/* Author:  G. Jungman
 * RCS:     $Id: bessel_Y1.c,v 1.23 1999/10/12 04:07:44 jungman Exp $
 */
#include <config.h>
#include <gsl_math.h>
#include <gsl_errno.h>
#include "bessel.h"
#include "bessel_amp_phase.h"
#include "gsl_sf_chebyshev.h"
#include "gsl_sf_trig.h"
#include "gsl_sf_bessel.h"


/*-*-*-*-*-*-*-*-*-*-*-* Private Section *-*-*-*-*-*-*-*-*-*-*-*/

/* based on SLATEC besy1, 1977 version, w. fullerton */

/* chebyshev expansions

 series for by1        on the interval  0.	    to  1.60000d+01
					with weighted error   1.87e-18
					 log weighted error  17.73
			       significant figures required  17.83
				    decimal places required  18.30
*/

static double by1_data[14] = {
  0.03208047100611908629,
  1.262707897433500450,
  0.00649996189992317500,
 -0.08936164528860504117,
  0.01325088122175709545,
 -0.00089790591196483523,
  0.00003647361487958306,
 -0.00000100137438166600,
  0.00000001994539657390,
 -0.00000000030230656018,
  0.00000000000360987815,
 -0.00000000000003487488,
  0.00000000000000027838,
 -0.00000000000000000186
};
static gsl_sf_cheb_series by1_cs = {
  by1_data,
  13,
  -1, 1,
  (double *)0,
  (double *)0,
  10
};


/*-*-*-*-*-*-*-*-*-*-*-* (semi)Private Implementations *-*-*-*-*-*-*-*-*-*-*-*/

int gsl_sf_bessel_Y1_impl(const double x, gsl_sf_result * result)
{
  const double two_over_pi = 2.0/M_PI;
  const double xmin = 1.571*GSL_DBL_MIN; /*exp ( amax1(alog(r1mach(1)), -alog(r1mach(2)))+.01) */
  const double x_small = 2.0 * GSL_SQRT_DBL_EPSILON;
  const double xmax    = 1.0/GSL_DBL_EPSILON;

  if(result == 0) {
    return GSL_EFAULT;
  }  
  else if(x <= 0.0) {
    result->val = 0.0;
    result->err = 0.0;
    return GSL_EDOM;
  }
  else if(x < xmin) {
    result->val = 0.0; /* FIXME: should be Inf */
    result->err = 0.0;
    return GSL_EOVRFLW;
  }
  else if(x < x_small) {
    const double lnterm = log(0.5*x);
    gsl_sf_result J1;
    gsl_sf_result c;
    int status = gsl_sf_bessel_J1_impl(x, &J1);
    gsl_sf_cheb_eval_impl(&by1_cs, -1.0, &c);
    result->val = two_over_pi * lnterm * J1.val + (0.5 + c.val)/x;
    result->err = fabs(lnterm) * (fabs(GSL_DBL_EPSILON * J1.val) + J1.err) + c.err/x;
    return status;
  }
  else if(x < 4.0) {
    const double lnterm = log(0.5*x);
    int status;
    gsl_sf_result J1;
    gsl_sf_result c;
    gsl_sf_cheb_eval_impl(&by1_cs, 0.125*x*x-1.0, &c);
    status = gsl_sf_bessel_J1_impl(x, &J1);
    result->val = two_over_pi * lnterm * J1.val + (0.5 + c.val)/x;
    result->err = fabs(lnterm) * (fabs(GSL_DBL_EPSILON * J1.val) + J1.err) + c.err/x;
    return status;
  }
  else if(x < xmax) {
    const double z = 32.0/(x*x) - 1.0;
    gsl_sf_result ca;
    gsl_sf_result ct;
    gsl_sf_result cp;
    const int stat_ca = gsl_sf_cheb_eval_impl(&_bessel_amp_phase_bm1_cs,  z, &ca);
    const int stat_ct = gsl_sf_cheb_eval_impl(&_bessel_amp_phase_bth1_cs, z, &ct);
    const int stat_cp = gsl_sf_bessel_cos_pi4_impl(x, ct.val/x, &cp);
    const double sqrtx = sqrt(x);
    const double ampl  = (0.75 + ca.val) / sqrtx;
    result->val  = -ampl * cp.val;
    result->err  = fabs(cp.val) * ca.err/sqrtx + fabs(ampl) * cp.err;
    result->err += GSL_DBL_EPSILON * fabs(result->val);
    return GSL_ERROR_SELECT_3(stat_ca, stat_ct, stat_cp);
  }
  else {
    result->val = 0.0;
    result->err = 0.0;
    return GSL_EUNDRFLW;
  }
}


/*-*-*-*-*-*-*-*-*-*-*-* Functions w/ Error Handling *-*-*-*-*-*-*-*-*-*-*-*/

int gsl_sf_bessel_Y1_e(const double x, gsl_sf_result * result)
{
  int status = gsl_sf_bessel_Y1_impl(x, result);
  if(status != GSL_SUCCESS) {
    GSL_ERROR("gsl_sf_bessel_Y1_e", status);
  }
  return status;
}