CocoRoboDesktop/pdf1.js/node_modules/cephes/cephes/j1.c

/*							j1.c
 *
 *	Bessel function of order one
 *
 *
 *
 * SYNOPSIS:
 *
 * double x, y, j1();
 *
 * y = j1( x );
 *
 *
 *
 * DESCRIPTION:
 *
 * Returns Bessel function of order one of the argument.
 *
 * The domain is divided into the intervals [0, 8] and
 * (8, infinity). In the first interval a 24 term Chebyshev
 * expansion is used. In the second, the asymptotic
 * trigonometric representation is employed using two
 * rational functions of degree 5/5.
 *
 *
 *
 * ACCURACY:
 *
 *                      Absolute error:
 * arithmetic   domain      # trials      peak         rms
 *    DEC       0, 30       10000       4.0e-17     1.1e-17
 *    IEEE      0, 30       30000       2.6e-16     1.1e-16
 *
 *
 */
/*							y1.c
 *
 *	Bessel function of second kind of order one
 *
 *
 *
 * SYNOPSIS:
 *
 * double x, y, y1();
 *
 * y = y1( x );
 *
 *
 *
 * DESCRIPTION:
 *
 * Returns Bessel function of the second kind of order one
 * of the argument.
 *
 * The domain is divided into the intervals [0, 8] and
 * (8, infinity). In the first interval a 25 term Chebyshev
 * expansion is used, and a call to j1() is required.
 * In the second, the asymptotic trigonometric representation
 * is employed using two rational functions of degree 5/5.
 *
 *
 *
 * ACCURACY:
 *
 *                      Absolute error:
 * arithmetic   domain      # trials      peak         rms
 *    DEC       0, 30       10000       8.6e-17     1.3e-17
 *    IEEE      0, 30       30000       1.0e-15     1.3e-16
 *
 * (error criterion relative when |y1| > 1).
 *
 */

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

/*
#define PIO4 .78539816339744830962
#define THPIO4 2.35619449019234492885
#define SQ2OPI .79788456080286535588
*/

#include "mconf.h"

#ifdef UNK
static double RP[4] = {
    -8.99971225705559398224E8,
    4.52228297998194034323E11,
    -7.27494245221818276015E13,
    3.68295732863852883286E15,
};
static double RQ[8] = {
    /* 1.00000000000000000000E0,*/
    6.20836478118054335476E2,  2.56987256757748830383E5,
    8.35146791431949253037E7,  2.21511595479792499675E10,
    4.74914122079991414898E12, 7.84369607876235854894E14,
    8.95222336184627338078E16, 5.32278620332680085395E18,
};
#endif
#ifdef DEC
static unsigned short RP[16] = {
    0147526, 0110742, 0063322, 0077052, 0051722, 0112720, 0065034, 0061530,
    0153604, 0052227, 0033147, 0105650, 0055121, 0055025, 0032276, 0022015,
};
static unsigned short RQ[32] = {
    /*0040200,0000000,0000000,0000000,*/
    0042433, 0032610, 0155604, 0033473, 0044572, 0173320, 0067270, 0006616,
    0046637, 0045246, 0162225, 0006606, 0050645, 0004773, 0157577, 0053004,
    0052612, 0033734, 0001667, 0176501, 0054462, 0054121, 0173147, 0121367,
    0056237, 0002777, 0121451, 0176007, 0057623, 0136253, 0131601, 0044710,
};
#endif
#ifdef IBMPC
static unsigned short RP[16] = {
    0x4fc5, 0x4cda, 0xd23c, 0xc1ca, 0x8c6b, 0x0d43, 0x52ba, 0x425a,
    0xf175, 0xe6cc, 0x8a92, 0xc2d0, 0xc482, 0xa697, 0x2b42, 0x432a,
};
static unsigned short RQ[32] = {
    /*0x0000,0x0000,0x0000,0x3ff0,*/
    0x86e7, 0x1b70, 0x66b1, 0x4083, 0x01b2, 0x0dd7, 0x5eda, 0x410f,
    0xa1b1, 0xdc92, 0xe954, 0x4193, 0xeac1, 0x7bef, 0xa13f, 0x4214,
    0xffa8, 0x8076, 0x46fb, 0x4291, 0xf45f, 0x3ecc, 0x4b0a, 0x4306,
    0x3f81, 0xf465, 0xe0bf, 0x4373, 0x2939, 0x7670, 0x7795, 0x43d2,
};
#endif
#ifdef MIEEE
static unsigned short RP[16] = {
    0xc1ca, 0xd23c, 0x4cda, 0x4fc5, 0x425a, 0x52ba, 0x0d43, 0x8c6b,
    0xc2d0, 0x8a92, 0xe6cc, 0xf175, 0x432a, 0x2b42, 0xa697, 0xc482,
};
static unsigned short RQ[32] = {
    /*0x3ff0,0x0000,0x0000,0x0000,*/
    0x4083, 0x66b1, 0x1b70, 0x86e7, 0x410f, 0x5eda, 0x0dd7, 0x01b2,
    0x4193, 0xe954, 0xdc92, 0xa1b1, 0x4214, 0xa13f, 0x7bef, 0xeac1,
    0x4291, 0x46fb, 0x8076, 0xffa8, 0x4306, 0x4b0a, 0x3ecc, 0xf45f,
    0x4373, 0xe0bf, 0xf465, 0x3f81, 0x43d2, 0x7795, 0x7670, 0x2939,
};
#endif

