libgivaro-dev 4.0.2-5 / usr / include / recint / rmgreduc.h

/* rmint/montgomery.h - Montgomery functions for rmint

Copyright Université Joseph Fourier - Grenoble
Contributors :
    Alexis BREUST (alexis.breust@gmail.com 2014)
    Christophe CHABOT (christophechabotcc@gmail.com 2011)


This software is a computer program whose purpose is to provide an fixed precision arithmetic library.

This software is governed by the CeCILL-B license under French law and
abiding by the rules of distribution of free software.  You can  use, 
modify and/ or redistribute the software under the terms of the CeCILL-B
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that may mean  that it is complicated to manipulate,  and  that  also
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*/


#ifndef RMINT_MG_REDUC_H
#define RMINT_MG_REDUC_H

#include "rutools.h" /* mod_n() */

// --------------------------------------------------------------
// ----------------------- DEFINITIONS --------------------------

namespace RecInt
{
    //-------- Reduction algorithms ----------
    
    // a is set to Montgomery representation of b
    template <size_t K> rmint<K, MGA>& to_mg(rmint<K, MGA>& a, const rmint<K, MGA>& b);
    template <size_t K> rmint<K, MGA>& to_mg(rmint<K, MGA>& a);

    // t = c * r1 mod p
    // where r1 = r^(-1) mod p, r = 2^(2^k) and p is the module of rmint
    template <size_t K> rmint<K, MGA>& reduction(rmint<K, MGA>& t, const ruint<K+1>& c);
    template <size_t K> rmint<K, MGA>& reduction(rmint<K, MGA>& t, const ruint<K>& c);
    template <size_t K> rmint<K, MGA>& reduction(rmint<K, MGA>& t, const rmint<K, MGA>& c);
    template <size_t K> rmint<K, MGA>& reduction(rmint<K, MGA>& t);
    
    //---------- Compatibility functions ----------
    
    // Returns a.Value, demontgomerized if necessary
    template <size_t K> ruint<K> get_ruint(const rmint<K, MGA>& a);
    
    // Reduction or montgomerizing
    template <size_t K> rmint<K, MGA>& get_ready(rmint<K, MGA>& a);
}


// --------------------------------------------------------------
// --------------------- Montgomerizing -------------------------

namespace RecInt
{
    // a is Montgomery representation of b
    template <size_t K>
    inline rmint<K, MGA>& to_mg(rmint<K, MGA>& a, const rmint<K, MGA>& b) {
        ruint<K+1> res;
        copy(res.High, b.Value);
        mod_n(a.Value, res, rmint<K, MGA>::p);
        return a;
    }

    template <size_t K>
    inline rmint<K, MGA>& to_mg(rmint<K, MGA>& a) {
        return to_mg(a, a);
    }
}


// --------------------------------------------------------------
// -------------------- Demontgomerizing ------------------------

namespace RecInt
{
    // t = a * r1 mod p
    // where r1 = r^(-1) mod p, r = 2^(2^k) and p is the module of rmint
    template <size_t K>
    inline rmint<K, MGA>& reduction(rmint<K, MGA>& t, const ruint<K+1>& a) {
        bool r;
        ruint<K> a0;

        // m = a * p1 mod r
        mul(a0, a.Low, rmint<K, MGA>::p1);
        // t|a0 = a * (p1 * p + 1)
        laddmul(r, t.Value, a0, a0, rmint<K, MGA>::p, a);

        if (r || t.Value >= rmint<K, MGA>::p) sub(t.Value, rmint<K, MGA>::p);
        return t;
    }

    // t = a * r1 mod p
    // where r1 = r^(-1) mod p, r = 2^(2^k)
    // Note: this function is safe, the result is correct
    // even if &a == &t.Value
    template <size_t K>
    inline rmint<K, MGA>& reduction(rmint<K, MGA>& t, const ruint<K>& a) {
        bool r;
        ruint<K> a0;

        // m = a * p1 mod r
        mul(a0, a, rmint<K, MGA>::p1);
        // t|a0 = a * (p1 * p + 1)
        laddmul(r, t.Value, a0, a0, rmint<K, MGA>::p, a);

        if (r || t.Value >= rmint<K, MGA>::p) sub(t.Value, rmint<K, MGA>::p);
        return t;
    }

    // t = a * r1 mod a.p
    // where r1 = r^(-1) mod p, r = 2^(2^k)
    template <size_t K>
    inline rmint<K, MGA>& reduction(rmint<K, MGA>& t, const rmint<K, MGA>& a) {
        return reduction(t, a.Value); 
    }

    // t = t * r1 mod a.p
    // where r1 = r^(-1) mod p, r = 2^(2^k)
    template <size_t K>
    inline rmint<K, MGA>& reduction(rmint<K, MGA>& t) {
        return reduction(t, t.Value); 
    }
}


// --------------------------------------------------------------
// ------------------ Compatibily functions ---------------------

namespace RecInt
{
    // Returns a.Value, demontgomerized if necessary
    template <size_t K>
    inline ruint<K> get_ruint(const rmint<K, MGA>& a) {
        rmint<K, MGA> ap(a);
        return reduction(ap).Value;
    }
    
    // Reduction or montgomerizing
    template <size_t K>
    inline rmint<K, MGA>& get_ready(rmint<K, MGA>& a) {
        return to_mg(a);
    }
}

#endif