1 files changed, 110 insertions, 0 deletions
diff --git a/gsl-1.9/poly/solve_cubic.c b/gsl-1.9/poly/solve_cubic.c
new file mode 100644
index 0000000..979e56a
--- /dev/null
+++ b/gsl-1.9/poly/solve_cubic.c
@@ -0,0 +1,110 @@
+/* poly/solve_cubic.c
+ * 
+ * Copyright (C) 1996, 1997, 1998, 1999, 2000 Brian Gough
+ * 
+ * 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.
+ */
+
+/* solve_cubic.c - finds the real roots of x^3 + a x^2 + b x + c = 0 */
+
+#include <config.h>
+#include <math.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_poly.h>
+
+#define SWAP(a,b) do { double tmp = b ; b = a ; a = tmp ; } while(0)
+
+int 
+gsl_poly_solve_cubic (double a, double b, double c, 
+                      double *x0, double *x1, double *x2)
+{
+  double q = (a * a - 3 * b);
+  double r = (2 * a * a * a - 9 * a * b + 27 * c);
+
+  double Q = q / 9;
+  double R = r / 54;
+
+  double Q3 = Q * Q * Q;
+  double R2 = R * R;
+
+  double CR2 = 729 * r * r;
+  double CQ3 = 2916 * q * q * q;
+
+  if (R == 0 && Q == 0)
+    {
+      *x0 = - a / 3 ;
+      *x1 = - a / 3 ;
+      *x2 = - a / 3 ;
+      return 3 ;
+    }
+  else if (CR2 == CQ3) 
+    {
+      /* this test is actually R2 == Q3, written in a form suitable
+         for exact computation with integers */
+
+      /* Due to finite precision some double roots may be missed, and
+         considered to be a pair of complex roots z = x +/- epsilon i
+         close to the real axis. */
+
+      double sqrtQ = sqrt (Q);
+
+      if (R > 0)
+        {
+          *x0 = -2 * sqrtQ  - a / 3;
+          *x1 = sqrtQ - a / 3;
+          *x2 = sqrtQ - a / 3;
+        }
+      else
+        {
+          *x0 = - sqrtQ  - a / 3;
+          *x1 = - sqrtQ - a / 3;
+          *x2 = 2 * sqrtQ - a / 3;
+        }
+      return 3 ;
+    }
+  else if (CR2 < CQ3) /* equivalent to R2 < Q3 */
+    {
+      double sqrtQ = sqrt (Q);
+      double sqrtQ3 = sqrtQ * sqrtQ * sqrtQ;
+      double theta = acos (R / sqrtQ3);
+      double norm = -2 * sqrtQ;
+      *x0 = norm * cos (theta / 3) - a / 3;
+      *x1 = norm * cos ((theta + 2.0 * M_PI) / 3) - a / 3;
+      *x2 = norm * cos ((theta - 2.0 * M_PI) / 3) - a / 3;
+      
+      /* Sort *x0, *x1, *x2 into increasing order */
+
+      if (*x0 > *x1)
+        SWAP(*x0, *x1) ;
+      
+      if (*x1 > *x2)
+        {
+          SWAP(*x1, *x2) ;
+          
+          if (*x0 > *x1)
+            SWAP(*x0, *x1) ;
+        }
+      
+      return 3;
+    }
+  else
+    {
+      double sgnR = (R >= 0 ? 1 : -1);
+      double A = -sgnR * pow (fabs (R) + sqrt (R2 - Q3), 1.0/3.0);
+      double B = Q / A ;
+      *x0 = A + B - a / 3;
+      return 1;
+    }
+}