File: [local] / OpenXM_contrib / gnuplot / Attic / specfun.c (download)
Revision 1.1.1.3 (vendor branch), Mon Sep 15 07:09:26 2003 UTC (20 years, 8 months ago) by ohara
Branch: GNUPLOT
CVS Tags: VERSION_3_7_3, RELEASE_1_2_3, RELEASE_1_2_2_KNOPPIX_b, RELEASE_1_2_2_KNOPPIX
Changes since 1.1.1.2: +1310 -248
lines
Import gnuplot 3.7.3
|
#ifndef lint
static char *RCSid = "$Id: specfun.c,v 1.8.2.7 2002/11/09 18:04:31 lhecking Exp $";
#endif
/* GNUPLOT - specfun.c */
/*[
* Copyright 1986 - 1993, 1998 Thomas Williams, Colin Kelley
*
* Permission to use, copy, and distribute this software and its
* documentation for any purpose with or without fee is hereby granted,
* provided that the above copyright notice appear in all copies and
* that both that copyright notice and this permission notice appear
* in supporting documentation.
*
* Permission to modify the software is granted, but not the right to
* distribute the complete modified source code. Modifications are to
* be distributed as patches to the released version. Permission to
* distribute binaries produced by compiling modified sources is granted,
* provided you
* 1. distribute the corresponding source modifications from the
* released version in the form of a patch file along with the binaries,
* 2. add special version identification to distinguish your version
* in addition to the base release version number,
* 3. provide your name and address as the primary contact for the
* support of your modified version, and
* 4. retain our contact information in regard to use of the base
* software.
* Permission to distribute the released version of the source code along
* with corresponding source modifications in the form of a patch file is
* granted with same provisions 2 through 4 for binary distributions.
*
* This software is provided "as is" without express or implied warranty
* to the extent permitted by applicable law.
]*/
/*
* AUTHORS
*
* Original Software:
* Jos van der Woude, jvdwoude@hut.nl
*
*/
#include "plot.h"
#include "fnproto.h"
extern struct value stack[STACK_DEPTH];
extern int s_p;
extern double zero;
#define ITMAX 200
#ifdef FLT_EPSILON
# define MACHEPS FLT_EPSILON /* 1.0E-08 */
#else
# define MACHEPS 1.0E-08
#endif
/* AS239 value, e^-88 = 2^-127 */
#define MINEXP -88.0
#ifdef FLT_MAX
# define OFLOW FLT_MAX /* 1.0E+37 */
#else
# define OFLOW 1.0E+37
#endif
/* AS239 value for igamma(a,x>=XBIG) = 1.0 */
#define XBIG 1.0E+08
/*
* Mathematical constants
*/
#define LNPI 1.14472988584940016
#define LNSQRT2PI 0.9189385332046727
#ifdef PI
# undef PI
#endif
#define PI 3.14159265358979323846
#define PNT68 0.6796875
#define SQRT_TWO 1.41421356237309504880168872420969809 /* JG */
/* Prefer lgamma */
#ifndef GAMMA
# ifdef HAVE_LGAMMA
# define GAMMA(x) lgamma (x)
# elif defined(HAVE_GAMMA)
# define GAMMA(x) gamma (x)
# else
# undef GAMMA
# endif
#endif
#ifndef GAMMA
int signgam = 0;
#else
extern int signgam; /* this is not always declared in math.h */
#endif
/* Global variables, not visible outside this file */
static long Xm1 = 2147483563L;
static long Xm2 = 2147483399L;
static long Xa1 = 40014L;
static long Xa2 = 40692L;
/* Local function declarations, not visible outside this file */
static int mtherr(char *name, int code);
static double polevl(double x, double coef[], int N);
static double p1evl(double x, double coef[], int N);
static double confrac __PROTO((double a, double b, double x));
static double ibeta __PROTO((double a, double b, double x));
static double igamma __PROTO((double a, double x));
static double ranf __PROTO((double init));
static double inverse_normal_func __PROTO((double p));
static double inverse_error_func __PROTO((double p));
/* UNKnown arithmetic, invokes coefficients given in
* normal decimal format. Beware of range boundary
* problems (MACHEP, MAXLOG, etc. in const.c) and
* roundoff problems in pow.c:
* (Sun SPARCstation)
*/
#define UNK 1
/* If you define UNK, then be sure to set BIGENDIAN properly. */
#ifdef FLOAT_WORDS_BIGENDIAN
#define BIGENDIAN 1
#else
#define BIGENDIAN 0
#endif
/* Define to support tiny denormal numbers, else undefine. */
#define DENORMAL 1
/* Define to ask for infinity support, else undefine. */
#define INFINITIES 1
/* Define to ask for support of numbers that are Not-a-Number,
else undefine. This may automatically define INFINITIES in some files. */
#define NANS 1
/* Define to distinguish between -0.0 and +0.0. */
#define MINUSZERO 1
/* Variable for error reporting. See mtherr.c. */
extern int merror;
/*
Cephes Math Library Release 2.0: April, 1987
Copyright 1984, 1987 by Stephen L. Moshier
Direct inquiries to 30 Frost Street, Cambridge, MA 02140
*/
#include <stdio.h>
int merror = 0;
/* Notice: the order of appearance of the following
* messages is bound to the error codes defined
* in mconf.h.
*/
static char *ermsg[7] = {
"unknown", /* error code 0 */
"domain", /* error code 1 */
"singularity", /* et seq. */
"overflow",
"underflow",
"total loss of precision",
"partial loss of precision"
};
#ifndef DOMAIN
/* HBB 20021103: copied this from Cephes mconf.h */
# define DOMAIN 1 /* argument domain error */
# define SING 2 /* argument singularity */
# define OVERFLOW 3 /* overflow range error */
# define UNDERFLOW 4 /* underflow range error */
# define TLOSS 5 /* total loss of precision */
# define PLOSS 6 /* partial loss of precision */
#endif
static int mtherr(char *name, int code)
{
/* Display string passed by calling program,
* which is supposed to be the name of the
* function in which the error occurred:
*/
printf("\n%s ", name);
/* Set global error message word */
merror = code;
/* Display error message defined
* by the code argument.
*/
if ((code <= 0) || (code >= 7))
code = 0;
printf("%s error\n", ermsg[code]);
/* Return to calling
* program
*/
return (0);
}
/* polevl.c
* p1evl.c
*
* Evaluate polynomial
*
*
*
* SYNOPSIS:
*
* int N;
* double x, y, coef[N+1], polevl[];
*
* y = polevl( x, coef, N );
*
*
*
* DESCRIPTION:
*
* Evaluates polynomial of degree N:
*
* 2 N
* y = C + C x + C x +...+ C x
* 0 1 2 N
*
* Coefficients are stored in reverse order:
*
* coef[0] = C , ..., coef[N] = C .
* N 0
*
* The function p1evl() assumes that coef[N] = 1.0 and is
* omitted from the array. Its calling arguments are
* otherwise the same as polevl().
