void CPositionOrbit::GetXYZ(double & x, double & y, double & z)
{
// Local variables (mostly renaming mParams variables for convenience).
// Remember to convert the angular parameters into radians.
double l1, l2, m1, m2, n1, n2;
double inc = mParams[0] * PI / 180.0;
double Omega = mParams[1] * PI / 180.0;
double omega = mParams[2] * PI / 180.0;
double alpha = mParams[3];
double e = mParams[4];
double tau = mParams[5];
double T = mParams[6];
double t = mTime;
// Pre-compute a few values
double n = ComputeN(T);
double M = ComputeM(tau, n, t);
double E = ComputeE(M, e);
double cos_E = cos(E);
double sin_E = sin(E);
double beta = sqrt(1 - e*e);
// Now compute the orbital coefficients
Compute_Coefficients(Omega, inc, omega, l1, m1, n1, l2, m2, n2);
Compute_xyz(alpha, beta, e, l1, l2, m1, m2, n1, n2, cos_E, sin_E, x, y, z);
}
void exp(RR& res, const RR& x)
{
if (x >= NTL_OVFBND || x <= -NTL_OVFBND)
Error("RR: overflow");
long p = RR::precision();
// step 0: write x = n + f, n an integer and |f| <= 1/2
// careful -- we want to compute f to > p bits of precision
RR f, nn;
RR::SetPrecision(NTL_BITS_PER_LONG);
round(nn, x);
RR::SetPrecision(p + 10);
sub(f, x, nn);
long n = to_long(nn);
// step 1: calculate t1 = e^n by repeated squaring
RR::SetPrecision(p + NumBits(n) + 10);
RR e;
ComputeE(e);
RR::SetPrecision(p + 10);
RR t1;
power(t1, e, n);
// step 2: calculate t2 = e^f using Taylor series expansion
RR::SetPrecision(p + NumBits(p) + 10);
RR t2, s, s1, t;
long i;
s = 0;
t = 1;
for (i = 1; ; i++) {
add(s1, s, t);
if (s == s1) break;
xcopy(s, s1);
mul(t, t, f);
div(t, t, i);
}
xcopy(t2, s);
RR::SetPrecision(p);
mul(res, t1, t2);
}