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quotient.go
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/
quotient.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 (
"math/big"
"math/bits"
"github.com/consensys/gnark-crypto/internal/parallel"
"github.com/consensys/gnark-crypto/ecc/bls12-377/fr"
"github.com/consensys/gnark-crypto/ecc/bls12-377/fr/fft"
)
// DivideByXMinusOne
// The input must be in LagrangeCoset.
// The result is in Canonical Regular.
func DivideByXMinusOne(a *Polynomial, domains [2]*fft.Domain) (*Polynomial, error) {
// check that the basis is LagrangeCoset
if a.Basis != LagrangeCoset {
return nil, ErrMustBeLagrangeCoset
}
// prepare the evaluations of x^n-1 on the big domain's coset
xnMinusOneInverseLagrangeCoset := evaluateXnMinusOneDomainBigCoset(domains)
rho := a.coefficients.Len() / a.size
nbElmts := a.coefficients.Len()
coeffs := make([]fr.Element, a.coefficients.Len())
res := NewPolynomial(&coeffs, Form{Layout: BitReverse, Basis: LagrangeCoset})
res.size = a.size
res.blindedSize = a.blindedSize
nn := uint64(64 - bits.TrailingZeros(uint(nbElmts)))
parallel.Execute(a.coefficients.Len(), func(start, end int) {
for i := start; i < end; i++ {
iRev := bits.Reverse64(uint64(i)) >> nn
c := a.GetCoeff(i)
(*res.coefficients)[iRev].
Mul(&c, &xnMinusOneInverseLagrangeCoset[i%rho])
}
})
res.ToCanonical(domains[1])
return res, nil
}
// evaluateXnMinusOneDomainBigCoset evaluates Xᵐ-1 on DomainBig coset
func evaluateXnMinusOneDomainBigCoset(domains [2]*fft.Domain) []fr.Element {
ratio := domains[1].Cardinality / domains[0].Cardinality
res := make([]fr.Element, ratio)
expo := big.NewInt(int64(domains[0].Cardinality))
res[0].Exp(domains[1].FrMultiplicativeGen, expo)
var t fr.Element
t.Exp(domains[1].Generator, big.NewInt(int64(domains[0].Cardinality)))
one := fr.One()
for i := 1; i < int(ratio); i++ {
res[i].Mul(&res[i-1], &t)
res[i-1].Sub(&res[i-1], &one)
}
res[len(res)-1].Sub(&res[len(res)-1], &one)
res = fr.BatchInvert(res)
return res
}