Fix Or && Xor

[liyue201]

Or and Xor return unexpected values

my circuit

package main

import (
	"fmt"
	"time"

	"github.com/consensys/gnark-crypto/ecc"
	"github.com/consensys/gnark/backend/groth16"
	"github.com/consensys/gnark/frontend"
	"github.com/consensys/gnark/frontend/cs/r1cs"
)

type TestCircuit struct {
	A frontend.Variable
	B frontend.Variable
}

func (t *TestCircuit) Define(api frontend.API) error {
	a := api.ToBinary(t.A, 8)
	b := api.ToBinary(t.B, 8)
	isZero := make([]frontend.Variable, 8)

	for i := 0; i < 8; i++ {
		isZero[i] = api.And(a[i], b[i])
	}

	api.Println(isZero...)

	// test or
	or := make([]frontend.Variable, 8)
	or[0] = api.Sub(1, isZero[0])
	for i := 1; i < 8; i++ {
		or[i] = api.Or(api.Sub(1, isZero[i]), or[i-1])
	}
	api.Println(or...)

	// test xor
	xor := make([]frontend.Variable, 8)
	xor[0] = api.Sub(1, isZero[0])
	for i := 1; i < 8; i++ {
		xor[i] = api.Xor(api.Sub(1, isZero[i]), xor[i-1])
	}
	api.Println(xor...)

	return nil
}

func main() {

	var circuit TestCircuit

	t := time.Now()
	_r1cs, err := frontend.Compile(ecc.BN254, r1cs.NewBuilder, &circuit, frontend.IgnoreUnconstrainedInputs())
	if err != nil {
		panic(err)
	}
	internal, secret, public := _r1cs.GetNbVariables()
	fmt.Printf("public, secret, internal %v, %v, %v\n", public, secret, internal)

	t0 := time.Now()
	fmt.Printf("Compilation time: %v\n", t0.Sub(t))
	pk, vk, _ := groth16.Setup(_r1cs)
	t1 := time.Now()
	fmt.Printf("Setup time: %v\n", t1.Sub(t0))

	witness, err := frontend.NewWitness(&TestCircuit{
		A: 7,
		B: 21,
	}, ecc.BN254)
	if err != nil {
		panic(err)
	}

	t2 := time.Now()
	fmt.Printf("Witness time: %v\n", t2.Sub(t1))
	proof, err := groth16.Prove(_r1cs, pk, witness)
	if err != nil {
		panic(err)
	}
	t3 := time.Now()
	fmt.Printf("Prove time: %v\n", t3.Sub(t2))
	pubwit, _ := witness.Public()
	if err := groth16.Verify(proof, vk, pubwit); err != nil {
		panic("verification failed")
	}
}

and the log

16:56:43 DBG main.go:27 > 1 0 1 0 0 0 0 0
16:56:43 DBG main.go:35 > 0 2 3 1 1 1 1 1
16:56:43 DBG main.go:43 > 0 2 3 -2 3 -2 3 -2

the expected value

17:00:07 DBG main.go:27 > 1 0 1 0 0 0 0 0
17:00:07 DBG main.go:35 > 0 1 1 1 1 1 1 1
17:00:07 DBG main.go:43 > 0 1 1 0 1 0 1 0