*
*
* SPEED:
*
* In the interest of speed, there are no checks for out
* of bounds arithmetic. This routine is used by most of
* the functions in the library. Depending on available
* equipment features, the user may wish to rewrite the
* program in microcode or assembly language.
*
*/
/*
Cephes Math Library Release 2.1: December, 1988
Copyright 1984, 1987, 1988 by Stephen L. Moshier
Direct inquiries to 30 Frost Street, Cambridge, MA 02140
*/
static double 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);
}
/* p1evl() */
/* N
* Evaluate polynomial when coefficient of x is 1.0.
* Otherwise same as polevl.
*/
static double 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);
}
#ifndef GAMMA
/* Provide GAMMA function for those who do not already have one */
static double lngamma __PROTO((double z));
int sgngam;
/* A[]: Stirling's formula expansion of log gamma
* B[], C[]: log gamma function between 2 and 3
*/
#ifdef UNK
static double A[] = {
8.11614167470508450300E-4,
-5.95061904284301438324E-4,
7.93650340457716943945E-4,
-2.77777777730099687205E-3,
8.33333333333331927722E-2
};
static double B[] = {
-1.37825152569120859100E3,
-3.88016315134637840924E4,
-3.31612992738871184744E5,
-1.16237097492762307383E6,
-1.72173700820839662146E6,
-8.53555664245765465627E5
};
static double C[] = {
/* 1.00000000000000000000E0, */
-3.51815701436523470549E2,
-1.70642106651881159223E4,
-2.20528590553854454839E5,
-1.13933444367982507207E6,
-2.53252307177582951285E6,
-2.01889141433532773231E6
};
/* log( sqrt( 2*pi ) ) */
static double LS2PI = 0.91893853320467274178;
#define MAXLGM 2.556348e305
#endif
#ifdef DEC
static unsigned short A[] = {
0035524, 0141201, 0034633, 0031405,
0135433, 0176755, 0126007, 0045030,
0035520, 0006371, 0003342, 0172730,
0136066, 0005540, 0132605, 0026407,
0037252, 0125252, 0125252, 0125132
};
static unsigned short B[] = {
0142654, 0044014, 0077633, 0035410,
0144027, 0110641, 0125335, 0144760,
0144641, 0165637, 0142204, 0047447,
0145215, 0162027, 0146246, 0155211,
0145322, 0026110, 0010317, 0110130,
0145120, 0061472, 0120300, 0025363
};
static unsigned short C[] = {
/*0040200,0000000,0000000,0000000*/
0142257, 0164150, 0163630, 0112622,
0143605, 0050153, 0156116, 0135272,
0144527, 0056045, 0145642, 0062332,
0145213, 0012063, 0106250, 0001025,
0145432, 0111254, 0044577, 0115142,
0145366, 0071133, 0050217, 0005122
};
/* log( sqrt( 2*pi ) ) */
static unsigned short LS2P[] = {040153, 037616, 041445, 0172645,};
#define LS2PI *(double *)LS2P
#define MAXLGM 2.035093e36
#endif
#ifdef IBMPC
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
};
/* log( sqrt( 2*pi ) ) */
static unsigned short LS2P[] = {
0xbeb5, 0xc864, 0x67f1, 0x3fed
};
#define LS2PI *(double *)LS2P
#define MAXLGM 2.556348e305
#endif
#ifdef MIEEE
static unsigned short A[] = {
0x3f4a, 0x9850, 0x2733, 0x6661,
0xbf43, 0x7fbd, 0xb580, 0xe943,
0x3f4a, 0x019f, 0x20dc, 0x5ebb,
0xbf66, 0xc16c, 0x16b0, 0xa5a1,
0x3fb5, 0x5555, 0x5555, 0x554b
};
static unsigned short B[] = {
0xc095, 0x8901, 0x8ff3, 0x6761,
0xc0e2, 0xf234, 0x355b, 0xb93e,
0xc114, 0x3d73, 0xf890, 0x89e5,
0xc131, 0xbc82, 0xf994, 0xdb51,
0xc13a, 0x4589, 0x0219, 0xf20b,
0xc12a, 0x0c67, 0x5418, 0x055e
};
static unsigned short C[] = {
0xc075, 0xfd0d, 0x1cf3, 0x12b2,
0xc0d0, 0xaa0d, 0x7b89, 0xd757,
0xc10a, 0xeb84, 0xb974, 0x4c9b,
0xc131, 0x6286, 0x7195, 0x0043,
0xc143, 0x5255, 0x892f, 0xf34c,
0xc13e, 0xce4b, 0x6a11, 0xe14a
};
/* log( sqrt( 2*pi ) ) */
static unsigned short LS2P[] = {
0x3fed, 0x67f1, 0xc864, 0xbeb5
};
#define LS2PI *(double *)LS2P
#define MAXLGM 2.556348e305
#endif
/* static const double PI = 3.1415926535897932384626433832795028841971693993751;*/
static const double LOGPI = 1.1447298858494001741434273513530587116472948129153;
int ISNAN(double x)
{
volatile double a = x;
if (a != a)
return 1;
return 0;
}
int ISFINITE(double x)
{
volatile double a = x;
if (a < DBL_MAX)
return 1;
return 0;
}
double lngamma(double x)
{
double p,
q,
u,
w,
z;
int i;
sgngam = 1;
#ifdef NANS
if (ISNAN(x))
return (x);
#endif
#ifdef INFINITIES
if (!ISFINITE((x)))
return (DBL_MAX * DBL_MAX);
#endif
if (x < -34.0) {
q = -x;
w = lngamma(q); /* note this modifies sgngam! */
p = floor(q);
if (p == q) {
lgsing:
#ifdef INFINITIES
mtherr("lngamma", SING);
return (DBL_MAX * DBL_MAX);
#else
goto loverf;
#endif
}
i = 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 = LOGPI - 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 * polevl(x, B, 5) / p1evl(x, C, 6);
return (log(z) + p);
}
if (x > MAXLGM) {
#ifdef INFINITIES
return (sgngam * (DBL_MAX * DBL_MAX));
#else
loverf:
mtherr("lngamma", OVERFLOW);
return (sgngam * MAXNUM);
#endif
}
q = (x - 0.5) * log(x) - x + LS2PI;
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 += polevl(p, A, 4) / x;
return (q);
}
#define GAMMA(x) lngamma ((x))
#endif /* !GAMMA */
void f_erf()
{
struct value a;
double x;
x = real(pop(&a));
#ifdef HAVE_ERF
x = erf(x);
#else
{
int fsign;
fsign = x >= 0 ? 1 : 0;
x = igamma(0.5, (x)*(x));
if (x == -1.0) {
undefined = TRUE;
x = 0.0;
} else {
if (fsign == 0)
x = -x;
}
}
#endif
push(Gcomplex(&a, x, 0.0));
}
void f_erfc()
{
struct value a;
double x;
x = real(pop(&a));
#ifdef HAVE_ERFC
x = erfc(x);
#else
{
int fsign;
fsign = x >= 0 ? 1 : 0;
x = igamma(0.5, (x)*(x));
if (x == 1.0) {
undefined = TRUE;
x = 0.0;
} else {
x = fsign > 0 ? 1.0 - x : 1.0 + x ;
}
}
#endif
push(Gcomplex(&a, x, 0.0));
}
void f_ibeta()
{
struct value a;
double x;
double arg1;
double arg2;
x = real(pop(&a));
arg2 = real(pop(&a));
arg1 = real(pop(&a));
x = ibeta(arg1, arg2, x);
if (x == -1.0) {
undefined = TRUE;
push(Ginteger(&a, 0));
} else
push(Gcomplex(&a, x, 0.0));
}
void f_igamma()
{
struct value a;
double x;
double arg1;
x = real(pop(&a));
arg1 = real(pop(&a));
x = igamma(arg1, x);
if (x == -1.0) {
undefined = TRUE;
push(Ginteger(&a, 0));
} else
push(Gcomplex(&a, x, 0.0));
}
void f_gamma()
{
register double y;
struct value a;
y = GAMMA(real(pop(&a)));
if (y > 88.0) {
undefined = TRUE;
push(Ginteger(&a, 0));
} else
push(Gcomplex(&a, signgam * gp_exp(y), 0.0));
}
void f_lgamma()
{
struct value a;
push(Gcomplex(&a, GAMMA(real(pop(&a))), 0.0));
}
#ifndef BADRAND
void f_rand()
{
struct value a;
push(Gcomplex(&a, ranf(real(pop(&a))), 0.0));
}
#else /* BADRAND */
/* Use only to observe the effect of a "bad" random number generator. */
void f_rand()
{
struct value a;
static unsigned int y = 0;
unsigned int maxran = 1000;
(void) real(pop(&a));
y = (781 * y + 387) % maxran;
push(Gcomplex(&a, (double) y / maxran, 0.0));
}
#endif /* BADRAND */
/* ** ibeta.c
*
* DESCRIB Approximate the incomplete beta function Ix(a, b).
