add numerical recipes library

lib/nr/cpp/recipes/expint.cpp

@@ -0,0 +1,61 @@
+#include <cmath>
+#include <limits>
+#include "nr.h"
+using namespace std;
+
+DP NR::expint(const int n, const DP x)
+{
+	const int MAXIT=100;
+	const DP EULER=0.577215664901533;
+	const DP EPS=numeric_limits<DP>::epsilon();
+	const DP BIG=numeric_limits<DP>::max()*EPS;
+	int i,ii,nm1;
+	DP a,b,c,d,del,fact,h,psi,ans;
+
+	nm1=n-1;
+	if (n < 0 || x < 0.0 || (x==0.0 && (n==0 || n==1)))
+	nrerror("bad arguments in expint");
+	else {
+		if (n == 0) ans=exp(-x)/x;
+		else {
+			if (x == 0.0) ans=1.0/nm1;
+			else {
+				if (x > 1.0) {
+					b=x+n;
+					c=BIG;
+					d=1.0/b;
+					h=d;
+					for (i=1;i<=MAXIT;i++) {
+						a = -i*(nm1+i);
+						b += 2.0;
+						d=1.0/(a*d+b);
+						c=b+a/c;
+						del=c*d;
+						h *= del;
+						if (fabs(del-1.0) <= EPS) {
+							ans=h*exp(-x);
+							return ans;
+						}
+					}
+					nrerror("continued fraction failed in expint");
+				} else {
+					ans = (nm1!=0 ? 1.0/nm1 : -log(x)-EULER);
+					fact=1.0;
+					for (i=1;i<=MAXIT;i++) {
+						fact *= -x/i;
+						if (i != nm1) del = -fact/(i-nm1);
+						else {
+							psi = -EULER;
+							for (ii=1;ii<=nm1;ii++) psi += 1.0/ii;
+							del=fact*(-log(x)+psi);
+						}
+						ans += del;
+						if (fabs(del) < fabs(ans)*EPS) return ans;
+					}
+					nrerror("series failed in expint");
+				}
+			}
+		}
+	}
+	return ans;
+}