UnreducedForeignField
Defined in: lib/provable/foreign-field.ts:454
Extends
Extended by
Constructors
new UnreducedForeignField()
new UnreducedForeignField(x: string | number | bigint | Field3 | ForeignField): UnreducedForeignField
Defined in: lib/provable/foreign-field.ts:91
Create a new ForeignField from a bigint, number, string or another ForeignField.
Parameters
x
string
| number
| bigint
| Field3
| ForeignField
Returns
Example
let x = new ForeignField(5);
Note: Inputs must be range checked if they originate from a different field with a different modulus or if they are not constants.
- When constructing from another ForeignField instance, ensure the modulus matches. If not, check the modulus using
Gadgets.ForeignField.assertLessThan()
and handle appropriately. - When constructing from a
Field3
array, ensure all elements are valid Field elements and range checked. - Ensure constants are correctly reduced to the modulus of the field.
Inherited from
Properties
type
type: "Unreduced" | "AlmostReduced" | "FullyReduced" = 'Unreduced';
Defined in: lib/provable/foreign-field.ts:455
value
value: Field3;
Defined in: lib/provable/foreign-field.ts:39
The internal representation of a foreign field element, as a tuple of 3 limbs.
Inherited from
_Bigint
static _Bigint: undefined | {} = undefined;
Defined in: lib/provable/foreign-field.ts:17
Inherited from
_modulus
static _modulus: undefined | bigint = undefined;
Defined in: lib/provable/foreign-field.ts:18
Inherited from
_provable
static _provable:
| undefined
| ProvablePureExtended<UnreducedForeignField, bigint, string> = undefined;
Defined in: lib/provable/foreign-field.ts:457
Overrides
_variants
static _variants:
| undefined
| {
almostReduced: typeof AlmostForeignField;
canonical: typeof CanonicalForeignField;
unreduced: typeof UnreducedForeignField;
} = undefined;
Defined in: lib/provable/foreign-field.ts:48
Sibling classes that represent different ranges of field elements.
Inherited from
Accessors
Constructor
Get Signature
get Constructor(): typeof ForeignField
Defined in: lib/provable/foreign-field.ts:41
Returns
typeof ForeignField
Inherited from
modulus
Get Signature
get modulus(): bigint
Defined in: lib/provable/foreign-field.ts:29
Returns
bigint
Inherited from
AlmostReduced
Get Signature
get static AlmostReduced(): typeof AlmostForeignField
Defined in: lib/provable/foreign-field.ts:66
Constructor for field elements that are "almost reduced", i.e. lie in the range [0, 2^ceil(log2(p))).
Returns
typeof AlmostForeignField
Inherited from
Bigint
Get Signature
get static Bigint(): {}
Defined in: lib/provable/foreign-field.ts:21
Returns
{}
Inherited from
Canonical
Get Signature
get static Canonical(): typeof CanonicalForeignField
Defined in: lib/provable/foreign-field.ts:73
Constructor for field elements that are fully reduced, i.e. lie in the range [0, p).
Returns
typeof CanonicalForeignField
Inherited from
modulus
Get Signature
get static modulus(): bigint
Defined in: lib/provable/foreign-field.ts:25
Returns
bigint
Inherited from
provable
Get Signature
get static provable(): ProvablePureExtended<UnreducedForeignField, bigint, string>
Defined in: lib/provable/foreign-field.ts:459
Provable<ForeignField>
, see Provable
Returns
ProvablePureExtended
<UnreducedForeignField
, bigint
, string
>
Overrides
sizeInBits
Get Signature
get static sizeInBits(): number
Defined in: lib/provable/foreign-field.ts:32
Returns
number
Inherited from
Unreduced
Get Signature
get static Unreduced(): typeof UnreducedForeignField
Defined in: lib/provable/foreign-field.ts:59
Constructor for unreduced field elements.
Returns
typeof UnreducedForeignField
Inherited from
Methods
add()
add(y: number | bigint | ForeignField): UnreducedForeignField
Defined in: lib/provable/foreign-field.ts:210
Finite field addition
Parameters
y
number
| bigint
| ForeignField
Returns
Example
x.add(2); // x + 2 mod p
Inherited from
assertAlmostReduced()
assertAlmostReduced(): AlmostForeignField
Defined in: lib/provable/foreign-field.ts:165
Assert that this field element lies in the range [0, 2^k), where k = ceil(log2(p)) and p is the foreign field modulus.
Returns the field element as a AlmostForeignField.
For a more efficient version of this for multiple field elements, see assertAlmostReduced.
Note: this does not ensure that the field elements is in the canonical range [0, p). To assert that stronger property, there is assertCanonical. You should typically use assertAlmostReduced though, because it is cheaper to prove and sufficient for ensuring validity of all our non-native field arithmetic methods.
Returns
Inherited from
ForeignField
.assertAlmostReduced
assertCanonical()
assertCanonical(): CanonicalForeignField
Defined in: lib/provable/foreign-field.ts:196
Assert that this field element is fully reduced, i.e. lies in the range [0, p), where p is the foreign field modulus.
Returns the field element as a CanonicalForeignField.
