math-funcs.c

/*
  liblrhsmm
  ===
  Copyright (c) 2016 Kanru Hua. All rights reserved.

  This file is part of liblrhsmm.

  liblrhsmm is free software: you can redistribute it and/or modify
  it under the terms of the GNU General Public License as published by
  the Free Software Foundation, either version 3 of the License, or
  (at your option) any later version.

  liblrhsmm is distributed in the hope that it will be useful,
  but WITHOUT ANY WARRANTY; without even the implied warranty of
  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  GNU General Public License for more details.

  You should have received a copy of the GNU General Public License
  along with liblrhsmm.  If not, see <http://www.gnu.org/licenses/>.
*/

#include "math-funcs.h"

FP_TYPE lrh_lse_table[lrh_lse_table_size] = {
  6.9314718e-01, 6.9264731e-01, 6.9214768e-01, 6.9164831e-01, 6.9114918e-01,
  6.9065031e-01, 6.9015168e-01, 6.8965331e-01, 6.8915518e-01, 6.8865731e-01,
  6.8815968e-01, 6.8766231e-01, 6.8716518e-01, 6.8666831e-01, 6.8617168e-01,
  6.8567531e-01, 6.8517918e-01, 6.8468331e-01, 6.8418768e-01, 6.8369230e-01,
  6.8319718e-01, 6.8270230e-01, 6.8220768e-01, 6.8171330e-01, 6.8121918e-01,
  6.8072530e-01, 6.8023168e-01, 6.7973830e-01, 6.7924518e-01, 6.7875230e-01,
  6.7825968e-01, 6.7776730e-01, 6.7727518e-01, 6.7678330e-01, 6.7629167e-01,
  6.7580030e-01, 6.7530917e-01, 6.7481830e-01, 6.7432767e-01, 6.7383729e-01,
  6.7334717e-01, 6.7285729e-01, 6.7236766e-01, 6.7187829e-01, 6.7138916e-01,
  6.7090028e-01, 6.7041166e-01, 6.6992328e-01, 6.6943515e-01, 6.6894728e-01,
  6.6845965e-01, 6.6797227e-01, 6.6748514e-01, 6.6699826e-01, 6.6651164e-01,
  6.6602526e-01, 6.6553913e-01, 6.6505325e-01, 6.6456762e-01, 6.6408224e-01,
  6.6359711e-01, 6.6311223e-01, 6.6262760e-01, 6.6214322e-01, 6.6165909e-01,
  6.6117521e-01, 6.6069158e-01, 6.6020820e-01, 6.5972507e-01, 6.5924219e-01,
  6.5875956e-01, 6.5827717e-01, 6.5779504e-01, 6.5731316e-01, 6.5683152e-01,
  6.5635014e-01, 6.5586901e-01, 6.5538812e-01, 6.5490749e-01, 6.5442710e-01,
  6.5394697e-01, 6.5346708e-01, 6.5298745e-01, 6.5250806e-01, 6.5202892e-01,
  6.5155003e-01, 6.5107140e-01, 6.5059301e-01, 6.5011487e-01, 6.4963698e-01,
  6.4915934e-01, 6.4868195e-01, 6.4820481e-01, 6.4772792e-01, 6.4725127e-01,
  6.4677488e-01, 6.4629874e-01, 6.4582284e-01, 6.4534720e-01, 6.4487181e-01,
  6.4439666e-01, 6.4392176e-01, 6.4344712e-01, 6.4297272e-01, 6.4249857e-01,
  6.4202467e-01, 6.4155102e-01, 6.4107762e-01, 6.4060447e-01, 6.4013157e-01,
  6.3965892e-01, 6.3918652e-01, 6.3871436e-01, 6.3824246e-01, 6.3777080e-01,
  6.3729940e-01, 6.3682824e-01, 6.3635733e-01, 6.3588667e-01, 6.3541626e-01,
  6.3494610e-01, 6.3447619e-01, 6.3400653e-01, 6.3353711e-01, 6.3306795e-01,
  6.3259904e-01, 6.3213037e-01, 6.3166195e-01, 6.3119378e-01, 6.3072586e-01,
  6.3025819e-01, 6.2979077e-01, 6.2932360e-01, 6.2885668e-01, 6.2839000e-01,
  6.2792358e-01, 6.2745740e-01, 6.2699147e-01, 6.2652579e-01, 6.2606036e-01,
  6.2559518e-01, 6.2513025e-01, 6.2466557e-01, 6.2420113e-01, 6.2373694e-01,
  6.2327301e-01, 6.2280932e-01, 6.2234588e-01, 6.2188269e-01, 6.2141974e-01,
  6.2095705e-01, 6.2049460e-01, 6.2003240e-01, 6.1957046e-01, 6.1910876e-01,
  6.1864730e-01, 6.1818610e-01, 6.1772515e-01, 6.1726444e-01, 6.1680398e-01,
  6.1634377e-01, 6.1588381e-01, 6.1542410e-01, 6.1496464e-01, 6.1450542e-01,
