/* Computation of the thermally averaged Gaunt factor and the corresponding Coulomb logarithm (for a hydrogen-like atom),
   according to the method and data presented in the paper of van Hoof et al. (MNRAS, 444, 420, 2014). */

#include "ExtMath.h"
#include <math.h>
#include "Plasma.h"

#define N_u 146     //number of grid points in u direction
#define N_g2 81     //number of grid points in gam2 direction
#define s_u (-16.0) //start value for lg(u)
#define s_g2 (-6.0) //start value for lg(gam2)
#define d 0.2       //step size in both directions

#define k_u (hPl/kB)
#define k_g2 (em_alpha*em_alpha*me*c*c/2/kB)

const double g_arr[N_u][N_g2]=
{{ 2.07575626e+01, 2.07575534e+01, 2.07575461e+01, 2.07575356e+01, 2.07574693e+01, 2.07574982e+01, 2.07574554e+01, 2.07573579e+01, 2.07572489e+01, 2.07571156e+01, 2.07569788e+01, 2.07566758e+01, 2.07561962e+01, 2.07555273e+01, 2.07545494e+01, 2.07531552e+01, 2.07510518e+01, 2.07479516e+01, 2.07435402e+01, 2.07372375e+01, 2.07283663e+01, 2.07159124e+01, 2.06988104e+01, 2.06756021e+01, 2.06447166e+01, 2.06044827e+01, 2.05534511e+01, 2.04904301e+01, 2.04148842e+01, 2.03271606e+01, 2.02284817e+01, 2.01207789e+01, 2.00063060e+01, 1.98870884e+01, 1.97648252e+01, 1.96407584e+01, 1.95155983e+01, 1.93897576e+01, 1.92634294e+01, 1.91369622e+01, 1.90103062e+01, 1.88834698e+01, 1.87566653e+01, 1.86298129e+01, 1.85028672e+01, 1.83759509e+01, 1.82490543e+01, 1.81220546e+01, 1.79951553e+01, 1.78682402e+01, 1.77412558e+01, 1.76142953e+01, 1.74873668e+01, 1.73604310e+01, 1.72334985e+01, 1.71065390e+01, 1.69795854e+01, 1.68526640e+01, 1.67256651e+01, 1.65987622e+01, 1.64717838e+01, 1.63448470e+01, 1.62179146e+01, 1.60909597e+01, 1.59640118e+01, 1.58370491e+01, 1.57101233e+01, 1.55831781e+01, 1.54562387e+01, 1.53292472e+01, 1.52023396e+01, 1.50753750e+01, 1.49484420e+01, 1.48215063e+01, 1.46945692e+01, 1.45675678e+01, 1.44406608e+01, 1.43136944e+01, 1.41867447e+01, 1.40598075e+01, 1.39328683e+01},
 { 2.05036528e+01, 2.05036480e+01, 2.05036407e+01, 2.05036175e+01, 2.05036006e+01, 2.05035695e+01, 2.05035357e+01, 2.05034704e+01, 2.05033818e+01, 2.05032577e+01, 2.05030551e+01, 2.05027511e+01, 2.05023037e+01, 2.05016501e+01, 2.05006727e+01, 2.04992342e+01, 2.04971230e+01, 2.04940744e+01, 2.04896581e+01, 2.04833921e+01, 2.04744959e+01, 2.04620643e+01, 2.04449380e+01, 2.04216979e+01, 2.03908457e+01, 2.03506592e+01, 2.02996050e+01, 2.02365724e+01, 2.01610259e+01, 2.00733019e+01, 1.99745887e+01, 1.98668770e+01, 1.97524146e+01, 1.96331597e+01, 1.95109656e+01, 1.93868639e+01, 1.92617155e+01, 1.91357986e+01, 1.90095905e+01, 1.88830500e+01, 1.87563534e+01, 1.86296009e+01, 1.85027941e+01, 1.83758782e+01, 1.82489837e+01, 1.81220629e+01, 1.79951194e+01, 1.78681683e+01, 1.77412926e+01, 1.76143067e+01, 1.74873471e+01, 1.73604193e+01, 1.72334839e+01, 1.71065513e+01, 1.69795577e+01, 1.68526265e+01, 1.67257171e+01, 1.65987277e+01, 1.64717993e+01, 1.63448373e+01, 1.62178955e+01, 1.60909679e+01, 1.59640167e+01, 1.58370652e+01, 1.57101026e+01, 1.55831719e+01, 1.54562360e+01, 1.53292920e+01, 1.52023353e+01, 1.50753994e+01, 1.49484285e+01, 1.48214777e+01, 1.46945196e+01, 1.45676224e+01, 1.44406307e+01, 1.43137164e+01, 1.41867480e+01, 1.40597984e+01, 1.39328612e+01, 1.38059217e+01, 1.36789688e+01},
