/*
 * This file is part of Deliantra, the Roguelike Realtime MMORPG.
 * 
 * Copyright (©) 2010 Marc Alexander Lehmann / Robin Redeker / the Deliantra team
 * 
 * Deliantra is free software: you can redistribute it and/or modify it under
 * the terms of the Affero GNU General Public License as published by the
 * Free Software Foundation, either version 3 of the License, or (at your
 * option) any later version.
 * 
 * This program 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 Affero GNU General Public License
 * and the GNU General Public License along with this program. If not, see
 * <http://www.gnu.org/licenses/>.
 * 
 * The authors can be reached via e-mail to <support@deliantra.net>
 */

#include "noise.h"

/////////////////////////////////////////////////////////////////////////////

// http://www-wales.ch.cam.ac.uk/~wales/CCD/Thomson/table.html, random permutation
static const float charges[256][3] = {
  6.32096444e-01, -6.11406706e-01, 4.76062943e-01, 5.19172442e-01, 8.08229585e-01, -2.77893708e-01,
  -8.81072422e-01, -4.68301230e-01, 6.63727731e-02, -1.92122323e-01, 9.81341519e-01, -7.60505942e-03,
  -2.57478265e-01, 9.34157733e-01, -2.47091628e-01, 8.75501090e-01, -1.48087600e-01, -4.59965112e-01,
  -6.44086082e-01, 3.21868600e-01, 6.93940720e-01, -4.42053435e-01, -1.94962529e-01, -8.75544615e-01,
  -6.86776297e-01, 5.34610386e-01, -4.92473403e-01, -8.45541961e-01, -2.41708225e-01, 4.76062943e-01,
  1.87301993e-01, 3.04913657e-01, 9.33780287e-01, -8.21274139e-01, 4.76841979e-01, -3.13257905e-01,
  1.82393582e-01, 9.78673695e-01, -9.45006918e-02, -5.13996405e-01, 5.64894294e-01, -6.45524695e-01,
  -2.85987088e-01, -5.27238900e-01, -8.00144067e-01, 3.72992508e-01, 8.73495087e-01, 3.12862464e-01,
  3.07149790e-02, -1.36108589e-01, 9.90217674e-01, -9.42965190e-01, -1.13726556e-01, 3.12862464e-01,
  -7.63495246e-01, -8.89713729e-02, -6.39655457e-01, -4.93181655e-01, 3.84537051e-01, -7.80322441e-01,
  9.59053138e-01, -6.07981062e-03, -2.83160934e-01, 8.47504655e-02, 6.82510620e-01, -7.25945323e-01,
  2.72233465e-01, 7.06503091e-01, 6.53255175e-01, -6.69781595e-01, 6.75521448e-01, -3.08323512e-01,
  -9.83646297e-01, 1.64266522e-01, -7.38679386e-02, -1.33230986e-01, 4.14543427e-02, 9.90217674e-01,
  -9.68112521e-01, -2.24691711e-01, 1.10778074e-01, 2.60286884e-01, 5.44444585e-01, -7.97390012e-01,
  -9.59533574e-01, 4.55017306e-02, -2.77893708e-01, 6.34082129e-01, 7.69729420e-01, -7.38679387e-02,
  8.71590956e-01, -4.57032412e-01, -1.77343115e-01, -5.65998169e-01, -6.84162385e-01, -4.59965112e-01,
  1.31348131e-01, -9.34573215e-01, 3.30636620e-01, 9.37743461e-01, -2.44096148e-01, -2.47091628e-01,
  -2.32019785e-03, -9.49665258e-01, -3.13257905e-01, 5.58257270e-01, -6.92564967e-01, -4.56839782e-01,
