add numerical recipes library

lib/nr/k_and_r/recipes/frenel.c

@@ -0,0 +1,87 @@
+
+#include <math.h>
+#include "complex.h"
+#define EPS 6.0e-8
+#define MAXIT 100
+#define FPMIN 1.0e-30
+#define XMIN 1.5
+#define PI 3.1415927
+#define PIBY2 (PI/2.0)
+#define TRUE 1
+#define ONE Complex(1.0,0.0)
+
+void frenel(x,s,c)
+float *c,*s,x;
+{
+	void nrerror();
+	int k,n,odd;
+	float a,ax,fact,pix2,sign,sum,sumc,sums,term,test;
+	fcomplex b,cc,d,h,del,cs;
+
+	ax=fabs(x);
+	if (ax < sqrt(FPMIN)) {
+		*s=0.0;
+		*c=ax;
+	} else if (ax <= XMIN) {
+		sum=sums=0.0;
+		sumc=ax;
+		sign=1.0;
+		fact=PIBY2*ax*ax;
+		odd=TRUE;
+		term=ax;
+		n=3;
+		for (k=1;k<=MAXIT;k++) {
+			term *= fact/k;
+			sum += sign*term/n;
+			test=fabs(sum)*EPS;
+			if (odd) {
+				sign = -sign;
+				sums=sum;
+				sum=sumc;
+			} else {
+				sumc=sum;
+				sum=sums;
+			}
+			if (term < test) break;
+			odd=!odd;
+			n += 2;
+		}
+		if (k > MAXIT) nrerror("series failed in frenel");
+		*s=sums;
+		*c=sumc;
+	} else {
+		pix2=PI*ax*ax;
+		b=Complex(1.0,-pix2);
+		cc=Complex(1.0/FPMIN,0.0);
+		d=h=Cdiv(ONE,b);
+		n = -1;
+		for (k=2;k<=MAXIT;k++) {
+			n += 2;
+			a = -n*(n+1);
+			b=Cadd(b,Complex(4.0,0.0));
+			d=Cdiv(ONE,Cadd(RCmul(a,d),b));
+			cc=Cadd(b,Cdiv(Complex(a,0.0),cc));
+			del=Cmul(cc,d);
+			h=Cmul(h,del);
+			if (fabs(del.r-1.0)+fabs(del.i) < EPS) break;
+		}
+		if (k > MAXIT) nrerror("cf failed in frenel");
+		h=Cmul(Complex(ax,-ax),h);
+		cs=Cmul(Complex(0.5,0.5),
+			Csub(ONE,Cmul(Complex(cos(0.5*pix2),sin(0.5*pix2)),h)));
+		*c=cs.r;
+		*s=cs.i;
+	}
+	if (x < 0.0) {
+		*c = -(*c);
+		*s = -(*s);
+	}
+}
+#undef EPS
+#undef MAXIT
+#undef FPMIN
+#undef XMIN
+#undef PI
+#undef PIBY2
+#undef TRUE
+#undef ONE