Merge commit 'upstream/4.6.1'

[debian/atlc] / src / gsl_sf_ellint_Kcomp.c

diff --git a/src/gsl_sf_ellint_Kcomp.c b/src/gsl_sf_ellint_Kcomp.c
new file mode 100644 (file)
index 0000000..4fcdde3
--- /dev/null
+++ b/src/gsl_sf_ellint_Kcomp.c
@@ -0,0 +1,136 @@
+
+
+#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;
+