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

/*							ellie.c
 *
 *	Incomplete elliptic integral of the second kind
 *
 *
 *
 * SYNOPSIS:
 *
 * double phi, m, y, ellie();
 *
 * y = ellie( phi, m );
 *
 *
 *
 * DESCRIPTION:
 *
 * Approximates the integral
 *
 *
 *                phi
 *                 -
 *                | |
 *                |                   2
 * E(phi_\m)  =    |    sqrt( 1 - m sin t ) dt
 *                |
 *              | |
 *               -
 *                0
 *
 * of amplitude phi and modulus m, using the arithmetic -
 * geometric mean algorithm.
 *
 *
 *
 * ACCURACY:
 *
 * Tested at random arguments with phi in [-10, 10] and m in
 * [0, 1].
 *                      Relative error:
 * arithmetic   domain     # trials      peak         rms
 *    DEC        0,2         2000       1.9e-16     3.4e-17
 *    IEEE     -10,10      150000       3.3e-15     1.4e-16
 *
 *
 */

/*
Cephes Math Library Release 2.8:  June, 2000
Copyright 1984, 1987, 1993, 2000 by Stephen L. Moshier
*/

/*	Incomplete elliptic integral of second kind	*/
#include "mconf.h"
extern double PI, PIO2, MACHEP;
#ifdef ANSIPROT
extern double sqrt(double);
extern double fabs(double);
extern double log(double);
extern double sin(double x);
extern double tan(double x);
extern double atan(double);
extern double floor(double);
extern double ellpe(double);
extern double ellpk(double);
double ellie(double, double);
#else
double sqrt(), fabs(), log(), sin(), tan(), atan(), floor();
double ellpe(), ellpk(), ellie();
#endif

double ellie(phi, m) double phi, m;
{
  double a, b, c, e, temp;
  double lphi, t, E;
  int d, mod, npio2, sign;

  if (m == 0.0)
    return (phi);
  lphi = phi;
  npio2 = floor(lphi / PIO2);
  if (npio2 & 1)
    npio2 += 1;
  lphi = lphi - npio2 * PIO2;
  if (lphi < 0.0) {
    lphi = -lphi;
    sign = -1;
  } else {
    sign = 1;
  }
  a = 1.0 - m;
  E = ellpe(a);
  if (a == 0.0) {
    temp = sin(lphi);
    goto done;
  }
  t = tan(lphi);
  b = sqrt(a);
  /* Thanks to Brian Fitzgerald <fitzgb@mml0.meche.rpi.edu>
     for pointing out an instability near odd multiples of pi/2.  */
  if (fabs(t) > 10.0) {
    /* Transform the amplitude */
    e = 1.0 / (b * t);
    /* ... but avoid multiple recursions.  */
    if (fabs(e) < 10.0) {
      e = atan(e);
      temp = E + m * sin(lphi) * sin(e) - ellie(e, m);
      goto done;
    }
  }
  c = sqrt(m);
  a = 1.0;
  d = 1;
  e = 0.0;
  mod = 0;

  while (fabs(c / a) > MACHEP) {
    temp = b / a;
    lphi = lphi + atan(t * temp) + mod * PI;
    mod = (lphi + PIO2) / PI;
    t = t * (1.0 + temp) / (1.0 - temp * t * t);
    c = (a - b) / 2.0;
    temp = sqrt(a * b);
    a = (a + b) / 2.0;
    b = temp;
    d += d;
    e += c * sin(lphi);
  }

  temp = E / ellpk(1.0 - m);
  temp *= (atan(t) + mod * PI) / (d * a);
  temp += e;

done:

  if (sign < 0)
    temp = -temp;
  temp += npio2 * E;
  return (temp);
}