#ifdef UNK
static double PP[7] = {
    7.62125616208173112003E-4, 7.31397056940917570436E-2,
    1.12719608129684925192E0,  5.11207951146807644818E0,
    8.42404590141772420927E0,  5.21451598682361504063E0,
    1.00000000000000000254E0,
};
static double PQ[7] = {
    5.71323128072548699714E-4, 6.88455908754495404082E-2,
    1.10514232634061696926E0,  5.07386386128601488557E0,
    8.39985554327604159757E0,  5.20982848682361821619E0,
    9.99999999999999997461E-1,
};
#endif
#ifdef DEC
static unsigned short PP[28] = {
    0035507, 0144542, 0061543, 0024326, 0037225, 0145105, 0017766,
    0022661, 0040220, 0043766, 0010254, 0133255, 0040643, 0113047,
    0142611, 0151521, 0041006, 0144344, 0055351, 0074261, 0040646,
    0156520, 0120574, 0006416, 0040200, 0000000, 0000000, 0000000,
};
static unsigned short PQ[28] = {
    0035425, 0142330, 0115041, 0165514, 0037214, 0177352, 0145105,
    0052026, 0040215, 0072515, 0141207, 0073255, 0040642, 0056427,
    0137222, 0106405, 0041006, 0062716, 0166427, 0165450, 0040646,
    0133352, 0035425, 0123304, 0040200, 0000000, 0000000, 0000000,
};
#endif
#ifdef IBMPC
static unsigned short PP[28] = {
    0x651b, 0x4c6c, 0xf92c, 0x3f48, 0xc4b6, 0xa3fe, 0xb948,
    0x3fb2, 0x96d6, 0xc215, 0x08fe, 0x3ff2, 0x3a6a, 0xf8b1,
    0x72c4, 0x4014, 0x2f16, 0x8b5d, 0xd91c, 0x4020, 0x81a2,
    0x142f, 0xdbaa, 0x4014, 0x0000, 0x0000, 0x0000, 0x3ff0,
};
static unsigned short PQ[28] = {
    0x3d69, 0x1344, 0xb89b, 0x3f42, 0xaa83, 0x5948, 0x9fdd,
    0x3fb1, 0xeed6, 0xb850, 0xaea9, 0x3ff1, 0x51a1, 0xf7d2,
    0x4ba2, 0x4014, 0xfd65, 0xdda2, 0xccb9, 0x4020, 0xb4d9,
    0x4762, 0xd6dd, 0x4014, 0x0000, 0x0000, 0x0000, 0x3ff0,
};
#endif
#ifdef MIEEE
static unsigned short PP[28] = {
    0x3f48, 0xf92c, 0x4c6c, 0x651b, 0x3fb2, 0xb948, 0xa3fe,
    0xc4b6, 0x3ff2, 0x08fe, 0xc215, 0x96d6, 0x4014, 0x72c4,
    0xf8b1, 0x3a6a, 0x4020, 0xd91c, 0x8b5d, 0x2f16, 0x4014,
    0xdbaa, 0x142f, 0x81a2, 0x3ff0, 0x0000, 0x0000, 0x0000,
};
static unsigned short PQ[28] = {
    0x3f42, 0xb89b, 0x1344, 0x3d69, 0x3fb1, 0x9fdd, 0x5948,
    0xaa83, 0x3ff1, 0xaea9, 0xb850, 0xeed6, 0x4014, 0x4ba2,
    0xf7d2, 0x51a1, 0x4020, 0xccb9, 0xdda2, 0xfd65, 0x4014,
    0xd6dd, 0x4762, 0xb4d9, 0x3ff0, 0x0000, 0x0000, 0x0000,
};
#endif

