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

/*							yn.c
 *
 *	Bessel function of second kind of integer order
 *
 *
 *
 * SYNOPSIS:
 *
 * double x, y, yn();
 * int n;
 *
 * y = yn( n, x );
 *
 *
 *
 * DESCRIPTION:
 *
 * Returns Bessel function of order n, where n is a
 * (possibly negative) integer.
 *
 * The function is evaluated by forward recurrence on
 * n, starting with values computed by the routines
 * y0() and y1().
 *
 * If n = 0 or 1 the routine for y0 or y1 is called
 * directly.
 *
 *
 *
 * ACCURACY:
 *
 *
 *                      Absolute error, except relative
 *                      when y > 1:
 * arithmetic   domain     # trials      peak         rms
 *    DEC       0, 30        2200       2.9e-16     5.3e-17
 *    IEEE      0, 30       30000       3.4e-15     4.3e-16
 *
 *
 * ERROR MESSAGES:
 *
 *   message         condition      value returned
 * yn singularity   x = 0              MAXNUM
 * yn overflow                         MAXNUM
 *
 * Spot checked against tables for x, n between 0 and 100.
 *
 */

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

#include "mconf.h"
#ifdef ANSIPROT
extern double y0(double);
extern double y1(double);
extern double log(double);
#else
double y0(), y1(), log();
#endif
extern double MAXNUM, MAXLOG;

double yn(n, x) int n;
double x;
{
  double an, anm1, anm2, r;
  int k, sign;

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

  if (n == 0)
    return (sign * y0(x));
  if (n == 1)
    return (sign * y1(x));

  /* test for overflow */
  if (x <= 0.0) {
    mtherr("yn", SING);
    return (-MAXNUM);
  }

  /* forward recurrence on n */

  anm2 = y0(x);
  anm1 = y1(x);
  k = 1;
  r = 2 * k;
  do {
    an = r * anm1 / x - anm2;
    anm2 = anm1;
    anm1 = an;
    r += 2.0;
    ++k;
  } while (k < n);

  return (sign * an);
}