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hints.go
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hints.go
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package emulated
import (
"fmt"
"math/big"
"github.com/consensys/gnark/backend/hint"
"github.com/consensys/gnark/frontend"
)
// TODO @gbotrel hint[T FieldParams] would simplify this . Issue is when registering hint, if QuoRem[T] was declared
// inside a func, then it becomes anonymous and hint identification is screwed.
func init() {
hint.Register(GetHints()...)
}
// GetHints returns all hint functions used in the package.
func GetHints() []hint.Function {
return []hint.Function{
DivHint,
QuoHint,
InverseHint,
MultiplicationHint,
RemHint,
NBitsShifted,
}
}
// computeMultiplicationHint packs the inputs for the MultiplicationHint hint function.
func (f *Field[T]) computeMultiplicationHint(leftLimbs, rightLimbs []frontend.Variable) (mulLimbs []frontend.Variable, err error) {
hintInputs := []frontend.Variable{
f.fParams.BitsPerLimb(),
len(leftLimbs),
len(rightLimbs),
}
hintInputs = append(hintInputs, leftLimbs...)
hintInputs = append(hintInputs, rightLimbs...)
return f.api.NewHint(MultiplicationHint, nbMultiplicationResLimbs(len(leftLimbs), len(rightLimbs)), hintInputs...)
}
// nbMultiplicationResLimbs returns the number of limbs which fit the
// multiplication result.
func nbMultiplicationResLimbs(lenLeft, lenRight int) int {
return lenLeft + lenRight - 1
}
// MultiplicationHint unpacks the factors and parameters from inputs, computes
// the product and stores it in output. See internal method
// computeMultiplicationHint for the input packing.
func MultiplicationHint(mod *big.Int, inputs []*big.Int, outputs []*big.Int) error {
if len(inputs) < 3 {
return fmt.Errorf("input must be at least three elements")
}
nbBits := int(inputs[0].Int64())
if 2*nbBits+1 >= mod.BitLen() {
return fmt.Errorf("can not fit multiplication result into limb of length %d", nbBits)
}
// TODO: check that the scalar field fits 2*nbBits + nbLimbs. 2*nbBits comes
// from multiplication and nbLimbs comes from additions.
// TODO: check that all limbs all fully reduced
nbLimbsLeft := int(inputs[1].Int64())
// TODO: get the limb length from the input instead of packing into input
nbLimbsRight := int(inputs[2].Int64())
if len(inputs) != 3+nbLimbsLeft+nbLimbsRight {
return fmt.Errorf("input invalid")
}
if len(outputs) < nbLimbsLeft+nbLimbsRight-1 {
return fmt.Errorf("can not fit multiplication result into %d limbs", len(outputs))
}
for _, oi := range outputs {
if oi == nil {
return fmt.Errorf("output not initialized")
}
oi.SetUint64(0)
}
tmp := new(big.Int)
for i, li := range inputs[3 : 3+nbLimbsLeft] {
for j, rj := range inputs[3+nbLimbsLeft:] {
outputs[i+j].Add(outputs[i+j], tmp.Mul(li, rj))
}
}
return nil
}
// computeRemHint packs inputs for the RemHint hint function.
// sets z to the remainder x%y for y != 0 and returns z.
func (f *Field[T]) computeRemHint(x, y *Element[T]) (z *Element[T], err error) {
var fp T
hintInputs := []frontend.Variable{
fp.BitsPerLimb(),
len(x.Limbs),
}
hintInputs = append(hintInputs, x.Limbs...)
hintInputs = append(hintInputs, y.Limbs...)
limbs, err := f.api.NewHint(RemHint, int(len(y.Limbs)), hintInputs...)
if err != nil {
return nil, err
}
return f.packLimbs(limbs, true), nil
}
// RemHint sets z to the remainder x%y for y != 0 and returns z.
// If y == 0, returns an error.
