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

/*							iv.c
 *
 *	Modified Bessel function of noninteger order
 *
 *
 *
 * SYNOPSIS:
 *
 * double v, x, y, iv();
 *
 * y = iv( v, x );
 *
 *
 *
 * DESCRIPTION:
 *
 * Returns modified Bessel function of order v of the
 * argument.  If x is negative, v must be integer valued.
 *
 * The function is defined as Iv(x) = Jv( ix ).  It is
 * here computed in terms of the confluent hypergeometric
 * function, according to the formula
 *
 *              v  -x
 * Iv(x) = (x/2)  e   hyperg( v+0.5, 2v+1, 2x ) / gamma(v+1)
 *
 * If v is a negative integer, then v is replaced by -v.
 *
 *
 * ACCURACY:
 *
 * Tested at random points (v, x), with v between 0 and
 * 30, x between 0 and 28.
 *                      Relative error:
 * arithmetic   domain     # trials      peak         rms
 *    DEC       0,30          2000      3.1e-15     5.4e-16
 *    IEEE      0,30         10000      1.7e-14     2.7e-15
 *
 * Accuracy is diminished if v is near a negative integer.
 *
 * See also hyperg.c.
 *
 */
/*							iv.c	*/
/*	Modified Bessel function of noninteger order		*/
/* If x < 0, then v must be an integer. */

/*
Cephes Math Library Release 2.8:  June, 2000
Copyright 1984, 1987, 1988, 2000 by Stephen L. Moshier
*/

#include "mconf.h"
#ifdef ANSIPROT
extern double hyperg(double, double, double);
extern double exp(double);
extern double gamma(double);
extern double log(double);
extern double fabs(double);
extern double floor(double);
#else
double hyperg(), exp(), gamma(), log(), fabs(), floor();
#endif
extern double MACHEP, MAXNUM;

double iv(v, x) double v, x;
{
  int sign;
  double t, ax;

  /* If v is a negative integer, invoke symmetry */
  t = floor(v);
  if (v < 0.0) {
    if (t == v) {
      v = -v; /* symmetry */
      t = -t;
    }
  }
  /* If x is negative, require v to be an integer */
  sign = 1;
  if (x < 0.0) {
    if (t != v) {
      mtherr("iv", DOMAIN);
      return (0.0);
    }
    if (v != 2.0 * floor(v / 2.0))
      sign = -1;
  }

  /* Avoid logarithm singularity */
  if (x == 0.0) {
    if (v == 0.0)
      return (1.0);
    if (v < 0.0) {
      mtherr("iv", OVERFLOW);
      return (MAXNUM);
    } else
      return (0.0);
  }

  ax = fabs(x);
  t = v * log(0.5 * ax) - x;
  t = sign * exp(t) / gamma(v + 1.0);
  ax = v + 0.5;
  return (t * hyperg(ax, 2.0 * ax, 2.0 * x));
}