summaryrefslogtreecommitdiff
path: root/gsl-1.9/specfunc/bessel_I1.c
diff options
context:
space:
mode:
Diffstat (limited to 'gsl-1.9/specfunc/bessel_I1.c')
-rw-r--r--gsl-1.9/specfunc/bessel_I1.c258
1 files changed, 258 insertions, 0 deletions
diff --git a/gsl-1.9/specfunc/bessel_I1.c b/gsl-1.9/specfunc/bessel_I1.c
new file mode 100644
index 0000000..18b2c0e
--- /dev/null
+++ b/gsl-1.9/specfunc/bessel_I1.c
@@ -0,0 +1,258 @@
+/* specfunc/bessel_I1.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_bessel.h>
+
+#include "error.h"
+
+#include "chebyshev.h"
+#include "cheb_eval.c"
+
+#define ROOT_EIGHT (2.0*M_SQRT2)
+
+
+/*-*-*-*-*-*-*-*-*-*-*-* Private Section *-*-*-*-*-*-*-*-*-*-*-*/
+
+/* based on SLATEC besi1(), besi1e() */
+
+/* chebyshev expansions
+
+ series for bi1 on the interval 0. to 9.00000d+00
+ with weighted error 2.40e-17
+ log weighted error 16.62
+ significant figures required 16.23
+ decimal places required 17.14
+
+ series for ai1 on the interval 1.25000d-01 to 3.33333d-01
+ with weighted error 6.98e-17
+ log weighted error 16.16
+ significant figures required 14.53
+ decimal places required 16.82
+
+ series for ai12 on the interval 0. to 1.25000d-01
+ with weighted error 3.55e-17
+ log weighted error 16.45
+ significant figures required 14.69
+ decimal places required 17.12
+*/
+
+static double bi1_data[11] = {
+ -0.001971713261099859,
+ 0.407348876675464810,
+ 0.034838994299959456,
+ 0.001545394556300123,
+ 0.000041888521098377,
+ 0.000000764902676483,
+ 0.000000010042493924,
+ 0.000000000099322077,
+ 0.000000000000766380,
+ 0.000000000000004741,
+ 0.000000000000000024
+};
+static cheb_series bi1_cs = {
+ bi1_data,
+ 10,
+ -1, 1,
+ 10
+};
+
+static double ai1_data[21] = {
+ -0.02846744181881479,
+ -0.01922953231443221,
+ -0.00061151858579437,
+ -0.00002069971253350,
+ 0.00000858561914581,
+ 0.00000104949824671,
+ -0.00000029183389184,
+ -0.00000001559378146,
+ 0.00000001318012367,
+ -0.00000000144842341,
+ -0.00000000029085122,
+ 0.00000000012663889,
+ -0.00000000001664947,
+ -0.00000000000166665,
+ 0.00000000000124260,
+ -0.00000000000027315,
+ 0.00000000000002023,
+ 0.00000000000000730,
+ -0.00000000000000333,
+ 0.00000000000000071,
+ -0.00000000000000006
+};
+static cheb_series ai1_cs = {
+ ai1_data,
+ 20,
+ -1, 1,
+ 11
+};
+
+static double ai12_data[22] = {
+ 0.02857623501828014,
+ -0.00976109749136147,
+ -0.00011058893876263,
+ -0.00000388256480887,
+ -0.00000025122362377,
+ -0.00000002631468847,
+ -0.00000000383538039,
+ -0.00000000055897433,
+ -0.00000000001897495,
+ 0.00000000003252602,
+ 0.00000000001412580,
+ 0.00000000000203564,
+ -0.00000000000071985,
+ -0.00000000000040836,
+ -0.00000000000002101,
+ 0.00000000000004273,
+ 0.00000000000001041,
+ -0.00000000000000382,
+ -0.00000000000000186,
+ 0.00000000000000033,
+ 0.00000000000000028,
+ -0.00000000000000003
+};
+static cheb_series ai12_cs = {
