add numerical recipes library

lib/nr/cpp/recipes/betai.cpp

@@ -0,0 +1,17 @@
+#include <cmath>
+#include "nr.h"
+using namespace std;
+
+DP NR::betai(const DP a, const DP b, const DP x)
+{
+	DP bt;
+
+	if (x < 0.0 || x > 1.0) nrerror("Bad x in routine betai");
+	if (x == 0.0 || x == 1.0) bt=0.0;
+	else
+		bt=exp(gammln(a+b)-gammln(a)-gammln(b)+a*log(x)+b*log(1.0-x));
+	if (x < (a+1.0)/(a+b+2.0))
+		return bt*betacf(a,b,x)/a;
+	else
+		return 1.0-bt*betacf(b,a,1.0-x)/b;
+}