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

/*							jn.c
 *
 *	Bessel function of integer order
 *
 *
 *
 * SYNOPSIS:
 *
 * int n;
 * double x, y, jn();
 *
 * y = jn( n, x );
 *
 *
 *
 * DESCRIPTION:
 *
 * Returns Bessel function of order n, where n is a
 * (possibly negative) integer.
 *
 * The ratio of jn(x) to j0(x) is computed by backward
 * recurrence.  First the ratio jn/jn-1 is found by a
 * continued fraction expansion.  Then the recurrence
 * relating successive orders is applied until j0 or j1 is
 * reached.
 *
 * If n = 0 or 1 the routine for j0 or j1 is called
 * directly.
 *
 *
 *
 * ACCURACY:
 *
 *                      Absolute error:
 * arithmetic   range      # trials      peak         rms
 *    DEC       0, 30        5500       6.9e-17     9.3e-18
 *    IEEE      0, 30        5000       4.4e-16     7.9e-17
 *
 *
 * Not suitable for large n or x. Use jv() instead.
 *
 */

/*							jn.c
Cephes Math Library Release 2.8:  June, 2000
Copyright 1984, 1987, 2000 by Stephen L. Moshier
*/
#include "mconf.h"
#ifdef ANSIPROT
extern double fabs(double);
extern double j0(double);
extern double j1(double);
#else
double fabs(), j0(), j1();
#endif
extern double MACHEP;

double jn(n, x) int n;
double x;
{
  double pkm2, pkm1, pk, xk, r, ans;
  int k, sign;

  if (n < 0) {
    n = -n;
    if ((n & 1) == 0) /* -1**n */
      sign = 1;
    else
      sign = -1;
  } else
    sign = 1;

  if (x < 0.0) {
    if (n & 1)
      sign = -sign;
    x = -x;
  }

  if (n == 0)
    return (sign * j0(x));
  if (n == 1)
    return (sign * j1(x));
  if (n == 2)
    return (sign * (2.0 * j1(x) / x - j0(x)));

  if (x < MACHEP)
    return (0.0);

/* continued fraction */
#ifdef DEC
  k = 56;
#else
  k = 53;
#endif

  pk = 2 * (n + k);
  ans = pk;
  xk = x * x;

  do {
    pk -= 2.0;
    ans = pk - (xk / ans);
  } while (--k > 0);
  ans = x / ans;

  /* backward recurrence */

  pk = 1.0;
  pkm1 = 1.0 / ans;
  k = n - 1;
  r = 2 * k;

  do {
    pkm2 = (pkm1 * r - pk * x) / x;
    pk = pkm1;
    pkm1 = pkm2;
    r -= 2.0;
  } while (--k > 0);

  if (fabs(pk) > fabs(pkm1))
    ans = j1(x) / pk;
  else
    ans = j0(x) / pkm1;
  return (sign * ans);
}