/*
 *  Mathlib : A C Library of Special Functions
 *  Copyright (C) 1998   Ross Ihaka
 *  Copyright (C) 2000-9 The R Development Core Team
 *
 *  This program 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 2 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 GNU General Public License
 *  along with this program; if not, a copy is available at
 *  http://www.r-project.org/Licenses/
 */
package jdistlib;

import static java.lang.Math.*;

import jdistlib.exception.PrecisionException;
import jdistlib.generic.GenericDistribution;
import jdistlib.rng.RandomEngine;
import jdistlib.util.Debug;

public class Spearman extends GenericDistribution {
	// From pspearman package
	private static final double[][] spearmanArray = {
		{0},
		{1.0},
		{1.0,2.0,0.0},
		{1.0,3.0,1.0,4.0,2.0,2.0},
		{1.0,4.0,3.0,6.0,7.0,6.0,4.0,10.0,6.0,10.0,6.0},
		{1.0,5.0,6.0,9.0,16.0,12.0,14.0,24.0,20.0,21.0,23.0,28.0,24.0,34.0,20.0,32.0,42.0,29.0},
		{1.0,6.0,10.0,14.0,29.0,26.0,35.0,46.0,55.0,54.0,74.0,70.0,84.0,90.0,78.0,90.0,129.0,106.0,123.0,134.0,147.0,98.0,168.0,
		130.0,175.0,144.0,168.0,144.0,184.0},
		{1.0,7.0,15.0,22.0,47.0,54.0,70.0,94.0,129.0,124.0,178.0,183.0,237.0,238.0,276.0,264.0,379.0,349.0,380.0,400.0,
		517.0,394.0,542.0,492.0,640.0,557.0,666.0,595.0,776.0,684.0,786.0,718.0,922.0,745.0,917.0,781.0,982.0,826.0,
		950.0,844.0,1066.0,845.0,936.0},
		{1.0,8.0,21.0,34.0,72.0,102.0,130.0,190.0,260.0,284.0,398.0,454.0,555.0,616.0,756.0,744.0,1022.0,1042.0,1159.0,
		1282.0,1555.0,1392.0,1719.0,1758.0,2009.0,2032.0,2282.0,2214.0,2676.0,2590.0,2878.0,2928.0,3397.0,3138.0,
		3647.0,3568.0,3921.0,3866.0,4311.0,4050.0,4852.0,4492.0,4816.0,4784.0,5505.0,4954.0,5638.0,5304.0,5890.0,
		5486.0,6188.0,5502.0,6436.0,5822.0,6233.0,6024.0,6697.0,5720.0,6672.0,6020.0,6688.0},
		{1.0,9.0,28.0,51.0,107.0,177.0,234.0,360.0,498.0,619.0,819.0,1040.0,1252.0,1528.0,1824.0,2010.0,2533.0,2837.0,
		3180.0,3676.0,4305.0,4493.0,5130.0,5672.0,6156.0,6909.0,7424.0,7830.0,8773.0,9392.0,9892.0,10678.0,
		11647.0,12141.0,13026.0,13918.0,14519.0,15611.0,16278.0,16780.0,18686.0,19280.0,19586.0,20795.0,
		22385.0,22896.0,23948.0,24970.0,26012.0,27096.0,28467.0,28427.0,30540.0,31272.0,31774.0,33264.0,
		34748.0,34499.0,36299.0,36596.0,38456.0,38926.0,39984.0,39386.0,42068.0,42848.0,42424.0,42925.0,
		45044.0,44584.0,46040.0,45496.0,46890.0,47036.0,47341.0,47646.0,48887.0,48840.0,48044.0,48540.0,
		50066.0,48970.0,49062.0},
		{1.0,10.0,36.0,74.0,156.0,288.0,409.0,644.0,930.0,1246.0,1636.0,2238.0,2714.0,3476.0,4198.0,5052.0,6027.0,
		7306.0,8207.0,9816.0,11384.0,12804.0,14193.0,16752.0,18079.0,20868.0,22580.0,25386.0,27333.0,31112.0,
		32448.0,36592.0,39140.0,43106.0,44778.0,50528.0,51964.0,57442.0,59348.0,65128.0,67870.0,74598.0,
		75264.0,82944.0,86123.0,93058.0,94220.0,103862.0,105313.0,114196.0,116213.0,125332.0,127623.0,
		138470.0,138317.0,150734.0,152353.0,162940.0,163331.0,176900.0,178020.0,190498.0,190152.0,
		203754.0,204867.0,220252.0,217045.0,232916.0,233434.0,248128.0,245488.0,262886.0,260963.0,
		277202.0,272844.0,292598.0,288389.0,306736.0,299406.0,319584.0,314926.0,333234.0,324357.0,
		345816.0,338295.0,360090.0,346910.0,369960.0,361215.0,381662.0,369447.0,391392.0,379327.0,
		402126.0,385304.0,411086.0,396552.0,418090.0,398919.0,425844.0,409927.0,429832.0,410407.0,