  5.79609682e-01, 2.34839316e-01, -7.80322441e-01, 5.21842141e-02, 4.80310769e-01, -8.75544615e-01,
  5.48696303e-01, -4.14651366e-01, -7.25945323e-01, -5.13713359e-02, -3.67059868e-01, 9.28777712e-01,
  -8.31597157e-01, -5.26303703e-01, -1.77343115e-01, 7.60006362e-01, -6.75440951e-02, -6.46396260e-01,
  -6.35840799e-01, -7.53287574e-01, 1.68119925e-01, 6.00789426e-01, 3.96860609e-01, 6.93940720e-01,
  -3.99937982e-02, 9.83336115e-01, -1.77343115e-01, -4.74261299e-01, 8.33604286e-01, -2.83160934e-01,
  8.74744319e-01, 8.54351386e-02, -4.76993934e-01, 2.64896284e-01, -6.69736874e-01, 6.93745254e-01,
  -2.24976555e-01, -1.01696579e-01, -9.69042494e-01, 6.08580404e-01, -2.06649545e-01, 7.66110865e-01,
  -2.32214607e-01, -7.27581091e-01, -6.45524695e-01, -1.14732673e-01, 7.81826288e-01, -6.12849141e-01,
  -5.46171508e-01, 5.27060305e-01, 6.51079195e-01, 1.70411976e-01, -3.14665113e-01, 9.33780287e-01,
  -1.14827108e-01, 9.66494440e-01, 2.29571847e-01, 6.62214703e-01, -4.23664923e-01, 6.18045079e-01,
  3.43568839e-01, 1.39041052e-01, 9.28777712e-01, 2.65015805e-01, 5.00565290e-01, 8.24136526e-01,
  -4.26259648e-01, -7.20031380e-01, 5.47592480e-01, 7.57191364e-01, -5.91945814e-01, 2.76154652e-01,
  9.94315593e-01, 4.60290452e-02, 9.60095232e-02, 9.70286575e-01, -1.74010497e-01, 1.68119925e-01,
  1.34044431e-01, 9.51719864e-01, 2.76154652e-01, -3.21508279e-01, 6.91956864e-01, -6.46396261e-01,
  -9.15927355e-01, 3.90047734e-01, -9.45507570e-02, -3.57713970e-01, 9.75145600e-03, 9.33780287e-01,
  4.58799092e-01, -6.16720593e-01, -6.39655457e-01, -4.06287592e-01, 9.10837959e-01, -7.28327195e-02,
  7.69084079e-01, -2.21547533e-01, 5.99521785e-01, 4.32966564e-02, -7.18729210e-01, 6.93940720e-01,
  7.91803580e-01, -4.28020920e-01, 4.35712270e-01, 3.04696154e-01, 7.05691965e-01, -6.39655457e-01,
  6.46420856e-01, 4.00281039e-01, -6.49549973e-01, 8.31864266e-01, -3.69542234e-01, -4.14053595e-01,
  8.23594337e-01, 4.72823279e-01, -3.13257905e-01, -5.85665015e-01, -8.07274355e-01, -7.28327193e-02,
  -5.65385161e-02, -4.32158277e-01, -9.00023678e-01, 2.06686552e-01, -8.22754465e-01, 5.29486316e-01,
  8.65928642e-01, 3.96271834e-01, 3.05182275e-01, 1.87431189e-02, 4.56064322e-01, 8.89749419e-01,
  -5.94715001e-01, -2.32669312e-01, 7.69531714e-01, 5.99595825e-01, 1.59473663e-02, -8.00144067e-01,
  9.58599657e-02, 6.31372955e-01, 7.69531714e-01, 3.20650220e-01, 8.29747462e-01, -4.56839782e-01,
  -3.13608737e-01, 5.11291534e-01, -8.00144067e-01, -8.67906788e-01, 4.85339988e-01, 1.05749252e-01,
  3.22455909e-01, 9.12507983e-01, -2.51696976e-01, 5.15563696e-01, 7.07202113e-01, -4.83796700e-01,
  7.50491607e-01, -5.66571271e-01, -3.40234247e-01, -2.58299208e-01, -3.23551155e-01, -9.10272580e-01,
  3.49564167e-01, -9.33995942e-01, -7.38679386e-02, 4.02529304e-01, 1.67115347e-01, -9.00023678e-01,
