[thirdparty/glibc.git] / sysdeps / ieee754 / dbl-64 / dosincos.c

/*
 * IBM Accurate Mathematical Library
 * written by International Business Machines Corp.
 * Copyright (C) 2001 Free Software Foundation
 *
 * 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, write to the Free Software
 * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
 */
/********************************************************************/
/*                                                                  */
/* 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 "sincos.tbl"
#include "dla.h"
#include "dosincos.h"
#include "math_private.h"

/***********************************************************************/
/* 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 __dubsin(double x, double dx, double v[]) {
  double r,s,p,hx,tx,hy,ty,q,c,cc,d,dd,d2,dd2,e,ee,
    sn,ssn,cs,ccs,ds,dss,dc,dcc;
#if 0
  double xx,y,yy,z,zz;
#endif
  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,p,hx,tx,hy,ty,q,c,cc);
  sn=sincos.x[k];     /*                                  */
  ssn=sincos.x[k+1];  /*      sin(Xi) and cos(Xi)         */
  cs=sincos.x[k+2];   /*                                  */
  ccs=sincos.x[k+3];  /*                                  */
  MUL2(d2,dd2,s7.x,ss7.x,ds,dss,p,hx,tx,hy,ty,q,c,cc);  /* Taylor    */
  ADD2(ds,dss,s5.x,ss5.x,ds,dss,r,s);
  MUL2(d2,dd2,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc);      /* series    */
  ADD2(ds,dss,s3.x,ss3.x,ds,dss,r,s);
  MUL2(d2,dd2,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc);      /* for sin   */
  MUL2(d,dd,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc);
  ADD2(ds,dss,d,dd,ds,dss,r,s);                         /* ds=sin(t) */

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

  MUL2(cs,ccs,ds,dss,e,ee,p,hx,tx,hy,ty,q,c,cc);
  MUL2(dc,dcc,sn,ssn,dc,dcc,p,hx,tx,hy,ty,q,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 __dubcos(double x, double dx, double v[]) {
  double r,s,p,hx,tx,hy,ty,q,c,cc,d,dd,d2,dd2,e,ee,
    sn,ssn,cs,ccs,ds,dss,dc,dcc;
#if 0
  double xx,y,yy,z,zz;
#endif
  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,p,hx,tx,hy,ty,q,c,cc);
  sn=sincos.x[k];     /*                                  */
  ssn=sincos.x[k+1];  /*      sin(Xi) and cos(Xi)         */
  cs=sincos.x[k+2];   /*                                  */
  ccs=sincos.x[k+3];  /*                                  */
  MUL2(d2,dd2,s7.x,ss7.x,ds,dss,p,hx,tx,hy,ty,q,c,cc);
  ADD2(ds,dss,s5.x,ss5.x,ds,dss,r,s);
  MUL2(d2,dd2,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc);
  ADD2(ds,dss,s3.x,ss3.x,ds,dss,r,s);
  MUL2(d2,dd2,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc);
  MUL2(d,dd,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc);
  ADD2(ds,dss,d,dd,ds,dss,r,s);

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

  MUL2(cs,ccs,ds,dss,e,ee,p,hx,tx,hy,ty,q,c,cc);
  MUL2(dc,dcc,sn,ssn,dc,dcc,p,hx,tx,hy,ty,q,c,cc);