*
* _
* |(a + b) /x (a-1) (b-1)
* Ix(a, b) = -_-------_--- * | t * (1 - t) dt (a,b > 0)
* |(a) * |(b) /0
*
*
*
* CALL p = ibeta(a, b, x)
*
* double a > 0
* double b > 0
* double x [0, 1]
*
* WARNING none
*
* RETURN double p [0, 1]
* -1.0 on error condition
*
* XREF lngamma()
*
* BUGS none
*
* REFERENCE The continued fraction expansion as given by
* Abramowitz and Stegun (1964) is used.
*
* Copyright (c) 1992 Jos van der Woude, jvdwoude@hut.nl
*
* Note: this function was translated from the Public Domain Fortran
* version available from http://lib.stat.cmu.edu/apstat/xxx
*
*/
static double ibeta(a, b, x)
double a, b, x;
{
/* Test for admissibility of arguments */
if (a <= 0.0 || b <= 0.0)
return -1.0;
if (x < 0.0 || x > 1.0)
return -1.0;;
/* If x equals 0 or 1, return x as prob */
if (x == 0.0 || x == 1.0)
return x;
/* Swap a, b if necessarry for more efficient evaluation */
return a < x * (a + b) ? 1.0 - confrac(b, a, 1.0 - x) : confrac(a, b, x);
}
static double confrac(a, b, x)
double a, b, x;
{
double Alo = 0.0;
double Ahi;
double Aev;
double Aod;
double Blo = 1.0;
double Bhi = 1.0;
double Bod = 1.0;
double Bev = 1.0;
double f;
double fold;
double Apb = a + b;
double d;
int i;
int j;
/* Set up continued fraction expansion evaluation. */
Ahi = gp_exp(GAMMA(Apb) + a * log(x) + b * log(1.0 - x) -
GAMMA(a + 1.0) - GAMMA(b));
/*
* Continued fraction loop begins here. Evaluation continues until
* maximum iterations are exceeded, or convergence achieved.
*/
for (i = 0, j = 1, f = Ahi; i <= ITMAX; i++, j++) {
d = a + j + i;
Aev = -(a + i) * (Apb + i) * x / d / (d - 1.0);
Aod = j * (b - j) * x / d / (d + 1.0);
Alo = Bev * Ahi + Aev * Alo;
Blo = Bev * Bhi + Aev * Blo;
Ahi = Bod * Alo + Aod * Ahi;
Bhi = Bod * Blo + Aod * Bhi;
if (fabs(Bhi) < MACHEPS)
Bhi = 0.0;
if (Bhi != 0.0) {
fold = f;
f = Ahi / Bhi;
if (fabs(f - fold) < fabs(f) * MACHEPS)
return f;
}
}
return -1.0;
}
/* ** igamma.c
*
* DESCRIB Approximate the incomplete gamma function P(a, x).
*
* 1 /x -t (a-1)
* P(a, x) = -_--- * | e * t dt (a > 0)
* |(a) /0
*
* CALL p = igamma(a, x)
*
* double a > 0
* double x >= 0
*
* WARNING none
*
* RETURN double p [0, 1]
* -1.0 on error condition
*
* XREF lngamma()
*
* BUGS Values 0 <= x <= 1 may lead to inaccurate results.
*
* REFERENCE ALGORITHM AS239 APPL. STATIST. (1988) VOL. 37, NO. 3
*
* Copyright (c) 1992 Jos van der Woude, jvdwoude@hut.nl
*
* Note: this function was translated from the Public Domain Fortran
* version available from http://lib.stat.cmu.edu/apstat/239
*
*/
/* Global variables, not visible outside this file */
static double pn1, pn2, pn3, pn4, pn5, pn6;
static double igamma(a, x)
double a, x;
{
double arg;
double aa;
double an;
double b;
int i;
/* Check that we have valid values for a and x */
if (x < 0.0 || a <= 0.0)
return -1.0;
/* Deal with special cases */
if (x == 0.0)
return 0.0;
if (x > XBIG)
return 1.0;
/* Check value of factor arg */
arg = a * log(x) - x - GAMMA(a + 1.0);
if (arg < MINEXP)
return -1.0;
arg = gp_exp(arg);
/* Choose infinite series or continued fraction. */
if ((x > 1.0) && (x >= a + 2.0)) {
/* Use a continued fraction expansion */
double rn;
double rnold;
aa = 1.0 - a;
b = aa + x + 1.0;
pn1 = 1.0;
pn2 = x;
pn3 = x + 1.0;
pn4 = x * b;
rnold = pn3 / pn4;
for (i = 1; i <= ITMAX; i++) {
aa++;
b += 2.0;
an = aa * (double) i;
pn5 = b * pn3 - an * pn1;
pn6 = b * pn4 - an * pn2;
if (pn6 != 0.0) {
rn = pn5 / pn6;
if (fabs(rnold - rn) <= GPMIN(MACHEPS, MACHEPS * rn))
return 1.0 - arg * rn * a;
rnold = rn;
}
pn1 = pn3;
pn2 = pn4;
pn3 = pn5;
pn4 = pn6;
/* Re-scale terms in continued fraction if terms are large */
if (fabs(pn5) >= OFLOW) {
pn1 /= OFLOW;
pn2 /= OFLOW;
pn3 /= OFLOW;
pn4 /= OFLOW;
}
}
} else {
/* Use Pearson's series expansion. */
for (i = 0, aa = a, an = b = 1.0; i <= ITMAX; i++) {
aa++;
an *= x / aa;
b += an;
if (an < b * MACHEPS)
return arg * b;
}
}
return -1.0;
}
/***********************************************************************
double ranf(double init)
RANDom number generator as a Function
Returns a random floating point number from a uniform distribution
over 0 - 1 (endpoints of this interval are not returned) using a
large integer generator.