		435898.0,416495.0,440086.0,416895.0,440380.0,421188.0,442248.0,420480.0},
		{1.0,11.0,45.0,104.0,224.0,447.0,691.0,1106.0,1685.0,2364.0,3204.0,4515.0,5696.0,7489.0,9349.0,11674.0,
		13990.0,17637.0,20224.0,24754.0,29017.0,33942.0,38126.0,45884.0,50335.0,58769.0,65357.0,74938.0,
		81377.0,94494.0,100563.0,115222.0,124120.0,139785.0,147928.0,168875.0,176242.0,197443.0,208076.0,
		230894.0,241008.0,270313.0,277189.0,307769.0,320330.0,351886.0,361038.0,400464.0,408638.0,
		449017.0,461014.0,503127.0,512780.0,563815.0,569548.0,623258.0,634516.0,688442.0,695523.0,
		760903.0,765072.0,832427.0,838450.0,908396.0,912804.0,993883.0,992831.0,1073538.0,1078809.0,
		1163135.0,1162148.0,1259822.0,1252655.0,1351968.0,1347572.0,1452294.0,1445058.0,1556327.0,
		1540961.0,1657338.0,1646459.0,1766307.0,1745370.0,1876868.0,1851978.0,1988308.0,1960781.0,
		2097330.0,2067296.0,2215579.0,2177879.0,2328850.0,2287815.0,2442657.0,2395528.0,2561776.0,
		2508162.0,2671633.0,2614400.0,2786853.0,2724111.0,2903732.0,2827376.0,3010422.0,2933732.0,
		3119473.0,3037478.0,3223085.0,3135126.0,3323377.0,3235030.0,3430056.0,3323582.0,3523672.0,
		3411922.0,3617531.0,3501633.0,3703255.0,3579168.0,3784866.0,3661664.0,3867119.0,3727644.0,
		3931625.0,3796200.0,4005139.0,3857556.0,4061582.0,3907440.0,4113107.0,3962844.0,4167834.0,
		3998147.0,4200614.0,4032778.0,4239762.0,4065521.0,4259186.0,4085197.0,4278553.0,4100572.0,
		4294448.0,4103817.0,4298664.0},
		{1.0,12.0,55.0,142.0,317.0,670.0,1127.0,1844.0,2951.0,4310.0,6088.0,8708.0,11587.0,15418.0,20016.0,
		25570.0,31667.0,40242.0,48025.0,59284.0,71102.0,85026.0,98320.0,118542.0,134958.0,158040.0,
		180310.0,208308.0,233236.0,269916.0,297048.0,339972.0,375937.0,424608.0,462228.0,524942.0,
		566979.0,633746.0,686047.0,761310.0,817107.0,909744.0,964800.0,1065992.0,1138521.0,1245730.0,
		1315174.0,1447024.0,1522702.0,1659552.0,1747046.0,1896492.0,1986407.0,2162212.0,2245621.0,
		2432194.0,2543828.0,2734866.0,2835400.0,3068180.0,3170585.0,3408592.0,3525861.0,3783196.0,
		3899774.0,4192938.0,4299258.0,4601094.0,4745784.0,5055532.0,5174632.0,5545970.0,5670088.0,
		6038506.0,6178310.0,6571596.0,6716042.0,7147558.0,7271677.0,7721884.0,7885235.0,8347042.0,
		8470600.0,9005120.0,9138310.0,9663102.0,9812493.0,10365234.0,10513307.0,11113646.0,
		11225392.0,11857744.0,12012468.0,12646038.0,12754458.0,13463796.0,13591198.0,14278576.0,
		14405617.0,15142336.0,15259324.0,16048214.0,16105588.0,16923958.0,17044118.0,17841050.0,
		17903636.0,18787058.0,18865804.0,19721254.0,19775610.0,20702900.0,20735025.0,21691788.0,
		21664773.0,22651060.0,22689798.0,23657946.0,23606072.0,24659546.0,24622080.0,25656300.0,
		25566045.0,26655856.0,26571587.0,27668176.0,27518320.0,28640222.0,28543471.0,29643286.0,
		29443599.0,30642576.0,30443509.0,31602636.0,31333301.0,32564446.0,32319917.0,33500618.0,
		33174681.0,34415424.0,34109507.0,35342166.0,34909036.0,36237988.0,35822933.0,37056530.0,
		36584269.0,37873230.0,37432685.0,38680992.0,38114667.0,39450896.0,38887382.0,40181032.0,
		39504908.0,40854118.0,40263517.0,41495420.0,40769221.0,42111970.0,41404913.0,42672592.0,
		41853652.0,43194552.0,42396485.0,43667268.0,42778281.0,44063462.0,43233261.0,44466370.0,
		43461804.0,44788938.0,43834189.0,45048558.0,43998971.0,45259500.0,44258181.0,45412672.0,