 { 2.02497421e+01, 2.02497373e+01, 2.02497300e+01, 2.02497077e+01, 2.02497207e+01, 2.02496842e+01, 2.02496314e+01, 2.02495855e+01, 2.02494970e+01, 2.02493757e+01, 2.02491649e+01, 2.02488663e+01, 2.02484310e+01, 2.02477677e+01, 2.02467907e+01, 2.02453521e+01, 2.02432487e+01, 2.02401935e+01, 2.02357552e+01, 2.02295111e+01, 2.02205687e+01, 2.02081258e+01, 2.01910156e+01, 2.01677847e+01, 2.01369167e+01, 2.00967264e+01, 2.00457370e+01, 1.99827049e+01, 1.99071585e+01, 1.98194347e+01, 1.97207627e+01, 1.96130191e+01, 1.94985008e+01, 1.93792802e+01, 1.92570523e+01, 1.91329782e+01, 1.90077670e+01, 1.88819592e+01, 1.87556740e+01, 1.86291446e+01, 1.85024946e+01, 1.83757402e+01, 1.82488556e+01, 1.81219649e+01, 1.79950895e+01, 1.78681727e+01, 1.77412583e+01, 1.76143392e+01, 1.74873626e+01, 1.73604314e+01, 1.72334712e+01, 1.71065364e+01, 1.69796038e+01, 1.68526110e+01, 1.67256797e+01, 1.65987308e+01, 1.64717883e+01, 1.63448526e+01, 1.62179019e+01, 1.60909544e+01, 1.59640212e+01, 1.58370665e+01, 1.57101188e+01, 1.55831860e+01, 1.54562254e+01, 1.53292895e+01, 1.52023521e+01, 1.50753546e+01, 1.49484529e+01, 1.48215163e+01, 1.46945241e+01, 1.45675732e+01, 1.44406551e+01, 1.43137014e+01, 1.41867700e+01, 1.40598110e+01, 1.39328576e+01, 1.38059150e+01, 1.36789752e+01, 1.35520224e+01, 1.34250670e+01},
 { 1.99958725e+01, 1.99958677e+01, 1.99958658e+01, 1.99958563e+01, 1.99958020e+01, 1.99957635e+01, 1.99957396e+01, 1.99956808e+01, 1.99955990e+01, 1.99954441e+01, 1.99952571e+01, 1.99949599e+01, 1.99945208e+01, 1.99938590e+01, 1.99928807e+01, 1.99914334e+01, 1.99893384e+01, 1.99862605e+01, 1.99818688e+01, 1.99755771e+01, 1.99666698e+01, 1.99542245e+01, 1.99371405e+01, 1.99138810e+01, 1.98830446e+01, 1.98428609e+01, 1.97918281e+01, 1.97287615e+01, 1.96532154e+01, 1.95655013e+01, 1.94668245e+01, 1.93591447e+01, 1.92446232e+01, 1.91254008e+01, 1.90031692e+01, 1.88790674e+01, 1.87538988e+01, 1.86280796e+01, 1.85017688e+01, 1.83752777e+01, 1.82486278e+01, 1.81218106e+01, 1.79949508e+01, 1.78681357e+01, 1.77411946e+01, 1.76142946e+01, 1.74873159e+01, 1.73603974e+01, 1.72334804e+01, 1.71065324e+01, 1.69795814e+01, 1.68526560e+01, 1.67256641e+01, 1.65987327e+01, 1.64717840e+01, 1.63448418e+01, 1.62179149e+01, 1.60909599e+01, 1.59640080e+01, 1.58370448e+01, 1.57101235e+01, 1.55831725e+01, 1.54562096e+01, 1.53292788e+01, 1.52023460e+01, 1.50754053e+01, 1.49484083e+01, 1.48215004e+01, 1.46945355e+01, 1.45675777e+01, 1.44406379e+01, 1.43137044e+01, 1.41867550e+01, 1.40598005e+01, 1.39328676e+01, 1.38059113e+01, 1.36789223e+01, 1.35520319e+01, 1.34250760e+01, 1.32981207e+01, 1.31711882e+01},
