github.com/consensys/gnark-crypto@v0.14.0/ecc/bn254/fr/iop/quotient.go (about)

     1  // Copyright 2020 Consensys Software Inc.
     2  //
     3  // Licensed under the Apache License, Version 2.0 (the "License");
     4  // you may not use this file except in compliance with the License.
     5  // You may obtain a copy of the License at
     6  //
     7  //     http://www.apache.org/licenses/LICENSE-2.0
     8  //
     9  // Unless required by applicable law or agreed to in writing, software
    10  // distributed under the License is distributed on an "AS IS" BASIS,
    11  // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
    12  // See the License for the specific language governing permissions and
    13  // limitations under the License.
    14  
    15  // Code generated by consensys/gnark-crypto DO NOT EDIT
    16  
    17  package iop
    18  
    19  import (
    20  	"math/big"
    21  	"math/bits"
    22  
    23  	"github.com/consensys/gnark-crypto/internal/parallel"
    24  
    25  	"github.com/consensys/gnark-crypto/ecc/bn254/fr"
    26  	"github.com/consensys/gnark-crypto/ecc/bn254/fr/fft"
    27  )
    28  
    29  // DivideByXMinusOne
    30  // The input must be in LagrangeCoset.
    31  // The result is in Canonical Regular.
    32  func DivideByXMinusOne(a *Polynomial, domains [2]*fft.Domain) (*Polynomial, error) {
    33  
    34  	// check that the basis is LagrangeCoset
    35  	if a.Basis != LagrangeCoset {
    36  		return nil, ErrMustBeLagrangeCoset
    37  	}
    38  
    39  	// prepare the evaluations of x^n-1 on the big domain's coset
    40  	xnMinusOneInverseLagrangeCoset := evaluateXnMinusOneDomainBigCoset(domains)
    41  
    42  	rho := a.coefficients.Len() / a.size
    43  
    44  	nbElmts := a.coefficients.Len()
    45  
    46  	coeffs := make([]fr.Element, a.coefficients.Len())
    47  	res := NewPolynomial(&coeffs, Form{Layout: BitReverse, Basis: LagrangeCoset})
    48  	res.size = a.size
    49  	res.blindedSize = a.blindedSize
    50  
    51  	nn := uint64(64 - bits.TrailingZeros(uint(nbElmts)))
    52  	parallel.Execute(a.coefficients.Len(), func(start, end int) {
    53  		for i := start; i < end; i++ {
    54  			iRev := bits.Reverse64(uint64(i)) >> nn
    55  			c := a.GetCoeff(i)
    56  			(*res.coefficients)[iRev].
    57  				Mul(&c, &xnMinusOneInverseLagrangeCoset[i%rho])
    58  		}
    59  	})
    60  
    61  	res.ToCanonical(domains[1])
    62  
    63  	return res, nil
    64  
    65  }
    66  
    67  // evaluateXnMinusOneDomainBigCoset evaluates Xᵐ-1 on DomainBig coset
    68  func evaluateXnMinusOneDomainBigCoset(domains [2]*fft.Domain) []fr.Element {
    69  
    70  	ratio := domains[1].Cardinality / domains[0].Cardinality
    71  
    72  	res := make([]fr.Element, ratio)
    73  
    74  	expo := big.NewInt(int64(domains[0].Cardinality))
    75  	res[0].Exp(domains[1].FrMultiplicativeGen, expo)
    76  
    77  	var t fr.Element
    78  	t.Exp(domains[1].Generator, big.NewInt(int64(domains[0].Cardinality)))
    79  
    80  	one := fr.One()
    81  
    82  	for i := 1; i < int(ratio); i++ {
    83  		res[i].Mul(&res[i-1], &t)
    84  		res[i-1].Sub(&res[i-1], &one)
    85  	}
    86  	res[len(res)-1].Sub(&res[len(res)-1], &one)
    87  
    88  	res = fr.BatchInvert(res)
    89  
    90  	return res
    91  }