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352 lines
10 KiB
C
352 lines
10 KiB
C
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/*
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* IBM Accurate Mathematical Library
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* Copyright (c) International Business Machines Corp., 2001
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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 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 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, write to the Free Software
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* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
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*/
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/****************************************************************/
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/* MODULE_NAME: sincos32.c */
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/* */
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/* FUNCTIONS: ss32 */
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/* cc32 */
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/* c32 */
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/* sin32 */
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/* cos32 */
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/* mpsin */
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/* mpcos */
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/* mpranred */
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/* mpsin1 */
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/* mpcos1 */
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/* */
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/* FILES NEEDED: endian.h mpa.h sincos32.h */
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/* mpa.c */
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/* */
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/* Multi Precision sin() and cos() function with p=32 for sin()*/
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/* cos() arcsin() and arccos() routines */
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/* In addition mpranred() routine performs range reduction of */
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/* a double number x into multi precision number y, */
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/* such that y=x-n*pi/2, abs(y)<pi/4, n=0,+-1,+-2,.... */
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/****************************************************************/
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#include "endian.h"
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#include "mpa.h"
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#include "sincos32.h"
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/****************************************************************/
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/* Compute Multi-Precision sin() function for given p. Receive */
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/* Multi Precision number x and result stored at y */
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/****************************************************************/
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static void ss32(mp_no *x, mp_no *y, int p) {
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int i;
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double a;
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#if 0
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double b;
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static const mp_no mpone = {1,{1.0,1.0}};
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#endif
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mp_no mpt1,x2,gor,sum ,mpk={1,{1.0}};
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#if 0
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mp_no mpt2;
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#endif
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for (i=1;i<=p;i++) mpk.d[i]=0;
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mul(x,x,&x2,p);
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cpy(&oofac27,&gor,p);
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cpy(&gor,&sum,p);
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for (a=27.0;a>1.0;a-=2.0) {
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mpk.d[1]=a*(a-1.0);
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mul(&gor,&mpk,&mpt1,p);
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cpy(&mpt1,&gor,p);
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mul(&x2,&sum,&mpt1,p);
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sub(&gor,&mpt1,&sum,p);
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}
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mul(x,&sum,y,p);
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}
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/**********************************************************************/
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/* Compute Multi-Precision cos() function for given p. Receive Multi */
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/* Precision number x and result stored at y */
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/**********************************************************************/
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static void cc32(mp_no *x, mp_no *y, int p) {
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int i;
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double a;
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#if 0
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double b;
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static const mp_no mpone = {1,{1.0,1.0}};
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#endif
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mp_no mpt1,x2,gor,sum ,mpk={1,{1.0}};
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#if 0
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mp_no mpt2;
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#endif
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for (i=1;i<=p;i++) mpk.d[i]=0;
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mul(x,x,&x2,p);
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mpk.d[1]=27.0;
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mul(&oofac27,&mpk,&gor,p);
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cpy(&gor,&sum,p);
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for (a=26.0;a>2.0;a-=2.0) {
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mpk.d[1]=a*(a-1.0);
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mul(&gor,&mpk,&mpt1,p);
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cpy(&mpt1,&gor,p);
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mul(&x2,&sum,&mpt1,p);
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sub(&gor,&mpt1,&sum,p);
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}
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mul(&x2,&sum,y,p);
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}
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/***************************************************************************/
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/* c32() computes both sin(x), cos(x) as Multi precision numbers */
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/***************************************************************************/
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void __c32(mp_no *x, mp_no *y, mp_no *z, int p) {
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static const mp_no mpt={1,{1.0,2.0}}, one={1,{1.0,1.0}};
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mp_no u,t,t1,t2,c,s;
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int i;
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cpy(x,&u,p);
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u.e=u.e-1;
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cc32(&u,&c,p);
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ss32(&u,&s,p);
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for (i=0;i<24;i++) {
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mul(&c,&s,&t,p);
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sub(&s,&t,&t1,p);
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add(&t1,&t1,&s,p);
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sub(&mpt,&c,&t1,p);
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mul(&t1,&c,&t2,p);
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add(&t2,&t2,&c,p);
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}
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sub(&one,&c,y,p);
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cpy(&s,z,p);
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}
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/************************************************************************/
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/*Routine receive double x and two double results of sin(x) and return */
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/*result which is more accurate */
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/*Computing sin(x) with multi precision routine c32 */
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/************************************************************************/
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double __sin32(double x, double res, double res1) {
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int p;
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mp_no a,b,c;
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p=32;
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dbl_mp(res,&a,p);
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dbl_mp(0.5*(res1-res),&b,p);
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add(&a,&b,&c,p);
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if (x>0.8)
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{ sub(&hp,&c,&a,p);
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__c32(&a,&b,&c,p);
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}
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else __c32(&c,&a,&b,p); /* b=sin(0.5*(res+res1)) */
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dbl_mp(x,&c,p); /* c = x */
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sub(&b,&c,&a,p);
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/* if a>0 return min(res,res1), otherwise return max(res,res1) */
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if (a.d[0]>0) return (res<res1)?res:res1;
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else return (res>res1)?res:res1;
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}
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/************************************************************************/
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/*Routine receive double x and two double results of cos(x) and return */
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/*result which is more accurate */
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/*Computing cos(x) with multi precision routine c32 */
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/************************************************************************/
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double __cos32(double x, double res, double res1) {
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int p;
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mp_no a,b,c;
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p=32;
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dbl_mp(res,&a,p);
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dbl_mp(0.5*(res1-res),&b,p);
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add(&a,&b,&c,p);
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if (x>2.4)
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{ sub(&pi,&c,&a,p);
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__c32(&a,&b,&c,p);
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b.d[0]=-b.d[0];
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}
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else if (x>0.8)
