/*
 *	Karinto Library Project
 *
 *	This software is distributed under a zlib-style license.
 *	See license.txt for more information.
 */

using System;
using System.Collections.Generic;
using System.Text;

namespace Karinto
{
    public static class MathEx
    {
        #region fields
        private static readonly Polynomial[] erfcTable = 
        {
            new Polynomial( //[0]: 1 <= x < 2
                4.7019003296642450457550391704e-1,
                -5.4129916560282193120142282350e-4,
                3.2466045488989207057247716494e-2,
                -1.5551574967900995569013129661e-3,
                1.2991371652846980287617056420e-3,
                -1.2476738559919909068871115854e-4,
                4.2164948133638407169423314936e-5,
                -5.5944555649744218134732620248e-6,
                1.2391258283306184550290288637e-6,
                -1.8629332352031266041799875695e-7,
                3.3508489330180889238527074083e-8,
                -5.1453759994172323811411458769e-9,
                8.2778054007509566713316121080e-10,
                -1.2419584612081402943997565209e-10,
                1.8628225410158766603724913483e-11,
                -2.6916642541339090011279256698e-12,
                3.8321798025710167662264220379e-13,
                -5.2985573947392393836199793226e-14,
                7.2214593891835651145391699616e-15,
                -1.0552316968012789176241975783e-15,
                1.3848365749828243613160210837e-16
                ),
            new Polynomial( //[1]: 2 <= x < 4
                0.28246919208993532,//2.8246919208993525100243945507e-1,
                1.0295429295263581287408466969e-4,
                2.6352174925955979906965931429e-2,
                -2.0840262584872572824603082922e-3,
                1.6107317263933041407504226538e-3,
                -2.6413257091217055241174636048e-4,
                9.3720096524725604112989062675e-5,
                -2.0394452777501772979594808178e-5,
                5.4818843984699154429750547408e-6,
                -1.2769242863171188612896799307e-6,
                3.0855108190100308040276886416e-7,
                -7.1110449954162265412516889674e-8,
                1.6277854940656666077194365644e-8,
                -3.6388350444865150940102551512e-9,
                8.0125451384130244729739875906e-10,
                -1.7333139256038089278659882792e-10,
                3.6913251414732819339098560977e-11,
                -7.7391112861863152629855204763e-12,
                1.5985771117554783386097643078e-12,
                -3.2558812235239520370430316160e-13,
                6.5474397002885039401566856717e-14,
                -1.2908539064863451579569117003e-14,
                2.4663418649675516649805424542e-15,
                -5.0102905606542145531985288605e-16,
                1.1637629874200535139854357149e-16,
                -1.7702372520803693617903759643e-17
                ),
            new Polynomial( //[2]: 4 <= x < 8
                2.6609916698112647641230096605e-1,
                1.0052997692961233689565319255e-1,
                0.063819586227166714,//6.3819586227166696717161903119e-2,
                1.6510111747337704484097091109e-2,
                6.7745775475928297665975539362e-3,
                1.2613799574673550665257600345e-3,
                4.6314050254419785813179921962e-4,
                5.4816124629655721757719475954e-5,
                2.5069740734847835425277961803e-5,
                7.6494811710229433994592919775e-7,
                1.3069891449561428965827894398e-6,
                -1.1211722505095090109921762128e-7,
                7.7627072370605473720667209070e-8,
                -1.5067764445724103557487307330e-8,
                5.3921138750029687859330065848e-9,
                -1.3591247804716958040748207366e-9,
                4.0341965879492537779635899830e-10,
                -1.0884398300756496354533131958e-10,
                3.0363217123340332343882922235e-11,
                -8.2439513886349055414081918841e-12,
                2.2756305305902268859393373330e-12,
                -6.1246789459726400033402401708e-13,
                1.4333003386843162197015125496e-13,
                -3.7815369812690037058307445308e-14,
                1.7401564599128446023009328203e-14,
                -4.5875278594765951588791904401e-15
                ),
            new Polynomial( //[3]: 8 <= x < 16
                4.6854221014893762619745618301e-2,
                -1.5511450952249084104775598329e-2,
                5.1178905303441648577722059649e-3,
                -1.6829798529769531049332840624e-3,
                5.5160777130644620308102757353e-4,
                -1.8020184996880086091090661904e-4,
                5.8678514133519807272309470851e-5,
                -1.9045977453678276537004114523e-5,
                6.1623270905278656151589976968e-6,
                -1.9875419915464967477768116933e-6,
                6.3904356643246431611609250453e-7,
                -2.0483278667408340516487849749e-7,
                6.5453904816333940501972558207e-8,
                -2.0852118199579889358624923805e-8,
                6.6229050456699429842283832512e-9,
                -2.0972627311983894339808366077e-9,
                6.6237821648144864340143708663e-10,
                -2.0853485442305791192334927397e-10,
                6.5162153190849185531320932146e-11,
                -2.0380108335416826794297357698e-11,
                6.6463403803777970165860627602e-12,
                -2.0777605497301746376639943675e-12,
                4.6614566309518191650253075708e-13,
                -1.4074713019480904125485292343e-13,
                1.0831110710204089408511450325e-13,
                -3.3906934201035073659517665140e-14
                ),
            new Polynomial( //[4]: 16 <= x < 28
                2.8262089312268317148835811995e-2,
                -5.4152623609484073274229170763e-3,
                1.6241399412435775154107409724e-3,
                -5.0744105591774430405597196162e-3,
                -1.7616157737971578130497741968e-2,
                2.3083427166129394399962687197e-2,
                1.1164742403248709989628167597e-1,
                -3.5273994341997794105095275190e-2,
                -3.0869428535741202544195312887e-1,
                -1.3020536214165453885942308553e-2,
                4.3332671745834241123676787595e-1,
                9.4385604975718760529994282754e-2,
                -3.0238469418692319645741714650e-1,
                -9.5995136295717931771565803096e-2,
                8.3313274670729987166299100438e-2,
                3.1593997744278794785645602547e-2
                )
        };
        #endregion