This is a transcription from Pascal to Fortran of routine
Uniform_01 from the paper
L'Ecuyer, P. and Cote, S. "Implementing a Random Number Package
with Splitting Facilities." ACM Transactions on Mathematical
Software, 17:98-111 (1991)
GeNerate LarGe Integer
Returns a random integer following a uniform distribution over
(1, 2147483562) using the generator.
This is a transcription from Pascal to Fortran of routine
Random from the paper
L'Ecuyer, P. and Cote, S. "Implementing a Random Number Package
with Splitting Facilities." ACM Transactions on Mathematical
Software, 17:98-111 (1991)
***********************************************************************/
static double ranf(init)
double init;
{
long k, z;
static int firsttime = 1;
static long s1, s2;
/* (Re)-Initialize seeds if necessary */
if (init < 0.0 || firsttime == 1) {
firsttime = 0;
s1 = 1234567890L;
s2 = 1234567890L;
}
/* Generate pseudo random integers */
k = s1 / 53668L;
s1 = Xa1 * (s1 - k * 53668L) - k * 12211;
if (s1 < 0)
s1 += Xm1;
k = s2 / 52774L;
s2 = Xa2 * (s2 - k * 52774L) - k * 3791;
if (s2 < 0)
s2 += Xm2;
z = s1 - s2;
if (z < 1)
z += (Xm1 - 1);
/*
* 4.656613057E-10 is 1/Xm1. Xm1 is set at the top of this file and is
* currently 2147483563. If Xm1 changes, change this also.
*/
return (double) 4.656613057E-10 *z;
}
/* ----------------------------------------------------------------
Following to specfun.c made by John Grosh (jgrosh@arl.mil)
on 28 OCT 1992.
---------------------------------------------------------------- */
void f_normal()
{ /* Normal or Gaussian Probability Function */
struct value a;
double x;
/* ref. Abramowitz and Stegun 1964, "Handbook of Mathematical
Functions", Applied Mathematics Series, vol 55,
Chapter 26, page 934, Eqn. 26.2.29 and Jos van der Woude
code found above */
x = real(pop(&a));
x = 0.5 * SQRT_TWO * x;
#ifdef HAVE_ERF
x = 0.5 * (1.0 + erf(x));
#else
{
int fsign;
fsign = x >= 0 ? 1 : 0;
x = igamma(0.5, (x)*(x));
if (x == 1.0) {
undefined = TRUE;
x = 0.0;
} else {
if (fsign == 0)
x = -(x);
x = 0.5 * (1.0 + x);
}
}
#endif
push(Gcomplex(&a, x, 0.0));
}
void f_inverse_normal()
{ /* Inverse normal distribution function */
struct value a;
double x;
x = real(pop(&a));
if (x <= 0.0 || x >= 1.0) {
undefined = TRUE;
push(Gcomplex(&a, 0.0, 0.0));
} else {
push(Gcomplex(&a, inverse_normal_func(x), 0.0));
}
}
void f_inverse_erf()
{ /* Inverse error function */
struct value a;
double x;
x = real(pop(&a));
if (fabs(x) >= 1.0) {
undefined = TRUE;
push(Gcomplex(&a, 0.0, 0.0));
} else {
push(Gcomplex(&a, inverse_error_func(x), 0.0));
}
}
/* ndtri.c
*
* Inverse of Normal distribution function
*
*
*
* SYNOPSIS:
*
* double x, y, ndtri();
*
* x = ndtri( y );
*
*
*
* DESCRIPTION:
*
* Returns the argument, x, for which the area under the
* Gaussian probability density function (integrated from
* minus infinity to x) is equal to y.
*
*
* For small arguments 0 < y < exp(-2), the program computes
* z = sqrt( -2.0 * log(y) ); then the approximation is
* x = z - log(z)/z - (1/z) P(1/z) / Q(1/z).
* There are two rational functions P/Q, one for 0 < y < exp(-32)
* and the other for y up to exp(-2). For larger arguments,
* w = y - 0.5, and x/sqrt(2pi) = w + w**3 R(w**2)/S(w**2)).
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* DEC 0.125, 1 5500 9.5e-17 2.1e-17
* DEC 6e-39, 0.135 3500 5.7e-17 1.3e-17
* IEEE 0.125, 1 20000 7.2e-16 1.3e-16
* IEEE 3e-308, 0.135 50000 4.6e-16 9.8e-17
*
*
* ERROR MESSAGES:
*
* message condition value returned
* ndtri domain x <= 0 -DBL_MAX
* ndtri domain x >= 1 DBL_MAX
*
*/
/*
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier
*/
#ifdef UNK
/* sqrt(2pi) */
static double s2pi = 2.50662827463100050242E0;
#endif
#ifdef DEC
static unsigned short s2p[] = {0040440, 0066230, 0177661, 0034055};
#define s2pi *(double *)s2p
#endif
#ifdef IBMPC
static unsigned short s2p[] = {0x2706, 0x1ff6, 0x0d93, 0x4004};
#define s2pi *(double *)s2p
#endif
#ifdef MIEEE
static unsigned short s2p[] = {
0x4004, 0x0d93, 0x1ff6, 0x2706
};
#define s2pi *(double *)s2p
#endif
/* approximation for 0 <= |y - 0.5| <= 3/8 */
#ifdef UNK
static double P0[5] = {
-5.99633501014107895267E1,
9.80010754185999661536E1,
-5.66762857469070293439E1,
1.39312609387279679503E1,
-1.23916583867381258016E0,
};
static double Q0[8] = {
/* 1.00000000000000000000E0,*/
1.95448858338141759834E0,
4.67627912898881538453E0,
8.63602421390890590575E1,
-2.25462687854119370527E2,
2.00260212380060660359E2,
-8.20372256168333339912E1,
1.59056225126211695515E1,
-1.18331621121330003142E0,
};
#endif
#ifdef DEC
