polynomial

Documentation

Index

• func EvalEq(api frontend.API, x, y []frontend.Variable) (eq frontend.Variable)
• func InterpolateLDE(api frontend.API, at frontend.Variable, values []frontend.Variable) frontend.Variable
• type MultiLin
  • func (m MultiLin) Clone() MultiLin
  • func (m MultiLin) Evaluate(api frontend.API, at []frontend.Variable) frontend.Variable
  • func (m MultiLin) NumVars() int
• type Polynomial
  • func (p Polynomial) Eval(api frontend.API, at frontend.Variable) (pAt frontend.Variable)

Examples

• MultiLin.Evaluate

Functions

func EvalEq

func EvalEq(api frontend.API, x, y []frontend.Variable) (eq frontend.Variable)

EvalEq returns Πⁿ₁ Eq(xᵢ, yᵢ) = Πⁿ₁ xᵢyᵢ + (1-xᵢ)(1-yᵢ) = Πⁿ₁ (1 + 2xᵢyᵢ - xᵢ - yᵢ). Is assumes len(x) = len(y) =: n

func InterpolateLDE

func InterpolateLDE(api frontend.API, at frontend.Variable, values []frontend.Variable) frontend.Variable

InterpolateLDE fits a polynomial f of degree len(values)-1 such that f(i) = values[i] whenever defined. Returns f(at)

Types

type MultiLin

type MultiLin []frontend.Variable

func (MultiLin) Clone

func (m MultiLin) Clone() MultiLin

func (MultiLin) Evaluate

func (m MultiLin) Evaluate(api frontend.API, at []frontend.Variable) frontend.Variable

Evaluate assumes len(m) = 1 << len(at) it doesn't modify m

Example

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

func (MultiLin) NumVars

func (m MultiLin) NumVars() int

type Polynomial

type Polynomial []frontend.Variable

func (Polynomial) Eval

func (p Polynomial) Eval(api frontend.API, at frontend.Variable) (pAt frontend.Variable)