Returns
Inherited from
assertEquals()
Call Signature
assertEquals(y: number | bigint | CanonicalForeignField, message?: string): CanonicalForeignField
Defined in: lib/provable/foreign-field.ts:288
Assert equality with a ForeignField-like value
Parameters
y
number
| bigint
| CanonicalForeignField
message?
string
Returns
Examples
x.assertEquals(0, "x is zero");
Since asserting equality can also serve as a range check,
this method returns x
with the appropriate type:
let xChecked = x.assertEquals(1, "x is 1");
xChecked satisfies CanonicalForeignField;
Inherited from
Call Signature
assertEquals(y: AlmostForeignField, message?: string): AlmostForeignField
Defined in: lib/provable/foreign-field.ts:289
Assert equality with a ForeignField-like value
Parameters
y
message?
string
Returns
Examples
x.assertEquals(0, "x is zero");
Since asserting equality can also serve as a range check,
this method returns x
with the appropriate type:
let xChecked = x.assertEquals(1, "x is 1");
xChecked satisfies CanonicalForeignField;
Inherited from
Call Signature
assertEquals(y: ForeignField, message?: string): ForeignField
Defined in: lib/provable/foreign-field.ts:290
Assert equality with a ForeignField-like value
Parameters
y
message?
string
Returns
Examples
x.assertEquals(0, "x is zero");
Since asserting equality can also serve as a range check,
this method returns x
with the appropriate type:
let xChecked = x.assertEquals(1, "x is 1");
xChecked satisfies CanonicalForeignField;
Inherited from
assertLessThan()
assertLessThan(c: number | bigint, message?: string): void
Defined in: lib/provable/foreign-field.ts:325
Assert that this field element is less than a constant c: x < c
.
The constant must satisfy 0 <= c < 2^264
, otherwise an error is thrown.
Parameters
c
number
| bigint
message?
string
Returns
void
Example
x.assertLessThan(10);
Inherited from
neg()
neg(): AlmostForeignField
Defined in: lib/provable/foreign-field.ts:221
Finite field negation
Returns
Example
x.neg(); // -x mod p = p - x
Inherited from
sub()
sub(y: number | bigint | ForeignField): UnreducedForeignField
Defined in: lib/provable/foreign-field.ts:236
Finite field subtraction
Parameters
y
number
| bigint
| ForeignField
Returns
Example
x.sub(1); // x - 1 mod p
Inherited from
toBigInt()
toBigInt(): bigint
Defined in: lib/provable/foreign-field.ts:148
Convert this field element to a bigint.
Returns
bigint
Inherited from
toBits()
toBits(length?: number): Bool[]
Defined in: lib/provable/foreign-field.ts:344
Unpack a field element to its bits, as a Bool[] array.
This method is provable!
Parameters
length?
number
Returns
Bool
[]
Inherited from
toFields()
toFields(): Field[]
Defined in: lib/provable/foreign-field.ts:392
Instance version of Provable<ForeignField>.toFields
, see Provable.toFields
Returns
Field
[]
Inherited from
assertAlmostReduced()
static assertAlmostReduced<T>(...xs: T): [...{ [i in string | number | symbol]: AlmostForeignField }[]]
Defined in: lib/provable/foreign-field.ts:179
Assert that one or more field elements lie in the range [0, 2^k), where k = ceil(log2(p)) and p is the foreign field modulus.
This is most efficient than when checking a multiple of 3 field elements at once.
Type Parameters
• T extends Tuple
<ForeignField
>
Parameters
xs
...T
Returns
[...{ [i in string | number | symbol]: AlmostForeignField }[]]
Inherited from
ForeignField
.assertAlmostReduced
check()
static check(x: ForeignField): void
Defined in: lib/provable/foreign-field.ts:464
Parameters
x
Returns
void
Overrides
from()
Call Signature
static from(x: string | number | bigint): CanonicalForeignField
Defined in: lib/provable/foreign-field.ts:114
Coerce the input to a ForeignField.
Parameters
x
string
| number
| bigint
Returns
Inherited from
Call Signature
static from(x: string | number | bigint | ForeignField): ForeignField
Defined in: lib/provable/foreign-field.ts:115
Coerce the input to a ForeignField.
Parameters
x
string
| number
| bigint
| ForeignField
Returns
Inherited from
fromBits()
static fromBits(bits: Bool[]): AlmostForeignField
Defined in: lib/provable/foreign-field.ts:374
Create a field element from its bits, as a Bool[]
array.
This method is provable!
Parameters
bits
Bool
[]
Returns
Inherited from
random()
static random(): CanonicalForeignField
Defined in: lib/provable/foreign-field.ts:385
Returns
Inherited from
sum()
static sum(xs: (number | bigint | ForeignField)[], operations: (-1 | 1)[]): UnreducedForeignField
Defined in: lib/provable/foreign-field.ts:261
Sum (or difference) of multiple finite field elements.
Parameters
xs
(number
| bigint
| ForeignField
)[]
operations
(-1
| 1
)[]
Returns
Example
let z = ForeignField.sum([3, 2, 1], [-1, 1]); // 3 - 2 + 1
z.assertEquals(2);
This method expects a list of ForeignField-like values, x0,...,xn
,
and a list of "operations" op1,...,opn
where every op is 1 or -1 (plus or minus),
and returns
x0 + op1*x1 + ... + opn*xn
where the sum is computed in finite field arithmetic.
Important: For more than two summands, this is significantly more efficient than chaining calls to ForeignField.add and ForeignField.sub.