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hints.go
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hints.go
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package fields_bn254
import (
"math/big"
"github.com/consensys/gnark-crypto/ecc/bn254"
"github.com/consensys/gnark/constraint/solver"
"github.com/consensys/gnark/std/math/emulated"
)
func init() {
solver.RegisterHint(GetHints()...)
}
// GetHints returns all hint functions used in the package.
func GetHints() []solver.Hint {
return []solver.Hint{
// E2
divE2Hint,
inverseE2Hint,
// E6
divE6Hint,
inverseE6Hint,
squareTorusHint,
// E12
divE12Hint,
inverseE12Hint,
}
}
func inverseE2Hint(nativeMod *big.Int, nativeInputs, nativeOutputs []*big.Int) error {
return emulated.UnwrapHint(nativeInputs, nativeOutputs,
func(mod *big.Int, inputs, outputs []*big.Int) error {
var a, c bn254.E2
a.A0.SetBigInt(inputs[0])
a.A1.SetBigInt(inputs[1])
c.Inverse(&a)
c.A0.BigInt(outputs[0])
c.A1.BigInt(outputs[1])
return nil
})
}
func divE2Hint(nativeMod *big.Int, nativeInputs, nativeOutputs []*big.Int) error {
return emulated.UnwrapHint(nativeInputs, nativeOutputs,
func(mod *big.Int, inputs, outputs []*big.Int) error {
var a, b, c bn254.E2
a.A0.SetBigInt(inputs[0])
a.A1.SetBigInt(inputs[1])
b.A0.SetBigInt(inputs[2])
b.A1.SetBigInt(inputs[3])
c.Inverse(&b).Mul(&c, &a)
c.A0.BigInt(outputs[0])
c.A1.BigInt(outputs[1])
return nil
})
}
// E6 hints
func inverseE6Hint(nativeMod *big.Int, nativeInputs, nativeOutputs []*big.Int) error {
return emulated.UnwrapHint(nativeInputs, nativeOutputs,
func(mod *big.Int, inputs, outputs []*big.Int) error {
var a, c bn254.E6
a.B0.A0.SetBigInt(inputs[0])
a.B0.A1.SetBigInt(inputs[1])
a.B1.A0.SetBigInt(inputs[2])
a.B1.A1.SetBigInt(inputs[3])
a.B2.A0.SetBigInt(inputs[4])
a.B2.A1.SetBigInt(inputs[5])
c.Inverse(&a)
c.B0.A0.BigInt(outputs[0])
c.B0.A1.BigInt(outputs[1])
c.B1.A0.BigInt(outputs[2])
c.B1.A1.BigInt(outputs[3])
c.B2.A0.BigInt(outputs[4])
c.B2.A1.BigInt(outputs[5])
return nil
})
}
func divE6Hint(nativeMod *big.Int, nativeInputs, nativeOutputs []*big.Int) error {
return emulated.UnwrapHint(nativeInputs, nativeOutputs,
func(mod *big.Int, inputs, outputs []*big.Int) error {
var a, b, c bn254.E6
a.B0.A0.SetBigInt(inputs[0])
a.B0.A1.SetBigInt(inputs[1])
a.B1.A0.SetBigInt(inputs[2])
a.B1.A1.SetBigInt(inputs[3])
a.B2.A0.SetBigInt(inputs[4])
a.B2.A1.SetBigInt(inputs[5])
b.B0.A0.SetBigInt(inputs[6])
b.B0.A1.SetBigInt(inputs[7])
b.B1.A0.SetBigInt(inputs[8])
b.B1.A1.SetBigInt(inputs[9])
b.B2.A0.SetBigInt(inputs[10])
b.B2.A1.SetBigInt(inputs[11])
c.Inverse(&b).Mul(&c, &a)
c.B0.A0.BigInt(outputs[0])
c.B0.A1.BigInt(outputs[1])
c.B1.A0.BigInt(outputs[2])
c.B1.A1.BigInt(outputs[3])
c.B2.A0.BigInt(outputs[4])
c.B2.A1.BigInt(outputs[5])
return nil
})
}
func squareTorusHint(nativeMod *big.Int, nativeInputs, nativeOutputs []*big.Int) error {
return emulated.UnwrapHint(nativeInputs, nativeOutputs,
