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AlmostForeignField

Extends

  • ForeignFieldWithMul

Constructors

new AlmostForeignField(x)

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

Parameters

x: | string | number | bigint | Field3 | AlmostForeignField

Returns

AlmostForeignField

Overrides

ForeignFieldWithMul.constructor

Source

lib/provable/foreign-field.ts:472

Properties

type

type: "AlmostReduced" | "FullyReduced" = 'AlmostReduced';

Source

lib/provable/foreign-field.ts:470


value

value: Field3;

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

Inherited from

ForeignFieldWithMul.value

Source

lib/provable/foreign-field.ts:50


_Bigint

static _Bigint: undefined | {} = undefined;

Inherited from

ForeignFieldWithMul._Bigint

Source

lib/provable/foreign-field.ts:28


_modulus

static _modulus: undefined | bigint = undefined;

Inherited from

ForeignFieldWithMul._modulus

Source

lib/provable/foreign-field.ts:29


_provable

static _provable: undefined | ProvablePureExtended<AlmostForeignField, bigint, string> = undefined;

Overrides

ForeignFieldWithMul._provable

Source

lib/provable/foreign-field.ts:476


_variants

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

Sibling classes that represent different ranges of field elements.

Inherited from

ForeignFieldWithMul._variants

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(): ProvablePureExtended<AlmostForeignField, bigint, string>

Returns

ProvablePureExtended\<AlmostForeignField, bigint, string>

Source

lib/provable/foreign-field.ts:479


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

Inherited from

ForeignFieldWithMul.add

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

Inherited from

ForeignFieldWithMul.assertAlmostReduced

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

Inherited from

ForeignFieldWithMul.assertCanonical

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

Inherited from

ForeignFieldWithMul.assertEquals

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

Inherited from

ForeignFieldWithMul.assertEquals

Source

lib/provable/foreign-field.ts:290

assertEquals(y, message)

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

y: ForeignField

message?: string

Returns

ForeignField

Inherited from

ForeignFieldWithMul.assertEquals

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

Inherited from

ForeignFieldWithMul.assertLessThan

Example

x.assertLessThan(10);

Source

lib/provable/foreign-field.ts:333


div()

div(y: number | bigint | AlmostForeignField): AlmostForeignField

Division in the finite field, i.e. x*y^(-1) mod p where y^(-1) is the finite field inverse.

Parameters

y: number | bigint | AlmostForeignField

Returns

AlmostForeignField

Inherited from

ForeignFieldWithMul.div

Example

let z = x.div(y); // x/y mod p
z.mul(y).assertEquals(x);

Source

lib/provable/foreign-field.ts:446


equals()

equals(y: number | bigint): Bool

Check equality with a constant value.

Parameters

y: number | bigint

Returns

Bool

Example

let isXZero = x.equals(0);

Source

lib/provable/foreign-field.ts:506


inv()

inv(): AlmostForeignField

Multiplicative inverse in the finite field

Returns

AlmostForeignField

Inherited from

ForeignFieldWithMul.inv

Example

let z = x.inv(); // 1/x mod p
z.mul(x).assertEquals(1);

Source

lib/provable/foreign-field.ts:432


isConstant()

isConstant(): boolean

Checks whether this field element is a constant.

See FieldVar to understand constants vs variables.

Returns

boolean

Inherited from

ForeignFieldWithMul.isConstant

Source

lib/provable/foreign-field.ts:126


mul()

mul(y: number | bigint | AlmostForeignField): UnreducedForeignField

Finite field multiplication

Parameters

y: number | bigint | AlmostForeignField

Returns

UnreducedForeignField

Inherited from

ForeignFieldWithMul.mul

Example

x.mul(y); // x*y mod p

Source

lib/provable/foreign-field.ts:418


neg()

neg(): AlmostForeignField

Finite field negation

Returns

AlmostForeignField

Inherited from

ForeignFieldWithMul.neg

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

Inherited from

ForeignFieldWithMul.sub

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

Inherited from

ForeignFieldWithMul.toBigInt

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[]

Inherited from

ForeignFieldWithMul.toBits

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

Inherited from

ForeignFieldWithMul.toConstant

Source

lib/provable/foreign-field.ts:138


toFields()

toFields(): Field[]

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

Returns

Field[]

Inherited from

ForeignFieldWithMul.toFields

Source

lib/provable/foreign-field.ts:391


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 }[]]

Inherited from

ForeignFieldWithMul.assertAlmostReduced

Source

lib/provable/foreign-field.ts:177


check()

static check(x: ForeignField): void

Parameters

x: ForeignField

Returns

void

Overrides

ForeignFieldWithMul.check

Source

lib/provable/foreign-field.ts:484


from()

from(x)

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

Coerce the input to a ForeignField.

Parameters

x: string | number | bigint

Returns

CanonicalForeignField

Inherited from

ForeignFieldWithMul.from

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

Inherited from

ForeignFieldWithMul.from

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

Inherited from

ForeignFieldWithMul.fromBits

Source

lib/provable/foreign-field.ts:373


random()

static random(): CanonicalForeignField

Returns

CanonicalForeignField

Inherited from

ForeignFieldWithMul.random

Source

lib/provable/foreign-field.ts:384


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

Inherited from

ForeignFieldWithMul.sum

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


unsafeFrom()

static unsafeFrom(x: ForeignField): AlmostForeignField

Coerce the input to an AlmostForeignField without additional assertions.

Warning: Only use if you know what you're doing.

Parameters

x: ForeignField

Returns

AlmostForeignField

Source

lib/provable/foreign-field.ts:494