add numerical recipes library

lib/nr/k_and_r/recipes/bessj.c

@@ -0,0 +1,57 @@
+
+#include <math.h>
+#define ACC 40.0
+#define BIGNO 1.0e10
+#define BIGNI 1.0e-10
+
+float bessj(n,x)
+float x;
+int n;
+{
+	float bessj0(),bessj1();
+	void nrerror();
+	int j,jsum,m;
+	float ax,bj,bjm,bjp,sum,tox,ans;
+
+	if (n < 2) nrerror("Index n less than 2 in bessj");
+	ax=fabs(x);
+	if (ax == 0.0)
+		return 0.0;
+	else if (ax > (float) 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=0;
+		bjp=ans=sum=0.0;
+		bj=1.0;
+		for (j=m;j>0;j--) {
+			bjm=j*tox*bj-bjp;
+			bjp=bj;
+			bj=bjm;
+			if (fabs(bj) > BIGNO) {
+				bj *= BIGNI;
+				bjp *= BIGNI;
+				ans *= BIGNI;
+				sum *= BIGNI;
+			}
+			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;
+}
+#undef ACC
+#undef BIGNO
+#undef BIGNI