/* 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;
}
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 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;
}
double __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;
}
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 */
}
void
SECTION
__mptan (double x, mp_no *mpy, int p)
{
int n;
mp_no mpw, mpc, mps;
/* Negative or positive result. */
n = __mpranred (x, &mpw, p) & 0x00000001;
/* Computing sin(x) and cos(x). */
__c32 (&mpw, &mpc, &mps, p);
/* Second or fourth quarter of unit circle. */
if (n)
{
__dvd (&mpc, &mps, mpy, p);
mpy->d[0] *= -1;
}
/* tan is negative in this area. */
else
__dvd (&mps, &mpc, mpy, p);
}
