/*
	Licensed to the Apache Software Foundation (ASF) under one
	or more contributor license agreements.  See the NOTICE file
	distributed with this work for additional information
	regarding copyright ownership.  The ASF licenses this file
	to you under the Apache License, Version 2.0 (the
	"License"); you may not use this file except in compliance
	with the License.  You may obtain a copy of the License at
	
	http://www.apache.org/licenses/LICENSE-2.0

	Unless required by applicable law or agreed to in writing,
	software distributed under the License is distributed on an
	"AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
	KIND, either express or implied.  See the License for the
	specific language governing permissions and limitations
	under the License.
*/

//
//  fp4.swift
//
//  Created by Michael Scott on 07/07/2015.
//  Copyright (c) 2015 Michael Scott. All rights reserved.
//

/* Finite Field arithmetic  Fp^4 functions */

/* FP4 elements are of the form a+ib, where i is sqrt(-1+sqrt(-1))  */

final class FP4 {
    private final var a:FP2
    private final var b:FP2

    /* constructors */
    init(_ c:Int)
    {
        a=FP2(c)
        b=FP2(0)
    }
    
    init(_ x:FP4)
    {
        a=FP2(x.a)
        b=FP2(x.b)
    }
    
    init(_ c:FP2,_ d:FP2)
    {
        a=FP2(c)
        b=FP2(d)
    }
    
    init(_ c:FP2)
    {
        a=FP2(c)
        b=FP2(0)
    }
    /* reduce all components of this mod Modulus */
    func reduce()
    {
        a.reduce()
        b.reduce()
    }
    /* normalise all components of this mod Modulus */
    func norm()
    {
        a.norm()
        b.norm()
    }
    /* test this==0 ? */
    func iszilch() -> Bool
    {
        reduce()
        return a.iszilch() && b.iszilch()
    }
    /* test this==1 ? */
    func isunity() -> Bool
    {
    let one=FP2(1);
    return a.equals(one) && b.iszilch()
    }
    
    /* test is w real? That is in a+ib test b is zero */
    func isreal() -> Bool
    {
        return b.iszilch();
    }
    /* extract real part a */
    func real() -> FP2
    {
        return a;
    }
    
    func geta() -> FP2
    {
        return a;
    }
    /* extract imaginary part b */
    func getb() -> FP2
    {
    return b;
    }
    /* test self=x? */
    func equals(_ x:FP4) -> Bool
    {
        return a.equals(x.a) && b.equals(x.b)
    }
    /* copy self=x */
    func copy(_ x:FP4)
    {
        a.copy(x.a)
        b.copy(x.b)
    }
    /* set this=0 */
    func zero()
    {
        a.zero()
        b.zero()
    }
    /* set this=1 */
    func one()
    {
        a.one()
        b.zero()
    }
    /* set self=-self */
    func neg()
    {
        let m=FP2(a)
        let t=FP2(0)
        m.add(b)
        m.neg()
        m.norm()
        t.copy(m); t.add(b)
        b.copy(m)
        b.add(a)
        a.copy(t)
    }
    /* self=conjugate(self) */
    func conj()
    {
        b.neg(); b.norm()
    }
    /* this=-conjugate(this) */
    func nconj()
    {
        a.neg(); a.norm()
    }
    /* self+=x */
    func add(_ x:FP4)
    {
        a.add(x.a)
        b.add(x.b)
    }
    /* self-=x */
    func sub(_ x:FP4)
    {
        let m=FP4(x)
        m.neg()
        add(m)
    }
    
