add numerical recipes library

lib/nr/cpp/recipes/midpnt.cpp

@@ -0,0 +1,27 @@
+#include "nr.h"
+
+DP NR::midpnt(DP func(const DP), const DP a, const DP b, const int n)
+{
+	int it,j;
+	DP x,tnm,sum,del,ddel;
+	static DP s;
+
+	if (n == 1) {
+		return (s=(b-a)*func(0.5*(a+b)));
+	} else {
+		for(it=1,j=1;j<n-1;j++) it *= 3;
+		tnm=it;
+		del=(b-a)/(3.0*tnm);
+		ddel=del+del;
+		x=a+0.5*del;
+		sum=0.0;
+		for (j=0;j<it;j++) {
+			sum += func(x);
+			x += ddel;
+			sum += func(x);
+			x += del;
+		}
+		s=(s+(b-a)*sum/tnm)/3.0;
+		return s;
+	}
+}