 { 1.97419688e+01, 1.97419640e+01, 1.97419637e+01, 1.97419460e+01, 1.97419228e+01, 1.97418972e+01, 1.97418636e+01, 1.97418049e+01, 1.97417226e+01, 1.97415841e+01, 1.97413842e+01, 1.97410901e+01, 1.97406433e+01, 1.97399825e+01, 1.97390043e+01, 1.97375654e+01, 1.97354619e+01, 1.97323708e+01, 1.97280135e+01, 1.97216767e+01, 1.97128027e+01, 1.97003502e+01, 1.96832449e+01, 1.96600072e+01, 1.96291279e+01, 1.95889543e+01, 1.95378932e+01, 1.94748607e+01, 1.93993142e+01, 1.93116040e+01, 1.92129755e+01, 1.91052637e+01, 1.89907406e+01, 1.88715278e+01, 1.87492962e+01, 1.86251834e+01, 1.85000012e+01, 1.83741412e+01, 1.82478676e+01, 1.81214110e+01, 1.79946940e+01, 1.78679262e+01, 1.77410863e+01, 1.76142056e+01, 1.74873133e+01, 1.73603416e+01, 1.72334401e+01, 1.71065008e+01, 1.69795632e+01, 1.68526323e+01, 1.67257131e+01, 1.65987256e+01, 1.64717854e+01, 1.63448370e+01, 1.62178952e+01, 1.60909680e+01, 1.59640132e+01, 1.58370658e+01, 1.57101032e+01, 1.55831768e+01, 1.54562320e+01, 1.53292925e+01, 1.52023322e+01, 1.50753966e+01, 1.49484585e+01, 1.48214710e+01, 1.46945540e+01, 1.45675890e+01, 1.44406385e+01, 1.43136804e+01, 1.41867579e+01, 1.40598044e+01, 1.39328163e+01, 1.38059211e+01, 1.36789636e+01, 1.35520458e+01, 1.34250854e+01, 1.32981326e+01, 1.31711996e+01, 1.30442417e+01, 1.29172852e+01},
 { 1.94880544e+01, 1.94880646e+01, 1.94880574e+01, 1.94880643e+01, 1.94880401e+01, 1.94880219e+01, 1.94879830e+01, 1.94879286e+01, 1.94878362e+01, 1.94877083e+01, 1.94875025e+01, 1.94871523e+01, 1.94867618e+01, 1.94861000e+01, 1.94851232e+01, 1.94836276e+01, 1.94815301e+01, 1.94785210e+01, 1.94741175e+01, 1.94678321e+01, 1.94589360e+01, 1.94464521e+01, 1.94293416e+01, 1.94061089e+01, 1.93752425e+01, 1.93350524e+01, 1.92840208e+01, 1.92209890e+01, 1.91454487e+01, 1.90577251e+01, 1.89590228e+01, 1.88513017e+01, 1.87367932e+01, 1.86175761e+01, 1.84953523e+01, 1.83712710e+01, 1.82460963e+01, 1.81202702e+01, 1.79940380e+01, 1.78674838e+01, 1.77408095e+01, 1.76140327e+01, 1.74871962e+01, 1.73603315e+01, 1.72333686e+01, 1.71064867e+01, 1.69795306e+01, 1.68526101e+01, 1.67256505e+01, 1.65987398e+01, 1.64717777e+01, 1.63448507e+01, 1.62179006e+01, 1.60909485e+01, 1.59640210e+01, 1.58370664e+01, 1.57101188e+01, 1.55831566e+01, 1.54562255e+01, 1.53292897e+01, 1.52023458e+01, 1.50753890e+01, 1.49484531e+01, 1.48215118e+01, 1.46945157e+01, 1.45676075e+01, 1.44406513e+01, 1.43136921e+01, 1.41867548e+01, 1.40598154e+01, 1.39328621e+01, 1.38058701e+01, 1.36789786e+01, 1.35520256e+01, 1.34250991e+01, 1.32981090e+01, 1.31712100e+01, 1.30442530e+01, 1.29172983e+01, 1.27903560e+01, 1.26634187e+01},
