add numerical recipes library

lib/nr/cpp/recipes/bessj.cpp

@@ -0,0 +1,52 @@
+#include <cmath>
+#include <limits>
+#include "nr.h"
+using namespace std;
+
+DP NR::bessj(const int n, const DP x)
+{
+	const DP ACC=160.0;
+	const int IEXP=numeric_limits<DP>::max_exponent/2;
+	bool jsum;
+	int j,k,m;
+	DP ax,bj,bjm,bjp,dum,sum,tox,ans;
+
+	if (n < 2) nrerror("Index n less than 2 in bessj");
+	ax=fabs(x);
+	if (ax*ax <= 8.0*numeric_limits<DP>::min()) return 0.0;
+	else if (ax > DP(n)) {
+		tox=2.0/ax;
+		bjm=bessj0(ax);
+		bj=bessj1(ax);
+		for (j=1;j<n;j++) {
+			bjp=j*tox*bj-bjm;
+			bjm=bj;
+			bj=bjp;
+		}
+		ans=bj;
+	} else {
+		tox=2.0/ax;
+		m=2*((n+int(sqrt(ACC*n)))/2);
+		jsum=false;
+		bjp=ans=sum=0.0;
+		bj=1.0;
+		for (j=m;j>0;j--) {
+			bjm=j*tox*bj-bjp;
+			bjp=bj;
+			bj=bjm;
+			dum=frexp(bj,&k);
+			if (k > IEXP) {
+				bj=ldexp(bj,-IEXP);
+				bjp=ldexp(bjp,-IEXP);
+				ans=ldexp(ans,-IEXP);
+				sum=ldexp(sum,-IEXP);
+			}
+			if (jsum) sum += bj;
+			jsum=!jsum;
+			if (j == n) ans=bjp;
+		}
+		sum=2.0*sum-bj;
+		ans /= sum;
+	}
+	return x < 0.0 && (n & 1) ? -ans : ans;
+}