int
gsl_sf_bessel_In_scaled_e(int n, const double x, gsl_sf_result * result)
{
const double ax = fabs(x);
n = abs(n); /* I(-n, z) = I(n, z) */
/* CHECK_POINTER(result) */
if(n == 0) {
return gsl_sf_bessel_I0_scaled_e(x, result);
}
else if(n == 1) {
return gsl_sf_bessel_I1_scaled_e(x, result);
}
else if(x == 0.0) {
result->val = 0.0;
result->err = 0.0;
return GSL_SUCCESS;
}
else if(x*x < 10.0*(n+1.0)/M_E) {
gsl_sf_result t;
double ex = exp(-ax);
int stat_In = gsl_sf_bessel_IJ_taylor_e((double)n, ax, 1, 50, GSL_DBL_EPSILON, &t);
result->val = t.val * ex;
result->err = t.err * ex;
result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
if(x < 0.0 && GSL_IS_ODD(n)) result->val = -result->val;
return stat_In;
}
else if(n < 150 && ax < 1e7) {
gsl_sf_result I0_scaled;
int stat_I0 = gsl_sf_bessel_I0_scaled_e(ax, &I0_scaled);
double rat;
int stat_CF1 = gsl_sf_bessel_I_CF1_ser((double)n, ax, &rat);
double Ikp1 = rat * GSL_SQRT_DBL_MIN;
double Ik = GSL_SQRT_DBL_MIN;
double Ikm1;
int k;
for(k=n; k >= 1; k--) {
Ikm1 = Ikp1 + 2.0*k/ax * Ik;
Ikp1 = Ik;
Ik = Ikm1;
}
result->val = I0_scaled.val * (GSL_SQRT_DBL_MIN / Ik);
result->err = I0_scaled.err * (GSL_SQRT_DBL_MIN / Ik);
result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
if(x < 0.0 && GSL_IS_ODD(n)) result->val = -result->val;
return GSL_ERROR_SELECT_2(stat_I0, stat_CF1);
}
else if( GSL_MIN( 0.29/(n*n), 0.5/(n*n + x*x) ) < 0.5*GSL_ROOT3_DBL_EPSILON) {
int stat_as = gsl_sf_bessel_Inu_scaled_asymp_unif_e((double)n, ax, result);
if(x < 0.0 && GSL_IS_ODD(n)) result->val = -result->val;
return stat_as;
}
else {
const int nhi = 2 + (int) (1.2 / GSL_ROOT6_DBL_EPSILON);
gsl_sf_result r_Ikp1;
gsl_sf_result r_Ik;
int stat_a1 = gsl_sf_bessel_Inu_scaled_asymp_unif_e(nhi+1.0, ax, &r_Ikp1);
int stat_a2 = gsl_sf_bessel_Inu_scaled_asymp_unif_e((double)nhi, ax, &r_Ik);
double Ikp1 = r_Ikp1.val;
double Ik = r_Ik.val;
double Ikm1;
int k;
for(k=nhi; k > n; k--) {
Ikm1 = Ikp1 + 2.0*k/ax * Ik;
Ikp1 = Ik;
Ik = Ikm1;
}
result->val = Ik;
result->err = Ik * (r_Ikp1.err/r_Ikp1.val + r_Ik.err/r_Ik.val);
if(x < 0.0 && GSL_IS_ODD(n)) result->val = -result->val;
return GSL_ERROR_SELECT_2(stat_a1, stat_a2);
}
}
int gsl_sf_bessel_il_scaled_e(const int l, double x, gsl_sf_result * result)
{
double sgn = 1.0;
double ax = fabs(x);
if(x < 0.0) {
/* i_l(-x) = (-1)^l i_l(x) */
sgn = ( GSL_IS_ODD(l) ? -1.0 : 1.0 );
x = -x;
}
if(l < 0) {
DOMAIN_ERROR(result);
}
else if(x == 0.0) {
result->val = 0.0;
result->err = 0.0;
return GSL_SUCCESS;
}
else if(l == 0) {
gsl_sf_result il;
int stat_il = gsl_sf_bessel_i0_scaled_e(x, &il);
result->val = sgn * il.val;
result->err = il.err;
return stat_il;
}
else if(l == 1) {
gsl_sf_result il;
int stat_il = gsl_sf_bessel_i1_scaled_e(x, &il);
result->val = sgn * il.val;
result->err = il.err;
return stat_il;
}
else if(l == 2) {
gsl_sf_result il;
int stat_il = gsl_sf_bessel_i2_scaled_e(x, &il);
result->val = sgn * il.val;
result->err = il.err;
return stat_il;
}
else if(x*x < 10.0*(l+1.5)/M_E) {
gsl_sf_result b;
int stat = gsl_sf_bessel_IJ_taylor_e(l+0.5, x, 1, 50, GSL_DBL_EPSILON, &b);
double pre = exp(-ax) * sqrt((0.5*M_PI)/x);
result->val = sgn * pre * b.val;
result->err = pre * b.err;
result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
return stat;
}
else if(l < 150) {
gsl_sf_result i0_scaled;
int stat_i0 = gsl_sf_bessel_i0_scaled_e(ax, &i0_scaled);
double rat;
int stat_CF1 = bessel_il_CF1(l, ax, GSL_DBL_EPSILON, &rat);
double iellp1 = rat * GSL_SQRT_DBL_MIN;
double iell = GSL_SQRT_DBL_MIN;
double iellm1;
int ell;
for(ell = l; ell >= 1; ell--) {
iellm1 = iellp1 + (2*ell + 1)/x * iell;
iellp1 = iell;
iell = iellm1;
}
result->val = sgn * i0_scaled.val * (GSL_SQRT_DBL_MIN / iell);
result->err = i0_scaled.err * (GSL_SQRT_DBL_MIN / iell);
result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
return GSL_ERROR_SELECT_2(stat_i0, stat_CF1);
}
else if(GSL_MIN(0.29/(l*l+1.0), 0.5/(l*l+1.0+x*x)) < 0.5*GSL_ROOT3_DBL_EPSILON) {
int status = gsl_sf_bessel_Inu_scaled_asymp_unif_e(l + 0.5, x, result);
double pre = sqrt((0.5*M_PI)/x);
result->val *= sgn * pre;
result->err *= pre;
return status;
}
else {
/* recurse down from safe values */
double rt_term = sqrt((0.5*M_PI)/x);
const int LMAX = 2 + (int) (1.2 / GSL_ROOT6_DBL_EPSILON);
gsl_sf_result r_iellp1;
gsl_sf_result r_iell;
int stat_a1 = gsl_sf_bessel_Inu_scaled_asymp_unif_e(LMAX + 1 + 0.5, x, &r_iellp1);
int stat_a2 = gsl_sf_bessel_Inu_scaled_asymp_unif_e(LMAX + 0.5, x, &r_iell);
double iellp1 = r_iellp1.val;
double iell = r_iell.val;
double iellm1 = 0.0;
int ell;
iellp1 *= rt_term;
iell *= rt_term;
for(ell = LMAX; ell >= l+1; ell--) {
iellm1 = iellp1 + (2*ell + 1)/x * iell;
iellp1 = iell;
iell = iellm1;
}
result->val = sgn * iellm1;
result->err = fabs(result->val)*(GSL_DBL_EPSILON + fabs(r_iellp1.err/r_iellp1.val) + fabs(r_iell.err/r_iell.val));
result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
return GSL_ERROR_SELECT_2(stat_a1, stat_a2);
}
}
