1 /*

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

     3 * All rights reserved.

     4 * This component and the accompanying materials are made available

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

     6 * which accompanies this distribution, and is available

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

     8 *

     9 * Initial Contributors:

    10 * Nokia Corporation - initial contribution.

    11 *

    12 * Contributors:

    13 *

    14 * Description: 

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

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

    17 * 

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

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

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

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

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

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

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

    25 */

    26 

    27 

    28 

    29 #include "openc.h"

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

    31 

    32 static const double	rel_error = 1E-12;

    33 

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

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

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

    37 double PI     = 3.14159265358979323846;			// pi, duh!

    38 

    39 static double big = 4.503599627370496e15;

    40 static double biginv =  2.22044604925031308085e-16;

    41 

    42 int sgngam = 0;

    43 

    44 double

    45 cephes_igamc(double a, double x)

    46 {

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

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

    49 

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

    51 		return( 1.0 );

    52 

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

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

    55 

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

    57 

    58 	if ( ax < -MAXLOG ) {

    59 		printf("igamc: UNDERFLOW\n");

    60 		return 0.0;

    61 	}

    62 	ax = exp(ax);

    63 

    64 	/* continued fraction */

    65 	y = 1.0 - a;

    66 	z = x + y + 1.0;

    67 	c = 0.0;

    68 	pkm2 = 1.0;

    69 	qkm2 = x;

    70 	pkm1 = x + 1.0;

    71 	qkm1 = z * x;

    72 	ans = pkm1/qkm1;

    73 

    74 	do {

    75 		c += 1.0;

    76 		y += 1.0;

    77 		z += 2.0;

    78 		yc = y * c;

    79 		pk = pkm1 * z  -  pkm2 * yc;

    80 		qk = qkm1 * z  -  qkm2 * yc;

    81 		if ( qk != 0 ) {

    82 			r = pk/qk;

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

    84 			ans = r;

    85 		}

    86 		else

    87 			t = 1.0;

    88 		pkm2 = pkm1;

    89 		pkm1 = pk;

    90 		qkm2 = qkm1;

    91 		qkm1 = qk;

    92 		if ( fabs(pk) > big ) {

    93 			pkm2 *= biginv;

    94 			pkm1 *= biginv;

    95 			qkm2 *= biginv;

    96 			qkm1 *= biginv;

    97 		}

    98 	} while ( t > MACHEP );

    99 

   100 	return ans*ax;

   101 }

   102 

   103 double

   104 cephes_igam(double a, double x)

   105 {

   106 	double ans, ax, c, r;

   107 

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

   109 		return 0.0;

   110 

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

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

   113 

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

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

   116 	if ( ax < -MAXLOG ) {

   117 		printf("igam: UNDERFLOW\n");

   118 		return 0.0;

   119 	}

   120 	ax = exp(ax);

   121 

   122 	/* power series */

   123 	r = a;

   124 	c = 1.0;

   125 	ans = 1.0;

   126 

   127 	do {

   128 		r += 1.0;

   129 		c *= x/r;

   130 		ans += c;

   131 	} while ( c/ans > MACHEP );

   132 

   133 	return ans * ax/a;

   134 }

   135 

   136 

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

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

   139  */

   140 static unsigned short A[] = {

   141 	0x6661,0x2733,0x9850,0x3f4a,

   142 	0xe943,0xb580,0x7fbd,0xbf43,

   143 	0x5ebb,0x20dc,0x019f,0x3f4a,

   144 	0xa5a1,0x16b0,0xc16c,0xbf66,

   145 	0x554b,0x5555,0x5555,0x3fb5

   146 };

   147 static unsigned short B[] = {

   148 	0x6761,0x8ff3,0x8901,0xc095,

   149 	0xb93e,0x355b,0xf234,0xc0e2,

   150 	0x89e5,0xf890,0x3d73,0xc114,

   151 	0xdb51,0xf994,0xbc82,0xc131,

   152 	0xf20b,0x0219,0x4589,0xc13a,

   153 	0x055e,0x5418,0x0c67,0xc12a

   154 };

   155 static unsigned short C[] = {

   156 	/*0x0000,0x0000,0x0000,0x3ff0,*/

   157 	0x12b2,0x1cf3,0xfd0d,0xc075,

   158 	0xd757,0x7b89,0xaa0d,0xc0d0,

   159 	0x4c9b,0xb974,0xeb84,0xc10a,

   160 	0x0043,0x7195,0x6286,0xc131,

   161 	0xf34c,0x892f,0x5255,0xc143,

   162 	0xe14a,0x6a11,0xce4b,0xc13e

   163 };