		44326704.0,45515922.0,44472111.0,45598614.0,44405142.0},
		{1.0,13.0,66.0,189.0,442.0,978.0,1778.0,3001.0,5004.0,7621.0,11185.0,16296.0,22714.0,30687.0,41329.0,
		53890.0,69000.0,88312.0,109936.0,136282.0,168065.0,203992.0,243089.0,293640.0,346170.0,406445.0,
		476376.0,555090.0,638435.0,737981.0,840101.0,958754.0,1089297.0,1231500.0,1377986.0,1558499.0,
		1736395.0,1931682.0,2146913.0,2383583.0,2623346.0,2901673.0,3179333.0,3489007.0,3821032.0,
		4169325.0,4524641.0,4942522.0,5353035.0,5789483.0,6258394.0,6765738.0,7268994.0,7836509.0,
		8393474.0,9007679.0,9653784.0,10315483.0,10980922.0,11756111.0,12493529.0,13284027.0,
		14104701.0,15002446.0,15857273.0,16829150.0,17759467.0,18799871.0,19840147.0,20936584.0,
		21994402.0,23257727.0,24416130.0,25674050.0,26933190.0,28337570.0,29660744.0,31142288.0,
		32538704.0,34131234.0,35657364.0,37303229.0,38866238.0,40713556.0,42390411.0,44226231.0,
		46026210.0,48052422.0,49928436.0,52010628.0,53959720.0,56242541.0,58338267.0,60610281.0,
		62777150.0,65299148.0,67603742.0,70103053.0,72486017.0,75242909.0,77757239.0,80514530.0,
		83095790.0,86134914.0,88853220.0,91786159.0,94654998.0,97905224.0,100842450.0,104081709.0,
		107061609.0,110610554.0,113799356.0,117211215.0,120417930.0,124247914.0,127581181.0,
		131238022.0,134726882.0,138693952.0,142228858.0,146213039.0,149744398.0,154011822.0,
		157834377.0,161825434.0,165621673.0,170242454.0,174034077.0,178290125.0,182365752.0,
		186984277.0,191021135.0,195611361.0,199527113.0,204460431.0,208828302.0,213250340.0,
		217440443.0,222729462.0,226759859.0,231569284.0,236032454.0,241135132.0,245439431.0,
		250504769.0,254612331.0,259997865.0,264665913.0,269356997.0,273667172.0,279524301.0,
		283593012.0,288632518.0,293226622.0,298545201.0,302967996.0,308339632.0,312258438.0,
		317978518.0,322597197.0,327295672.0,331561587.0,337672699.0,341420019.0,346487453.0,
		351068351.0,356335035.0,360417294.0,365857944.0,369305338.0,375044914.0,379452513.0,
		383842057.0,387658144.0,393682784.0,396981304.0,401710452.0,405882413.0,410776076.0,
		414306115.0,419446656.0,422214081.0,427562490.0,431456290.0,435111738.0,438382275.0,
		443994124.0,446432305.0,450450697.0,453988014.0,458174232.0,461002239.0,465343459.0,
		467281490.0,471745412.0,474948799.0,477641982.0,480006472.0,484827139.0,486253544.0,
		489242049.0,492039840.0,494978045.0,496952466.0,500110514.0,501161877.0,504454988.0,
		506848516.0,508065797.0,509425844.0,513061847.0,513585323.0,515102059.0,516978459.0,
		518489286.0,519535434.0,521182527.0,521270191.0,523036325.0,524433229.0,524177317.0,
		524632679.0,526655128.0,526115720.0,525983713.0,527033785.0,526902688.0},
		{1.0,14.0,78.0,246.0,607.0,1398.0,2723.0,4778.0,8249.0,13116.0,19925.0,29744.0,42977.0,59494.0,82394.0,
		110038.0,144988.0,188338.0,241827.0,303424.0,383424.0,472472.0,578006.0,703844.0,851648.0,
		1010232.0,1209450.0,1423616.0,1672638.0,1948968.0,2270978.0,2605684.0,3021630.0,3440504.0,
		3931304.0,4458672.0,5075461.0,5675284.0,6426995.0,7165964.0,8036349.0,8914408.0,9962103.0,
		10955498.0,12213818.0,13374904.0,14782820.0,16160026.0,17829199.0,19328362.0,21255960.0,
		23012680.0,25165370.0,27156104.0,29620688.0,31791190.0,34644351.0,37086304.0,40166496.0,
		42954596.0,46470939.0,49423256.0,53357428.0,56696414.0,60980460.0,64632006.0,69395071.0,
