add numerical recipes library

lib/nr/k_and_r/recipes/ei.c

@@ -0,0 +1,47 @@
+
+#include <math.h>
+#define EULER 0.57721566
+#define MAXIT 100
+#define FPMIN 1.0e-30
+#define EPS 6.0e-8
+
+float ei(x)
+float x;
+{
+	void nrerror();
+	int k;
+	float fact,prev,sum,term;
+
+	if (x <= 0.0) nrerror("Bad argument in ei");
+	if (x < FPMIN) return log(x)+EULER;
+	if (x <= -log(EPS)) {
+		sum=0.0;
+		fact=1.0;
+		for (k=1;k<=MAXIT;k++) {
+			fact *= x/k;
+			term=fact/k;
+			sum += term;
+			if (term < EPS*sum) break;
+		}
+		if (k > MAXIT) nrerror("Series failed in ei");
+		return sum+log(x)+EULER;
+	} else {
+		sum=0.0;
+		term=1.0;
+		for (k=1;k<=MAXIT;k++) {
+			prev=term;
+			term *= k/x;
+			if (term < EPS) break;
+			if (term < prev) sum += term;
+			else {
+				sum -= prev;
+				break;
+			}
+		}
+		return exp(x)*(1.0+sum)/x;
+	}
+}
+#undef EPS
+#undef EULER
+#undef MAXIT
+#undef FPMIN