/*

* Portions Copyright (c) 2009 Nokia Corporation and/or its subsidiary(-ies).

* All rights reserved.

* This component and the accompanying materials are made available

* under the terms of "Eclipse Public License v1.0"

* which accompanies this distribution, and is available

* at the URL "http://www.eclipse.org/legal/epl-v10.html".

*

* Initial Contributors:

* Nokia Corporation - initial contribution.

*

* Contributors:

*

* Description: 

* The original NIST Statistical Test Suite code is placed in public domain.

* (http://csrc.nist.gov/groups/ST/toolkit/rng/documentation_software.html) 

* 

* This software was developed at the National Institute of Standards and Technology by 

* employees of the Federal Government in the course of their official duties. Pursuant

* to title 17 Section 105 of the United States Code this software is not subject to 

* copyright protection and is in the public domain. The NIST Statistical Test Suite is

* an experimental system. NIST assumes no responsibility whatsoever for its use by other 

* parties, and makes no guarantees, expressed or implied, about its quality, reliability, 

* or any other characteristic. We would appreciate acknowledgment if the software is used.

*/

#include "openc.h"

#include "../include/cephes.h"

static const double	rel_error = 1E-12;

double MACHEP = 1.11022302462515654042E-16;		// 2**-53

double MAXLOG = 7.09782712893383996732224E2;	// log(MAXNUM)

double MAXNUM = 1.7976931348623158E308;			// 2**1024*(1-MACHEP)

double PI     = 3.14159265358979323846;			// pi, duh!

static double big = 4.503599627370496e15;

static double biginv =  2.22044604925031308085e-16;

int sgngam = 0;

double

cephes_igamc(double a, double x)

{

	double ans, ax, c, yc, r, t, y, z;

	double pk, pkm1, pkm2, qk, qkm1, qkm2;

	if ( (x <= 0) || ( a <= 0) )

		return( 1.0 );

	if ( (x < 1.0) || (x < a) )

		return( 1.e0 - cephes_igam(a,x) );

	ax = a * log(x) - x - cephes_lgam(a);

	if ( ax < -MAXLOG ) {

		printf("igamc: UNDERFLOW\n");

		return 0.0;

	}

	ax = exp(ax);

	/* continued fraction */

	y = 1.0 - a;

	z = x + y + 1.0;

	c = 0.0;

	pkm2 = 1.0;

	qkm2 = x;

	pkm1 = x + 1.0;

	qkm1 = z * x;

	ans = pkm1/qkm1;

	do {

		c += 1.0;

		y += 1.0;

		z += 2.0;

		yc = y * c;

		pk = pkm1 * z  -  pkm2 * yc;

		qk = qkm1 * z  -  qkm2 * yc;

		if ( qk != 0 ) {

			r = pk/qk;

			t = fabs( (ans - r)/r );

			ans = r;

		}

		else

			t = 1.0;

		pkm2 = pkm1;

		pkm1 = pk;

		qkm2 = qkm1;

		qkm1 = qk;

		if ( fabs(pk) > big ) {

			pkm2 *= biginv;

			pkm1 *= biginv;

			qkm2 *= biginv;

			qkm1 *= biginv;

		}

	} while ( t > MACHEP );

	return ans*ax;

}

double

cephes_igam(double a, double x)

{

	double ans, ax, c, r;

	if ( (x <= 0) || ( a <= 0) )

		return 0.0;

	if ( (x > 1.0) && (x > a ) )

		return 1.e0 - cephes_igamc(a,x);

	/* Compute  x**a * exp(-x) / gamma(a)  */

	ax = a * log(x) - x - cephes_lgam(a);

	if ( ax < -MAXLOG ) {

		printf("igam: UNDERFLOW\n");

		return 0.0;

	}

	ax = exp(ax);

	/* power series */

	r = a;

	c = 1.0;

	ans = 1.0;

	do {

		r += 1.0;

		c *= x/r;

		ans += c;

	} while ( c/ans > MACHEP );

	return ans * ax/a;

}

/* A[]: Stirling's formula expansion of log gamma

 * B[], C[]: log gamma function between 2 and 3

 */

static unsigned short A[] = {

	0x6661,0x2733,0x9850,0x3f4a,

	0xe943,0xb580,0x7fbd,0xbf43,

	0x5ebb,0x20dc,0x019f,0x3f4a,

	0xa5a1,0x16b0,0xc16c,0xbf66,

	0x554b,0x5555,0x5555,0x3fb5

};

static unsigned short B[] = {

	0x6761,0x8ff3,0x8901,0xc095,

	0xb93e,0x355b,0xf234,0xc0e2,

	0x89e5,0xf890,0x3d73,0xc114,

	0xdb51,0xf994,0xbc82,0xc131,

	0xf20b,0x0219,0x4589,0xc13a,

	0x055e,0x5418,0x0c67,0xc12a

};

static unsigned short C[] = {

	/*0x0000,0x0000,0x0000,0x3ff0,*/

	0x12b2,0x1cf3,0xfd0d,0xc075,

	0xd757,0x7b89,0xaa0d,0xc0d0,

	0x4c9b,0xb974,0xeb84,0xc10a,

	0x0043,0x7195,0x6286,0xc131,

	0xf34c,0x892f,0x5255,0xc143,

	0xe14a,0x6a11,0xce4b,0xc13e

};