  6.1404645e-01, 6.1358773e-01, 6.1312926e-01, 6.1267104e-01, 6.1221307e-01,
  6.1175534e-01, 6.1129786e-01, 6.1084063e-01, 6.1038365e-01, 6.0992692e-01,
  6.0947043e-01, 6.0901419e-01, 6.0855820e-01, 6.0810246e-01, 6.0764697e-01,
  6.0719172e-01, 6.0673673e-01, 6.0628198e-01, 6.0582748e-01, 6.0537322e-01,
  6.0491922e-01, 6.0446546e-01, 6.0401195e-01, 6.0355869e-01, 6.0310568e-01,
  6.0265291e-01, 6.0220039e-01, 6.0174812e-01, 6.0129610e-01, 6.0084432e-01,
  6.0039279e-01, 5.9994151e-01, 5.9949048e-01, 5.9903970e-01, 5.9858916e-01,
  5.9813887e-01, 5.9768883e-01, 5.9723903e-01, 5.9678949e-01, 5.9634019e-01,
  5.9589113e-01, 5.9544233e-01, 5.9499377e-01, 5.9454546e-01, 5.9409740e-01,
  5.9364958e-01, 5.9320201e-01, 5.9275469e-01, 5.9230762e-01, 5.9186079e-01,
  5.9141421e-01, 5.9096788e-01, 5.9052179e-01, 5.9007595e-01, 5.8963036e-01,
  5.8918502e-01, 5.8873992e-01, 5.8829507e-01, 5.8785047e-01, 5.8740611e-01,
  5.8696200e-01, 5.8651814e-01, 5.8607452e-01, 5.8563115e-01, 5.8518803e-01,
  5.8474516e-01, 5.8430253e-01, 5.8386015e-01, 5.8341801e-01, 5.8297612e-01,
  5.8253448e-01, 5.8209308e-01, 5.8165193e-01, 5.8121103e-01, 5.8077038e-01,
  5.8032997e-01, 5.7988980e-01, 5.7944989e-01, 5.7901022e-01, 5.7857079e-01,
  5.7813161e-01, 5.7769268e-01, 5.7725400e-01, 5.7681556e-01, 5.7637737e-01,
  5.7593942e-01, 5.7550172e-01, 5.7506427e-01, 5.7462706e-01, 5.7419009e-01,
  5.7375338e-01, 5.7331691e-01, 5.7288068e-01, 5.7244471e-01, 5.7200897e-01,
  5.7157349e-01, 5.7113825e-01, 5.7070325e-01, 5.7026850e-01, 5.6983400e-01,
  5.6939974e-01, 5.6896573e-01, 5.6853196e-01, 5.6809844e-01, 5.6766516e-01,
  5.6723214e-01, 5.6679935e-01, 5.6636681e-01, 5.6593452e-01, 5.6550247e-01,
  5.6507067e-01, 5.6463911e-01, 5.6420780e-01, 5.6377673e-01, 5.6334591e-01,
  5.6291533e-01, 5.6248500e-01, 5.6205492e-01, 5.6162508e-01, 5.6119548e-01,
  5.6076613e-01, 5.6033702e-01, 5.5990816e-01, 5.5947955e-01, 5.5905117e-01,
  5.5862305e-01, 5.5819517e-01, 5.5776753e-01, 5.5734014e-01, 5.5691299e-01,
  5.5648609e-01, 5.5605943e-01, 5.5563302e-01, 5.5520685e-01, 5.5478092e-01,
  5.5435524e-01, 5.5392981e-01, 5.5350462e-01, 5.5307967e-01, 5.5265497e-01,
  5.5223051e-01, 5.5180630e-01, 5.5138233e-01, 5.5095860e-01, 5.5053512e-01,
  5.5011189e-01, 5.4968889e-01, 5.4926615e-01, 5.4884364e-01, 5.4842138e-01,
  5.4799936e-01, 5.4757759e-01, 5.4715606e-01, 5.4673478e-01, 5.4631373e-01,
  5.4589294e-01, 5.4547238e-01, 5.4505207e-01, 5.4463201e-01, 5.4421218e-01,
  5.4379260e-01, 5.4337327e-01, 5.4295418e-01, 5.4253533e-01, 5.4211672e-01,
  5.4169836e-01, 5.4128024e-01, 5.4086236e-01, 5.4044473e-01, 5.4002734e-01,
  5.3961020e-01, 5.3919329e-01, 5.3877663e-01, 5.3836022e-01, 5.3794404e-01,
  5.3752811e-01, 5.3711242e-01, 5.3669698e-01, 5.3628178e-01, 5.3586682e-01,
  5.3545210e-01, 5.3503763e-01, 5.3462339e-01, 5.3420941e-01, 5.3379566e-01,
  5.3338216e-01, 5.3296889e-01, 5.3255588e-01, 5.3214310e-01, 5.3173057e-01,
  5.3131827e-01, 5.3090622e-01, 5.3049442e-01, 5.3008285e-01, 5.2967153e-01,
  5.2926045e-01, 5.2884961e-01, 5.2843901e-01, 5.2802866e-01, 5.2761855e-01,
  5.2720868e-01, 5.2679905e-01, 5.2638966e-01, 5.2598052e-01, 5.2557161e-01,
  5.2516295e-01, 5.2475453e-01, 5.2434635e-01, 5.2393841e-01, 5.2353072e-01,
  5.2312326e-01, 5.2271605e-01, 5.2230908e-01, 5.2190235e-01, 5.2149586e-01,