static unsigned short P0[20] = {
0141557, 0155170, 0071360, 0120550,
0041704, 0000214, 0172417, 0067307,
0141542, 0132204, 0040066, 0156723,
0041136, 0163161, 0157276, 0007747,
0140236, 0116374, 0073666, 0051764,
};
static unsigned short Q0[32] = {
/*0040200,0000000,0000000,0000000,*/
0040372, 0026256, 0110403, 0123707,
0040625, 0122024, 0020277, 0026661,
0041654, 0134161, 0124134, 0007244,
0142141, 0073162, 0133021, 0131371,
0042110, 0041235, 0043516, 0057767,
0141644, 0011417, 0036155, 0137305,
0041176, 0076556, 0004043, 0125430,
0140227, 0073347, 0152776, 0067251,
};
#endif
#ifdef IBMPC
static unsigned short P0[20] = {
0x142d, 0x0e5e, 0xfb4f, 0xc04d,
0xedd9, 0x9ea1, 0x8011, 0x4058,
0xdbba, 0x8806, 0x5690, 0xc04c,
0xc1fd, 0x3bd7, 0xdcce, 0x402b,
0xca7e, 0x8ef6, 0xd39f, 0xbff3,
};
static unsigned short Q0[36] = {
/*0x0000,0x0000,0x0000,0x3ff0,*/
0x74f9, 0xd220, 0x4595, 0x3fff,
0xe5b6, 0x8417, 0xb482, 0x4012,
0x81d4, 0x350b, 0x970e, 0x4055,
0x365f, 0x56c2, 0x2ece, 0xc06c,
0xcbff, 0xa8e9, 0x0853, 0x4069,
0xb7d9, 0xe78d, 0x8261, 0xc054,
0x7563, 0xc104, 0xcfad, 0x402f,
0xcdd5, 0xfabf, 0xeedc, 0xbff2,
};
#endif
#ifdef MIEEE
static unsigned short P0[20] = {
0xc04d, 0xfb4f, 0x0e5e, 0x142d,
0x4058, 0x8011, 0x9ea1, 0xedd9,
0xc04c, 0x5690, 0x8806, 0xdbba,
0x402b, 0xdcce, 0x3bd7, 0xc1fd,
0xbff3, 0xd39f, 0x8ef6, 0xca7e,
};
static unsigned short Q0[32] = {
/*0x3ff0,0x0000,0x0000,0x0000,*/
0x3fff, 0x4595, 0xd220, 0x74f9,
0x4012, 0xb482, 0x8417, 0xe5b6,
0x4055, 0x970e, 0x350b, 0x81d4,
0xc06c, 0x2ece, 0x56c2, 0x365f,
0x4069, 0x0853, 0xa8e9, 0xcbff,
0xc054, 0x8261, 0xe78d, 0xb7d9,
0x402f, 0xcfad, 0xc104, 0x7563,
0xbff2, 0xeedc, 0xfabf, 0xcdd5,
};
#endif
/* Approximation for interval z = sqrt(-2 log y ) between 2 and 8
* i.e., y between exp(-2) = .135 and exp(-32) = 1.27e-14.
*/
#ifdef UNK
static double P1[9] = {
4.05544892305962419923E0,
3.15251094599893866154E1,
5.71628192246421288162E1,
4.40805073893200834700E1,
1.46849561928858024014E1,
2.18663306850790267539E0,
-1.40256079171354495875E-1,
-3.50424626827848203418E-2,
-8.57456785154685413611E-4,
};
static double Q1[8] = {
/* 1.00000000000000000000E0,*/
1.57799883256466749731E1,
4.53907635128879210584E1,
4.13172038254672030440E1,
1.50425385692907503408E1,
2.50464946208309415979E0,
-1.42182922854787788574E-1,
-3.80806407691578277194E-2,
-9.33259480895457427372E-4,
};
#endif
#ifdef DEC
static unsigned short P1[36] = {
0040601, 0143074, 0150744, 0073326,
0041374, 0031554, 0113253, 0146016,
0041544, 0123272, 0012463, 0176771,
0041460, 0051160, 0103560, 0156511,
0041152, 0172624, 0117772, 0030755,
0040413, 0170713, 0151545, 0176413,
0137417, 0117512, 0022154, 0131671,
0137017, 0104257, 0071432, 0007072,
0135540, 0143363, 0063137, 0036166,
};
static unsigned short Q1[32] = {
/*0040200,0000000,0000000,0000000,*/
0041174, 0075325, 0004736, 0120326,
0041465, 0110044, 0047561, 0045567,
0041445, 0042321, 0012142, 0030340,
0041160, 0127074, 0166076, 0141051,
0040440, 0046055, 0040745, 0150400,
0137421, 0114146, 0067330, 0010621,
0137033, 0175162, 0025555, 0114351,
0135564, 0122773, 0145750, 0030357,
};
#endif
#ifdef IBMPC
static unsigned short P1[36] = {
0x8edb, 0x9a3c, 0x38c7, 0x4010,
0x7982, 0x92d5, 0x866d, 0x403f,
0x7fbf, 0x42a6, 0x94d7, 0x404c,
0x1ba9, 0x10ee, 0x0a4e, 0x4046,
0x463e, 0x93ff, 0x5eb2, 0x402d,
0xbfa1, 0x7a6c, 0x7e39, 0x4001,
0x9677, 0x448d, 0xf3e9, 0xbfc1,
0x41c7, 0xee63, 0xf115, 0xbfa1,
0xe78f, 0x6ccb, 0x18de, 0xbf4c,
};
static unsigned short Q1[32] = {
/*0x0000,0x0000,0x0000,0x3ff0,*/
0xd41b, 0xa13b, 0x8f5a, 0x402f,
0x296f, 0x89ee, 0xb204, 0x4046,
0x461c, 0x228c, 0xa89a, 0x4044,
0xd845, 0x9d87, 0x15c7, 0x402e,
0xba20, 0xa83c, 0x0985, 0x4004,
0x0232, 0xcddb, 0x330c, 0xbfc2,
0xb31d, 0x456d, 0x7f4e, 0xbfa3,
0x061e, 0x797d, 0x94bf, 0xbf4e,
};
#endif
#ifdef MIEEE
static unsigned short P1[36] = {
0x4010, 0x38c7, 0x9a3c, 0x8edb,
0x403f, 0x866d, 0x92d5, 0x7982,
0x404c, 0x94d7, 0x42a6, 0x7fbf,
0x4046, 0x0a4e, 0x10ee, 0x1ba9,
0x402d, 0x5eb2, 0x93ff, 0x463e,
0x4001, 0x7e39, 0x7a6c, 0xbfa1,
0xbfc1, 0xf3e9, 0x448d, 0x9677,
0xbfa1, 0xf115, 0xee63, 0x41c7,
0xbf4c, 0x18de, 0x6ccb, 0xe78f,
};
static unsigned short Q1[32] = {
/*0x3ff0,0x0000,0x0000,0x0000,*/
0x402f, 0x8f5a, 0xa13b, 0xd41b,
0x4046, 0xb204, 0x89ee, 0x296f,
0x4044, 0xa89a, 0x228c, 0x461c,
0x402e, 0x15c7, 0x9d87, 0xd845,
0x4004, 0x0985, 0xa83c, 0xba20,
0xbfc2, 0x330c, 0xcddb, 0x0232,
0xbfa3, 0x7f4e, 0x456d, 0xb31d,
0xbf4e, 0x94bf, 0x797d, 0x061e,
};
#endif
/* Approximation for interval z = sqrt(-2 log y ) between 8 and 64
* i.e., y between exp(-32) = 1.27e-14 and exp(-2048) = 3.67e-890.