		73329050.0,78653930.0,82935378.0,88586235.0,93363616.0,99685403.0,104635768.0,111515217.0,
		116974276.0,124425214.0,130284666.0,138328420.0,144583466.0,153390644.0,160051970.0,
		169396667.0,176626760.0,186854457.0,194316512.0,205262725.0,213380408.0,225159341.0,
		233639864.0,246107869.0,255271718.0,268795401.0,278227458.0,292535146.0,302629396.0,
		318072065.0,328557272.0,344727709.0,355956562.0,373398179.0,384885612.0,403210562.0,
		415622824.0,435161655.0,447652676.0,468425726.0,481703380.0,503678298.0,517550828.0,
		540225670.0,554885368.0,579618738.0,594150034.0,619660115.0,635544616.0,662512419.0,
		678357768.0,706929737.0,723397128.0,753272921.0,770668216.0,801318839.0,819270010.0,
		852679809.0,869971540.0,904129039.0,923710534.0,959146548.0,977983620.0,1015733723.0,
		1035167042.0,1074357293.0,1094896006.0,1134506034.0,1155283444.0,1198843691.0,
		1218536240.0,1262164158.0,1284902046.0,1329685208.0,1351189690.0,1399328856.0,
		1420675522.0,1470119887.0,1492937788.0,1542396790.0,1565421300.0,1619799389.0,
		1640729582.0,1694461356.0,1719650638.0,1774614738.0,1797158122.0,1856311266.0,
		1878180378.0,1938469061.0,1962938958.0,2022139752.0,2045968196.0,2111358815.0,
		2132040756.0,2196584624.0,2222493548.0,2287428235.0,2309480198.0,2380088834.0,
		2401110522.0,2471798762.0,2496002546.0,2564518188.0,2587603222.0,2664604978.0,
		2682692304.0,2757384075.0,2782008170.0,2857045326.0,2876898986.0,2957939999.0,
		2975776954.0,3056145115.0,3078496002.0,3156159871.0,3175928724.0,3263525385.0,
		3276477908.0,3360962613.0,3382751912.0,3465833975.0,3481027850.0,3571749127.0,
		3584194978.0,3673999368.0,3691289922.0,3776640628.0,3790212494.0,3887582735.0,
		3893712272.0,3985719650.0,4001970014.0,4091800490.0,4100049906.0,4199450612.0,
		4203209244.0,4300414700.0,4309954112.0,4401608453.0,4407365050.0,4512145601.0,
		4508069904.0,4605646320.0,4614221808.0,4709677147.0,4707664058.0,4813372529.0,
		4805490064.0,4908592591.0,4908603480.0,5003679733.0,4998400272.0,5107975635.0,
		5092349102.0,5194265531.0,5191369394.0,5289507506.0,5274566644.0,5384678058.0,
		5364098636.0,5469291271.0,5457357380.0,5552940649.0,5535155390.0,5648077592.0,
		5617102862.0,5720161421.0,5703803962.0,5802598697.0,5774153012.0,5884320975.0,
		5849017536.0,5953542186.0,5928097702.0,6022508658.0,5989707406.0,6101899315.0,
		6054659148.0,6156493730.0,6126608764.0,6221940927.0,6178217062.0,6285232986.0,
		6234671836.0,6336190338.0,6295878162.0,6385551002.0,6336755374.0,6445998622.0,
		6383574762.0,6479377408.0,6434506552.0,6523050060.0,6465019476.0,6566986368.0,
		6500314872.0,6595476897.0,6539582206.0,6622153512.0,6559510856.0,6660313955.0,
		6583022892.0,6669719910.0,6611763532.0,6691930320.0,6618812738.0,6711815053.0,
		6630235054.0,6716291184.0,6647688784.0,6719002762.0,6642826900.0,6732621476.0},
		{1.0,15.0,91.0,314.0,821.0,1964.0,4064.0,7450.0,13274.0,22012.0,34558.0,53017.0,78913.0,112511.0,
		159259.0,218617.0,294940.0,390960.0,513571.0,657686.0,845620.0,1061931.0,1326562.0,1637732.0,
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		2255850433736791930.0,2256164913113768153.0,2256485510267024143.0,
		2256828831902121348.0,2256961328932287467.0,2257136647230667004.0,
		2257323403728064042.0,2257287926517768227.0}};

