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210 lines
7.7 KiB
C
210 lines
7.7 KiB
C
/*
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* IBM Accurate Mathematical Library
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* written by International Business Machines Corp.
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* Copyright (C) 2001, 2011 Free Software Foundation
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU Lesser General Public License as published by
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* the Free Software Foundation; either version 2.1 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU Lesser General Public License for more details.
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*
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* You should have received a copy of the GNU Lesser General Public License
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* along with this program; if not, see <http://www.gnu.org/licenses/>.
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*/
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/********************************************************************/
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/* */
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/* MODULE_NAME: dosincos.c */
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/* */
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/* */
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/* FUNCTIONS: dubsin */
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/* dubcos */
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/* docos */
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/* FILES NEEDED: endian.h mydefs.h dla.h dosincos.h */
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/* sincos.tbl */
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/* */
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/* Routines compute sin() and cos() as Double-Length numbers */
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/********************************************************************/
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#include "endian.h"
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#include "mydefs.h"
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#include <dla.h>
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#include "dosincos.h"
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#include <math_private.h>
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#ifndef SECTION
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# define SECTION
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#endif
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extern const union
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{
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int4 i[880];
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double x[440];
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} __sincostab attribute_hidden;
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/***********************************************************************/
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/* Routine receive Double-Length number (x+dx) and computing sin(x+dx) */
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/* as Double-Length number and store it at array v .It computes it by */
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/* arithmetic action on Double-Length numbers */
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/*(x+dx) between 0 and PI/4 */
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/***********************************************************************/
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void
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SECTION
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__dubsin(double x, double dx, double v[]) {
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double r,s,c,cc,d,dd,d2,dd2,e,ee,
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sn,ssn,cs,ccs,ds,dss,dc,dcc;
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#ifndef DLA_FMS
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double p,hx,tx,hy,ty,q;
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#endif
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#if 0
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double xx,y,yy,z,zz;
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#endif
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mynumber u;
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int4 k;
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u.x=x+big.x;
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k = u.i[LOW_HALF]<<2;
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x=x-(u.x-big.x);
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d=x+dx;
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dd=(x-d)+dx;
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/* sin(x+dx)=sin(Xi+t)=sin(Xi)*cos(t) + cos(Xi)sin(t) where t ->0 */
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MUL2(d,dd,d,dd,d2,dd2,p,hx,tx,hy,ty,q,c,cc);
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sn=__sincostab.x[k]; /* */
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ssn=__sincostab.x[k+1]; /* sin(Xi) and cos(Xi) */
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cs=__sincostab.x[k+2]; /* */
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ccs=__sincostab.x[k+3]; /* */
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MUL2(d2,dd2,s7.x,ss7.x,ds,dss,p,hx,tx,hy,ty,q,c,cc); /* Taylor */
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ADD2(ds,dss,s5.x,ss5.x,ds,dss,r,s);
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MUL2(d2,dd2,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc); /* series */
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ADD2(ds,dss,s3.x,ss3.x,ds,dss,r,s);
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MUL2(d2,dd2,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc); /* for sin */
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MUL2(d,dd,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc);
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ADD2(ds,dss,d,dd,ds,dss,r,s); /* ds=sin(t) */
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MUL2(d2,dd2,c8.x,cc8.x,dc,dcc,p,hx,tx,hy,ty,q,c,cc); ;/* Taylor */
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ADD2(dc,dcc,c6.x,cc6.x,dc,dcc,r,s);
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MUL2(d2,dd2,dc,dcc,dc,dcc,p,hx,tx,hy,ty,q,c,cc); /* series */
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ADD2(dc,dcc,c4.x,cc4.x,dc,dcc,r,s);
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MUL2(d2,dd2,dc,dcc,dc,dcc,p,hx,tx,hy,ty,q,c,cc); /* for cos */
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ADD2(dc,dcc,c2.x,cc2.x,dc,dcc,r,s);
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MUL2(d2,dd2,dc,dcc,dc,dcc,p,hx,tx,hy,ty,q,c,cc); /* dc=cos(t) */
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MUL2(cs,ccs,ds,dss,e,ee,p,hx,tx,hy,ty,q,c,cc);
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MUL2(dc,dcc,sn,ssn,dc,dcc,p,hx,tx,hy,ty,q,c,cc);
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SUB2(e,ee,dc,dcc,e,ee,r,s);
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ADD2(e,ee,sn,ssn,e,ee,r,s); /* e+ee=sin(x+dx) */
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v[0]=e;
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v[1]=ee;
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}
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/**********************************************************************/
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/* Routine receive Double-Length number (x+dx) and computes cos(x+dx) */
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/* as Double-Length number and store it in array v .It computes it by */
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/* arithmetic action on Double-Length numbers */
