/*
* 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);
}