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{ sub(&hp,&c,&a,p);
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__c32(&a,&c,&b,p);
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}
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else __c32(&c,&b,&a,p); /* b=cos(0.5*(res+res1)) */
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dbl_mp(x,&c,p); /* c = x */
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sub(&b,&c,&a,p);
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/* if a>0 return max(res,res1), otherwise return min(res,res1) */
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if (a.d[0]>0) return (res>res1)?res:res1;
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else return (res<res1)?res:res1;
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}
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/*******************************************************************/
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/*Compute sin(x+dx) as Multi Precision number and return result as */
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/* double */
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/*******************************************************************/
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double __mpsin(double x, double dx) {
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int p;
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double y;
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mp_no a,b,c;
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p=32;
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dbl_mp(x,&a,p);
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dbl_mp(dx,&b,p);
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add(&a,&b,&c,p);
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if (x>0.8) { sub(&hp,&c,&a,p); __c32(&a,&b,&c,p); }
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else __c32(&c,&a,&b,p); /* b = sin(x+dx) */
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__mp_dbl(&b,&y,p);
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return y;
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}
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/*******************************************************************/
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/* Compute cos()of double-length number (x+dx) as Multi Precision */
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/* number and return result as double */
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/*******************************************************************/
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double __mpcos(double x, double dx) {
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int p;
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double y;
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mp_no a,b,c;
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p=32;
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dbl_mp(x,&a,p);
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dbl_mp(dx,&b,p);
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add(&a,&b,&c,p);
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if (x>0.8)
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{ sub(&hp,&c,&b,p);
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__c32(&b,&a,&c,p);
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}
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else __c32(&c,&a,&b,p); /* a = cos(x+dx) */
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__mp_dbl(&a,&y,p);
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return y;
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}
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/******************************************************************/
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/* mpranred() performs range reduction of a double number x into */
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/* multi precision number y, such that y=x-n*pi/2, abs(y)<pi/4, */
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/* n=0,+-1,+-2,.... */
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/* Return int which indicates in which quarter of circle x is */
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/******************************************************************/
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int mpranred(double x, mp_no *y, int p)
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{
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number v;
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double t,xn;
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int i,k,n;
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static const mp_no one = {1,{1.0,1.0}};
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mp_no a,b,c;
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if (ABS(x) < 2.8e14) {
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t = (x*hpinv.d + toint.d);
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xn = t - toint.d;
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v.d = t;
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n =v.i[LOW_HALF]&3;
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dbl_mp(xn,&a,p);
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mul(&a,&hp,&b,p);
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dbl_mp(x,&c,p);
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sub(&c,&b,y,p);
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return n;
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}
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else { /* if x is very big more precision required */
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dbl_mp(x,&a,p);
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a.d[0]=1.0;
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k = a.e-5;
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if (k < 0) k=0;
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b.e = -k;
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b.d[0] = 1.0;
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for (i=0;i<p;i++) b.d[i+1] = toverp[i+k];
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mul(&a,&b,&c,p);
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t = c.d[c.e];
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for (i=1;i<=p-c.e;i++) c.d[i]=c.d[i+c.e];
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for (i=p+1-c.e;i<=p;i++) c.d[i]=0;
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c.e=0;
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if (c.d[1] >= 8388608.0)
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{ t +=1.0;
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sub(&c,&one,&b,p);
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mul(&b,&hp,y,p);
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}
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else mul(&c,&hp,y,p);
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n = (int) t;
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if (x < 0) { y->d[0] = - y->d[0]; n = -n; }
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return (n&3);
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}
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}
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/*******************************************************************/
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/* Multi-Precision sin() function subroutine, for p=32. It is */
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/* based on the routines mpranred() and c32(). */
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/*******************************************************************/
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double mpsin1(double x)
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{
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int p;
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int n;
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mp_no u,s,c;
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double y;
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p=32;
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n=mpranred(x,&u,p); /* n is 0, 1, 2 or 3 */
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__c32(&u,&c,&s,p);
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switch (n) { /* in which quarter of unit circle y is*/
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case 0:
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__mp_dbl(&s,&y,p);
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return y;
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break;
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case 2:
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__mp_dbl(&s,&y,p);
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return -y;
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break;
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case 1:
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__mp_dbl(&c,&y,p);
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return y;
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break;
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case 3:
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__mp_dbl(&c,&y,p);
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return -y;
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break;
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}
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return 0; /* unreachable, to make the compiler happy */
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}
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/*****************************************************************/
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/* Multi-Precision cos() function subroutine, for p=32. It is */
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/* based on the routines mpranred() and c32(). */
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/*****************************************************************/
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double mpcos1(double x)
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{
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int p;
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int n;
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mp_no u,s,c;
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double y;
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p=32;
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n=mpranred(x,&u,p); /* n is 0, 1, 2 or 3 */
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__c32(&u,&c,&s,p);
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switch (n) { /* in what quarter of unit circle y is*/
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case 0:
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__mp_dbl(&c,&y,p);
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return y;
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break;
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case 2:
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__mp_dbl(&c,&y,p);
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return -y;
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break;
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case 1:
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__mp_dbl(&s,&y,p);
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return -y;
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break;
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case 3:
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__mp_dbl(&s,&y,p);
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return y;
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break;
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}
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return 0; /* unreachable, to make the compiler happy */
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}
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/******************************************************************/
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