add numerical recipes library

lib/nr/k_and_r/recipes/airy.c

@@ -0,0 +1,41 @@
+
+#include <math.h>
+#define PI 3.1415927
+#define THIRD (1.0/3.0)
+#define TWOTHR (2.0*THIRD)
+#define ONOVRT 0.57735027
+
+void airy(x,ai,bi,aip,bip)
+float *ai,*aip,*bi,*bip,x;
+{
+	void bessik(),bessjy();
+	float absx,ri,rip,rj,rjp,rk,rkp,rootx,ry,ryp,z;
+
+	absx=fabs(x);
+	rootx=sqrt(absx);
+	z=TWOTHR*absx*rootx;
+	if (x > 0.0) {
+		bessik(z,THIRD,&ri,&rk,&rip,&rkp);
+		*ai=rootx*ONOVRT*rk/PI;
+		*bi=rootx*(rk/PI+2.0*ONOVRT*ri);
+		bessik(z,TWOTHR,&ri,&rk,&rip,&rkp);
+		*aip = -x*ONOVRT*rk/PI;
+		*bip=x*(rk/PI+2.0*ONOVRT*ri);
+	} else if (x < 0.0) {
+		bessjy(z,THIRD,&rj,&ry,&rjp,&ryp);
+		*ai=0.5*rootx*(rj-ONOVRT*ry);
+		*bi = -0.5*rootx*(ry+ONOVRT*rj);
+		bessjy(z,TWOTHR,&rj,&ry,&rjp,&ryp);
+		*aip=0.5*absx*(ONOVRT*ry+rj);
+		*bip=0.5*absx*(ONOVRT*rj-ry);
+	} else {
+		*ai=0.35502805;
+		*bi=(*ai)/ONOVRT;
+		*aip = -0.25881940;
+		*bip = -(*aip)/ONOVRT;
+	}
+}
+#undef PI
+#undef THIRD
+#undef TWOTHR
+#undef ONOVRT