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