new inverse method of PackScalarToVar (UnpackVarToScalar) and test

utils/utils.go

@@ -4,6 +4,7 @@ import (
 	"math/big"
 
 	"github.com/consensys/gnark/frontend"
+	"github.com/consensys/gnark/std/math/bits"
 	"github.com/consensys/gnark/std/math/emulated"
 	"github.com/consensys/gnark/std/math/uints"
 )
@@ -29,6 +30,33 @@ func PackScalarToVar[S emulated.FieldParams](api frontend.API, s *emulated.Eleme
 	return res, nil
 }
 
+// UnpackVarToScalar function converts a frontend.Variable to an emulated
+// element of the S field. It is the inverse of PackScalarToVar. The variable
+// is transformed into a binary representation and then grouped into limbs of
+// nbBits until all limbs are filled or all bits are used. Then the limbs are
+// converted to an emulated element of the field. If something goes wrong, an
+// error is returned.
+func UnpackVarToScalar[S emulated.FieldParams](api frontend.API, v frontend.Variable) (*emulated.Element[S], error) {
+	// get field parameters
+	var fr S
+	nBits := int(fr.BitsPerLimb())
+	nLimbs := int(fr.NbLimbs())
+	limbs := make([]frontend.Variable, nLimbs)
+	// get binary representation of the variable
+	vBin := bits.ToBinary(api, v, bits.WithNbDigits(nBits*nLimbs))
+	// group bits into limbs of nbBits until fill all limbs or all bits
+	for i := 0; i < nLimbs; i++ {
+		g := vBin[i*nBits : (i+1)*nBits]
+		limbs[i] = bits.FromBinary(api, g)
+	}
+	// convert limbs to emulated element of the field
+	field, err := emulated.NewField[S](api)
+	if err != nil {
+		return nil, err
+	}
+	return field.NewElement(limbs), nil
+}
+
 // ElemToU8 converts a field element to a slice of uint8 by converting each
 // limb to a slice of uint8 and concatenating them.
 func ElemToU8[T emulated.FieldParams](api frontend.API, elem emulated.Element[T]) ([]uints.U8, error) {

utils/utils_test.go

@@ -0,0 +1,47 @@
+package utils
+
+import (
+	"crypto/rand"
+	"testing"
+
+	"github.com/consensys/gnark-crypto/ecc"
+	"github.com/consensys/gnark/backend"
+	"github.com/consensys/gnark/frontend"
+	"github.com/consensys/gnark/std/algebra/native/sw_bls12377"
+	"github.com/consensys/gnark/std/math/emulated"
+	"github.com/consensys/gnark/std/recursion/groth16"
+	"github.com/consensys/gnark/test"
+)
+
+type testPackUnpackCircuit struct {
+	Input emulated.Element[sw_bls12377.ScalarField]
+}
+
+func (c *testPackUnpackCircuit) Define(api frontend.API) error {
+	// pack the emulated element to a variable
+	packed, err := PackScalarToVar[sw_bls12377.ScalarField](api, &c.Input)
+	if err != nil {
+		return err
+	}
+	// unpack the variable to an emulated element
+	unpacked, err := UnpackVarToScalar[sw_bls12377.ScalarField](api, packed)
+	if err != nil {
+		return err
+	}
+	// compare the limbs of the input and the unpacked element
+	for i, limb := range c.Input.Limbs {
+		api.AssertIsEqual(limb, unpacked.Limbs[i])
+	}
+	return nil
+}
+
+func TestUnpackPackVar(t *testing.T) {
+	assert := test.NewAssert(t)
+	// generate a random big number
+	r, err := rand.Int(rand.Reader, ecc.BLS12_377.ScalarField())
+	assert.NoError(err)
+
+	assert.SolvingSucceeded(&testPackUnpackCircuit{}, &testPackUnpackCircuit{Input: emulated.ValueOf[sw_bls12377.ScalarField](r)},
+		test.WithCurves(ecc.BW6_761), test.WithBackends(backend.GROTH16),
+		test.WithProverOpts(groth16.GetNativeProverOptions(ecc.BN254.ScalarField(), ecc.BW6_761.ScalarField())))
+}