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

/*							ellpe.c
 *
 *	Complete elliptic integral of the second kind
 *
 *
 *
 * SYNOPSIS:
 *
 * double m1, y, ellpe();
 *
 * y = ellpe( m1 );
 *
 *
 *
 * DESCRIPTION:
 *
 * Approximates the integral
 *
 *
 *            pi/2
 *             -
 *            | |                 2
 * E(m)  =    |    sqrt( 1 - m sin t ) dt
 *          | |
 *           -
 *            0
 *
 * Where m = 1 - m1, using the approximation
 *
 *      P(x)  -  x log x Q(x).
 *
 * Though there are no singularities, the argument m1 is used
 * rather than m for compatibility with ellpk().
 *
 * E(1) = 1; E(0) = pi/2.
 *
 *
 * ACCURACY:
 *
 *                      Relative error:
 * arithmetic   domain     # trials      peak         rms
 *    DEC        0, 1       13000       3.1e-17     9.4e-18
 *    IEEE       0, 1       10000       2.1e-16     7.3e-17
 *
 *
 * ERROR MESSAGES:
 *
 *   message         condition      value returned
 * ellpe domain      x<0, x>1            0.0
 *
 */

/*							ellpe.c		*/

/* Elliptic integral of second kind */

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

#include "mconf.h"

#ifdef UNK
static double P[] = {1.53552577301013293365E-4, 2.50888492163602060990E-3,
                     8.68786816565889628429E-3, 1.07350949056076193403E-2,
                     7.77395492516787092951E-3, 7.58395289413514708519E-3,
                     1.15688436810574127319E-2, 2.18317996015557253103E-2,
                     5.68051945617860553470E-2, 4.43147180560990850618E-1,
                     1.00000000000000000299E0};
static double Q[] = {3.27954898576485872656E-5, 1.00962792679356715133E-3,
                     6.50609489976927491433E-3, 1.68862163993311317300E-2,
                     2.61769742454493659583E-2, 3.34833904888224918614E-2,
                     4.27180926518931511717E-2, 5.85936634471101055642E-2,
                     9.37499997197644278445E-2, 2.49999999999888314361E-1};
#endif

#ifdef DEC
static unsigned short P[] = {
    0035041, 0001364, 0141572, 0117555, 0036044, 0066032, 0130027, 0033404,
    0036416, 0053617, 0064456, 0102632, 0036457, 0161100, 0061177, 0122612,
    0036376, 0136251, 0012403, 0124162, 0036370, 0101316, 0151715, 0131613,
    0036475, 0105477, 0050317, 0133272, 0036662, 0154232, 0024645, 0171552,
    0037150, 0126220, 0047054, 0030064, 0037742, 0162057, 0167645, 0165612,
    0040200, 0000000, 0000000, 0000000};
static unsigned short Q[] = {
    0034411, 0106743, 0115771, 0055462, 0035604, 0052575, 0155171, 0045540,
    0036325, 0030424, 0064332, 0167756, 0036612, 0052366, 0063006, 0115175,
    0036726, 0070430, 0004533, 0124654, 0037011, 0022741, 0030675, 0030711,
    0037056, 0174452, 0127062, 0132122, 0037157, 0177750, 0142041, 0072523,
    0037277, 0177777, 0173137, 0002627, 0037577, 0177777, 0177777, 0101101};
#endif

#ifdef IBMPC
static unsigned short P[] = {
    0x53ee, 0x986f, 0x205e, 0x3f24, 0xe6e0, 0x5602, 0x8d83, 0x3f64, 0xd0b3,
    0xed25, 0xcaf1, 0x3f81, 0xf4b1, 0x0c4f, 0xfc48, 0x3f85, 0x750e, 0x22a0,
    0xd795, 0x3f7f, 0xb671, 0xda79, 0x1059, 0x3f7f, 0xf6d7, 0xea19, 0xb167,
    0x3f87, 0xbe6d, 0x4534, 0x5b13, 0x3f96, 0x8607, 0x09c5, 0x1592, 0x3fad,
    0xbd71, 0xfdf4, 0x5c85, 0x3fdc, 0x0000, 0x0000, 0x0000, 0x3ff0};
static unsigned short Q[] = {
    0x2b66, 0x737f, 0x31bc, 0x3f01, 0x296c, 0xbb4f, 0x8aaf, 0x3f50,
    0x5dfe, 0x8d1b, 0xa622, 0x3f7a, 0xd350, 0xccc0, 0x4a9e, 0x3f91,
    0x7535, 0x012b, 0xce23, 0x3f9a, 0xa639, 0x2637, 0x24bc, 0x3fa1,
    0x568a, 0x55c6, 0xdf25, 0x3fa5, 0x2eaa, 0x1884, 0xfffd, 0x3fad,
    0xe0b3, 0xfecb, 0xffff, 0x3fb7, 0xf048, 0xffff, 0xffff, 0x3fcf};
#endif

#ifdef MIEEE
static unsigned short P[] = {
    0x3f24, 0x205e, 0x986f, 0x53ee, 0x3f64, 0x8d83, 0x5602, 0xe6e0, 0x3f81,
    0xcaf1, 0xed25, 0xd0b3, 0x3f85, 0xfc48, 0x0c4f, 0xf4b1, 0x3f7f, 0xd795,
    0x22a0, 0x750e, 0x3f7f, 0x1059, 0xda79, 0xb671, 0x3f87, 0xb167, 0xea19,
    0xf6d7, 0x3f96, 0x5b13, 0x4534, 0xbe6d, 0x3fad, 0x1592, 0x09c5, 0x8607,
    0x3fdc, 0x5c85, 0xfdf4, 0xbd71, 0x3ff0, 0x0000, 0x0000, 0x0000};
static unsigned short Q[] = {
    0x3f01, 0x31bc, 0x737f, 0x2b66, 0x3f50, 0x8aaf, 0xbb4f, 0x296c,
    0x3f7a, 0xa622, 0x8d1b, 0x5dfe, 0x3f91, 0x4a9e, 0xccc0, 0xd350,
    0x3f9a, 0xce23, 0x012b, 0x7535, 0x3fa1, 0x24bc, 0x2637, 0xa639,
    0x3fa5, 0xdf25, 0x55c6, 0x568a, 0x3fad, 0xfffd, 0x1884, 0x2eaa,
    0x3fb7, 0xffff, 0xfecb, 0xe0b3, 0x3fcf, 0xffff, 0xffff, 0xf048};
#endif

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

double ellpe(x) double x;
{

  if ((x <= 0.0) || (x > 1.0)) {
    if (x == 0.0)
      return (1.0);
    mtherr("ellpe", DOMAIN);
    return (0.0);
  }
  return (polevl(x, P, 10) - log(x) * (x * polevl(x, Q, 9)));
}