add numerical recipes library

lib/nr/k_and_r/recipes/mpsqrt.c

@@ -0,0 +1,54 @@
+
+#include <math.h>
+#include "nrutil.h"
+#define MF 3
+#define BI (1.0/256)
+
+void mpsqrt(w,u,v,n,m)
+int m,n;
+unsigned char u[],v[],w[];
+{
+	void mplsh(),mpmov(),mpmul(),mpneg(),mpsdv();
+	int i,ir,j,mm;
+	float fu,fv;
+	unsigned char *r,*s;
+
+	r=cvector(1,n<<1);
+	s=cvector(1,n<<1);
+	mm=IMIN(m,MF);
+	fv=(float) v[mm];
+	for (j=mm-1;j>=1;j--) {
+		fv *= BI;
+		fv += v[j];
+	}
+	fu=1.0/sqrt(fv);
+	for (j=1;j<=n;j++) {
+		i=(int) fu;
+		u[j]=(unsigned char) i;
+		fu=256.0*(fu-i);
+	}
+	for (;;) {
+		mpmul(r,u,u,n,n);
+		mplsh(r,n);
+		mpmul(s,r,v,n,IMIN(m,n));
+		mplsh(s,n);
+		mpneg(s,n);
+		s[1] -= 253;
+		mpsdv(s,s,n,2,&ir);
+		for (j=2;j<n;j++) {
+			if (s[j]) {
+				mpmul(r,s,u,n,n);
+				mpmov(u,&r[1],n);
+				break;
+			}
+		}
+		if (j<n) continue;
+		mpmul(r,u,v,n,IMIN(m,n));
+		mpmov(w,&r[1],n);
+		free_cvector(s,1,n<<1);
+		free_cvector(r,1,n<<1);
+		return;
+	}
+}
+#undef MF
+#undef BI