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/*
almabench
Standard C version
17 April 2003
Written by Scott Robert Ladd.
No rights reserved. This is public domain software, for use by anyone.
A number-crunching benchmark that can be used as a fitness test for
evolving optimal compiler options via genetic algorithm.
This program calculates the daily ephemeris (at noon) for the years
2000-2099 using an algorithm developed by J.L. Simon, P. Bretagnon, J.
Chapront, M. Chapront-Touze, G. Francou and J. Laskar of the Bureau des
Longitudes, Paris, France), as detailed in Astronomy & Astrophysics
282, 663 (1994)
Note that the code herein is design for the purpose of testing
computational performance; error handling and other such "niceties"
is virtually non-existent.
Actual benchmark results can be found at:
http://www.coyotegulch.com
Please do not use this information or algorithm in any way that might
upset the balance of the universe or otherwise cause planets to impact
upon one another.
*/
#include <math.h>
#include <string.h>
#define PI 3.14159265358979323846
#define J2000 2451545.0
#define JCENTURY 36525.0
#define JMILLENIA 365250.0
#define TWOPI (2.0 * PI)
#define A2R (PI / 648000.0)
#define R2H (12.0 / PI)
#define R2D (180.0 / PI)
#define GAUSSK 0.01720209895
#define TEST_LOOPS 20
#define TEST_LENGTH 36525
#define sineps 0.3977771559319137
#define coseps 0.9174820620691818
extern double amas[8];
extern double a[8][3], dlm[8][3], e[8][3], pi[8][3], dinc[8][3], omega[8][3];
extern double kp[8][9], ca[8][9], sa[8][9], kq[8][10], cl[8][10], sl[8][10];
extern double cos_static(double), sin_static(double),
atan2_static(double, double), asin_static(double), sqrt_static(double),
fmod_static(double, double), fabs_static(double);
#define cos cos_static
#define sin sin_static
#define atan2 atan2_static
#define asin asin_static
#define sqrt sqrt_static
#define fmod fmod_static
#define fabs fabs_static
//---------------------------------------------------------------------------
// Normalize angle into the range -pi <= A < +pi.
double anpm (double a)
{
double w = fmod(a,TWOPI);
if (fabs(w) >= PI)
w = w - ((a < 0) ? -TWOPI : TWOPI);
return w;
}
//---------------------------------------------------------------------------
// The reference frame is equatorial and is with respect to the
// mean equator and equinox of epoch j2000.
void planetpv (double epoch[2], int np, double pv[2][3])
{
// working storage
int i, j, k;
double t, da, dl, de, dp, di, doh, dmu, arga, argl, am;
double ae, dae, ae2, at, r, v, si2, xq, xp, tl, xsw;
double xcw, xm2, xf, ci2, xms, xmc, xpxq2, x, y, z;
// time: julian millennia since j2000.
t = ((epoch[0] - J2000) + epoch[1]) / JMILLENIA;
// compute the mean elements.
da = a[np][0] + (a[np][1] + a[np][2] * t ) * t;
dl = (3600.0 * dlm[np][0] + (dlm[np][1] + dlm[np][2] * t ) * t ) * A2R;
de = e[np][0] + (e[np][1] + e[np][2] * t ) * t;
dp = anpm((3600.0 * pi[np][0] + (pi[np][1] + pi[np][2] * t ) * t ) * A2R );
di = (3600.0 * dinc[np][0] + (dinc[np][1] + dinc[np][2] * t ) * t ) * A2R;
doh = anpm((3600.0 * omega[np][0] + (omega[np][1] + omega[np][2] * t ) * t ) * A2R );
// apply the trigonometric terms.
dmu = 0.35953620 * t;
for (k = 0; k < 8; ++k)
{
arga = kp[np][k] * dmu;
argl = kq[np][k] * dmu;
da = da + (ca[np][k] * cos(arga) + sa[np][k] * sin(arga)) * 0.0000001;
dl = dl + (cl[np][k] * cos(argl) + sl[np][k] * sin(argl)) * 0.0000001;
}
arga = kp[np][8] * dmu;
da = da + t * (ca[np][8] * cos(arga) + sa[np][8] * sin(arga)) * 0.0000001;
for (k = 8; k <= 9; ++k)
{
argl = kq[np][k] * dmu;
dl = dl + t * ( cl[np][k] * cos(argl) + sl[np][k] * sin(argl) ) * 0.0000001;
}
dl = fmod(dl,TWOPI);
// iterative solution of kepler's equation to get eccentric anomaly.
am = dl - dp;
ae = am + de * sin(am);
k = 0;
while (1)
{
dae = (am - ae + de * sin(ae)) / (1.0 - de * cos(ae));
ae = ae + dae;
k = k + 1;
if ((k >= 10) || (fabs(dae) < 1e-12))
break;
}
// true anomaly.
ae2 = ae / 2.0;
at = 2.0 * atan2(sqrt((1.0 + de)/(1.0 - de)) * sin(ae2), cos(ae2));
// distance (au) and speed (radians per day).
r = da * (1.0 - de * cos(ae));
v = GAUSSK * sqrt((1.0 + 1.0 / amas[np] ) / (da * da * da));
si2 = sin(di / 2.0);
xq = si2 * cos(doh);
xp = si2 * sin(doh);
tl = at + dp;
xsw = sin(tl);
xcw = cos(tl);
xm2 = 2.0 * (xp * xcw - xq * xsw );
xf = da / sqrt(1.0 - de*de);
ci2 = cos(di / 2.0);
xms = (de * sin(dp) + xsw) * xf;
xmc = (de * cos(dp) + xcw) * xf;
xpxq2 = 2.0 * xp * xq;
// position (j2000 ecliptic x,y,z in au).
x = r * (xcw - xm2 * xp);
y = r * (xsw + xm2 * xq);
z = r * (-xm2 * ci2);
// rotate to equatorial.
pv[0][0] = x;
pv[0][1] = y * coseps - z * sineps;
pv[0][2] = y * sineps + z * coseps;
// velocity (j2000 ecliptic xdot,ydot,zdot in au/d).
x = v * ((-1.0 + 2.0 * xp * xp) * xms + xpxq2 * xmc);
y = v * (( 1.0 - 2.0 * xq * xq ) * xmc - xpxq2 * xms);
z = v * (2.0 * ci2 * (xp * xms + xq * xmc));
// rotate to equatorial.
pv[1][0] = x;
pv[1][1] = y * coseps - z * sineps;
pv[1][2] = y * sineps + z * coseps;
}
//---------------------------------------------------------------------------
// Computes RA, Declination, and distance from a state vector returned by
// planetpv.
void radecdist(double state[2][3], double rdd[3])
{
// distance
rdd[2] = sqrt(state[0][0] * state[0][0] + state[0][1] * state[0][1] + state[0][2] * state[0][2]);
// RA
rdd[0] = atan2(state[0][1], state[0][0]) * R2H;
if (rdd[0] < 0.0) rdd[0] += 24.0;
// Declination
rdd[1] = asin(state[0][2] / rdd[2]) * R2D;
}
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