#define MAXLGM 2.556348e305

/* Logarithm of gamma function */

double

cephes_lgam(double x)

{

	double	p, q, u, w, z;

	int		i;

	sgngam = 1;

	if ( x < -34.0 ) {

		q = -x;

		w = cephes_lgam(q); /* note this modifies sgngam! */

		p = floor(q);

		if ( p == q ) {

lgsing:

			goto loverf;

		}

		i = (int)p;

		if ( (i & 1) == 0 )

			sgngam = -1;

		else

			sgngam = 1;

		z = q - p;

		if ( z > 0.5 ) {

			p += 1.0;

			z = p - q;

		}

		z = q * sin( PI * z );

		if ( z == 0.0 )

			goto lgsing;

		/*      z = log(PI) - log( z ) - w;*/

		z = log(PI) - log( z ) - w;

		return z;

	}

	if ( x < 13.0 ) {

		z = 1.0;

		p = 0.0;

		u = x;

		while ( u >= 3.0 ) {

			p -= 1.0;

			u = x + p;

			z *= u;

		}

		while ( u < 2.0 ) {

			if ( u == 0.0 )

				goto lgsing;

			z /= u;

			p += 1.0;

			u = x + p;

		}

		if ( z < 0.0 ) {

			sgngam = -1;

			z = -z;

		}

		else

			sgngam = 1;

		if ( u == 2.0 )

			return( log(z) );

		p -= 2.0;

		x = x + p;

		p = x * cephes_polevl( x, (double *)B, 5 ) / cephes_p1evl( x, (double *)C, 6);

		return log(z) + p;

	}

	if ( x > MAXLGM ) {

loverf:

		printf("lgam: OVERFLOW\n");

		return sgngam * MAXNUM;

	}

	q = ( x - 0.5 ) * log(x) - x + log( sqrt( 2*PI ) );

	if ( x > 1.0e8 )

		return q;

	p = 1.0/(x*x);

	if ( x >= 1000.0 )

		q += ((   7.9365079365079365079365e-4 * p

		        - 2.7777777777777777777778e-3) *p

				+ 0.0833333333333333333333) / x;

	else

		q += cephes_polevl( p, (double *)A, 4 ) / x;

	return q;

}

double

cephes_polevl(double x, double *coef, int N)

{

	double	ans;

	int		i;

	double	*p;

	p = coef;

	ans = *p++;

	i = N;

	do

		ans = ans * x  +  *p++;

	while ( --i );

	return ans;

}

double

cephes_p1evl(double x, double *coef, int N)

{

	double	ans;

	double	*p;

	int		i;

	p = coef;

	ans = x + *p++;

	i = N-1;

	do

		ans = ans * x  + *p++;

	while ( --i );

	return ans;

}

double

cephes_erf(double x)

{

	static const double two_sqrtpi = 1.128379167095512574;

	double	sum = x, term = x, xsqr = x * x;

	int		j = 1;

	if ( fabs(x) > 2.2 )

		return 1.0 - cephes_erfc(x);

	do {

		term *= xsqr/j;

		sum -= term/(2*j+1);

		j++;

		term *= xsqr/j;

		sum += term/(2*j+1);

		j++;

	} while ( fabs(term)/sum > rel_error );

	return two_sqrtpi*sum;

}

double

cephes_erfc(double x)

{

	static const double one_sqrtpi = 0.564189583547756287;

	double	a = 1, b = x, c = x, d = x*x + 0.5;

	double	q1, q2 = b/d, n = 1.0, t;

	if ( fabs(x) < 2.2 )

		return 1.0 - cephes_erf(x);

	if ( x < 0 )

		return 2.0 - cephes_erfc(-x);

	do {

		t = a*n + b*x;

		a = b;

		b = t;

		t = c*n + d*x;

		c = d;

		d = t;

		n += 0.5;

		q1 = q2;

		q2 = b/d;

	} while ( fabs(q1-q2)/q2 > rel_error );

	return one_sqrtpi*exp(-x*x)*q2;

}

double

cephes_normal(double x)

{

	double arg, result, sqrt2=1.414213562373095048801688724209698078569672;

	if (x > 0) {

		arg = x/sqrt2;

		result = 0.5 * ( 1 + erf(arg) );

	}

	else {

		arg = -x/sqrt2;

		result = 0.5 * ( 1 - erf(arg) );

	}

	return( result);

}