  MUL2(d2,dd2,s7.x,ss7.x,ds,dss,p,hx,tx,hy,ty,q,c,cc);
  ADD2(ds,dss,s5.x,ss5.x,ds,dss,r,s);
  MUL2(d2,dd2,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc);
  ADD2(ds,dss,s3.x,ss3.x,ds,dss,r,s);
  MUL2(d2,dd2,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc);
  MUL2(d,dd,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc);
  ADD2(ds,dss,d,dd,ds,dss,r,s);
  MUL2(d2,dd2,c8.x,cc8.x,dc,dcc,p,hx,tx,hy,ty,q,c,cc);
  ADD2(dc,dcc,c6.x,cc6.x,dc,dcc,r,s);
  MUL2(d2,dd2,dc,dcc,dc,dcc,p,hx,tx,hy,ty,q,c,cc);
  ADD2(dc,dcc,c4.x,cc4.x,dc,dcc,r,s);
  MUL2(d2,dd2,dc,dcc,dc,dcc,p,hx,tx,hy,ty,q,c,cc);
  ADD2(dc,dcc,c2.x,cc2.x,dc,dcc,r,s);
  MUL2(d2,dd2,dc,dcc,dc,dcc,p,hx,tx,hy,ty,q,c,cc);
  MUL2(sn,ssn,ds,dss,e,ee,p,hx,tx,hy,ty,q,c,cc);
  MUL2(dc,dcc,cs,ccs,dc,dcc,p,hx,tx,hy,ty,q,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 __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];
  }
}
Commit	Line	Data
e4d82761 UD	1	/*
e4d82761 UD	2	* IBM Accurate Mathematical Library
aeb25823 AJ	3	* written by International Business Machines Corp.
aeb25823 AJ	4	* Copyright (C) 2001 Free Software Foundation
e4d82761 UD	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
cc7375ce	8	* the Free Software Foundation; either version 2.1 of the License, or
e4d82761	9	* (at your option) any later version.
50944bca	10	*
e4d82761 UD	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
c6c6dd48	14	* GNU Lesser General Public License for more details.
e4d82761 UD	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
50944bca	18	* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
e4d82761 UD	19	*/
e4d82761 UD	20	/********************************************************************/
50944bca	21	/* */
e4d82761 UD	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"
50944bca	37	#include "mydefs.h"
e4d82761 UD	38	#include "sincos.tbl"
	39	#include "dla.h"
	40	#include "dosincos.h"
15b3c029 AJ	41	#include "math_private.h"
15b3c029 AJ	42
e4d82761 UD	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 */
50944bca	47	/(x+dx) between 0 and PI/4 /
e4d82761 UD	48	/***********************************************************************/
e4d82761 UD	49
ca58f1db	50	void __dubsin(double x, double dx, double v[]) {
50944bca	51	double r,s,p,hx,tx,hy,ty,q,c,cc,d,dd,d2,dd2,e,ee,
e4d82761	52	sn,ssn,cs,ccs,ds,dss,dc,dcc;
50944bca UD	53	#if 0
	54	double xx,y,yy,z,zz;
	55	#endif
e4d82761 UD	56	mynumber u;
e4d82761 UD	57	int4 k;
50944bca	58
e4d82761 UD	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 */
50944bca	71	ADD2(ds,dss,s5.x,ss5.x,ds,dss,r,s);
e4d82761	72	MUL2(d2,dd2,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc); /* series */
50944bca	73	ADD2(ds,dss,s3.x,ss3.x,ds,dss,r,s);
e4d82761 UD	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) */
50944bca	77
e4d82761	78	MUL2(d2,dd2,c8.x,cc8.x,dc,dcc,p,hx,tx,hy,ty,q,c,cc); ;/* Taylor */
50944bca	79	ADD2(dc,dcc,c6.x,cc6.x,dc,dcc,r,s);
e4d82761	80	MUL2(d2,dd2,dc,dcc,dc,dcc,p,hx,tx,hy,ty,q,c,cc); /* series */
50944bca	81	ADD2(dc,dcc,c4.x,cc4.x,dc,dcc,r,s);
e4d82761	82	MUL2(d2,dd2,dc,dcc,dc,dcc,p,hx,tx,hy,ty,q,c,cc); /* for cos */
50944bca	83	ADD2(dc,dcc,c2.x,cc2.x,dc,dcc,r,s);