  9.45927846e-01, -3.24287947e-01, -7.60505937e-03, -4.04334848e-01, -2.11800144e-01, 8.89749419e-01,
  3.41359400e-01, -4.97637347e-01, -7.97390012e-01, 7.43690080e-01, 5.81037425e-01, 3.30636620e-01,
  -8.15869544e-01, 2.32381428e-01, 5.29486316e-01, -2.73993936e-01, -4.03941386e-01, 8.72787878e-01,
  -1.14485896e-01, -9.85759380e-01, -1.23172337e-01, -6.69863977e-01, 3.59676363e-01, -6.49549972e-01,
  -7.96449717e-01, 5.92027384e-01, -1.23172337e-01, -6.19715090e-01, -4.90274553e-01, -6.12849141e-01,
  -8.65910917e-01, -3.66659161e-01, -3.40234247e-01, 8.46096973e-01, -5.28880485e-01, 6.63727731e-02,
  -8.91235794e-01, -3.59774050e-01, 2.76154652e-01, 4.20417732e-01, 3.46935142e-01, 8.38382334e-01,
  -6.38459078e-01, 7.23512413e-01, 2.62487703e-01, -7.53805524e-01, -6.57053571e-01, -7.60505938e-03,
  4.47561005e-01, 5.64275348e-01, 6.93745254e-01, 3.49754488e-02, 9.97181715e-01, 6.63727730e-02,
  -1.28749619e-01, -5.72643486e-01, 8.09631381e-01, -6.36032129e-01, -6.58092804e-01, 4.02960285e-01,
  -5.37020119e-01, 8.38088040e-01, 9.60095232e-02, -8.78907490e-01, -1.37182495e-01, -4.56839782e-01,
  -9.33228374e-01, 1.34065997e-01, 3.33333333e-01, 6.80411181e-01, 5.47277055e-01, -4.87368906e-01,
  -7.12457289e-01, 1.05461526e-01, 6.93745254e-01, 2.30586085e-01, 3.30051738e-01, -9.15366543e-01,
  2.34431211e-02, -7.59957402e-01, -6.49549973e-01, -6.98011937e-01, -3.61662294e-01, 6.18045079e-01,
  8.59171516e-01, 2.05105173e-01, 4.68781584e-01, 7.11862181e-01, 6.90797320e-01, 1.26693714e-01,
  -2.12826534e-01, 4.39256402e-01, 8.72787878e-01, -3.62298594e-01, -9.25543476e-01, -1.10040912e-01,
  -3.63383159e-01, -8.00268371e-01, -4.76993934e-01, -7.76145796e-01, 5.51780285e-01, 3.05182275e-01,
  -1.92676248e-01, 7.76820116e-01, 5.99521785e-01, -9.19690664e-01, 2.65359911e-01, -2.89401453e-01,
  -2.52247996e-02, 8.99732475e-01, 4.35712270e-01, 7.52676085e-01, 4.12472645e-01, 5.13171539e-01,
  -1.19598027e-01, -8.62070913e-01, -4.92473403e-01, 9.40191063e-01, -1.58443230e-02, 3.40278890e-01,
  -9.89903836e-01, 3.37653035e-02, 1.37660085e-01, 3.00994355e-01, -4.79793064e-01, 8.24136526e-01,
  4.35219899e-01, 8.98427220e-01, -5.84137724e-02, -9.54179119e-01, 2.71092073e-01, 1.26693714e-01,
  9.02457799e-02, -5.37560007e-01, 8.38382334e-01, -9.58991702e-02, 9.05186704e-01, -4.14053596e-01,
  -8.97828463e-02, -9.48052118e-01, 3.05182275e-01, -7.79595183e-01, -5.82690413e-01, 2.29571847e-01,
  -6.01646284e-01, -4.68072388e-02, -7.97390012e-01, -6.80265196e-01, -6.90061585e-01, -2.47091628e-01,
  6.89653756e-01, 6.63795523e-01, -2.89401453e-01, -7.35965096e-01, -5.35644470e-01, -4.14053595e-01,
  -4.83817118e-01, -8.06307183e-01, 3.40278890e-01, -2.51959468e-01, -8.46616946e-01, 4.68781584e-01,
