CocoRoboDesktop/pdf1.js/node_modules/cephes/cephes/ndtr.c

/*							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 with care to avoid error amplification in computing exp(-x^2).
 *
 *
 * ACCURACY:
 *
 *                      Relative error:
 * arithmetic   domain     # trials      peak         rms
 *    IEEE     -13,0        30000       1.3e-15     2.2e-16
 *
 *
 * 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.
 *
 * A special function expx2.c is used to suppress error amplification
 * in computing exp(-x^2).
 *
 *
 * ACCURACY:
 *
 *                      Relative error:
 * arithmetic   domain     # trials      peak         rms
 *    IEEE      0,26.6417   30000       1.3e-15     2.2e-16
 *
 *
 * ERROR MESSAGES:
 *
 *   message         condition              value returned
 * erfc underflow    x > 9.231948545 (DEC)       0.0
 *
 *
 */

/*
Cephes Math Library Release 2.9:  November, 2000
Copyright 1984, 1987, 1988, 1992, 2000 by Stephen L. Moshier
*/

#include "mconf.h"

extern double SQRTH;
extern double MAXLOG;

/* Define this macro to suppress error propagation in exp(x^2)
   by using the expx2 function.  The tradeoff is that doing so
   generates two calls to the exponential function instead of one.  */
#define USE_EXPXSQ 1

#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

#ifdef ANSIPROT
extern double polevl(double, void *, int);
extern double p1evl(double, void *, int);
extern double exp(double);
extern double log(double);
extern double fabs(double);
extern double sqrt(double);
extern double expx2(double, int);
double erf(double);
double erfc(double);
static double erfce(double);
#else
double polevl(), p1evl(), exp(), log(), fabs();
double erf(), erfc(), expx2(), sqrt();
static double erfce();
#endif

double ndtr(a) double a;
{
  double x, y, z;

  x = a * SQRTH;
  z = fabs(x);

  /* if( z < SQRTH ) */
  if (z < 1.0)
    y = 0.5 + 0.5 * erf(x);

  else {
#ifdef USE_EXPXSQ
    /* See below for erfce. */
    y = 0.5 * erfce(z);
    /* Multiply by exp(-x^2 / 2)  */
    z = expx2(a, -1);
    y = y * sqrt(z);
#else
    y = 0.5 * erfc(z);
#endif
    if (x > 0)
      y = 1.0 - y;
  }

  return (y);
}

double erfc(a) 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 < -MAXLOG) {
  under:
    mtherr("erfc", UNDERFLOW);
    if (a < 0)
      return (2.0);
    else
      return (0.0);
  }

#ifdef USE_EXPXSQ
  /* Compute z = exp(z).  */
  z = expx2(a, -1);
#else
  z = exp(z);
#endif
  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);
}

/* Exponentially scaled erfc function
   exp(x^2) erfc(x)
   valid for x > 1.
   Use with ndtr and expx2.  */
static double erfce(x) double x;
{
  double p, q;

  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);
  }
  return (p / q);
}

double erf(x) 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);
}