/*  slflsqrt.cpp  by K.Tsuru  */
// function ID = 2004   DRADIX
/*******************************************
 SLong class
 Get a square root of SLong N.
 *sgn = sign of (N - q*q).  sgn >= 0
 If N is a complete square number, sgn = 0.
*******************************************/
#ifndef SN_H
#include "sn.h"
#endif
SLong LSqrt(const SLong& N, int* sgn){
    RealSize C;
    // change the effective figures for a time.
    uint ef = N.Head() + 1u;
    C.SetEffFig(ef, C.TEMP_EXTEND);
    SDouble sq(N);
    sq = DDAdd(Sqrt(sq), ROUND_DBL_INT);    // use Newton method.

    SLong q, r;
    q = sq;         // need the information of effective figures.
    C.SetEffFig(0); // restore the effective figures.
    r = N - q*q;

    if(r.Sign(2004) < 0){
        q -= 1.0;   r = N - q*q;
        if( r.Sign() < 0 ) r.SetError(r.VERIFY, "LSqrt", 2004);
    }
    if(sgn != NULL) *sgn = r.Sign();    // = 1 or 0
    return q;
}