  2.89467531e-01, 9.50755892e-01, 1.10778074e-01, -4.31548997e-01, 3.97822184e-01, 8.09631381e-01,
  1.03460411e-01, 8.29768433e-01, -5.48434400e-01, -7.70330748e-01, -3.25284873e-01, -5.48434400e-01,
  4.75732892e-01, -5.89012642e-01, 6.53255175e-01, -4.56373945e-01, 8.22151506e-01, 3.40278890e-01,
  -7.47966357e-01, -1.17490449e-01, 6.53255175e-01, -4.84791839e-01, -8.27524476e-01, -2.83160934e-01,
  -8.75038211e-01, 3.53535790e-01, 3.30636620e-01, 4.09353123e-01, -6.19180984e-02, -9.10272580e-01,
  -9.95670746e-01, -7.23021212e-02, -5.84137724e-02, -4.57295474e-01, -8.84117086e-01, 9.60095233e-02,
  -8.64280276e-02, -6.19376367e-01, -7.80322441e-01, 2.44164564e-02, 2.45683701e-01, -9.69042494e-01,
  8.94422292e-01, -3.83804027e-01, 2.29571847e-01, -8.62566691e-01, 4.52816156e-03, 5.05923116e-01,
  9.19909533e-01, 2.42287152e-01, -3.08323512e-01, -4.01126232e-01, 3.46675383e-02, -9.15366543e-01,
  9.51367455e-01, 2.99880902e-01, 7.05082324e-02, -5.61852646e-01, 1.73058019e-01, -8.08932956e-01,
  5.60450847e-01, -8.26125099e-01, -5.84137724e-02, -4.83253958e-01, -4.23721318e-01, 7.66110865e-01,
  -1.91262533e-02, -8.58072933e-01, 5.13171539e-01, 4.27361843e-01, -7.49268748e-01, 5.05923116e-01,
  8.06374324e-01, 3.27460527e-01, -4.92473403e-01, -3.49075205e-01, -5.94876216e-01, 7.24064077e-01,
  1.70540147e-01, -3.64719277e-01, -9.15366543e-01, -9.51483049e-01, -1.76998983e-01, -2.51696976e-01,
  -3.34445776e-01, 9.27298072e-01, 1.68119925e-01, -2.58769450e-02, -2.24111854e-01, -9.74219821e-01,
  3.50509628e-01, -8.75232478e-01, 3.33333333e-01, -5.11361160e-01, 7.14833233e-01, -4.76993934e-01,
  2.13445517e-01, 8.53114931e-01, 4.76062943e-01, -7.35388206e-01, 6.73967933e-01, 7.05082324e-02,
  -5.10663512e-01, 1.90624866e-01, 8.38382334e-01, 2.07025032e-01, 8.96458354e-02, -9.74219821e-01,
  2.30036908e-01, -9.29155434e-01, -2.89401453e-01, -4.38498083e-01, -6.24412769e-01, -6.46396260e-01,
  7.56359490e-01, -6.47294323e-01, -9.45006918e-02, -7.33549832e-01, 4.45600288e-01, 5.13171539e-01,
  5.69972682e-01, -7.59768531e-01, 3.12862464e-01, 1.36366351e-02, -9.94299320e-01, 1.05749252e-01,
  -1.20108971e-01, 6.12129242e-01, -7.81582770e-01, -6.20394866e-01, 7.76531524e-01, -1.10040912e-01,
  3.85591729e-01, -2.44264178e-01, 8.89749420e-01, -8.14161423e-01, 3.15614840e-01, -4.87368906e-01,
  1.15419311e-01, 9.33230432e-01, -3.40234248e-01, 5.90173960e-01, -2.02047201e-01, -7.81582770e-01,
  8.54270153e-01, 5.08959332e-01, 1.05749252e-01, 7.95754924e-01, 5.98192490e-01, -9.45507571e-02,
  3.54673147e-01, -8.00092315e-01, -4.83796700e-01, 9.91952607e-01, -1.03563604e-01, -7.28327194e-02,
  -6.21935152e-02, 2.58972647e-01, 9.63880249e-01, -3.09502921e-01, 8.32249985e-01, -4.59965112e-01,
  4.65710308e-01, -8.74164521e-01, 1.37660085e-01, 1.33750242e-01, -8.62891895e-01, -4.87368906e-01,