  5.2108961e-01, 5.2068361e-01, 5.2027784e-01, 5.1987232e-01, 5.1946704e-01,
  5.1906199e-01, 5.1865719e-01, 5.1825263e-01, 5.1784831e-01, 5.1744423e-01,
  5.1704040e-01, 5.1663680e-01, 5.1623344e-01, 5.1583033e-01, 5.1542745e-01,
  5.1502482e-01, 5.1462242e-01, 5.1422027e-01, 5.1381836e-01, 5.1341668e-01,
  5.1301525e-01, 5.1261406e-01, 5.1221311e-01, 5.1181240e-01, 5.1141192e-01,
  5.1101169e-01, 5.1061170e-01, 5.1021195e-01, 5.0981244e-01, 5.0941317e-01,
  5.0901413e-01, 5.0861534e-01, 5.0821679e-01, 5.0781848e-01, 5.0742040e-01,
  5.0702257e-01, 5.0662498e-01, 5.0622762e-01, 5.0583051e-01, 5.0543363e-01,
  5.0503699e-01, 5.0464060e-01, 5.0424444e-01, 5.0384852e-01, 5.0345284e-01,
  5.0305740e-01, 5.0266220e-01, 5.0226724e-01, 5.0187251e-01, 5.0147803e-01,
  5.0108378e-01, 5.0068978e-01, 5.0029601e-01, 4.9990248e-01, 4.9950919e-01,
  4.9911613e-01, 4.9872332e-01, 4.9833075e-01, 4.9793841e-01, 4.9754631e-01,
  4.9715445e-01, 4.9676283e-01, 4.9637144e-01, 4.9598030e-01, 4.9558939e-01,
  4.9519872e-01, 4.9480829e-01, 4.9441810e-01, 4.9402814e-01, 4.9363843e-01,
  4.9324895e-01, 4.9285970e-01, 4.9247070e-01, 4.9208193e-01, 4.9169340e-01,
  4.9130511e-01, 4.9091706e-01, 4.9052924e-01, 4.9014166e-01, 4.8975432e-01,
  4.8936722e-01, 4.8898035e-01, 4.8859372e-01, 4.8820733e-01, 4.8782117e-01,
  4.8743525e-01, 4.8704957e-01, 4.8666413e-01, 4.8627892e-01, 4.8589395e-01,
  4.8550921e-01, 4.8512471e-01, 4.8474045e-01, 4.8435643e-01, 4.8397264e-01,
  4.8358909e-01, 4.8320577e-01, 4.8282269e-01, 4.8243985e-01, 4.8205724e-01,
  4.8167487e-01, 4.8129274e-01, 4.8091084e-01, 4.8052918e-01, 4.8014775e-01,
  4.7976656e-01, 4.7938561e-01, 4.7900489e-01, 4.7862441e-01, 4.7824416e-01,
  4.7786415e-01, 4.7748437e-01, 4.7710483e-01, 4.7672553e-01, 4.7634646e-01,
  4.7596763e-01, 4.7558903e-01, 4.7521066e-01, 4.7483254e-01, 4.7445464e-01,
  4.7407698e-01, 4.7369956e-01, 4.7332237e-01, 4.7294542e-01, 4.7256870e-01,
  4.7219222e-01, 4.7181597e-01, 4.7143995e-01, 4.7106417e-01, 4.7068863e-01,
  4.7031332e-01, 4.6993824e-01, 4.6956340e-01, 4.6918879e-01, 4.6881442e-01,
  4.6844028e-01, 4.6806637e-01, 4.6769270e-01, 4.6731927e-01, 4.6694606e-01,
  4.6657309e-01, 4.6620036e-01, 4.6582786e-01, 4.6545559e-01, 4.6508356e-01,
  4.6471175e-01, 4.6434019e-01, 4.6396885e-01, 4.6359775e-01, 4.6322689e-01,
  4.6285625e-01, 4.6248585e-01, 4.6211569e-01, 4.6174575e-01, 4.6137605e-01,
  4.6100658e-01, 4.6063735e-01, 4.6026835e-01, 4.5989958e-01, 4.5953104e-01,
  4.5916274e-01, 4.5879466e-01, 4.5842683e-01, 4.5805922e-01, 4.5769185e-01,
  4.5732470e-01, 4.5695780e-01, 4.5659112e-01, 4.5622467e-01, 4.5585846e-01,
  4.5549248e-01, 4.5512673e-01, 4.5476122e-01, 4.5439593e-01, 4.5403088e-01,
  4.5366606e-01, 4.5330147e-01, 4.5293711e-01, 4.5257299e-01, 4.5220909e-01,
  4.5184543e-01, 4.5148200e-01, 4.5111880e-01, 4.5075583e-01, 4.5039309e-01,
  4.5003058e-01, 4.4966831e-01, 4.4930626e-01, 4.4894445e-01, 4.4858286e-01,
  4.4822151e-01, 4.4786039e-01, 4.4749950e-01, 4.4713884e-01, 4.4677841e-01,
  4.4641821e-01, 4.4605824e-01, 4.4569850e-01, 4.4533899e-01, 4.4497972e-01,
  4.4462067e-01, 4.4426185e-01, 4.4390326e-01, 4.4354491e-01, 4.4318678e-01,
  4.4282888e-01, 4.4247121e-01, 4.4211378e-01, 4.4175657e-01, 4.4139959e-01,
  4.4104284e-01, 4.4068632e-01, 4.4033003e-01, 4.3997397e-01, 4.3961813e-01,
