glibc/sysdeps/ieee754/dbl-64/dosincos.c

/*
 * IBM Accurate Mathematical Library
 * written by International Business Machines Corp.
 * Copyright (C) 2001-2021 Free Software Foundation, Inc.
 *
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU Lesser General Public License as published by
 * the Free Software Foundation; either version 2.1 of the License, or
 * (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public License
 * along with this program; if not, see <https://www.gnu.org/licenses/>.
 */
/********************************************************************/
/*                                                                  */
/* MODULE_NAME: dosincos.c                                          */
/*                                                                  */
/*                                                                  */
/* FUNCTIONS:   dubsin                                              */
/*              dubcos                                              */
/*              docos                                               */
/* FILES NEEDED: endian.h mydefs.h dla.h dosincos.h                 */
/*               sincos.tbl                                         */
/*                                                                  */
/* Routines compute sin() and cos() as Double-Length numbers         */
/********************************************************************/



#include "endian.h"
#include "mydefs.h"
#include <dla.h>
#include "dosincos.h"
#include <math_private.h>

#ifndef SECTION
# define SECTION
#endif

extern const union
{
  int4 i[880];
  double x[440];
} __sincostab attribute_hidden;

/***********************************************************************/
/* Routine receive Double-Length number (x+dx) and computing sin(x+dx) */
/* as Double-Length number and store it at array v .It computes it by  */
/* arithmetic action on Double-Length numbers                          */
/*(x+dx) between 0 and PI/4                                            */
/***********************************************************************/

void
SECTION
__dubsin (double x, double dx, double v[])
{
  double r, s, c, cc, d, dd, d2, dd2, e, ee,
	 sn, ssn, cs, ccs, ds, dss, dc, dcc;
  mynumber u;
  int4 k;

  u.x = x + big.x;
  k = u.i[LOW_HALF] << 2;
  x = x - (u.x - big.x);
  d = x + dx;
  dd = (x - d) + dx;
  /* sin(x+dx)=sin(Xi+t)=sin(Xi)*cos(t) + cos(Xi)sin(t) where t ->0 */
  MUL2 (d, dd, d, dd, d2, dd2, c, cc);
  sn = __sincostab.x[k];       /*                                  */
  ssn = __sincostab.x[k + 1];  /*      sin(Xi) and cos(Xi)         */
  cs = __sincostab.x[k + 2];   /*                                  */
  ccs = __sincostab.x[k + 3];  /*                                  */
  /* Taylor series for sin ds=sin(t) */
  MUL2 (d2, dd2, s7.x, ss7.x, ds, dss, c, cc);
  ADD2 (ds, dss, s5.x, ss5.x, ds, dss, r, s);
  MUL2 (d2, dd2, ds, dss, ds, dss, c, cc);
  ADD2 (ds, dss, s3.x, ss3.x, ds, dss, r, s);
  MUL2 (d2, dd2, ds, dss, ds, dss, c, cc);
  MUL2 (d, dd, ds, dss, ds, dss, c, cc);
  ADD2 (ds, dss, d, dd, ds, dss, r, s);

  /* Taylor series for cos dc=cos(t) */
  MUL2 (d2, dd2, c8.x, cc8.x, dc, dcc, c, cc);
  ADD2 (dc, dcc, c6.x, cc6.x, dc, dcc, r, s);
  MUL2 (d2, dd2, dc, dcc, dc, dcc, c, cc);
  ADD2 (dc, dcc, c4.x, cc4.x, dc, dcc, r, s);
  MUL2 (d2, dd2, dc, dcc, dc, dcc, c, cc);
  ADD2 (dc, dcc, c2.x, cc2.x, dc, dcc, r, s);
  MUL2 (d2, dd2, dc, dcc, dc, dcc, c, cc);

  MUL2 (cs, ccs, ds, dss, e, ee, c, cc);
  MUL2 (dc, dcc, sn, ssn, dc, dcc, c, cc);
  SUB2 (e, ee, dc, dcc, e, ee, r, s);
  ADD2 (e, ee, sn, ssn, e, ee, r, s);                    /* e+ee=sin(x+dx) */

  v[0] = e;
  v[1] = ee;
}
/**********************************************************************/
/* Routine receive Double-Length number (x+dx) and computes cos(x+dx) */
/* as Double-Length number and store it in array v .It computes it by */
/* arithmetic action on Double-Length numbers                         */
/*(x+dx) between 0 and PI/4                                           */
/**********************************************************************/

