CocoRoboDesktop/pdf1.js/node_modules/cephes/cephes/j0.c

/*							j0.c
 *
 *	Bessel function of order zero
 *
 *
 *
 * SYNOPSIS:
 *
 * double x, y, j0();
 *
 * y = j0( x );
 *
 *
 *
 * DESCRIPTION:
 *
 * Returns Bessel function of order zero of the argument.
 *
 * The domain is divided into the intervals [0, 5] and
 * (5, infinity). In the first interval the following rational
 * approximation is used:
 *
 *
 *        2         2
 * (w - r  ) (w - r  ) P (w) / Q (w)
 *       1         2    3       8
 *
 *            2
 * where w = x  and the two r's are zeros of the function.
 *
 * In the second interval, the Hankel asymptotic expansion
 * is employed with two rational functions of degree 6/6
 * and 7/7.
 *
 *
 *
 * ACCURACY:
 *
 *                      Absolute error:
 * arithmetic   domain     # trials      peak         rms
 *    DEC       0, 30       10000       4.4e-17     6.3e-18
 *    IEEE      0, 30       60000       4.2e-16     1.1e-16
 *
 */
/*							y0.c
 *
 *	Bessel function of the second kind, order zero
 *
 *
 *
 * SYNOPSIS:
 *
 * double x, y, y0();
 *
 * y = y0( x );
 *
 *
 *
 * DESCRIPTION:
 *
 * Returns Bessel function of the second kind, of order
 * zero, of the argument.
 *
 * The domain is divided into the intervals [0, 5] and
 * (5, infinity). In the first interval a rational approximation
 * R(x) is employed to compute
 *   y0(x)  = R(x)  +   2 * log(x) * j0(x) / PI.
 * Thus a call to j0() is required.
 *
 * In the second interval, the Hankel asymptotic expansion
 * is employed with two rational functions of degree 6/6
 * and 7/7.
 *
 *
 *
 * ACCURACY:
 *
 *  Absolute error, when y0(x) < 1; else relative error:
 *
 * arithmetic   domain     # trials      peak         rms
 *    DEC       0, 30        9400       7.0e-17     7.9e-18
 *    IEEE      0, 30       30000       1.3e-15     1.6e-16
 *
 */

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

/* Note: all coefficients satisfy the relative error criterion
 * except YP, YQ which are designed for absolute error. */

#include "mconf.h"