	/**
	 * Spearman exact cumulative distribution function for n <= 22. For n > 22,
	 * cumulative_as89 is invoked. Taken from pspearman package.
	 * @param is
	 * @param n
	 * @param lower_tail
	 * @return CDF
	 */
	public static final double cumulative(double is, int n, boolean lower_tail) {
		if (n > spearmanArray.length)
			return cumulative_as89(is, n, lower_tail);
		int m = n * (n * n - 1) / 6 + 1;
		double[]
			freq = new double[m],
			g = spearmanArray[n - 1];
		int l = g.length;
		System.arraycopy(g, 0, freq, 0, l);
		for (int i = 0; i < l; i++)
			freq[m - i - 1] = g[i];
		if (!lower_tail)
			is = n * (n * n - 1) / 3 - is;
		int k = ((int) is) / 2 + 1;
		double sumk = 0, sum;
		for (int i = 0; i < k; i++)
			sumk += freq[i];
		sum = sumk;
		for (int i = k; i < m; i++)
			sum += freq[i];
		return sumk / sum;
	}

	/**
	 * Spearman cumulative distribution. (taken from src/library/stats/src/prho.c)
	 * Algorithm AS89 -- actually an approximation
	 * @param is
	 * @param n
	 * @param lower_tail
	 * @return CDF
	 */
	public static final double cumulative_as89(double is, int n, boolean lower_tail) {
		final double
		c1 = .2274,
		c2 = .2531,
		c3 = .1745,
		c4 = .0758,
		c5 = .1033,
		c6 = .3932,
		c7 = .0879,
		c8 = .0151,
		c9 = .0072,
		c10= .0831,
		c11= .0131,
		c12= 4.6e-4;
		final int n_small = 9;