func(mod *big.Int, inputs, outputs []*big.Int) error {
var a, c bn254.E6
a.B0.A0.SetBigInt(inputs[0])
a.B0.A1.SetBigInt(inputs[1])
a.B1.A0.SetBigInt(inputs[2])
a.B1.A1.SetBigInt(inputs[3])
a.B2.A0.SetBigInt(inputs[4])
a.B2.A1.SetBigInt(inputs[5])
_c := a.DecompressTorus()
_c.CyclotomicSquare(&_c)
c, _ = _c.CompressTorus()
c.B0.A0.BigInt(outputs[0])
c.B0.A1.BigInt(outputs[1])
c.B1.A0.BigInt(outputs[2])
c.B1.A1.BigInt(outputs[3])
c.B2.A0.BigInt(outputs[4])
c.B2.A1.BigInt(outputs[5])
return nil
})
}
// E12 hints
func inverseE12Hint(nativeMod *big.Int, nativeInputs, nativeOutputs []*big.Int) error {
return emulated.UnwrapHint(nativeInputs, nativeOutputs,
func(mod *big.Int, inputs, outputs []*big.Int) error {
var a, c bn254.E12
a.C0.B0.A0.SetBigInt(inputs[0])
a.C0.B0.A1.SetBigInt(inputs[1])
a.C0.B1.A0.SetBigInt(inputs[2])
a.C0.B1.A1.SetBigInt(inputs[3])
a.C0.B2.A0.SetBigInt(inputs[4])
a.C0.B2.A1.SetBigInt(inputs[5])
a.C1.B0.A0.SetBigInt(inputs[6])
a.C1.B0.A1.SetBigInt(inputs[7])
a.C1.B1.A0.SetBigInt(inputs[8])
a.C1.B1.A1.SetBigInt(inputs[9])
a.C1.B2.A0.SetBigInt(inputs[10])
a.C1.B2.A1.SetBigInt(inputs[11])
c.Inverse(&a)
c.C0.B0.A0.BigInt(outputs[0])
c.C0.B0.A1.BigInt(outputs[1])
c.C0.B1.A0.BigInt(outputs[2])
c.C0.B1.A1.BigInt(outputs[3])
c.C0.B2.A0.BigInt(outputs[4])
c.C0.B2.A1.BigInt(outputs[5])
c.C1.B0.A0.BigInt(outputs[6])
c.C1.B0.A1.BigInt(outputs[7])
c.C1.B1.A0.BigInt(outputs[8])
c.C1.B1.A1.BigInt(outputs[9])
c.C1.B2.A0.BigInt(outputs[10])
c.C1.B2.A1.BigInt(outputs[11])
return nil
})
}
func divE12Hint(nativeMod *big.Int, nativeInputs, nativeOutputs []*big.Int) error {
return emulated.UnwrapHint(nativeInputs, nativeOutputs,
func(mod *big.Int, inputs, outputs []*big.Int) error {
var a, b, c bn254.E12
a.C0.B0.A0.SetBigInt(inputs[0])
a.C0.B0.A1.SetBigInt(inputs[1])
a.C0.B1.A0.SetBigInt(inputs[2])
a.C0.B1.A1.SetBigInt(inputs[3])
a.C0.B2.A0.SetBigInt(inputs[4])
a.C0.B2.A1.SetBigInt(inputs[5])
a.C1.B0.A0.SetBigInt(inputs[6])
a.C1.B0.A1.SetBigInt(inputs[7])
a.C1.B1.A0.SetBigInt(inputs[8])
a.C1.B1.A1.SetBigInt(inputs[9])
a.C1.B2.A0.SetBigInt(inputs[10])
a.C1.B2.A1.SetBigInt(inputs[11])
b.C0.B0.A0.SetBigInt(inputs[12])
b.C0.B0.A1.SetBigInt(inputs[13])
b.C0.B1.A0.SetBigInt(inputs[14])
b.C0.B1.A1.SetBigInt(inputs[15])
b.C0.B2.A0.SetBigInt(inputs[16])
b.C0.B2.A1.SetBigInt(inputs[17])
b.C1.B0.A0.SetBigInt(inputs[18])
b.C1.B0.A1.SetBigInt(inputs[19])
b.C1.B1.A0.SetBigInt(inputs[20])
b.C1.B1.A1.SetBigInt(inputs[21])
b.C1.B2.A0.SetBigInt(inputs[22])
b.C1.B2.A1.SetBigInt(inputs[23])
c.Inverse(&b).Mul(&c, &a)
c.C0.B0.A0.BigInt(outputs[0])
c.C0.B0.A1.BigInt(outputs[1])
c.C0.B1.A0.BigInt(outputs[2])
c.C0.B1.A1.BigInt(outputs[3])
c.C0.B2.A0.BigInt(outputs[4])
c.C0.B2.A1.BigInt(outputs[5])
c.C1.B0.A0.BigInt(outputs[6])
c.C1.B0.A1.BigInt(outputs[7])
c.C1.B1.A0.BigInt(outputs[8])
c.C1.B1.A1.BigInt(outputs[9])
c.C1.B2.A0.BigInt(outputs[10])
c.C1.B2.A1.BigInt(outputs[11])
return nil
})
}