*/
#ifdef UNK
static double P2[9] = {
3.23774891776946035970E0,
6.91522889068984211695E0,
3.93881025292474443415E0,
1.33303460815807542389E0,
2.01485389549179081538E-1,
1.23716634817820021358E-2,
3.01581553508235416007E-4,
2.65806974686737550832E-6,
6.23974539184983293730E-9,
};
static double Q2[8] = {
/* 1.00000000000000000000E0,*/
6.02427039364742014255E0,
3.67983563856160859403E0,
1.37702099489081330271E0,
2.16236993594496635890E-1,
1.34204006088543189037E-2,
3.28014464682127739104E-4,
2.89247864745380683936E-6,
6.79019408009981274425E-9,
};
#endif
#ifdef DEC
static unsigned short P2[36] = {
0040517, 0033507, 0036236, 0125641,
0040735, 0044616, 0014473, 0140133,
0040574, 0012567, 0114535, 0102541,
0040252, 0120340, 0143474, 0150135,
0037516, 0051057, 0115361, 0031211,
0036512, 0131204, 0101511, 0125144,
0035236, 0016627, 0043160, 0140216,
0033462, 0060512, 0060141, 0010641,
0031326, 0062541, 0101304, 0077706,
};
static unsigned short Q2[32] = {
/*0040200,0000000,0000000,0000000,*/
0040700, 0143322, 0132137, 0040501,
0040553, 0101155, 0053221, 0140257,
0040260, 0041071, 0052573, 0010004,
0037535, 0066472, 0177261, 0162330,
0036533, 0160475, 0066666, 0036132,
0035253, 0174533, 0027771, 0044027,
0033502, 0016147, 0117666, 0063671,
0031351, 0047455, 0141663, 0054751,
};
#endif
#ifdef IBMPC
static unsigned short P2[36] = {
0xd574, 0xe793, 0xe6e8, 0x4009,
0x780b, 0xc327, 0xa931, 0x401b,
0xb0ac, 0xf32b, 0x82ae, 0x400f,
0x9a0c, 0x18e7, 0x541c, 0x3ff5,
0x2651, 0xf35e, 0xca45, 0x3fc9,
0x354d, 0x9069, 0x5650, 0x3f89,
0x1812, 0xe8ce, 0xc3b2, 0x3f33,
0x2234, 0x4c0c, 0x4c29, 0x3ec6,
0x8ff9, 0x3058, 0xccac, 0x3e3a,
};
static unsigned short Q2[32] = {
/*0x0000,0x0000,0x0000,0x3ff0,*/
0xe828, 0x568b, 0x18da, 0x4018,
0x3816, 0xaad2, 0x704d, 0x400d,
0x6200, 0x2aaf, 0x0847, 0x3ff6,
0x3c9b, 0x5fd6, 0xada7, 0x3fcb,
0xc78b, 0xadb6, 0x7c27, 0x3f8b,
0x2903, 0x65ff, 0x7f2b, 0x3f35,
0xccf7, 0xf3f6, 0x438c, 0x3ec8,
0x6b3d, 0xb876, 0x29e5, 0x3e3d,
};
#endif
#ifdef MIEEE
static unsigned short P2[36] = {
0x4009, 0xe6e8, 0xe793, 0xd574,
0x401b, 0xa931, 0xc327, 0x780b,
0x400f, 0x82ae, 0xf32b, 0xb0ac,
0x3ff5, 0x541c, 0x18e7, 0x9a0c,
0x3fc9, 0xca45, 0xf35e, 0x2651,
0x3f89, 0x5650, 0x9069, 0x354d,
0x3f33, 0xc3b2, 0xe8ce, 0x1812,
0x3ec6, 0x4c29, 0x4c0c, 0x2234,
0x3e3a, 0xccac, 0x3058, 0x8ff9,
};
static unsigned short Q2[32] = {
/*0x3ff0,0x0000,0x0000,0x0000,*/
0x4018, 0x18da, 0x568b, 0xe828,
0x400d, 0x704d, 0xaad2, 0x3816,
0x3ff6, 0x0847, 0x2aaf, 0x6200,
0x3fcb, 0xada7, 0x5fd6, 0x3c9b,
0x3f8b, 0x7c27, 0xadb6, 0xc78b,
0x3f35, 0x7f2b, 0x65ff, 0x2903,
0x3ec8, 0x438c, 0xf3f6, 0xccf7,
0x3e3d, 0x29e5, 0xb876, 0x6b3d,
};
#endif
static double inverse_normal_func(double y0)
{
double x,
y,
z,
y2,
x0,
x1;
int code;
if (y0 <= 0.0) {
mtherr("inverse_normal_func", DOMAIN);
return (-DBL_MAX);
}
if (y0 >= 1.0) {
mtherr("inverse_normal_func", DOMAIN);
return (DBL_MAX);
}
code = 1;
y = y0;
if (y > (1.0 - 0.13533528323661269189)) { /* 0.135... = exp(-2) */
y = 1.0 - y;
code = 0;
}
if (y > 0.13533528323661269189) {
y = y - 0.5;
y2 = y * y;
x = y + y * (y2 * polevl(y2, P0, 4) / p1evl(y2, Q0, 8));
x = x * s2pi;
return (x);
}
x = sqrt(-2.0 * log(y));
x0 = x - log(x) / x;
z = 1.0 / x;
if (x < 8.0) /* y > exp(-32) = 1.2664165549e-14 */
x1 = z * polevl(z, P1, 8) / p1evl(z, Q1, 8);
else
x1 = z * polevl(z, P2, 8) / p1evl(z, Q2, 8);
x = x0 - x1;
if (code != 0)
x = -x;
return (x);
}
/* ndtr.c
*
* Normal distribution function
*
*
*
* SYNOPSIS:
*
* double x, y, ndtr();
*
* y = ndtr( x );
*
*
*
* DESCRIPTION:
*
* Returns the area under the Gaussian probability density
* function, integrated from minus infinity to x:
*
* x
* -
* 1 | | 2
* ndtr(x) = --------- | exp( - t /2 ) dt
* sqrt(2pi) | |
* -
* -inf.
*
* = ( 1 + erf(z) ) / 2
* = erfc(z) / 2
*
* where z = x/sqrt(2). Computation is via the functions
* erf and erfc.
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* DEC -13,0 8000 2.1e-15 4.8e-16
* IEEE -13,0 30000 3.4e-14 6.7e-15
*
*
* ERROR MESSAGES:
*
* message condition value returned
* erfc underflow x > 37.519379347 0.0
*
*/
/* erf.c
*
* Error function
*
*
*
* SYNOPSIS:
*
* double x, y, erf();
*
* y = erf( x );
*
*
*
* DESCRIPTION:
*
* The integral is
*
* x
* -
* 2 | | 2
* erf(x) = -------- | exp( - t ) dt.
* sqrt(pi) | |
* -
* 0
*
* The magnitude of x is limited to 9.231948545 for DEC
* arithmetic; 1 or -1 is returned outside this range.
*
* For 0 <= |x| < 1, erf(x) = x * P4(x**2)/Q5(x**2); otherwise
* erf(x) = 1 - erfc(x).
