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diff --git a/gsl-1.9/specfunc/bessel_i.c b/gsl-1.9/specfunc/bessel_i.c
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+/* specfunc/bessel_i.c
+ *
+ * Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman
+ *
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or (at
+ * your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ * General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+/* Author: G. Jungman */
+
+#include <config.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_sf_pow_int.h>
+#include <gsl/gsl_sf_bessel.h>
+
+#include "error.h"
+
+#include "bessel.h"
+
+
+/* i_{l+1}/i_l
+ */
+static
+int
+bessel_il_CF1(const int l, const double x, const double threshold, double * ratio)
+{
+ const int kmax = 2000;
+ double tk = 1.0;
+ double sum = 1.0;
+ double rhok = 0.0;
+ int k;
+
+ for(k=1; k<=kmax; k++) {
+ double ak = (x/(2.0*l+1.0+2.0*k)) * (x/(2.0*l+3.0+2.0*k));
+ rhok = -ak*(1.0 + rhok)/(1.0 + ak*(1.0 + rhok));
+ tk *= rhok;
+ sum += tk;
+ if(fabs(tk/sum) < threshold) break;
+ }
+
+ *ratio = x/(2.0*l+3.0) * sum;
+
+ if(k == kmax)
+ GSL_ERROR ("error", GSL_EMAXITER);
+ else
+ return GSL_SUCCESS;
+}
+
+
+/*-*-*-*-*-*-*-*-*-*-*-* Functions with Error Codes *-*-*-*-*-*-*-*-*-*-*-*/
+
+int gsl_sf_bessel_i0_scaled_e(const double x, gsl_sf_result * result)
+{
+ double ax = fabs(x);
+
+ /* CHECK_POINTER(result) */
+
+ if(x == 0.0) {
+ result->val = 1.0;
+ result->err = 0.0;
+ return GSL_SUCCESS;
+ }
+ else if(ax < 0.2) {
+ const double eax = exp(-ax);
+ const double y = ax*ax;
+ const double c1 = 1.0/6.0;
+ const double c2 = 1.0/120.0;
+ const double c3 = 1.0/5040.0;
+ const double c4 = 1.0/362880.0;
+ const double c5 = 1.0/39916800.0;
+ const double sum = 1.0 + y*(c1 + y*(c2 + y*(c3 + y*(c4 + y*c5))));
+ result->val = eax * sum;
+ result->err = 2.0 * GSL_DBL_EPSILON * result->val;
+ }
+ else if(ax < -0.5*GSL_LOG_DBL_EPSILON) {
+ result->val = (1.0 - exp(-2.0*ax))/(2.0*ax);
+ result->err = 2.0 * GSL_DBL_EPSILON * result->val;
+ }
+ else {
+ result->val = 1.0/(2.0*ax);
+ result->err = 2.0 * GSL_DBL_EPSILON * result->val;
+ }
+ return GSL_SUCCESS;
+}
+
+
+int gsl_sf_bessel_i1_scaled_e(const double x, gsl_sf_result * result)
+{
+ double ax = fabs(x);
+
+ /* CHECK_POINTER(result) */
+
+ if(x == 0.0) {
+ result->val = 0.0;
+ result->err = 0.0;
+ return GSL_SUCCESS;
+ }
+ else if(ax < 3.0*GSL_DBL_MIN) {
+ UNDERFLOW_ERROR(result);
+ }
+ else if(ax < 0.25) {
+ const double eax = exp(-ax);
+ const double y = x*x;
+ const double c1 = 1.0/10.0;
+ const double c2 = 1.0/280.0;
+ const double c3 = 1.0/15120.0;
+ const double c4 = 1.0/1330560.0;
+ const double c5 = 1.0/172972800.0;
+ const double sum = 1.0 + y*(c1 + y*(c2 + y*(c3 + y*(c4 + y*c5))));
+ result->val = eax * x/3.0 * sum;
+ result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val);
+ return GSL_SUCCESS;
+ }
+ else {
+ double ex = exp(-2.0*ax);
+ result->val = 0.5 * (ax*(1.0+ex) - (1.0-ex)) / (ax*ax);
+ result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val);
+ if(x < 0.0) result->val = -result->val;
+ return GSL_SUCCESS;
+ }
+}
+
+
+int gsl_sf_bessel_i2_scaled_e(const double x, gsl_sf_result * result)
+{
+ double ax = fabs(x);
+
+ /* CHECK_POINTER(result) */
+
+ if(x == 0.0) {
+ result->val = 0.0;
+ result->err = 0.0;
+ return GSL_SUCCESS;
+ }
+ else if(ax < 4.0*GSL_SQRT_DBL_MIN) {
+ UNDERFLOW_ERROR(result);
+ }
+ else if(ax < 0.25) {
+ const double y = x*x;
+ const double c1 = 1.0/14.0;
+ const double c2 = 1.0/504.0;
+ const double c3 = 1.0/33264.0;
+ const double c4 = 1.0/3459456.0;
+ const double c5 = 1.0/518918400.0;
+ const double sum = 1.0 + y*(c1 + y*(c2 + y*(c3 + y*(c4 + y*c5))));
+ const double pre = exp(-ax) * x*x/15.0;
+ result->val = pre * sum;
+ result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val);
+ return GSL_SUCCESS;
+ }
+ else {
+ double ex = exp(-2.0*ax);
+ double x2 = x*x;
+ result->val = 0.5 * ((3.0+x2)*(1.0-ex) - 3.0*ax*(1.0+ex))/(ax*ax*ax);
+ result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val);
+ return GSL_SUCCESS;
+ }
+}
+
+
+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 = ( l == 0 ? 1.0 : 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);
+ }
+}
+
+
+int gsl_sf_bessel_il_scaled_array(const int lmax, const double x, double * result_array)
+{
+ if(x == 0.0) {
+ int ell;
+ result_array[0] = 1.0;
+ for (ell = lmax; ell >= 1; ell--) {
+ result_array[ell] = 0.0;
+ };
+ return GSL_SUCCESS;
+ } else {
+ int ell;
+ gsl_sf_result r_iellp1;
+ gsl_sf_result r_iell;
+ int stat_0 = gsl_sf_bessel_il_scaled_e(lmax+1, x, &r_iellp1);
+ int stat_1 = gsl_sf_bessel_il_scaled_e(lmax, x, &r_iell);
+ double iellp1 = r_iellp1.val;
+ double iell = r_iell.val;
+ double iellm1;
+ result_array[lmax] = iell;
+ for(ell = lmax; ell >= 1; ell--) {
+ iellm1 = iellp1 + (2*ell + 1)/x * iell;
+ iellp1 = iell;
+ iell = iellm1;
+ result_array[ell-1] = iellm1;
+ }
+ return GSL_ERROR_SELECT_2(stat_0, stat_1);
+ }
+}
+
+
+/*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/
+
+#include "eval.h"
+
+double gsl_sf_bessel_i0_scaled(const double x)
+{
+ EVAL_RESULT(gsl_sf_bessel_i0_scaled_e(x, &result));
+}
+
+double gsl_sf_bessel_i1_scaled(const double x)
+{
+ EVAL_RESULT(gsl_sf_bessel_i1_scaled_e(x, &result));
+}
+
+double gsl_sf_bessel_i2_scaled(const double x)
+{
+ EVAL_RESULT(gsl_sf_bessel_i2_scaled_e(x, &result));
+}
+
+double gsl_sf_bessel_il_scaled(const int l, const double x)
+{
+ EVAL_RESULT(gsl_sf_bessel_il_scaled_e(l, x, &result));
+}
+
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