  -2.51909022e-01, 8.79866384e-01, 4.02960285e-01, -6.67371446e-11, -8.00239945e-11, -1.00000000e+00,
  -5.76407831e-01, -5.55272584e-01, 5.99521785e-01, -4.70064989e-01, -4.10082041e-01, -7.81582770e-01,
  8.36695291e-01, -9.13599363e-03, 5.47592480e-01, 5.24193529e-01, 8.40399218e-01, 1.37660085e-01,
  2.48438744e-01, -7.05895175e-01, -6.63317565e-01, 1.20172431e-01, -9.88240224e-01, -9.45507569e-02,
  4.30798964e-01, 4.00049655e-01, -8.08932956e-01, -2.50127938e-01, -9.17808600e-01, -3.08323512e-01,
  6.09182992e-01, 5.90373037e-01, 5.29486316e-01, -3.40640313e-01, 5.99746104e-01, 7.24064077e-01,
  4.40361132e-01, -8.53731316e-01, -2.77893708e-01, -1.83361859e-01, -7.36528553e-01, 6.51079195e-01,
  9.82693460e-01, 1.49011952e-01, -1.10040912e-01, 6.29027140e-01, -7.35509000e-01, -2.51696976e-01,
  -8.70236843e-01, 9.28902018e-02, -4.83796700e-01, 9.45809668e-01, 1.91165575e-01, 2.62487703e-01,
  2.00560098e-01, -1.43987122e-01, -9.69042494e-01, 1.02516007e-01, 9.46542469e-02, 9.90217674e-01,
  -6.07212048e-01, 6.41511773e-01, 4.68781584e-01, 2.42316938e-01, -9.61889393e-01, 1.26693714e-01,
  4.87103783e-01, 5.68101851e-01, -6.63317565e-01, -9.38753073e-01, -3.31379371e-01, -9.45006918e-02,
  3.89869221e-01, -2.85348240e-01, -8.75544615e-01, -6.33446768e-01, -2.67859254e-01, -7.25945323e-01,
  5.82718746e-01, 7.41166481e-01, 3.33333333e-01, 6.66870337e-01, -5.04483561e-01, -5.48434400e-01,
  7.34447763e-01, -2.91551734e-01, -6.12849141e-01, 9.10935613e-01, 3.93731996e-01, -1.23172337e-01,
  3.57972341e-02, 7.85327217e-01, 6.18045079e-01, -2.92197503e-01, 2.28018816e-01, 9.28777712e-01
  -1.93180133e-01, -1.83347487e-01, 9.63880249e-01, -2.15979248e-01, -9.73848835e-01, 7.05082325e-02,
  8.87941151e-01, -2.21773580e-01, 4.02960285e-01, 6.89715518e-01, -4.86988739e-03, 7.24064077e-01,
  -4.10435643e-01, 7.29167374e-01, 5.47592480e-01, 7.46211012e-01, 1.62686797e-01, -6.45524695e-01,
  -1.81148087e-01, 1.34466019e-01, -9.74219821e-01, -7.66578780e-01, -4.71711555e-01, 4.35712270e-01,
  -5.66010160e-01, -2.07722258e-02, 8.24136526e-01, 7.29533368e-01, 2.09468249e-01, 6.51079195e-01,
  -3.45990788e-01, 2.65042929e-01, -9.00023678e-01, -7.35542526e-01, 1.37793324e-01, -6.63317565e-01,
  -1.25326447e-01, 6.30370863e-01, 7.66110865e-01, 1.31053682e-01, -5.73107674e-01, -8.08932955e-01,
  4.86820470e-01, -3.53150162e-02, 8.72787878e-01, 4.35204849e-01, 7.44740586e-01, 5.05923116e-01,
  4.98855035e-01, -3.98703643e-01, 7.69531714e-01, 2.55373649e-01, -7.56251592e-02, 9.63880249e-01,
  -1.51053916e-01, 3.85469253e-01, -9.10272580e-01, 6.78644990e-01, -7.26064181e-01, 1.10778074e-01,
  -3.07350590e-01, -9.14677987e-01, 2.62487703e-01, 5.60298616e-01, 1.74821302e-01, 8.09631381e-01,
};