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* DEC 0,1 14000 4.7e-17 1.5e-17
* IEEE 0,1 30000 3.7e-16 1.0e-16
*
*/
/* erfc.c
*
* Complementary error function
*
*
*
* SYNOPSIS:
*
* double x, y, erfc();
*
* y = erfc( x );
*
*
*
* DESCRIPTION:
*
*
* 1 - erf(x) =
*
* inf.
* -
* 2 | | 2
* erfc(x) = -------- | exp( - t ) dt
* sqrt(pi) | |
* -
* x
*
*
* For small x, erfc(x) = 1 - erf(x); otherwise rational
* approximations are computed.
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* DEC 0, 9.2319 12000 5.1e-16 1.2e-16
* IEEE 0,26.6417 30000 5.7e-14 1.5e-14
*
*
* ERROR MESSAGES:
*
* message condition value returned
* erfc underflow x > 9.231948545 (DEC) 0.0
*
*
*/
/*
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1987, 1988, 1992, 2000 by Stephen L. Moshier
*/
static const double SQRTH = 0.70710678118654752440084436210484903928483593768845;
#ifdef UNK
static double P[] = {
2.46196981473530512524E-10,
5.64189564831068821977E-1,
7.46321056442269912687E0,
4.86371970985681366614E1,
1.96520832956077098242E2,
5.26445194995477358631E2,
9.34528527171957607540E2,
1.02755188689515710272E3,
5.57535335369399327526E2
};
static double Q[] = {
/* 1.00000000000000000000E0,*/
1.32281951154744992508E1,
8.67072140885989742329E1,
3.54937778887819891062E2,
9.75708501743205489753E2,
1.82390916687909736289E3,
2.24633760818710981792E3,
1.65666309194161350182E3,
5.57535340817727675546E2
};
static double R[] = {
5.64189583547755073984E-1,
1.27536670759978104416E0,
5.01905042251180477414E0,
6.16021097993053585195E0,
7.40974269950448939160E0,
2.97886665372100240670E0
};
static double S[] = {
/* 1.00000000000000000000E0,*/
2.26052863220117276590E0,
9.39603524938001434673E0,
1.20489539808096656605E1,
1.70814450747565897222E1,
9.60896809063285878198E0,
3.36907645100081516050E0
};
static double T[] = {
9.60497373987051638749E0,
9.00260197203842689217E1,
2.23200534594684319226E3,
7.00332514112805075473E3,
5.55923013010394962768E4
};
static double U[] = {
/* 1.00000000000000000000E0,*/
3.35617141647503099647E1,
5.21357949780152679795E2,
4.59432382970980127987E3,
2.26290000613890934246E4,
4.92673942608635921086E4
};
#define UTHRESH 37.519379347
#endif
#ifdef DEC
static unsigned short P[] = {
0030207, 0054445, 0011173, 0021706,
0040020, 0067272, 0030661, 0122075,
0040756, 0151236, 0173053, 0067042,
0041502, 0106175, 0062555, 0151457,
0042104, 0102525, 0047401, 0003667,
0042403, 0116176, 0011446, 0075303,
0042551, 0120723, 0061641, 0123275,
0042600, 0070651, 0007264, 0134516,
0042413, 0061102, 0167507, 0176625
};
static unsigned short Q[] = {
/*0040200,0000000,0000000,0000000,*/
0041123, 0123257, 0165741, 0017142,
0041655, 0065027, 0173413, 0115450,
0042261, 0074011, 0021573, 0004150,
0042563, 0166530, 0013662, 0007200,
0042743, 0176427, 0162443, 0105214,
0043014, 0062546, 0153727, 0123772,
0042717, 0012470, 0006227, 0067424,
0042413, 0061103, 0003042, 0013254
};
static unsigned short R[] = {
0040020, 0067272, 0101024, 0155421,
0040243, 0037467, 0056706, 0026462,
0040640, 0116017, 0120665, 0034315,
0040705, 0020162, 0143350, 0060137,
0040755, 0016234, 0134304, 0130157,
0040476, 0122700, 0051070, 0015473
};
static unsigned short S[] = {
/*0040200,0000000,0000000,0000000,*/
0040420, 0126200, 0044276, 0070413,
0041026, 0053051, 0007302, 0063746,
0041100, 0144203, 0174051, 0061151,
0041210, 0123314, 0126343, 0177646,
0041031, 0137125, 0051431, 0033011,
0040527, 0117362, 0152661, 0066201
};
static unsigned short T[] = {
0041031, 0126770, 0170672, 0166101,
0041664, 0006522, 0072360, 0031770,
0043013, 0100025, 0162641, 0126671,
0043332, 0155231, 0161627, 0076200,
0044131, 0024115, 0021020, 0117343
};
static unsigned short U[] = {
/*0040200,0000000,0000000,0000000,*/
0041406, 0037461, 0177575, 0032714,
0042402, 0053350, 0123061, 0153557,
0043217, 0111227, 0032007, 0164217,
0043660, 0145000, 0004013, 0160114,
0044100, 0071544, 0167107, 0125471
};
#define UTHRESH 14.0
#endif
#ifdef IBMPC
static unsigned short P[] = {
0x6479, 0xa24f, 0xeb24, 0x3df0,
0x3488, 0x4636, 0x0dd7, 0x3fe2,
0x6dc4, 0xdec5, 0xda53, 0x401d,
0xba66, 0xacad, 0x518f, 0x4048,
0x20f7, 0xa9e0, 0x90aa, 0x4068,
0xcf58, 0xc264, 0x738f, 0x4080,
0x34d8, 0x6c74, 0x343a, 0x408d,
0x972a, 0x21d6, 0x0e35, 0x4090,
0xffb3, 0x5de8, 0x6c48, 0x4081
};
static unsigned short Q[] = {
/*0x0000,0x0000,0x0000,0x3ff0,*/
0x23cc, 0xfd7c, 0x74d5, 0x402a,
0x7365, 0xfee1, 0xad42, 0x4055,
0x610d, 0x246f, 0x2f01, 0x4076,
0x41d0, 0x02f6, 0x7dab, 0x408e,
0x7151, 0xfca4, 0x7fa2, 0x409c,
0xf4ff, 0xdafa, 0x8cac, 0x40a1,
0xede2, 0x0192, 0xe2a7, 0x4099,
0x42d6, 0x60c4, 0x6c48, 0x4081