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/*(x+dx) between 0 and PI/4 */
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/**********************************************************************/
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void
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SECTION
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__dubcos(double x, double dx, double v[]) {
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double r,s,c,cc,d,dd,d2,dd2,e,ee,
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sn,ssn,cs,ccs,ds,dss,dc,dcc;
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#ifndef DLA_FMS
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double p,hx,tx,hy,ty,q;
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#endif
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#if 0
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double xx,y,yy,z,zz;
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#endif
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mynumber u;
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int4 k;
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u.x=x+big.x;
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k = u.i[LOW_HALF]<<2;
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x=x-(u.x-big.x);
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d=x+dx;
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dd=(x-d)+dx; /* cos(x+dx)=cos(Xi+t)=cos(Xi)cos(t) - sin(Xi)sin(t) */
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MUL2(d,dd,d,dd,d2,dd2,p,hx,tx,hy,ty,q,c,cc);
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sn=__sincostab.x[k]; /* */
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ssn=__sincostab.x[k+1]; /* sin(Xi) and cos(Xi) */
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cs=__sincostab.x[k+2]; /* */
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ccs=__sincostab.x[k+3]; /* */
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MUL2(d2,dd2,s7.x,ss7.x,ds,dss,p,hx,tx,hy,ty,q,c,cc);
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ADD2(ds,dss,s5.x,ss5.x,ds,dss,r,s);
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MUL2(d2,dd2,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc);
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ADD2(ds,dss,s3.x,ss3.x,ds,dss,r,s);
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MUL2(d2,dd2,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc);
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MUL2(d,dd,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc);
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ADD2(ds,dss,d,dd,ds,dss,r,s);
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MUL2(d2,dd2,c8.x,cc8.x,dc,dcc,p,hx,tx,hy,ty,q,c,cc);
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ADD2(dc,dcc,c6.x,cc6.x,dc,dcc,r,s);
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MUL2(d2,dd2,dc,dcc,dc,dcc,p,hx,tx,hy,ty,q,c,cc);
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ADD2(dc,dcc,c4.x,cc4.x,dc,dcc,r,s);
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MUL2(d2,dd2,dc,dcc,dc,dcc,p,hx,tx,hy,ty,q,c,cc);
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ADD2(dc,dcc,c2.x,cc2.x,dc,dcc,r,s);
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MUL2(d2,dd2,dc,dcc,dc,dcc,p,hx,tx,hy,ty,q,c,cc);
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MUL2(cs,ccs,ds,dss,e,ee,p,hx,tx,hy,ty,q,c,cc);
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MUL2(dc,dcc,sn,ssn,dc,dcc,p,hx,tx,hy,ty,q,c,cc);
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MUL2(d2,dd2,s7.x,ss7.x,ds,dss,p,hx,tx,hy,ty,q,c,cc);
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ADD2(ds,dss,s5.x,ss5.x,ds,dss,r,s);
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MUL2(d2,dd2,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc);
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ADD2(ds,dss,s3.x,ss3.x,ds,dss,r,s);
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MUL2(d2,dd2,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc);
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MUL2(d,dd,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc);
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ADD2(ds,dss,d,dd,ds,dss,r,s);
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MUL2(d2,dd2,c8.x,cc8.x,dc,dcc,p,hx,tx,hy,ty,q,c,cc);
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ADD2(dc,dcc,c6.x,cc6.x,dc,dcc,r,s);
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MUL2(d2,dd2,dc,dcc,dc,dcc,p,hx,tx,hy,ty,q,c,cc);
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ADD2(dc,dcc,c4.x,cc4.x,dc,dcc,r,s);
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MUL2(d2,dd2,dc,dcc,dc,dcc,p,hx,tx,hy,ty,q,c,cc);
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ADD2(dc,dcc,c2.x,cc2.x,dc,dcc,r,s);
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MUL2(d2,dd2,dc,dcc,dc,dcc,p,hx,tx,hy,ty,q,c,cc);
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MUL2(sn,ssn,ds,dss,e,ee,p,hx,tx,hy,ty,q,c,cc);
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MUL2(dc,dcc,cs,ccs,dc,dcc,p,hx,tx,hy,ty,q,c,cc);
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ADD2(e,ee,dc,dcc,e,ee,r,s);
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SUB2(cs,ccs,e,ee,e,ee,r,s);
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v[0]=e;
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v[1]=ee;
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}
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/**********************************************************************/
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/* Routine receive Double-Length number (x+dx) and computes cos(x+dx) */
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/* as Double-Length number and store it in array v */
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/**********************************************************************/
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void
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SECTION
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__docos(double x, double dx, double v[]) {
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double y,yy,p,w[2];
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if (x>0) {y=x; yy=dx;}
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else {y=-x; yy=-dx;}
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if (y<0.5*hp0.x) /* y< PI/4 */
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{__dubcos(y,yy,w); v[0]=w[0]; v[1]=w[1];}
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else if (y<1.5*hp0.x) { /* y< 3/4 * PI */
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p=hp0.x-y; /* p = PI/2 - y */
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yy=hp1.x-yy;
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y=p+yy;
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yy=(p-y)+yy;
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if (y>0) {__dubsin(y,yy,w); v[0]=w[0]; v[1]=w[1];}
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/* cos(x) = sin ( 90 - x ) */
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else {__dubsin(-y,-yy,w); v[0]=-w[0]; v[1]=-w[1];
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}
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}
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else { /* y>= 3/4 * PI */
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p=2.0*hp0.x-y; /* p = PI- y */
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yy=2.0*hp1.x-yy;
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y=p+yy;
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yy=(p-y)+yy;
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__dubcos(y,yy,w);
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v[0]=-w[0];
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v[1]=-w[1];
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}
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}
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