static vec2d
floor (vec2d v)
{
  return vec2d (std::floor (v[0]), std::floor (v[1]));
}

static vec3d
floor (vec3d v)
{
  return vec3d (std::floor (v[0]), std::floor (v[1]), std::floor (v[2]));
}

noise_gen<vec2d>::noise_gen (uint32_t seed)
{
  seedable_rand_gen rng (seed);

#if 1
  for (int i = 0; i < 256; ++i)
    {
      vec2d rv (rng () - 0.5f, rng () - 0.5f);

      // normalise
      float mag = 1.f / sqrtf (dot (rv, rv));

      rv[0] *= mag;
      rv[1] *= mag;

      rvec[i] = rv;
    }
#endif

#if 0
  float offset = rng () * 3.14159265;

  for (int i = 0; i < 256; ++i)
    {
      float phi = i * (3.14159265 * 2 / 256) + offset;

      rvec[i][0] =  sinf (phi);
      rvec[i][1] = -cosf (phi);
    }

  // fisher-yates to randomly perturb
  for (int i = 256; --i; )
    ::swap (rvec [i], rvec [rng (i + 1)]);
#endif

  rvmap[0].seed (rng);
  rvmap[1].seed (rng);
}

vec2d::T_numtype
noise_gen<vec2d>::operator() (vec2d P)
{
  vec2d I = floor (P);
  vec2d F = P - I;

  float v = 0;

  for (int j = -1; j <= 2; ++j)
    for (int i = -1; i <= 2; ++i)
      {
        vec2d A = F - vec2d (i, j);

        float d = dot (A, A);
  
        if (d < 4)
          {
            float t1 = 1 - d / 4;
            float t2 = t1 * t1;
            float t4 = t2 * t2;

            float p = (4 * t1 - 3) * t4;

            int h = rvmap [0](I[0] + i) ^ rvmap [1](I[1] + j);
            vec2d G = rvec [h & 0xff];
  
            v += dot (A, G) * p;
          }
      }

  return clamp (v, -.9999999f, .9999999f);
} 

/////////////////////////////////////////////////////////////////////////////

noise_gen<vec3d>::noise_gen (uint32_t seed)
{
  seedable_rand_gen rng (seed);

  rvmap [0].seed (rng);
  rvmap [1].seed (rng);
  rvmap [2].seed (rng);
}

vec3d::T_numtype
noise_gen<vec3d>::operator() (vec3d P)
{
  vec3d I = floor (P);
  vec3d F = P - I;

  float v = 0;

  for (int j = -1; j <= 2; ++j)
    for (int i = -1; i <= 2; ++i)
      for (int k = -1; k <= 2; ++k)
        {
          vec3d A = F - vec3d (i, j, k);
          float d = dot (A, A);

          if (d < 4)
            {
              float t1 = 1 - d / 4;
              float t2 = t1 * t1;
              float t4 = t2 * t2;

              // (4t⁵ - 3t⁴)
              float p = (4 * t1 - 3) * t4;

              int h = rvmap[0](I[0] + i) ^ rvmap[1](I[1] + j) ^ rvmap[2](I[2] + k);
              const float *G = charges[h & 0xff];

              v += dot (A, vec3d (G[0], G[1], G[2])) * p;
            }
        }

  return clamp (v * 2, -.9999999f, .9999999f);
}

vec3d::T_numtype
noise_gen<vec3d>::operator() (vec3d P, vec3d N)
{
  vec3d I = floor (P);
  vec3d F = P - I;

  float v = 0;

  for (int j = -1; j <= 2; ++j)
    for (int i = -1; i <= 2; ++i)
      for (int k = -1; k <= 2; ++k)
        {
          vec3d D = F - vec3d (i, j, k);
          float e = dot (D, N);
          float o = 1 - abs (e);

          if (o > 0)
            {
              vec3d A = D - e * N;
              float d = dot (A, A);

              if (d < 4)
                {
                  float t1 = 1 - d / 4;
                  float t2 = t1 * t1;
                  float t4 = t2 * t2;

                  float o2 = o * o;