#ifdef UNK
static double QP[8] = {
    5.10862594750176621635E-2, 4.98213872951233449420E0,
    7.58238284132545283818E1,  3.66779609360150777800E2,
    7.10856304998926107277E2,  5.97489612400613639965E2,
    2.11688757100572135698E2,  2.52070205858023719784E1,
};
static double QQ[7] = {
    /* 1.00000000000000000000E0,*/
    7.42373277035675149943E1, 1.05644886038262816351E3,
    4.98641058337653607651E3, 9.56231892404756170795E3,
    7.99704160447350683650E3, 2.82619278517639096600E3,
    3.36093607810698293419E2,
};
#endif
#ifdef DEC
static unsigned short QP[32] = {
    0037121, 0037723, 0055605, 0151004, 0040637, 0066656, 0031554, 0077264,
    0041627, 0122714, 0153170, 0161466, 0042267, 0061712, 0036520, 0140145,
    0042461, 0133315, 0131573, 0071176, 0042425, 0057525, 0147500, 0013201,
    0042123, 0130122, 0061245, 0154131, 0041311, 0123772, 0064254, 0172650,
};
static unsigned short QQ[28] = {
    /*0040200,0000000,0000000,0000000,*/
    0041624, 0074603, 0002112, 0101670, 0042604, 0007135, 0010162,
    0175565, 0043233, 0151510, 0157757, 0172010, 0043425, 0064506,
    0112006, 0104276, 0043371, 0164125, 0032271, 0164242, 0043060,
    0121425, 0122750, 0136013, 0042250, 0005773, 0053472, 0146267,
};
#endif
#ifdef IBMPC
static unsigned short QP[32] = {
    0xba40, 0x6b70, 0x27fa, 0x3faa, 0x8fd6, 0xc66d, 0xedb5, 0x4013,
    0x1c67, 0x9acf, 0xf4b9, 0x4052, 0x180d, 0x47aa, 0xec79, 0x4076,
    0x6e50, 0xb66f, 0x36d9, 0x4086, 0x02d0, 0xb9e8, 0xabea, 0x4082,
    0xbb0b, 0x4c54, 0x760a, 0x406a, 0x9eb5, 0x4d15, 0x34ff, 0x4039,
};
static unsigned short QQ[28] = {
    /*0x0000,0x0000,0x0000,0x3ff0,*/
    0x5077, 0x6089, 0x8f30, 0x4052, 0x5f6f, 0xa20e, 0x81cb,
    0x4090, 0xfe81, 0x1bfd, 0x7a69, 0x40b3, 0xd118, 0xd280,
    0xad28, 0x40c2, 0x3d14, 0xa697, 0x3d0a, 0x40bf, 0x1781,
    0xb4bd, 0x1462, 0x40a6, 0x5997, 0x6ae7, 0x017f, 0x4075,
};
#endif
#ifdef MIEEE
static unsigned short QP[32] = {
    0x3faa, 0x27fa, 0x6b70, 0xba40, 0x4013, 0xedb5, 0xc66d, 0x8fd6,
    0x4052, 0xf4b9, 0x9acf, 0x1c67, 0x4076, 0xec79, 0x47aa, 0x180d,
    0x4086, 0x36d9, 0xb66f, 0x6e50, 0x4082, 0xabea, 0xb9e8, 0x02d0,
    0x406a, 0x760a, 0x4c54, 0xbb0b, 0x4039, 0x34ff, 0x4d15, 0x9eb5,
};
static unsigned short QQ[28] = {
    /*0x3ff0,0x0000,0x0000,0x0000,*/
    0x4052, 0x8f30, 0x6089, 0x5077, 0x4090, 0x81cb, 0xa20e,
    0x5f6f, 0x40b3, 0x7a69, 0x1bfd, 0xfe81, 0x40c2, 0xad28,
    0xd280, 0xd118, 0x40bf, 0x3d0a, 0xa697, 0x3d14, 0x40a6,
    0x1462, 0xb4bd, 0x1781, 0x4075, 0x017f, 0x6ae7, 0x5997,
};
#endif

