sfun.java

This is a Java library for performing floating-point calculations on small devices such as mobile p

package com.imsl.math;

/*
 * -------------------------------------------------------------------------
 *	$Id: Sfun.java,v 1.1 2004/08/01 18:01:48 Dave Exp $
 * -------------------------------------------------------------------------
 * Copyright (c) 1997 - 1998 by Visual Numerics, Inc. All rights reserved.
 *
 * Permission to use, copy, modify, and distribute this software is freely
 * granted by Visual Numerics, Inc., provided that the copyright notice
 * above and the following warranty disclaimer are preserved in human
 * readable form.
 *
 * Because this software is licenses free of charge, it is provided
 * "AS IS", with NO WARRANTY.  TO THE EXTENT PERMITTED BY LAW, VNI
 * DISCLAIMS ALL WARRANTIES, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED
 * TO ITS PERFORMANCE, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
 * VNI WILL NOT BE LIABLE FOR ANY DAMAGES WHATSOEVER ARISING OUT OF THE USE
 * OF OR INABILITY TO USE THIS SOFTWARE, INCLUDING BUT NOT LIMITED TO DIRECT,
 * INDIRECT, SPECIAL, CONSEQUENTIAL, PUNITIVE, AND EXEMPLARY DAMAGES, EVEN
 * IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGES. 
 *
 * -------------------------------------------------------------------------
 */

/**
 *	Collection of special functions.
 */
public class Sfun
{
	/** The smallest relative spacing for doubles.*/
	public final static double EPSILON_SMALL = 1.1102230246252e-16;
	
	/** The largest relative spacing for doubles. */
	public final static double EPSILON_LARGE = 2.2204460492503e-16;

	
	// Series on [0,0.0625]
	private static final double	COT_COEF[] = {
		.240259160982956302509553617744970e+0,
		-.165330316015002278454746025255758e-1,
		-.429983919317240189356476228239895e-4,
		-.159283223327541046023490851122445e-6,
		-.619109313512934872588620579343187e-9,
		-.243019741507264604331702590579575e-11,
		-.956093675880008098427062083100000e-14,
		-.376353798194580580416291539706666e-16,
		-.148166574646746578852176794666666e-18
	};

	// Series on the interval [0,1]
	private static final double	SINH_COEF[] = {
		0.1730421940471796,
		0.08759422192276048,
		0.00107947777456713,
		0.00000637484926075,
		0.00000002202366404,
		0.00000000004987940,
		0.00000000000007973,
		0.00000000000000009};

	// Series on [0,1]
	private static final double	TANH_COEF[] = {
		-.25828756643634710,
		-.11836106330053497,
		.009869442648006398,
		-.000835798662344582,
		.000070904321198943,
		-.000006016424318120,
		.000000510524190800,
		-.000000043320729077,
		.000000003675999055,
		-.000000000311928496,
		.000000000026468828,
		-.000000000002246023,
		.000000000000190587,
		-.000000000000016172,
		.000000000000001372,
		-.000000000000000116,
		.000000000000000009};

	// Series on the interval [0,1]
	private static final double	ASINH_COEF[] = {
		 -.12820039911738186343372127359268e+0,
		-.58811761189951767565211757138362e-1,
		.47274654322124815640725249756029e-2,
		-.49383631626536172101360174790273e-3,
		.58506207058557412287494835259321e-4,
		-.74669983289313681354755069217188e-5,
		.10011693583558199265966192015812e-5,
		-.13903543858708333608616472258886e-6,
		.19823169483172793547317360237148e-7,
		-.28847468417848843612747272800317e-8,
		.42672965467159937953457514995907e-9,
		-.63976084654366357868752632309681e-10,
		.96991686089064704147878293131179e-11,
		-.14844276972043770830246658365696e-11,
		.22903737939027447988040184378983e-12,
		-.35588395132732645159978942651310e-13,
		.55639694080056789953374539088554e-14,
		-.87462509599624678045666593520162e-15,
		.13815248844526692155868802298129e-15,
		-.21916688282900363984955142264149e-16,
		.34904658524827565638313923706880e-17
	};

	// Series on the interval [0,0.25]
	private static final double	ATANH_COEF[] = {
		.9439510239319549230842892218633e-1,
		.4919843705578615947200034576668e-1,
		.2102593522455432763479327331752e-2,
		.1073554449776116584640731045276e-3,
		.5978267249293031478642787517872e-5,
		.3505062030889134845966834886200e-6,
		.2126374343765340350896219314431e-7,
		.1321694535715527192129801723055e-8,
		.8365875501178070364623604052959e-10,
		.5370503749311002163881434587772e-11,
		.3486659470157107922971245784290e-12,
		.2284549509603433015524024119722e-13,
		.1508407105944793044874229067558e-14,
		.1002418816804109126136995722837e-15,
		.6698674738165069539715526882986e-17,
		.4497954546494931083083327624533e-18
	};