                  // (4t⁵ - 3t⁴) * (3o³ - 2o²)
                  // alternative?  ((o * 6 - 15) * o + 10) * o³
                  float p = (4 * t1 - 3) * t4 * (3 * o2 - 2 * o2 * o);

                  int h = rvmap[0](I[0] + i) ^ rvmap[1](I[1] + j) ^ rvmap[2](I[2] + k);
                  const float *G = charges[h & 0xff];

                  v += dot (A, vec3d (G[0], G[1], G[2])) * p;
                }
            }
        }

  return clamp (v, -.9999999f, .9999999f);
}

template class noise_gen<vec2d>;
template class noise_gen<vec3d>;

/////////////////////////////////////////////////////////////////////////////

template<class vec_t>
static vec_t
ith_octave (vec_t P, int i)
{
  vec_t r = P;
  r[0] += i;
  return r;
}

template<class vec_t>
frac_gen<vec_t>::frac_gen (value_t hurst_expo, value_t lacunarity)
: h (hurst_expo), lac (lacunarity), noise_gen<vec_t> (0)
{
  value_t exsum = 0;

  for (int i = 0; i < MAX_OCTAVES; ++i)
    {
      ex [i] = powf (lac, -h * i);
      exsum += ex [i];
      fbm_mul [i] = 0.5f / (exsum * 0.75f); // .75f is a heuristic
      rot [i].set (0.4488f * i);
    }
}

template<class vec_t>
typename frac_gen<vec_t>::value_t
frac_gen<vec_t>::fBm (vec_t P, int octaves)
{
  value_t v = 0.f;

  for (int i = 0; i < octaves; ++i)
    {
      rot [i](P);
      v += noise (ith_octave (P, i)) * ex [i];
      P *= lac;
    }

  return clamp (v * fbm_mul [octaves - 1] + 0.5f, 0.f, .9999999f);
}

template<class vec_t>
typename frac_gen<vec_t>::value_t
frac_gen<vec_t>::turbulence (vec_t P, int octaves)
{
  value_t v = 0.f;

  for (int i = 0; i < octaves; ++i)
    {
      rot [i](P);
      v += abs (noise (ith_octave (P, i))) * ex [i];
      P *= lac;
    }

  return clamp (v * fbm_mul [octaves - 1] * 2.f, 0.f, .9999999f);
}

template<class vec_t>
typename frac_gen<vec_t>::value_t
frac_gen<vec_t>::multifractal (vec_t P, int octaves, value_t offset)
{
  value_t v = 1.f;

  for (int i = 0; i < octaves; ++i)
    {
      rot [i](P);
      v *= noise (P) * ex [i] + offset;
      P *= lac;
    }

  return clamp (v * 0.5f, 0.f, .9999999f);
}

template<class vec_t>
typename frac_gen<vec_t>::value_t
frac_gen<vec_t>::heterofractal (vec_t P, int octaves, value_t offset)
{
  value_t v = noise (P) + offset;
  int i;

  for (i = 1; i < octaves; ++i)
    {
      rot [i](P);
      P *= lac;
      v += v * (noise (P) * ex [i] + offset);
    }

  return v / powf (2., octaves);
}

template<class vec_t>
typename frac_gen<vec_t>::value_t
frac_gen<vec_t>::hybridfractal (vec_t P, int octaves, value_t offset, value_t gain)
{
  value_t v = (noise (P) + offset) * ex [0];
  value_t weight = v;
  int i;

  for (i = 1; i < octaves; ++i)
    {
      rot [i](P);
      P *= lac;

      min_it (weight, 1.f);

      value_t sig = (noise (P) + offset) * ex [i];
      v += weight * sig;
      weight *= gain * sig;
    }

  return clamp (v * 0.5f + 0.5f, 0.f, .9999999f);
}

template<class vec_t>
typename frac_gen<vec_t>::value_t
frac_gen<vec_t>::ridgedmultifractal (vec_t P, int octaves, value_t offset, value_t gain)
{
  value_t sig = offset - abs (noise (P));
  sig *= sig;
  value_t v = sig;

  for (int i = 1; i < octaves; ++i)
    {
      rot [i](P);
      P *= lac;

      value_t w = clamp (sig * gain, 0.f, 1.f);

      sig = offset - abs (noise (P));
      sig *= sig;
      sig *= w;