void
SECTION
__dubcos (double x, double dx, double v[])
{
  double r, s, c, cc, d, dd, d2, dd2, e, ee,
	 sn, ssn, cs, ccs, ds, dss, dc, dcc;
  mynumber u;
  int4 k;
  u.x = x + big.x;
  k = u.i[LOW_HALF] << 2;
  x = x - (u.x - big.x);
  d = x + dx;
  dd = (x - d) + dx;  /* cos(x+dx)=cos(Xi+t)=cos(Xi)cos(t) - sin(Xi)sin(t) */
  MUL2 (d, dd, d, dd, d2, dd2, c, cc);
  sn = __sincostab.x[k];     /*                                  */
  ssn = __sincostab.x[k + 1];  /*      sin(Xi) and cos(Xi)         */
  cs = __sincostab.x[k + 2];   /*                                  */
  ccs = __sincostab.x[k + 3];  /*                                  */
  MUL2 (d2, dd2, s7.x, ss7.x, ds, dss, c, cc);
  ADD2 (ds, dss, s5.x, ss5.x, ds, dss, r, s);
  MUL2 (d2, dd2, ds, dss, ds, dss, c, cc);
  ADD2 (ds, dss, s3.x, ss3.x, ds, dss, r, s);
  MUL2 (d2, dd2, ds, dss, ds, dss, c, cc);
  MUL2 (d, dd, ds, dss, ds, dss, c, cc);
  ADD2 (ds, dss, d, dd, ds, dss, r, s);

  MUL2 (d2, dd2, c8.x, cc8.x, dc, dcc, c, cc);
  ADD2 (dc, dcc, c6.x, cc6.x, dc, dcc, r, s);
  MUL2 (d2, dd2, dc, dcc, dc, dcc, c, cc);
  ADD2 (dc, dcc, c4.x, cc4.x, dc, dcc, r, s);
  MUL2 (d2, dd2, dc, dcc, dc, dcc, c, cc);
  ADD2 (dc, dcc, c2.x, cc2.x, dc, dcc, r, s);
  MUL2 (d2, dd2, dc, dcc, dc, dcc, c, cc);

  MUL2 (cs, ccs, ds, dss, e, ee, c, cc);
  MUL2 (dc, dcc, sn, ssn, dc, dcc, c, cc);

  MUL2 (d2, dd2, s7.x, ss7.x, ds, dss, c, cc);
  ADD2 (ds, dss, s5.x, ss5.x, ds, dss, r, s);
  MUL2 (d2, dd2, ds, dss, ds, dss, c, cc);
  ADD2 (ds, dss, s3.x, ss3.x, ds, dss, r, s);
  MUL2 (d2, dd2, ds, dss, ds, dss, c, cc);
  MUL2 (d, dd, ds, dss, ds, dss, c, cc);
  ADD2 (ds, dss, d, dd, ds, dss, r, s);
  MUL2 (d2, dd2, c8.x, cc8.x, dc, dcc, c, cc);
  ADD2 (dc, dcc, c6.x, cc6.x, dc, dcc, r, s);
  MUL2 (d2, dd2, dc, dcc, dc, dcc, c, cc);
  ADD2 (dc, dcc, c4.x, cc4.x, dc, dcc, r, s);
  MUL2 (d2, dd2, dc, dcc, dc, dcc, c, cc);
  ADD2 (dc, dcc, c2.x, cc2.x, dc, dcc, r, s);
  MUL2 (d2, dd2, dc, dcc, dc, dcc, c, cc);
  MUL2 (sn, ssn, ds, dss, e, ee, c, cc);
  MUL2 (dc, dcc, cs, ccs, dc, dcc, c, cc);
  ADD2 (e, ee, dc, dcc, e, ee, r, s);
  SUB2 (cs, ccs, e, ee, e, ee, r, s);

  v[0] = e;
  v[1] = ee;
}
/**********************************************************************/
/* Routine receive Double-Length number (x+dx) and computes cos(x+dx) */
/* as Double-Length number and store it in array v                    */
/**********************************************************************/
void
SECTION
__docos (double x, double dx, double v[])
{
  double y, yy, p, w[2];
  if (x > 0)
    {
      y = x; yy = dx;
    }
  else
    {
      y = -x; yy = -dx;
    }
  if (y < 0.5 * hp0.x)                                 /*  y< PI/4    */
    {
      __dubcos (y, yy, w); v[0] = w[0]; v[1] = w[1];
    }
  else if (y < 1.5 * hp0.x)                        /* y< 3/4 * PI */
    {
      p = hp0.x - y; /* p = PI/2 - y */
      yy = hp1.x - yy;
      y = p + yy;
      yy = (p - y) + yy;
      if (y > 0)
	{
	  __dubsin (y, yy, w); v[0] = w[0]; v[1] = w[1];
	}
      /* cos(x) = sin ( 90 -  x ) */
      else
	{
	  __dubsin (-y, -yy, w); v[0] = -w[0]; v[1] = -w[1];
	}
    }
  else   /* y>= 3/4 * PI */
    {
      p = 2.0 * hp0.x - y; /* p = PI- y */
      yy = 2.0 * hp1.x - yy;
      y = p + yy;
      yy = (p - y) + yy;
      __dubcos (y, yy, w);
      v[0] = -w[0];
      v[1] = -w[1];
    }
}