	// Series on the interval [0,1]
	private static final double	GAMMA_COEF[] = {
		.8571195590989331421920062399942e-2,
		.4415381324841006757191315771652e-2,
		.5685043681599363378632664588789e-1,
		-.4219835396418560501012500186624e-2,
		.1326808181212460220584006796352e-2,
		-.1893024529798880432523947023886e-3,
		.3606925327441245256578082217225e-4,
		-.6056761904460864218485548290365e-5,
		.1055829546302283344731823509093e-5,
		-.1811967365542384048291855891166e-6,
		.3117724964715322277790254593169e-7,
		-.5354219639019687140874081024347e-8,
		.9193275519859588946887786825940e-9,
		-.1577941280288339761767423273953e-9,
		.2707980622934954543266540433089e-10,
		-.4646818653825730144081661058933e-11,
		.7973350192007419656460767175359e-12,
		-.1368078209830916025799499172309e-12,
		.2347319486563800657233471771688e-13,
		-.4027432614949066932766570534699e-14,
		.6910051747372100912138336975257e-15,
		-.1185584500221992907052387126192e-15,
		.2034148542496373955201026051932e-16,
		-.3490054341717405849274012949108e-17,
		.5987993856485305567135051066026e-18,
		-.1027378057872228074490069778431e-18
	};

	//	Series for the interval [0,0.01]
	private static final double	R9LGMC_COEF[] =
	{
		.166638948045186324720572965082e0,
		-.138494817606756384073298605914e-4,
		.981082564692472942615717154749e-8,
		-.180912947557249419426330626672e-10,
		.622109804189260522712601554342e-13,
		-.339961500541772194430333059967e-15,
		.268318199848269874895753884667e-17
	};

	// Series on [-0.375,0.375]
	final private static double ALNRCS_COEF[] = {
	   .103786935627437698006862677191e1,
	  -.133643015049089180987660415531,
	  .194082491355205633579261993748e-1,
	  -.301075511275357776903765377766e-2,
	  .486946147971548500904563665091e-3,
	  -.810548818931753560668099430086e-4,
	  .137788477995595247829382514961e-4,
	  -.238022108943589702513699929149e-5,
	  .41640416213865183476391859902e-6,
	  -.73595828378075994984266837032e-7,
	  .13117611876241674949152294345e-7,
	  -.235467093177424251366960923302e-8,
	  .425227732760349977756380529626e-9,
	  -.771908941348407968261081074933e-10,
	  .140757464813590699092153564722e-10,
	  -.257690720580246806275370786276e-11,
	  .473424066662944218491543950059e-12,
	  -.872490126747426417453012632927e-13,
	  .161246149027405514657398331191e-13,
	  -.298756520156657730067107924168e-14,
	  .554807012090828879830413216973e-15,
	  -.103246191582715695951413339619e-15,
	  .192502392030498511778785032449e-16,
	  -.359550734652651500111897078443e-17,
	  .672645425378768578921945742268e-18,
	  -.126026241687352192520824256376e-18
	};
	
	// Series on [0,1]
	private static final double	ERFC_COEF[] = {
	 -.490461212346918080399845440334e-1,
	 -.142261205103713642378247418996e0,
	 .100355821875997955757546767129e-1,
	 -.576876469976748476508270255092e-3,
	 .274199312521960610344221607915e-4,
	 -.110431755073445076041353812959e-5,
	 .384887554203450369499613114982e-7,
	 -.118085825338754669696317518016e-8,
	 .323342158260509096464029309534e-10,
	 -.799101594700454875816073747086e-12,
	 .179907251139614556119672454866e-13,
	 -.371863548781869263823168282095e-15,
	 .710359900371425297116899083947e-17,
	 -.126124551191552258324954248533e-18
	};

	// Series on [0.25,1.00]
	private static final double	ERFC2_COEF[] = {
	 -.69601346602309501127391508262e-1,
	 -.411013393626208934898221208467e-1,
	 .391449586668962688156114370524e-2,
	 -.490639565054897916128093545077e-3,
	 .715747900137703638076089414183e-4,
	 -.115307163413123283380823284791e-4,
	 .199467059020199763505231486771e-5,
	 -.364266647159922287393611843071e-6,
	 .694437261000501258993127721463e-7,
	 -.137122090210436601953460514121e-7,
	 .278838966100713713196386034809e-8,
	 -.581416472433116155186479105032e-9,
	 .123892049175275318118016881795e-9,
	 -.269063914530674343239042493789e-10,
	 .594261435084791098244470968384e-11,
	 -.133238673575811957928775442057e-11,
	 .30280468061771320171736972433e-12,
	 -.696664881494103258879586758895e-13,
	 .162085454105392296981289322763e-13,
	 -.380993446525049199987691305773e-14,
	 .904048781597883114936897101298e-15,
	 -.2164006195089607347809812047e-15,
	 .522210223399585498460798024417e-16,
	 -.126972960236455533637241552778e-16,
	 .310914550427619758383622741295e-17,
	 -.766376292032038552400956671481e-18,
	 .190081925136274520253692973329e-18
  	};

