl_mp(xn,&a,p);
 263     __mul(&a,&hp,&b,p);
 264     __dbl_mp(x,&c,p);
 265     __sub(&c,&b,y,p);
 266     return n;
 267   }
 268   else {                      /* if x is very big more precision required */
 269     __dbl_mp(x,&a,p);
 270     a.d[0]=1.0;
 271     k = a.e-5;
 272     if (k < 0) k=0;
 273     b.e = -k;
 274     b.d[0] = 1.0;
 275     for (i=0;i<p;i++) b.d[i+1] = toverp[i+k];
 276     __mul(&a,&b,&c,p);
 277     t = c.d[c.e];
 278     for (i=1;i<=p-c.e;i++) c.d[i]=c.d[i+c.e];
 279     for (i=p+1-c.e;i<=p;i++) c.d[i]=0;
 280     c.e=0;
 281     if (c.d[1] >=  8388608.0)
 282     { t +=1.0;
 283       __sub(&c,&one,&b,p);
 284       __mul(&b,&hp,y,p);
 285     }
 286     else __mul(&c,&hp,y,p);
 287     n = (int) t;
 288     if (x < 0) { y->d[0] = - y->d[0]; n = -n; }
 289     return (n&3);
 290   }
 291 }
 292
 293 /*******************************************************************/
 294 /* Multi-Precision sin() function subroutine, for p=32.  It is     */
 295 /* based on the routines mpranred() and c32().                     */
 296 /*******************************************************************/
 297 double
 298 SECTION
 299 __mpsin1(double x)
 300 {
 301   int p;
 302   int n;
 303   mp_no u,s,c;
 304   double y;
 305   p=32;
 306   n=__mpranred(x,&u,p);               /* n is 0, 1, 2 or 3 */
 307   __c32(&u,&c,&s,p);
 308   switch (n) {                      /* in which quarter of unit circle y is*/
 309   case 0:
 310     __mp_dbl(&s,&y,p);
 311     return y;
 312     break;
 313
 314   case 2:
 315     __mp_dbl(&s,&y,p);
 316     return -y;
 317     break;
 318
 319   case 1:
 320     __mp_dbl(&c,&y,p);
 321     return y;
 322     break;
 323
 324   case 3:
 325     __mp_dbl(&c,&y,p);
 326     return -y;
 327     break;
 328
 329   }
 330   return 0;                     /* unreachable, to make the compiler happy */
 331 }
 332
 333 /*****************************************************************/
 334 /* Multi-Precision cos() function subroutine, for p=32.  It is   */
 335 /* based  on the routines mpranred() and c32().                  */
 336 /*****************************************************************/
 337
 338 double
 339 SECTION
 340 __mpcos1(double x)
 341 {
 342   int p;
 343   int n;
 344   mp_no u,s,c;
 345   double y;
 346
 347   p=32;
 348   n=__mpranred(x,&u,p);              /* n is 0, 1, 2 or 3 */
 349   __c32(&u,&c,&s,p);
 350   switch (n) {                     /* in what quarter of unit circle y is*/
 351
 352   case 0:
 353     __mp_dbl(&c,&y,p);
 354     return y;
 355     break;
 356
 357   case 2:
 358     __mp_dbl(&c,&y,p);
 359     return -y;
 360     break;
 361
 362   case 1:
 363     __mp_dbl(&s,&y,p);
 364     return -y;
 365     break;
 366
 367   case 3:
 368     __mp_dbl(&s,&y,p);
 369     return y;
 370     break;
 371
 372   }
 373   return 0;                     /* unreachable, to make the compiler happy */
 374 }
 375 /******************************************************************/