  4.3926253e-01, 4.3890716e-01, 4.3855201e-01, 4.3819710e-01, 4.3784241e-01,
  4.3748795e-01, 4.3713372e-01, 4.3677972e-01, 4.3642595e-01, 4.3607241e-01,
  4.3571909e-01, 4.3536600e-01, 4.3501315e-01, 4.3466052e-01, 4.3430811e-01,
  4.3395594e-01, 4.3360400e-01, 4.3325228e-01, 4.3290079e-01, 4.3254953e-01,
  4.3219850e-01, 4.3184769e-01, 4.3149711e-01, 4.3114676e-01, 4.3079664e-01,
  4.3044674e-01, 4.3009708e-01, 4.2974764e-01, 4.2939842e-01, 4.2904944e-01,
  4.2870068e-01, 4.2835215e-01, 4.2800384e-01, 4.2765576e-01, 4.2730791e-01,
  4.2696029e-01, 4.2661289e-01, 4.2626572e-01, 4.2591878e-01, 4.2557206e-01,
  4.2522557e-01, 4.2487931e-01, 4.2453327e-01, 4.2418746e-01, 4.2384187e-01,
  4.2349651e-01, 4.2315138e-01, 4.2280647e-01, 4.2246179e-01, 4.2211733e-01,
  4.2177310e-01, 4.2142910e-01, 4.2108532e-01, 4.2074177e-01, 4.2039844e-01,
  4.2005534e-01, 4.1971246e-01, 4.1936981e-01, 4.1902738e-01, 4.1868518e-01,
  4.1834320e-01, 4.1800145e-01, 4.1765993e-01, 4.1731862e-01, 4.1697755e-01,
  4.1663670e-01, 4.1629607e-01, 4.1595567e-01, 4.1561549e-01, 4.1527553e-01,
  4.1493580e-01, 4.1459630e-01, 4.1425702e-01, 4.1391796e-01, 4.1357913e-01,
  4.1324052e-01, 4.1290213e-01, 4.1256397e-01, 4.1222604e-01, 4.1188832e-01,
  4.1155083e-01, 4.1121357e-01, 4.1087652e-01, 4.1053970e-01, 4.1020311e-01,
  4.0986673e-01, 4.0953059e-01, 4.0919466e-01, 4.0885896e-01, 4.0852347e-01,
  4.0818822e-01, 4.0785318e-01, 4.0751837e-01, 4.0718378e-01, 4.0684941e-01,
  4.0651527e-01, 4.0618135e-01, 4.0584765e-01, 4.0551417e-01, 4.0518092e-01,
  4.0484788e-01, 4.0451507e-01, 4.0418248e-01, 4.0385012e-01, 4.0351797e-01,
  4.0318605e-01, 4.0285435e-01, 4.0252287e-01, 4.0219161e-01, 4.0186057e-01,
  4.0152976e-01, 4.0119916e-01, 4.0086879e-01, 4.0053864e-01, 4.0020871e-01,
  3.9987900e-01, 3.9954951e-01, 3.9922024e-01, 3.9889120e-01, 3.9856237e-01,
  3.9823377e-01, 3.9790538e-01, 3.9757722e-01, 3.9724927e-01, 3.9692155e-01,
  3.9659405e-01, 3.9626676e-01, 3.9593970e-01, 3.9561286e-01, 3.9528624e-01,
  3.9495983e-01, 3.9463365e-01, 3.9430769e-01, 3.9398194e-01, 3.9365642e-01,
  3.9333111e-01, 3.9300603e-01, 3.9268116e-01, 3.9235652e-01, 3.9203209e-01,
  3.9170788e-01, 3.9138389e-01, 3.9106012e-01, 3.9073657e-01, 3.9041324e-01,
  3.9009013e-01, 3.8976723e-01, 3.8944456e-01, 3.8912210e-01, 3.8879986e-01,
  3.8847784e-01, 3.8815604e-01, 3.8783445e-01, 3.8751308e-01, 3.8719194e-01,
  3.8687101e-01, 3.8655029e-01, 3.8622980e-01, 3.8590952e-01, 3.8558946e-01,
  3.8526962e-01, 3.8495000e-01, 3.8463059e-01, 3.8431140e-01, 3.8399243e-01,
  3.8367367e-01, 3.8335514e-01, 3.8303682e-01, 3.8271871e-01, 3.8240083e-01,
  3.8208316e-01, 3.8176570e-01, 3.8144847e-01, 3.8113145e-01, 3.8081464e-01,
  3.8049805e-01, 3.8018168e-01, 3.7986553e-01, 3.7954959e-01, 3.7923387e-01,
  3.7891836e-01, 3.7860307e-01, 3.7828800e-01, 3.7797314e-01, 3.7765849e-01,
  3.7734407e-01, 3.7702985e-01, 3.7671586e-01, 3.7640208e-01, 3.7608851e-01,
  3.7577516e-01, 3.7546202e-01, 3.7514910e-01, 3.7483640e-01, 3.7452391e-01,
  3.7421163e-01, 3.7389957e-01, 3.7358772e-01, 3.7327609e-01, 3.7296467e-01,
  3.7265347e-01, 3.7234248e-01, 3.7203171e-01, 3.7172114e-01, 3.7141080e-01,
  3.7110067e-01, 3.7079075e-01, 3.7048104e-01, 3.7017155e-01, 3.6986227e-01,
  3.6955321e-01, 3.6924436e-01, 3.6893572e-01, 3.6862730e-01, 3.6831909e-01,