#ifdef UNK
static double YP[6] = {
    1.26320474790178026440E9,  -6.47355876379160291031E11,
    1.14509511541823727583E14, -8.12770255501325109621E15,
    2.02439475713594898196E17, -7.78877196265950026825E17,
};
static double YQ[8] = {
    /* 1.00000000000000000000E0,*/
    5.94301592346128195359E2,  2.35564092943068577943E5,
    7.34811944459721705660E7,  1.87601316108706159478E10,
    3.88231277496238566008E12, 6.20557727146953693363E14,
    6.87141087355300489866E16, 3.97270608116560655612E18,
};
#endif
#ifdef DEC
static unsigned short YP[24] = {
    0047626, 0112763, 0013715, 0133045, 0152026, 0134552, 0142033, 0024411,
    0053720, 0045245, 0102210, 0077565, 0155347, 0000321, 0136415, 0102031,
    0056463, 0146550, 0055633, 0032605, 0157054, 0171012, 0167361, 0054265,
};
static unsigned short YQ[32] = {
    /*0040200,0000000,0000000,0000000,*/
    0042424, 0111515, 0044773, 0153014, 0044546, 0005405, 0171307, 0075774,
    0046614, 0023575, 0047105, 0063556, 0050613, 0143034, 0101533, 0156026,
    0052541, 0175367, 0166514, 0114257, 0054415, 0014466, 0134350, 0171154,
    0056164, 0017436, 0025075, 0022101, 0057534, 0103614, 0103663, 0121772,
};
#endif
#ifdef IBMPC
static unsigned short YP[24] = {
    0xb6c5, 0x62f9, 0xd2be, 0x41d2, 0x6521, 0x5883, 0xd72d, 0xc262,
    0x0fef, 0xb091, 0x0954, 0x42da, 0xb083, 0x37a1, 0xe01a, 0xc33c,
    0x66b1, 0x0b73, 0x79ad, 0x4386, 0x2b17, 0x5dde, 0x9e41, 0xc3a5,
};
static unsigned short YQ[32] = {
    /*0x0000,0x0000,0x0000,0x3ff0,*/
    0x7ac2, 0xa93f, 0x9269, 0x4082, 0xef7f, 0xbe58, 0xc160, 0x410c,
    0xacee, 0xa9c8, 0x84ef, 0x4191, 0x7b83, 0x906b, 0x78c3, 0x4211,
    0x9316, 0xfda9, 0x3f5e, 0x428c, 0x1e4e, 0xd71d, 0xa326, 0x4301,
    0xa488, 0xc547, 0x83e3, 0x436e, 0x747f, 0x90f6, 0x90f1, 0x43cb,
};
#endif
#ifdef MIEEE
static unsigned short YP[24] = {
    0x41d2, 0xd2be, 0x62f9, 0xb6c5, 0xc262, 0xd72d, 0x5883, 0x6521,
    0x42da, 0x0954, 0xb091, 0x0fef, 0xc33c, 0xe01a, 0x37a1, 0xb083,
    0x4386, 0x79ad, 0x0b73, 0x66b1, 0xc3a5, 0x9e41, 0x5dde, 0x2b17,
};
static unsigned short YQ[32] = {
    /*0x3ff0,0x0000,0x0000,0x0000,*/
    0x4082, 0x9269, 0xa93f, 0x7ac2, 0x410c, 0xc160, 0xbe58, 0xef7f,
    0x4191, 0x84ef, 0xa9c8, 0xacee, 0x4211, 0x78c3, 0x906b, 0x7b83,
    0x428c, 0x3f5e, 0xfda9, 0x9316, 0x4301, 0xa326, 0xd71d, 0x1e4e,
    0x436e, 0x83e3, 0xc547, 0xa488, 0x43cb, 0x90f1, 0x90f6, 0x747f,
};
#endif

