/**
 * \file CircularEngine.cpp
 * \brief Implementation for GeographicLib::CircularEngine class
 *
 * Copyright (c) Charles Karney (2011) <charles@karney.com> and licensed under
 * the MIT/X11 License. For more information, see
 * https://geographiclib.sourceforge.io/
 **********************************************************************/

#include <GeographicLib/CircularEngine.hpp>

namespace GeographicLib {

 using namespace std;

 Math::real CircularEngine::Value(bool gradp, real sl, real cl,
 real& gradx, real& grady, real& gradz) const
 {
 gradp = _gradp && gradp;
 const vector<real>& root( SphericalEngine::sqrttable() );

 // Initialize outer sum
 real vc = 0, vc2 = 0, vs = 0, vs2 = 0; // v [N + 1], v [N + 2]
 // vr, vt, vl and similar w variable accumulate the sums for the
 // derivatives wrt r, theta, and lambda, respectively.
 real vrc = 0, vrc2 = 0, vrs = 0, vrs2 = 0; // vr[N + 1], vr[N + 2]
 real vtc = 0, vtc2 = 0, vts = 0, vts2 = 0; // vt[N + 1], vt[N + 2]
 real vlc = 0, vlc2 = 0, vls = 0, vls2 = 0; // vl[N + 1], vl[N + 2]
 for (int m = _M; m >= 0; --m) { // m = M .. 0
 // Now Sc[m] = wc, Ss[m] = ws
 // Sc'[m] = wtc, Ss'[m] = wtc
 if (m) {
 real v, A, B; // alpha[m], beta[m + 1]
 switch (_norm) {
 case FULL:
 v = root[2] * root[2 * m + 3] / root[m + 1];
 A = cl * v * _uq;
 B = - v * root[2 * m + 5] / (root[8] * root[m + 2]) * _uq2;
 break;
 case SCHMIDT:
 v = root[2] * root[2 * m + 1] / root[m + 1];
 A = cl * v * _uq;
 B = - v * root[2 * m + 3] / (root[8] * root[m + 2]) * _uq2;
 break;
 default:
 A = B = 0;
 }
 v = A * vc + B * vc2 + _wc[m] ; vc2 = vc ; vc = v;
 v = A * vs + B * vs2 + _ws[m] ; vs2 = vs ; vs = v;
 if (gradp) {
 v = A * vrc + B * vrc2 + _wrc[m]; vrc2 = vrc; vrc = v;
 v = A * vrs + B * vrs2 + _wrs[m]; vrs2 = vrs; vrs = v;
 v = A * vtc + B * vtc2 + _wtc[m]; vtc2 = vtc; vtc = v;
 v = A * vts + B * vts2 + _wts[m]; vts2 = vts; vts = v;
 v = A * vlc + B * vlc2 + m*_ws[m]; vlc2 = vlc; vlc = v;
 v = A * vls + B * vls2 - m*_wc[m]; vls2 = vls; vls = v;
 }
 } else {
 real A, B, qs;
 switch (_norm) {
 case FULL:
 A = root[3] * _uq; // F[1]/(q*cl) or F[1]/(q*sl)
 B = - root[15]/2 * _uq2; // beta[1]/q
 break;
 case SCHMIDT:
 A = _uq;
 B = - root[3]/2 * _uq2;
 break;
 default:
 A = B = 0;
 }
 qs = _q / SphericalEngine::scale();
 vc = qs * (_wc[m] + A * (cl * vc + sl * vs ) + B * vc2);
 if (gradp) {
 qs /= _r;
 // The components of the gradient in circular coordinates are
 // r: dV/dr
 // theta: 1/r * dV/dtheta
 // lambda: 1/(r*u) * dV/dlambda
 vrc = - qs * (_wrc[m] + A * (cl * vrc + sl * vrs) + B * vrc2);
 vtc = qs * (_wtc[m] + A * (cl * vtc + sl * vts) + B * vtc2);
 vlc = qs / _u * ( A * (cl * vlc + sl * vls) + B * vlc2);
 }
 }
 }

 if (gradp) {
 // Rotate into cartesian (geocentric) coordinates
 gradx = cl * (_u * vrc + _t * vtc) - sl * vlc;
 grady = sl * (_u * vrc + _t * vtc) + cl * vlc;
 gradz = _t * vrc - _u * vtc ;
 }
 return vc;
 }

} // namespace GeographicLib