add numerical recipes library

lib/nr/k_and_r/recipes/cisi.c

@@ -0,0 +1,82 @@
+
+#include <math.h>
+#include "complex.h"
+#define EPS 6.0e-8
+#define EULER 0.57721566
+#define MAXIT 100
+#define PIBY2 1.5707963
+#define FPMIN 1.0e-30
+#define TMIN 2.0
+#define TRUE 1
+#define ONE Complex(1.0,0.0)
+
+void cisi(x,ci,si)
+float *ci,*si,x;
+{
+	void nrerror();
+	int i,k,odd;
+	float a,err,fact,sign,sum,sumc,sums,t,term;
+	fcomplex h,b,c,d,del;
+
+	t=fabs(x);
+	if (t == 0.0) {
+		*si=0.0;
+		*ci = -1.0/FPMIN;
+		return;
+	}
+	if (t > TMIN) {
+		b=Complex(1.0,t);
+		c=Complex(1.0/FPMIN,0.0);
+		d=h=Cdiv(ONE,b);
+		for (i=2;i<=MAXIT;i++) {
+			a = -(i-1)*(i-1);
+			b=Cadd(b,Complex(2.0,0.0));
+			d=Cdiv(ONE,Cadd(RCmul(a,d),b));
+			c=Cadd(b,Cdiv(Complex(a,0.0),c));
+			del=Cmul(c,d);
+			h=Cmul(h,del);
+			if (fabs(del.r-1.0)+fabs(del.i) < EPS) break;
+		}
+		if (i > MAXIT) nrerror("cf failed in cisi");
+		h=Cmul(Complex(cos(t),-sin(t)),h);
+		*ci = -h.r;
+		*si=PIBY2+h.i;
+	} 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");
+		}
+		*si=sums;
+		*ci=sumc+log(t)+EULER;
+	}
+	if (x < 0.0) *si = -(*si);
+}
+#undef EPS
+#undef EULER
+#undef MAXIT
+#undef PIBY2
+#undef FPMIN
+#undef TMIN
+#undef TRUE
+#undef ONE