#ifdef UNK
static double PP[7] = {
    7.96936729297347051624E-4, 8.28352392107440799803E-2,
    1.23953371646414299388E0,  5.44725003058768775090E0,
    8.74716500199817011941E0,  5.30324038235394892183E0,
    9.99999999999999997821E-1,
};
static double PQ[7] = {
    9.24408810558863637013E-4, 8.56288474354474431428E-2,
    1.25352743901058953537E0,  5.47097740330417105182E0,
    8.76190883237069594232E0,  5.30605288235394617618E0,
    1.00000000000000000218E0,
};
#endif
#ifdef DEC
static unsigned short PP[28] = {
    0035520, 0164604, 0140733, 0054470, 0037251, 0122605, 0115356,
    0107170, 0040236, 0124412, 0071500, 0056303, 0040656, 0047737,
    0045720, 0045263, 0041013, 0172143, 0045004, 0142103, 0040651,
    0132045, 0026241, 0026406, 0040200, 0000000, 0000000, 0000000,
};
static unsigned short PQ[28] = {
    0035562, 0052006, 0070034, 0134666, 0037257, 0057055, 0055242,
    0123424, 0040240, 0071626, 0046630, 0032371, 0040657, 0011077,
    0032013, 0012731, 0041014, 0030307, 0050331, 0006414, 0040651,
    0145457, 0065021, 0150304, 0040200, 0000000, 0000000, 0000000,
};
#endif
#ifdef IBMPC
static unsigned short PP[28] = {
    0x6b27, 0x983b, 0x1d30, 0x3f4a, 0xd1cf, 0xb35d, 0x34b0,
    0x3fb5, 0x0b98, 0x4e68, 0xd521, 0x3ff3, 0x0956, 0xe97a,
    0xc9fb, 0x4015, 0x9888, 0x6940, 0x7e8c, 0x4021, 0x25a1,
    0xa594, 0x3684, 0x4015, 0x0000, 0x0000, 0x0000, 0x3ff0,
};
static unsigned short PQ[28] = {
    0x9737, 0xce03, 0x4a80, 0x3f4e, 0x54e3, 0xab54, 0xebc5,
    0x3fb5, 0x069f, 0xc9b3, 0x0e72, 0x3ff4, 0x62bb, 0xe681,
    0xe247, 0x4015, 0x21a1, 0xea1b, 0x8618, 0x4021, 0x3a19,
    0xed42, 0x3965, 0x4015, 0x0000, 0x0000, 0x0000, 0x3ff0,
};
#endif
#ifdef MIEEE
static unsigned short PP[28] = {
    0x3f4a, 0x1d30, 0x983b, 0x6b27, 0x3fb5, 0x34b0, 0xb35d,
    0xd1cf, 0x3ff3, 0xd521, 0x4e68, 0x0b98, 0x4015, 0xc9fb,
    0xe97a, 0x0956, 0x4021, 0x7e8c, 0x6940, 0x9888, 0x4015,
    0x3684, 0xa594, 0x25a1, 0x3ff0, 0x0000, 0x0000, 0x0000,
};
static unsigned short PQ[28] = {
    0x3f4e, 0x4a80, 0xce03, 0x9737, 0x3fb5, 0xebc5, 0xab54,
    0x54e3, 0x3ff4, 0x0e72, 0xc9b3, 0x069f, 0x4015, 0xe247,
    0xe681, 0x62bb, 0x4021, 0x8618, 0xea1b, 0x21a1, 0x4015,
    0x3965, 0xed42, 0x3a19, 0x3ff0, 0x0000, 0x0000, 0x0000,
};
#endif

#ifdef UNK
static double QP[8] = {
    -1.13663838898469149931E-2, -1.28252718670509318512E0,
    -1.95539544257735972385E1,  -9.32060152123768231369E1,