  3.6801109e-01, 3.6770331e-01, 3.6739574e-01, 3.6708838e-01, 3.6678123e-01,
  3.6647430e-01, 3.6616758e-01, 3.6586108e-01, 3.6555478e-01, 3.6524870e-01,
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  1.2739448e-03, 1.2726723e-03, 1.2714011e-03, 1.2701311e-03, 1.2688624e-03,
  1.2675950e-03, 1.2663289e-03, 1.2650640e-03, 1.2638003e-03, 1.2625380e-03,
  1.2612768e-03, 1.2600170e-03, 1.2587584e-03, 1.2575011e-03, 1.2562450e-03,
  1.2549901e-03, 1.2537366e-03, 1.2524842e-03, 1.2512332e-03, 1.2499833e-03,
  1.2487348e-03, 1.2474874e-03, 1.2462413e-03, 1.2449965e-03, 1.2437529e-03,
  1.2425105e-03, 1.2412694e-03, 1.2400295e-03, 1.2387909e-03, 1.2375535e-03,
  1.2363173e-03, 1.2350824e-03, 1.2338487e-03, 1.2326162e-03, 1.2313850e-03,
  1.2301550e-03, 1.2289262e-03, 1.2276986e-03, 1.2264723e-03, 1.2252472e-03,
  1.2240233e-03, 1.2228006e-03, 1.2215792e-03, 1.2203590e-03, 1.2191399e-03,
  1.2179222e-03, 1.2167056e-03, 1.2154902e-03, 1.2142761e-03, 1.2130631e-03,
  1.2118514e-03, 1.2106409e-03, 1.2094316e-03, 1.2082235e-03, 1.2070166e-03,
  1.2058109e-03, 1.2046064e-03, 1.2034032e-03, 1.2022011e-03, 1.2010002e-03,
  1.1998005e-03, 1.1986020e-03, 1.1974048e-03, 1.1962087e-03, 1.1950138e-03,
  1.1938201e-03, 1.1926276e-03, 1.1914362e-03, 1.1902461e-03, 1.1890572e-03,
  1.1878694e-03, 1.1866828e-03, 1.1854974e-03, 1.1843132e-03, 1.1831302e-03,
  1.1819484e-03, 1.1807677e-03, 1.1795882e-03, 1.1784099e-03, 1.1772328e-03,
  1.1760569e-03, 1.1748821e-03, 1.1737085e-03, 1.1725360e-03, 1.1713648e-03,
  1.1701947e-03, 1.1690257e-03, 1.1678580e-03, 1.1666914e-03, 1.1655260e-03,
  1.1643617e-03, 1.1631986e-03, 1.1620367e-03, 1.1608759e-03, 1.1597163e-03,
  1.1585578e-03, 1.1574005e-03, 1.1562443e-03, 1.1550893e-03, 1.1539355e-03,
  1.1527828e-03, 1.1516312e-03, 1.1504808e-03, 1.1493316e-03, 1.1481835e-03,
  1.1470366e-03, 1.1458907e-03, 1.1447461e-03, 1.1436026e-03, 1.1424602e-03,
  1.1413189e-03, 1.1401788e-03, 1.1390399e-03, 1.1379021e-03, 1.1367654e-03,
  1.1356298e-03, 1.1344954e-03, 1.1333621e-03, 1.1322300e-03, 1.1310989e-03,
  1.1299690e-03, 1.1288403e-03, 1.1277126e-03, 1.1265861e-03, 1.1254607e-03,
  1.1243365e-03, 1.1232133e-03, 1.1220913e-03, 1.1209704e-03, 1.1198506e-03,
  1.1187320e-03, 1.1176144e-03, 1.1164980e-03, 1.1153827e-03, 1.1142685e-03,
  1.1131554e-03, 1.1120434e-03, 1.1109325e-03, 1.1098227e-03, 1.1087141e-03,
  1.1076065e-03, 1.1065001e-03, 1.1053948e-03, 1.1042905e-03, 1.1031874e-03,
  1.1020854e-03, 1.1009845e-03, 1.0998846e-03, 1.0987859e-03, 1.0976883e-03,
  1.0965917e-03, 1.0954963e-03, 1.0944019e-03, 1.0933087e-03, 1.0922165e-03,
  1.0911254e-03, 1.0900354e-03, 1.0889465e-03, 1.0878587e-03, 1.0867720e-03,
  1.0856864e-03, 1.0846018e-03, 1.0835183e-03, 1.0824360e-03, 1.0813546e-03,
  1.0802744e-03, 1.0791953e-03, 1.0781172e-03, 1.0770402e-03, 1.0759643e-03,
  1.0748894e-03, 1.0738156e-03, 1.0727429e-03, 1.0716713e-03, 1.0706007e-03,
  1.0695312e-03, 1.0684628e-03, 1.0673955e-03, 1.0663292e-03, 1.0652639e-03,
  1.0641998e-03, 1.0631367e-03, 1.0620746e-03, 1.0610137e-03, 1.0599537e-03,
  1.0588949e-03, 1.0578371e-03, 1.0567803e-03, 1.0557246e-03, 1.0546700e-03,
  1.0536164e-03, 1.0525639e-03, 1.0515124e-03, 1.0504619e-03, 1.0494125e-03,
  1.0483642e-03, 1.0473169e-03, 1.0462707e-03, 1.0452255e-03, 1.0441813e-03,
  1.0431382e-03, 1.0420961e-03, 1.0410551e-03, 1.0400151e-03, 1.0389761e-03,
