add numerical recipes library

lib/nr/cpp/recipes/cisi.cpp

@@ -0,0 +1,69 @@
+#include <cmath>
+#include <complex>
+#include <limits>
+#include "nr.h"
+using namespace std;
+
+void NR::cisi(const DP x, complex<DP> &cs)
+{
+	const int MAXIT=100;
+	const DP EULER=0.577215664901533, PIBY2=1.570796326794897, TMIN=2.0;
+	const DP EPS=numeric_limits<DP>::epsilon();
+	const DP FPMIN=numeric_limits<DP>::min()*4.0;
+	const DP BIG=numeric_limits<DP>::max()*EPS;
+	int i,k;
+	bool odd;
+	DP a,err,fact,sign,sum,sumc,sums,t,term;
+	complex<DP> h,b,c,d,del;
+
+	t=fabs(x);
+	if (t == 0.0) {
+		cs= -BIG;
+		return;
+	}
+	if (t > TMIN) {
+		b=complex<DP>(1.0,t);
+		c=complex<DP>(BIG,0.0);
+		d=h=1.0/b;
+		for (i=1;i<MAXIT;i++) {
+			a= -i*i;
+			b += 2.0;
+			d=1.0/(a*d+b);
+			c=b+a/c;
+			del=c*d;
+			h *= del;
+			if (fabs(real(del)-1.0)+fabs(imag(del)) <= EPS) break;
+		}
+		if (i >= MAXIT) nrerror("cf failed in cisi");
+		h=complex<DP>(cos(t),-sin(t))*h;
+		cs= -conj(h)+complex<DP>(0.0,PIBY2);
+	} else {
+		if (t < sqrt(FPMIN)) {
+			sumc=0.0;
+			sums=t;
+		} else {
+			sum=sums=sumc=0.0;
+			sign=fact=1.0;
+			odd=true;
+			for (k=1;k<=MAXIT;k++) {
+				fact *= t/k;
+				term=fact/k;
+				sum += sign*term;
+				err=term/fabs(sum);
+				if (odd) {
+					sign = -sign;
+					sums=sum;
+					sum=sumc;
+				} else {
+					sumc=sum;
+					sum=sums;
+				}
+				if (err < EPS) break;
+				odd=!odd;
+			}
+			if (k > MAXIT) nrerror("maxits exceeded in cisi");
+		}
+		cs=complex<DP>(sumc+log(t)+EULER,sums);
+	}
+	if (x < 0.0) cs = conj(cs);
+}