    /* self*=s where s is FP2 */
    func pmul(_ s:FP2)
    {
        a.mul(s)
        b.mul(s)
    }
    /* self*=c where c is int */
    func imul(_ c:Int)
    {
        a.imul(c)
        b.imul(c)
    }
    /* self*=self */
    func sqr()
    {
        norm();
    
        let t1=FP2(a)
        let t2=FP2(b)
        let t3=FP2(a)
    
        t3.mul(b)
        t1.add(b)
        t2.mul_ip()
    
        t2.add(a)
        a.copy(t1)
    
        a.mul(t2)
    
        t2.copy(t3)
        t2.mul_ip()
        t2.add(t3)
        t2.neg()
        a.add(t2)
    
        b.copy(t3)
        b.add(t3)
    
        norm()
    }
    /* self*=y */
    func mul(_ y:FP4)
    {
        norm();
    
        let t1=FP2(a)
        let t2=FP2(b)
        let t3=FP2(0)
        let t4=FP2(b)
    
        t1.mul(y.a)
        t2.mul(y.b)
        t3.copy(y.b)
        t3.add(y.a)
        t4.add(a)
    
        t4.mul(t3)
        t4.sub(t1)
        t4.norm()
    
        b.copy(t4)
        b.sub(t2)
        t2.mul_ip()
        a.copy(t2)
        a.add(t1)
    
        norm()
    }
    /* convert this to hex string */
    func toString() -> String
    {
        return ("["+a.toString()+","+b.toString()+"]")
    }
    
    func toRawString() -> String
    {
        return ("["+a.toRawString()+","+b.toRawString()+"]")
    }
    /* self=1/self */
    func inverse()
    {
        norm();
    
        let t1=FP2(a)
        let t2=FP2(b)
    
        t1.sqr()
        t2.sqr()
        t2.mul_ip()
        t1.sub(t2)
        t1.inverse()
        a.mul(t1)
        t1.neg()
        b.mul(t1)
    }
    
    /* self*=i where i = sqrt(-1+sqrt(-1)) */
    func times_i()
    {
        norm();
        let s=FP2(b)
        let t=FP2(b)
        s.times_i()
        t.add(s)
        t.norm()
        b.copy(a)
        a.copy(t)
    }
    
    /* self=self^p using Frobenius */
    func frob(_ f:FP2)
    {
        a.conj()
        b.conj()
        b.mul(f)
    }
    /* self=self^e */
    func pow(_ e:BIG) -> FP4
    {
        norm()
        e.norm()
        let w=FP4(self)
        let z=BIG(e)
        let r=FP4(1)
        while (true)
        {
            let bt=z.parity()
            z.fshr(1)
            if bt==1 {r.mul(w)}
            if z.iszilch() {break}
            w.sqr()
        }
        r.reduce()
        return r
    }
    /* XTR xtr_a function */
    func xtr_A(_ w:FP4,_ y:FP4,_ z:FP4)
    {
        let r=FP4(w)
        let t=FP4(w)
        r.sub(y)
        r.pmul(a)
        t.add(y)
        t.pmul(b)
        t.times_i()
    
        copy(r)
        add(t)
        add(z)
    
        norm()
    }
    /* XTR xtr_d function */
    func xtr_D()
    {
        let w=FP4(self)
        sqr(); w.conj()
        w.add(w)
        sub(w)
        reduce()
    }
    /* r=x^n using XTR method on traces of FP12s */
    func xtr_pow(_ n:BIG) -> FP4
    {
        let a=FP4(3)
        let b=FP4(self)
        let c=FP4(b)
        c.xtr_D()
        let t=FP4(0)
        let r=FP4(0)
    
        n.norm();
        let par=n.parity()
        let v=BIG(n); v.fshr(1)
        if par==0 {v.dec(1); v.norm()}
    
        let nb=v.nbits()
        //for i in (0...nb-1).reverse()
        var i=nb-1
        //for var i=nb-1;i>=0;i--
        while i>=0
        {
            if (v.bit(UInt(i)) != 1)
            {
				t.copy(b)
				conj()
				c.conj()
				b.xtr_A(a,self,c)
				conj()
				c.copy(t)
				c.xtr_D()
				a.xtr_D()
            }
            else
            {
				t.copy(a); t.conj()
				a.copy(b)
				a.xtr_D()
				b.xtr_A(c,self,t)
				c.xtr_D()
            }
            i-=1
        }
        if par==0 {r.copy(c)}
        else {r.copy(b)}
        r.reduce()
        return r
    }
    