+ ai12_data,
+ 21,
+ -1, 1,
+ 9
+};
+
+
+/*-*-*-*-*-*-*-*-*-*-*-* Functions with Error Codes *-*-*-*-*-*-*-*-*-*-*-*/
+
+int gsl_sf_bessel_I1_scaled_e(const double x, gsl_sf_result * result)
+{
+ const double xmin = 2.0 * GSL_DBL_MIN;
+ const double x_small = ROOT_EIGHT * GSL_SQRT_DBL_EPSILON;
+ const double y = fabs(x);
+
+ /* CHECK_POINTER(result) */
+
+ if(y == 0.0) {
+ result->val = 0.0;
+ result->err = 0.0;
+ return GSL_SUCCESS;
+ }
+ else if(y < xmin) {
+ UNDERFLOW_ERROR(result);
+ }
+ else if(y < x_small) {
+ result->val = 0.5*x;
+ result->err = 0.0;
+ return GSL_SUCCESS;
+ }
+ else if(y <= 3.0) {
+ const double ey = exp(-y);
+ gsl_sf_result c;
+ cheb_eval_e(&bi1_cs, y*y/4.5-1.0, &c);
+ result->val = x * ey * (0.875 + c.val);
+ result->err = ey * c.err + y * GSL_DBL_EPSILON * fabs(result->val);
+ result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
+ return GSL_SUCCESS;
+ }
+ else if(y <= 8.0) {
+ const double sy = sqrt(y);
+ gsl_sf_result c;
+ double b;
+ double s;
+ cheb_eval_e(&ai1_cs, (48.0/y-11.0)/5.0, &c);
+ b = (0.375 + c.val) / sy;
+ s = (x > 0.0 ? 1.0 : -1.0);
+ result->val = s * b;
+ result->err = c.err / sy;
+ result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
+ return GSL_SUCCESS;
+ }
+ else {
+ const double sy = sqrt(y);
+ gsl_sf_result c;
+ double b;
+ double s;
+ cheb_eval_e(&ai12_cs, 16.0/y-1.0, &c);
+ b = (0.375 + c.val) / sy;
+ s = (x > 0.0 ? 1.0 : -1.0);
+ result->val = s * b;
+ result->err = c.err / sy;
+ result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
+ return GSL_SUCCESS;
+ }
+}
+
+
+int gsl_sf_bessel_I1_e(const double x, gsl_sf_result * result)
+{
+ const double xmin = 2.0 * GSL_DBL_MIN;
+ const double x_small = ROOT_EIGHT * GSL_SQRT_DBL_EPSILON;
+ const double y = fabs(x);
+
+ /* CHECK_POINTER(result) */
+
+ if(y == 0.0) {
+ result->val = 0.0;
+ result->err = 0.0;
+ return GSL_SUCCESS;
+ }
+ else if(y < xmin) {
+ UNDERFLOW_ERROR(result);
+ }
+ else if(y < x_small) {
+ result->val = 0.5*x;
+ result->err = 0.0;
+ return GSL_SUCCESS;
+ }
+ else if(y <= 3.0) {
+ gsl_sf_result c;
+ cheb_eval_e(&bi1_cs, y*y/4.5-1.0, &c);
+ result->val = x * (0.875 + c.val);
+ result->err = y * c.err;
+ result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
+ return GSL_SUCCESS;
+ }
+ else if(y < GSL_LOG_DBL_MAX) {
+ const double ey = exp(y);
+ gsl_sf_result I1_scaled;
+ gsl_sf_bessel_I1_scaled_e(x, &I1_scaled);
+ result->val = ey * I1_scaled.val;
+ result->err = ey * I1_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);
+ }
+}
+
+/*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/
+
+#include "eval.h"
+
+double gsl_sf_bessel_I1_scaled(const double x)
+{
+ EVAL_RESULT(gsl_sf_bessel_I1_scaled_e(x, &result));
+}
+
+double gsl_sf_bessel_I1(const double x)
+{
+ EVAL_RESULT(gsl_sf_bessel_I1_e(x, &result));
+}
generated by cgit v1.2.3 (git 2.25.1) at 2024-05-01 04:36:23 +0000