// Rem implements truncated modulus (like Go); see QuoRem for more details.
func RemHint(_ *big.Int, inputs []*big.Int, outputs []*big.Int) error {
nbBits, _, x, y, err := parseHintDivInputs(inputs)
if err != nil {
return err
}
r := new(big.Int)
r.Rem(x, y)
if err := decompose(r, nbBits, outputs); err != nil {
return fmt.Errorf("decompose remainder: %w", err)
}
return nil
}
// computeQuoHint packs the inputs for QuoHint function and returns z = x / y
// (discards remainder)
func (f *Field[T]) computeQuoHint(x *Element[T]) (z *Element[T], err error) {
var fp T
resLen := (uint(len(x.Limbs))*fp.BitsPerLimb() + x.overflow + 1 - // diff total bitlength
uint(fp.Modulus().BitLen()) + // subtract modulus bitlength
fp.BitsPerLimb() - 1) / // to round up
fp.BitsPerLimb()
hintInputs := []frontend.Variable{
fp.BitsPerLimb(),
len(x.Limbs),
}
p := f.Modulus()
hintInputs = append(hintInputs, x.Limbs...)
hintInputs = append(hintInputs, p.Limbs...)
limbs, err := f.api.NewHint(QuoHint, int(resLen), hintInputs...)
if err != nil {
return nil, err
}
return f.packLimbs(limbs, false), nil
}
// QuoHint sets z to the quotient x/y for y != 0 and returns z.
// If y == 0, returns an error.
// Quo implements truncated division (like Go); see QuoRem for more details.
func QuoHint(_ *big.Int, inputs []*big.Int, outputs []*big.Int) error {
nbBits, _, x, y, err := parseHintDivInputs(inputs)
if err != nil {
return err
}
z := new(big.Int)
z.Quo(x, y) //.Mod(z, y)
if err := decompose(z, nbBits, outputs); err != nil {
return fmt.Errorf("decompose: %w", err)
}
return nil
}
// computeInverseHint packs the inputs for the InverseHint hint function.
func (f *Field[T]) computeInverseHint(inLimbs []frontend.Variable) (inverseLimbs []frontend.Variable, err error) {
var fp T
hintInputs := []frontend.Variable{
fp.BitsPerLimb(),
fp.NbLimbs(),
}
p := f.Modulus()
hintInputs = append(hintInputs, p.Limbs...)
hintInputs = append(hintInputs, inLimbs...)
return f.api.NewHint(InverseHint, int(fp.NbLimbs()), hintInputs...)
}
// InverseHint computes the inverse x^-1 for the input x and stores it in outputs.
func InverseHint(mod *big.Int, inputs []*big.Int, outputs []*big.Int) error {
if len(inputs) < 2 {
return fmt.Errorf("input must be at least two elements")
}
nbBits := uint(inputs[0].Uint64())
nbLimbs := int(inputs[1].Int64())
if len(inputs[2:]) < 2*nbLimbs {
return fmt.Errorf("inputs missing")
}
if len(outputs) != nbLimbs {
return fmt.Errorf("result does not fit into output")
}
p := new(big.Int)
if err := recompose(inputs[2:2+nbLimbs], nbBits, p); err != nil {
return fmt.Errorf("recompose emulated order: %w", err)
}
x := new(big.Int)
if err := recompose(inputs[2+nbLimbs:], nbBits, x); err != nil {
return fmt.Errorf("recompose value: %w", err)
}
if x.ModInverse(x, p) == nil {
return fmt.Errorf("input and modulus not relatively primes")
}
if err := decompose(x, nbBits, outputs); err != nil {
return fmt.Errorf("decompose: %w", err)
}
return nil
}
// computeDivisionHint packs the inputs for DivisionHint hint function.
func (f *Field[T]) computeDivisionHint(nomLimbs, denomLimbs []frontend.Variable) (divLimbs []frontend.Variable, err error) {
var fp T
hintInputs := []frontend.Variable{
fp.BitsPerLimb(),
fp.NbLimbs(),
len(denomLimbs),
len(nomLimbs),
}
p := f.Modulus()
hintInputs = append(hintInputs, p.Limbs...)
hintInputs = append(hintInputs, nomLimbs...)
hintInputs = append(hintInputs, denomLimbs...)
return f.api.NewHint(DivHint, int(fp.NbLimbs()), hintInputs...)
