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ratios.go
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ratios.go
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// Copyright 2020 ConsenSys Software Inc.
//
// 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.
// Code generated by consensys/gnark-crypto DO NOT EDIT
package iop
import (
"errors"
"math/bits"
"github.com/consensys/gnark-crypto/internal/parallel"
"github.com/consensys/gnark-crypto/ecc/bw6-756/fr"
"github.com/consensys/gnark-crypto/ecc/bw6-756/fr/fft"
)
// errors related to the computation of the quotient and the ratios.
var (
ErrMustBeRegular = errors.New("the layout must be Regular")
ErrMustBeCanonical = errors.New("the basis must be Canonical")
ErrMustBeLagrangeCoset = errors.New("the basis must be LagrangeCoset")
ErrInconsistentFormat = errors.New("the format of the polynomials must be the same")
ErrInconsistentSize = errors.New("the sizes of the polynomial must be the same as the size of the domain")
ErrNumberPolynomials = errors.New("the number of polynomials in the denominator and the numerator must be the same")
ErrSizeNotPowerOfTwo = errors.New("the size of the polynomials must be a power of two")
ErrInconsistentSizeDomain = errors.New("the size of the domain must be consistent with the size of the polynomials")
ErrIncorrectNumberOfVariables = errors.New("the number of variables is incorrect")
)
// Build an 'accumulating ratio' polynomial.
// * numerator list of polynomials that will form the numerator of the ratio
// * denominator list of polynomials that will form the denominator of the ratio
// The polynomials in the denominator and the numerator are expected to be of
// the same size and the size must be a power of 2. The polynomials are given as
// pointers in case the caller wants to FFTInv the polynomials during the process.
// * beta variable at which the numerator and denominators are evaluated
// * expectedForm expected form of the resulting polynomial
// * Return: say beta=β, numerator = [P₁,...,P_m], denominator = [Q₁,..,Q_m]. The function
// returns a polynomial whose evaluation on the j-th root of unity is
// (Π_{k<j}Π_{i<m}(β-Pᵢ(ωᵏ)))/(β-Qᵢ(ωᵏ))
func BuildRatioShuffledVectors(numerator, denominator []*Polynomial, beta fr.Element, expectedForm Form, domain *fft.Domain) (*Polynomial, error) {
// check that len(numerator)=len(denominator)
if len(numerator) != len(denominator) {
return nil, ErrNumberPolynomials
}
nbPolynomials := len(numerator)
// check that the sizes are consistent
err := checkSize(numerator, denominator)
if err != nil {
return nil, err
}
// create the domain + some checks on the sizes of the polynomials
n := numerator[0].coefficients.Len()
domain, err = buildDomain(n, domain)
if err != nil {
return nil, err
}
// put every polynomials in Lagrange form. Also make sure
// that we don't modify the slices numerator and denominator, but
// only their entries. If the polynomials are unlocked, the
// entries of the slices numerator and denominator will be
// modified.
for i := 0; i < nbPolynomials; i++ {
numerator[i].ToLagrange(domain)
denominator[i].ToLagrange(domain)
}
// build the ratio (careful with the indices of
// the polynomials which are bit reversed)
coeffs := make([]fr.Element, n)
t := make([]fr.Element, n)
coeffs[0].SetOne()
t[0].SetOne()
var a, b, c, d fr.Element
nn := uint64(64 - bits.TrailingZeros(uint(n)))
for i := 0; i < n-1; i++ {
b.SetOne()
d.SetOne()
iRev := bits.Reverse64(uint64(i)) >> nn
for j := 0; j < nbPolynomials; j++ {
if numerator[j].Layout == BitReverse {
a.Sub(&beta, &numerator[j].Coefficients()[iRev])
} else {
a.Sub(&beta, &numerator[j].Coefficients()[i])
}
b.Mul(&b, &a)
if denominator[j].Layout == BitReverse {
c.Sub(&beta, &denominator[j].Coefficients()[iRev])
} else {
c.Sub(&beta, &denominator[j].Coefficients()[i])
}
d.Mul(&d, &c)
}
// b = Πₖ (β-Pₖ(ωⁱ⁻¹))
// d = Πₖ (β-Qₖ(ωⁱ⁻¹))
coeffs[i+1].Mul(&coeffs[i], &b)
t[i+1].Mul(&t[i], &d)
}
t = fr.BatchInvert(t)
for i := 1; i < n; i++ {
coeffs[i].Mul(&coeffs[i], &t[i])
}
res := NewPolynomial(&coeffs, expectedForm)
// at this stage the result is in Lagrange form, Regular layout
putInExpectedFormFromLagrangeRegular(res, domain, expectedForm)
return res, nil
}
// BuildRatioCopyConstraint builds the accumulating ratio polynomial to prove that
// [P₁ ∥ .. ∥ P_{n—1}] is invariant by the permutation \sigma.
