1package field
 2
 3import (
 4	"github.com/consensys/gnark-crypto/ecc"
 5	"github.com/consensys/gnark-crypto/field/goldilocks"
 6	"github.com/consensys/gnark/frontend"
 7	"github.com/consensys/gnark/std/math/emulated"
 8)
 9
10type EmulatedField = emulated.Goldilocks
11type F = *emulated.Element[EmulatedField]
12type FieldAPI = *emulated.Field[emulated.Goldilocks]
13
14var TEST_CURVE = ecc.BN254
15
16func NewFieldAPI(api frontend.API) FieldAPI {
17	fieldAPI, err := emulated.NewField[EmulatedField](api)
18	if err != nil {
19		panic(err)
20	}
21	return fieldAPI
22}
23
24func NewFieldConst(x uint64) F {
25	val := emulated.ValueOf[EmulatedField](x)
26	return &val
27}
28
29func NewFieldConstFromString(x string) F {
30	val := emulated.ValueOf[EmulatedField](x)
31	return &val
32}
33
34var ONE_F = NewFieldConst(1)
35var ZERO_F = NewFieldConst(0)
36var NEG_ONE_F = NewFieldConst(EmulatedField{}.Modulus().Uint64() - 1)
37
38var GOLDILOCKS_MULTIPLICATIVE_GROUP_GENERATOR = goldilocks.NewElement(7)
39var GOLDILOCKS_TWO_ADICITY = uint64(32)
40var GOLDILOCKS_POWER_OF_TWO_GENERATOR = goldilocks.NewElement(1753635133440165772)
41
42func GoldilocksPrimitiveRootOfUnity(nLog uint64) goldilocks.Element {
43	if nLog > GOLDILOCKS_TWO_ADICITY {
44		panic("nLog is greater than GOLDILOCKS_TWO_ADICITY")
45	}
46
47	res := goldilocks.NewElement(GOLDILOCKS_POWER_OF_TWO_GENERATOR.Uint64())
48	for i := 0; i < int(GOLDILOCKS_TWO_ADICITY-nLog); i++ {
49		res.Square(&res)
50	}
51
52	return res
53}
54
55func TwoAdicSubgroup(nLog uint64) []goldilocks.Element {
56	if nLog > GOLDILOCKS_TWO_ADICITY {
57		panic("nLog is greater than GOLDILOCKS_TWO_ADICITY")
58	}
59
60	var res []goldilocks.Element
61	rootOfUnity := GoldilocksPrimitiveRootOfUnity(nLog)
62	res = append(res, goldilocks.NewElement(1))
63
64	for i := 0; i < (1 << nLog); i++ {
65		lastElement := res[len(res)-1]
66		res = append(res, *lastElement.Mul(&lastElement, &rootOfUnity))
67	}
68
69	return res
70}
71
72func IsZero(api frontend.API, fieldAPI *emulated.Field[emulated.Goldilocks], x F) frontend.Variable {
73	reduced := fieldAPI.Reduce(x)
74	limbs := reduced.Limbs
75
76	isZero := api.IsZero(limbs[0])
77	for i := 1; i < len(limbs); i++ {
78		isZero = api.Mul(isZero, api.IsZero(limbs[i]))
79	}
80
81	return isZero
82
83}