e4d82761	84	MUL2(d2,dd2,dc,dcc,dc,dcc,p,hx,tx,hy,ty,q,c,cc); /* dc=cos(t) */
50944bca	85
e4d82761 UD	86	MUL2(cs,ccs,ds,dss,e,ee,p,hx,tx,hy,ty,q,c,cc);
e4d82761 UD	87	MUL2(dc,dcc,sn,ssn,dc,dcc,p,hx,tx,hy,ty,q,c,cc);
50944bca	88	SUB2(e,ee,dc,dcc,e,ee,r,s);
e4d82761	89	ADD2(e,ee,sn,ssn,e,ee,r,s); /* e+ee=sin(x+dx) */
50944bca	90
e4d82761 UD	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
ca58f1db	101	void __dubcos(double x, double dx, double v[]) {
50944bca	102	double r,s,p,hx,tx,hy,ty,q,c,cc,d,dd,d2,dd2,e,ee,
e4d82761	103	sn,ssn,cs,ccs,ds,dss,dc,dcc;
50944bca UD	104	#if 0
	105	double xx,y,yy,z,zz;
	106	#endif
e4d82761	107	mynumber u;
50944bca UD	108	int4 k;
50944bca UD	109	u.x=x+big.x;
e4d82761 UD	110	k = u.i[LOW_HALF]<<2;
e4d82761 UD	111	x=x-(u.x-big.x);
50944bca	112	d=x+dx;
e4d82761	113	dd=(x-d)+dx; /* cos(x+dx)=cos(Xi+t)=cos(Xi)cos(t) - sin(Xi)sin(t) */
50944bca	114	MUL2(d,dd,d,dd,d2,dd2,p,hx,tx,hy,ty,q,c,cc);
e4d82761 UD	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);
50944bca	120	ADD2(ds,dss,s5.x,ss5.x,ds,dss,r,s);
e4d82761	121	MUL2(d2,dd2,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc);
50944bca	122	ADD2(ds,dss,s3.x,ss3.x,ds,dss,r,s);
e4d82761 UD	123	MUL2(d2,dd2,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc);
e4d82761 UD	124	MUL2(d,dd,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc);
50944bca UD	125	ADD2(ds,dss,d,dd,ds,dss,r,s);
50944bca UD	126
e4d82761	127	MUL2(d2,dd2,c8.x,cc8.x,dc,dcc,p,hx,tx,hy,ty,q,c,cc);
50944bca	128	ADD2(dc,dcc,c6.x,cc6.x,dc,dcc,r,s);
e4d82761	129	MUL2(d2,dd2,dc,dcc,dc,dcc,p,hx,tx,hy,ty,q,c,cc);
50944bca	130	ADD2(dc,dcc,c4.x,cc4.x,dc,dcc,r,s);
e4d82761	131	MUL2(d2,dd2,dc,dcc,dc,dcc,p,hx,tx,hy,ty,q,c,cc);
50944bca	132	ADD2(dc,dcc,c2.x,cc2.x,dc,dcc,r,s);
e4d82761	133	MUL2(d2,dd2,dc,dcc,dc,dcc,p,hx,tx,hy,ty,q,c,cc);
50944bca	134
e4d82761 UD	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);
50944bca	141	ADD2(ds,dss,s3.x,ss3.x,ds,dss,r,s);
e4d82761	142	MUL2(d2,dd2,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc);
50944bca UD	143	MUL2(d,dd,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc);
50944bca UD	144	ADD2(ds,dss,d,dd,ds,dss,r,s);
e4d82761 UD	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);
50944bca UD	154	ADD2(e,ee,dc,dcc,e,ee,r,s);
	155	SUB2(cs,ccs,e,ee,e,ee,r,s);
	156
e4d82761 UD	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	/**********************************************************************/
ca58f1db	164	void __docos(double x, double dx, double v[]) {
e4d82761 UD	165	double y,yy,p,w[2];
	166	if (x>0) {y=x; yy=dx;}
	167	else {y=-x; yy=-dx;}
	168	if (y<0.5hp0.x) / y< PI/4 */
ca58f1db	169	{__dubcos(y,yy,w); v[0]=w[0]; v[1]=w[1];}
e4d82761 UD	170	else if (y<1.5hp0.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;
ca58f1db	175	if (y>0) {__dubsin(y,yy,w); v[0]=w[0]; v[1]=w[1];}
e4d82761	176	/* cos(x) = sin ( 90 - x ) */
ca58f1db	177	else {__dubsin(-y,-yy,w); v[0]=-w[0]; v[1]=-w[1];
e4d82761 UD	178	}
	179	}
	180	else { /* y>= 3/4 * PI */
	181	p=2.0hp0.x-y; / p = PI- y */
50944bca	182	yy=2.0*hp1.x-yy;
e4d82761 UD	183	y=p+yy;
e4d82761 UD	184	yy=(p-y)+yy;
ca58f1db	185	__dubcos(y,yy,w);
e4d82761 UD	186	v[0]=-w[0];
	187	v[1]=-w[1];
	188	}
	189	}