      v += sig * ex [i];
    }

  return clamp (v * 0.25f, 0.f, .9999999f);
}

// http://www.gamasutra.com/view/feature/3098/a_realtime_procedural_universe_.php?page=2
template<class vec_t>
typename frac_gen<vec_t>::value_t
frac_gen<vec_t>::terrain (vec_t P, int octaves)
{
  value_t v = 0.f;

  for (int i = 0; i < octaves; ++i)
    {
      rot [i](P);
      v += noise (P) * ex [i];
      P *= lac;
    }

  v *= fbm_mul [octaves - 1];

  return v <= 0.f ? - powf (-v, 0.7f) : powf (v, 1. + noise (P) * v);
}

template<class vec_t>
typename frac_gen<vec_t>::value_t
frac_gen<vec_t>::terrain2 (vec_t P, int octaves)
{
  value_t a = fBm (P, octaves);
  value_t b = ridgedmultifractal (P, octaves, 1, 8);
  value_t fade = fBm (P + vec_t(10.3), octaves);

  const value_t width = 0.05f;

  if (fade > 0.5f + width)
    return a;
  else if (fade < 0.5f - width)
    return b;

  fade = (fade - 0.5f + width) / (width * 2);

  // sigmoidal curve
  fade = fade * fade * 2 * (1.5f - fade);

  return a * fade + b * (1 - fade);
}

template class frac_gen<vec2d>;
template class frac_gen<vec3d>;

/////////////////////////////////////////////////////////////////////////////

#if 0
void hack(); void hack()
{
  frac_gen<vec2d> gen (0.5, 2);
  frac_gen<vec3d> gen3;

#if 0
  int N = 1024;

  printf ("P5 %d %d 255\n", N, N);
  // pmake&&server/deliantra-server >x&&convert -depth 8 -size 512xx512 gray:x x.ppm&& cv x.ppm
  for (int y = 0; y < N; ++y)
    {
      if (!(y&63))fprintf (stderr, "y %d\n", y);//D
    for (int x = 0; x < N; ++x)
      {
        //putc (127 * n.noise (x * 0.1, y * 0.1, 0, 0,0,1) + 128, stdout);
        //putc (256 * gen.terrain2 (x * 0.004, y * 0.004, 8), stdout);
        //putc (256 * gen.fBm (x * 0.01, y * 0.01, 3), stdout);
        //putc (256 * gen.turbulence (x * 0.004 - 1, y * 0.004 - 1, 8), stdout);
        //putc (256 * gen.heterofractal (x * 0.008, y * 0.008, 8, 0.9), stdout);

        // mountais or somesuch(?)
        //putc (256 * gen.hybridfractal (x * 0.01, y * 0.01, 8, -.4, -4), stdout);

        // temperature
        //putc (256 * gen.fBm (x * 0.002, y * 0.002, 2), stdout);
        // rain
        //putc (256 * gen.ridgedmultifractal (x * 0.01, y * 0.01, 3, 1.03, 2), stdout);
      }
    }
#else
  int N = 512;

  //printf ("P6 %d %d 255\n", N, N);
  // pmake&&server/deliantra-server >x&&convert -depth 8 -size 512xx512 gray:x x.ppm&& cv x.ppm
  for (int z = 0; z < N; ++z)
    {
      if (!(z&7))fprintf (stderr, "z %d\n", z);//D
  for (int y = 0; y < N; ++y)
    for (int x = 0; x < N; ++x)
      {
        float v = gen3.ridgedmultifractal (vec3d (x * 0.01 + 0.2, y * 0.01 + 0.2, z * 0.01 + 0.2), 3, 1.03, 2) * 2;

#if 0
        if (z < 64)
          v = v * (z * z) / (64 * 64);
#endif

        if (v <= 0.9999)
          continue;

        float r[4];
        int i[4];

        r[0] = x;
        r[1] = y;
        r[2] = z;
        r[3] = v;

        memcpy (i, r, 16);

        i[0] = htonl (i[0]);
        i[1] = htonl (i[1]);
        i[2] = htonl (i[2]);
        i[3] = htonl (i[3]);

        fwrite (i, 4*4, 1, stdout);
      }
    }
#endif

  exit (0);
}
#endif