add numerical recipes library

lib/nr/cpp/recipes/betacf.cpp

@@ -0,0 +1,43 @@
+#include <cmath>
+#include <limits>
+#include "nr.h"
+using namespace std;
+
+DP NR::betacf(const DP a, const DP b, const DP x)
+{
+	const int MAXIT=100;
+	const DP EPS=numeric_limits<DP>::epsilon();
+	const DP FPMIN=numeric_limits<DP>::min()/EPS;
+	int m,m2;
+	DP aa,c,d,del,h,qab,qam,qap;
+
+	qab=a+b;
+	qap=a+1.0;
+	qam=a-1.0;
+	c=1.0;
+	d=1.0-qab*x/qap;
+	if (fabs(d) < FPMIN) d=FPMIN;
+	d=1.0/d;
+	h=d;
+	for (m=1;m<=MAXIT;m++) {
+		m2=2*m;
+		aa=m*(b-m)*x/((qam+m2)*(a+m2));
+		d=1.0+aa*d;
+		if (fabs(d) < FPMIN) d=FPMIN;
+		c=1.0+aa/c;
+		if (fabs(c) < FPMIN) c=FPMIN;
+		d=1.0/d;
+		h *= d*c;
+		aa = -(a+m)*(qab+m)*x/((a+m2)*(qap+m2));
+		d=1.0+aa*d;
+		if (fabs(d) < FPMIN) d=FPMIN;
+		c=1.0+aa/c;
+		if (fabs(c) < FPMIN) c=FPMIN;
+		d=1.0/d;
+		del=d*c;
+		h *= del;
+		if (fabs(del-1.0) <= EPS) break;
+	}
+	if (m > MAXIT) nrerror("a or b too big, or MAXIT too small in betacf");
+	return h;
+}