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

/*							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        -MAXNUM
 * ndtri domain       x >= 1         MAXNUM
 *
 */

/*
Cephes Math Library Release 2.8:  June, 2000
Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier
*/

#include "mconf.h"
extern double MAXNUM;

#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

#ifdef ANSIPROT
extern double polevl(double, void *, int);
extern double p1evl(double, void *, int);
extern double log(double);
extern double sqrt(double);
#else
double polevl(), p1evl(), log(), sqrt();
#endif

double ndtri(y0) double y0;
{
  double x, y, z, y2, x0, x1;
  int code;

  if (y0 <= 0.0) {
    mtherr("ndtri", DOMAIN);
    return (-MAXNUM);
  }
  if (y0 >= 1.0) {
    mtherr("ndtri", DOMAIN);
    return (MAXNUM);
  }
  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);
}