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ForeignField

Constructors

new ForeignField()

new ForeignField(x: 
| string
| number
| bigint
| Field3
| ForeignField): ForeignField

Create a new ForeignField from a bigint, number, string or another ForeignField.

Parameters

x: | string | number | bigint | Field3 | ForeignField

Returns

ForeignField

Example

let x = new ForeignField(5);

Source

lib/provable/foreign-field.ts:96

Properties

value

value: Field3;

The internal representation of a foreign field element, as a tuple of 3 limbs.

Source

lib/provable/foreign-field.ts:50


_Bigint

static _Bigint: undefined | {} = undefined;

Source

lib/provable/foreign-field.ts:28


_modulus

static _modulus: undefined | bigint = undefined;

Source

lib/provable/foreign-field.ts:29


_provable

static _provable: any = undefined;

Source

lib/provable/foreign-field.ts:408


_variants

static _variants: undefined | {
"almostReduced": typeof AlmostForeignField;
"canonical": typeof CanonicalForeignField;
"unreduced": typeof UnreducedForeignField;
} = undefined;

Sibling classes that represent different ranges of field elements.

Source

lib/provable/foreign-field.ts:59

Accessors

Constructor

get Constructor(): typeof ForeignField

Returns

typeof ForeignField

Source

lib/provable/foreign-field.ts:52


modulus

get modulus(): bigint

Returns

bigint

Source

lib/provable/foreign-field.ts:40


AlmostReduced

get static AlmostReduced(): typeof AlmostForeignField

Constructor for field elements that are "almost reduced", i.e. lie in the range [0, 2^ceil(log2(p))).

Returns

typeof AlmostForeignField

Source

lib/provable/foreign-field.ts:77


Bigint

get static Bigint(): {}

Returns

{}

Source

lib/provable/foreign-field.ts:32


Canonical

get static Canonical(): typeof CanonicalForeignField

Constructor for field elements that are fully reduced, i.e. lie in the range [0, p).

Returns

typeof CanonicalForeignField

Source

lib/provable/foreign-field.ts:84


Unreduced

get static Unreduced(): typeof UnreducedForeignField

Constructor for unreduced field elements.

Returns

typeof UnreducedForeignField

Source

lib/provable/foreign-field.ts:70


modulus

get static modulus(): bigint

Returns

bigint

Source

lib/provable/foreign-field.ts:36


provable

get static provable(): any

Provable<ForeignField>, see Provable

Returns

any

Source

lib/provable/foreign-field.ts:413


sizeInBits

get static sizeInBits(): number

Returns

number

Source

lib/provable/foreign-field.ts:43

Methods

add()

add(y: number | bigint | ForeignField): UnreducedForeignField

Finite field addition

Parameters

y: number | bigint | ForeignField

Returns

UnreducedForeignField

Example

x.add(2); // x + 2 mod p

Source

lib/provable/foreign-field.ts:208


assertAlmostReduced()

assertAlmostReduced(): AlmostForeignField

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

AlmostForeignField

Source

lib/provable/foreign-field.ts:163


assertCanonical()

assertCanonical(): CanonicalForeignField

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

CanonicalForeignField

Source

lib/provable/foreign-field.ts:194


assertEquals()

assertEquals(y, message)

assertEquals(y: number | bigint | CanonicalForeignField, message?: string): CanonicalForeignField

Assert equality with a ForeignField-like value

Parameters

y: number | bigint | CanonicalForeignField

message?: string

Returns

CanonicalForeignField

Example
x.assertEquals(0, "x is zero");

Since asserting equality can also serve as a range check, this method returns x with the appropriate type:

Example
let xChecked = x.assertEquals(1, "x is 1");
xChecked satisfies CanonicalForeignField;
Source

lib/provable/foreign-field.ts:286

assertEquals(y, message)

assertEquals(y: AlmostForeignField, message?: string): AlmostForeignField
Parameters

y: AlmostForeignField

message?: string

Returns

AlmostForeignField

Source

lib/provable/foreign-field.ts:290

assertEquals(y, message)

assertEquals(y: ForeignField, message?: string): ForeignField
Parameters

y: ForeignField

message?: string

Returns

ForeignField

Source

lib/provable/foreign-field.ts:291


assertLessThan()

assertLessThan(c: number | bigint, message?: string): void

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);

Source

lib/provable/foreign-field.ts:333


isConstant()

isConstant(): boolean

Checks whether this field element is a constant.

See FieldVar to understand constants vs variables.

Returns

boolean

Source

lib/provable/foreign-field.ts:126


neg()

neg(): AlmostForeignField

Finite field negation

Returns

AlmostForeignField

Example

x.neg(); // -x mod p = p - x

Source

lib/provable/foreign-field.ts:219


sub()

sub(y: number | bigint | ForeignField): UnreducedForeignField

Finite field subtraction

Parameters

y: number | bigint | ForeignField

Returns

UnreducedForeignField

Example

x.sub(1); // x - 1 mod p

Source

lib/provable/foreign-field.ts:234


toBigInt()

toBigInt(): bigint

Convert this field element to a bigint.

Returns

bigint

Source

lib/provable/foreign-field.ts:146


toBits()

toBits(length?: number): Bool[]

Unpack a field element to its bits, as a Bool[] array.

This method is provable!

Parameters

length?: number

Returns

Bool[]

Source

lib/provable/foreign-field.ts:352


toConstant()

toConstant(): ForeignField

Convert this field element to a constant.

See FieldVar to understand constants vs variables.

Warning: This function is only useful in Provable.witness or Provable.asProver blocks, that is, in situations where the prover computes a value outside provable code.

Returns

ForeignField

Source

lib/provable/foreign-field.ts:138


toFields()

toFields(): Field[]

Instance version of Provable<ForeignField>.toFields, see Provable.toFields

Returns

Field[]

Source

lib/provable/foreign-field.ts:400


assertAlmostReduced()

static assertAlmostReduced<T>(...xs: T): [...{ [i in string | number | symbol]: AlmostForeignField }[]]

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 }[]]

Source

lib/provable/foreign-field.ts:177


check()

static check(_: ForeignField): void

Parameters

_: ForeignField

Returns

void

Source

lib/provable/foreign-field.ts:404


from()

from(x)

static from(x: string | number | bigint): CanonicalForeignField

Coerce the input to a ForeignField.

Parameters

x: string | number | bigint

Returns

CanonicalForeignField

Source

lib/provable/foreign-field.ts:114

from(x)

static from(x: string | number | bigint | ForeignField): ForeignField
Parameters

x: string | number | bigint | ForeignField

Returns

ForeignField

Source

lib/provable/foreign-field.ts:115


fromBits()

static fromBits(bits: Bool[]): AlmostForeignField

Create a field element from its bits, as a Bool[] array.

This method is provable!

Parameters

bits: Bool[]

Returns

AlmostForeignField

Source

lib/provable/foreign-field.ts:382


random()

static random(): CanonicalForeignField

Returns

CanonicalForeignField

Source

lib/provable/foreign-field.ts:393


sum()

static sum(xs: (number | bigint | ForeignField)[], operations: (-1 | 1)[]): UnreducedForeignField

Sum (or difference) of multiple finite field elements.

Parameters

xs: (number | bigint | ForeignField)[]

operations: (-1 | 1)[]

Returns

UnreducedForeignField

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.

Source

lib/provable/foreign-field.ts:259