/*
 * Copyright (c) 2012-2020 MIRACL UK Ltd.
 *
 * This file is part of MIRACL Core
 * (see https://github.com/miracl/core).
 *
 * Licensed 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.
 */

use crate::bls12381::big::BIG;
use crate::bls12381::fp;
use crate::bls12381::fp::FP;
use crate::bls12381::fp2::FP2;

use crate::rand::RAND;

#[derive(Copy, Clone)]
pub struct FP4 {
    a: FP2,
    b: FP2,
}

impl FP4 {
    pub const fn new() -> FP4 {
        FP4 {
            a: FP2::new(),
            b: FP2::new(),
        }
    }

    pub fn new_int(a: isize) -> FP4 {
        let mut f = FP4::new();
        f.a.copy(&FP2::new_int(a));
        f.b.zero();
        return f;
    }

    pub fn new_ints(a: isize,b: isize) -> FP4 {
        let mut f = FP4::new();
        f.a.copy(&FP2::new_int(a));
        f.b.copy(&FP2::new_int(b));
        return f;
    }

    pub fn new_copy(x: &FP4) -> FP4 {
        let mut f = FP4::new();
        f.a.copy(&x.a);
        f.b.copy(&x.b);
        return f;
    }

    pub fn new_fp2s(c: &FP2, d: &FP2) -> FP4 {
        let mut f = FP4::new();
        f.a.copy(c);
        f.b.copy(d);
        return f;
    }

    pub fn new_fp2(c: &FP2) -> FP4 {
        let mut f = FP4::new();
        f.a.copy(c);
        f.b.zero();
        return f;
    }

    pub fn new_fp(c: &FP) -> FP4 {
        let mut f = FP4::new();
        f.a.set_fp(c);
        f.b.zero();
        return f;
    }

    pub fn new_rand(rng: &mut RAND) -> FP4 {
        return FP4::new_fp2s(&FP2::new_rand(rng),&FP2::new_rand(rng));
    }

    pub fn set_fp2s(&mut self, c: &FP2, d: &FP2) {
        self.a.copy(&c);
        self.b.copy(&d);
    }

    pub fn set_fp(&mut self, c: &FP) {
        self.a.set_fp(&c);
        self.b.zero();
    }

    pub fn set_fp2(&mut self, c: &FP2) {
        self.a.copy(&c);
        self.b.zero();
    }

    pub fn set_fp2h(&mut self, c: &FP2) {
        self.b.copy(&c);
        self.a.zero();
    }

    /* reduce components mod Modulus */
    pub fn reduce(&mut self) {
        self.a.reduce();
        self.b.reduce();
    }

    /* normalise components of w */
    pub fn norm(&mut self) {
        self.a.norm();
        self.b.norm();
    }

    pub fn cmove(&mut self, g: &FP4, d: isize) {
        self.a.cmove(&g.a, d);
        self.b.cmove(&g.b, d);
    }

    /* test self=0 ? */
    pub fn iszilch(&self) -> bool {
        return self.a.iszilch() && self.b.iszilch();
    }

    /* test self=1 ? */
    pub fn isunity(&self) -> bool {
        let one = FP2::new_int(1);
        return self.a.equals(&one) && self.b.iszilch();
    }

    /* test is w real? That is in a+ib test b is zero */
    pub fn isreal(&mut self) -> bool {
        return self.b.iszilch();
    }
    /* extract real part a */
    pub fn real(&self) -> FP2 {
        let f = FP2::new_copy(&self.a);
        return f;
    }

    pub fn geta(&self) -> FP2 {
        let f = FP2::new_copy(&self.a);
        return f;
    }
    /* extract imaginary part b */
    pub fn getb(&self) -> FP2 {
        let f = FP2::new_copy(&self.b);
        return f;
    }

    /* test self=x */
    pub fn equals(&self, x: &FP4) -> bool {
        return self.a.equals(&x.a) && self.b.equals(&x.b);
    }
    /* copy self=x */
    pub fn copy(&mut self, x: &FP4) {
        self.a.copy(&x.a);
        self.b.copy(&x.b);
    }

    /* set self=0 */
    pub fn zero(&mut self) {
        self.a.zero();
        self.b.zero();
    }

    /* set self=1 */
    pub fn one(&mut self) {
        self.a.one();
        self.b.zero();
    }

    pub fn sign(&self)  -> isize {
        let mut p1=self.a.sign();
        let mut p2=self.b.sign();
        if fp::BIG_ENDIAN_SIGN {
            let u=self.b.iszilch() as isize;
	        p2^=(p1^p2)&u;
	        return p2;
        } else {
            let u=self.a.iszilch() as isize;
	        p1^=(p1^p2)&u;
	        return p1;
        }
    }