  1.0379382e-03, 1.0369013e-03, 1.0358655e-03, 1.0348307e-03, 1.0337969e-03,
  1.0327642e-03, 1.0317324e-03, 1.0307018e-03, 1.0296721e-03, 1.0286435e-03,
  1.0276159e-03, 1.0265893e-03, 1.0255637e-03, 1.0245392e-03, 1.0235157e-03,
  1.0224932e-03, 1.0214718e-03, 1.0204513e-03, 1.0194319e-03, 1.0184135e-03,
  1.0173961e-03, 1.0163797e-03, 1.0153644e-03, 1.0143500e-03, 1.0133367e-03,
  1.0123244e-03, 1.0113131e-03, 1.0103028e-03, 1.0092935e-03, 1.0082852e-03,
  1.0072780e-03, 1.0062717e-03, 1.0052664e-03, 1.0042622e-03, 1.0032589e-03,
  1.0022567e-03, 1.0012554e-03, 1.0002551e-03, 9.9925589e-04, 9.9825763e-04,
  9.9726037e-04, 9.9626410e-04, 9.9526883e-04, 9.9427455e-04, 9.9328127e-04,
  9.9228898e-04, 9.9129768e-04, 9.9030736e-04, 9.8931804e-04, 9.8832971e-04,
  9.8734236e-04, 9.8635600e-04, 9.8537062e-04, 9.8438622e-04, 9.8340281e-04,
  9.8242039e-04, 9.8143894e-04, 9.8045847e-04, 9.7947898e-04, 9.7850047e-04,
  9.7752294e-04, 9.7654638e-04, 9.7557080e-04, 9.7459619e-04, 9.7362255e-04,
  9.7264989e-04, 9.7167820e-04, 9.7070748e-04, 9.6973773e-04, 9.6876894e-04,
  9.6780113e-04, 9.6683428e-04, 9.6586839e-04, 9.6490347e-04, 9.6393952e-04,
  9.6297652e-04, 9.6201449e-04, 9.6105342e-04, 9.6009331e-04, 9.5913415e-04,
  9.5817596e-04, 9.5721872e-04, 9.5626243e-04, 9.5530711e-04, 9.5435273e-04,
  9.5339931e-04, 9.5244684e-04, 9.5149532e-04, 9.5054476e-04, 9.4959514e-04,
  9.4864647e-04, 9.4769874e-04, 9.4675197e-04, 9.4580614e-04, 9.4486125e-04,
  9.4391731e-04, 9.4297430e-04, 9.4203225e-04, 9.4109113e-04, 9.4015095e-04,
  9.3921171e-04, 9.3827341e-04, 9.3733604e-04, 9.3639961e-04, 9.3546412e-04,
  9.3452956e-04, 9.3359593e-04, 9.3266324e-04, 9.3173147e-04, 9.3080064e-04,
  9.2987074e-04, 9.2894176e-04, 9.2801372e-04, 9.2708660e-04, 9.2616040e-04,
  9.2523513e-04, 9.2431079e-04, 9.2338737e-04, 9.2246487e-04, 9.2154329e-04,
  9.2062263e-04, 9.1970289e-04, 9.1878407e-04, 9.1786616e-04, 9.1694918e-04,
  9.1603311e-04, 9.1511795e-04, 9.1420371e-04, 9.1329038e-04, 9.1237796e-04
};

FP_TYPE lrh_exp_table[lrh_exp_table_size] = {
  1.0000000e+00, 9.9800200e-01, 9.9600799e-01, 9.9401796e-01, 9.9203191e-01,
  9.9004983e-01, 9.8807171e-01, 9.8609754e-01, 9.8412732e-01, 9.8216103e-01,
  9.8019867e-01, 9.7824024e-01, 9.7628571e-01, 9.7433509e-01, 9.7238837e-01,
  9.7044553e-01, 9.6850658e-01, 9.6657150e-01, 9.6464029e-01, 9.6271294e-01,
  9.6078944e-01, 9.5886978e-01, 9.5695396e-01, 9.5504196e-01, 9.5313379e-01,
  9.5122942e-01, 9.4932887e-01, 9.4743211e-01, 9.4553914e-01, 9.4364995e-01,
  9.4176453e-01, 9.3988289e-01, 9.3800500e-01, 9.3613086e-01, 9.3426047e-01,
  9.3239382e-01, 9.3053090e-01, 9.2867169e-01, 9.2681621e-01, 9.2496443e-01,
  9.2311635e-01, 9.2127196e-01, 9.1943126e-01, 9.1759423e-01, 9.1576088e-01,
  9.1393119e-01, 9.1210515e-01, 9.1028276e-01, 9.0846402e-01, 9.0664890e-01,
  9.0483742e-01, 9.0302955e-01, 9.0122530e-01, 8.9942465e-01, 8.9762760e-01,
  8.9583414e-01, 8.9404426e-01, 8.9225796e-01, 8.9047522e-01, 8.8869605e-01,
  8.8692044e-01, 8.8514837e-01, 8.8337984e-01, 8.8161485e-01, 8.7985338e-01,
  8.7809543e-01, 8.7634100e-01, 8.7459006e-01, 8.7284263e-01, 8.7109869e-01,
  8.6935824e-01, 8.6762126e-01, 8.6588775e-01, 8.6415770e-01, 8.6243111e-01,
  8.6070798e-01, 8.5898828e-01, 8.5727202e-01, 8.5555919e-01, 8.5384978e-01,
