/*  slfdivnw.cpp  by K.Tsuru  */
// function ID = 214  DRADIX
/*************************************************
SLong class only
This is a protected member function which user cannot access.
m/n by Newton method    m and n both positive.
 q = m/n, r = m - q*n;
m > n > 0, n > 1 etc. has been checked in LLDiv().
*************************************************/
#ifndef SN_H
#include "sn.h"
#endif
static const char* const func = "NewtonLLDiv";
Ldiv_t SLong::NewtonLLDiv(const SLong& m, const SLong& n, bool needRem){
    if( (m.Head() < n.Head()) || (m.Sign() <= 0) || (n.Sign() <= 0) ){
        m.SetError(m.SYNTAX_ERR, func, 214);
    }
//check the radix
    if( (m.Radix() != DRADIX) || (n.Radix() != DRADIX) ){
        m.SetError(m.RADIX_ERR, func, 214);
    }
    uint inv_fig = m.Head()-n.Head()+2u;    //necessary figures of 1/n
    RealSize C;
    C.SetEffFig(inv_fig);

// SLong ---> SDouble conversion
    SDouble M(m), N(n);
    SLong q, r, one(1.0);

    M = M/N;
    q = M;              // SDouble --> SLong conversion
    C.SetEffFig(0);

//It corrects the quotient and remainder.
//Almost an exact result is obtained.
    r = m - n*q;
    if(r.Sign(214) < 0){
        while(r.Sign(214) < 0){ // q is too large.
            q -= one;   r += n;
        }
    } else {
        while(r >= n){      // q is too small.
            q += one;   r -= n;
        }
    }

    if(!needRem) return q;
    return Ldiv_t(q, r);    //The verify is done in LLDiv.
}