/*
Copyright 2018 0kims association
This file is part of zksnark javascript library.
zksnark javascript library is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
zksnark javascript library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with zksnark javascript library. If not, see .
*/
/*
This library do operations on polinomials where their coefficients are in field F
The polynomial P(x) = p0 + p1 * x + p2 * x^2 + p3 * x^3, ...
is represented by the array [ p0, p1, p2, p3, ... ]
*/
const bigInt = require("./bigint.js");
class PolField {
constructor (F) {
this.F = F;
const q = this.F.q;
let rem = q.sub(bigInt(1));
let s = 0;
while (!rem.isOdd()) {
s ++;
rem = rem.shr(1);
}
const five = this.F.add(this.F.add(this.F.two, this.F.two), this.F.one);
this.w = new Array(s+1);
this.wi = new Array(s+1);
this.w[s] = this.F.exp(five, rem);
this.wi[s] = this.F.inverse(this.w[s]);
let n=s-1;
while (n>=0) {
this.w[n] = this.F.square(this.w[n+1]);
this.wi[n] = this.F.square(this.wi[n+1]);
n--;
}
}
add(a, b) {
const m = Math.max(a.length, b.length);
const res = new Array(m);
for (let i=0; i a.length) {
[b, a] = [a, b];
}
if ((b.length <= 2) || (b.length < log2(a.length))) {
return this.mulNormal(a,b);
} else {
return this.mulFFT(a,b);
}
}
mulNormal(a, b) {
let res = [];
b = this.affine(b);
for (let i=0; i0) {
const z = new Array(n).fill(this.F.zero);
return z.concat(p);
} else {
if (-n >= p.length) return [];
return p.slice(-n);
}
}
eval(p, x) {
let v = this.F.zero;
let ix = this.F.one;
for (let i=0; i> 1;
const p1 = this._fft(pall, bits-1, offset, step*2);
const p2 = this._fft(pall, bits-1, offset+step, step*2);
const out = new Array(n);
let m= this.F.one;
for (let i=0; i0 && this.F.isZero(p[i]) ) i--;
return p.slice(0, i+1);
}
affine(p) {
for (let i=0; i=0; i--) {
res[i] = this.F.add(this.F.mul(res[i+1], r), p[i+1]);
}
return res;
}
_next2Power(v) {
v--;
v |= v >> 1;
v |= v >> 2;
v |= v >> 4;
v |= v >> 8;
v |= v >> 16;
v++;
return v;
}
toString(p) {
const ap = this.affine(p);
let S = "";
for (let i=ap.length-1; i>=0; i--) {
if (!this.F.isZero(p[i])) {
if (S!="") S += " + ";
S = S + p[i].toString(10);
if (i>0) {
S = S + "x";
if (i>1) {
S = S + "^" +i;
}
}
}
}
return S;
}
_reciprocal(p, bits) {
const k = 1 << bits;
if (k==1) {
return [ this.F.inverse(p[0]) ];
}
const np = this.scaleX(p, -k/2);
const q = this._reciprocal(np, bits-1);
const a = this.scaleX(this.double(q), 3*k/2-2);
const b = this.mul( this.square(q), p);
return this.scaleX(this.sub(a,b), -(k-2));
}
// divides x^m / v
_div2(m, v) {
const kbits = log2(v.length-1)+1;
const k = 1 << kbits;
const scaleV = k - v.length;
// rec = x^(k - 2) / v* x^scaleV =>
// rec = x^(k-2-scaleV)/ v
//
// res = x^m/v = x^(m + (2*k-2 - scaleV) - (2*k-2 - scaleV)) /v =>
// res = rec * x^(m - (2*k-2 - scaleV)) =>
// res = rec * x^(m - 2*k + 2 + scaleV)
const rec = this._reciprocal(this.scaleX(v, scaleV), kbits);
const res = this.scaleX(rec, m - 2*k + 2 + scaleV);
return res;
}
div(_u, _v) {
if (_u.length < _v.length) return [];
const kbits = log2(_v.length-1)+1;
const k = 1 << kbits;
const u = this.scaleX(_u, k-_v.length);
const v = this.scaleX(_v, k-_v.length);
const n = v.length-1;
let m = u.length-1;
const s = this._reciprocal(v, kbits);
let t;
if (m>2*n) {
t = this.sub(this.scaleX([this.F.one], 2*n), this.mul(s, v));
}
let q = [];
let rem = u;
let us, ut;
let finish = false;
while (!finish) {
us = this.mul(rem, s);
q = this.add(q, this.scaleX(us, -2*n));
if ( m > 2*n ) {
ut = this.mul(rem, t);
rem = this.scaleX(ut, -2*n);
m = rem.length-1;
} else {
finish = true;
}
}
return q;
}
}
function log2( V )
{
return( ( ( V & 0xFFFF0000 ) !== 0 ? ( V &= 0xFFFF0000, 16 ) : 0 ) | ( ( V & 0xFF00FF00 ) !== 0 ? ( V &= 0xFF00FF00, 8 ) : 0 ) | ( ( V & 0xF0F0F0F0 ) !== 0 ? ( V &= 0xF0F0F0F0, 4 ) : 0 ) | ( ( V & 0xCCCCCCCC ) !== 0 ? ( V &= 0xCCCCCCCC, 2 ) : 0 ) | ( ( V & 0xAAAAAAAA ) !== 0 ) );
}
module.exports = PolField;