bivariate_seq/bivariate_lin_seq.cpp at master · ke456/bivariate_seq · GitHub

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
#include "bivariate_lin_seq.h"
#include <iostream>
#include <NTL/BasicThreadPool.h>

Vec<int> get_binary(const long &t){
  Vec<int> result;
	auto n = t;
	while (n != 0){
		result.append(n % 2);
		n = n/2;
	}
	return result;
}

void repeated_sq_mod(zz_pX &result, const zz_pX &p,
                              const zz_pX &h, const long &k){
	auto bin = get_binary(k);
	zz_pX b = p % h;
	zz_pX p_mod = b;
	for (long i = bin.length()-2; i>=0; i--){
		MulMod(b,b,b,h);
		if (bin[i] == 1)
			MulMod(b,b,p_mod,h);
	}
	result = b;
}

zz_p get_elem (const long& D, const zz_pX &P, const Vec<zz_p>& init){
    zz_pX mod;
	SetCoeff(mod,1,1);
	repeated_sq_mod(mod, mod, P, D);
	zz_p result{0};
	for (long i = 0; i < init.length(); i++)
			result = result + coeff(mod,i) * init[i];
    return result;
}

Vec<zz_p> get_init(const long& n, const zz_pX &num, const zz_pX &den){
    zz_pX partial_series;
    MulTrunc(partial_series, num,
            InvTrunc(den, n),n);
   Vec<zz_p> init;
   for (long t = 0; t <= deg(partial_series); t++)
        init.append(coeff(partial_series,t));
   return init;
}

bivariate_lin_seq::bivariate_lin_seq(const Vec<Vec<long>>& num,Vec<Vec<long>>& den, int d1, int d2):
num_coeffs{num}, den_coeffs{den},d1{d1},d2{d2}{}

void create_poly(Vec<zz_pX> &res, const Vec<Vec<long>> &coeffs){
    res.SetLength(coeffs.length());

    for (long i = 0; i < coeffs.length(); i++){
        zz_pX tmp;
        for (long j = 0; j < coeffs[i].length(); j++){
            SetCoeff(tmp,j,zz_p(coeffs[i][j]));
        }
        res[i] = tmp;
    }
}

void bivariate_lin_seq::eval_x(zz_pX &res, const zz_p& x, const Vec<zz_pX> &poly){
    for (int i = 0; i < poly.length(); i++){
        zz_p val;
        eval(val,poly[i],x);
        SetCoeff(res, i, val);
    }
}

void bivariate_lin_seq::find_row(zz_pX &num, zz_pX &den, const long& D){
    long degree = (D+1) * d1; // total degree on the bottom
    zz_p x_i = zz_p(0);
    Vec<zz_p> pointsX;
    Vec<zz_p> pointsY;

    pointsX.SetLength(degree);
    pointsY.SetLength(degree);

    Vec<zz_pX> polX_num, polX_den;

    create_poly(polX_num, num_coeffs);
    create_poly(polX_den, den_coeffs);

    for (long i = 0; i < degree; i++){
        zz_pX eval_num;
        zz_pX eval_den;
        do{
            eval_x(eval_num, x_i, polX_num);
            eval_x(eval_den, x_i, polX_den);
            x_i += zz_p(1);
        }while(ConstTerm(eval_den) == zz_p(0));

        // find initial conditions
        Vec<zz_p> init = get_init(d2,eval_num,eval_den);

        // find the point
        auto rp = get_elem(D,reverse(eval_den),init);
        auto p_pow = power(ConstTerm(eval_den), D+1);

        pointsX[i] = (x_i - zz_p(1));
        pointsY[i] = (rp*p_pow);
    }

    // interpolate
    interpolate(num, pointsX, pointsY);
    power(den,polX_den[0],D+1);
}

void bivariate_lin_seq::get_entry_sq_ZZ
                        (Vec<ZZ> &entries_num,
                         Vec<ZZ> &entries_den,
                         const long a,
                         const long b,
                         const long L,
                         const long nbits,
                         const long steps){
     Vec<long> primes;
     primes.SetLength(steps);

     long init_prime = GenPrime_long(nbits);
     primes[0] = init_prime;

     Vec<Vec<Vec<zz_p>>> coeffs;
     coeffs.SetLength(steps);

     for (long i = 1; i < steps; i++){
        primes[i] = NextPrime(primes[i-1]+1);
     }

    for (long i = 0; i < steps; i++){
        cout << "prime: " << primes[i] << endl;
        zz_p::init(primes[i]);

        zz_pX n,d;

        coeffs[i].SetLength(2*L+1);
        long at_D = 0;
        for (long D = b-L; D < b+L+1; D++, at_D++){
            find_row(n,d,D);
            cout << "D: " << D << endl;
            cout << "n: " << n << endl;
            cout << "d: " << d << endl;
            Vec<zz_p> init = get_init(deg(d), n, d);
            coeffs[i][at_D].SetLength(2*L+1);

             long at_N = 0;
            for (long N = a-L; N < a+L+1; N++, at_N++)
                coeffs[i][at_D][at_N] = get_elem(N, reverse(d), init);

            cout << "coeffs[" << i << "][" << at_D << "]="
                 << coeffs[i][at_D] << endl;

        }
        cout << endl;
    }


}


// g++ -std=c++14 *.cpp -g -lntl -lgmp -lm -lpthread -march=native