    -1.77681167980488050595E2,  -1.47077505154951170175E2,
    -5.14105326766599330220E1,  -6.05014350600728481186E0,
};
static double QQ[7] = {
    /*  1.00000000000000000000E0,*/
    6.43178256118178023184E1, 8.56430025976980587198E2,
    3.88240183605401609683E3, 7.24046774195652478189E3,
    5.93072701187316984827E3, 2.06209331660327847417E3,
    2.42005740240291393179E2,
};
#endif
#ifdef DEC
static unsigned short QP[32] = {
    0136472, 0035021, 0142451, 0141115, 0140244, 0024731, 0150620, 0105642,
    0141234, 0067177, 0124161, 0060141, 0141672, 0064572, 0151557, 0043036,
    0142061, 0127141, 0003127, 0043517, 0142023, 0011727, 0060271, 0144544,
    0141515, 0122142, 0126620, 0143150, 0140701, 0115306, 0106715, 0007344,
};
static unsigned short QQ[28] = {
    /*0040200,0000000,0000000,0000000,*/
    0041600, 0121272, 0004741, 0026544, 0042526, 0015605, 0105654,
    0161771, 0043162, 0123155, 0165644, 0062645, 0043342, 0041675,
    0167576, 0130756, 0043271, 0052720, 0165631, 0154214, 0043000,
    0160576, 0034614, 0172024, 0042162, 0000570, 0030500, 0051235,
};
#endif
#ifdef IBMPC
static unsigned short QP[32] = {
    0x384a, 0x38a5, 0x4742, 0xbf87, 0x1174, 0x3a32, 0x853b, 0xbff4,
    0x2c0c, 0xf50e, 0x8dcf, 0xc033, 0xe8c4, 0x5a6d, 0x4d2f, 0xc057,
    0xe8ea, 0x20ca, 0x35cc, 0xc066, 0x392d, 0xec17, 0x627a, 0xc062,
    0x18cd, 0x55b2, 0xb48c, 0xc049, 0xa1dd, 0xd1b9, 0x3358, 0xc018,
};
static unsigned short QQ[28] = {
    /*0x0000,0x0000,0x0000,0x3ff0,*/
    0x25ac, 0x413c, 0x1457, 0x4050, 0x9c7f, 0xb175, 0xc370,
    0x408a, 0x8cb5, 0xbd74, 0x54cd, 0x40ae, 0xd63e, 0xbdef,
    0x4877, 0x40bc, 0x3b11, 0x1d73, 0x2aba, 0x40b7, 0x9e82,
    0xc731, 0x1c2f, 0x40a0, 0x0a54, 0x0628, 0x402f, 0x406e,
};
#endif
#ifdef MIEEE
static unsigned short QP[32] = {
    0xbf87, 0x4742, 0x38a5, 0x384a, 0xbff4, 0x853b, 0x3a32, 0x1174,
    0xc033, 0x8dcf, 0xf50e, 0x2c0c, 0xc057, 0x4d2f, 0x5a6d, 0xe8c4,
    0xc066, 0x35cc, 0x20ca, 0xe8ea, 0xc062, 0x627a, 0xec17, 0x392d,
    0xc049, 0xb48c, 0x55b2, 0x18cd, 0xc018, 0x3358, 0xd1b9, 0xa1dd,
};
static unsigned short QQ[28] = {
    /*0x3ff0,0x0000,0x0000,0x0000,*/
    0x4050, 0x1457, 0x413c, 0x25ac, 0x408a, 0xc370, 0xb175,
    0x9c7f, 0x40ae, 0x54cd, 0xbd74, 0x8cb5, 0x40bc, 0x4877,
    0xbdef, 0xd63e, 0x40b7, 0x2aba, 0x1d73, 0x3b11, 0x40a0,
    0x1c2f, 0xc731, 0x9e82, 0x406e, 0x402f, 0x0628, 0x0a54,
};
#endif

