polynomial

package main

import (
	"fmt"

	"github.com/consensys/gnark-crypto/ecc"
	"github.com/consensys/gnark/frontend"
	"github.com/consensys/gnark/frontend/cs/r1cs"
	"github.com/consensys/gnark/frontend/cs/scs"
	"github.com/consensys/gnark/std/polynomial"
)

type evalMultiLinCircuit struct {
	M          []frontend.Variable `gnark:",public"`
	At         []frontend.Variable `gnark:",secret"`
	Evaluation frontend.Variable   `gnark:",secret"`
}

func (c *evalMultiLinCircuit) Define(api frontend.API) error {
	m := polynomial.MultiLin(c.M)
	evaluation := m.Evaluate(api, c.At)
	api.AssertIsEqual(evaluation, c.Evaluation)
	return nil
}

func main() {
	const logSize = 20
	const size = 1 << logSize
	m := polynomial.MultiLin(make([]frontend.Variable, size))
	e := polynomial.MultiLin(make([]frontend.Variable, logSize))

	cs, err := frontend.Compile(ecc.BN254.ScalarField(), r1cs.NewBuilder, &evalMultiLinCircuit{M: m, At: e, Evaluation: 0})
	if err != nil {
		panic(err)
	}
	fmt.Println("r1cs size:", cs.GetNbConstraints())

	cs, err = frontend.Compile(ecc.BN254.ScalarField(), scs.NewBuilder, &evalMultiLinCircuit{M: m, At: e, Evaluation: 0})
	if err != nil {
		panic(err)
	}
	fmt.Println("scs size:", cs.GetNbConstraints())

}

Output:

r1cs size: 1048627
scs size: 2097226