 { 1.92342031e+01, 1.92342011e+01, 1.92341266e+01, 1.92341474e+01, 1.92341305e+01, 1.92341093e+01, 1.92340929e+01, 1.92339746e+01, 1.92339457e+01, 1.92337536e+01, 1.92335725e+01, 1.92332505e+01, 1.92328078e+01, 1.92321460e+01, 1.92311874e+01, 1.92297257e+01, 1.92276590e+01, 1.92246177e+01, 1.92202060e+01, 1.92139138e+01, 1.92050123e+01, 1.91925940e+01, 1.91754732e+01, 1.91522576e+01, 1.91213785e+01, 1.90811797e+01, 1.90301471e+01, 1.89670988e+01, 1.88915632e+01, 1.88038317e+01, 1.87051547e+01, 1.85974284e+01, 1.84829244e+01, 1.83637069e+01, 1.82414402e+01, 1.81174010e+01, 1.79921947e+01, 1.78664034e+01, 1.77401015e+01, 1.76136030e+01, 1.74868744e+01, 1.73601425e+01, 1.72333172e+01, 1.71063907e+01, 1.69795031e+01, 1.68525672e+01, 1.67256464e+01, 1.65987294e+01, 1.64717889e+01, 1.63448454e+01, 1.62179080e+01, 1.60909529e+01, 1.59640066e+01, 1.58370057e+01, 1.57101195e+01, 1.55831723e+01, 1.54562100e+01, 1.53292789e+01, 1.52023432e+01, 1.50754057e+01, 1.49484090e+01, 1.48215066e+01, 1.46945698e+01, 1.45675783e+01, 1.44406612e+01, 1.43136959e+01, 1.41867457e+01, 1.40597641e+01, 1.39328688e+01, 1.38059157e+01, 1.36789611e+01, 1.35520281e+01, 1.34250792e+01, 1.32981467e+01, 1.31711914e+01, 1.30442633e+01, 1.29172874e+01, 1.27903377e+01, 1.26634096e+01, 1.25364764e+01, 1.24094926e+01},
 { 1.89803014e+01, 1.89802776e+01, 1.89802579e+01, 1.89802697e+01, 1.89802285e+01, 1.89802038e+01, 1.89801989e+01, 1.89801064e+01, 1.89800517e+01, 1.89798849e+01, 1.89796973e+01, 1.89794180e+01, 1.89789722e+01, 1.89783117e+01, 1.89772890e+01, 1.89758797e+01, 1.89737627e+01, 1.89707076e+01, 1.89663174e+01, 1.89600261e+01, 1.89511284e+01, 1.89386861e+01, 1.89215708e+01, 1.88983650e+01, 1.88674858e+01, 1.88272952e+01, 1.87762364e+01, 1.87132375e+01, 1.86376232e+01, 1.85499699e+01, 1.84512567e+01, 1.83435811e+01, 1.82290626e+01, 1.81098494e+01, 1.79876135e+01, 1.78635435e+01, 1.77383646e+01, 1.76124768e+01, 1.74862164e+01, 1.73596994e+01, 1.72330190e+01, 1.71062170e+01, 1.69793769e+01, 1.68525139e+01, 1.67256066e+01, 1.65986898e+01, 1.64717721e+01, 1.63448311e+01, 1.62178899e+01, 1.60909586e+01, 1.59640079e+01, 1.58370733e+01, 1.57100588e+01, 1.55831760e+01, 1.54562317e+01, 1.53292634e+01, 1.52023322e+01, 1.50753967e+01, 1.49484589e+01, 1.48214627e+01, 1.46945541e+01, 1.45675897e+01, 1.44406319e+01, 1.43136925e+01, 1.41867582e+01, 1.40597993e+01, 1.39328624e+01, 1.38059223e+01, 1.36789721e+01, 1.35520147e+01, 1.34250816e+01, 1.32981246e+01, 1.31712058e+01, 1.30442449e+01, 1.29173026e+01, 1.27903698e+01, 1.26633915e+01, 1.25364645e+01, 1.24095124e+01, 1.22825466e+01, 1.21556235e+01},
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double lnC1(double T, double f)
{
 double log_u=log10(k_u*f/T);
 double log_g2=log10(k_g2/T);

 double idx_u=(log_u-s_u)/d;
 double idx_g2=(log_g2-s_g2)/d;

 double G=InterpolateBilinear((double*)g_arr, idx_u, idx_g2, N_u, N_g2, dNaN);

 return G*M_PI/sqrt(3.0);
}