add numerical recipes library

lib/nr/cpp/recipes/sncndn.cpp

@@ -0,0 +1,61 @@
+#include <cmath>
+#include "nr.h"
+using namespace std;
+
+void NR::sncndn(const DP uu, const DP emmc, DP &sn, DP &cn, DP &dn)
+{
+	const DP CA=1.0e-8;
+	bool bo;
+	int i,ii,l;
+	DP a,b,c,d,emc,u;
+	Vec_DP em(13),en(13);
+
+	emc=emmc;
+	u=uu;
+	if (emc != 0.0) {
+		bo=(emc < 0.0);
+		if (bo) {
+			d=1.0-emc;
+			emc /= -1.0/d;
+			u *= (d=sqrt(d));
+		}
+		a=1.0;
+		dn=1.0;
+		for (i=0;i<13;i++) {
+			l=i;
+			em[i]=a;
+			en[i]=(emc=sqrt(emc));
+			c=0.5*(a+emc);
+			if (fabs(a-emc) <= CA*a) break;
+			emc *= a;
+			a=c;
+		}
+		u *= c;
+		sn=sin(u);
+		cn=cos(u);
+		if (sn != 0.0) {
+			a=cn/sn;
+			c *= a;
+			for (ii=l;ii>=0;ii--) {
+				b=em[ii];
+				a *= c;
+				c *= dn;
+				dn=(en[ii]+a)/(b+a);
+				a=c/b;
+			}
+			a=1.0/sqrt(c*c+1.0);
+			sn=(sn >= 0.0 ? a : -a);
+			cn=c*sn;
+		}
+		if (bo) {
+			a=dn;
+			dn=cn;
+			cn=a;
+			sn /= d;
+		}
+	} else {
+		cn=1.0/cosh(u);
+		dn=cn;
+		sn=tanh(u);
+	}
+}