	// Series on [0,0.25]
	private static final double	ERFCC_COEF[] = {
	 .715179310202924774503697709496e-1,
	 -.265324343376067157558893386681e-1,
	 .171115397792085588332699194606e-2,
	 -.163751663458517884163746404749e-3,
	 .198712935005520364995974806758e-4,
	 -.284371241276655508750175183152e-5,
	 .460616130896313036969379968464e-6,
	 -.822775302587920842057766536366e-7,
	 .159214187277090112989358340826e-7,
	 -.329507136225284321486631665072e-8,
	 .72234397604005554658126115389e-9,
	 -.166485581339872959344695966886e-9,
	 .401039258823766482077671768814e-10,
	 -.100481621442573113272170176283e-10,
	 .260827591330033380859341009439e-11,
	 -.699111056040402486557697812476e-12,
	 .192949233326170708624205749803e-12,
	 -.547013118875433106490125085271e-13,
	 .158966330976269744839084032762e-13,
	 -.47268939801975548392036958429e-14,
	 .14358733767849847867287399784e-14,
	 -.444951056181735839417250062829e-15,
	 .140481088476823343737305537466e-15,
	 -.451381838776421089625963281623e-16,
	 .147452154104513307787018713262e-16,
	 -.489262140694577615436841552532e-17,
	 .164761214141064673895301522827e-17,
	 -.562681717632940809299928521323e-18,
	 .194744338223207851429197867821e-18
  	};



	/**
	 *	Private contructor, so nobody can make an instance of this class.
	 */
	private Sfun()
	{
	}
	/**
	 *	Returns the inverse (arc) hyperbolic cosine of a double.
	 *	@param	x	A double value.
	 *	@return  The arc hyperbolic cosine of x.
	 *	If x is NaN or less than one, the result is NaN.
	 */
	static public double acosh(double x)
	{
		double ans;
		
		if (Double.isNaN(x) || x < 1) {
			ans = Double.NaN;
		} else if (x < 94906265.62) {
			// 94906265.62 = 1.0/Math.sqrt(EPSILON_SMALL)
			ans = Math.log(x+Math.sqrt(x*x-1.0));
		} else {
			ans = 0.69314718055994530941723212145818 + Math.log(x);
		}
		return ans;
	}
	/**
	 *	Returns the inverse (arc) hyperbolic sine of a double.
	 *	@param	x	A double value.
	 *	@return  The arc hyperbolic sine of x.
	 *	If x is NaN, the result is NaN.
	 */
	static public double asinh(double x)
	{
		double	ans;
		double	y = Math.abs(x);
	
		if (Double.isNaN(x)) {
			ans = Double.NaN;
		} else if (y <= 1.05367e-08) {
			// 1.05367e-08 = Math.sqrt(EPSILON_SMALL)
			ans = x;
		} else if (y <= 1.0) {			
			ans = x*(1.0+csevl(2.0*x*x-1.0,ASINH_COEF));
		} else if (y < 94906265.62) {
			// 94906265.62 = 1/Math.sqrt(EPSILON_SMALL)
			ans = Math.log(y+Math.sqrt(y*y+1.0));
		} else {	
			ans = 0.69314718055994530941723212145818 + Math.log(y);
		}
		if (x < 0.0) ans = -ans;
		return ans;
	}
	/**
	 *	Returns the inverse (arc) hyperbolic tangent of a double.
	 *	@param	x	A double value.
	 *	@return  The arc hyperbolic tangent of x.
	 *	If x is NaN or |x|>1, the result is NaN.
	 */
	static public double atanh(double x)
	{
		double	y = Math.abs(x);
		double	ans;

		if (Double.isNaN(x)) {
			ans = Double.NaN;
		} else if (y < 1.82501e-08) {
			// 1.82501e-08 = Math.sqrt(3.0*EPSILON_SMALL)
			ans = x;
		} else if (y <= 0.5) {
			ans = x*(1.0+csevl(8.0*x*x-1.0,ATANH_COEF));
		} else if (y < 1.0) {
			ans = 0.5*Math.log((1.0+x)/(1.0-x));
		} else if (y == 1.0) {
			ans = x*Double.POSITIVE_INFINITY;
		} else {
			ans = Double.NaN;
		}
		return ans;
	}
	/**
	 *	Returns the hyperbolic cosine of a double.
	 *	@param	x	A double value.
	 *	@return  The hyperbolic cosine of x.
	 *	If x is NaN, the result is NaN.
	 */
	static public double cosh(double x)
	{
		double	ans;
		double	y = Math.exp(Math.abs(x));

		if (Double.isNaN(x)) {
			ans = Double.NaN;
		} else if (Double.isInfinite(x)) {
			ans = x;
		} else if (y < 94906265.62) {
			// 94906265.62 = 1.0/Math.sqrt(EPSILON_SMALL)
			ans = 0.5*(y+1.0/y);
		} else {
			ans = 0.5*y;
		}
		return ans;
	}