}
// DivHint computes the value z = x/y for inputs x and y and stores z in
// outputs.
func DivHint(mod *big.Int, inputs []*big.Int, outputs []*big.Int) error {
if len(inputs) < 3 {
return fmt.Errorf("input must be at least three elements")
}
nbBits := uint(inputs[0].Uint64())
nbLimbs := int(inputs[1].Int64())
nbDenomLimbs := int(inputs[2].Int64())
// nominator does not have to be reduced and can be more than nbLimbs.
// Denominator and order have to be nbLimbs long.
nbNomLimbs := int(inputs[3].Int64())
if len(inputs[4:]) != nbLimbs+nbNomLimbs+nbDenomLimbs {
return fmt.Errorf("input length mismatch")
}
if len(outputs) != nbLimbs {
return fmt.Errorf("result does not fit into output")
}
p := new(big.Int)
if err := recompose(inputs[4:4+nbLimbs], nbBits, p); err != nil {
return fmt.Errorf("recompose emulated order: %w", err)
}
nominator := new(big.Int)
if err := recompose(inputs[4+nbLimbs:4+nbLimbs+nbNomLimbs], nbBits, nominator); err != nil {
return fmt.Errorf("recompose nominator: %w", err)
}
denominator := new(big.Int)
if err := recompose(inputs[4+nbLimbs+nbNomLimbs:], nbBits, denominator); err != nil {
return fmt.Errorf("recompose denominator: %w", err)
}
res := new(big.Int).ModInverse(denominator, p)
if res == nil {
return fmt.Errorf("no modular inverse")
}
res.Mul(res, nominator)
res.Mod(res, p)
if err := decompose(res, nbBits, outputs); err != nil {
return fmt.Errorf("decompose division: %w", err)
}
return nil
}
// input[0] = nbBits per limb
// input[1] = nbLimbs(x)
// input[2:2+nbLimbs(x)] = limbs(x)
// input[2+nbLimbs(x):] = limbs(y)
// errors if y == 0
func parseHintDivInputs(inputs []*big.Int) (uint, int, *big.Int, *big.Int, error) {
if len(inputs) < 2 {
return 0, 0, nil, nil, fmt.Errorf("at least 2 inputs required")
}
nbBits := uint(inputs[0].Uint64())
nbLimbs := int(inputs[1].Int64())
if len(inputs[2:]) < nbLimbs {
return 0, 0, nil, nil, fmt.Errorf("x limbs missing")
}
x, y := new(big.Int), new(big.Int)
if err := recompose(inputs[2:2+nbLimbs], nbBits, x); err != nil {
return 0, 0, nil, nil, fmt.Errorf("recompose x: %w", err)
}
if err := recompose(inputs[2+nbLimbs:], nbBits, y); err != nil {
return 0, 0, nil, nil, fmt.Errorf("recompose y: %w", err)
}
if y.IsUint64() && y.Uint64() == 0 {
return 0, 0, nil, nil, fmt.Errorf("y == 0")
}
return nbBits, nbLimbs, x, y, nil
}
// NBitsShifted returns the first bits of the input, with a shift. The number of returned bits is
// defined by the length of the results slice.
func NBitsShifted(_ *big.Int, inputs []*big.Int, results []*big.Int) error {
n := inputs[0]
shift := inputs[1].Uint64() // TODO @gbotrel validate input vs perf in large circuits.
for i := 0; i < len(results); i++ {
results[i].SetUint64(uint64(n.Bit(i + int(shift))))
}
return nil
}