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glibc/sysdeps/ieee754/dbl-64/sincos32.c
Paul Eggert 59ba27a63a Replace FSF snail mail address with URLs.
2012-02-09 23:18:22 +00:00

376 lines
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C
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/*
* IBM Accurate Mathematical Library
* written by International Business Machines Corp.
* Copyright (C) 2001, 2011 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, see <http://www.gnu.org/licenses/>.
*/
/****************************************************************/
/* MODULE_NAME: sincos32.c */
/* */
/* FUNCTIONS: ss32 */
/* cc32 */
/* c32 */
/* sin32 */
/* cos32 */
/* mpsin */
/* mpcos */
/* mpranred */
/* mpsin1 */
/* mpcos1 */
/* */
/* FILES NEEDED: endian.h mpa.h sincos32.h */
/* mpa.c */
/* */
/* Multi Precision sin() and cos() function with p=32 for sin()*/
/* cos() arcsin() and arccos() routines */
/* In addition mpranred() routine performs range reduction of */
/* a double number x into multi precision number y, */
/* such that y=x-n*pi/2, abs(y)<pi/4, n=0,+-1,+-2,.... */
/****************************************************************/
#include "endian.h"
#include "mpa.h"
#include "sincos32.h"
#include "math_private.h"
#ifndef SECTION
# define SECTION
#endif
/****************************************************************/
/* Compute Multi-Precision sin() function for given p. Receive */
/* Multi Precision number x and result stored at y */
/****************************************************************/
static void
SECTION
ss32(mp_no *x, mp_no *y, int p) {
int i;
double a;
#if 0
double b;
static const mp_no mpone = {1,{1.0,1.0}};
#endif
mp_no mpt1,x2,gor,sum ,mpk={1,{1.0}};
#if 0
mp_no mpt2;
#endif
for (i=1;i<=p;i++) mpk.d[i]=0;
__mul(x,x,&x2,p);
__cpy(&oofac27,&gor,p);
__cpy(&gor,&sum,p);
for (a=27.0;a>1.0;a-=2.0) {
mpk.d[1]=a*(a-1.0);
__mul(&gor,&mpk,&mpt1,p);
__cpy(&mpt1,&gor,p);
__mul(&x2,&sum,&mpt1,p);
__sub(&gor,&mpt1,&sum,p);
}
__mul(x,&sum,y,p);
}
/**********************************************************************/
/* Compute Multi-Precision cos() function for given p. Receive Multi */
/* Precision number x and result stored at y */
/**********************************************************************/
static void
SECTION
cc32(mp_no *x, mp_no *y, int p) {
int i;
double a;
#if 0
double b;
static const mp_no mpone = {1,{1.0,1.0}};
#endif
mp_no mpt1,x2,gor,sum ,mpk={1,{1.0}};
#if 0
mp_no mpt2;
#endif
for (i=1;i<=p;i++) mpk.d[i]=0;
__mul(x,x,&x2,p);
mpk.d[1]=27.0;
__mul(&oofac27,&mpk,&gor,p);
__cpy(&gor,&sum,p);
for (a=26.0;a>2.0;a-=2.0) {
mpk.d[1]=a*(a-1.0);
__mul(&gor,&mpk,&mpt1,p);
__cpy(&mpt1,&gor,p);
__mul(&x2,&sum,&mpt1,p);
__sub(&gor,&mpt1,&sum,p);
}
__mul(&x2,&sum,y,p);
}
/***************************************************************************/
/* c32() computes both sin(x), cos(x) as Multi precision numbers */
/***************************************************************************/
void
SECTION
__c32(mp_no *x, mp_no *y, mp_no *z, int p) {
static const mp_no mpt={1,{1.0,2.0}}, one={1,{1.0,1.0}};
mp_no u,t,t1,t2,c,s;
int i;
__cpy(x,&u,p);
u.e=u.e-1;
cc32(&u,&c,p);
ss32(&u,&s,p);
for (i=0;i<24;i++) {
__mul(&c,&s,&t,p);
__sub(&s,&t,&t1,p);
__add(&t1,&t1,&s,p);
__sub(&mpt,&c,&t1,p);
__mul(&t1,&c,&t2,p);
__add(&t2,&t2,&c,p);
}
__sub(&one,&c,y,p);
__cpy(&s,z,p);
}
/************************************************************************/
/*Routine receive double x and two double results of sin(x) and return */
/*result which is more accurate */
/*Computing sin(x) with multi precision routine c32 */
/************************************************************************/
double
SECTION
__sin32(double x, double res, double res1) {
int p;
mp_no a,b,c;
p=32;
__dbl_mp(res,&a,p);
__dbl_mp(0.5*(res1-res),&b,p);
__add(&a,&b,&c,p);
if (x>0.8)
{ __sub(&hp,&c,&a,p);
__c32(&a,&b,&c,p);
}
else __c32(&c,&a,&b,p); /* b=sin(0.5*(res+res1)) */
__dbl_mp(x,&c,p); /* c = x */
__sub(&b,&c,&a,p);
/* if a>0 return min(res,res1), otherwise return max(res,res1) */
if (a.d[0]>0) return (res<res1)?res:res1;
else return (res>res1)?res:res1;
}
/************************************************************************/
/*Routine receive double x and two double results of cos(x) and return */
/*result which is more accurate */