};
static unsigned short R[] = {
0x9b62, 0x5042, 0x0dd7, 0x3fe2,
0xc5a6, 0xebb8, 0x67e6, 0x3ff4,
0xa71a, 0xf436, 0x1381, 0x4014,
0x0c0c, 0x58dd, 0xa40e, 0x4018,
0x960e, 0x9718, 0xa393, 0x401d,
0x0367, 0x0a47, 0xd4b8, 0x4007
};
static unsigned short S[] = {
/*0x0000,0x0000,0x0000,0x3ff0,*/
0xce21, 0x0917, 0x1590, 0x4002,
0x4cfd, 0x21d8, 0xcac5, 0x4022,
0x2c4d, 0x7f05, 0x1910, 0x4028,
0x7ff5, 0x959c, 0x14d9, 0x4031,
0x26c1, 0xaa63, 0x37ca, 0x4023,
0x2d90, 0x5ab6, 0xf3de, 0x400a
};
static unsigned short T[] = {
0x5d88, 0x1e37, 0x35bf, 0x4023,
0x067f, 0x4e9e, 0x81aa, 0x4056,
0x35b7, 0xbcb4, 0x7002, 0x40a1,
0xef90, 0x3c72, 0x5b53, 0x40bb,
0x13dc, 0xa442, 0x2509, 0x40eb
};
static unsigned short U[] = {
/*0x0000,0x0000,0x0000,0x3ff0,*/
0xa6ba, 0x3fef, 0xc7e6, 0x4040,
0x3aee, 0x14c6, 0x4add, 0x4080,
0xfd12, 0xe680, 0xf252, 0x40b1,
0x7c0a, 0x0101, 0x1940, 0x40d6,
0xf567, 0x9dc8, 0x0e6c, 0x40e8
};
#define UTHRESH 37.519379347
#endif
#ifdef MIEEE
static unsigned short P[] = {
0x3df0, 0xeb24, 0xa24f, 0x6479,
0x3fe2, 0x0dd7, 0x4636, 0x3488,
0x401d, 0xda53, 0xdec5, 0x6dc4,
0x4048, 0x518f, 0xacad, 0xba66,
0x4068, 0x90aa, 0xa9e0, 0x20f7,
0x4080, 0x738f, 0xc264, 0xcf58,
0x408d, 0x343a, 0x6c74, 0x34d8,
0x4090, 0x0e35, 0x21d6, 0x972a,
0x4081, 0x6c48, 0x5de8, 0xffb3
};
static unsigned short Q[] = {
0x402a, 0x74d5, 0xfd7c, 0x23cc,
0x4055, 0xad42, 0xfee1, 0x7365,
0x4076, 0x2f01, 0x246f, 0x610d,
0x408e, 0x7dab, 0x02f6, 0x41d0,
0x409c, 0x7fa2, 0xfca4, 0x7151,
0x40a1, 0x8cac, 0xdafa, 0xf4ff,
0x4099, 0xe2a7, 0x0192, 0xede2,
0x4081, 0x6c48, 0x60c4, 0x42d6
};
static unsigned short R[] = {
0x3fe2, 0x0dd7, 0x5042, 0x9b62,
0x3ff4, 0x67e6, 0xebb8, 0xc5a6,
0x4014, 0x1381, 0xf436, 0xa71a,
0x4018, 0xa40e, 0x58dd, 0x0c0c,
0x401d, 0xa393, 0x9718, 0x960e,
0x4007, 0xd4b8, 0x0a47, 0x0367
};
static unsigned short S[] = {
0x4002, 0x1590, 0x0917, 0xce21,
0x4022, 0xcac5, 0x21d8, 0x4cfd,
0x4028, 0x1910, 0x7f05, 0x2c4d,
0x4031, 0x14d9, 0x959c, 0x7ff5,
0x4023, 0x37ca, 0xaa63, 0x26c1,
0x400a, 0xf3de, 0x5ab6, 0x2d90
};
static unsigned short T[] = {
0x4023, 0x35bf, 0x1e37, 0x5d88,
0x4056, 0x81aa, 0x4e9e, 0x067f,
0x40a1, 0x7002, 0xbcb4, 0x35b7,
0x40bb, 0x5b53, 0x3c72, 0xef90,
0x40eb, 0x2509, 0xa442, 0x13dc
};
static unsigned short U[] = {
0x4040, 0xc7e6, 0x3fef, 0xa6ba,
0x4080, 0x4add, 0x14c6, 0x3aee,
0x40b1, 0xf252, 0xe680, 0xfd12,
0x40d6, 0x1940, 0x0101, 0x7c0a,
0x40e8, 0x0e6c, 0x9dc8, 0xf567
};
#define UTHRESH 37.519379347
#endif
/*
double ndtr(double a)
{
double x,
y,
z;
x = a * SQRTH;
z = fabs(x);
if (z < SQRTH)
y = 0.5 + 0.5 * erf(x);
else {
y = 0.5 * erfc(z);
if (x > 0)
y = 1.0 - y;
}
return (y);
}
*/
double erf(double);
double erfc(double a)
{
double p,
q,
x,
y,
z;
if (a < 0.0)
x = -a;
else
x = a;
if (x < 1.0)
return (1.0 - erf(a));
z = -a * a;
if (z < DBL_MIN_10_EXP) {
under:
mtherr("erfc", UNDERFLOW);
if (a < 0)
return (2.0);
else
return (0.0);
}
z = exp(z);
if (x < 8.0) {
p = polevl(x, P, 8);
q = p1evl(x, Q, 8);
} else {
p = polevl(x, R, 5);
q = p1evl(x, S, 6);
}
y = (z * p) / q;
if (a < 0)
y = 2.0 - y;
if (y == 0.0)
goto under;
return (y);
}
double erf(double x)
{
double y,
z;
if (fabs(x) > 1.0)
return (1.0 - erfc(x));
z = x * x;
y = x * polevl(z, T, 4) / p1evl(z, U, 5);
return (y);
}
static double inverse_error_func(double y)
{
double x = 0.0; /* The output */
double z = 0.0; /* Intermadiate variable */
double y0 = 0.7; /* Central range variable */
/* Coefficients in rational approximations. */
double a[4] = {0.886226899, -1.645349621, 0.914624893, -0.140543331};
double b[4] = {-2.118377725, 1.442710462, -0.329097515, 0.012229801};
double c[4] = {-1.970840454, -1.624906493, 3.429567803, 1.641345311};
double d[2] = {3.543889200, 1.637067800};
if ((y < -1.0) || (1.0 < y)) {
printf("inverse_error_func: The value out of the range of the function");
x = log(-1.0);
} else if ((y == -1.0) || (1.0 == y)) {
x = -y * log(0.0);
} else if ((-1.0 < y) && (y < -y0)) {
z = sqrt(-log((1.0 + y) / 2.0));
x = -(((c[3] * z + c[2]) * z + c[1]) * z + c[0]) / ((d[1] * z + d[0]) * z + 1.0);
} else {
if ((-y0 < y) && (y < y0)) {
z = y * y;
x = y * (((a[3] * z + a[2]) * z + a[1]) * z + a[0]) /
((((b[3] * z + b[3]) * z + b[1]) * z + b[0]) * z + 1.0);
} else if ((y0 < y) && (y < 1.0)) {
z = sqrt(-log((1.0 - y) / 2.0));
x = (((c[3] * z + c[2]) * z + c[1]) * z + c[0]) / ((d[1] * z + d[0]) * z + 1.0);
}
/* Two steps of Newton-Raphson correction to full accuracy. */
x = x - (erf(x) - y) / (2.0 / sqrt(PI) * exp(-x * x));
x = x - (erf(x) - y) / (2.0 / sqrt(PI) * exp(-x * x));
}
return (x);
}
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