   164 

   165 #define MAXLGM 2.556348e305

   166 

   167 

   168 /* Logarithm of gamma function */

   169 double

   170 cephes_lgam(double x)

   171 {

   172 	double	p, q, u, w, z;

   173 	int		i;

   174 

   175 	sgngam = 1;

   176 

   177 	if ( x < -34.0 ) {

   178 		q = -x;

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

   180 		p = floor(q);

   181 		if ( p == q ) {

   182 lgsing:

   183 			goto loverf;

   184 		}

   185 		i = (int)p;

   186 		if ( (i & 1) == 0 )

   187 			sgngam = -1;

   188 		else

   189 			sgngam = 1;

   190 		z = q - p;

   191 		if ( z > 0.5 ) {

   192 			p += 1.0;

   193 			z = p - q;

   194 		}

   195 		z = q * sin( PI * z );

   196 		if ( z == 0.0 )

   197 			goto lgsing;

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

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

   200 		return z;

   201 	}

   202 

   203 	if ( x < 13.0 ) {

   204 		z = 1.0;

   205 		p = 0.0;

   206 		u = x;

   207 		while ( u >= 3.0 ) {

   208 			p -= 1.0;

   209 			u = x + p;

   210 			z *= u;

   211 		}

   212 		while ( u < 2.0 ) {

   213 			if ( u == 0.0 )

   214 				goto lgsing;

   215 			z /= u;

   216 			p += 1.0;

   217 			u = x + p;

   218 		}

   219 		if ( z < 0.0 ) {

   220 			sgngam = -1;

   221 			z = -z;

   222 		}

   223 		else

   224 			sgngam = 1;

   225 		if ( u == 2.0 )

   226 			return( log(z) );

   227 		p -= 2.0;

   228 		x = x + p;

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

   230 

   231 		return log(z) + p;

   232 	}

   233 

   234 	if ( x > MAXLGM ) {

   235 loverf:

   236 		printf("lgam: OVERFLOW\n");

   237 

   238 		return sgngam * MAXNUM;

   239 	}

   240 

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

   242 	if ( x > 1.0e8 )

   243 		return q;

   244 

   245 	p = 1.0/(x*x);

   246 	if ( x >= 1000.0 )

   247 		q += ((   7.9365079365079365079365e-4 * p

   248 		        - 2.7777777777777777777778e-3) *p

   249 				+ 0.0833333333333333333333) / x;

   250 	else

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

   252 

   253 	return q;

   254 }

   255 

   256 double

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

   258 {

   259 	double	ans;

   260 	int		i;

   261 	double	*p;

   262 

   263 	p = coef;

   264 	ans = *p++;

   265 	i = N;

   266 

   267 	do

   268 		ans = ans * x  +  *p++;

   269 	while ( --i );

   270 

   271 	return ans;

   272 }

   273 

   274 double

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

   276 {

   277 	double	ans;

   278 	double	*p;

   279 	int		i;

   280 

   281 	p = coef;

   282 	ans = x + *p++;

   283 	i = N-1;

   284 

   285 	do

   286 		ans = ans * x  + *p++;

   287 	while ( --i );

   288 

   289 	return ans;

   290 }

   291 

   292 double

   293 cephes_erf(double x)

   294 {

   295 	static const double two_sqrtpi = 1.128379167095512574;

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

   297 	int		j = 1;

   298 

   299 	if ( fabs(x) > 2.2 )

   300 		return 1.0 - cephes_erfc(x);

   301 

   302 	do {

   303 		term *= xsqr/j;

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

   305 		j++;

   306 		term *= xsqr/j;

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

   308 		j++;

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

   310 

   311 	return two_sqrtpi*sum;

   312 }

   313 

   314 double

   315 cephes_erfc(double x)

   316 {

   317 	static const double one_sqrtpi = 0.564189583547756287;

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

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

   320 

   321 	if ( fabs(x) < 2.2 )

   322 		return 1.0 - cephes_erf(x);

   323 	if ( x < 0 )

   324 		return 2.0 - cephes_erfc(-x);

   325 

   326 	do {

   327 		t = a*n + b*x;

   328 		a = b;

   329 		b = t;

   330 		t = c*n + d*x;

   331 		c = d;

   332 		d = t;

   333 		n += 0.5;

   334 		q1 = q2;

   335 		q2 = b/d;

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

   337 

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

   339 }

   340 

   341 

   342 double

   343 cephes_normal(double x)

   344 {

   345 	double arg, result, sqrt2=1.414213562373095048801688724209698078569672;

   346 

   347 	if (x > 0) {

   348 		arg = x/sqrt2;

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

   350 	}

   351 	else {

   352 		arg = -x/sqrt2;

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

   354 	}

   355 

   356 	return( result);

   357 }