		/* Local variables */
		double b, u, x, y, n3;/*, js */
		int l[] = new int[n_small];
		int nfac, i, m, mt, ifr, ise, n1;
		double pv = lower_tail ? 0. : 1.;

		if (is <= 0)
			return pv;
		n3 = n;
		n3 *= (n3 * n3 - 1.) / 3.;/* = (n^3 - n)/3 */
		if (is > n3)
			return 1 - pv;

		if (n <= n_small) { /* 2 <= n <= n_small :
		 * Exact evaluation of probability */
			nfac = 1;
			for (i = 1; i <= n; ++i) {
				nfac *= i;
				l[i - 1] = i;
			}
			/* KH mod next line: was `!=' in the code but `.eq.' in the paper */
			if (is == n3) {
				ifr = 1;
			}
			else {
				ifr = 0;
				for (m = 0; m < nfac; ++m) {
					ise = 0;
					for (i = 0; i < n; ++i) {
						n1 = i + 1 - l[i];
						ise += n1 * n1;
					}
					if (is <= ise)
						++ifr;

					n1 = n;
					do {
						mt = l[0];
						for (i = 1; i < n1; ++i)
							l[i - 1] = l[i];
						--n1;
						l[n1] = mt;
					} while (mt == n1+1 && n1 > 1);
				}
			}
			pv = (lower_tail ? nfac-ifr : ifr) / (double) nfac;
		} /* exact for n <= n_small */
		else { /* n >= n_small : Evaluation by Edgeworth series expansion */
			y = (double) (n);
			b = 1 / y;
			x = (6. * (is - 1) * b / (y * y - 1) - 1) * sqrt(y - 1);
			/* = rho * sqrt(n-1)  ==  rho / sqrt(var(rho))  ~  (0,1) */
			y = x * x;
			u = x * b * (c1 + b * (c2 + c3 * b) +
					y * (-c4 + b * (c5 + c6 * b) -
							y * b * (c7 + c8 * b -
									y * (c9 - c10 * b + y * b * (c11 - c12 * y))
									)));
			y = u / exp(y / 2.);
			pv = (lower_tail ? -y : y) + Normal.cumulative(x, 0., 1., lower_tail, /*log_p = */false);
			/* above was call to alnorm() [algorithm AS 66] */
			if (pv < 0) pv = 0.;
			if (pv > 1) pv = 1.;
		}
		return pv;
	}

	/**
	 * Spearman cumulative distribution function, approximation using T (df=n-2)
	 * @param is
	 * @param n
	 * @param lower_tail
	 * @return CDF
	 */
	public static final double cumulative_t(double is, int n, boolean lower_tail) {
		double r = 1 - (6.0 / n) * (is / (n * n - 1.0));
		return T.cumulative(r / sqrt((1 - r * r) / (n - 2.0)), n-2, !lower_tail, false);
	}

	/**
	 * Density. Minimally tested! Implemented as a differential, i.e. (f(x+h) - f(x)) / h
	 * @param is
	 * @param n
	 * @return density value
	 */
	public static final double density(double is, int n) {
		if (n <= spearmanArray.length) {
			if (is > 0)
				return min(1, max(0, cumulative(is, n, true) - cumulative(is - 1, n, true)));
			return min(1, max(0, cumulative(is + 1, n, true) - cumulative(is, n, true)));
		}
		double
			lo = cumulative_as89(is, n, true),
			hi = cumulative_as89(is + 1e-8, n, true);
		return min(1, max(0, (hi - lo) * 1e8));
	}

