/*
* IBM Accurate Mathematical Library
* written by International Business Machines Corp.
* Copyright (C) 2001-2018 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 <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.h>
#include <math_private.h>
#include <stap-probe.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;
mp_no mpt1, x2, gor, sum, mpk = {1, {1.0}};
for (i = 1; i <= p; i++)
mpk.d[i] = 0;
__sqr (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;
mp_no mpt1, x2, gor, sum, mpk = {1, {1.0}};
for (i = 1; i <= p; i++)
mpk.d[i] = 0;
__sqr (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);
}
/* Compute both sin(x), cos(x) as Multi precision numbers. */
void
SECTION
__c32 (mp_no *x, mp_no *y, mp_no *z, int p)
{
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 (&__mptwo, &c, &t1, p);
__mul (&t1, &c, &t2, p);
__add (&t2, &t2, &c, p);
}
__sub (&__mpone, &c, y, p);
__cpy (&s, z, p);
}
/* 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 && res >= res1) || (a.d[0] <= 0 && res <= res1))
res = res1;
LIBC_PROBE (slowasin, 2, &res, &x);
return res;
}
/* 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 && res <= res1) || (a.d[0] <= 0 && res >= res1))
res = res1;
LIBC_PROBE (slowacos, 2, &res, &x);
return res;
}
/* Compute sin() of double-length number (X + DX) as Multi Precision number and
return result as double. If REDUCE_RANGE is true, X is assumed to be the
original input and DX is ignored. */
double
SECTION
__mpsin (double x, double dx, bool reduce_range)
{
double y;
mp_no a, b, c, s;
int n;
int p = 32;
if (reduce_range)
{
n = __mpranred (x, &a, p); /* n is 0, 1, 2 or 3. */
__c32 (&a, &c, &s, p);
}
else
{
n = -1;
__dbl_mp (x, &b, p);
__dbl_mp (dx, &c, p);
__add (&b, &c, &a, p);
if (x > 0.8)
{
__sub (&hp, &a, &b, p);
__c32 (&b, &s, &c, p);
}
else
__c32 (&a, &c, &s, p); /* b = sin(x+dx) */
}
/* Convert result based on which quarter of unit circle y is in. */
switch (n)
{
case 1:
__mp_dbl (&c, &y, p);
break;
case 3:
__mp_dbl (&c, &y, p);
y = -y;
break;
case 2:
__mp_dbl (&s, &y, p);
y = -y;
break;
/* Quadrant not set, so the result must be sin (X + DX), which is also in
S. */
case 0:
default:
__mp_dbl (&s, &y, p);
}
LIBC_PROBE (slowsin, 3, &x, &dx, &y);
return y;
}
/* Compute cos() of double-length number (X + DX) as Multi Precision number and
return result as double. If REDUCE_RANGE is true, X is assumed to be the
original input and DX is ignored. */
double
SECTION
__mpcos (double x, double dx, bool reduce_range)
{
double y;
mp_no a, b, c, s;
int n;
int p = 32;
if (reduce_range)
{
n = __mpranred (x, &a, p); /* n is 0, 1, 2 or 3. */
__c32 (&a, &c, &s, p);
}
else
{
n = -1;
__dbl_mp (x, &b, p);
__dbl_mp (dx, &c, p);
__add (&b, &c, &a, p);
if (x > 0.8)
{
__sub (&hp, &a, &b, p);
__c32 (&b, &s, &c, p);
}
else
__c32 (&a, &c, &s, p); /* a = cos(x+dx) */
}
/* Convert result based on which quarter of unit circle y is in. */
switch (n)
{
case 1:
__mp_dbl (&s, &y, p);
y = -y;
break;
case 3:
__mp_dbl (&s, &y, p);
break;
case 2:
__mp_dbl (&c, &y, p);
y = -y;
break;
/* Quadrant not set, so the result must be cos (X + DX), which is also
stored in C. */
case 0:
default:
__mp_dbl (&c, &y, p);
}
LIBC_PROBE (slowcos, 3, &x, &dx, &y);
return y;
}
/* Perform 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;
mp_no a, b, c;
if (fabs (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] >= HALFRAD)
{
t += 1.0;
__sub (&c, &__mpone, &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);
}
}