add numerical recipes library

lib/nr/cpp/recipes/mpsqrt.cpp

@@ -0,0 +1,49 @@
+#include <cmath>
+#include "nr.h"
+using namespace std;
+
+void NR::mpsqrt(Vec_O_UCHR &w, Vec_O_UCHR &u, Vec_I_UCHR &v)
+{
+	const int MF=3;
+	const DP BI=1.0/256.0;
+	int i,ir,j,mm;
+	DP fu,fv;
+
+	int n=u.size();
+	int m=v.size();
+	Vec_UCHR r(2*n),x(n+m),s(2*n+m),t(3*n+m);
+	mm=MIN(m,MF);
+	fv=DP(v[mm-1]);
+	for (j=mm-2;j>=0;j--) {
+		fv *= BI;
+		fv += v[j];
+	}
+	fu=1.0/sqrt(fv);
+	for (j=0;j<n;j++) {
+		i=int(fu);
+		u[j]=(unsigned char) i;
+		fu=256.0*(fu-i);
+	}
+	for (;;) {
+		mpmul(r,u,u);
+		mplsh(r);
+		mpmul(s,r,v);
+		mplsh(s);
+		mpneg(s);
+		s[0] += (unsigned char) 3;
+		mpsdv(s,s,2,ir);
+		for (j=1;j<n-1;j++) {
+			if (s[j] != 0) {
+				mpmul(t,s,u);
+				mplsh(t);
+				mpmov(u,t);
+				break;
+			}
+		}
+		if (j<n-1) continue;
+		mpmul(x,u,v);
+		mplsh(x);
+		mpmov(w,x);
+		return;
+	}
+}