// Namely it returns the polynomial Z whose evaluation on the j-th root of unity is
// Z(ω^j) = Π_{i<j}(Π_{k<n}(P_k(ω^i)+β*u^k+γ))/(P_k(ω^i)+σ(kn+i)+γ)))
// * entries list of polynomials whose evaluation are invariant under \sigma
// * beta, gamma challenges
// * expectedForm expected form of the resulting polynomial
func BuildRatioCopyConstraint(
entries []*Polynomial,
permutation []int64,
beta, gamma fr.Element,
expectedForm Form,
domain *fft.Domain) (*Polynomial, error) {
nbPolynomials := len(entries)
// check that the sizes are consistent
err := checkSize(entries)
if err != nil {
return nil, err
}
// create the domain + some checks on the sizes of the polynomials
n := entries[0].coefficients.Len()
domain, err = buildDomain(n, domain)
if err != nil {
return nil, err
}
// put every polynomials in Lagrange form. Also make sure
// that we don't modify the slice entries
for i := 0; i < nbPolynomials; i++ {
entries[i].ToLagrange(domain)
}
// get the support for the permutation
evaluationIDSmallDomain := getSupportIdentityPermutation(nbPolynomials, domain)
// build the ratio (careful with the indices of
// the polynomials which are bit reversed)
coeffs := make([]fr.Element, n)
t := make([]fr.Element, n)
coeffs[0].SetOne()
t[0].SetOne()
parallel.Execute(n-1, func(start, end int) {
var a, b, c, d fr.Element
nn := uint64(64 - bits.TrailingZeros(uint(n)))
for i := start; i < end; i++ {
b.SetOne()
d.SetOne()
iRev := int(bits.Reverse64(uint64(i)) >> nn)
for j, p := range entries {
idx := i
if p.Layout == BitReverse {
idx = iRev
}
a.Mul(&beta, &evaluationIDSmallDomain[i+j*n]).
Add(&a, &gamma).
Add(&a, &p.Coefficients()[idx])
b.Mul(&b, &a)
c.Mul(&beta, &evaluationIDSmallDomain[permutation[i+j*n]]).
Add(&c, &gamma).
Add(&c, &p.Coefficients()[idx])
d.Mul(&d, &c)
}
// b = Πⱼ(Pⱼ(ωⁱ)+β*ωⁱνʲ+γ)
// d = Πⱼ(Qⱼ(ωⁱ)+β*σ(j*n+i)+γ)
coeffs[i+1].Set(&b)
t[i+1].Set(&d)
}
})
for i := 0; i < n-1; i++ {
coeffs[i+1].Mul(&coeffs[i+1], &coeffs[i])
t[i+1].Mul(&t[i+1], &t[i])
}
t = fr.BatchInvert(t)
for i := 1; i < n; i++ {
coeffs[i].Mul(&coeffs[i], &t[i])
}
res := NewPolynomial(&coeffs, expectedForm)
// at this stage the result is in Lagrange form, Regular layout
putInExpectedFormFromLagrangeRegular(res, domain, expectedForm)
return res, nil
}
func putInExpectedFormFromLagrangeRegular(p *Polynomial, domain *fft.Domain, expectedForm Form) {
p.Basis = expectedForm.Basis
p.Layout = expectedForm.Layout
if expectedForm.Basis == Canonical {
domain.FFTInverse(p.Coefficients(), fft.DIF)
if expectedForm.Layout == Regular {
fft.BitReverse(p.Coefficients())
}
return
}
if expectedForm.Basis == LagrangeCoset {
domain.FFTInverse(p.Coefficients(), fft.DIF)
domain.FFT(p.Coefficients(), fft.DIT, true)
if expectedForm.Layout == BitReverse {
fft.BitReverse(p.Coefficients())
}
return
}
if expectedForm.Layout == BitReverse {
fft.BitReverse(p.Coefficients())
}
}
// check that the polynomials are of the same size.
// It assumes that pols contains slices of the same size.
func checkSize(pols ...[]*Polynomial) error {
// check sizes between one another
m := len(pols)
n := pols[0][0].coefficients.Len()
for i := 0; i < m; i++ {
for j := 0; j < len(pols); j++ {
if pols[i][j].coefficients.Len() != n {
return ErrInconsistentSize
}
}
}
return nil
}
// buildDomain builds the fft domain necessary to do FFTs.
// n is the cardinality of the domain, it must be a power of 2.
func buildDomain(n int, domain *fft.Domain) (*fft.Domain, error) {
// check if the sizes are a power of 2
if n&(n-1) != 0 {
return nil, ErrSizeNotPowerOfTwo
}
// if the domain doesn't exist we create it.
if domain == nil {
domain = fft.NewDomain(uint64(n))
}
// in case domain was not nil, it must match the size of the polynomials.
if domain.Cardinality != uint64(n) {
return nil, ErrInconsistentSizeDomain
}
return domain, nil
}
// getSupportIdentityPermutation returns the support on which the permutation acts.
// Concretely it's X evaluated on
// [1,ω,..,ωˢ⁻¹,g,g*ω,..,g*ωˢ⁻¹,..,gⁿ⁻¹,gⁿ⁻¹*ω,..,gⁿ⁻¹*ωˢ⁻¹]
// nbCopies is the number of cosets of the roots of unity that are needed, including the set of
// roots of unity itself.
func getSupportIdentityPermutation(nbCopies int, domain *fft.Domain) []fr.Element {
res := make([]fr.Element, uint64(nbCopies)*domain.Cardinality)
sizePoly := int(domain.Cardinality)
res[0].SetOne()
for i := 0; i < sizePoly-1; i++ {
res[i+1].Mul(&res[i], &domain.Generator)
}
for i := 1; i < nbCopies; i++ {
copy(res[i*sizePoly:], res[(i-1)*sizePoly:i*int(domain.Cardinality)])
for j := 0; j < sizePoly; j++ {
res[i*sizePoly+j].Mul(&res[i*sizePoly+j], &domain.FrMultiplicativeGen)
}
}
return res
}