	/**
	 * Uses bisection. 
	 * @param q
	 * @param n
	 * @param lower_tail
	 * @param log_p
	 * @return quantile value
	 */
	public static final double quantile(double q, int n, boolean lower_tail, boolean log_p) {
		if (Double.isNaN(q) || n <= 0 || q < 0 || q > 1) return Double.NaN;
		if (log_p) q = exp(q);
		double lo = 0, hi = n * (n * n - 1) / 3 + 1,
			f_lo = cumulative(lo, n, true), f_hi = cumulative(hi, n, true), mid, f_mid;
		boolean pathological = false;
		do {
			mid = floor((lo + hi) / 2);
			f_mid = cumulative(mid, n, true);
			// When the case is pathological, prefer to shrink the
			// upper bound when lower_tail == true (shrink the lower bound otherwise)
			if (f_mid == q && (f_hi == q || f_lo == q) && (hi - lo > 2))
				pathological = true;
			if (lower_tail) {
				if (f_lo >= q) return lo;
				if (f_mid > q) {
					hi = mid;
					f_hi = f_mid;
				} else {
					lo = mid;
					f_lo = f_mid;
				}
			} else {
				if (f_hi <= q) return hi;
				if (f_mid < q) {
					lo = mid;
					f_lo = f_mid;
				} else {
					hi = mid;
					f_hi = f_mid;
				}
			}
		} while (hi - lo > 1);
		if (pathological) {
			System.err.println("Pathological case of Spearman.quantile! Quantile estimate may not be accurate!");
			if (Debug.warningAsError) {
				double ans = (lower_tail) ? (f_hi <= q ? hi : f_mid <= q ? mid : lo) : (f_lo >= q ? lo : f_mid >= q ? mid : hi);
				throw new PrecisionException("Pathological case of Spearman.quantile! Quantile estimate may not be accurate!", ans);
			}
		}
		if (lower_tail)
			return f_hi <= q ? hi : f_mid <= q ? mid : lo;
		return f_lo >= q ? lo : f_mid >= q ? mid : hi;
	}

	/**
	 * Inverse CDF lookup
	 * @param n
	 * @param random
	 * @return random variate
	 */
	public static final double random(int n, RandomEngine random) {
		double u1 = random.nextDouble();
		u1 = (int) (134217728 * u1) + random.nextDouble();
		u1 = quantile(u1 / 134217728, n, true, false);
		return u1;
	}

	public static final double[] random(int count, int n, RandomEngine random) {
		double[] rand = new double[count];
		for (int i = 0; i < count; i++)
			rand[i] = random(n, random);
		return rand;
	}

	protected int n;

	public Spearman(int n) {
		this.n = n;
	}

	/**
	 * Density. Minimally tested!
	 * @param x
	 * @param log set true for log
	 * @return density value
	 */
	@Override
	public double density(double x, boolean log) {
		x = density(x, n);
		return log ? log(x) : x;
	}

	@Override
	public double cumulative(double p, boolean lower_tail, boolean log_p) {
		p = cumulative(p, n, lower_tail);
		return log_p ? log(p) : p;
	}

	/**
	 * Uses numerical optimization to get approximate value, then followed by manual search. 
	 * @param q
	 * @param lower_tail
	 * @param log_p Whether q is in log value
	 * @return quantile value
	 */
	@Override
	public double quantile(double q, boolean lower_tail, boolean log_p) {
		return quantile(q, n, lower_tail, log_p);
	}

	/**
	 * Inverse CDF lookup
	 * @return random variate
	 */
	@Override
	public double random() {
		return random(n, random);
	}

	public static final void main(String[] args) {
		System.out.println(cumulative(0, 10, true));
		int n = 10, q = 36;
		double v = cumulative(q, n, true);
		System.out.println(v);
		System.out.println(quantile(v, n, true, false));
		System.out.println(density(q, n));
		System.out.println(density(3000, 25));
	}
}