-
-
-#include "config.h"
-
-#ifdef HAVE_MATH_H
-#include <math.h>
-#endif
-
-#include "definitions.h"
-#include "gsl_types.h"
-#include "gsl_definitions.h"
-#include "exit_codes.h"
-
-/* This part of atlc is a copy from the code in the GPL'ed
-GNU Scientific Library, gsl. By including this code, it saves
-the user having to like with gsl. */
-
-const double gsl_prec_eps[3];
-
-
-
-double gsl_sf_ellint_Kcomp(double k, gsl_mode_t mode)
-{
- gsl_sf_result result;
- gsl_sf_ellint_Kcomp_e(k, mode, &result);
- return result.val;
-}
-
-
-/* [Carlson, Numer. Math. 33 (1979) 1, (4.5)] */
-int gsl_sf_ellint_Kcomp_e(double k, gsl_mode_t mode, gsl_sf_result * result)
-{
- int return_val=0;
- if(k*k >= 1.0) {
- exit_with_msg_and_exit_code("domain error in gsl_sf_Kcomp_e", DOMAIN_ERROR);
- }
- else if(k*k >= 1.0 - GSL_SQRT_DBL_EPSILON) {
- /* [Abramowitz+Stegun, 17.3.33] */
- const double y = 1.0 - k*k;
- const double a[] = { 1.38629436112, 0.09666344259, 0.03590092383 };
- const double b[] = { 0.5, 0.12498593597, 0.06880248576 };
- const double ta = a[0] + y*(a[1] + y*a[2]);
- const double tb = -log(y) * (b[0] * y*(b[1] + y*b[2]));
- result->val = ta + tb;
- result->err = 2.0 * GSL_DBL_EPSILON * result->val;
- return_val=GSL_SUCCESS;
- }
- else {
- /* This was previously computed as,
-
- return gsl_sf_ellint_RF_e(0.0, 1.0 - k*k, 1.0, mode, result);
-
- but this underestimated the total error for small k, since the
- argument y=1-k^2 is not exact (there is an absolute error of
- GSL_DBL_EPSILON near y=0 due to cancellation in the subtraction).
- Taking the singular behavior of -log(y) above gives an error
- of 0.5*epsilon/y near y=0. (BJG) */
-
- double y = 1.0 - k*k;
- int status = gsl_sf_ellint_RF_e(0.0, y, 1.0, mode, result);
- result->err += 0.5 * GSL_DBL_EPSILON / y;
- return_val=status ;
- }
- return(return_val);
-}
-
-int gsl_sf_ellint_RF_e(double x, double y, double z, gsl_mode_t mode, gsl_sf_result * result)
-{
- int return_val=0;
- const double lolim = 5.0 * GSL_DBL_MIN;
- const double uplim = 0.2 * GSL_DBL_MAX;
- const gsl_prec_t goal = GSL_MODE_PREC(mode);
- const double errtol = ( goal == GSL_PREC_DOUBLE ? 0.001 : 0.03 );
- const double prec = gsl_prec_eps[goal];
-
- if(x < 0.0 || y < 0.0 || z < 0.0) {
- exit_with_msg_and_exit_code("domain error in gsl_sf_ellint_RF_e", DOMAIN_ERROR);
- }
- else if(x+y < lolim || x+z < lolim || y+z < lolim) {
- exit_with_msg_and_exit_code("domain error in gsl_sf_ellint_RF_e", DOMAIN_ERROR);
- }
- else if(locMAX3(x,y,z) < uplim) {
- const double c1 = 1.0 / 24.0;
- const double c2 = 3.0 / 44.0;
- const double c3 = 1.0 / 14.0;
- double xn = x;
- double yn = y;
- double zn = z;
- double mu, xndev, yndev, zndev, e2, e3, s;
- while(1) {
- double epslon, lamda;
- double xnroot, ynroot, znroot;
- mu = (xn + yn + zn) / 3.0;
- xndev = 2.0 - (mu + xn) / mu;
- yndev = 2.0 - (mu + yn) / mu;
- zndev = 2.0 - (mu + zn) / mu;
- epslon = locMAX3(fabs(xndev), fabs(yndev), fabs(zndev));
- if (epslon < errtol) break;
- xnroot = sqrt(xn);
- ynroot = sqrt(yn);
- znroot = sqrt(zn);
- lamda = xnroot * (ynroot + znroot) + ynroot * znroot;
- xn = (xn + lamda) * 0.25;
- yn = (yn + lamda) * 0.25;
- zn = (zn + lamda) * 0.25;
- }
- e2 = xndev * yndev - zndev * zndev;
- e3 = xndev * yndev * zndev;
- s = 1.0 + (c1 * e2 - 0.1 - c2 * e3) * e2 + c3 * e3;
- result->val = s / sqrt(mu);
- result->err = prec * fabs(result->val);
- return_val= GSL_SUCCESS;
- }
- else {
- exit_with_msg_and_exit_code("domain error in gsl_sf_ellint_RF_e", DOMAIN_ERROR);
- }
- return(return_val);
-}
-
-
-/* static double locMAX3(double x, double y, double z) */
-double locMAX3(double x, double y, double z)
-{
- double xy = GSL_MAX(x, y);
- return GSL_MAX(xy, z);
-}
-
-
-#define EVAL_RESULT(fn) \
- gsl_sf_result result; \
- int status = fn; \
- if (status != GSL_SUCCESS) { \
- GSL_ERROR_VAL(#fn, status, result.val); \
- } ; \
-return result.val;
-