    /* negate self mod Modulus */
    pub fn neg(&mut self) {
        self.norm();
        let mut m = FP2::new_copy(&self.a);
        let mut t = FP2::new();

        m.add(&self.b);
        m.neg();
        t.copy(&m);
        t.add(&self.b);
        self.b.copy(&m);
        self.b.add(&self.a);
        self.a.copy(&t);
        self.norm();
    }

    /* set to a-ib */
    pub fn conj(&mut self) {
        self.b.neg();
        self.norm();
    }

    /* self=-conjugate(self) */
    pub fn nconj(&mut self) {
        self.a.neg();
        self.norm();
    }

    /* self+=a */
    pub fn add(&mut self, x: &FP4) {
        self.a.add(&x.a);
        self.b.add(&x.b);
    }

    pub fn padd(&mut self, x: &FP2) {
        self.a.add(x);
    }

    pub fn dbl(&mut self) {
        self.a.dbl();
        self.b.dbl();
    }

    /* self-=a */
    pub fn sub(&mut self, x: &FP4) {
        let mut m = FP4::new_copy(x);
        m.neg();
        self.add(&m);
    }

    /* self-=a */
    pub fn rsub(&mut self, x: &FP4) {
        self.neg();
        self.add(x);
    }

    /* self*=s, where s is an FP2 */
    pub fn pmul(&mut self, s: &FP2) {
        self.a.mul(s);
        self.b.mul(s);
    }

    /* self*=s, where s is an FP */
    pub fn qmul(&mut self, s: &FP) {
        self.a.pmul(s);
        self.b.pmul(s);
    }

    /* self*=i, where i is an int */
    pub fn imul(&mut self, c: isize) {
        self.a.imul(c);
        self.b.imul(c);
    }

    /* self*=self */

    pub fn sqr(&mut self) {
        let mut t1 = FP2::new_copy(&self.a);
        let mut t2 = FP2::new_copy(&self.b);
        let mut t3 = FP2::new_copy(&self.a);

        t3.mul(&self.b);
        t1.add(&self.b);
        t2.mul_ip();

        t2.add(&self.a);

        t1.norm();
        t2.norm();

        self.a.copy(&t1);

        self.a.mul(&t2);

        t2.copy(&t3);
        t2.mul_ip();
        t2.add(&t3);
        t2.norm();
        t2.neg();
        self.a.add(&t2);

        t3.dbl();
        self.b.copy(&t3);

        self.norm();
    }

    /* self*=y */
    pub fn mul(&mut self, y: &FP4) {
        //self.norm();

        let mut t1 = FP2::new_copy(&self.a);
        let mut t2 = FP2::new_copy(&self.b);
        let mut t3 = FP2::new();
        let mut t4 = FP2::new_copy(&self.b);

        t1.mul(&y.a);
        t2.mul(&y.b);
        t3.copy(&y.b);
        t3.add(&y.a);
        t4.add(&self.a);

        t3.norm();
        t4.norm();

        t4.mul(&t3);

        t3.copy(&t1);
        t3.neg();
        t4.add(&t3);
        t4.norm();

        t3.copy(&t2);
        t3.neg();
        self.b.copy(&t4);
        self.b.add(&t3);

        t2.mul_ip();
        self.a.copy(&t2);
        self.a.add(&t1);

        self.norm();
    }

    /* output to hex string */
    pub fn tostring(&self) -> String {
        return format!("[{},{}]", self.a.tostring(), self.b.tostring());
    }

    /* self=1/self */
    pub fn inverse(&mut self) {
        //self.norm();

        let mut t1 = FP2::new_copy(&self.a);
        let mut t2 = FP2::new_copy(&self.b);

        t1.sqr();
        t2.sqr();
        t2.mul_ip();
        t2.norm();
        t1.sub(&t2);
        t1.inverse();
        self.a.mul(&t1);
        t1.neg();
        t1.norm();
        self.b.mul(&t1);
    }

    /* self*=i where i = sqrt(-1+sqrt(-1)) */
    pub fn times_i(&mut self) {
        let mut t = FP2::new_copy(&self.b);
        self.b.copy(&self.a);
        t.mul_ip();
        self.a.copy(&t);
        self.norm();
        if fp::TOWER == fp::POSITOWER {
            self.neg();
            self.norm();
        }
    }

    /* self=self^p using Frobenius */
    pub fn frob(&mut self, f: &FP2) {
        self.a.conj();
        self.b.conj();
        self.b.mul(f);
    }