#ifdef UNK
static double YP[8] = {
    1.55924367855235737965E4,  -1.46639295903971606143E7,
    5.43526477051876500413E9,  -9.82136065717911466409E11,
    8.75906394395366999549E13, -3.46628303384729719441E15,
    4.42733268572569800351E16, -1.84950800436986690637E16,
};
static double YQ[7] = {
    /* 1.00000000000000000000E0,*/
    1.04128353664259848412E3,  6.26107330137134956842E5,
    2.68919633393814121987E8,  8.64002487103935000337E10,
    2.02979612750105546709E13, 3.17157752842975028269E15,
    2.50596256172653059228E17,
};
#endif
#ifdef DEC
static unsigned short YP[32] = {
    0043563, 0120677, 0042264, 0046166, 0146137, 0140371, 0113444, 0042260,
    0050241, 0175707, 0100502, 0063344, 0152144, 0125737, 0007265, 0164526,
    0053637, 0051621, 0163035, 0060546, 0155105, 0004416, 0107306, 0060023,
    0056035, 0045133, 0030132, 0000024, 0155603, 0065132, 0144061, 0131732,
};
static unsigned short YQ[28] = {
    /*0040200,0000000,0000000,0000000,*/
    0042602, 0024422, 0135557, 0162663, 0045030, 0155665, 0044075,
    0160135, 0047200, 0035432, 0105446, 0104005, 0051240, 0167331,
    0056063, 0022743, 0053223, 0127746, 0025764, 0012160, 0055064,
    0044206, 0177532, 0145545, 0056536, 0111375, 0163715, 0127201,
};
#endif
#ifdef IBMPC
static unsigned short YP[32] = {
    0x898f, 0xe896, 0x7437, 0x40ce, 0x8896, 0x32e4, 0xf81f, 0xc16b,
    0x4cdd, 0xf028, 0x3f78, 0x41f4, 0xbd2b, 0xe1d6, 0x957b, 0xc26c,
    0xac2d, 0x3cc3, 0xea72, 0x42d3, 0xcc02, 0xd1d8, 0xa121, 0xc328,
    0x4003, 0x660b, 0xa94b, 0x4363, 0x367b, 0x5906, 0x6d4b, 0xc350,
};
static unsigned short YQ[28] = {
    /*0x0000,0x0000,0x0000,0x3ff0,*/
    0xfcb6, 0x576d, 0x4522, 0x4090, 0xbc0c, 0xa907, 0x1b76,
    0x4123, 0xd101, 0x5164, 0x0763, 0x41b0, 0x64bc, 0x2b86,
    0x1ddb, 0x4234, 0x828e, 0xc57e, 0x75fc, 0x42b2, 0x596d,
    0xdfeb, 0x8910, 0x4326, 0xb5d0, 0xbcf9, 0xd25f, 0x438b,
};
#endif
#ifdef MIEEE
static unsigned short YP[32] = {
    0x40ce, 0x7437, 0xe896, 0x898f, 0xc16b, 0xf81f, 0x32e4, 0x8896,
    0x41f4, 0x3f78, 0xf028, 0x4cdd, 0xc26c, 0x957b, 0xe1d6, 0xbd2b,
    0x42d3, 0xea72, 0x3cc3, 0xac2d, 0xc328, 0xa121, 0xd1d8, 0xcc02,
    0x4363, 0xa94b, 0x660b, 0x4003, 0xc350, 0x6d4b, 0x5906, 0x367b,
};
static unsigned short YQ[28] = {
    /*0x3ff0,0x0000,0x0000,0x0000,*/
    0x4090, 0x4522, 0x576d, 0xfcb6, 0x4123, 0x1b76, 0xa907,
    0xbc0c, 0x41b0, 0x0763, 0x5164, 0xd101, 0x4234, 0x1ddb,
    0x2b86, 0x64bc, 0x42b2, 0x75fc, 0xc57e, 0x828e, 0x4326,
    0x8910, 0xdfeb, 0x596d, 0x438b, 0xd25f, 0xbcf9, 0xb5d0,
};
#endif

