1package prover
  2
  3import (
  4	"math"
  5	"math/big"
  6
  7	"github.com/iden3/go-iden3-crypto/ff"
  8)
  9
 10type rootsT struct {
 11	roots [][]*ff.Element
 12	w     []*ff.Element
 13}
 14
 15func newRootsT() rootsT {
 16	var roots rootsT
 17
 18	rem := new(big.Int).Sub(R, big.NewInt(1))
 19	s := 0
 20	for rem.Bit(0) == 0 { // rem.Bit==0 when even
 21		s++
 22		rem = new(big.Int).Rsh(rem, 1)
 23	}
 24	roots.w = make([]*ff.Element, s+1)
 25	roots.w[s] = ff.NewElement().SetBigInt(fExp(big.NewInt(5), rem))
 26
 27	n := s - 1
 28	for n >= 0 {
 29		roots.w[n] = ff.NewElement().Mul(roots.w[n+1], roots.w[n+1])
 30		n--
 31	}
 32	roots.roots = make([][]*ff.Element, 50) // TODO WIP
 33
 34	roots.setRoots(15)
 35	return roots
 36}
 37
 38func (roots rootsT) setRoots(n int) {
 39	for i := n; i >= 0 && nil == roots.roots[i]; i-- { // TODO tmp i<=len(r)
 40		r := ff.NewElement().SetBigInt(big.NewInt(1))
 41		nroots := 1 << i
 42		var rootsi []*ff.Element
 43		for j := 0; j < nroots; j++ {
 44			rootsi = append(rootsi, r)
 45			r = ff.NewElement().Mul(r, roots.w[i])
 46		}
 47		roots.roots[i] = rootsi
 48	}
 49}
 50
 51func fftroots(roots rootsT, pall []*ff.Element, bits, offset, step int) []*ff.Element {
 52	n := 1 << bits
 53	if n == 1 {
 54		return []*ff.Element{pall[offset]}
 55	} else if n == 2 {
 56		return []*ff.Element{
 57			ff.NewElement().Add(pall[offset], pall[offset+step]), // TODO tmp
 58			ff.NewElement().Sub(pall[offset], pall[offset+step]),
 59		}
 60	}
 61
 62	ndiv2 := n >> 1
 63	p1 := fftroots(roots, pall, bits-1, offset, step*2)
 64	p2 := fftroots(roots, pall, bits-1, offset+step, step*2)
 65
 66	out := make([]*ff.Element, n)
 67	for i := 0; i < ndiv2; i++ {
 68		out[i] = ff.NewElement().Add(p1[i], ff.NewElement().Mul(roots.roots[bits][i], p2[i]))
 69		out[i+ndiv2] = ff.NewElement().Sub(p1[i], ff.NewElement().Mul(roots.roots[bits][i], p2[i]))
 70	}
 71	return out
 72}
 73
 74func fft(p []*ff.Element) []*ff.Element {
 75	if len(p) <= 1 {
 76		return p
 77	}
 78	bits := math.Log2(float64(len(p)-1)) + 1
 79	roots := newRootsT()
 80	roots.setRoots(int(bits))
 81	m := 1 << int(bits)
 82	ep := extend(p, m)
 83	res := fftroots(roots, ep, int(bits), 0, 1)
 84	return res
 85}
 86
 87func ifft(p []*ff.Element) []*ff.Element {
 88	res := fft(p)
 89	bits := math.Log2(float64(len(p)-1)) + 1
 90	m := 1 << int(bits)
 91
 92	twoinvm := ff.NewElement().SetBigInt(fInv(fMul(big.NewInt(1), big.NewInt(int64(m)))))
 93
 94	var resn []*ff.Element
 95	for i := 0; i < m; i++ {
 96		resn = append(resn, ff.NewElement().Mul(res[(m-i)%m], twoinvm))
 97	}
 98
 99	return resn
100}
101
102func extend(p []*ff.Element, e int) []*ff.Element {
103	if e == len(p) {
104		return p
105	}
106	z := arrayOfZeroesE(e - len(p))
107	return append(p, z...)
108}