/*Computing cos(x) with multi precision routine c32 */
/************************************************************************/
double
SECTION
__cos32(double x, double res, double res1) {
int p;
mp_no a,b,c;
p=32;
__dbl_mp(res,&a,p);
__dbl_mp(0.5*(res1-res),&b,p);
__add(&a,&b,&c,p);
if (x>2.4)
{ __sub(&pi,&c,&a,p);
__c32(&a,&b,&c,p);
b.d[0]=-b.d[0];
}
else if (x>0.8)
{ __sub(&hp,&c,&a,p);
__c32(&a,&c,&b,p);
}
else __c32(&c,&b,&a,p); /* b=cos(0.5*(res+res1)) */
__dbl_mp(x,&c,p); /* c = x */
__sub(&b,&c,&a,p);
/* if a>0 return max(res,res1), otherwise return min(res,res1) */
if (a.d[0]>0) return (res>res1)?res:res1;
else return (res<res1)?res:res1;
}
/*******************************************************************/
/*Compute sin(x+dx) as Multi Precision number and return result as */
/* double */
/*******************************************************************/
double
SECTION
__mpsin(double x, double dx) {
int p;
double y;
mp_no a,b,c;
p=32;
__dbl_mp(x,&a,p);
__dbl_mp(dx,&b,p);
__add(&a,&b,&c,p);
if (x>0.8) { __sub(&hp,&c,&a,p); __c32(&a,&b,&c,p); }
else __c32(&c,&a,&b,p); /* b = sin(x+dx) */
__mp_dbl(&b,&y,p);
return y;
}
/*******************************************************************/
/* Compute cos()of double-length number (x+dx) as Multi Precision */
/* number and return result as double */
/*******************************************************************/
double
SECTION
__mpcos(double x, double dx) {
int p;
double y;
mp_no a,b,c;
p=32;
__dbl_mp(x,&a,p);
__dbl_mp(dx,&b,p);
__add(&a,&b,&c,p);
if (x>0.8)
{ __sub(&hp,&c,&b,p);
__c32(&b,&c,&a,p);
}
else __c32(&c,&a,&b,p); /* a = cos(x+dx) */
__mp_dbl(&a,&y,p);
return y;
}
/******************************************************************/
/* mpranred() performs range reduction of a double number x into */
/* multi precision number y, such that y=x-n*pi/2, abs(y)<pi/4, */
/* n=0,+-1,+-2,.... */
/* Return int which indicates in which quarter of circle x is */
/******************************************************************/
int
SECTION
__mpranred(double x, mp_no *y, int p)
{
number v;
double t,xn;
int i,k,n;
static const mp_no one = {1,{1.0,1.0}};
mp_no a,b,c;
if (ABS(x) < 2.8e14) {
t = (x*hpinv.d + toint.d);
xn = t - toint.d;
v.d = t;
n =v.i[LOW_HALF]&3;
__dbl_mp(xn,&a,p);
__mul(&a,&hp,&b,p);
__dbl_mp(x,&c,p);
__sub(&c,&b,y,p);
return n;
}
else { /* if x is very big more precision required */
__dbl_mp(x,&a,p);
a.d[0]=1.0;
k = a.e-5;
if (k < 0) k=0;
b.e = -k;
b.d[0] = 1.0;
for (i=0;i<p;i++) b.d[i+1] = toverp[i+k];
__mul(&a,&b,&c,p);
t = c.d[c.e];
for (i=1;i<=p-c.e;i++) c.d[i]=c.d[i+c.e];
for (i=p+1-c.e;i<=p;i++) c.d[i]=0;
c.e=0;
if (c.d[1] >= 8388608.0)
{ t +=1.0;
__sub(&c,&one,&b,p);
__mul(&b,&hp,y,p);
}
else __mul(&c,&hp,y,p);
n = (int) t;
if (x < 0) { y->d[0] = - y->d[0]; n = -n; }
return (n&3);
}
}
/*******************************************************************/
/* Multi-Precision sin() function subroutine, for p=32. It is */
/* based on the routines mpranred() and c32(). */
/*******************************************************************/
double
SECTION
__mpsin1(double x)
{
int p;
int n;
mp_no u,s,c;
double y;
p=32;
n=__mpranred(x,&u,p); /* n is 0, 1, 2 or 3 */
__c32(&u,&c,&s,p);
switch (n) { /* in which quarter of unit circle y is*/
case 0:
__mp_dbl(&s,&y,p);
return y;
break;
case 2:
__mp_dbl(&s,&y,p);
return -y;
break;
case 1:
__mp_dbl(&c,&y,p);
return y;
break;
case 3:
__mp_dbl(&c,&y,p);
return -y;
break;
}
return 0; /* unreachable, to make the compiler happy */
}
/*****************************************************************/
/* Multi-Precision cos() function subroutine, for p=32. It is */
/* based on the routines mpranred() and c32(). */
/*****************************************************************/
double
SECTION
__mpcos1(double x)
{
int p;
int n;
mp_no u,s,c;
double y;
p=32;
n=__mpranred(x,&u,p); /* n is 0, 1, 2 or 3 */
__c32(&u,&c,&s,p);
switch (n) { /* in what quarter of unit circle y is*/
case 0:
__mp_dbl(&c,&y,p);
return y;
break;
case 2:
__mp_dbl(&c,&y,p);
return -y;
break;
case 1:
__mp_dbl(&s,&y,p);
return -y;
break;
case 3:
__mp_dbl(&s,&y,p);
return y;
break;
}
return 0; /* unreachable, to make the compiler happy */
}
/******************************************************************/
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