int gsl_sf_bessel_I0_e(const double x, gsl_sf_result * result)
{
double y = fabs(x);
/* CHECK_POINTER(result) */
if(y < 2.0 * GSL_SQRT_DBL_EPSILON) {
result->val = 1.0;
result->err = 0.5*y*y;
return GSL_SUCCESS;
}
else if(y <= 3.0) {
gsl_sf_result c;
cheb_eval_e(&bi0_cs, y*y/4.5-1.0, &c);
result->val = 2.75 + c.val;
result->err = GSL_DBL_EPSILON * (2.75 + fabs(c.val));
result->err += c.err;
result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
return GSL_SUCCESS;
}
else if(y < GSL_LOG_DBL_MAX - 1.0) {
const double ey = exp(y);
gsl_sf_result b_scaled;
gsl_sf_bessel_I0_scaled_e(x, &b_scaled);
result->val = ey * b_scaled.val;
result->err = ey * b_scaled.err + y*GSL_DBL_EPSILON*fabs(result->val);
result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
return GSL_SUCCESS;
}
else {
OVERFLOW_ERROR(result);
}
}
int
gsl_sf_bessel_In_scaled_array(const int nmin, const int nmax, const double x, double * result_array)
{
/* CHECK_POINTER(result_array) */
if(nmax < nmin || nmin < 0) {
int j;
for(j=0; j<=nmax-nmin; j++) result_array[j] = 0.0;
GSL_ERROR ("domain error", GSL_EDOM);
}
else if(x == 0.0) {
int j;
for(j=0; j<=nmax-nmin; j++) result_array[j] = 0.0;
if(nmin == 0) result_array[0] = 1.0;
return GSL_SUCCESS;
}
else if(nmax == 0) {
gsl_sf_result I0_scaled;
int stat = gsl_sf_bessel_I0_scaled_e(x, &I0_scaled);
result_array[0] = I0_scaled.val;
return stat;
}
else {
const double ax = fabs(x);
const double two_over_x = 2.0/ax;
/* starting values */
gsl_sf_result r_Inp1;
gsl_sf_result r_In;
int stat_0 = gsl_sf_bessel_In_scaled_e(nmax+1, ax, &r_Inp1);
int stat_1 = gsl_sf_bessel_In_scaled_e(nmax, ax, &r_In);
double Inp1 = r_Inp1.val;
double In = r_In.val;
double Inm1;
int n;
for(n=nmax; n>=nmin; n--) {
result_array[n-nmin] = In;
Inm1 = Inp1 + n * two_over_x * In;
Inp1 = In;
In = Inm1;
}
/* deal with signs */
if(x < 0.0) {
for(n=nmin; n<=nmax; n++) {
if(GSL_IS_ODD(n)) result_array[n-nmin] = -result_array[n-nmin];
}
}
return GSL_ERROR_SELECT_2(stat_0, stat_1);
}
}
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);
}
}