        #region public methods
        public static double Erf(double x)
        {
            double a = Math.Abs(x);
            if (a >= 1.0)
            {
                return 1.0 - Erfc(x);
            }
            double y;
            double aa = a * a;
            if (a < 0.0625)
            {
                double c1 = a * aa;
                double c2 = c1 * aa;
                double c3 = c2 * aa;
                double c4 = c3 * aa;

                double s1 = c1 * -315.0;// (3*5*7*9 / -3 / 1!);
                double s2 = s1 * 0 + c2 * 189.0 / 2.0;// (3*5*7*9 / +5 / 2!)
                double s3 = s2 * 0 + c3 * -45.0 / 2.0;// (3*5*7*9 / -7 / 3!)
                double s4 = s3 * 0 + c4 * 35.0 / 8.0;// (3*5*7*9 / 9 / 4!)
                y = a + (s1 + s2 + s3 + s4) / 945.0; //(3*5*7*9);
            }
            else
            {
                double c = a;
                double s = 0;
                double b = 1.0;
                for (double i = -1.0; i > -20.0; i-=1.0)
                {
                    c *= aa / i;
                    b += 2.0;
                    s += c / b;
                }
                y = a + s;
            }
            y *= 1.1283791670955126;     // 2 / pi^0.5
            return Math.Sign(x) > 0 ? y : -y;
        }

        public static double Erfc(double x)
        {
            double a = Math.Abs(x);
            if (a < 1.0)
            {
                return 1.0 - Erf(x);
            }
            if (a > 27.226017111108501)
            {
                return x > 0 ? 0 : 2.0;
            }
            double y = 0.0;

            if (a < 2.0)
            {
                y = Math.Exp(-1.1688327773406599 * a * a);
                y *= erfcTable[0].GetValueAt(a + a - 3.0);
            }
            else if (a < 4.0)
            {
                decimal b = -1.05068636145441m * (decimal)a * (decimal)a;
                y = Math.Exp((double)b);
                y *= erfcTable[1].GetValueAt(a - 3.0);
            }
            else if (a < 8.0)
            {
                decimal b = -1.0292687483818601m * (decimal)a * (decimal)a;
                y = Math.Exp((double)b);
                y *= erfcTable[2].GetValueAt(a * 0.5 - 3);
            }
            else if (a < 16.0)
            {
                y = Math.Exp(-a * a);
                y *= erfcTable[3].GetValueAt(a * 0.25 - 3);
            }
            else
            {
                y = Math.Exp(-a * a);
                y *= erfcTable[4].GetValueAt(a * 0.125 - 3);
            }
            return x > 0 ? y : 2.0 - y;
        }
        #endregion
    }
}