    /* r=ck^a.cl^n using XTR double exponentiation method on traces of FP12s. See Stam thesis. */
    func xtr_pow2(_ ck:FP4,_ ckml:FP4,_ ckm2l:FP4,_ a:BIG,_ b:BIG) -> FP4
    {
        a.norm(); b.norm()
        let e=BIG(a)
        let d=BIG(b)
        let w=BIG(0)
    
        let cu=FP4(ck)  // can probably be passed in w/o copying
        let cv=FP4(self)
        let cumv=FP4(ckml)
        let cum2v=FP4(ckm2l)
        var r=FP4(0)
        let t=FP4(0)
    
        var f2:Int=0
        while d.parity()==0 && e.parity()==0
        {
            d.fshr(1);
            e.fshr(1);
            f2 += 1;
        }
    
        while (BIG.comp(d,e) != 0)
        {
            if BIG.comp(d,e)>0
            {
				w.copy(e); w.imul(4); w.norm()
				if BIG.comp(d,w)<=0
				{
                    w.copy(d); d.copy(e)
                    e.rsub(w); e.norm()
    
                    t.copy(cv)
                    t.xtr_A(cu,cumv,cum2v)
                    cum2v.copy(cumv)
                    cum2v.conj()
                    cumv.copy(cv)
                    cv.copy(cu)
                    cu.copy(t)
    
				}
				else if d.parity()==0
				{
                    d.fshr(1)
                    r.copy(cum2v); r.conj()
                    t.copy(cumv)
                    t.xtr_A(cu,cv,r)
                    cum2v.copy(cumv)
                    cum2v.xtr_D()
                    cumv.copy(t)
                    cu.xtr_D()
				}
				else if e.parity()==1
				{
                    d.sub(e); d.norm()
                    d.fshr(1)
                    t.copy(cv)
                    t.xtr_A(cu,cumv,cum2v)
                    cu.xtr_D()
                    cum2v.copy(cv)
                    cum2v.xtr_D()
                    cum2v.conj()
                    cv.copy(t)
				}
				else
				{
                    w.copy(d)
                    d.copy(e); d.fshr(1)
                    e.copy(w)
                    t.copy(cumv)
                    t.xtr_D()
                    cumv.copy(cum2v); cumv.conj()
                    cum2v.copy(t); cum2v.conj()
                    t.copy(cv)
                    t.xtr_D()
                    cv.copy(cu)
                    cu.copy(t)
				}
            }
            if BIG.comp(d,e)<0
            {
				w.copy(d); w.imul(4); w.norm()
				if BIG.comp(e,w)<=0
				{
                    e.sub(d); e.norm()
                    t.copy(cv)
                    t.xtr_A(cu,cumv,cum2v)
                    cum2v.copy(cumv)
                    cumv.copy(cu)
                    cu.copy(t)
				}
				else if e.parity()==0
				{
                    w.copy(d)
                    d.copy(e); d.fshr(1)
                    e.copy(w)
                    t.copy(cumv)
                    t.xtr_D()
                    cumv.copy(cum2v); cumv.conj()
                    cum2v.copy(t); cum2v.conj()
                    t.copy(cv)
                    t.xtr_D()
                    cv.copy(cu)
                    cu.copy(t)
				}
				else if d.parity()==1
				{
                    w.copy(e)
                    e.copy(d)
                    w.sub(d); w.norm()
                    d.copy(w); d.fshr(1)
                    t.copy(cv)
                    t.xtr_A(cu,cumv,cum2v)
                    cumv.conj()
                    cum2v.copy(cu)
                    cum2v.xtr_D()
                    cum2v.conj()
                    cu.copy(cv)
                    cu.xtr_D()
                    cv.copy(t)
				}
				else
				{
                    d.fshr(1)
                    r.copy(cum2v); r.conj()
                    t.copy(cumv)
                    t.xtr_A(cu,cv,r)
                    cum2v.copy(cumv)
                    cum2v.xtr_D()
                    cumv.copy(t)
                    cu.xtr_D()
				}
            }
        }
        r.copy(cv)
        r.xtr_A(cu,cumv,cum2v)
        for _ in 0 ..< f2
            {r.xtr_D()}
        r=r.xtr_pow(d)
        return r
    }
    
}