/* y=0 is not permitted if x<=0. No error messages are given. */
void __mpatan2(mp_no *y, mp_no *x, mp_no *z, int p) {
static const double ZERO = 0.0, ONE = 1.0;
mp_no mpone = {0,{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0}};
mp_no mpt1,mpt2,mpt3;
if (X[0] <= ZERO) {
mpone.e = 1; mpone.d[0] = mpone.d[1] = ONE;
__dvd(x,y,&mpt1,p); __mul(&mpt1,&mpt1,&mpt2,p);
if (mpt1.d[0] != ZERO) mpt1.d[0] = ONE;
__add(&mpt2,&mpone,&mpt3,p); __mpsqrt(&mpt3,&mpt2,p);
__add(&mpt1,&mpt2,&mpt3,p); mpt3.d[0]=Y[0];
__mpatan(&mpt3,&mpt1,p); __add(&mpt1,&mpt1,z,p);
}
else
{ __dvd(y,x,&mpt1,p);
__mpatan(&mpt1,z,p);
}
return;
}
void
SECTION
__mpatan(mp_no *x, mp_no *y, int p) {
int i,m,n;
double dx;
mp_no
mpone = {0,{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0}},
mptwo = {0,{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0}},
mptwoim1 = {0,{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0}};
mp_no mps,mpsm,mpt,mpt1,mpt2,mpt3;
/* Choose m and initiate mpone, mptwo & mptwoim1 */
if (EX>0) m=7;
else if (EX<0) m=0;
else {
__mp_dbl(x,&dx,p); dx=ABS(dx);
for (m=6; m>0; m--)
{if (dx>__atan_xm[m].d) break;}
}
mpone.e = mptwo.e = mptwoim1.e = 1;
mpone.d[0] = mpone.d[1] = mptwo.d[0] = mptwoim1.d[0] = ONE;
mptwo.d[1] = TWO;
/* Reduce x m times */
__mul(x,x,&mpsm,p);
if (m==0) __cpy(x,&mps,p);
else {
for (i=0; i<m; i++) {
__add(&mpone,&mpsm,&mpt1,p);
__mpsqrt(&mpt1,&mpt2,p);
__add(&mpt2,&mpt2,&mpt1,p);
__add(&mptwo,&mpsm,&mpt2,p);
__add(&mpt1,&mpt2,&mpt3,p);
__dvd(&mpsm,&mpt3,&mpt1,p);
__cpy(&mpt1,&mpsm,p);
}
__mpsqrt(&mpsm,&mps,p); mps.d[0] = X[0];
}
/* Evaluate a truncated power series for Atan(s) */
n=__atan_np[p]; mptwoim1.d[1] = __atan_twonm1[p].d;
__dvd(&mpsm,&mptwoim1,&mpt,p);
for (i=n-1; i>1; i--) {
mptwoim1.d[1] -= TWO;
__dvd(&mpsm,&mptwoim1,&mpt1,p);
__mul(&mpsm,&mpt,&mpt2,p);
__sub(&mpt1,&mpt2,&mpt,p);
}
__mul(&mps,&mpt,&mpt1,p);
__sub(&mps,&mpt1,&mpt,p);
/* Compute Atan(x) */
mptwoim1.d[1] = __atan_twom[m].d;
__mul(&mptwoim1,&mpt,y,p);
return;
}
