add numerical recipes library

lib/nr/ansi/recipes/gauher.c

@@ -0,0 +1,48 @@
+
+#include <math.h>
+#define EPS 3.0e-14
+#define PIM4 0.7511255444649425
+#define MAXIT 10
+
+void gauher(float x[], float w[], int n)
+{
+	void nrerror(char error_text[]);
+	int i,its,j,m;
+	double p1,p2,p3,pp,z,z1;
+
+	m=(n+1)/2;
+	for (i=1;i<=m;i++) {
+		if (i == 1) {
+			z=sqrt((double)(2*n+1))-1.85575*pow((double)(2*n+1),-0.16667);
+		} else if (i == 2) {
+			z -= 1.14*pow((double)n,0.426)/z;
+		} else if (i == 3) {
+			z=1.86*z-0.86*x[1];
+		} else if (i == 4) {
+			z=1.91*z-0.91*x[2];
+		} else {
+			z=2.0*z-x[i-2];
+		}
+		for (its=1;its<=MAXIT;its++) {
+			p1=PIM4;
+			p2=0.0;
+			for (j=1;j<=n;j++) {
+				p3=p2;
+				p2=p1;
+				p1=z*sqrt(2.0/j)*p2-sqrt(((double)(j-1))/j)*p3;
+			}
+			pp=sqrt((double)2*n)*p2;
+			z1=z;
+			z=z1-p1/pp;
+			if (fabs(z-z1) <= EPS) break;
+		}
+		if (its > MAXIT) nrerror("too many iterations in gauher");
+		x[i]=z;
+		x[n+1-i] = -z;
+		w[i]=2.0/(pp*pp);
+		w[n+1-i]=w[i];
+	}
+}
+#undef EPS
+#undef PIM4
+#undef MAXIT