  8.5214379e-01, 8.5044120e-01, 8.4874202e-01, 8.4704623e-01, 8.4535383e-01,
  8.4366482e-01, 8.4197917e-01, 8.4029690e-01, 8.3861798e-01, 8.3694242e-01,
  8.3527021e-01, 8.3360134e-01, 8.3193580e-01, 8.3027359e-01, 8.2861471e-01,
  8.2695913e-01, 8.2530687e-01, 8.2365790e-01, 8.2201223e-01, 8.2036985e-01,
  8.1873075e-01, 8.1709493e-01, 8.1546237e-01, 8.1383308e-01, 8.1220704e-01,
  8.1058425e-01, 8.0896470e-01, 8.0734839e-01, 8.0573530e-01, 8.0412544e-01,
  8.0251880e-01, 8.0091536e-01, 7.9931513e-01, 7.9771810e-01, 7.9612426e-01,
  7.9453360e-01, 7.9294612e-01, 7.9136182e-01, 7.8978067e-01, 7.8820269e-01,
  7.8662786e-01, 7.8505618e-01, 7.8348763e-01, 7.8192222e-01, 7.8035994e-01,
  7.7880078e-01, 7.7724474e-01, 7.7569180e-01, 7.7414197e-01, 7.7259523e-01,
  7.7105159e-01, 7.6951102e-01, 7.6797354e-01, 7.6643913e-01, 7.6490778e-01,
  7.6337949e-01, 7.6185426e-01, 7.6033208e-01, 7.5881293e-01, 7.5729682e-01,
  7.5578374e-01, 7.5427368e-01, 7.5276664e-01, 7.5126262e-01, 7.4976159e-01,
  7.4826357e-01, 7.4676854e-01, 7.4527649e-01, 7.4378743e-01, 7.4230134e-01,
  7.4081822e-01, 7.3933806e-01, 7.3786087e-01, 7.3638662e-01, 7.3491532e-01,
  7.3344696e-01, 7.3198153e-01, 7.3051903e-01, 7.2905945e-01, 7.2760279e-01,
  7.2614904e-01, 7.2469819e-01, 7.2325024e-01, 7.2180519e-01, 7.2036302e-01,
  7.1892373e-01, 7.1748732e-01, 7.1605378e-01, 7.1462311e-01, 7.1319529e-01,
  7.1177032e-01, 7.1034820e-01, 7.0892893e-01, 7.0751249e-01, 7.0609888e-01,
  7.0468809e-01, 7.0328012e-01, 7.0187497e-01, 7.0047262e-01, 6.9907308e-01,
  6.9767633e-01, 6.9628237e-01, 6.9489119e-01, 6.9350280e-01, 6.9211718e-01,
  6.9073433e-01, 6.8935424e-01, 6.8797691e-01, 6.8660233e-01, 6.8523050e-01,
  6.8386141e-01, 6.8249505e-01, 6.8113143e-01, 6.7977053e-01, 6.7841234e-01,
  6.7705687e-01, 6.7570411e-01, 6.7435406e-01, 6.7300670e-01, 6.7166203e-01,
  6.7032005e-01, 6.6898075e-01, 6.6764412e-01, 6.6631017e-01, 6.6497888e-01,
  6.6365025e-01, 6.6232428e-01, 6.6100095e-01, 6.5968027e-01, 6.5836223e-01,
  6.5704682e-01, 6.5573404e-01, 6.5442388e-01, 6.5311634e-01, 6.5181141e-01,
  6.5050909e-01, 6.4920938e-01, 6.4791226e-01, 6.4661773e-01, 6.4532578e-01,
  6.4403642e-01, 6.4274964e-01, 6.4146542e-01, 6.4018377e-01, 6.3890468e-01,
  6.3762815e-01, 6.3635417e-01, 6.3508273e-01, 6.3381384e-01, 6.3254748e-01,
  6.3128365e-01, 6.3002234e-01, 6.2876355e-01, 6.2750728e-01, 6.2625352e-01,
  6.2500227e-01, 6.2375351e-01, 6.2250725e-01, 6.2126348e-01, 6.2002220e-01,
  6.1878339e-01, 6.1754706e-01, 6.1631320e-01, 6.1508181e-01, 6.1385287e-01,
  6.1262639e-01, 6.1140237e-01, 6.1018078e-01, 6.0896164e-01, 6.0774493e-01,
  6.0653066e-01, 6.0531881e-01, 6.0410938e-01, 6.0290237e-01, 6.0169777e-01,
  6.0049558e-01, 5.9929579e-01, 5.9809839e-01, 5.9690339e-01, 5.9571078e-01,
  5.9452055e-01, 5.9333270e-01, 5.9214722e-01, 5.9096410e-01, 5.8978336e-01,
  5.8860497e-01, 5.8742894e-01, 5.8625525e-01, 5.8508391e-01, 5.8391492e-01,
  5.8274825e-01, 5.8158392e-01, 5.8042192e-01, 5.7926223e-01, 5.7810486e-01,
  5.7694981e-01, 5.7579706e-01, 5.7464662e-01, 5.7349848e-01, 5.7235263e-01,
  5.7120906e-01, 5.7006779e-01, 5.6892879e-01, 5.6779207e-01, 5.6665762e-01,
  5.6552544e-01, 5.6439552e-01, 5.6326786e-01, 5.6214245e-01, 5.6101928e-01,
  5.5989837e-01, 5.5877969e-01, 5.5766325e-01, 5.5654903e-01, 5.5543705e-01,