#ifdef UNK
/*  5.783185962946784521175995758455807035071 */
static double DR1 = 5.78318596294678452118E0;
/* 30.47126234366208639907816317502275584842 */
static double DR2 = 3.04712623436620863991E1;
#endif

#ifdef DEC
static unsigned short R1[] = {0040671, 0007734, 0001061, 0056734};
#define DR1 *(double *)R1
static unsigned short R2[] = {0041363, 0142445, 0030416, 0165567};
#define DR2 *(double *)R2
#endif

#ifdef IBMPC
static unsigned short R1[] = {0x2bbb, 0x8046, 0x21fb, 0x4017};
#define DR1 *(double *)R1
static unsigned short R2[] = {0xdd6f, 0xa621, 0x78a4, 0x403e};
#define DR2 *(double *)R2
#endif

#ifdef MIEEE
static unsigned short R1[] = {0x4017, 0x21fb, 0x8046, 0x2bbb};
#define DR1 *(double *)R1
static unsigned short R2[] = {0x403e, 0x78a4, 0xa621, 0xdd6f};
#define DR2 *(double *)R2
#endif

#ifdef UNK
static double RP[4] = {
    -4.79443220978201773821E9,
    1.95617491946556577543E12,
    -2.49248344360967716204E14,
    9.70862251047306323952E15,
};
static double RQ[8] = {
    /* 1.00000000000000000000E0,*/
    4.99563147152651017219E2,  1.73785401676374683123E5,
    4.84409658339962045305E7,  1.11855537045356834862E10,
    2.11277520115489217587E12, 3.10518229857422583814E14,
    3.18121955943204943306E16, 1.71086294081043136091E18,
};
#endif
#ifdef DEC
static unsigned short RP[16] = {
    0150216, 0161235, 0064344, 0014450, 0052343, 0135216, 0035624, 0144153,
    0154142, 0130247, 0003310, 0003667, 0055411, 0173703, 0047772, 0176635,
};
static unsigned short RQ[32] = {
    /*0040200,0000000,0000000,0000000,*/
    0042371, 0144025, 0032265, 0136137, 0044451, 0133131, 0132420, 0151466,
    0046470, 0144641, 0072540, 0030636, 0050446, 0126600, 0045042, 0044243,
    0052365, 0172633, 0110301, 0071063, 0054215, 0032424, 0062272, 0043513,
    0055742, 0005013, 0171731, 0072335, 0057275, 0170646, 0036663, 0013134,
};
#endif
#ifdef IBMPC
static unsigned short RP[16] = {
    0x8325, 0xad1c, 0xdc53, 0xc1f1, 0x990d, 0xc772, 0x7751, 0x427c,
    0x00f7, 0xe0d9, 0x5614, 0xc2ec, 0x5fb4, 0x69ff, 0x3ef8, 0x4341,
};
static unsigned short RQ[32] = {
    /*0x0000,0x0000,0x0000,0x3ff0,*/
    0xb78c, 0xa696, 0x3902, 0x407f, 0x1a67, 0x36a2, 0x36cb, 0x4105,
    0x0634, 0x2eac, 0x1934, 0x4187, 0x4914, 0x0944, 0xd5b0, 0x4204,
    0x2e46, 0x7218, 0xbeb3, 0x427e, 0x48e9, 0x8c97, 0xa6a2, 0x42f1,
    0x2e9c, 0x7e7b, 0x4141, 0x435c, 0x62cc, 0xc7b6, 0xbe34, 0x43b7,
};
#endif
#ifdef MIEEE
static unsigned short RP[16] = {
    0xc1f1, 0xdc53, 0xad1c, 0x8325, 0x427c, 0x7751, 0xc772, 0x990d,
    0xc2ec, 0x5614, 0xe0d9, 0x00f7, 0x4341, 0x3ef8, 0x69ff, 0x5fb4,
};
static unsigned short RQ[32] = {
    /*0x3ff0,0x0000,0x0000,0x0000,*/
    0x407f, 0x3902, 0xa696, 0xb78c, 0x4105, 0x36cb, 0x36a2, 0x1a67,
    0x4187, 0x1934, 0x2eac, 0x0634, 0x4204, 0xd5b0, 0x0944, 0x4914,
    0x427e, 0xbeb3, 0x7218, 0x2e46, 0x42f1, 0xa6a2, 0x8c97, 0x48e9,
    0x435c, 0x4141, 0x7e7b, 0x2e9c, 0x43b7, 0xbe34, 0xc7b6, 0x62cc,
};
#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 j0(double);
#else
double polevl(), p1evl(), log(), sin(), cos(), sqrt();
double j0();
#endif
extern double TWOOPI, SQ2OPI, PIO4;

double j0(x) double x;
{
  double w, z, p, q, xn;

  if (x < 0)
    x = -x;

  if (x <= 5.0) {
    z = x * x;
    if (x < 1.0e-5)
      return (1.0 - z / 4.0);

    p = (z - DR1) * (z - DR2);
    p = p * polevl(z, RP, 3) / p1evl(z, RQ, 8);
    return (p);
  }

  w = 5.0 / x;
  q = 25.0 / (x * x);
  p = polevl(q, PP, 6) / polevl(q, PQ, 6);
  q = polevl(q, QP, 7) / p1evl(q, QQ, 7);
  xn = x - PIO4;
  p = p * cos(xn) - w * q * sin(xn);
  return (p * SQ2OPI / sqrt(x));
}

/*							y0() 2	*/
/* Bessel function of second kind, order zero	*/

/* Rational approximation coefficients YP[], YQ[] are used here.
 * The function computed is  y0(x)  -  2 * log(x) * j0(x) / PI,
 * whose value at x = 0 is  2 * ( log(0.5) + EUL ) / PI
 * = 0.073804295108687225.
 */

/*
#define PIO4 .78539816339744830962
#define SQ2OPI .79788456080286535588
*/
extern double MAXNUM;

double y0(x) double x;
{
  double w, z, p, q, xn;

  if (x <= 5.0) {
    if (x <= 0.0) {
      mtherr("y0", DOMAIN);
      return (-MAXNUM);
    }
    z = x * x;
    w = polevl(z, YP, 7) / p1evl(z, YQ, 7);
    w += TWOOPI * log(x) * j0(x);
    return (w);
  }

  w = 5.0 / x;
  z = 25.0 / (x * x);
  p = polevl(z, PP, 6) / polevl(z, PQ, 6);
  q = polevl(z, QP, 7) / p1evl(z, QQ, 7);
  xn = x - PIO4;
  p = p * sin(xn) + w * q * cos(xn);
  return (p * SQ2OPI / sqrt(x));
}