    /* self=self^e */
/*
    pub fn pow(&self, e: &BIG) -> FP4 {
        let mut w = FP4::new_copy(self);
        w.norm();
        let mut z = BIG::new_copy(&e);
        let mut r = FP4::new_int(1);
        z.norm();
        loop {
            let bt = z.parity();
            z.fshr(1);
            if bt == 1 {
                r.mul(&mut w)
            };
            if z.iszilch() {
                break;
            }
            w.sqr();
        }
        r.reduce();
        return r;
    }
*/
    /* XTR xtr_a function */
    pub fn xtr_a(&mut self, w: &FP4, y: &FP4, z: &FP4) {
        let mut r = FP4::new_copy(w);
        let mut t = FP4::new_copy(w);
        r.sub(y);
        r.norm();
        r.pmul(&self.a);
        t.add(y);
        t.norm();
        t.pmul(&self.b);
        t.times_i();

        self.copy(&r);
        self.add(&t);
        self.add(z);

        self.norm();
    }

    /* XTR xtr_d function */
    pub fn xtr_d(&mut self) {
        let mut w = FP4::new_copy(self);
        self.sqr();
        w.conj();
        w.dbl();
        w.norm();
        self.sub(&w);
        self.reduce();
    }

    /* r=x^n using XTR method on traces of FP12s */
    pub fn xtr_pow(&self, n: &BIG) -> FP4 {
        let mut sf = FP4::new_copy(self);
        sf.norm();
        let mut a = FP4::new_int(3);
        let mut b = FP4::new_copy(&sf);
        let mut c = FP4::new_copy(&b);
        c.xtr_d();
        let mut t = FP4::new();
        let mut r = FP4::new();

        let par = n.parity();
        let mut v = BIG::new_copy(n);
        v.norm();
        v.fshr(1);
        if par == 0 {
            v.dec(1);
            v.norm();
        }

        let nb = v.nbits();
        for i in (0..nb).rev() {
            if v.bit(i) != 1 {
                t.copy(&b);
                sf.conj();
                c.conj();
                b.xtr_a(&a, &sf, &c);
                sf.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, &sf, &t);
                c.xtr_d();
            }
        }
        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. */
    pub fn xtr_pow2(&mut self, ck: &FP4, ckml: &FP4, ckm2l: &FP4, a: &BIG, b: &BIG) -> FP4 {
        let mut e = BIG::new_copy(a);
        let mut d = BIG::new_copy(b);
        let mut w = BIG::new();
        e.norm();
        d.norm();

        let mut cu = FP4::new_copy(ck); // can probably be passed in w/o copying
        let mut cv = FP4::new_copy(self);
        let mut cumv = FP4::new_copy(ckml);
        let mut cum2v = FP4::new_copy(ckm2l);
        let mut r = FP4::new();
        let mut t = FP4::new();

        let mut f2: usize = 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(&mut d);
        return r;
    }

    /* this/=2 */
    pub fn div2(&mut self) {
        self.a.div2();
        self.b.div2();
    }

    pub fn div_i(&mut self) {
        let mut u = FP2::new_copy(&self.a);
        let v = FP2::new_copy(&self.b);
        u.div_ip();
        self.a.copy(&v);
        self.b.copy(&u);
        if fp::TOWER == fp::POSITOWER {
            self.neg();
            self.norm();
        }
    }
/*
    pub fn pow(&mut self, e: &BIG) {
        let mut w = FP4::new_copy(self);
        let mut z = BIG::new_copy(&e);
        let mut r = FP4::new_int(1);
        loop {
            let bt = z.parity();
            z.fshr(1);
            if bt == 1 {
                r.mul(&mut w)
            };
            if z.iszilch() {
                break;
            }
            w.sqr();
        }
        r.reduce();
        self.copy(&r);
    }
*/
    pub fn qr(&mut self) -> isize {
        let mut c=FP4::new_copy(self);
        c.conj();
        c.mul(self);
        return c.geta().qr();
    }

    /* sqrt(a+ib) = sqrt(a+sqrt(a*a-n*b*b)/2)+ib/(2*sqrt(a+sqrt(a*a-n*b*b)/2)) */
    /* returns true if this is QR */
    pub fn sqrt(&mut self)  {
        if self.iszilch() {
            return;
        }

        let mut a = FP2::new_copy(&self.a);
        let mut b = FP2::new_copy(&self.a);
        let mut s = FP2::new_copy(&self.b);
        let mut t = FP2::new_copy(&self.a);

        s.sqr();
        a.sqr();
        s.mul_ip();
        s.norm();
        a.sub(&s);

        s.copy(&a); s.norm();

        s.sqrt();

        a.copy(&t);
        a.add(&s);
        a.norm();
        a.div2();

        b.copy(&t);
        b.sub(&s);
        b.norm();
        b.div2();

        let d=b.qr();
        a.cmove(&b,d);

        a.sqrt();
        t.copy(&self.b);
        s.copy(&a);
        s.add(&a); s.norm();
        s.inverse();

        t.mul(&s);
        self.a.copy(&a);
        self.b.copy(&t);

        let sgn=self.sign();
        let mut nr=FP4::new_copy(&self);
        nr.neg(); nr.norm();
        self.cmove(&nr,sgn); 
    }
}