  5.5432728e-01, 5.5321974e-01, 5.5211440e-01, 5.5101128e-01, 5.4991036e-01,
  5.4881164e-01, 5.4771511e-01, 5.4662077e-01, 5.4552863e-01, 5.4443866e-01,
  5.4335087e-01, 5.4226525e-01, 5.4118181e-01, 5.4010052e-01, 5.3902140e-01,
  5.3794444e-01, 5.3686962e-01, 5.3579696e-01, 5.3472643e-01, 5.3365805e-01,
  5.3259180e-01, 5.3152768e-01, 5.3046569e-01, 5.2940582e-01, 5.2834806e-01,
  5.2729242e-01, 5.2623889e-01, 5.2518747e-01, 5.2413814e-01, 5.2309091e-01,
  5.2204578e-01, 5.2100273e-01, 5.1996176e-01, 5.1892288e-01, 5.1788607e-01,
  5.1685133e-01, 5.1581866e-01, 5.1478806e-01, 5.1375951e-01, 5.1273302e-01,
  5.1170858e-01, 5.1068618e-01, 5.0966583e-01, 5.0864752e-01, 5.0763124e-01,
  5.0661699e-01, 5.0560477e-01, 5.0459457e-01, 5.0358639e-01, 5.0258023e-01,
  5.0157607e-01, 5.0057392e-01, 4.9957377e-01, 4.9857562e-01, 4.9757947e-01,
  4.9658530e-01, 4.9559313e-01, 4.9460293e-01, 4.9361471e-01, 4.9262847e-01,
  4.9164420e-01, 4.9066189e-01, 4.8968155e-01, 4.8870316e-01, 4.8772673e-01,
  4.8675226e-01, 4.8577972e-01, 4.8480914e-01, 4.8384049e-01, 4.8287377e-01,
  4.8190899e-01, 4.8094614e-01, 4.7998520e-01, 4.7902619e-01, 4.7806910e-01,
  4.7711392e-01, 4.7616064e-01, 4.7520927e-01, 4.7425980e-01, 4.7331223e-01,
  4.7236655e-01, 4.7142276e-01, 4.7048086e-01, 4.6954084e-01, 4.6860270e-01,
  4.6766643e-01, 4.6673203e-01, 4.6579950e-01, 4.6486883e-01, 4.6394002e-01,
  4.6301307e-01, 4.6208797e-01, 4.6116472e-01, 4.6024331e-01, 4.5932374e-01,
  4.5840601e-01, 4.5749012e-01, 4.5657605e-01, 4.5566381e-01, 4.5475339e-01,
  4.5384480e-01, 4.5293801e-01, 4.5203304e-01, 4.5112988e-01, 4.5022852e-01,
  4.4932896e-01, 4.4843120e-01, 4.4753524e-01, 4.4664106e-01, 4.4574867e-01,
  4.4485807e-01, 4.4396924e-01, 4.4308219e-01, 4.4219691e-01, 4.4131340e-01,
  4.4043165e-01, 4.3955167e-01, 4.3867345e-01, 4.3779698e-01, 4.3692226e-01,
  4.3604929e-01, 4.3517806e-01, 4.3430857e-01, 4.3344082e-01, 4.3257481e-01,
  4.3171052e-01, 4.3084797e-01, 4.2998713e-01, 4.2912802e-01, 4.2827062e-01,
  4.2741493e-01, 4.2656096e-01, 4.2570869e-01, 4.2485812e-01, 4.2400925e-01,
  4.2316208e-01, 4.2231660e-01, 4.2147281e-01, 4.2063071e-01, 4.1979029e-01,
  4.1895155e-01, 4.1811448e-01, 4.1727909e-01, 4.1644537e-01, 4.1561331e-01,
  4.1478291e-01, 4.1395417e-01, 4.1312709e-01, 4.1230167e-01, 4.1147789e-01,
  4.1065575e-01, 4.0983526e-01, 4.0901641e-01, 4.0819920e-01, 4.0738361e-01,
  4.0656966e-01, 4.0575733e-01, 4.0494663e-01, 4.0413755e-01, 4.0333008e-01,
  4.0252422e-01, 4.0171998e-01, 4.0091734e-01, 4.0011631e-01, 3.9931688e-01,
  3.9851904e-01, 3.9772280e-01, 3.9692815e-01, 3.9613509e-01, 3.9534361e-01,
  3.9455371e-01, 3.9376539e-01, 3.9297865e-01, 3.9219348e-01, 3.9140987e-01,
  3.9062784e-01, 3.8984736e-01, 3.8906844e-01, 3.8829109e-01, 3.8751528e-01,
  3.8674102e-01, 3.8596831e-01, 3.8519715e-01, 3.8442752e-01, 3.8365944e-01,
  3.8289289e-01, 3.8212787e-01, 3.8136437e-01, 3.8060241e-01, 3.7984196e-01,
  3.7908304e-01, 3.7832563e-01, 3.7756973e-01, 3.7681535e-01, 3.7606247e-01,
  3.7531110e-01, 3.7456123e-01, 3.7381285e-01, 3.7306597e-01, 3.7232059e-01,
  3.7157669e-01, 3.7083428e-01, 3.7009335e-01, 3.6935391e-01, 3.6861594e-01,
  3.6787944e-01, 3.6714442e-01, 3.6641086e-01, 3.6567877e-01, 3.6494815e-01,
  3.6421898e-01, 3.6349127e-01, 3.6276501e-01, 3.6204021e-01, 3.6131685e-01,
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