#ifdef UNK
static double Z1 = 1.46819706421238932572E1;
static double Z2 = 4.92184563216946036703E1;
#endif

#ifdef DEC
static unsigned short DZ1[] = {0041152, 0164532, 0006114, 0010540};
static unsigned short DZ2[] = {0041504, 0157663, 0001625, 0020621};
#define Z1 (*(double *)DZ1)
#define Z2 (*(double *)DZ2)
#endif

#ifdef IBMPC
static unsigned short DZ1[] = {0x822c, 0x4189, 0x5d2b, 0x402d};
static unsigned short DZ2[] = {0xa432, 0x6072, 0x9bf6, 0x4048};
#define Z1 (*(double *)DZ1)
#define Z2 (*(double *)DZ2)
#endif

#ifdef MIEEE
static unsigned short DZ1[] = {0x402d, 0x5d2b, 0x4189, 0x822c};
static unsigned short DZ2[] = {0x4048, 0x9bf6, 0x6072, 0xa432};
#define Z1 (*(double *)DZ1)
#define Z2 (*(double *)DZ2)
#endif

#ifdef ANSIPROT
extern double polevl(double, void *, int);
extern double p1evl(double, void *, int);
extern double log(double);
extern double sin(double);
extern double cos(double);
extern double sqrt(double);
double j1(double);
#else
double polevl(), p1evl(), log(), sin(), cos(), sqrt();
double j1();
#endif
extern double TWOOPI, THPIO4, SQ2OPI;

double j1(x) double x;
{
  double w, z, p, q, xn;

  w = x;
  if (x < 0)
    w = -x;

  if (w <= 5.0) {
    z = x * x;
    w = polevl(z, RP, 3) / p1evl(z, RQ, 8);
    w = w * x * (z - Z1) * (z - Z2);
    return (w);
  }

  w = 5.0 / x;
  z = w * w;
  p = polevl(z, PP, 6) / polevl(z, PQ, 6);
  q = polevl(z, QP, 7) / p1evl(z, QQ, 7);
  xn = x - THPIO4;
  p = p * cos(xn) - w * q * sin(xn);
  return (p * SQ2OPI / sqrt(x));
}

extern double MAXNUM;

double y1(x) double x;
{
  double w, z, p, q, xn;

  if (x <= 5.0) {
    if (x <= 0.0) {
      mtherr("y1", DOMAIN);
      return (-MAXNUM);
    }
    z = x * x;
    w = x * (polevl(z, YP, 5) / p1evl(z, YQ, 8));
    w += TWOOPI * (j1(x) * log(x) - 1.0 / x);
    return (w);
  }

  w = 5.0 / x;
  z = w * w;
  p = polevl(z, PP, 6) / polevl(z, PQ, 6);
  q = polevl(z, QP, 7) / p1evl(z, QQ, 7);
  xn = x - THPIO4;
  p = p * sin(xn) + w * q * cos(xn);
  return (p * SQ2OPI / sqrt(x));
}